Thessalian Personal Names and the Greek Lexicon

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Thessalian Personal Names and the Greek Lexicon"

Transcript

1 3 Thessalian Personal Names and the Greek Lexicon JOSÉ-LUIS GARCÍA RAMÓN 1. Aims and scope of this study 1.1. Exclusions: non-greek names; Macedonian variants? 1.2. Dialectal and non-dialectal forms 1.3. Difficulties encountered in interpreting names 2. The Greek lexicon in Thessalian compound names 2.1. Compound names based on compound epithets found in poetry and prose 2.2. Compounds attested exclusively in names reflecting junctures in poetry or prose 2.3. Compounds attested exclusively in names but intelligible as Greek phrases 3. Names interpretable only in the light of IE comparison 4. Short forms of compound names or mere derivatives? 5. Nicknames reflecting aspects of everyday life 5.1. Physical appearance 5.2. Human character and behaviour 5.3. Animals 5.4. Plants 5.5. Utensils 5.6. Pastry- and bread-making 6. The Greek lexicon in Thessalian names 7. Thessalian names and the Thessalian lexicon 8. Concluding remarks Proceedings of the British Academy 148, The British Academy 2007.

2 30 José-Luis García Ramón 1. AIMS AND SCOPE OF THIS STUDY 1 AN OVERVIEW OF THE PROPER NAMES OF EVERY GREEK REGION offers an extremely variegated picture. It is true that many of them (especially religious and geographical names, but also personal names) defy interpretation in terms of Greek, and are simply evidence of the existence of prehistoric and/or foreign populations. When the names are intelligible, either from the Greek language itself or with the help of comparative philology, they reflect, directly or indirectly, all conceivable aspects of the Greek world; mythology, religion, history, and literature, as well as Greek Weltanschauung (including moral values and taboos) appear repeatedly in personal names, and the same holds true for even the most prosaic details of daily life, as is shown especially, but not exclusively, by names based on common nouns. Names in this last category, which can also occur as compounds, often sound rather bizarre and display an impressive degree of creativity: they are in fact first-hand evidence for the more prosaic aspects of daily life, not usually found in Greek literary records. It should be stressed at the outset that Thessalian personal names, now readily available in LGPN III B, present a picture which is not fundamentally different from that of other regions: naming patterns are basically the same, including the strong presence of poetic (especially Homeric) names; the lexicon concealed by proper names (what we might call latent vocabulary) is for the most part either of a literary or of a supra-dialectal character (i.e. common to other regions), and dialectal words in the strict sense are not very numerous. The same holds good for the names based on them. The most one 1 For alphabetic Greek names reference is made to the corresponding entries in LGPN: I, II, III A, and III B, and to Bechtel, HP. See also H. Frisk, Griechisches etymologisches Wörterbuch (Heidelberg, ) and especially Chantraine, DELG; for zoonyms, see R. Strömberg, Studien zur Etymologie und Bildung der griechischen Fischnamen (Göteborg, 1943) and W. d A. Thompson, A Glossary of Greek Birds (London, 1936), A Glossary of Greek Fishes (London, 1947); for verbal roots see Lexikon der indogermanischen Verben: die Wurzeln und ihre Primärstammbildungen, ed. H. Rix (Wiesbaden, 1998). Quotations follow the current conventions. References to IG are IG IX (2) unless otherwise stated. Unpublished texts are quoted according to their number in GHW: the unpublished database (Lyon) by V. von Graeve, B. Helly, and C. Wolters, Dossier de documentation thessalienne; I.Thess is J.-C. Decourt, Inscriptions de Thessalie, I: Les Cités de la vallée de l Enipeus (Athens, 1995). Place-names are abbreviated according to the Greek form of the name: AINis, ANTHion, ARGoussa, ATRax, AZORos, CHALai, DEMetrias, ERIKinion, GOMPHoi, GONNoi, GYRTon, HALos, HERakleia, HYPata, KIERion, KONDaia, KRANNon, LAMia, LARissa, LIMNaion, MATRopolis, MELITaia, MOPSion, NARTHakion, OITaia, OLOOson, PARasopia, PELina, PEUma, PHALanna, PHARSalos, PHAYttos, PHERai, PYTHion, SKOToussa, THAUmakion, THEBai, TRIKka. All centuries are BC unless otherwise stated.

3 THESSALIAN PERSONAL NAMES 31 can say is that some names are especially frequent, e.g. Πετθαλ ς and its variants (over twenty instances) or Λέων (over seventy attestations), and the very numerous names in Ιππο-: that the ethnic of the region is used as a personal name is easily understandable, that lions were known in Thessaly has been shown by Bruno Helly, 2 and that horses were common in the Thessalian plain is a well-known fact. But things are not always so transparent: for instance, the fact that Φρ νος and its variants are surprisingly frequent in Thessaly (over twenty-five occurrences) does not necessarily imply that toads are more characteristic of Thessaly than of other regions. The possibility that names based on zoonyms or phytonyms reflect the fauna or flora of the region 3 must be examined in each instance. On the other hand, as far as we know, there are no major differences from one Thessalian city to another. The present contribution will deal with Thessalian personal names based on words which may be understood or explained in terms of Greek; names which remain opaque from the linguistic point of view will be left out of consideration. My aim is twofold: on the one hand, an overview of Thessalian personal names according to the current conventional classification (compound names and short forms, simplicia); on the other, a more detailed analysis of some nicknames belonging to a variety of concrete semantic groups (physical appearance, human character and behaviour, zoonyms, phytonyms, utensils, pastry- and bread-making), which will cast light on the Greek lexicon in Thessaly, and, conversely, on the contribution of Thessalian latent vocabulary to our knowledge of the Greek lexicon. On the basis of the names discussed, I shall attempt to determine which lexical items underlying Thessalian names may be understood as properly Thessalian and which of them may be assumed to be specifically Thessalian. For obvious reasons the present paper does not attempt to be exhaustive. I have selected a set of names which are, in my opinion, especially interesting because of their morphology or semantics, or because they are (so far) attested exclusively in Thessaly. Within the framework of this inevitably arbitrary selection of nomina potiora, some original interpretations will be suggested. As a rule, only names which are securely attested will be taken into account: exception is made only in the case of the woman s name (WN) Οκορναλίς probably noted OKORMALIS, cf. below B. Helly, Des lions dans l Olympe, REA 70 (1968), 270 ff. 3 Cf. the thorough study for Boiotia by G. Vottéro, Milieu naturel, littérature et anthroponymie en Béotie à l époque dialectale (7 e 1 e s. av. J.-C.), in id., Dialectologica Graeca. Actas del II Coloquio Internacional de Dialectología Griega, Miraflores de la Sierra (Madrid), June 1991 (Madrid, 1993),

4 32 José-Luis García Ramón 1.1. Exclusions: Non-Greek Names; Macedonian Variants? This study excludes from consideration a significant number of personal names attested in Thessaly which defy interpretation in terms of Greek, or of any specific non-greek language: for example, the man s name (MN) Τορ ββας (HYP, 2nd cent.), and Τορ μβας (PHARS, 424 BC; cf. Thuc ), which point to Macedonia or Epiros, 4 but remain linguistically opaque. The number of such names is higher than one could wish: all one can say about them is that they are simply non-greek. The extremely interesting question of the Macedonian element in Thessalian anthroponymy also falls outside of the framework of this paper. It is true that some names attested in Thessaly may be the Macedonian variant of a Greek name, for they show the main phonetic peculiarity which is recognizably Macedonian, namely the presence of voiced occlusives corresponding to Greek voiceless aspirates as the reflex of IE voiced aspirates. 5 For example, the MN Βερέκκας (or Βερεκκα ς) and the WN Βερενίκη, which correspond to Φερέκκας (or Φερεκκα ς), a short form of Φερε-κρα της or Φερε-κ δης, and to the MN Φερέ-νικος respectively. The same holds for Β λιππος (LAR, 4th/3rd cent.), which may correspond to Φ λιππος (attested also in Attica, 405 BC); the MN Β λος (patron. adj. Β λειος LAR?, 3rd cent.) may be interpreted as a short form of it. 6 On the other hand, some proper names conceal terms which are transmitted by Greek Glossaries as Macedonian, e.g. the byname Θα λιος of Zeus in Pharsalos (Διος Θαυλιου I.Thess 63, 4th cent. GHW 4242; also 62 GHW 4241) corresponds to the Gloss Θα λιος Θα λος. Αρης Μακεδ νιος, even if it does not refer to the same god. In other cases, variants and deviations from the form attested in Greek may be due to a non-greek, but not precisely Macedonian, component. This is, for instance, the case with the WN Τολ βα (ATR, 4th cent.), which we might plausibly interpret as a variant of τολ πη clew, ball of wool 7 (Ar.; Hsch.), a pre-greek word. Further speculations about Macedonian linguistic elements in Thessalian anthroponymy will be avoided in this paper. 4 Cf. O. Masson, Quelques anthroponymes rares chez Thucydide, in Φιλίας χάριν: miscellanea di studi classici in onore di Eugenio Manni (Rome, 1980), iv ff. OGS II, 328 ff. 5 On this point, and on the whole problem of Macedonian, cf. C. Brixhe and A. Panayotou, Le macédonien, in F. Bader (ed.), Les Langues indo-européennes (Paris, 1994), and, especially, C. Brixhe, Un nouveau champ de la dialectologie grecque: le macédonien, in Katà Diálekton (Atti Napoli Faiano d Ischia, September 1996) AION 19 (1997), 41 71; I. Hajnal, Methodische Vorbemerkungen zu einer Paleolinguistik des Balkanraums, in A. Bammesberger and T. Venneman (eds.), Languages in Prehistoric Europe (Heidelberg, 2001), 123 ff. 6 On the Thess. MN Κορραβο - ν as possibly a Macedonian form for Gr. *Κορραφ ν, see below n On this term cf. N. Maurice, Τολ πη ou les écheveaux de l étymologie, in Étymologie diachronique et étymologie synchronique en grec ancien (Actes du Colloque de Rouen, November 1991 Revue de Philologie 65 (1993)),

