03 an introduction to ancient greek language:

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "03 an introduction to ancient greek language:"

Transcript

1 01 an introduction to ancient greek language: we shall attempt to introduce this language in an oversimplified manner. in this introductory coverage, we shall attempt to make a comparison with modern greek and/or latin, whenever feasible. Nouns: in gender they have 3 which are masculine, feminine and neuter (similar to modern greek and latin). in number, they have 3 which are singular plural and dual (modern greek and latin do not have the dual, but arabic has it). nouns declined similar to latin and have 3 different groups (while latin has five and modern greek nouns are first divided into masculine, feminine and neuter before being declined). with regards to verbs, the have 3 singular persons, 3 plural and 2 dual (as mentioned before this dual issue does not exist neither in latin nor modern greek). 02 an introduction to ancient greek language: Th ancient greek alphabet has 24 letters of which there are seven vowels, vowels can be short or long, open or close. vowels and diphthongs can be hard or soft (breathing) when they fall in the beginning of the word. there are 8 diphthongs and 3 imperfect diphthongs. there are 3 classes of consonants which are mutes (silent consonants) i.e. cannot be pronounced without a vowel, semivowels which can be pronounced without a vowel and double consonants. there are 3 accents (in modern greek there is only one, while in french there are the same three accents). they were invented by grammarians at about 200 BC. fyi: modern greek debut was in the eleventh century. 03 an introduction to ancient greek language: το ελληνικό αλφάβητο: α (short as in mat or long as in hate), β (b), γ (hard as in get), δ (d), ε (always short as in met), ζ (z), η (always long as the first e in here), θ (th), ι (short as in sit or long as in bite), κ (k), λ (l), μ (m), ν (n), ξ (x, pronounced xi), ο, (short as in spot) π (p), ρ (r), σ (s) ή ς (at the end od the word), τ (t), υ (generally long as in tune, sometimes short as in hut), φ ((pf), χ (kh), ψ (ps), ω (long as in tone). Α, ε, η, ο and ω are called open vowels while ι and υ are closed vowels. the 8 diphthongs (δίφθογγοι - double sounding) are: αι (like ai in aisle), αυ (au in taught), ει (ei in height), ευ (eu in feudal), οι (oi in oil), ου (ou in sound), ηυ (eu in feudal), υι (wi in wine), which are formed by a combination of an open vowel with a closed one with 1 exception which is the last one. the 3 imperfect (improper) diphthongs are formed by union of α, η, ω with ι that is written beneath the vowel and is called Iota subscript. the pronounciation of ancien greek diphthongs differs than the modern greek ones. the modern greek diphthongs are: ει, οι, αι, ου. 04 an introduction to ancient greek language: Consonants: the double consonts are: ξ (κ + σ), ψ (π + σ) & ζ (δ + σ). the simple consonants can be divided into labials (π, β, φ, μ), palatals (κ, λ, χ) and linguals (τ, δ, θ, σ, λ, ν & ρ). by another classification, they are divided into semivowels and mutes. the semivowels are λ, μ, ν, ρ, σ. nasal γ they are subclassified into liquids (λ, μ, ν, ρ), nasals (μ, ν, nasal γ) and spirant (σ). the mutes are of 3 orders: smooth (π, κ, τ), middld mute (β, γ, δ) and rough mute (φ, χ, θ). they also correspond to the following classes: labial mutes (π, β, φ), palatal mutes (κ, γ, χ), lingual mutes(τ, δ, θ).

2 fyi: the ionic greek alphabet was first introduced officialy in Athens in 403 BC. the only consonants which can end a greek word are: ν, ρ, ς, if others are left at the end of a word, they are dropped. 05 an introduction to ancient greek language: Euphony of vowels: a succession of 2 vowels (not forming a diphthong) apparently was in general displeasing to the Athenians. collision of vowels was avoided through the following techniques: contraction (when it happens in the middle of a word) and when it happens between 2 words (hiatus), it was avoided by any of the following: crasis, elision, aphaeresis or adding a movable consonant to the former word. crasis means mixture, when a vowel or diphthong appears at the end of the word, it may be contracted with the one at the beginning of the following word. elision is the action of dropping a final vowel i a word when the next word begins with a vowel. an apostrophe marks the omission. aphaeresis which means taking off happens when a short vowel at the beginning of the word is dropped after a long vowel or a diphthong at the end of the preceding word.. movable consonants. example for a movable cobsonant is ν, generally it is added to the word ending in a vowel (example ε) when the next word begins with a vowel. 06 an introduction to ancient greek language: indefinite article declension: in ancient greek, the definite article has gender (masc., fem. & neuter), has number (sing., dual & plural) and has case for each gender/number combination (nominative, accusative, genitive & dative). 1) nominative case: 1-1) singular: ο, η (aspired,rough breathing), τό 1-2) plural: οι, αι, τά. 1-3) dual: τώ, τώ, τώ. 2) accusative case: 2-1) τόν, τήν, τό. 2-2) τούς, τάς, τά 2-3) τώ, τώ, τώ. 3) genitive case: 3-1) του, της, του (the υ & η have the circumflex accent) 3-2) των, των, των (the ω has the circumflex accent). 3-3) τοιν, τοιν, τοιν (the i has the circumflex accent). 4) dative case: 4-1) τω, τη, τω (the ω & η have the circumflex accent and the iota subscript beneath the character). 4-2) τοις, ταις, τοις (the ι has the circumflex accent). 4-3) τοιν, τοιν, τοιν (the ι has the circumflex accent). In modern greek: οδιστικό άρθρο/definite article ο, η, το, οι, οι, τα το (ν), τη (ν), το, τους, τις, τα του, της, του, των αόριστο άρθρο/indefinite article ένας, μια, ένα

