Is Husband of One Wife in 1 Timothy 3:2 Gender-Specific? Clinton Wahlen, Ph.D. Theology of Ordination Study Committee Columbia, Md.

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Is Husband of One Wife in 1 Timothy 3:2 Gender-Specific? Clinton Wahlen, Ph.D. Theology of Ordination Study Committee Columbia, Md."

Transcript

1 0 0 0 Is Husand of One Wife in Timothy : Gender-Specific? Clinton Wahlen, Ph.D. Theology of Ordination Study Committee Columia, Md. January, 0 Introduction From Clarity to Uncertainty Limiting Bilical Authority Two Different Approaches to Bilical Interpretation The Hermeneutics of Evangelical Feminism A Remarkale Similarity Two Methods Two Outcomes A False Dichotomy 0 Historical and Literary Contets The Witness of - Timothy Management Plan for the Church Reasons for Church Order Etra-ilical Historical Contet The New Roman Woman Structure of Timothy Contet of Timothy : Church Order Principles Applied 0 Household Codes and Church Codes Slavery A Human Institution The Family Social Structure Sumission to God Seeking Peace and Harmony Authoritative Teaching in the Church Eegesis of Timothy : The Overseer/Elder

2 The Husand of One Wife Meaning of Anēr in Timothy : Paul Not Limited y the Greek Language Conclusion Appendi : English Bile Translations of Timothy : Appendi : Similarities etween Timothy and Titus 0 Appendi : Use of Masculine and Feminine Forms of τις (tis) in the New Testament Appendi : Use of ἀνήρ (anēr) in the New Testament Appendi : Use of ἄρσην (arsēn) and θῆλυς (thēlys) in the New Testament

3 0 0 Is Husand of One Wife in Timothy : Gender-Specific? Clinton Wahlen, Ph.D. January, 0 The question posed y the title of this study may seem so straightforward as to e answered quite easily, without the need of a detailed eamination. Unless we would redefine these commonly accepted terms so that a husand may e female and a wife may e male, most readers of the Bile would naturally answer the question in the affirmative. But, over the past forty years, this seemingly ovious conclusion has een increasingly questioned y ilical scholars, a fact that has ecome evident in the way the Greek phrase of this verse has een translated in a few recent versions of the Bile. An understanding of how apparently plain language, which is as clear in Greek as it is in English, can now e read so differently from the way it has een understood across languages and cultures for nearly,000 years requires consideration of some new hermeneutical assumptions and methods that have made this leap of language possile. In this paper, these new hermeneutical approaches will e considered as well as how the methodology that has generally een employed within the Adventist church differs from these recent approaches. After this discussion of interpretative approaches, we will proceed to our major task: a study of Timothy : in its historical-grammatical contets. From Clarity to Uncertainty There are a numer of ways that husand of one wife (mias gynaikos andra) has een interpreted in recent scholarly literature. However, apart from one reading that spiritualizes the wife to mean the church, to which the ishop must consider himself to e married, most of the other suggested interpretations understand the phrase in See Appendi : English Bile Translations of Timothy :, eginning on p. 0 elow. Only four offer gender neutral translations: NAB (0), NRSV (), CEV (), and CEB (0). Interesting also is the shift evident in the more recent revision of a given version. For eample, the RSV s () the husand of one wife has ecome in the NRSV married only once ; the original NIV () translation must e the husand of ut one wife ecame in the 0 edition is to e faithful to his wife, significantly softening the stipulation and only a small step away from faithful to one s spouse. See Benjamin Fiore, The Pastoral Epistles: First Timothy, Second Timothy, Titus (SP ; Collegeville, Minn.: Liturgical Press, 00), -; Ekkehardt Mueller, Husand of One Wife Tim : (June 00),. Cited Decemer 0. Online: les/pdf/husandof%0one%0wife.pdf. See also Jay Twomey, The Pastoral Epistles through the Centuries (Blackwell Bile Commentaries; Malden, Mass.: Wiley-Blackwell, 00), -. Homer A. Kent, The Pastoral Epistles: Studies in and Timothy and Titus (Chicago: Moody Press,

4 0 terms of a literal marriage relationship. They differ only with regard to how husand of one wife is to e interpreted in certain eceptional cases. Should a ishop/overseer not e a divorcé or remarried? Or is Paul only requiring faithfulness to one s (present) wife? Certainly, as one commentator points out, it can hardly e taken to mean that polygamy was otherwise acceptale. Another suggests that the specification is clear enough in requiring marital fidelity while wisely avoiding eing more precise. Such nuanced interpretations are rather common. But few commentators, until recently, would categorically deny that gender has any role at all in determining a person s qualifications for the office of overseer. This fact is evident from the unwillingness of many recent versions to alter the standard literal translation husand of one wife. 0 Of the sity-one English versions surveyed, only four adopt gender neutral language, while fifty-seven ),, an interpretation at least as old as Augustine, Bon. conj., [NPNF :0]. Fiore, ; y contrast, according to Roert W. Wall with Richard B. Steel, and Timothy and Titus (The Two Horizons New Testament Commentary; Grand Rapids, Mich.: Eerdmans, 0), 0, the episkopos of a Pauline congregation would pledge not to remarry if his wife should die. However, there was a Greek equivalent for widows who did not remarry (monandros), ut this term is not used where it would then most certainly e epected (:). The Greek phrase whether of men (:, ) or of women (:) is not found in inscriptions (Philip H. Towner, The Letters to Timothy and Titus [NICNT; Grand Rapids, Mich.: Eerdmans, 00], n. ); E.g., C. H. Dodd, New Testament Translation Prolems II, BT (): - here ; George W. Knight III, The Pastoral Epistles: A Commentary on the Greek Tet (NIGTC; Grand Rapids, Mich.: Eerdmans, ), -; Sydney Page, Marital Epectations of Church Leaders in the Pastoral Epistles, JSNT 0 () -; Towner, 0-. James D. G. Dunn, The First and Second Letters to Timothy and the Letter to Titus: Introduction, Commentary, and Reflections (NIB ; Nashville, Tenn.: Aingdon, 000), 0; although polygamy might have een practiced in some Jewish circles [see CD IV.0-V.; Josephus, Ant..; War.], monogamy was the generally accepted norm in Greco-Roman and Jewish culture y the time, and prohiition of polygamy in Christian circles would have een unnecessary (Towner, 0 n. ). Similarly Towner, 0- and n.. For a useful discussion of this passage in view of the compleity of marital issues in modern society see Walter L. Liefeld, The NIV Application Commentary: & Timothy, Titus (Grand Rapids, Mich.: Zondervan, ), -0. See, e.g., the reference to the perspective of feminist readers who, on the asis of Tim : ( the woman of one man ) consider that the virtue of having one spouse represents no gender eclusivity ut adherence to the social norm of faithfulness to the household (Wall and Steel, 0). Commentators supporting the traditional interpretation that limits elders to men married to one wife include Thomas D. Lea and Hayne P. Griffin, Jr., Timothy, Titus (NAC ; Nashville, Tenn.: Broadman, ), 0-0; Donald Guthrie, The Pastoral Epistles (TNTC; London: Tyndale, 00),. Others, while acknowledging this meaning, point out that the instruction presupposes a patriarchal culture and is therefore not directly applicale to all societies (e.g., Craig S. Keener, The IVP Bile Background Commentary: New Testament [Downers Grove: InterVarsity, ], ). William D. Mounce, Pastoral Epistles (WBC ; Nashville: Nelson, 000), -, considers the list ad hoc in response to a specific situation in the church of Ephesus, ut also admits that the requirement suggests that the overseers and elders were men (). Martin Dielius and Hans Conzelmann, The Pastoral Epistles: A Commentary on the Pastoral Epistles (Hermeneia; Philadelphia: Fortress, ) consider that the verse does not give special instruction for ishops () ut is similar to lists of virtues mentioned y Greek and Roman writers (0-). 0 E.g., NKJV (), NASB (rev. ), ESV (00), NET (00), HCSB (00).