5 1.2. Dialectal and Non-Dialectal Forms THESSALIAN PERSONAL NAMES 33 Two further preliminary remarks at this point: the first on the relation between dialectal and koine forms, the second on the existence of old words underlying names. Whether a Thessalian name displays dialectal or Attic phonetics is entirely irrelevant as regards the lexical items it conceals, and their value as a naming motif: forms recognizable as dialectal, with characteristic spellings ει, ου for Attic η, ω make no difference in this respect. As a rule, Thessalian names appear in Attic form when they occur in metrical texts and in inscriptions written in Attic or North-West koine, and in their dialectal form when the inscription as a whole is in dialect. This is, for instance, the case with names with Αστο or Ασστο for Αριστο, 8 with τ- for πτ- (Τολεμα ος for Πτολεμα ος), or with Περρ for Περι, and one interesting case of Ερρ for Ερι ( Ερρ-αίνας, cf. 2.3). Hybrid forms are also common: a very instructive case is that of the representation of labiovelars, especially evident in the Greek form for IE *ĝ h ũer- wild animal (: Att. θήρ), which occurs both as Φειρ (Φείρουν, Φειρο νδας) and φειρος (Φιλ -φειρος), with labial representation of the labiovelar, alongside forms in Θηρ- and -θηρος; there are also examples of compromise forms with Θειρ (Θειραμένεις, Θειροκράτεις, Θειρίων). Similarly with compounds whose first element is Πεισι and Τεισι (Πεισι-κρα τεις vs. Τεισικρα τεις), for IE *k ũ eĩ- pay (Att. τίνω), or Πειλε/ο along with Τηλε/ο (Πειλο-κλίας vs. Τηλέ-μαχος, -φα νης, -φαντος), for *k ũ ēle- far. For our purposes it is important to remember that the fact that a name is attested in its dialectal form does not in itself mean that the word(s) on which it is based belonged to the Thessalian dialect, still less that it may be considered as specifically Thessalian. Conversely, words labelled as Thessalian by grammarians and in Glosses, or quoted as such by poets or historians, are transmitted in their Attic form, yet turn out to be absolutely reliable, as I have tried to show recently. 9 The question is to determine which words among those underlying Thessalian names may be taken to be Thessalian, i.e. as 8 From *arsto-, with dialectal syncope of unaccented -i- in *áristo-, J.-L. García Ramón, Geografía intradialectal tesalia, Actes de la première rencontre internationale de dialectologie grecque (Nancy, July 1986) ( Verbum 10 (1987)), Cf. J.-L. García Ramón, Del trabajo en una gramática del tesalio: Para una valoración lingüística de las glosas, Colloquio Internazionale de Glottologia Dialetti, dialettismi, generi letterari e funzioni sociali (Milan, Sept. 2002) (Alessandria, 2004), In the cases where the words transmitted as glosses may be checked on the inscriptions (or in the literary sources) they turn out to be amazingly authentic, irrespective of whether they are Greek or pre-greek, exclusively Thessalian or not. Cf. also my Lexicographica Graeca: algunos nuevos lemmata a la luz de las glosas y la onomástica, Myrtia 22 (2007), 5 18.

6 34 José-Luis García Ramón belonging to the lexical stock of the Thessalian dialect. This point will be dealt with below ( 7). Thessalian onomastics (like those of every Greek region) provide us with formal variants of well-attested words, or with old words not attested elsewhere. It does not follow that these anomalous forms may be understood as dialectal, even less as specifically Thessalian. Such is the case, for instance, with the MN Βρεχα ς (PHARS, 3rd/2nd cent.), which presupposes a form *mréĝ h -u- short (Lat. breuis) as against Βροχ- in MN Βροχα ς (PYTH, 3rd cent.), Βρ χυς (KRANN, 2nd cent.), WN Μροχο- (PHAL, 2nd cent.), 10 which presuppose the zero-grade form *mrĝ h -ú- (: Att. βραχ ς, Litt. Lesb. βρ χυς). The MN Βρεχα ς reflects an archaic type of root-alternance to be traced back to Proto-Greek, rather than a specifically Thessalian form of the epithet βραχ ς. The same applies to the MN Στρείβουν* (patron. adj. Στρειβο νειος, LAR, 3rd cent.), which points to *στρείβω turn : the present is not attested, but its existence is indirectly guaranteed by the glosses στροιβ ς. δ νος, στροιβα ν. α ντιστρέφειν, which clearly underlie the Athenian MN Στρο βος (Thuc ). Though both names are only attested in Thessaly, it is highly improbable that an adjective *βρεχ ς or a present στρείβο/ε- existed as common terms in the Thessalian dialect in the classical period. This is well illustrated by another old term which is attested in names in Thessaly, though this one also occurs in other regions. The MN Κ ρρος (and the first element Κορρ(ο) in compounds such as Κορρίμαχος : Κοιρ μαχος) reflects an old term IE κ ρρος* army 11 (i.e. a synonym of στρατ ς or Hom. λα ς): the form is not attested as a common appellative in Thessaly or elsewhere, but the name is attested, not only in Thessaly but also in Macedonia and in Athens. Further instances of old, inherited words will be discussed below ( 3) Difficulties Encountered in Interpreting Names A final remark before proceeding: the fact that a name may be interpreted in terms of Greek does not of course mean that that is the only interpretation possible. We may note two difficulties which may confront philologists trying to interpret names. First, it is not always easy to assign a name to one single group, either because the underlying appellative is not clearly recognizable as belonging to 10 Cf. also the variants Βορχ- (with metathesis) and (supra-dialectal) Βραχ- (both from *mr ĝ h -ú-) in Βορχίδας Βραχ λλου (LAR). 11 On this form cf. 3.

7 THESSALIAN PERSONAL NAMES 35 a given class, or because it designates different appellatives. For instance, Φα λαρος (KRANN, 3rd/2nd cent.) and Φαλαρίουν (PHARS, 3rd cent.) 12 may be based on one of two possible forms: Hom. φα λαρον metal boss of a helmet, or cheek-pieces of a horse s head-stall (Hdt. ), whence later bandages and ornaments, which is a derivative of φα λος horn of a helmet ; or alternatively, on the adjective φα ληρος patched with white (κ ων (Theocr.), ρος (Nic.)), which is based on φαλ ς 13 (same word?, 14 cf. φαλ ς. λευκ ς Hsch.); this form is also used as a ram s name (Theocr ), and as a zoonym φαλᾱρίς coot : Fulica atra with white head (Ar. ). A remarkably complicated example is provided by compound and derivative names containing Δρουπ- (: Δρωπ-), such as Δρουπ λος (cf. Δρωπο λος Boiotia, Δρωπ λος West Lokris), Δρο πακος* in patron. adj. Δρουπάκειος (both PHARS, BC), Δρουπακίδας (PHARS, 4th cent.), and Δρω πακος (LAM 3rd/2nd cent.). These names are currently assumed to contain the appellative man transmitted in the gloss δρω ψ. α νθρωπος; the form is generally believed to go back to *nr-op-, taken to be a compound with a first element *h 2 ner- (α νήρ, Hom. νω ροπι χαλκ, νω ροψ. λαμπρ ς). On this assumption, Δρουπ λος and Δρο πακος are onomastic forms in - λος and -αξ (or -ακος) based on the old term δρω ψ man. 15 However, the existence of the common appellative δρω παξ pitchplaster (Hipp. ), with the verb δρωπακίζω apply a depilatory clearly related to δρέπω pull out (assuming the existence of a root form δρωπ-), allows a rather less poetic interpretation, at least for Δρο πακος*, namely a nickname the pitch-plaster or the depilated one. There is, however, a third possibility suggested by the Glosses δρω πτης. πλανήτης, πτωχ ς, δρωπάζειν. μβλέπειν, δρώπτειν. [διακ πτειν. ] διασκοπε ν. Α σχ λος Ψυχαγωγο ς, which point to a variant of δέρκομαι, in which case, the Thessalian names formed on Δρουπ- could be nicknames meaning vagabond or spy. Whatever the etymology and meaning of δρωπ-, the difficulties of interpretation are evident. This statement of facts and difficulties brings us to the WN Δρουττα.λίς (ATR, 4th cent.), which also underlies the patron. adj. Δρου[ταλ]ίδαιος (PHARS, 4th cent.). 16 Since the spelling ττ is usual in Thessaly to note the outcome of *(-)pt-, 17 it is 12 The names are attested elsewhere; cf. also Φα λαρις in Boiotia. 13 Gr. φαλ- goes back to the zero-grade of IE *b h el-, cf. Sanskrit bhālam forehead, brightness, Gaul, balio- and Welsh bal ( φα ληρος), OCS bĕlŭ white. 14 The MN Φαλ-ια δας (KRANN, 3rd cent.) may be based on either of the meanings of φαλ ς. 15 Cf. O. Masson, Anthroponymie, dialectes et histoire, Actes de la première rencontre... Verbum 10 (1987), 257 ff. OGS II, 597 ff. 16 The reading Διο τταλις, as quoted in LGPN III B (following I.Thess I 80) must be discarded. 17 Cf. Thess. αρχιττολι-αρχεντος for αρχιπτολι-, and the new forms εττασθειν, ετταμενος for Att. κτ σθαι, κτημένος, in an unpublished decree from Larissa (GHW 5800), which I had

8 36 José-Luis García Ramón easily conceivable that Δρουττα- conceals a former *Drōptā-, or *Drōp-tā-, corresponding to the gloss δρω πτης (see above). 18 A second, strictly linguistic difficulty concerns the identification of a name as a short form of a compound or as a simplex. Some significant instances of this type will be dealt with below, THE GREEK LEXICON IN THESSALIAN COMPOUND NAMES Let us turn now to the different types of names attested in Thessaly. As in every Greek region, Thessalian personal names show a strong presence of Homeric (and Mycenaean) and literary names of more of less heroic character (with or without Thessalian phonetics), which are not specifically Thessalian. We may note briefly the compounds Βαθυκλ ς, Ιπποδάμας, Ιππ λοχος, Πρωτεσίλαος (and Πρωτ λαος), Τήλεφος, Τηλέμαχος, Τλαπ λεμος, Υπεράνωρ, and Προμαθε ς (ATR, 3rd cent.) with etymological -ā-, 19 as against Προμηθε ς, which is also attested. Among the non-compound names (and/or non-greek), cf. Α μων (and dialectal Ε μουν), Θέστουρ, Νειλε ς (if not a short form of Myc. ne-e-ra-wo /Ne h elāwos/), Πέλοψ, Πτολεμα ος, Σίσυφος, Τηρε ς. Many compound personal names which are not specifically Thessalian deserve attention because they illustrate the influence of poetry in Greek onomastics. Of those which can be interpreted with certainty ex graeco ipso, a threefold classification is possible, which I set out in 2.1, 2.2, and Compound Names Based on Compound Epithets Some compound names are based directly on compound epithets, especially those found in poetry (whether or not they are appropriate for people). New the opportunity of discussing with Bruno Helly on the occasion of his visit to Cologne in May As we shall try to show elsewhere (García Ramón and Helly in preparation), the WN Δρουττα. λίς (*Δρωπταλίς) would stand to δρώπτης in the same relation as WN Ακροταλίς to α κρ της, and have the meaning the vagabond one or the depilated one (if ultimately belonging to δρωπ-, and δρώπαξ). 19 Non-Attic-Ionic μᾱθ (προ-μᾱθ-) has convincingly been related to Ved. (pra-)math steal by J. Narten, Das vedische Verbum math, Indo-Iranian Journal 4 (1995), 135 n. 40 ( id., Kleine Schriften i (Wiesbaden, 1995), The comparison with Māthava- in the Śatapatha- Brāhmaṇa, the king who bears fire in his mouth, points to an inherited myth, cf. T. Gotō, Purūravas und Urvaśī aus dem neuentdeckten Vadhula-Anvakhyana (Ed. Ikari), in Anusantatyai: Festschrift für Johanna Narten, ed. A. Hintze and E. Tichy, Münchener Studien zur Sprachwissenschaft, Beiheft 19 (Dettelbach, 2000), 110.