3 ένα (ν), μια, ένα ενός, μιας, ενός nouns' declension: when it comes to the declension of nouns, nouns are divided into 3 groups, stem ending in a, stems ending in o and stems ending in one of the following: consonant, vowels (ι, υ, ο, ω) or diphthongs (αυ, ευ, ου). on the other hand, the latin nouns are divided into 5 groups: a-declension, o-declension, consonant declension, u-declension and e-declension. 07 an introduction to ancient greek language: a-declension: are either feminines or masculines: examples: for feminine nouns: stem: χωρα, φιλια, γλωσσα, τιμα. nom: sing /plural/dual: χώρα/χωραι/χώρα, φιλία/φιλιαι/φιλία, γλωσσα/γλωσσαι/γλωσσα, τιμή/τιμαί/τιμα. acc: χώραν/χώρας/χώρα, φιλίαν/φιλίας/φιλία, γλωσσαν/γλωσσας/γλώσσα, τιμήν/τιμας/τιμα. gen: χώρας/χωρων/χώραιν, φιλίας/φιλιων/φιλίαιν, γλώσσης/γλωσσων/γλώσσαιν, τιμης/τιμων/τιμαιν dat: χώρα/χώραις/χώραιν, φιλία/φιλίαις/φιλίαιν, γλώσση/γλώσσαις/γλώσσαιν, τιμη/τιμαις. voc: χώρα/χώραι/χώρα, φιλία/φίλιαι/φιλία, γλωσσα/γλωσσαι/γλώσσα, τιμή/τιμαί/τιμα for masc. nouns: nom.: νεανίας/νεανίαι/νεανία, πολίτης/πολιται/πολιτα. acc.: νεανίαν/νεανίας/νεανία, πολίτην/πολίτας/πολίτα. gen.: νεανίου/νεανιων/νεανίαιν, πολίτου/πολιτων/πολίταιν. dat.: νεανία/νεανίαις/νεανίαιν, πολίτη/πολιταις/πολίταιν. voc.: νεανία/νεανίαι/νεανία, πολιτα/πολιται/πολίτα. Note: not all signs are shown, like accents, breathing or iota-subscript, as the modern greek keyboard lack such signs. in modern greek, the endings are function of the noun in the nominative singular. example endings are α, η (fem) και ας, ης (masc.). α, ες nominative, sing.: ταβέρνα nominative, plural: ταβέρνες accusative, sing.: ταβέρνα accusative, plural: ταβέρνες genitive, sing.: ταβέρνας genitive, plural: ταβερνών vocative, sing: ταβέρνα vocative, plural: ταβέρνες η, ες nominative, sing.: ψυχή nominative, plural: ψυχές

4 accusative, sing.: ψυχή accusative, plural: ψυχές genitive, sing.: ψυχής genitive, plural: ψυχών vocative, sing: ψυχή vocative, plural: ψυχές ας, ες nominative, sing.: ο αναπτήρας nominative, plural: οι αναπτήρες accusative, sing.: τον αναπτήρα accusative, plural: τους αναπτήρες genitive, sing.: του αναπτήρα genitive, plural: των αναπτήρων vocative, sing: απαπτήρα, vocative, plural: αναπτήρες ης, ες nominative, sing.: υπολογιστής nominative, plural: υπολογιστές accusative, sing.:υπολογιστή accusative, plural: υπολογιστές genitive, sing.: υπολογιστή genitive, plural: υπολογιστών vocative, sing.: υπολογιστή vocative, plural: υπολογιστές in latin the a-declension nouns are feminine with few exceptions, there are some similarity in the endings' sounds with ancient greek. 08 an introduction to ancient greek language: the second declension or the o-declension: these nouns could be masculine or neuter with few feminine ones. the masculine nouns could be equivalent to those ending in ος in the nominative singular in modern greek. a few feminine nouns in modern greek (like οδός) also come from this group. in modern greek, the neuter nouns ending in o also were originated from this group, for example δώρο, νόσος. for masculine nouns: nom.: ανθδωπος/ανθρωποι/ανθρώπω. acc: ανθρωπον/ανθρώπους/ανθρώπω. gen: ανθρώπου/ανθρώπων/ανθρώποιν. dat: ανθρώπω/ανθρώποις/ανθρώποιν voc: ανθρωπε/ανθρωποι/ανθρώπω. for neuter nouns: nom: δωρον/δωρα/δώρω.