5 0 0 retain the male-specific language of the underlying Greek term anēr. How then are we to understand the shift away from the traditional interpretation of this phrase in some strands of recent scholarship? Limiting Bilical Authority Underlying discussion over the years of the ordination of women are issues of ilical authority and consistency of interpretation. As Gerhard Hasel pointed out in the 0s and 0s, two distinct ut similar strands of scholarship dealing with women and the Bile were discernile: Christian feminists, who employed the historical-critical method, and certain evangelicals referred to as Bilical feminists. This latter group, although they employed the historical-grammatical method and held to a high view of Scripture, nevertheless limited the Bile s authority y assigning troulesome passages such as Timothy :-, Corinthians :- and :- to local situations of the time. Hasel concluded that the impact on ilical authority is similar in oth cases and that the only alternative position is one which upholds the full authority of Scripture: Basically there are ut two positions on the authority of the Bile. One position maintains the full and unlimited authority of the Bile without qualification and the other holds to some kind of limited authority of the Bile. In reflecting on the serious implications of limiting ilical authority, warning ells were sounded: Once the pandora s o of limited authority is opened, who can close it? If we use the principles or norms of our culture for decisions as to what in the Bile is or is not of a inding and lasting transcultural nature, then the Bile no longer transforms culture ut culture transforms the Bile. See n. aove. See Gerhard F. Hasel, Bilical Authority, Hermeneutics, and the Role of Women (paper presented at the Commission on the Role of Women I, Washington, D.C., March -, ); cf. idem, Bilical Authority and Feminist Interpretation, Adventists Affirm / (Fall ), -. Iid, -; Hasel, Bilical Authority, Hermeneutics, and the Role of Women, 0. According to the Estate of Gerhard F. Hasel, he later distriuted the full paper under a different title: Hermeneutical Issues Relating to the Ordination of Women: Methodological Reflections on Key Passages. The most recent copy is dated May,. Other than the title page with the date, the paper itself is unchanged which means that he did not change his position against women s ordination to that date, less than three months efore the car accident that took his life. Letter to Dr. Jan Paulsen, June, 0. Hasel, Bilical Authority, Hermeneutics, and the Role of Women,. Iid.,.

6 0 0 Those who wish to insist that the entire Bile consists of historically conditioned (i.e. culturally conditioned) tets need to have norms outside of the Bile to determine which tets or parts of the Bile contain principles of a directly transcultural or universal nature. In this case the asic and historic rule of the self-interpretation of the Bile is compromised to such a degree so as to render it meaningless. Sujectivity and relativity will in these areas replace Bilical authority. A few years earlier, George W. Reid, then director of the Bilical Research Institute, concluded in a similar vein that, in relation to the question of the ordination of women,... genuine decisions too often are made outside the Scriptures. There is a reasonale level of agreement aout what each tet is saying ut sustantial disagreement aout how to use its contriution in constructing an overall synthesis. Two Different Approaches to Bilical Interpretation While the hermeneutical landscape has undergone considerale change over the past several decades, with its consequent impact on methods of ilical interpretation, recognizale similarities to the theological situation descried y Hasel remain. New methods have given irth to some different paradigms for interpreting Scripture, some of which have seemed especially attractive to evangelicals ecause, in allowing them to work with the tet in its canonical form, they can maintain their high view of Scripture. However, these newer methods still retain the principle of criticism, which suordinates the Bile to human reason. A more recent analysis of hermeneutics in terms of the women s ordination deate identifies seven interpretative principles used y evangelical feminists, a designation roughly equivalent to Bilical feminists. Iid., 0, citing David M. Scholer, Tim :- and the Place of Women in the Church s Ministry, in Women, Authority, and the Bile (ed. A. Mickelsen; Downers Grove, Ill.: IVP, ),. George W. Reid, The Ordination of Women: A Review of the Principal Arguments for and against the Ordination of Women to the Gospel Ministry, Bilical Research Institute, January,. Methods of Bile Study Committee (GCC-A) Report, Adventist Review, January,,,, par.. Cited January 0. Online: Further see Clinton Wahlen, Hermeneutics and Scripture in the Twenty-First Century (paper presented at the Lake Union Conference Eecutive Committee, Berrien Springs, Mich., Feruary, 0). Cited January 0. Online: See Paul W. Feli, The Hermeneutics of Evangelical Feminism, JBMW / (Fall 00): - here n.. Cited January 0. Online: Sally K. Gallagher, The Marginalization of Evangelical Feminism, Sociology Of Religion / (00): -, herself a feminist researcher, uses oth terms interchangealy and non-pejoratively. She also notes the persistence of the elief among evangelicals that male leadership in oth the home and the church is the ilical model, with.% still suscriing to this idea (): This vision of a hierarchically ordered

7 0 These principles, which are identified and discussed in detail y New Testament scholar Paul Feli, are conveniently summarized y him in taular form. 0 The first and second columns present the feminist hermeneutical principle and how it operates within the evangelical feminist perspective, while the third column contrasts this approach with the historical-grammatical perspective. It should e kept in mind, when considering this tale, that not all ilical scholars consistently adhere to one perspective or the other. Furthermore, even interpreters sympathetic to a feminist reading of the tet may not employ every principle listed in the tale; in fact, they may oject to some of them. For the most part, however, the tale can help us recognize when certain principles are guiding an interpretation that would seem to e at odds with a plain reading of the tet. THE HERMENEUTICS OF EVANGELICAL FEMINISM Feminist Principle Evangelical Feminist Perspective Historical-Grammatical Response Ad Hoc Documents An Interpretive Center Privileging Clear Passages Slavery as a Model Culturally-Based Interpretation Cultural Relativity in Revelation Patriarchal and Seist Tets teaching restricted to original audience; no universal application a starting point used to filter out some tets in analyzing the NT view supposedly clear passages ecome the focus while oscure tets are ignored or given little weight cultural growth in applying ilical principles rings change of understanding ojective interpretation a myth; each reader determines what is universal and what is culturally specific tet is culturally limited; widespread distinction etween universal principles and localized applications tet seen as limited y writers cultural assumptions of a negative view of females teaching is normative, with application to Christians of all times and places equal weight given to each tet in arriving at the NT view equal attention to all passages, allowing eegesis to identify the clear from the oscure role of women rooted in Creation ordinance, not culture; role of slaves different advocates ojectivity in interpretation; interpreters try to keep cultural prejudices from influencing results tet is transcultural; Scripture presents what is normative unless Scripture itself indicates otherwise patriarchal culture not synonymous with ias against females universe has een drawn on with great success historically and continues as the orienting gender story among the majority of conservative Protestants today (). On the reasons for the intractaility of oth sides as well as for the continued resistance to feminist claims y the vast majority of evangelicals, see A Duane Litfin, Evangelical Feminism: Why Traditionalists Reject It, BSac / (): -. 0 Feli,. The tale has een modified in places for clarity. The historical-grammatical perspective or method is also referred to as the historical-ilical method. See Richard M. Davidson, Bilical Interpretation, in Handook of Seventh-day Adventist Theology (Commentary Reference Series ; Hagerstown, Md.: Review and Herald, 000),.