9 THESSALIAN PERSONAL NAMES 37 names may subsequently be created by substituting one of the elements with a synonymous term. Excellent examples are provided by compound names with -πρέπης, -πρ πος, and snyonymous -φαντος. 20 An example of the first is Εσπρέπεις* in patron. adj. Εσπρέπεια (LAR, 3rd cent.), which reproduces Hom. κπρεπής highly distinguished, obviously with the same meaning as Εκπροπος (Boiotia); of the second, Θε προπος (DEM, 130 BC), Θεοπροπίδας* (patron. adj. Θεοπροπίδαιος, LAR, 4th cent. ), Θεοπροπίδης (LAR, 108 BC), for which compare Hom. θεοπρ πος prophetic (θεοπρ πος ο ωνιστής Il ), θεοπροπία prophecy, oracle, also θεοπρεπής meet for a god (of δ μα Pind. Nem ). 21 The MN Εκφαντος (4th cent. ) reflects a synonymous epithet: cf. κφαντον. φανερ ν (Hsch.). Further Examples Α χμαίρετος* (patron. adj. Α χμαιρέτειος LAR, 3rd/2nd cent.), Α χμαρέτα (attested once, as Αιχναρετα I.Thess I 9, LIMN 3rd cent.), short forms Α χνουν (KRANN), Α χνα (LAR), Α χμων (MOPS), all 3rd cent.: there is no corresponding compound attested, but the names are obviously built on Hom. α χμάλωτος captured by the spear and provide interesting examples of substitution of one of the elements of a poetic compound, namely άλωτος, by synonymous αίρετος. Αμω μητος (passim, 3rd cent. ), Αμωμήτα (TRIK?, 2nd cent.): Hom. α μω μητος blameless (Πολυδάμαντος α μωμήτοιο Il ). Αφθ νητος/-α (around thirty attestations passim): α φθ νητος beyond the reach of envy, of αι νος praise (Pind. Ol ). Τέρπνος (ARG, 2nd 1st cent.): τερπν ς delightful, pleasant (Pind. ). A feminine form Τέρπνη is attested once in Cyprus (Imperial). The adjective is used very seldom for persons, e.g. Soph. Ai Εμο πικρ ς τέθνηκεν κείνοις γλυκ ς, / α τ δ τερπν ς to his own content. The following four compound names are attested so far only in Thessaly. Ελανδρος* (patron. adj. Ελα νδρειος, ATR, 3rd cent.): pejorative adjective λανδρος men-destroying, used of Helen (Aesch. Ag λανδρος, λέ πτολις). The epithet obviously reflects Hom. α νδρα λε ν, as well as 20 Both lexemes are built on IE roots: πρεπής, πρ πος and Hom. πρέπει go back to IE *prep- (Arm. erewim φαίνομαι ), φα ντος (Hom. φαίνεται) to IE *b h an- (Ved. bhán-a- declārāre, Arm. ban ο γειν from *b h n h 2 -o/e-, causative to IE *b h eh 2 - be visible ). 21 On πρ πος cf. the short form Προπέας (PEU, 2nd cent.); cf. Πρ πος (LAR, 2nd cent. AD), Πρ ππει, Προππίδας (Boiotia).

10 38 José-Luis García Ramón synonymous ζωγρε ν, which in its turn is reflected in the MN Ζ γρος (Lakonia). B. Forssman 22 showed that the collocation may be traced back to Indo-European. Παρτ νας (ATR, 4th/3rd cent.): dialectal form of the adjective παρα τονος stretched beside, with Thessalian apocope of παρα and masculine suffix -ας. The adjective is used of hands (παρα τονοι χέρες Eur. Alc. 399), but may also have the sense ill-sounding (Hsch. s.v. βαρβαρισμ ς. παρα τονος δια λεκτος). Περπ λας (LAR, 4th cent.): dialectal variant of *Περίπολας, with apocope of περι, reflecting περίπολος watchman, as Bechtel correctly saw, 23 or περιπολα ος open all round (the eyes), cf. Arist., Physiogn. 810 a στι γὰρ χον πρ σωπον μικρ ν, στ μα μέγα, φθαλμο ς μικρο ς, κλε κους, γκοίλους, α το ς δ περιπολαιοτέρους. The Thessalian name reflects probably the poetic sense, for in Thessaly the term for watchman is φρουρ ς. 24 The form Πειρι is simply the Homeric variant, without apocope, of Περι with metrical lengthening (cf. Πειρίθοον for non-metrical Περίθοον). WN Υπανεμίς (ATR, 3rd cent.): reflects πήνεμος sheltered from the wind (Soph. ) and/or πηνέμιος lifted by the wind (Soph.), or full of wind (of eggs which do not produce a chicken, Ar. frg. 186 πηνέμια τίκτουσιν α` πολλα κις). Whether the meaning of the name is the poetic or the pejorative one, we cannot say. At any rate, the name evokes poetic reminiscences, in the light of the Homeric phrase π λιγείων α νέμων (Il ) Compound Names Reflecting Junctures in Poetry or Prose Some compounds are attested exclusively in names, but reflect junctures in poetry or prose, and their equivalents, with replacement of one or both of the elements by synonyms. Some examples follow. Φαιναρέτα (LAR, ARG, 3rd cent.), Φαινα ρετος (ATR, 4th/3rd cent.): cf. Od α ρετ ν σ ν φαινέμεν. Φειδέλαος (PHER, c.311 BC), Φειδέστρατος (PHER, 4th cent.?), with the variants Φειδ λας (LAR, 4th cent., also Φειδ λαος c BC): cf. such 22 B. Forssman, Ved. jīvagr bh, jīvagr ham, gr.ζωγρέω, Studien zur Indologie und Iranistik 13/4 (1987), 69 76, who invokes the perfect semantic parallel of Ved. jīvagr bh, jīvagrāham: the first element is the same as Gr. Ζωο, the second grabh is synonymous with Gr. α ρέω. 23 Bechtel, HP 515, who quotes also the MNΠειρίπολος (Chalkis) under the label Heereswesen. 24 Cf. B. Helly, Gonnoi, i:la cité et son histoire. ii: Les inscriptions (Amsterdam, 1973), i Cf. also πανεμ ω breathe over (Liban. Descr ρωτι τὰς παρειάς).

11 THESSALIAN PERSONAL NAMES 39 phrases such as Od σ δ φείδεο λα ν / σ ν save your own people, or Soph. Ai. 844 μ φείδεσθε...στρατο. Φείδιππος 26 (PHER, 4th cent., ATR, NARTH; also in Hom. Il ): cf. the Homeric phrase: Il ππων φειδ μενος using the horses sparingly. 27 Φρασιμήδα (PHER, c BC): cf. Il κακὰ δ φρεσ μήδετο ργα. Two names which are attested only in Thessaly show clear Homeric reminiscences: Βο πλαγος (four examples, PYTH, 4th/3rd cent.) reflects the Hom. hapax βουπλ γι in Il θειν μεναι βουπλ γι struck with an ox-goad, rather than the late compound βουπλήξ* attested in causal forms (βουπλ γος, βουπλ γες, βουπλ γας) in late Epics. Σ λανδρος* (patron. adj. Συλα νδρειος, LAR, 3rd cent.) is readily intelligible (cf. Il τινα συλήσων νεκ ων strip the bodies of the dead ), even if the exact phrase is not attested Compounds Attested Exclusively in Names but Intelligible as Greek Phrases We also find compound names which are intelligible in the light of common Greek phraseology, even if the actual combinations are not attested elsewhere. The following names occur exclusively in Thessaly, and some show a remarkable familiarity with Greek literature. The patron. adj. Αργολα ειος (PHER c.303 BC), of which Αργουν (KRANN, PHARS 3rd cent. ) may, but need not, be a short form, raises difficulties as to the name (and noun) on which it is based. In my opinion, the underlying name was Αργ λᾱς, 28 reflecting α ργ λας, a kind of snake, which was also called α ργ ς (Hipp. ), Dor. α ργαˆς. The Suda explains that the α ργ λαι were native to Pelasgian Argos ( Αργ λαι. ει δος φεων, ο ς 26 Φείδας (PHARS, 3rd cent. ), Φειδίουν may be short forms of both Φειδέλαος and Φείδιππος. 27 The comic effect produced by the Aristophanic Φειδιππίδης (Nub. 60 ff.) is due to the context, not to the compound itself, cf. O. Panagl, Zur Problematik der semantischen Rekonstruktion in der Etymologie, Lautgeschichte und Etymologie. Akten der IX. Fachtagung der Indogermanischen Gesellschaft (Vienna, 1978), The form Αργ λαος (LGPN) has no clear support: the assumed names Αργέ-λαος and Αργί-λαος (Bechtel, HP, 64, s.v. Αργε-, Αργι-) are mere conjectures on the basis of inconclusive short forms, as the author himself admits ( Αργέ-λαος vielleicht wegen Αργέας, and Αργί-λαος vielleicht wegen Αργι-λίας ).