5 acc: δωρον/δωρα/δώρω. gen: δώρου/δώρων/δώροιν. dat: δώρω/δώροις/δώροιν. voc: δωρον/δωρα/δώρω. note: we are not going to cover the attic second declension here. 09 an introduction to ancient greek language: the stem of the third declension nouns may end in consonants, vowels or diphthongs. the nouns could be masculine, feminine or neuter. the neuter nouns' stems may end in a consonant or in υ. the masculine and feminine nouns may end in any of the guttural or labial mutes (κ, γ, χ, π, β φ), dental mutes (τ, δ θ), αντ, οντ, liquid (λ,ρ), nasal ν, σ, vowels (ι, υ), diphthongs (ευ, αυ, ου), vowels (ο, ω). examples: 1) stems in κ, γ, χ, π, β, φ: (φυλακ, μαστιγ, ονυχ, φλεβ: nom: ο/η φύλαξ/φύλακες/δύλακε, η μάστιξ/μάστιγες/μάστιγε, ο ονυξ/ονυχες/ονυχε, η φλέψ/φλέβες/φλέβε. acc: φύλακα/φύλακας/φύλακε, μάστιγα/μάστιγας/μάστιγε, ονυχα/ονυχας/ονυχε, φλέβα/φλέβας/φλέβε. gen: φύλακος/φυλάκων/φυλάλοιν, μάστιγος/μαστίγων/μαστίγοιν, ονυχος/ονύχων/ονύχοιν, φλεβός/φλεβων/φλεβοιν dat: φύλακι/φύλαξιν/φυλάκοιν, μάστιγι/μάστιξιν/μαστίγοιν, ονυχι/ονυξιν/ονύχοιν, φλεβί/φλεψίν/φλεβοιν. voc: same as nominative. 2) stems ending on τ, δ θ: λαμπαδ, εριδ, πατριδ: nom: η λαμπάς/λαμπάδες/λαμπάδε, η ερις/εριδες/εριδε, η πατρίς/πατρίδες/πατρίδε. acc: λαμπάδα/λαμπάδας/λαμπάδε, εριν/εριδας/εριδε, πατρίδα/πατρίδας/πατρίδε. gen: λαμπάδος/λαμπάδων/λαμπάδοιν, εριδος/ερίδων/ερίδοιν, πατρίδος/πατρίδων/πατρίδοιν. dat: λαμπάδι/λαμπάσιν/λαμπάδοιν, εριδι/ερισιν/ερίδοιν, πατρίδι/πατρίσιν/πατρίδοιν. voc: same as nominative case. 3) stems which end in αντ, οντ. γιγαντ, οδονυ, λροντ. nom: ο γίγας/γίγαντες/γίγαντε, ο οδούς/οδόντες/οδόντε, ο λέων/λέοντες/λέοντε. acc: γίγαντα/γίγαντας/γίγαντε, οδόντα/οδόντας/οδόντε, λέοντα/λέοντας/λέοντε. gen: γίγαντος/γιγάντων/γιγάντοιν, οδόντος/οδόντων/οδόντοιν, λέοντος/λεόντων/λεόντοιν. dat: γίγαντι/γίγασιν/γιγάντοιν, οδόντι/οδουσιν/οδόντοιν, λέοντι/λέουσιν/λεόντοιν voc: same as nominative case with one exception with certain nouns, eg. λέων & λέον. 4) stems which end in λ, ρ (liquids): stems are: αλ, θηρ, ρητορ, μητερ. nom: ο αλς/αλες/αλε, ο θήρ/θήρες/θηρε, ο ρήτορ/ρήτορεσ/ρήτορε, η μήτηρ/μητέρες/μητέρρ acc: αλα/αλας/αλε, θηρα/θηρας/θηρε, ρήτορα/ρήτορας/ρήτορε, μητέρα/μητέρας/μητέρε. gen: αλός/αλων/αλοιν, θηρος/θηρων/θηροιν, ρήτορος/ρητόρων/ρητόροιν, μητρός/μητέρων/μητέροιν. dat: αλί/αλσίν/αλοιν, θηρί/θηρσίν/θηροιν, ρήτορι/ρήτορσιν/ρητόροιν, μητρί/μητρασιν/μητέροιν.