8 0 0 The first four principles limit the authority, scope or application of particular Bile passages while the last three concern how Scripture itself is understood. Feli also shows how these principles operate and illustrates their use y interpreters who read Scripture from an evangelical perspective: The Ad Hoc Documents principle is used to limit the application of Timothy :- to the local situation in the first-century on the asis of an alleged Ephesian heresy that Timothy faced. The principle of An Interpretive Center elevates a clear ilical passage or concept to the level of a theological and hermeneutical key. Eamples given y Feli include Galatians : ( there is no male and female, for you are all one in Christ Jesus ) and Creation-Redemption. The Privileging Clear Passages principle identifies some tets as clearer than others and uses these as a asis for relativizing oscure passages. In other words, the eegesis of the less clear passages does not proceed on the same asis their authority or scope must e restricted in order to harmonize with the theological principle that has already een identified on the asis of a limited selection of supposedly clear Bile tets. The fourth principle (Slavery as a Model) is essentially the same as the notion that a trajectory can e seen in Scripture wherey God leads His people to a etter understanding of His will through time so that, as the social and cultural conditions permit, a higher ethic than was possile in Bile times can e implemented. Feli,, quoting Scholer,. Credited with originating and popularizing use of this principle (iid., n. ) is Gordon D. Fee, Reflections on Church Order in the Pastoral Epistles, with Further Reflection on the Hermeneutics of Ad Hoc Documents, JETS (June ): - esp. : It must e noted again that Timothy is not intended to estalish church order ut to respond in a very ad hoc way to the Ephesian situation with its straying elders. Feli,, citing Grant R. Osorne, Hermeneutics and Women in the Church, JETS 0 (Decemer ):. Feli,. Iid.,. Feli, somewhat confusingly, refers to this as the Analogy of Faith principle (which all interpreters employ to some etent); the real prolem is when supposedly clear passages are privileged to such an etent that other passages, which might have corrected a wrong interpretation, are pushed into the ackground and not allowed to influence the interpreter s conclusions. Further, see Edwin Reynolds and Clinton Wahlen, Minority Report, in North American Division Theology of Ordination Study Committee Report [NADTOSC Report] (Novemer 0), -. Cited

9 0 0 The last three principles all reflect a fundamental difference in how the nature of Scripture is understood. For this reason, they are less frequently encountered among evangelical interpreters ut do nevertheless appear occasionally. The Culturally-Based Interpretation principle denies that Scripture has one unamiguous ojective meaning ecause each of us reads the Bile from our own perspective; there is only the veneer of ojectivity. The Cultural Relativity in Revelation principle distinguishes etween the permanent, universal, normative teaching of Scripture on the one hand and, on the other hand that which is transient, not applicale to every people in every culture, not intended to function as a mandate for normative ehavior. As the third column of the tale indicates, this principle is not prolematic in itself ecause sometimes the Bile makes clear that certain elements are cultural and not intended for permanent, universal, normative application divorce, circumcision, and slavery eing three ovious eamples. The prolem is one of degree. Evangelical feminist hermeneutics advocate widespread distinctions etween universal principles and localized applications. 0 The final principle, Patriarchal and Seist Tets, is far less common among evangelicals since it seems to imply a negative value judgment on portions of the Bile and most feminist theologians with a high view of Scripture would e unwilling to engage in this. Nevertheless, at least one evangelical has ventured to Feruary 0. Online: 0/nad-ordination--minority.pdf. Feli,, quoting Roert K. Johnston, Bilical Authority and Interpretation: The Test Case of Women s Role in the Church and Home Updated, in Women, Authority and the Bile,. Feli, 0, quoting J. Roertson McQuilkin, Prolems of Normativeness in Scripture: Cultural Versus Permanent, in Hermeneutics, Inerrancy and the Bile (ed. Earl D. Radmacher and Roert D. Preus; Grand Rapids, Mich.: Zondervan, ),. For a more in-depth discussion of these eamples in connection with this principle, see Wahlen, Hermeneutics and Scripture, -0. McQuilkin, 0-, presents seven criteria for distinguishing the Bile s normative teaching from that which is cultural:. Does the contet limit the recipient or application?. Does susequent revelation limit the recipient or the application?. Is this specific teaching in conflict with other ilical teaching?. Is the reason for a norm given in Scripture, and is that reason treated as normative?. Is the specific teaching normative as well as the principle?. Does the Bile treat the historic contet as normative?. Does the Bile treat the cultural contet as limited? (Feli, ). 0 Iid., 0.

10 0 0 classify parts of the New Testament as patriarchal, androcentric and possily misogynist (Rev :-; Tim :-; Cor :-; Eph :). A Remarkale Similarity Turning to recent Adventist perspectives on passages of Scripture relevant to the issue of the ordination of women, such as Timothy :, what happens when two groups of scholars who hold a high view of Scripture as the word of God and love the Lord arrive at opposite conclusions in their interpretation? The answer to this important question may e found in the fact that some scholars have proposed a refinement to our traditional hermeneutic. As one writes: A plain and literal reading strategy would e sufficient to understand most of the Bile. Yet... there are occasions when we should employ principle ased reading ecause the passage calls for an understanding of the historical and cultural settings. These occasions arise when considering difficult passages or issues such as the ordination of women, ecause otherwise interpretation may ecome a power issue. A careful eamination of how this refinement operates in practice reveals a remarkale similarity to the hermeneutical principles of evangelical feminists. Rather than recognizing that the Bile transcends its cultural ackgrounds to serve as God s word for all cultural, racial, and situational contets in all ages, the Ad Hoc Documents principle is employed to limit the scope of Tim :- to a local prolem having little relevance eyond the first-century church of Ephesus. Rather than ringing all the scriptures together on the suject and letting every word have its proper influence, the Interpretive Center principle of the overall picture of God and the major driving themes of the Bile is used to filter out tets that do not fit this metanarrative, and the Privileging Clear Passages principle is utilized so that Gal : determines the meaning Iid.,, citing David M. Scholer, Feminist Hermeneutics and Evangelical Bilical Interpretation, JETS 0 (Decemer ): -, as an eample. Kyoshin Ahn, Hermeneutics and the Ordination of Women, in NADTOSC Report,. Iid., -. On p., the situations in which the principle-ased approach is needed are enumerated. These include when: () conflicting interpretations eist, () understanding the historical (and/or cultural) ackground is essential for a correct interpretation, () interpretation of a specific passage contradicts the overall teaching of Scripture on a suject; () an interpretation does not make sense and human reason must step in; () the Holy Spirit enales a new understanding of what is revealed in Scripture. Methods of Bile Study,,.a.. Ellen G. White, Notes of Travel, The Advent Review and Saath Herald [RH], Nov.,, par.. Ahn,.

11 of supposedly unclear tets. Slavery, although not rooted in creation ut symptomatic of the fall, is used as a model in connection with discussion of the redemptive movement hermeneutic and the importance of recognizing the notion of a trajectory. This principle-ased historical cultural approach, as the majority of the North American Division (NAD) study committee descries it, enales the Bile to e read as supporting women s ordination even though some passages on a plain reading suggest otherwise. It is essentially arguing for pluralism in hermeneutical method as the diagram accompanying the NAD majority report makes clear: 0 A continuum of hermeneutical approaches NO INSPIRATION THOUGHT INSPIRATION BIBLICAL INERRANCY Historical-Critical Principle-Based Historical-Cultural Historical-Grammatical Literalistic 0 Two Methods Two Outcomes Methods-of-Bile-Study Document 0 Certainly we must recognize ilical principles and the eistence within Scripture, ased on the plan of salvation, of a progression from Creation to Re-Creation. But, when Bile tets seem to e saying different things, what constraints can e put in place to prevent human reason from elevating one or two passages to a position of unwarranted importance over all the others? Ellen White provides some important guidance on this question: To understand doctrine, ring all the scriptures together on the suject you wish to know, then let every word have its proper influence; and if you can form your theory without a contradiction, you cannot e in error. Before aritrarily elevating some tets aove others, all the scriptures on a given suject should e carefully studied and every word must e carefully considered. In determining whether the ordination of women is ilical, a particular word may in fact make a crucial contriution to a correct Kendra Haloviak Valentine, Is Headship Theology Bilical? in NADTOSC Report,. Further, see Wahlen, Hermeneutics and Scripture, 0. Ahn,, citing William J. We, Slaves, Women, & Homoseuals: Eploring the Hermeneutics of Cultural Analysis (Downers Grove, Ill.: InterVarsity Press, 00). 0 Report Summary, in NADTOSC Report,. Ellen G. White (quoting approvingly of William Miller s hermeneutic), Notes of Travel, RH, Nov.,, par..