12 40 José-Luis García Ramón νεγκε Μακεδω` ν Αλέξανδρος κ το Αργους το Πελασγικο ε ς Αλεξάνδρειαν), and etymologizes the word ingeniously (... α ργ λαι ο ν κ το Αργους λαιοί) by resorting to the term λαι ς (Arist. ) designating a kind of thrush. The appellative α ργ λας seems to be a compound with α ργο- bright as its first element, though its second element remains obscure. That this bird-name might be used as a nickname finds strong support in the fact that the synonymous α ργ ς is attested precisely as a nickname of Demosthenes (Aeschin ; Plu. Dem. 4). Its occurrence in Thessaly fits well with the allusion to Pelasgian Argos. It should be noted that Αργ λας is also the name of a hill in Lokris:... κον ε ς τ ν Λοκρίδα κα συνάψαντες μα χην το ς Φωκε σι περ λ φον Αργ λαν νομαζ μενον ττήθησαν (Diod. Sic ). The second element of the personal name Αργ λας, surely λα ας, λαˆς stone, rock, provides a conceivable meaning for the place-name, namely white rock or the like. But it does not necessarily follow that the second element of the bird name α ργ λᾱς is the same. 29 I do not think that the Thessalian anthroponym is based on this place-name, for in that case we would expect a derivative * Αργολα ιος (or Αργολα ος) as the name, and a formation in -ειος (* Αργολαίειος) as the patronymic adjective. Ερραίνας occurs in the recently published stele of the Menandridai (KRANN, 3rd cent.). 30 The name is to be interpreted as Ερί-αινας, with dialectal representation of prevocalic -ri- as ρρ 31 (cf. Thess. κυρρον, Περρανδρος κυρίον, Περίανδρος); in which case it is the first attestation of the combination in a compound of emphatic ρι and αι νος tale, praise, or decree. The MN Ερραίνας with its peculiar formation in -ᾱς, may be understood as having high/good thoughts/expressions. Semantic parallels might be names of the type Αρίστ-αινος (patron. adj. Αρισταίνειος GYRT 2nd cent.), Αριστ-αίνα, Αριστ-αίνετος, Αριστ-αινέτα/η, or Ευ αινος (Ευ ηνος in Boiotia), Ε αίνετος (CHAL, THEB, 2nd/1st cent.); all these names are attested outside Thessaly. Λιμέναρχος (PHAL, 3rd cent.) reflects the characteristically Thessalian (and Cypriot) meaning of λιμήν square 32 (corresponding to Attic α γορά), as 29 The gloss α ργος. τ πεδίον λέγεται παρὰ το ς νεωτέροις, παρ Ομήρ δ ο δ α παξ. μα λιστα μ ν ο ονται, μακεδονικ ν κα θεσσαλικ ν ει ναι (Strabo ) does not apply here. 30 J.-C. Decourt and A. Tzafalias, Une liste civique à Crannon: la stèle dite des Ménandridai, ZPE 137 (2001), (Tables IX XII). The name is listed by the editors among those unanalysable (150, peut-être dérivé d un autre mot en ρρ- ou ρσ- ). 31 The spelling ρρ instead of ρι notes a geminate -rr-, as the result of *-ri which in its turn goes back to the iotization of /i/ before vowel in Thessalian, cf. García Ramón, ˆ-, Geografía intradialecta tesalia, 135 f. 32 Cf. B. Helly, Accord de sympolitie entre Gomphoi et Tamiai, Dialectologica Graeca Miraflores. Actas del II Coloquio Internacional de Dialectología Griega, June Madrid,

13 THESSALIAN PERSONAL NAMES 41 shown by the glosses λιμήν. ο ονε τ ν α γορὰν κάλει λιμένα Θετταλ ν α κο σας (Dio Chr ), and λιμήν. α γορὰ κα νδιατριβή. Πάφιοι. The glosses are confirmed by the evidence of the great inscription of Larissa (τος ταγος... εσθεμεν αυτος εν τον λιμενα IG 517, 42: 214 BC), and in a fragmentary text from Hestiaiotis (late 3rd cent.): 33 εν τει λιμενι line 2, εις το λιμενεν line 6, ενλιμενα line 11 Att. ν τ λιμένι, ε ς τ λιμένιον, νλιμένια. On this assumption, the MN Λιμέναρχος is synonymous with * Αγ ραρχος, which is itself unattested, but the MN Αρχάγορος (a compound of the type φερέ-οικος, Φερε-κ δης), conveys the same meaning, and is thus a perfect semantic parallel to Thessalian Λιμέναρχος. 34 However, this interpretation encounters a serious difficulty in the participle λιμεναρχήσας attested in Boiotia (IG VII 1826, 2: Thespiai): λιμεναρχησας δις / Διοσκουροιν και τη πολι. The form seems to refer to the activity of the manager of the harbour, as suggested by Hiller von Gaertringen, followed by Bechtel. 35 Σπ ραγος, attested in the politography decree IG (PHARS, BC), has reappeared in Thessaly under the form Σπουραγος (MATR, 3rd cent.), in which ου denotes [ū]. 36 Since ᾱγος may be understood as the second element of the compound, namely a nomen agentis of α γω, the only possible interpretation of the name is that its first element is σπ ρ ς, a variant of π ρ ς wheat, attested in some Doric dialects. 37 This 176. The same probably holds good for λίμνη pool, marshy lake (Hom. ), which may conceal the special meaning square in the Thessalian epiclesis Πανλίμνιος (Απολλονι Πανλιμνιωι SEG XXIX 515. GONN). As to the pair λίμνη : λίμνιος, cf. τιμή : τίμιος. A similar situation may be assumed for Lakonian in view of the place-name Λίμναι, a name for a square in Sparta (Paus ; Strabo et al.). The synonymity of λιμήν (and λίμνη) with Attic α γορα suggests that meetings were held originally in an area close to a meadow or to the harbour (F. Gschnitzer, Zu griech. λιμήν: Hafen, *Wiese, Versammlungsplatz, in Sprachwissenschaftliche Forschungen: Festschrift für Johann Knobloch, ed. H. M. Ölberg and G. Schmidt (Innsbruck, 1985), 123 ff. ( Kl. Schr. I, ); García Ramón, Cuestiones de léxico y onomástica tesalios. Katà Diálekton (Atti Napoli Faiano d Ischia, September 1996) AION 19 (1997), 531 ff. 33 Edited by B. Helly, Accord de sympolitie entre Gomphoi et Tamiai, Once the equivalence of λιμήν with Attic α γορα is established, the same argument can be applied to a further Thessalian gloss, νορμος. α γορὰ παρὰ Θετταλο ς. Although νορμος is a hapax, its synonymity with λιμήν is assured by its derivatives e.g. νορμίζω bring a ship to land (C. Thg ), νορμέω ride at anchor in a harbour (Plb. ); cf. García Ramón Del trabajo en una gramática del tesalio, 241 ff. 35 Bechtel, HP, 514 ( Verwaltung und Rechtspflege ). Cf. also MN Λιμεν-ο[χ]ος (rather than -ο χος. Megara BC, SEG XIII 300). 36 Line 17 of the text, published by B. Helly, La convention des Basaidai, BCH 94 (1970), ; cf. García Ramón Geografía intradialectal tesalia, 117 ff. 37 Cf. J.-L. García Ramón, Der thessalische Name Σπ ραγος, σπυρ ς Weizen(korn) und att. πυρ ς, πυρο ς α γειν Weizen(korn) zu Wasser transportieren, in Indogermanica: Festschrift für Gert Klingenschmitt, ed. G. Schweiger (Regensburg, 2006), Since σπ may

14 42 José-Luis García Ramón is strongly supported by the well-attested collocation π ρο ς (and κριθὰς) α γειν transport wheat (and barley) by sea (cf. Thuc τ ν δ κα α τ θεν σ τον ν λκάσι, πυρο ς κα πεφρυγμένας κριθάς, α γειν,... to transport from there grain, and wheat and dried barley in merchant vessels ) 38 as against π ρο ς (and κριθὰς) φέρειν, which designates transport by land, as well as by parallel combinations with σ τος, namely σ τον α γειν, σιτηγ ς, and σιταγωγ ς (of ships) in contrast to σ τον φέρειν, σιτοφ ροι. It is possible that the MN Σπ ραγος reflects a title, like Λιμέναρχος ( 2.3), or even Κ ρραγος ( 3). Χαν λαος* (patron. adj. Χανυλα ειος), with the short forms Χα νυς* (patron. adj. Χαν ειος, both PHARS, 3rd cent.), Χα νος (KRANN, 3rd cent.), and Χαναˆς (Pelasgiotis, 1st cent.) is not easy to interpret. Its first element Χανυ- surely conceals a verb χαν ω call, shout, attested in the glosses χαν ειν. βοαˆν, χαν σσει. βία καλε (Hsch.). 39 The meaning of the verb finds a semantic parallel in the construction of βοα ω with accusative of the person called, first attested in Pindar (Pyth Μεσσανίου δ γέροντος / δονηθε σα φρ ν β ασε πα δα ν), and common in classical prose (cf. Hdt βώσας τ ν Θεμιστοκλέα). 40 The clearest semantic parallel of the juncture *χαν ω λα ν is the phrase τ ν α λλην στρατι ν πεβώσαντο they called the rest of the army for help (Hdt ), which provides a possible, post-homeric model for the creation of the compound name. Ψίλαυχος (MATR, 3rd cent.) combines the adjective ψιλ ς bare (of land), smooth, stripped of hair (Hom. ), and αυ χη boasting, αυ χημα (Pind.), α χέω boast, exult (cf. Hitt. h ṷek - swear ). The meaning of the juncture is clear in the light of synonyms ψιλ ς λ γος prose, pl. unsupported speech, ψιλ ς λέγειν speak without proofs (Plat. ), and of compounds with κενε(ο), μεγαλ, such as κενεαυχής (Hom.), μεγα λαυχος represent not only [sp] but also [sp h ] in Thessalian (cf. García Ramón, Geografía intradialectal tesalia, 144) as well as in Boiotian and in the West Greek dialects (cf. J. Méndez, Los dialectos dorios del Noroeste (Salamanca, 1985), 348 ff.), the first element of the compound could be σπυρίς large basket, creel (Hdt., with late variant σφυρίς Papp.), or σφυρ ν ankle (Hom.), or σφ ρα hammer (Od. ), beetle, mallet (Hes. ), balk between the furrows of ploughed land (Poll ), whence a land measure (cf. Hsch. s.v. μ σφυρος. α δελφή. τ ς δ τρίτης συλλαβ ς κτεινομένης, δηλο τ ν μ χωρον. Σφ ρα γὰρ τ ς σπορίμου γ ς τ μέτρον), or even the name of a fish. None of these forms, however, is attested (or conceivable) as the first element of a compound with αγος, i.e. as the object of α γω. 38 Cf. also Herond ξ Ακης λήλουθα / πυρ]ο ς α γων κ στησα τ ν κακ ν λιμ ν I have come from Ake, bringing a last of wheat and I have stopped the bad famine. 39 Bechtel, HP, 464; Chantraine, DELG s.v. χαίνω. On the phraseological background cf. García Ramón, Lexicographica Graeca, 14 ff. 40 The current meanings of χαίνω open, χα σκω yawn, gape (Hom. ), also speak with open mouth, utter (Soph. ), also swallow (Paus χανε ν...τ ν γ ν...τ α ρμα). The form χα νος mouth (Com.) can hardly be assumed for χανυ.