6 voc: same as nom with few exceptions, with ρ stem, when ρ is preceded by a short vowel and the word is not accented on the last syllable, the voc. case does not change it, eg. μητερ: μήτηρ/μητερ, when the last syllable is accented, the acc is the same as nom (with few exceptions,. πατήρ πατέρ, 5) stems which end in nasal ν: stems are: Έλλην, ηγεμον, δελφιν. nom: ο Έλλην/Έλληνες/Έλληνε, ο ηγεμών/ηγεμόνες/ηγεμόνε, ο δελφίς/δελφινες/δελφινε. acc: Έλληνα/Έλληνας/Έλληνε, ηγεμόνα/ηγεμόνας/ηγεμόνε, δελφινα/δελφινας/δελφινε. gen: Έλληνος/Έλλήνων/Ελλήνοιν, ηγεμόνος/ηγεμόνων/ηγεμόνοιν, δελφινος/δελφίνων/δελφίνοιν. dat: Έλληνι/Έλλησιν/Ελλήνοιν, ηγεμόνι/ηγεμόσιν/ηγεμόνοιν, δελφινι/δελφισιν/δελφίνοιν. voc: the same like the nom. 6) stems which end in vowels υ, ι: πολι, συ, πηζυ nom: η πόλις/πόλεις/πόλει, ο/η συς//συες/συε, ο πηχυς/πήχεις/πήχει. acc: πόλιν/πόλεις/πόλει, συν/συς/συε, πηχυν/πήχεις/πήχει. gen: πόλεως/πόλεων/πολέοιν, συός/συων/συοιν, πήχεως/πήχεων. dat: πόλει/πόλεσιν/πολέοιν, συί/συσίν/συσοιν, πήχει/πήχεσιν. voc: it similar to the nominative case except for the sing.: πόλι, συ, πηχυ. 7) stems which end in diphthongs (ευ, αυ, ου): βασιλευ, γραυ, βου nom: ο βασιλευς/βασιλς/βασιλη, η γραυς/γραες/γραε, ο/η βους/βοές/βόε. acc: βασιλέα/βασιλέας/βασιλη, γραυν, γραυς, γραε, βουν/βους/βόε. gen: βασιλέως/βασιλέων/βασιλέοιν, γραός/γραων/γραοιν, βοός/βοων/βοοιν. dat: βασιλει/βασιλευσιν/βασιλέοιν, γραί/γραυσιν/γραοιν, βοί/βουσιν/βοοιν. voc: βασιλευ, γραυ, βου, for thd plural and the dual, they are identical to the nominative case. 8) stems which end in vowels ο, ω: πειθο, ήρω nom: η πειθώ, ο ηρως/ηρωες/ηρωε acc: πειθώ, ηρω (ηρωα)/ηρως (ηρωας)/ηρωε. gen: πειθους, ηρωος/ηρώων/ηφώοιν dat: πειθοι, ηρωι (ηρω)/ηρωσιν/ηρώοιν. voc: same like above only the singular is different: πειθοι. 9) stems which end in σ: Δημοσθενες, Ηρακλης, τριήρης. nom: ο Δημοσθένης, ο Ηρακλης, η τριήρης/τριήρρις/τδιήρει. acc: Δημοσθένη, Ηρακλέα, τριήρι/τριήρεις/τριήρει. gen: Δημοσθένους, Ηρακλέους, τριήρους/τριήρων/τριηροιν. dat: Δημοσθένει, Ηρακλει, τριήρει/τριήρεσιντρηροιν. voc: τριηρες for voc. Sing. Neuter nouns: examples: 1) stems which end in a consonant. the stems are: σωματ, τερατ, κρεας, γενες. nom: το σωμα/σώματα/σώματε, το τέρας/τέρατα/τέρατε, το κρεας/κρεα, το γένος/γένη/γένει acc: σωμα/σώματα/σώματε, τέρας/τέρατα/τέρατε, κρέας/κρέα, γένος/γένη/γένει. gen: σώματος/σωμάτων/σωμάτοιν, τέρατοε/τεράτων/τεράτοιν, κρέως/κρεων, γενους/γενων/γενοιν dat: σώματι/σώμασιν/αωμάτοιν, τέρατι/τέρασιν/τεράτοιν, κρέα/κρέασιν, γένει/γένεσιν/γενοιν. voc: same as nom. case.

7 2) stem which end in υ. αστυ nom: το αστυ/αστη/αστει acc: αστυ/αστη/αστει gen: αστεως/αστέων/αστέοιν dat: αστει/αστεσιν/αστέοιν voc: same as nom. case.

03 an introduction to ancient greek language:

03 an introduction to ancient greek language: 01 an introduction to ancient greek language: we shall attempt to introduce this language in an oversimplified manner. in this introductory coverage, we shall attempt to make a comparison with modern greek

Διαβάστε περισσότερα

03 an introduction to ancient greek language:

03 an introduction to ancient greek language: 01 an introduction to ancient greek language: we shall attempt to introduce this language in an oversimplified manner. in this introductory coverage, we shall attempt to make a comparison with modern greek

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

Galatia SIL Keyboard Information

Galatia SIL Keyboard Information Galatia SIL Keyboard Information Keyboard ssignments The main purpose of the keyboards is to provide a wide range of keying options, so many characters can be entered in multiple ways. If you are typing

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

The Accusative Case. A Target for the Action. A lesson for the Paideia web-app Ian W. Scott, 2015

The Accusative Case. A Target for the Action. A lesson for the Paideia web-app Ian W. Scott, 2015 The Accusative Case A Target for the Action A lesson for the Paideia web-app Ian W. Scott, 2015 The Accusative Case So far we've seen three noun cases Nominative Genitive Vocative We need one more case

Διαβάστε περισσότερα

Croy Lesson 18. First Declension. THIRD Declension. Second Declension. SINGULAR PLURAL NOM -α / -η [-ης]* -αι. GEN -ας / -ης [-ου]* -ων

Croy Lesson 18. First Declension. THIRD Declension. Second Declension. SINGULAR PLURAL NOM -α / -η [-ης]* -αι. GEN -ας / -ης [-ου]* -ων Croy Lesson 18 First Declension SINGULAR PLURAL NOM -α / -η [-ης]* -αι GEN -ας / -ης [-ου]* -ων DAT -ᾳ / -ῃ -αις ACC -αν / -ην -ας VOC -α / -η -αι *Masculine Nouns of First Declension Second Declension

Διαβάστε περισσότερα

LESSON TEN: THE ADJECTIVE. Memorization of vocabulary ten

LESSON TEN: THE ADJECTIVE. Memorization of vocabulary ten LESSON TEN: THE ADJECTIVE Memorization of vocabulary ten ἀγαθος good ἁγιος holy, set apart ἀλλα but (the regular contrasting particle, with δε used at times) ἀληθεια truth ἀληθινος true/genuine αὐτος he