12 0 0 0 understanding of the Bile s teaching on the topic. According to the Methods of Bile Study document: Human reason is suject to the Bile, not equal to or aove it. God intends that human reason e used to its fullest etent, ut within the contet and under the authority of His Word rather than independent of it. The Bile is its own est interpreter and when studied as a whole it depicts a consistent, harmonious truth.... Although it was given to those who lived in an ancient Near Eastern/Mediterranean contet, the Bile transcends its cultural ackgrounds to serve as God s Word for all cultural, racial, and situational contets in all ages. This affirmation stands in direct opposition to the Culturally-Based Interpretation and Cultural Relativity in Revelation principles (see p. aove). Nevertheless, the application of these principles is now eginning to e seen among some Adventist interpreters, which has led to a difference in hermeneutical method within the church. A False Dichotomy The Culturally-Based Interpretation principle presupposes that all readers of the Bile distinguish the universal from the cultural ased on their own individual criteria and personal preferences. According to some, the different conclusions reached stems from whether the ilical tet is read literalistically or in a principled way. This is hardly a fair representation of interpretative options inasmuch as those who find no ilical support for ordaining women would likewise reject a literalistic approach. Such a characterization of method among Seventh-day Adventists is a false dichotomy. The emphasis on principled versus literalistic readings of the Bile effectively removes the issue from what Scripture says to how it is read. Thus, each reader determines what is universal and what is culturally specific and the limitations of the reader of Scripture control the process of interpretation. Under the sith principle, Cultural Relativity, the interpreter distinguishes what is normative from what is Methods of Bile Study,,... Iid.,.a.- (emphasis supplied). John C. Brunt, Ordination of women: a hermeneutical question, Ministry (Septemer ), -. Similarly, Ján Barna, Ordination of Women in Seventh-day Adventist Theology: A Bilical and Theological Analysis and Synthesis of the Deate with Special Attention to Hermeneutical Matters (Ph.D. diss., Trinity College, University of Bristol, 00), 0, -. Feli,. See the warning in Ahn,, that language represents a perception of reality, which may e understood in more than one way.... The author attempts to persuade us to see things his or her way, while readers decipher meaning from their own contets.

13 0 0 descriptive or temporary, rather than recognizing the Bile s own authority to define this within its pages. Having riefly considered the hermeneutical method found in oth the larger evangelical world and among Seventh-day Adventists, we can see that a polarization has taken place within oth groups. Among those finding ilical support for the ordination of women (egalitarians) are some who employ the hermeneutics of evangelical feminism while those finding no ilical support for it (complementarians) eclusively employ the historical-grammatical method. Among Adventists, however, only recently has there een a recognition y egalitarians that some change was needed in hermeneutical methods. We will now proceed to study Timothy : y employing the historicalgrammatical method of ilical interpretation 0 with the intent of validating its use in eplaining the tet and contrasting its use with the new hermeneutics eing employed in support of women s ordination. Historical and Literary Contets Scripture itself provides the key to understanding Scripture. This principle applies not just to the study of words, concepts, and grammatical constructions; it is just as important in investigating the historical contet of a passage. As Richard M. Davidson affirms: The historical contet of ilical accounts is accepted as true, with no attempt to reconstruct history in a different way from that presented in the ilical record. The Methods of Bile Study document urges: As far as possile ascertain the historical circumstances in which the passage was written y the ilical writers under the guidance Iid., : the twenty-first century Christian is responsile for assessing the normative status of commands and practices in the Bile. Cf. Ellen G. White, Testimonies for the Church ( vols.; Mountain View, Calif.: Pacific Press, ), :-: In His providence the Lord has seen fit to teach and warn His people in various ways. By direct command, y the sacred writings, and y the spirit of prophecy has He made known unto them His will. Throughout the inspired writings and not only through definite commands is God s normative will made known. Cf. Barna, 0: Unless oth sides make conscious attempts to address the lack of epistemological and critical clarification of their hermeneutical positions, there is every chance that the theological differences etween the two camps will remain unresolved. It is therefore the proposition of this research that fuller awareness of the prolems of hermeneutics may provide a defense against interpretations that may e largely echoes of one's own attitudes or pre-judgements; furthermore, at the same time, such a fuller awareness may provide a useful platform for further constructive reflection. 0 The method is succinctly summarized in Methods of Bile Study, -0. Davidson, Bilical Interpretation, 0.

14 0 of the Holy Spirit. This does not mean that we cannot gain useful information from outside the Bile. Archaeology, anthropology, and history may contriute to understanding the meaning of the tet, ut it will supplement and enlarge upon the historical and cultural information that can e gleaned from the Bile itself rather than challenge or overthrow it. The Witness of - Timothy In the study of Paul s epistles to Timothy, we can learn a great deal aout the historical contet and purpose from the epistles themselves. Both are clearly designed to help Timothy in his work with the church in Ephesus. The first epistle addresses the needs of the church more generally and is said to e written from Macedonia ( Tim :), apparently susequent to the history recorded in Acts and after Paul s release from Roman custody following his first successful defense ( Tim :-). Sometime later Paul was seized again, apparently at Troas (cf. Tim :), and imprisoned in Rome, from which he writes the second epistle in view of his impending death. It takes the Methods of Bile Study,,.g. Iid.,.k. Further see Wahlen, Hermeneutics and Scripture, -. Conveniently on what can e gleaned from their self-testimony, see Knight, The Pastoral Epistles, -, who is among a growing numer of recent commentators supporting Pauline authorship of Timothy. Iid.,, oserving that the aorist enemeinen in Acts :0 implies Paul s imprisonment was past. An epectation of release appears already in the Prison Epistles usually dated to this first Roman confinement (Phil :, -; :; Phlm ). Cf. Ellen G. White, The Acts of the Apostles (Mountain View, Calif.: Pacific Press, ), 0, 0: At Paul s eamination the charges against him were not sustained, and, contrary to the general epectation, with a regard for justice wholly at variance with his character, Nero declared the prisoner guiltless. Paul s fetters were struck off, and he was again a free man. This last precious interval of freedom was earnestly improved in laoring among the churches. He sought to estalish a firmer union etween the Greek and Eastern churches which he had raised up, and to guard them against the sutle heresies that were creeping in to corrupt the faith. This reconstruction is generally accepted y scholars who accept Pauline authorship of the Pastoral Epistles. See F. F. Bruce, Commentary on the Book of Acts: The English Tet with Introduction, Eposition and Notes (Grand Rapids, Mich.: Eerdmans, ), - and n. ; Knight, The Pastoral Epistles, -0, -. Luke Timothy Johnson, The First and Second Letters to Timothy (AB A; New York: Douleday, 00), locates Timothy earlier, following the Ephesian uproar (Acts ) when Paul left for Macedonia (0:-). The reference to two winters, the first which Paul will spend at Nicopolis (Titus :) and the second with Paul again imprisoned in Rome and epecting death ( Tim :), suggests his freedom lasted at least a year, and it could have een longer. The Seventh-day Adventist Bile Commentary [SDABC] (ed. Francis D. Nichol; vols.; Washington, D.C.: Review and Herald, ), :0, dates Paul s first Roman imprisonment to AD - and his second imprisonment to AD -: This leaves aout three years for his last journeys, A.D. -. Since Paul had indicated in his prison epistles that he was anious to see the churches in Asia and Macedonia as soon as possile (Phil. :; Philemon ), it may e assumed that he traveled to those eastern lands shortly after his release. He visited Ephesus, the main city of the province of Asia, efore he proceeded to Macedonia ( Tim. :), where the eloved church of Philippi was located.