15 THESSALIAN PERSONAL NAMES 43 vainglorious (Pind. Pyth.8.15 ), μεγαλαυχία (Plat.), μεγαυχής (Aesch.): the name characterizes its bearer as someone who speaks vain, unsupported words. A parallel of ψίλαυχος is the MN Πα νταυχος (KRANN, 2nd cent., and in other regions), which reproduces the synonymous πάνταυχος (Plb. ). We may note other compound names, of diverse character and difficulty, which are attested only in Thessaly: Καιριμένεις (LAR, c.200 BC; its short form Καίριμος occurs in Attica): cf. Καιρογενής Ν σσανδρος (LAR, 2nd cent.), and Ν σανδρος (ATR, 4th cent.), with short form Νυσσίλος (LAR, 109 BC), which is usually connected with Ν σα 41 Τα ξιππος (PHER 371 BC, quoted by Val. Max ) Φιλοπ τας* (patron. adj. Φιλοπ ταιος, KRANN 215 BC?), with -π τας drinker 42 (or lord, cf. δεσπ της house lord?, cf. MN Μανδρο-π της). 3. NAMES INTERPRETABLE ONLY IN THE LIGHT OF IE COMPARISON Thessaly provides names which are only interpretable with the aid of IE comparisons, for they conserve inherited words which were not immediately intelligible from Greek itself. Compound names provide nice instances of semantic continuity, with old words lexically renewed, i.e. replaced by synonymous new terms. Let us look at three remarkable instances. Μενέκορρος (ATR, PHARS, 3rd cent.), of which Μενεκκ ας 43 (KRANN, GONN: 3rd cent.) may be a short form, has as its second element *κ ρρος army (IE *koriˆo- : Goth. harjis, Gaul. corii, Lit. ka ~ rias), which probably underlies Hom. κοίρανος. 44 The term also occurs in the MN Κορρα ος, Κορράτας and is equivalent to στρατ ς or to Hom. λα ς. The compound MN Μενέκορρος turns out to mean who withstands the (foreign) army, a theme continued by Μενέλαος, Μενέστρατος (passim 2nd cent.), fem. 41 So Bechtel, HP, 338. One may wonder if the first element reflects the present stem of ν σσω touch with a sharp point, although one would a priori expect Νυξι based on aor. ν ξε (Il ). 42 So Bechtel, HP, 382 ( aus einem Spitznamen erwachsen ), with reference to the MN Μεθ στας. 43 The MN Μενεκκαˆς may be a short form of Μενέκορρος, or of Μενε-κλ ς, or of Μενεκρα της. 44 Cf.A.Heubeck, Κοίρανος, Κ ρραγος und Verwandtes, Würzburger Jahrbücher für die Altertumswissenschaft 4 (1978), 91 8.

16 44 José-Luis García Ramón Μενεστράτα (PHER), and Μενεστράτης (LAR, 1st cent.). The name is reflected in the Homeric phrase, Il ο τ πάρος περ / μίμνομεν ξ ν Αρηα παρ α λλήλοισι μένοντες; cf ς Δαναο Τρ ας μένον μπεδον ο δ φέβοντο. The correspondence between compound names with Κορρο- or -κορρος and those with Λαο-, Στρατο- or -λαος, -στρατος make a coherent group, irrespective of whether their internal syntax is understandable. On the one hand, Νικ ρρας (LAR, 3rd cent.) and patron. adj. Νικ ρραιος (KRANN, 3rd cent.) presuppose a haplology of *Νικ -κορρας, which matches semantically the well-attested names Νικ λαος (-λας), Νικ -στρατος and inversely, Λα -νικος, Στρατ -νικος (and, in another type of compound, Νικησί-λας). On the other hand, Κ ρραγος (DEM, 3rd cent., GONN, KIER, 2nd cent.), matches the widely attested MN Λαˆγος (in Thessaly only in OLOO, 2nd cent. AD), Λαγέτας (PHER, 4th cent. ), and Στρα τ-αγος. Finally, Κορρίμαχος (LAR, 3rd cent.) matches Λα μαχος passim, and Στρατ μαχος in other regions. 45 Κα σσανδρος, Κασσα νδρα, both attested in other regions, show in Thessaly an interesting short form, namely the feminine Κασσώ (PYTH, 125 BC). The name conceals a compound with a first element κασσ( ), which goes back to Καστι (cf. Hom. Καστι-α νειρα). The underlying root *kˆend- (i.e. *kˆ n d-ti- in the compound) is obviously that of Hom. κέκασμαι excel and may be traced back to IE *(s)kˆend- become visible. 46 The meaning is transparent, who excels among men, which indicates that the name was originally masculine, with the feminine form a secondary creation. The evolution from *kast(i) to *kass(i), is parallel to (and guaranted by) the pair *Nest(i) ::Ness(i) (cf. Myc. ne-ti-ja-no : : alph. Gr. Νέσσανδρος, see below). The existence of a compound name with a second element καστος or κάστα, namely *Ναυσικάστας, is assured by the short form Ναυσικκαˆ ς* (patron. adj. Ναυσίκκαιος, PHAL, 3rd cent.), cf. Ναυσικα α. κεκασμένη ( στι κεκοσμημένη) τα ς ναυσί, cf.myc.na-u-si-ke-re[-we (dat. /Nausiklewei/ (: Ναυσικλέης). Obvious semantic parallels are the names with πρέπης and φαντος, φα νης ( 2.1 above), for example Λαπρέπεις (PHER, c.224 BC), which is equivalent to Πρεπέλαος (cf. Il κυδι ων, παˆσιν δ μετέπρεπεν ρώεσσιν). Νέσσανδρος (ATR, c BC) is the formal outcome of the Myc. name from Pylos ne-ti-ja-no /Nesti-ānōr/ (Dat. -a-no-re /ānorei/), as M. Peters 45 It is possible that Κορραβο ν (Macedonia) reflects a Greek name *Κορρα-φ ν; cf. Heubeck, Κοίρανος, Κ ρραγος und Verwandtes, 95; in this case, it would be a perfect parallel to the compound names Λεω-φ ν ( short forms of Λᾱ-φάντης, Λεώ-φαντης or of Λεω-φ ντης) and Στρατο-φ ν. 46 Cf. García Ramón Homérico κέκασμαι : védico śaśad, protoario *sćand-, IE *(s)kˆ end- aparecer, hacerse visible, Die Sprache 34 ( ), 27 58, with discussion of the Greek and Vedic material.

17 THESSALIAN PERSONAL NAMES 45 recognized. 47 A short form Νεσσ λος (LAR, 1st cent.?) stands along with Νέσσανδρος, which evokes Νέστωρ (in its turn a short form of ne-ti-ja-no). The first element Nes-ti conceals IE *nes- come home, escape (: νέομαι, and Causat. *nos-éiˆo/e- save, cf. Goth. nasjan σ σαι, OE nerian). As I have tried to show elsewhere, 48 the juncture is continued as an onomastic motif in classical Greek. The verbal lexeme is replaced by the contemporary term for save, namely σώζω, in the first element Σωσι. Νέσσανδρος who brings his men home matches perfectly Σο σανδρος (GYRT, MATR 3rd cent. ). The onomastic juncture reflects Homeric phraseology, as in Od (Athena to Telemachos): ρ ε α θε ς γ θέλων κα τηλ θεν α νδρα σαώσαι. βουλοίμην δ α ν γώ γε κα α λγεα πολλὰ μογήσας ο καδέ τ λθέμεναι κα ν στιμον μαρ δέσθαι where explicit allusion is made to returning (ν στιμον μαρ). Other names attested in Thessaly reflect similar Homeric junctures. 4. SHORT FORMS OF COMPOUND NAMES OR MERE DERIVATIVES? It is sometimes difficult to know whether a particular name apparently based on a common adjective or substantive is derived from it, or is the short form of a compound the second element of which has disappeared. A name may confidently be interpreted as a short form of a compound only when the first (and/or second) phoneme of the second element of the compound has been retained (types Φιλομμ ας : Φιλομήδης or Πάτροκλος : Πατροκλέ1ης). This is the case with Βο δουν, Π ρκος, and Ξοροννο. Let us consider some instances of this type, which is very common throughout Greece. Αγορα ος (HYP, late 3rd cent., THEB, 1st cent.) may be based on α γορά, or it may conceal the first element of a compound. It is important to remember that the name may reflect α γορα meaning assembly, which is characteristic of the Thessalian dialect, as shown by the Gloss α γορα. νομα τ που λιμένος. Θετταλο δ κα τ ν λιμένα α γορὰν καλο σιν. Κρ τες δ τ ν κκλησίαν. παρ Ομήρ δ κα πα ντα α θροισμ ν. 49 The 47 M. Peters, Indogermanische Chronik 32b, Die Sprache 32:2 (1986), no J.-L. García Ramón, Mycenaean Greek personal names: a 2000 survey, Proceedings of the XII Colloquium for Mycenaean Studies (May 2000) (Colloquium Austin) (forthcoming). 49 On the wrong use of the article by Hesychius cf. García Ramón, Del trabajo en una gramática del tesalio, 239 n. 7.

18 46 José-Luis García Ramón Thessalian α γορα is thus the same as that of Homer (Il ) and the λευθέρα α γορα (Arist. Pol a ). 50 The form is also attested in dialectal inscriptions in the formula αγορας ενσας. 51 The byname Αγοραία attested in Atrax (Αθαναι Αγοραια SEG XXVII 184.1, Θεμιστι Αγοραιαι SEG XXVII 183.1, both 4th cent.), 52 suggests Athena as protector goddess of the assembly, rather than of the square or market (which would correspond to the meaning of Attic α γορα, α γορα ζω buy in the market ). Αριθε ς (ATR, 3rd cent.) is a variant of the bird name ριθε ς robinredbreast (Theophr. Sign. 39; Arat. 1025), with a first element α ρι instead of ρι. The appellative ριθε ς is synonymous with ρίθακος (Arist. HA 592 b 22 ) and with ρίθυλος, as shown by the gloss ριθε ς. ρίθακος, τ ρνεον (Hsch.) and by Schol. ad Ar. Vesp. 927 ο τρέφει μία λ χμη δ ο ριθάκους. στι δ ρνεον π μέν τινων καλο μενον ριθε ς, π δ τέρων ρίθυλος. Formations in -ε ς, in -ακος and in -υλος are common both as morphemes derived from a basic word and as onomastic suffixes of short forms of compound names. The coexistence of all three formations in the case of ριθ-, at least in the common noun, may point, in the case of the MN Αριθε ς, either to a (rather enigmatic) basic form with different derivatives, or to short forms of a compound of the type ρίθαυλος (Schol. Ar. Vesp. 922), ριθαλής or the like. Non liquet. 53 Βατθείας (PHARS, 3rd/2nd cent.) presupposes *Βατθε ς, i.e. *Βαθ-ε ς, rather than Βαθίας, which is actually attested (HER, 4th cent.). The name shows dialectal notation τθ for θ, θθ and may be a nickname based on βαθ ς profound, or a short form of Hom. βαθυ-κλ ς or the like. Βο δουν (PHARS, 3rd cent.), corresponding to Βο δων (and parallel to Βο δας, Βουδίων) in other regions, immediately evokes the names Βουδήμων, Βουδ ρκα attested in other regions: in both cases, the second element begins with δ-, which is retained in the corresponding short form Βο δ-. Other compounds with βου of the same type are attested in two glosses of Hesychius, namely βουδάκη. βο πρηστις (a poisonous beetle which kills cows, Hipp.), and βουδ ρ. ν μ, βο ς δέρουσιν. It is irrelevant at this point whether Βου in Βου-δήμων, Βου-δ ρκα has the 50 B. Helly, À Larisa. Bouleversement et remise en ordre des sanctuaires, Mnemosyne 23 (1970), LAR, IG 512, 22 (SEG XXXI 574: 2nd cent.) et passim, SEG XXIX 529, 7 8 (αγορας εονσας); cf. XXXI 575, 8 9 (171 BC). 52 Even if SEG XXVII 183 is earlier (first half of 5th cent. according to K. I. Gallis, Athens Annals of Archaeology 7 (1974), 273 ff.), its first line (Θεμιστι Αγοραια) is to be dated to the first half of 4th cent. 53 The illuminating discussion of ριθε ς by J. L. Perpillou, Les Substantifs grecs en -ε ς (Paris, 1973), 319 ff. does not allow any optimism: Les problèmes posés... sont insolubles.