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

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

Present Participles. Verbal Adjectives with Present Aspect. A lesson for the Paideia web-app Ian W. Scott, 2015

Present Participles. Verbal Adjectives with Present Aspect. A lesson for the Paideia web-app Ian W. Scott, 2015 Present Participles Verbal Adjectives with Present Aspect A lesson for the Paideia web-app Ian W. Scott, 2015 Participles with Present Aspect Participle = a verbal adjective Allows a whole clause to tell

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

Modern Greek Grammar Konstantinos Athanasiou

Modern Greek Grammar Konstantinos Athanasiou 7. Nouns / Ουσιαστικά Nouns in Greek are declinable words and may be classified as masculine, feminine or neuter. Although the determination of the grammatical gender of the Greek words is often arbitrary,

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

Declension of the definite article

Declension of the definite article Greek alphabet Α α Alpha Ν ν Nu Β β Beta Ξ ξ Xi Γ γ Gamma Ο ο Omicron Δ δ Delta Π π Pi Ε ε Epsilon Ρ ρ Rho Ζ ζ Zeta Σ σ ς Sigma Η η Eta Τ τ Tau Θ θ Theta Υ υ Upsilon Ι ι Iota Φ φ Phi Κ κ Kappa Χ χ Khi

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

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

Περισσότερα ουσιαστικά

Περισσότερα ουσιαστικά 5 Περισσότερα ουσιαστικά (More nouns) Α. Plural in -εις There is a subgroup of feminine nouns ending in -η that have different forms. Θα ψωνίσω στις εκπτώσεις γιατί βρίσκω καλύτερες τιμές Σήμερα θα δούμε

Διαβάστε περισσότερα

NOM -**- [**] -ες / -εις [-α ] GEN -ος / -ως / -ους -ων. DAT -ι -σι. ACC -α / -ιν [**] -ας / -εις [-α ]

NOM -**- [**] -ες / -εις [-α ] GEN -ος / -ως / -ους -ων. DAT -ι -σι. ACC -α / -ιν [**] -ας / -εις [-α ] Croy Lesson 18 First Declension SINGULAR PLURAL NOM -α / -η [-ης]* -αι GEN -ας / -ης [-ου]* -ων DAT -ᾳ / -ῃ -αις ACC -αν / -ην -ας VOC -α / -η -αι *Masculine Nouns of First Declension Second Declension

Διαβάστε περισσότερα

Επίθετα. (Adjectives)

Επίθετα. (Adjectives) 6 Επίθετα (Adjectives) Greek adjectives are inflected words which either modify nouns (τα κόκκινα τριαντάφυλλα) or attribute a property to them (τα τριαντάφυλλα είναι ακριβά). Adjectives must agree with

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

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

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

CHAPTER 2: THE FARMER

CHAPTER 2: THE FARMER 10 Elementary Ancient Greek CHAPTER 2: THE FARMER DECLENSION PARADIGMS The Definite Article, Masculine sing. pl. Nom. ὁ οἱ Gen. τοῦ τῶν Dat. τῷ τοῖς Acc. τόν τούς -ος Declension Endings sing. pl. Nom.

Διαβάστε περισσότερα

Summer Greek. Lesson 3. NOUNS GENDER (does not refer to fe/male) masculine feminine neuter NUMBER singular plural. NOUNS -Case.

Summer Greek. Lesson 3. NOUNS GENDER (does not refer to fe/male) masculine feminine neuter NUMBER singular plural. NOUNS -Case. A Summer Greek Lesson 3 Ω Parts of Speech NOUN- person, place, thing, quality, idea, or action ARTICLE Indefinite = a / an ; Definite = the ADJECTIVE- describes a noun (includes in/definite articles) PRONOUN-word

Διαβάστε περισσότερα

Λέξεις, φράσεις και προτάσεις

Λέξεις, φράσεις και προτάσεις 1 Λέξεις, φράσεις και προτάσεις (Words, phrases and clauses) The Greek language, like all human languages, has a Lexicon and a Grammar that are used to create sentences. The Lexicon consists of the words

Διαβάστε περισσότερα

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

LESSON SEVEN: A BREAK FROM THE VERB AND INTRODUCTION OF THE NOUN

LESSON SEVEN: A BREAK FROM THE VERB AND INTRODUCTION OF THE NOUN LESSON SEVEN: A BREAK FROM THE VERB AND INTRODUCTION OF THE NOUN A. Summary on the verb So far we have been focused on the verb, and particularly the verb in the indicative mood and active voice. There

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

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

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

22.1: Root Aorist (Athematic Long-Vowel Aorist)

22.1: Root Aorist (Athematic Long-Vowel Aorist) 22.1: Root Aorist (Athematic Long-Vowel Aorist) A THIRD AORIST? In previous lessons you learned the following types of active aorist conjugations: ἔπαυσα First aorist (Lesson 9). A regular tense that we

Διαβάστε περισσότερα

LESSON EIGHT: FIRST DECLENSION NOUNS. lawlessness, wickedness (νοµος is law) ἀντιχριστος anti-christ beginning, origin