15 0 0 form of a last will and testament, focusing even more particularly on Timothy s ministerial laors. The torch is eing passed, history is eing made and we see Paul preparing the church and Timothy himself for laor in his asence. Earlier, Paul had written to the Corinthians to e imitators of me. That is why I sent you Timothy, my eloved and faithful child in the Lord, to remind you of my ways in Christ, as I teach them everywhere in every church ( Cor :-). 0 Paul s letters to Timothy are designed first and foremost as instruction on an effective ministry in Ephesus where Timothy happens to e located at the time of writing, ut also more roadly as guidance for the church in general, otherwise they would not elong to the ilical canon. Management Plan for the Church As is typical for Pauline epistles, the suject of Timothy is made clear from the eginning. Concern to strengthen the church is prominent. Interestingly in this connection, Paul refers to God s oikonomia or management plan for the church (:) : Oikonomia refers to the organization and ordering of a household or the responsiility of management that maintains order (as used in Cor :; Col :). This translation fits well the description of the church as the household of God (oikō theou, Tim :) and Paul s use of a modified household code to delineate church life and administration, a kind of church code (see p. elow). Significantly, he also descries the overseer (or elder) as God s church manager (oikonomos theou, Titus :; cf. Cor :). In fact, immediately after detailing the qualifications for church offices, Paul indicates clearly that the purpose of the epistle is connected with maintaining order in the church: I am writing these things to you so that, The first letter to Timothy was written after these visits, and so may e dated aout a year following his release, proaly A.D.. Charles E. Bradford, Timothy and Titus: Counsels to Young Pastors for Struggling Churches (The Aundant Life Bile Amplifier; Boise, Id.: Pacific Press, ), ; cf. Towner,. 0 All Scripture quotations are from the English Standard Version (00), unless otherwise indicated; the translation is that of the author if a transliteration of the original tet is given in the tet or in a footnote. LSJ 0 gives management of a household or family and principles of government as prominent meanings, oth of which fit well Timothy; cf. God s order (Fiore, ). Towner ; similarly Johnson,, translates the word God s way of ordering things (citing enophon, Oecumenicus :; Aristotle, Politics B); cf. its translation y the ESV here as the good order from God (marg.).

16 0 0 if I delay, you may know how one ought to ehave in the household of God, which is the church of the living God, a pillar and uttress of the truth ( Tim :-). The same sentiment is epressed to Titus: This is why I left you in Crete, so that you might put what remained into order, and appoint elders in every town as I directed you (:). It appears that Paul has personally instituted some church order there already and that he has left Titus ehind to manage the church and apply the pattern already estalished to the other towns throughout the island. There is no indication here of a crisis and the close similarity of the instructions Paul gives to oth Timothy and Titus, including the cautions regarding false teachers, suggests that the difficulty was not much greater in Ephesus than in Crete (see Appendi, p. elow). In fact, the reason for a perceived difference in tone etween the letters to these ministers may reside not so much in the condition of their respective churches ut in the differences etween the two men themselves in temperament ( Tim :-), as well as in age and eperience ( Tim :). Reasons for Church Order Several reasons for the emphasis in Timothy on church order are apparent. One has already een mentioned. As with Titus, there was a need to prepare for a post-pauline ministry. This must have weighed heavily on Paul s mind after release from his first Roman imprisonment. The words, if I delay (:) reinforce the sense of uncertainty the apostle clearly felt aout his aility in the future to personally oversee the churches he had estalished. On the other hand, it would e misleading to suggest that all was calm in Ephesus; it clearly was not. Besides the pressures from outside the church that threatened its unity, Paul had already warned the overseers there that wolves would come in to destroy the flock, adding that even from your own numer men will arise and distort the truth in order to draw away disciples after them (Acts 0:-0, NIV). Thus, Paul instructs Timothy not only as to the qualifications for overseers ut also urges him not to ordain The mention of elders ut not deacons suggests a younger church on Crete (Mounce, ). The word left (apoleipō) is used also in Timothy to suggest something or someone that Paul personally left ehind ( Tim :, 0). For further reasons to affirm Paul s presence with Titus on Crete, see iid.

17 0 0 anyone to this office too hastily and eplains when and how to correct those elders who err ( Tim :-). According to Paul, certain men (tines, :,, ) were wanting (thelontes) to e teachers ut they neither understand what they are saying nor the things aout which they speak so confidently (:). It seems they had a very high opinion of themselves and their teachings, since they styled themselves teachers of the law (nomodidaskalos). Paul employs here a very rare and significant word used only twice more in the New Testament: of the eperts in the law who sought a asis for having Jesus arrested (Luke :) and of Gamaliel (Acts :), recognized y Jews and Christians alike as one of the most important Jewish scholars in history (cf. Acts :; m. Sotah :). This fact, together with the references in Titus to those of the circumcision teaching Jewish myths (:0, ) and the association in oth Timothy and Titus (:) of genealogies with disputes over the law strongly suggest that the false teachers in oth Ephesus and Crete were promoting Jewish ideas (cf. Acts :-; 0:0). Clear evidence from Josephus for a sizeale Jewish population in Ephesus also supports this conclusion. If we include the statements in Timothy aout false teachers as applicale to those referred to in the first epistle, there were some in Ephesus at this time who were undermining the doctrine of the resurrection, just as some had een doing in Corinth. In Corinth they had denied its reality altogether ( Cor :), while in Ephesus it had supposedly already occurred ( Tim :). Elder and overseer were used interchangealy for the same office in this early period of the Christian church (Acts 0:, ; Titus :, ). But cf. George W. Knight III, Two Offices (Elders/Bishops and Deacons) and Two Orders of Elders (Preaching/Teaching Elders and Ruling Elders): A New Testament Study, Presyterion / (): -, finding two distinct offices the duties of which somewhat overlap. Gk. mē noountes mēte ha legousin mēte peri tinōn diaeaiountai. Two of these men are named in :-0 (Hymenaeus and Aleander). It does not occur in the Septuagint, Josephus, Philo or secular Greek. It may also e significant in light of the Jewish concept that the student of an epert teacher of the law is called a son (.Sanh. : When a man teaches the son of another the Torah, the scripture treats him as if he had egotten him. ; cf. ) and Paul s reference to Timothy as his eloved child and to oth him and Titus as his true child (Tim :; Tim :; Titus :; cf. Gal :; Cor :, ). Further, see Karl Heinrich Rengstorf, νοµοδιδάσκαλος, TDNT :; cf. -. So Roert J. Karris, The Background and Significance of the Polemic of the Pastoral Epistles, JBL / (): ; Towner, 0; similarly Lea and Griffin, ; Craig S. Keener, And Marries Another: Divorce and Remarriage in the Teaching of the New Testament (Peaody, Mass.: Hendrickson, ), 0. Cf. Appendi : Similarities etween Timothy and Titus, p. elow. So influential were the Jews in Ephesus that a special law was passed to protect their right to Saath oservance (Josephus, Ant..-), they were eempted from serving in the armed forces (.0), and given other legal considerations (.0, -;.-, etc.).