19 THESSALIAN PERSONAL NAMES 47 same augmentative function as it has in such compounds as βο -παις big young child (Ar.) or βο -συκον big fig. 54 Βο μουν* (patron. adj. Βουμο νειος, KOND? 3rd cent.) may be based on βωμ ς platform, altar, or may be a short form of a compound of the type βωμο-νίκης, βωμο-λ χος and the like. Δαυχνα ος (PHAL, 3rd cent.) is based on δα χνα, which is equivalent to δα φνη, bay (cf. Hsch. δα χνα. δα φνη): the term, being itself pre-greek, may be considered as belonging to the Thessalian lexical stock, 55 for it is attested in dialectal texts, cf. συνδαυχναφοροι (LAR, 5th cent., IG 1027 a, 22), αρχιδαυχναφορεισας (PHAL, 2nd cent., IG 1234, 4). 56 The name may be based on the common appellative, or reflect the first element of a compound. Π ρκος* (patron. adj. Π ρκειος, ATR, 3rd cent.) is a short form of *πυρ-κα1- ς, cf.myc.pu-ka-wo /pūrkawoi/ (Pylos), as the designation of a trade used as a title, and alph. Gr. πυρκαε ς fire kindler (cf. Hom. πυρκαιή pyre ). The name may also be built on πυρκαι ς for burnt-offerings (Myc. MN pu-ko-wo [Pylos]), on πυρ-κ ος watcher of sacrificial fire or on π ρκορος (lex sacra of Argoussa: GHW 4270); the form occurs in Mycenaean, cf. the MN pu-ko-ro (Knossos, Pylos). Χα δας* or Χαδαˆς* (patron. adj. Χαδα ος, Perrhaibia, 3rd cent.), is based on a compound with χα δης of the type πολυ-χαδής (Theocr., Nic.), ε ρυ-χαδής wide-gasping (of cups, Anth. Pal. Luc.), which are the only attested nominal formations corresponding to χανδα νω take. 57 Χοροννο WN (ATR, 3rd cent.) is a short form of Χορονίκη (attested in Attica), with banal gemination of ν, and is the feminine counterpart of Χορ νικος (THEB, 4th 3rd cent.), which reflects the compound χορ νικος victorious with the chorus (Alex. 19: Χορ νικος ποιητ ς δί). 5. NICKNAMES REFLECTING ASPECTS OF EVERYDAY LIFE As in other regions, Thessalian names based on common nouns are extremely informative about what we may call the latent vocabulary. Here we are 54 The existence of an Athena Βουδουνεία (as B. Helly points out to me) and of a place name Βωδώνη in Perrhaibia, as transmitted by Stephanus of Byzantium (Βωδώνη, π λις Περραιβική, ς Απολλ δωρος, ο δ ρθ ς Θετταλίας, α π Βωδωνο ρωος. πολίτης Βωδωνα ος) are not enough, in my opinion, to justify assuming that Βο δουν is a short form of one of them. 55 The form is also Cypriot, cf. ta-u-ka-na-po-ri-o /Dauk h nāp h oriō/ (gen.) as a byname of Apollo. 56 García Ramón, Del trabajo en una gramática del tesalio, 249. The magistrate s title shows both variants of the phytonym in a text from Atrax (SEG XLVII 679: end of the 5th cent.): Ευφορβος αρχιδαυχν αφορες και σ υνδαφναφο ροι. It remains open whether the presence of δα φνη precisely in the local title συνδαφναφ ρος is due to the literary influence. 57 The nasal present goes back to IE *g h ed-, cf. Lat. prae-hendō, praeda, Goth. bi-gitan find.

20 48 José-Luis García Ramón dealing basically with nicknames, dialectal or not, which conceal appellatives belonging either to the common Greek lexical stock or to the specifically regional lexicon. 58 Needless to say, the motifs of the nicknames embrace all aspects of human life. We shall deal with some rather heterogeneous groups: those referring to physical appearance, to human peculiarities and behaviour, to zoonyms, phytonyms, utensils, and bakery. The choice of names is inevitably arbitrary, and should be understood as a sample to illustrate the contribution of Thessalian onomastics to our knowledge of the Greek lexicon. In each group distinction will be made between (1) names which are attested in other regions and (2) names which are (for the present) exclusively attested in Thessaly. Words underlying names of type 2 are not necessarily specifically Thessalian: each instance must be discussed separately Physical Appearance First, some names referring to physical appearance. 59 For the sake of simplicity the names will be given in alphabetical order, 60 irrespective of whether they are based on parts of the body, physical characteristics and disabilities, or personal care or fashion Thessalian Names which are also Attested in Other Regions Βάττας or Βαττας (ATR, 4th cent.), Βαττάρακος* (patron. adj. Βατταράκειος, THEB, 2nd cent.): βάττος and βατταρ ς stammerer ; βατταρίζω stammer, βαττ λογος NT. 61 The existence of an adjective βατταρ ς is plausible in view of the MN Βάτταρος (Herondas), Βατταρας Cf. García Ramón, Cuestiones de léxico y onomástica tesalios, 523 ff. 59 To this list may be added the compound Π ρρανδρος (Achaia Phthiotis, 1st cent.), an individualizing hypostasis of πυρρ ς reddish and α νήρ of the type Θοα νωρ (Hom., also Myc. to-wa-no /T h owānōr/ as the individualization of [θο ς α νήρ]; cf. J.-L. García Ramón, Anthroponymica Mycenaea: 3. Mykenisch to-wa-no /T h owānōr/, homerisch Πρ θοος and Προθοήνωρ, Z iva Antika 50 (2000), The MN Π ρρος, Πυρρέας, Πυρρίας, Πυρρ νος and the like, which may be short forms of compound or nicknames based on simplicia. 60 Several names referring to physical appearance are attested in the Politography Decree of Pharsalos IG 234 ( I.Thess 50: ): Βρεχ ας, Γα σστρουν, Δενδίλος*, Μιλτίας*, Σίμουν, Φ ξινος, or Φοξ νος. 61 For the names based on Βα ττος, which are frequent in Cyrene and recall the founder of the colony and the dynasty of the Βαττι αδαι, cf. O. Masson, Le nom de Battos, fondateur de Cyrène, et un groupe de mots grecs apparentés, Glotta 54 (1976), 84 ff. OGS I, 269 ff. The Thessalian names must be added to the dossier. 62 Cf. O. Masson, En marge du Mime II d Herondas: les surnoms Ioniens Βα τταρος et Βατταρ ας, REG 83 (1970), 356 ff. OGS I, 111 ff.

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

Adjectives. Describing the Qualities of Things. A lesson for the Paideia web-app Ian W. Scott, 2015

Adjectives. Describing the Qualities of Things. A lesson for the Paideia web-app Ian W. Scott, 2015 Adjectives Describing the Qualities of Things A lesson for the Paideia web-app Ian W. Scott, 2015 Getting Started with Adjectives It's hard to say much using only nouns and pronouns Simon is a father.

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΝΟΜΙΚΟ ΚΑΙ ΘΕΣΜΙΚΟ ΦΟΡΟΛΟΓΙΚΟ ΠΛΑΙΣΙΟ ΚΤΗΣΗΣ ΚΑΙ ΕΚΜΕΤΑΛΛΕΥΣΗΣ ΠΛΟΙΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που υποβλήθηκε στο

Διαβάστε περισσότερα

Every set of first-order formulas is equivalent to an independent set

Every set of first-order formulas is equivalent to an independent set Every set of first-order formulas is equivalent to an independent set May 6, 2008 Abstract A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent

Διαβάστε περισσότερα

C.S. 430 Assignment 6, Sample Solutions

C.S. 430 Assignment 6, Sample Solutions C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

Concrete Mathematics Exercises from 30 September 2016

Concrete Mathematics Exercises from 30 September 2016 Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)

Διαβάστε περισσότερα

Συντακτικές λειτουργίες

Συντακτικές λειτουργίες 2 Συντακτικές λειτουργίες (Syntactic functions) A. Πτώσεις και συντακτικές λειτουργίες (Cases and syntactic functions) The subject can be identified by asking ποιος (who) or τι (what) the sentence is about.

Διαβάστε περισσότερα

EE512: Error Control Coding

EE512: Error Control Coding EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

Example Sheet 3 Solutions

Example Sheet 3 Solutions Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note

Διαβάστε περισσότερα

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

the total number of electrons passing through the lamp.

the total number of electrons passing through the lamp. 1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy

Διαβάστε περισσότερα

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ»

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ» I ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΗ ΝΟΜΙΚΩΝ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΠΟΛΙΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ «ΔΙΟΙΚΗΣΗ ΚΑΙ ΟΙΚΟΝΟΜΙΑ» ΚΑΤΕΥΘΥΝΣΗ: ΟΙΚΟΝΟΜΙΚΗ

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

14 Lesson 2: The Omega Verb - Present Tense

14 Lesson 2: The Omega Verb - Present Tense Lesson 2: The Omega Verb - Present Tense Day one I. Word Study and Grammar 1. Most Greek verbs end in in the first person singular. 2. The present tense is formed by adding endings to the present stem.