LESSON EIGHT: FIRST DECLENSION NOUNS. lawlessness, wickedness (νοµος is law) ἀντιχριστος anti-christ beginning, origin LESSON EIGHT: FIRST DECLENSION NOUNS Memorization of Vocabulary eight ἀλαζονεια pride, arrogance ἀληθεια truth ἀκουω I hear ἁµαρτια sin ἀνοµια lawlessness, wickedness (νοµος is law) ἀντιχριστος anti-christ

Διαβάστε περισσότερα

2018 Greek Language Final Assessment Review and Study-guide 2 nd Grade:

2018 Greek Language Final Assessment Review and Study-guide 2 nd Grade: 2018 Greek Language Final Assessment Review and Study-guide 2 nd Grade: TABLE OF CONTENTS Q. # SUBJECT Pg. # 1) -Date: Full Greek Date 2 2) -Name: Greek First and Last Name 2 3) -Q&A: Frequently used Questions

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

Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1

Main source: Discrete-time systems and computer control by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 A Brief History of Sampling Research 1915 - Edmund Taylor Whittaker (1873-1956) devised a

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

Herodian and the Greek language: rules of thumb for accenting Greek enclitics. Stephanie Roussou (a joint project with Philomen Probert)

Herodian and the Greek language: rules of thumb for accenting Greek enclitics. Stephanie Roussou (a joint project with Philomen Probert) Herodian and the Greek language: rules of thumb for accenting Greek enclitics Stephanie Roussou (a joint project with Philomen Probert) What are enclitics? Enclitics are small words forming close-knit

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

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

Croy Lessons Second Declension. First Declension PARTICIPLES. THIRD Declension. -αι -ας. -ον. -οι. -ος. / -ης. -ων. -ου. -αν. / -ον.

Croy Lessons Second Declension. First Declension PARTICIPLES. THIRD Declension. -αι -ας. -ον. -οι. -ος. / -ης. -ων. -ου. -αν. / -ον. Croy Lessons 18-20 Greek Verb Formation Αug Redp STEM Tense Theme Ending PRES ACT -- STEM -- o/ε PRES M/P/D -- STEM -- o/ε IMPF ACT ἐ STEM -- o/ε ΙΜPF M/P ἐ STEM -- o/ε FUT ACT -- STEM σ o/ε FUT M/D --

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 11: The Unreal Past Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

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

Subject - Students love Greek.

Subject - Students love Greek. A Summer Greek 2009 Ω Parts of Speech NOUN - person, place, thing, quality, idea, or action ARTICLE Indefinite = a / an ; Definite = the ADJECTIVE - describes a noun (includes in/definite articles) VERB

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

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0. DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec

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

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

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

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

two-case nominative two-case nominative forms accusative forms accusative genitive genitive three-case forms nominative accusative genitive

two-case nominative two-case nominative forms accusative forms accusative genitive genitive three-case forms nominative accusative genitive 4 Ουσιαστικά (Nouns) Greek nouns can be masculine, feminine or neuter. They have different case forms (,, and ) which are associated with different functions (cf. syntactic functions, nouns as complements).

Διαβάστε περισσότερα

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΣΥΓΚΡΙΤΙΚΗ ΜΕΛΕΤΗ ΤΗΣ ΣΥΓΚΡΑΤΗΤΙΚΗΣ ΙΚΑΝΟΤΗΤΑΣ ΟΡΙΣΜΕΝΩΝ ΠΡΟΚΑΤΑΣΚΕΥΑΣΜΕΝΩΝ ΣΥΝΔΕΣΜΩΝ ΑΚΡΙΒΕΙΑΣ

Διαβάστε περισσότερα

CRASH COURSE IN PRECALCULUS

CRASH COURSE IN PRECALCULUS CRASH COURSE IN PRECALCULUS Shiah-Sen Wang The graphs are prepared by Chien-Lun Lai Based on : Precalculus: Mathematics for Calculus by J. Stuwart, L. Redin & S. Watson, 6th edition, 01, Brooks/Cole Chapter

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

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

Παρελθόν. (Past) Formation. past imperfective. past perfective. active forms Α / Β Α Β

Παρελθόν. (Past) Formation. past imperfective. past perfective. active forms Α / Β Α Β 12 Παρελθόν (Past) In Greek there are three different sets of forms (both active and medio-passive), which refer to the past: the past perfective (αόριστος), the past imperfective (παρατατικός) and the

Διαβάστε περισσότερα

d. Case endings (Active follows declension patterns, Middle follows declension patterns)

d. Case endings (Active follows declension patterns, Middle follows declension patterns) Mounce 8 Handout: Aorist-stem PTCs Dr. Phillip Marshall. st Aorist Active and Middle PTC formations: a. Use Aorist Active stem, UN-augmented (not indicative!) b. Tense formative: -σα- c. Participle morpheme:

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

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

HW 13 Due THURSDAY May 3, 2018

HW 13 Due THURSDAY May 3, 2018 Όνομα: Τάξη: Αριθμό# (Greek First and Last name) Name: HW 13 Due THURSDAY May 3, 2018 For My HW 13: - PRINT HW 13 packet and bring to class on THURSDAY May 3, 2018! - Write my name (Greek and English),

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

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

Ονοματική Φράση (Noun Phrase)

Ονοματική Φράση (Noun Phrase) 3 Ονοματική Φράση (Noun Phrase) Άρθρα (Articles) The articles are definite (ο, η, το) and indefinite (ένας, μία, ένα). They agree in gender, number and case with the noun they modify. Είναι ο φίλος μου