18 0 0 This realized eschatology also ears some similarity to the false teachings eing spread in Thessalonica ( Thess :-). Many suggest that Paul s teaching of spiritual death and rising to life ( Tim :; Rom :-; Col :0-:; cf. Eph :; :) had een perverted y replacing the odily with spiritual resurrection and hence denying the odily resurrection. 0 In other words, on the asis of Timothy, there is no reason to think that the false teachers in Ephesus were strikingly different from the opponents Paul faced in other important cities as we find the same false ideas surfacing in epistles directed to other places. Etra-ilical Historical Contet Recently, some have egun to argue for quite a different situation in the Ephesian church compared to other Pauline churches, ased primarily on three sets of etra-ilical sources: Gnostic writings, the cult of Artemis (Diana), and socio-historical findings aout the new Roman woman. When it comes to connecting these disparate sources to the actual words of Paul, it is difficult to see any clear link. Admissions must e made such as although the evidence is not entirely clear and the sparseness of information and the comple construction of the passage [ Tim :-] make it difficult for modern readers to know precisely what Paul had in mind. Still, an attempt is made to link this reconstructed setting with the situation in the church: Gentile converts would not have needed to have een initiated memers of the cult of Artemis to have associated aspects of the role of women in the worship of Artemis along with those of their new found [sic] faith in Christ. 0 Guthrie, and the literature cited. See Carl P. Cosaert, Paul, Women, and the Ephesian Church: An Eamination of Timothy :- (paper presented at the Theology of Ordination Study Committee, Linthicum Heights, Md., July, 0), -0. Cited Feruary 0. Online: Eamples of heroines from apocryphal and pseudepigraphal Jewish literature and the political eploits of Bernice (cf. Acts :, ; :0) are also mentioned in order to show the diverse attitudes toward women that may have eisted in Jewish circles of the first century. Mention of Rufina is too late to e relevant (dated to the late second century or third century). See Andrew D. Clarke, Serve the Community of the Church: Christians as Leaders and Ministers (First Century Christians in the Greco- Roman World; Grand Rapids, Mich.: Eerdmans, 000), 0-. Cosaert,,. Also, while it is asserted that two particular prolems were undermining the unity of the church, only one is mentioned: the ehavior of men and women in worship (). Cosaert,.

19 0 0 There are many difficulties with such a reconstruction. First, as James D. G. Dunn points out, calling the heresy a Judaizing Gnosticism (as many suggest) is not very helpful, since Judaizing means living as a Jew, and no gnostic system that we know of taught the need to Judaize. Furthermore, the notion that cult prostitutes at the temple of Artemis may present an important ackground to understanding the Ephesian heresy that Paul comated has een convincingly refuted y what has een called the most detailed and latest word on the ackground in Ephesus. Another prolem with this duious reconstruction is its reliance on sources dated long after the New Testament period anywhere from one to three centuries after Paul. If the cultural pressures in Ephesus were so ovious and influential within the church, why is there no clear attestation of it dating to the first century? So far no such sources that might provide evidence for the influence of Artemis on first-century Christianity in Ephesus or anywhere else have een produced, and until such sources can e shown to eist we must look elsewhere to find a credile ackground for the prolems the Ephesian church faced. Of course, it is also helpful to ear in mind that many of those doing original research on etra-ilical sources for Timothy dout its Pauline authorship and place the date of the epistle much later in the first century. The New Roman Woman Those who emphasize the pagan influence on the church also refer to the new Roman woman, Rome s equivalent to our modern women s lieration movement. Dunn,, in apparent reuttal to the suggestion that a Gnostic form of Jewish Christianity was present in Ephesus as maintained y Sharon Hodgin Gritz, Paul, Women Teachers, and the Mother Goddess at Ephesus: A Study of Timothy :- in Light of the Religious and Cultural Milieu of the First Century (New York: University Press of America, ),. See esp. S. M. Baugh, Cult Prostitution in New Testament Ephesus: A Reappraisal, JETS / (): -0, a comprehensive study that remarks on the proposal of Gritz (cf. n. aove) as follows: if one removes the historical errors from the material supporting Gritz s conclusions, very little remains ecept modern fancy. She refers to ancient sources ut cites none (0); See also idem, A Foreign World: Ephesus in the First Century, in Women in the Church: An Analysis of Timothy :- (ed. Andreas J. Köstenerger and Thomas R. Schreiner; d ed.; Grand Rapids, Mich.: Baker, 00), -. Liefeld, 0. Of the commentaries housed in the lirary of the Bilical Research Institute pulished since Sharon Gritz s dissertation was written, less than one third refer to her (some only in the iliography), those making reference eing Liefeld (the only one seemingly aware of Baugh s treatments of the suject, given in n. aove), Fiore, Johnson, Lea and Griffin, Mounce, I. Howard Marshall, A Critical and Eegetical Commentary on the Pastoral Epistles (ICC; New York: T. & T. Clark, ), and Ben Witherington III, Letters and Homilies for Hellenized Christians. : A Socio-Rhetorical Commentary on Titus, - Timothy and - John (Downers Grove: IVP, 00). See, e.g., Cosaert, -, who, apart from Gos. Eg. and Gos. Thom., quotes works dating to the third and fourth centuries.

20 0 0 Lieralizing cultural trends had influenced a generation of women/wives to reject the traditional modest attire of a Roman matron for the more sensual and epensive dress of the courtesan. However, the eistence of these new women in the Ephesian church is likewise without evidence. Many of those who quote Bruce Winter, the acknowledged epert on this suject, overlook the careful and limited way he descries the relevance of this social and cultural contet to the church in Ephesus: the aim [of Timothy :-] appears to have een preventative and not remedial; the reason for the concern was the possile influence on that community of the norms of the new woman. These insights into the social faric of the Roman world, rather than illuminating the prolems within the church, show the challenge faced y Christians as they sought to live soerly, righteously, and godly, in this present world (Titus :, KJV). Consistently, the Christian lifestyle advocated in the New Testament is far aove worldly standards such as those legislated y Augustus 0 as well as those of our own time, as we look for our lessed hope, the appearing of the glory of our great God and Savior Jesus Christ (v. ). In summary, Paul wrote Timothy with a view to preparing him to minister in his etended asence. A careful reading of the epistle reveals nothing that is of eclusively local relevance. Even the polemic against false teachers ears striking similarity to the stock polemics of the Greco-Roman era and therefore must e used judiciously in seeking to understand the false teachings eing opposed. The most pertinent historical and social information for interpreting Paul s instruction is found within the epistle itself. Still more important are the ilical contets to which Paul refers to eplain his own meaning. Structure of Timothy The structure of the epistle supports the conclusion that church order constitutes one of the primary concerns of Timothy: Iid.,. Bruce W. Winter, Roman Wives, Roman Widows: The Appearance of the New Women and the Pauline Communities (Grand Rapids: Eerdmans, 00), 0 (emphasis supplied). 0 Roman standards of morality permitted men to fornicate freely, not only with courtesans and slavemaids ut with married women too (iid.,, 0, ). The new Roman women were simply seeking equal access to the privileges that Roman law already accorded to men. Karris, -. Outline condensed from Towner, i-i.