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

Finite Field Problems: Solutions

Finite Field Problems: Solutions Finite Field Problems: Solutions 1. Let f = x 2 +1 Z 11 [x] and let F = Z 11 [x]/(f), a field. Let Solution: F =11 2 = 121, so F = 121 1 = 120. The possible orders are the divisors of 120. Solution: The

Διαβάστε περισσότερα

Strain gauge and rosettes

Strain gauge and rosettes Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified

Διαβάστε περισσότερα

Instruction Execution Times

Instruction Execution Times 1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables

Διαβάστε περισσότερα

Lecture 2. Soundness and completeness of propositional logic

Lecture 2. Soundness and completeness of propositional logic Lecture 2 Soundness and completeness of propositional logic February 9, 2004 1 Overview Review of natural deduction. Soundness and completeness. Semantics of propositional formulas. Soundness proof. Completeness

Διαβάστε περισσότερα

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας»

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας» ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΠΡΟΣΧΟΛΙΚΗΣ ΑΓΩΓΗΣ ΚΑΙ ΤΟΥ ΕΚΠΑΙ ΕΥΤΙΚΟΥ ΣΧΕ ΙΑΣΜΟΥ «ΠΑΙ ΙΚΟ ΒΙΒΛΙΟ ΚΑΙ ΠΑΙ ΑΓΩΓΙΚΟ ΥΛΙΚΟ» ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που εκπονήθηκε για τη

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

forms This gives Remark 1. How to remember the above formulas: Substituting these into the equation we obtain with

forms This gives Remark 1. How to remember the above formulas: Substituting these into the equation we obtain with Week 03: C lassification of S econd- Order L inear Equations In last week s lectures we have illustrated how to obtain the general solutions of first order PDEs using the method of characteristics. We

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

Chapter 29. Adjectival Participle

Chapter 29. Adjectival Participle Chapter 29 Adjectival Participle Overview (29.3-5) Definition: Verbal adjective Function: they may function adverbially or adjectivally Forms: No new forms because adverbial and adjectival participles

Διαβάστε περισσότερα

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required) Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts

Διαβάστε περισσότερα

Partial Differential Equations in Biology The boundary element method. March 26, 2013

Partial Differential Equations in Biology The boundary element method. March 26, 2013 The boundary element method March 26, 203 Introduction and notation The problem: u = f in D R d u = ϕ in Γ D u n = g on Γ N, where D = Γ D Γ N, Γ D Γ N = (possibly, Γ D = [Neumann problem] or Γ N = [Dirichlet

Διαβάστε περισσότερα

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11 Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and

Διαβάστε περισσότερα

Démographie spatiale/spatial Demography

Démographie spatiale/spatial Demography ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΙΑΣ Démographie spatiale/spatial Demography Session 1: Introduction to spatial demography Basic concepts Michail Agorastakis Department of Planning & Regional Development Άδειες Χρήσης

Διαβάστε περισσότερα

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι She selects the option. Jenny starts with the al listing. This has employees listed within She drills down through the employee. The inferred ER sttricture relates this to the redcords in the databasee

Διαβάστε περισσότερα

Section 7.6 Double and Half Angle Formulas

Section 7.6 Double and Half Angle Formulas 09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)

Διαβάστε περισσότερα

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ting Zhang Stanford May 11, 2001 Stanford, 5/11/2001 1 Outline Ordinal Classification Ordinal Addition Ordinal Multiplication Ordinal

Διαβάστε περισσότερα

Statistical Inference I Locally most powerful tests

Statistical Inference I Locally most powerful tests Statistical Inference I Locally most powerful tests Shirsendu Mukherjee Department of Statistics, Asutosh College, Kolkata, India. shirsendu st@yahoo.co.in So far we have treated the testing of one-sided

Διαβάστε περισσότερα

ST5224: Advanced Statistical Theory II

ST5224: Advanced Statistical Theory II ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known

Διαβάστε περισσότερα

Other Test Constructions: Likelihood Ratio & Bayes Tests

Other Test Constructions: Likelihood Ratio & Bayes Tests Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :

Διαβάστε περισσότερα

Math221: HW# 1 solutions

Math221: HW# 1 solutions Math: HW# solutions Andy Royston October, 5 7.5.7, 3 rd Ed. We have a n = b n = a = fxdx = xdx =, x cos nxdx = x sin nx n sin nxdx n = cos nx n = n n, x sin nxdx = x cos nx n + cos nxdx n cos n = + sin

Διαβάστε περισσότερα

6.1. Dirac Equation. Hamiltonian. Dirac Eq.

6.1. Dirac Equation. Hamiltonian. Dirac Eq. 6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 1: Elements of Syntactic Structure Το περιεχόμενο του μαθήματος διατίθεται με άδεια

Διαβάστε περισσότερα

Συστήματα Διαχείρισης Βάσεων Δεδομένων

Συστήματα Διαχείρισης Βάσεων Δεδομένων ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Συστήματα Διαχείρισης Βάσεων Δεδομένων Φροντιστήριο 9: Transactions - part 1 Δημήτρης Πλεξουσάκης Τμήμα Επιστήμης Υπολογιστών Tutorial on Undo, Redo and Undo/Redo

Διαβάστε περισσότερα

Uniform Convergence of Fourier Series Michael Taylor

Uniform Convergence of Fourier Series Michael Taylor Uniform Convergence of Fourier Series Michael Taylor Given f L 1 T 1 ), we consider the partial sums of the Fourier series of f: N 1) S N fθ) = ˆfk)e ikθ. k= N A calculation gives the Dirichlet formula

Διαβάστε περισσότερα

Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in

Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in : tail in X, head in A nowhere-zero Γ-flow is a Γ-circulation such that

Διαβάστε περισσότερα

Matrices and Determinants

Matrices and Determinants Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z

Διαβάστε περισσότερα

Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your

Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your GP practice in Islington Σε όλα τα Ιατρεία Οικογενειακού

Διαβάστε περισσότερα

Approximation of distance between locations on earth given by latitude and longitude

Approximation of distance between locations on earth given by latitude and longitude Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth

Διαβάστε περισσότερα

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =? Teko Classes IITJEE/AIEEE Maths by SUHAAG SIR, Bhopal, Ph (0755) 3 00 000 www.tekoclasses.com ANSWERSHEET (TOPIC DIFFERENTIAL CALCULUS) COLLECTION # Question Type A.Single Correct Type Q. (A) Sol least

Διαβάστε περισσότερα

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8  questions or comments to Dan Fetter 1 Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test

Διαβάστε περισσότερα

Policy Coherence. JEL Classification : J12, J13, J21 Key words :

Policy Coherence. JEL Classification : J12, J13, J21 Key words : ** 80%1.89 2005 7 35 Policy Coherence JEL Classification : J12, J13, J21 Key words : ** Family Life and Family Policy in France and Germany: Implications for Japan By Tomoko Hayashi and Rieko Tamefuji

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΨΥΧΟΛΟΓΙΚΕΣ ΕΠΙΠΤΩΣΕΙΣ ΣΕ ΓΥΝΑΙΚΕΣ ΜΕΤΑ ΑΠΟ ΜΑΣΤΕΚΤΟΜΗ ΓΕΩΡΓΙΑ ΤΡΙΣΟΚΚΑ Λευκωσία 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ

Διαβάστε περισσότερα

Code Breaker. TEACHER s NOTES

Code Breaker. TEACHER s NOTES TEACHER s NOTES Time: 50 minutes Learning Outcomes: To relate the genetic code to the assembly of proteins To summarize factors that lead to different types of mutations To distinguish among positive,

Διαβάστε περισσότερα

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014 LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV 18 February 2014 Slowly/quietly Clear/clearly Clean Quickly/quick/fast Hurry (in a hurry) Driver Attention/caution/notice/care Dance Σιγά Καθαρά Καθαρός/η/ο

Διαβάστε περισσότερα

Physical DB Design. B-Trees Index files can become quite large for large main files Indices on index files are possible.

Physical DB Design. B-Trees Index files can become quite large for large main files Indices on index files are possible. B-Trees Index files can become quite large for large main files Indices on index files are possible 3 rd -level index 2 nd -level index 1 st -level index Main file 1 The 1 st -level index consists of pairs

Διαβάστε περισσότερα

Solutions to Exercise Sheet 5

Solutions to Exercise Sheet 5 Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X

Διαβάστε περισσότερα

Right Rear Door. Let's now finish the door hinge saga with the right rear door

Right Rear Door. Let's now finish the door hinge saga with the right rear door Right Rear Door Let's now finish the door hinge saga with the right rear door You may have been already guessed my steps, so there is not much to describe in detail. Old upper one file:///c /Documents

Διαβάστε περισσότερα

The Simply Typed Lambda Calculus

The Simply Typed Lambda Calculus Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and

Διαβάστε περισσότερα

Congruence Classes of Invertible Matrices of Order 3 over F 2

Congruence Classes of Invertible Matrices of Order 3 over F 2 International Journal of Algebra, Vol. 8, 24, no. 5, 239-246 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.2988/ija.24.422 Congruence Classes of Invertible Matrices of Order 3 over F 2 Ligong An and

Διαβάστε περισσότερα

The challenges of non-stable predicates

The challenges of non-stable predicates The challenges of non-stable predicates Consider a non-stable predicate Φ encoding, say, a safety property. We want to determine whether Φ holds for our program. The challenges of non-stable predicates

Διαβάστε περισσότερα

6.3 Forecasting ARMA processes

6.3 Forecasting ARMA processes 122 CHAPTER 6. ARMA MODELS 6.3 Forecasting ARMA processes The purpose of forecasting is to predict future values of a TS based on the data collected to the present. In this section we will discuss a linear

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΦΙΛΟΛΟΓΙΑΣ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΦΙΛΟΛΟΓΙΑΣ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΦΙΛΟΛΟΓΙΑΣ Π.Μ.Σ: «Σύγχρονες Προσεγγίσεις στη γλώσσα και στα κείμενα» ΚΑΤΕΥΘΥΝΣΗ ΓΛΩΣΣΟΛΟΓΙΑΣ ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΑΤΡΙΒΗ Το φωνηεντικό

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS

LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS 1. Developing a grammar fragment...1 2. A formalism that is too strong and too weak at the same time...3 3. References...4 1. Developing a grammar fragment The

Διαβάστε περισσότερα

Chapter 2 * * * * * * * Introduction to Verbs * * * * * * *

Chapter 2 * * * * * * * Introduction to Verbs * * * * * * * Chapter 2 * * * * * * * Introduction to Verbs * * * * * * * In the first chapter, we practiced the skill of reading Greek words. Now we want to try to understand some parts of what we read. There are a

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

Διαβάστε περισσότερα

ω ω ω ω ω ω+2 ω ω+2 + ω ω ω ω+2 + ω ω+1 ω ω+2 2 ω ω ω ω ω ω ω ω+1 ω ω2 ω ω2 + ω ω ω2 + ω ω ω ω2 + ω ω+1 ω ω2 + ω ω+1 + ω ω ω ω2 + ω

ω ω ω ω ω ω+2 ω ω+2 + ω ω ω ω+2 + ω ω+1 ω ω+2 2 ω ω ω ω ω ω ω ω+1 ω ω2 ω ω2 + ω ω ω2 + ω ω ω ω2 + ω ω+1 ω ω2 + ω ω+1 + ω ω ω ω2 + ω 0 1 2 3 4 5 6 ω ω + 1 ω + 2 ω + 3 ω + 4 ω2 ω2 + 1 ω2 + 2 ω2 + 3 ω3 ω3 + 1 ω3 + 2 ω4 ω4 + 1 ω5 ω 2 ω 2 + 1 ω 2 + 2 ω 2 + ω ω 2 + ω + 1 ω 2 + ω2 ω 2 2 ω 2 2 + 1 ω 2 2 + ω ω 2 3 ω 3 ω 3 + 1 ω 3 + ω ω 3 +