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

LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG. 4 March 2014

LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG. 4 March 2014 LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG 4 March 2014 Family η οικογένεια a/one(fem.) μία a/one(masc.) ένας father ο πατέρας mother η μητέρα man/male/husband ο άντρας letter το γράμμα brother ο

Διαβάστε περισσότερα

Perfect Participles. A lesson for the Paideia web-app Ian W. Scott, 2015

Perfect Participles. A lesson for the Paideia web-app Ian W. Scott, 2015 Perfect Participles A lesson for the Paideia web-app Ian W. Scott, 2015 Remember the Components of a Participle Stem Tense marker Connecting vowel Voice indicator Case ending Resulting form λυ σ α ντ ος

Διαβάστε περισσότερα

The Dative Case. Nouns that Act Like Adverbs. A lesson for the Paideia web-app Ian W. Scott, 2015

The Dative Case. Nouns that Act Like Adverbs. A lesson for the Paideia web-app Ian W. Scott, 2015 The Dative Case Nouns that Act Like Adverbs A lesson for the Paideia web-app Ian W. Scott, 2015 The Dative Case The last of the five jobs for nominals nominative: identify the clause's subject genitive:

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

Croy Lesson 10. Kind of action and time of action. and/or Redup. using the verb λύω

Croy Lesson 10. Kind of action and time of action. and/or Redup. using the verb λύω A Lesson 10 Vocabulary Summer Greek Croy Lesson 10 Ω ἄγω αἴρω ἀναβαίνω ἀπέρχοµαι ἀποθνῄσκω ἀποκτείνω καταβαίνω µέλλω ὀφείλω συνάγω ἀπόστολος, ὁ ἱερόν, τό παρά (G,D,A) (+ gen.) from; (+ dat.) beside, with,

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

LESSON ELEVEN: COMPARISON OF ADJECTIVES AND FORMATION OF ADVERBS

LESSON ELEVEN: COMPARISON OF ADJECTIVES AND FORMATION OF ADVERBS LESSON ELEVEN: COMPARISON OF ADJECTIVES AND FORMATION OF ADVERBS Memorization of Vocabulary Eleven ἀγαθος ἁγιος ἁγνος ἀληθης ἀξιος δεισδαιµων διαβολος δικαιος ἐσθλος ἡδυς κακος καρδια µεγας µικρος ὀλιγος

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011 Διάρκεια Διαγωνισμού: 3 ώρες Απαντήστε όλες τις ερωτήσεις Μέγιστο Βάρος (20 Μονάδες) Δίνεται ένα σύνολο από N σφαιρίδια τα οποία δεν έχουν όλα το ίδιο βάρος μεταξύ τους και ένα κουτί που αντέχει μέχρι

Διαβάστε περισσότερα

LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013

LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013 LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV 10 December 2013 I get up/i stand up I wash myself I shave myself I comb myself I dress myself Once (one time) Twice (two times) Three times Salary/wage/pay Alone/only

Διαβάστε περισσότερα

Mounce Handout: Introduction to Participles (PTCs), Present-stem PTCs Dr. Phillip Marshall

Mounce Handout: Introduction to Participles (PTCs), Present-stem PTCs Dr. Phillip Marshall Mounce 26-27 Handout: Introduction to Participles (PTCs), Present-stem PTCs Dr. Phillip Marshall What are PTCs?. Participles are verbal adjectives!! They have verbal characteristics (can be marked in Greek

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

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

Croy Lessons PARTICIPLES PARTICIPLES PARTICIPLES PARTICIPLES PARTICIPLES. >> CIRCUMSTANTIAL (ADVERBIAL) Under the circumstance of (UTC )

Croy Lessons PARTICIPLES PARTICIPLES PARTICIPLES PARTICIPLES PARTICIPLES. >> CIRCUMSTANTIAL (ADVERBIAL) Under the circumstance of (UTC ) Croy Lessons 18-20 Greek Verb Formation Αug Redp STEM Tense Theme Ending PRES ACT -- STEM -- o/ε PRES M/P/D -- STEM -- o/ε IMPF ACT ἐ STEM -- o/ε ΙΜPF M/P ἐ STEM -- o/ε FUT ACT -- STEM σ o/ε FUT M/D --

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

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

HW 15 Due MONDAY April 22, TEST on TUESDAY April 23, 2019

HW 15 Due MONDAY April 22, TEST on TUESDAY April 23, 2019 Όνομα: Τάξη: Αριθμό# (Greek First and Last name) Name: HW 5 Due MONDAY April 22, 209 TEST on TUESDAY April 23, 209 For My HW 5: Part A page 2: - Grammar - Use Grammar notes (p.3) to answer Part A questions

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

TMA4115 Matematikk 3

TMA4115 Matematikk 3 TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet

Διαβάστε περισσότερα

Croy Lessons GEN GEN. Αug Redp STEM Tense Theme Ending. *Masculine Nouns of First Declension

Croy Lessons GEN GEN. Αug Redp STEM Tense Theme Ending. *Masculine Nouns of First Declension Croy Lessons 18-20 Greek Verb Formation Αug Redp STEM Tense Theme Ending PRES ACT -- STEM -- o/ε PRES M/P/D -- STEM -- o/ε IMPF ACT ἐ STEM -- o/ε ΙΜPF M/P ἐ STEM -- o/ε FUT ACT -- STEM σ o/ε FUT M/D --