Επιβλέπουσα Καθηγήτρια: ΣΟΦΙΑ ΑΡΑΒΟΥ ΠΑΠΑΔΑΤΟΥ

Επιβλέπουσα Καθηγήτρια: ΣΟΦΙΑ ΑΡΑΒΟΥ ΠΑΠΑΔΑΤΟΥ EΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΕΚΠΑΙΔΕΥΤΙΚΟ ΤΕΧΝΟΛΟΓΙΚΟ ΙΔΡΥΜΑ ΤΕΙ ΙΟΝΙΩΝ ΝΗΣΩΝ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : Λεωφ. Αντ.Τρίτση, Αργοστόλι Κεφαλληνίας Τ.Κ. 28 100 τηλ. : 26710-27311 fax : 26710-27312

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

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

ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ

ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ Ενότητα 1β: Principles of PS Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης

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

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

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

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

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

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

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

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

Η ΠΡΟΣΩΠΙΚΗ ΟΡΙΟΘΕΤΗΣΗ ΤΟΥ ΧΩΡΟΥ Η ΠΕΡΙΠΤΩΣΗ ΤΩΝ CHAT ROOMS

Η ΠΡΟΣΩΠΙΚΗ ΟΡΙΟΘΕΤΗΣΗ ΤΟΥ ΧΩΡΟΥ Η ΠΕΡΙΠΤΩΣΗ ΤΩΝ CHAT ROOMS ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ Ι Ο Ν Ι Ω Ν Ν Η Σ Ω Ν ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : ΑΤΕΙ Ιονίων Νήσων- Λεωφόρος Αντώνη Τρίτση Αργοστόλι Κεφαλληνίας, Ελλάδα 28100,+30

Διαβάστε περισσότερα

ΑΓΓΛΙΚΑ IV. Ενότητα 8: Analysis of Consumerism and Consumers Rights. Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών

ΑΓΓΛΙΚΑ IV. Ενότητα 8: Analysis of Consumerism and Consumers Rights. Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών Ενότητα 8: Analysis of Consumerism and Consumers Rights Ιφιγένεια Μαχίλη Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative Commons. Για εκπαιδευτικό υλικό, όπως εικόνες, που

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

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

1999 MODERN GREEK 2 UNIT Z

1999 MODERN GREEK 2 UNIT Z STUDENT NUMBER CENTRE NUMBER HIGHER SCHOOL CERTIFICATE EXAMINATION 1999 MODERN GREEK 2 UNIT Z (55 Marks) Time allowed Two hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Write your Student

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

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

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

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

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

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

Test Data Management in Practice

Test Data Management in Practice Problems, Concepts, and the Swisscom Test Data Organizer Do you have issues with your legal and compliance department because test environments contain sensitive data outsourcing partners must not see?

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 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

Ακαδημαϊκός Λόγος Εισαγωγή

Ακαδημαϊκός Λόγος Εισαγωγή - In this essay/paper/thesis I shall examine/investigate/evaluate/analyze Γενική εισαγωγή για μια εργασία/διατριβή Σε αυτήν την εργασία/διατριβή θα αναλύσω/εξετάσω/διερευνήσω/αξιολογήσω... To answer this

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

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

Ακαδημαϊκός Λόγος Εισαγωγή

Ακαδημαϊκός Λόγος Εισαγωγή - Σε αυτήν την εργασία/διατριβή θα αναλύσω/εξετάσω/διερευνήσω/αξιολογήσω... Γενική εισαγωγή για μια εργασία/διατριβή In this essay/paper/thesis I shall examine/investigate/evaluate/analyze Για να απαντήσουμε

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

Η ΨΥΧΙΑΤΡΙΚΗ - ΨΥΧΟΛΟΓΙΚΗ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΗ ΣΤΗΝ ΠΟΙΝΙΚΗ ΔΙΚΗ

Η ΨΥΧΙΑΤΡΙΚΗ - ΨΥΧΟΛΟΓΙΚΗ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΗ ΣΤΗΝ ΠΟΙΝΙΚΗ ΔΙΚΗ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΝΟΜΙΚΗ ΣΧΟΛΗ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΤΟΜΕΑΣ ΙΣΤΟΡΙΑΣ ΦΙΛΟΣΟΦΙΑΣ ΚΑΙ ΚΟΙΝΩΝΙΟΛΟΓΙΑΣ ΤΟΥ ΔΙΚΑΙΟΥ Διπλωματική εργασία στο μάθημα «ΚΟΙΝΩΝΙΟΛΟΓΙΑ ΤΟΥ ΔΙΚΑΙΟΥ»

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

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

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

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

LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV. 4 February 2014

LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV. 4 February 2014 LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV 4 February 2014 Somewhere κάπου (kapoo) Nowhere πουθενά (poothena) Elsewhere αλλού (aloo) Drawer το συρτάρι (sirtari) Page η σελίδα (selida) News τα νέα (nea)

Διαβάστε περισσότερα

þÿ»±íº »¹ Áà  : É º±¹ Ä þÿ Á³ Ä Å : ¼¹± ºÁ¹Ä¹º ±À Ä ¼

þÿ»±íº »¹ Áà  : É º±¹ Ä þÿ Á³ Ä Å : ¼¹± ºÁ¹Ä¹º ±À Ä ¼ Neapolis University HEPHAESTUS Repository School of Health Sciences http://hephaestus.nup.ac.cy Master Degree Thesis 2015 þÿ»±íº »¹ Áà  : É º±¹ Ä þÿ Á³ Ä Å : ¼¹± ºÁ¹Ä¹º ±À Ä ¼ þÿ Ä Æ Á Â, Á ÃÄ Â þÿ Á̳Á±¼¼±

Διαβάστε περισσότερα

ΔΗΜΟΚΡΙΤΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΡΑΚΗΣ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΑΓΩΓΗΣ

ΔΗΜΟΚΡΙΤΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΡΑΚΗΣ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΑΓΩΓΗΣ ΔΗΜΟΚΡΙΤΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΡΑΚΗΣ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΑΓΩΓΗΣ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΕΚΠΑΙΔΕΥΣΗΣ ΣΤΗΝ ΠΡΟΣΧΟΛΙΚΗ ΗΛΙΚΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Διαπολιτισμική Εκπαίδευση και Θρησκευτική Ετερότητα: εθνικές και θρησκευτικές

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

Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ

Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ Νικόλας Χριστοδούλου Λευκωσία, 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ

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

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

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

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 4: English a Language of Economy Το περιεχόμενο του μαθήματος διατίθεται με άδεια

Διαβάστε περισσότερα

105 Verses in the Critical Greek Text of the New Testament Without Any Manuscript Support

105 Verses in the Critical Greek Text of the New Testament Without Any Manuscript Support 105 Verses in the Critical Greek Text of the New Testament Without Any Manuscript Support These notes were sent to me by Dr. Maurice Robinson and detail 105 places in the Critical Greek Text of the New

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ Πτυχιακή Εργασία "Η ΣΗΜΑΝΤΙΚΟΤΗΤΑ ΤΟΥ ΜΗΤΡΙΚΟΥ ΘΗΛΑΣΜΟΥ ΣΤΗ ΠΡΟΛΗΨΗ ΤΗΣ ΠΑΙΔΙΚΗΣ ΠΑΧΥΣΑΡΚΙΑΣ" Ειρήνη Σωτηρίου Λεμεσός 2014 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ

Διαβάστε περισσότερα

Advanced Subsidiary Unit 1: Understanding and Written Response

Advanced Subsidiary Unit 1: Understanding and Written Response Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes

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

Business English. Ενότητα # 9: Financial Planning. Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων

Business English. Ενότητα # 9: Financial Planning. Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα Business English Ενότητα # 9: Financial Planning Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων Άδειες Χρήσης Το παρόν εκπαιδευτικό