Διαβάστε περισσότερα

Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς

Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς We review side by side a model of stems ending in ι: πόλις, πόλεως, ἡ = city-state and a masculine model of stems ending in υ: πρέσβυς,

Διαβάστε περισσότερα

PARTIAL NOTES for 6.1 Trigonometric Identities

PARTIAL NOTES for 6.1 Trigonometric Identities PARTIAL NOTES for 6.1 Trigonometric Identities tanθ = sinθ cosθ cotθ = cosθ sinθ BASIC IDENTITIES cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ PYTHAGOREAN IDENTITIES sin θ + cos θ =1 tan θ +1= sec θ 1 + cot

Διαβάστε περισσότερα

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης Α.Τ.Ε.Ι. ΙΟΝΙΩΝ ΝΗΣΩΝ ΠΑΡΑΡΤΗΜΑ ΑΡΓΟΣΤΟΛΙΟΥ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ «Η διαμόρφωση επικοινωνιακής στρατηγικής (και των τακτικών ενεργειών) για την ενδυνάμωση της εταιρικής

Διαβάστε περισσότερα

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 1 State vector space and the dual space Space of wavefunctions The space of wavefunctions is the set of all

Διαβάστε περισσότερα

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

About these lecture notes. Simply Typed λ-calculus. Types

About these lecture notes. Simply Typed λ-calculus. Types About these lecture notes Simply Typed λ-calculus Akim Demaille akim@lrde.epita.fr EPITA École Pour l Informatique et les Techniques Avancées Many of these slides are largely inspired from Andrew D. Ker

Διαβάστε περισσότερα

SCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions

SCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions SCHOOL OF MATHEMATICAL SCIENCES GLMA Linear Mathematics 00- Examination Solutions. (a) i. ( + 5i)( i) = (6 + 5) + (5 )i = + i. Real part is, imaginary part is. (b) ii. + 5i i ( + 5i)( + i) = ( i)( + i)

Διαβάστε περισσότερα

Πτυχιακή Εργασία. Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους

Πτυχιακή Εργασία. Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους ΑΛΕΞΑΝΔΡΕΙΟ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΣΧΟΛΗ ΤΕΧΝΟΛΟΓΙΑΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΜΗΜΑ ΔΙΑΤΡΟΦΗΣ ΚΑΙ ΔΙΑΙΤΟΛΟΓΙΑΣ Πτυχιακή Εργασία Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους Εκπόνηση:

Διαβάστε περισσότερα

Second Order Partial Differential Equations

Second Order Partial Differential Equations Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y

Διαβάστε περισσότερα

Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ

Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ Τμήμα Δημοσίων Σχέσεων & Επικοινωνίας Τεχνολογικό Εκπαιδευτικό Ίδρυμα Ιονίων

Διαβάστε περισσότερα

Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live.

Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live. Topic 1: Describe yourself Write your name, your nationality, your hobby, your pet. Write where you live. Χρησιμοποίησε το and. WRITE your paragraph in 40-60 words... 1 Topic 2: Describe your room Χρησιμοποίησε

Διαβάστε περισσότερα

GREECE BULGARIA 6 th JOINT MONITORING

GREECE BULGARIA 6 th JOINT MONITORING GREECE BULGARIA 6 th JOINT MONITORING COMMITTEE BANSKO 26-5-2015 «GREECE BULGARIA» Timeline 02 Future actions of the new GR-BG 20 Programme June 2015: Re - submission of the modified d Programme according

Διαβάστε περισσότερα

Calculating the propagation delay of coaxial cable

Calculating the propagation delay of coaxial cable Your source for quality GNSS Networking Solutions and Design Services! Page 1 of 5 Calculating the propagation delay of coaxial cable The delay of a cable or velocity factor is determined by the dielectric

Διαβάστε περισσότερα

A Note on Intuitionistic Fuzzy. Equivalence Relation

A Note on Intuitionistic Fuzzy. Equivalence Relation International Mathematical Forum, 5, 2010, no. 67, 3301-3307 A Note on Intuitionistic Fuzzy Equivalence Relation D. K. Basnet Dept. of Mathematics, Assam University Silchar-788011, Assam, India dkbasnet@rediffmail.com

Διαβάστε περισσότερα

Bounding Nonsplitting Enumeration Degrees

Bounding Nonsplitting Enumeration Degrees Bounding Nonsplitting Enumeration Degrees Thomas F. Kent Andrea Sorbi Università degli Studi di Siena Italia July 18, 2007 Goal: Introduce a form of Σ 0 2-permitting for the enumeration degrees. Till now,

Διαβάστε περισσότερα

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Section 1: Listening and Responding/ Aκουστική εξέταση Στο πρώτο μέρος της

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΓΕΩΠΟΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΒΙΟΤΕΧΝΟΛΟΓΙΑΣ ΚΑΙ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ. Πτυχιακή εργασία

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΓΕΩΠΟΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΒΙΟΤΕΧΝΟΛΟΓΙΑΣ ΚΑΙ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ. Πτυχιακή εργασία ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΓΕΩΠΟΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΒΙΟΤΕΧΝΟΛΟΓΙΑΣ ΚΑΙ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ Πτυχιακή εργασία ΜΕΛΕΤΗ ΠΟΛΥΦΑΙΝΟΛΩΝ ΚΑΙ ΑΝΤΙΟΞΕΙΔΩΤΙΚΗΣ ΙΚΑΝΟΤΗΤΑΣ ΣΟΚΟΛΑΤΑΣ Αναστασία Σιάντωνα Λεμεσός

Διαβάστε περισσότερα

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ "ΠΟΛΥΚΡΙΤΗΡΙΑ ΣΥΣΤΗΜΑΤΑ ΛΗΨΗΣ ΑΠΟΦΑΣΕΩΝ. Η ΠΕΡΙΠΤΩΣΗ ΤΗΣ ΕΠΙΛΟΓΗΣ ΑΣΦΑΛΙΣΤΗΡΙΟΥ ΣΥΜΒΟΛΑΙΟΥ ΥΓΕΙΑΣ "

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΠΟΛΥΚΡΙΤΗΡΙΑ ΣΥΣΤΗΜΑΤΑ ΛΗΨΗΣ ΑΠΟΦΑΣΕΩΝ. Η ΠΕΡΙΠΤΩΣΗ ΤΗΣ ΕΠΙΛΟΓΗΣ ΑΣΦΑΛΙΣΤΗΡΙΟΥ ΣΥΜΒΟΛΑΙΟΥ ΥΓΕΙΑΣ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΚΑΛΑΜΑΤΑΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΜΟΝΑΔΩΝ ΥΓΕΙΑΣ ΚΑΙ ΠΡΟΝΟΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ "ΠΟΛΥΚΡΙΤΗΡΙΑ ΣΥΣΤΗΜΑΤΑ ΛΗΨΗΣ ΑΠΟΦΑΣΕΩΝ. Η ΠΕΡΙΠΤΩΣΗ ΤΗΣ ΕΠΙΛΟΓΗΣ ΑΣΦΑΛΙΣΤΗΡΙΟΥ ΣΥΜΒΟΛΑΙΟΥ

Διαβάστε περισσότερα

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS EXERCISE 01 Page 545 1. Use matrices to solve: 3x + 4y x + 5y + 7 3x + 4y x + 5y 7 Hence, 3 4 x 0 5 y 7 The inverse of 3 4 5 is: 1 5 4 1 5 4 15 8 3

Διαβάστε περισσότερα

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- ----------------- Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin

Διαβάστε περισσότερα

Assalamu `alaikum wr. wb.

Assalamu `alaikum wr. wb. LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 7: More about gerunds Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

Διαβάστε περισσότερα

Problem Set 3: Solutions

Problem Set 3: Solutions CMPSCI 69GG Applied Information Theory Fall 006 Problem Set 3: Solutions. [Cover and Thomas 7.] a Define the following notation, C I p xx; Y max X; Y C I p xx; Ỹ max I X; Ỹ We would like to show that C

Διαβάστε περισσότερα

Homework 8 Model Solution Section

Homework 8 Model Solution Section MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx

Διαβάστε περισσότερα

ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α. Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:.

ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α.  Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:. ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α 2 ειδήσεις από ελληνικές εφημερίδες: 1. Τα Νέα, 13-4-2010, Σε ανθρώπινο λάθος αποδίδουν τη συντριβή του αεροσκάφους, http://www.tanea.gr/default.asp?pid=2&artid=4569526&ct=2 2. Τα Νέα,

Διαβάστε περισσότερα

Μηχανική Μάθηση Hypothesis Testing

Μηχανική Μάθηση Hypothesis Testing ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Μηχανική Μάθηση Hypothesis Testing Γιώργος Μπορμπουδάκης Τμήμα Επιστήμης Υπολογιστών Procedure 1. Form the null (H 0 ) and alternative (H 1 ) hypothesis 2. Consider

Διαβάστε περισσότερα

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS ΟΜΗΡΟΥ ΙΛΙΑΔΑ ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS www.scooltime.gr [- 2 -] The Project Gutenberg EBook of Iliad, by Homer This ebook is for the use of anyone anywhere at no cost and with almost no restrictions

Διαβάστε περισσότερα

Living and Nonliving Created by: Maria Okraska

Living and Nonliving Created by: Maria Okraska Living and Nonliving Created by: Maria Okraska http://enchantingclassroom.blogspot.com Living Living things grow, change, and reproduce. They need air, water, food, and a place to live in order to survive.

Διαβάστε περισσότερα

Modern Greek Extension

Modern Greek Extension Centre Number 2017 HIGHER SCHOOL CERTIFICATE EXAMINATION Student Number Modern Greek Extension Written Examination General Instructions Reading time 10 minutes Working time 1 hour and 50 minutes Write

Διαβάστε περισσότερα

Η αλληλεπίδραση ανάμεσα στην καθημερινή γλώσσα και την επιστημονική ορολογία: παράδειγμα από το πεδίο της Κοσμολογίας

Η αλληλεπίδραση ανάμεσα στην καθημερινή γλώσσα και την επιστημονική ορολογία: παράδειγμα από το πεδίο της Κοσμολογίας Η αλληλεπίδραση ανάμεσα στην καθημερινή γλώσσα και την επιστημονική ορολογία: παράδειγμα από το πεδίο της Κοσμολογίας ΠΕΡΙΛΗΨΗ Αριστείδης Κοσιονίδης Η κατανόηση των εννοιών ενός επιστημονικού πεδίου απαιτεί

Διαβάστε περισσότερα

5.4 The Poisson Distribution.

5.4 The Poisson Distribution. The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable

Διαβάστε περισσότερα

Ρηματική άποψη. (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect)

Ρηματική άποψη. (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect) 15 Ρηματική άποψη (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect) imperfective perfective Verb forms in Modern Greek are based either on the imperfective or the perfective

Διαβάστε περισσότερα