Διαβάστε περισσότερα

Summer Greek Lesson 3 - Vocabulary

Summer Greek Lesson 3 - Vocabulary A Summer Greek 2006 Ω ἀδελφή, ἡ ἀλήθεια, ἡ βασιλεία, ἡ δόξα, ἡ ἐκκλησία, ἡ ἔχω ζωή, ἡ ἡμέρα, ἡ θάλασσα, ἡ καρδία, ἡ φωνή, ἡ ὥρα, ἡ Parts of Speech NOUN - person, place, thing, quality, idea, or action

Διαβάστε περισσότερα

On a four-dimensional hyperbolic manifold with finite volume

On a four-dimensional hyperbolic manifold with finite volume BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Numbers 2(72) 3(73), 2013, Pages 80 89 ISSN 1024 7696 On a four-dimensional hyperbolic manifold with finite volume I.S.Gutsul Abstract. In

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

ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΠΛΗΡΟΦΟΡΙΚΗΣ. ΕΠΛ342: Βάσεις Δεδομένων. Χειμερινό Εξάμηνο Φροντιστήριο 10 ΛΥΣΕΙΣ. Επερωτήσεις SQL

ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΠΛΗΡΟΦΟΡΙΚΗΣ. ΕΠΛ342: Βάσεις Δεδομένων. Χειμερινό Εξάμηνο Φροντιστήριο 10 ΛΥΣΕΙΣ. Επερωτήσεις SQL ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΠΛΗΡΟΦΟΡΙΚΗΣ ΕΠΛ342: Βάσεις Δεδομένων Χειμερινό Εξάμηνο 2013 Φροντιστήριο 10 ΛΥΣΕΙΣ Επερωτήσεις SQL Άσκηση 1 Για το ακόλουθο σχήμα Suppliers(sid, sname, address) Parts(pid, pname,

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

GREEK GRAMMAR I Future Active and Middle-Deponent Indicative Tense Dr. Marshall

GREEK GRAMMAR I Future Active and Middle-Deponent Indicative Tense Dr. Marshall GREEK GRAMMAR I Future Active and Middle-Deponent Indicative Tense Dr. Marshall I. Future Active Indicative A. Basics: Stem: The Greek future tense uses the Future Active Stem (sometimes the same as the

Διαβάστε περισσότερα

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται

Διαβάστε περισσότερα

Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author.

Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author. Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author. 2012, Γεράσιμος Χρ. Σιάσος / Gerasimos Siasos, All rights reserved. Στοιχεία επικοινωνίας συγγραφέα / Author

Διαβάστε περισσότερα

In this lesson, we learn how to identify and pronounce the letters of

In this lesson, we learn how to identify and pronounce the letters of Lesson 1 the Greek alphabet & Pronunciation In this lesson, we learn how to identify and pronounce the letters of the Greek alphabet. We also distinguish smooth and rough breathing marks and learn the

Διαβάστε περισσότερα

Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων. Εξάμηνο 7 ο

Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων. Εξάμηνο 7 ο Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων Εξάμηνο 7 ο Procedures and Functions Stored procedures and functions are named blocks of code that enable you to group and organize a series of SQL and PL/SQL

Διαβάστε περισσότερα

Svetlana Berikashvili (Tbilisi) FOR ALTERNATIVE CLASSIFICATION OF DECLENSION SYSTEM IN MODERN GREEK

Svetlana Berikashvili (Tbilisi) FOR ALTERNATIVE CLASSIFICATION OF DECLENSION SYSTEM IN MODERN GREEK Svetlana Berikashvili (Tbilisi) FOR ALTERNATIVE CLASSIFICATION OF DECLENSION SYSTEM IN MODERN GREEK Since Antiquity the classification of the declension system in Greek language had been essentially changed.

Διαβάστε περισσότερα

Passive and Middle Voices. A lesson for the Paideia web-app Ian W. Scott, 2015

Passive and Middle Voices. A lesson for the Paideia web-app Ian W. Scott, 2015 Passive and Middle Voices A lesson for the Paideia web-app Ian W. Scott, 2015 The Passive Voice So far all of our Greek verbs have been in the active voice Subject performs the verbal action "Clare is

Διαβάστε περισσότερα

5. Choice under Uncertainty

5. Choice under Uncertainty 5. Choice under Uncertainty Daisuke Oyama Microeconomics I May 23, 2018 Formulations von Neumann-Morgenstern (1944/1947) X: Set of prizes Π: Set of probability distributions on X : Preference relation

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

Croy Lessons Second Declension. First Declension PARTICIPLES. THIRD Declension SINGULAR PLURAL SINGULAR PLURAL. NOM -α / -η [-ης]* -αι

Croy Lessons Second Declension. First Declension PARTICIPLES. THIRD Declension SINGULAR PLURAL SINGULAR PLURAL. NOM -α / -η [-ης]* -αι Croy Lessons 18-20 Greek Verb Formation Αug Redp STEM Tense Theme Ending PRES ACT -- STEM -- o/ε PrimAct PRES M/P/D -- STEM -- o/ε PrimMP IMPF ACT ἐ STEM -- o/ε SecAct ΙΜPF M/P ἐ STEM -- o/ε SecMP FUT

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