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

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

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΠΕΛΟΠΟΝΝΗΣΟΥ

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΠΕΛΟΠΟΝΝΗΣΟΥ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΠΕΛΟΠΟΝΝΗΣΟΥ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΔΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΚΑΙ ΟΡΓΑΝΙΣΜΩΝ Κατ/νση Τοπικής Αυτοδιοίκησης ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ «Μοντέλα στρατηγικής διοίκησης και

Διαβάστε περισσότερα

ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «ΘΕΜΑ»

ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «ΘΕΜΑ» ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΠΡΟΣΧΟΛΙΚΗΣ ΑΓΩΓΗΣ ΚΑΙ ΤΟΥ ΕΚΠΑΙΔΕΥΤΙΚΟΥ ΣΧΕΔΙΑΣΜΟΥ Π.Μ.Σ. «ΠΕΡΙΒΑΛΛΟΝΤΙΚΗ ΕΚΠΑΙΔΕΥΣΗ» ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «ΘΕΜΑ» «Εφαρμογή

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

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

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

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

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού)

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Προσδοκώμενα αποτελέσματα Περιεχόμενο Ενδεικτικές δραστηριότητες

Διαβάστε περισσότερα

Τμήμα Πολιτικών και Δομικών Έργων

Τμήμα Πολιτικών και Δομικών Έργων Τμήμα Πολιτικών και Δομικών Έργων Πτυχιακή Εργασία: Τοπογραφικό διάγραμμα σε ηλεκτρονική μορφή κεντρικού λιμένα Κέρκυρας και κτιρίου νέου επιβατικού σταθμού σε τρισδιάστατη μορφή και σχεδίαση με AutoCAD

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

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

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

Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ

Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Η προβολή επιστημονικών θεμάτων από τα ελληνικά ΜΜΕ : Η κάλυψή τους στον ελληνικό ημερήσιο τύπο Σαραλιώτου

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

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

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

I haven t fully accepted the idea of growing older

I haven t fully accepted the idea of growing older I haven t fully accepted the idea of growing older 1 Peter Authorship Questions Πέτρος ἀπόστολος Ἰησοῦ Χριστοῦ ἐκλεκτοῖς παρεπιδήμοις διασπορᾶς Πόντου, Γαλατίας, Καππαδοκίας, Ἀσίας 1 Peter Authorship

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ιπλωµατική Εργασία του φοιτητή του τµήµατος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Ηλεκτρονικών

Διαβάστε περισσότερα

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

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

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΗΡΑΚΛΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΗΡΑΚΛΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΗΡΑΚΛΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ Π Τ Υ Χ Ι Α Κ Η Ε Ρ Γ Α Σ Ι Α: Ο ΡΟΛΟΣ ΤΗΣ ΣΥΝΑΙΣΘΗΜΑΤΙΚΗΣ ΝΟΗΜΟΣΥΝΗΣ ΣΤΗΝ ΑΠΟΤΕΛΕΣΜΑΤΙΚΗ ΗΓΕΣΙΑ ΕΠΙΜΕΛΕΙΑ

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

Το κοινωνικό στίγμα της ψυχικής ασθένειας

Το κοινωνικό στίγμα της ψυχικής ασθένειας Διεπιζηημονική Φρονηίδα Υγείας(2015) Τόμος 7,Τεύχος 1, 8-18 ISSN 1791-9649 Το κοινωνικό στίγμα της ψυχικής ασθένειας Κνξδώζε Α 1, Σαξίδε Μ 2, Σνπιηώηεο Κ 3 1 Ννζειεύηξηα ΤΔ, MSc, Γεληθό Ννζνθνκείν Κνξίλζνπ.

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

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ Γηπισκαηηθή Δξγαζία ηνπ Φνηηεηή ηνπ ηκήκαηνο Ζιεθηξνιόγσλ Μεραληθώλ θαη Σερλνινγίαο Ζιεθηξνληθώλ

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

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

«Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων. Η μεταξύ τους σχέση και εξέλιξη.»

«Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων. Η μεταξύ τους σχέση και εξέλιξη.» ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΑΓΡΟΝΟΜΩΝ ΚΑΙ ΤΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΓΕΩΓΡΑΦΙΑΣ ΚΑΙ ΠΕΡΙΦΕΡΕΙΑΚΟΥ ΣΧΕΔΙΑΣΜΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ: «Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων.

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

ΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥ ΩΝ ΣΤΗ ΙΟΙΚΗΣΗ ΕΠΙΧΕΙΡΗΣΕΩΝ. ιπλωµατική Εργασία. της ΘΕΟ ΟΣΟΠΟΥΛΟΥ ΕΛΕΝΗΣ ΜΣ:5411

ΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥ ΩΝ ΣΤΗ ΙΟΙΚΗΣΗ ΕΠΙΧΕΙΡΗΣΕΩΝ. ιπλωµατική Εργασία. της ΘΕΟ ΟΣΟΠΟΥΛΟΥ ΕΛΕΝΗΣ ΜΣ:5411 Παρακίνηση εργαζοµένων: Ο ρόλος του ηγέτη στην παρακίνηση των εργαζοµένων. ΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥ ΩΝ ΣΤΗ ΙΟΙΚΗΣΗ ΕΠΙΧΕΙΡΗΣΕΩΝ ιπλωµατική Εργασία της ΘΕΟ ΟΣΟΠΟΥΛΟΥ ΕΛΕΝΗΣ ΜΣ:5411 ΠΑΡΑΚΙΝΗΣΗ

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

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

[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

Dynamic types, Lambda calculus machines Section and Practice Problems Apr 21 22, 2016

Dynamic types, Lambda calculus machines Section and Practice Problems Apr 21 22, 2016 Harvard School of Engineering and Applied Sciences CS 152: Programming Languages Dynamic types, Lambda calculus machines Apr 21 22, 2016 1 Dynamic types and contracts (a) To make sure you understand the

Διαβάστε περισσότερα

Όλνκα πνπδάζηξηαο: Γξεγνξία αββίδνπ Α.Δ.Μ:7859. Δπηβιέπνλ Καζεγεηήο: Παζραιίδεο Αζαλάζηνο ΑΝΩΣΑΣΟ ΣΔΥΝΟΛΟΓΗΚΟ ΔΚΠΑΗΓΔΤΣΗΚΟ ΗΓΡΤΜΑ ΚΑΒΑΛΑ

Όλνκα πνπδάζηξηαο: Γξεγνξία αββίδνπ Α.Δ.Μ:7859. Δπηβιέπνλ Καζεγεηήο: Παζραιίδεο Αζαλάζηνο ΑΝΩΣΑΣΟ ΣΔΥΝΟΛΟΓΗΚΟ ΔΚΠΑΗΓΔΤΣΗΚΟ ΗΓΡΤΜΑ ΚΑΒΑΛΑ ΑΝΩΣΑΣΟ ΣΔΥΝΟΛΟΓΗΚΟ ΔΚΠΑΗΓΔΤΣΗΚΟ ΗΓΡΤΜΑ ΚΑΒΑΛΑ ΥΟΛΖ ΓΗΟΗΚΖΖ ΚΑΗ ΟΗΚΟΝΟΜΗΑ ΣΜΖΜΑ ΛΟΓΗΣΗΚΖ Εςπωπαϊϊκή Εταιιπείία,, ο θεσμόρ καιι η ανάπτςξη τηρ. Όλνκα πνπδάζηξηαο: Γξεγνξία αββίδνπ Α.Δ.Μ:7859 Δπηβιέπνλ Καζεγεηήο:

Διαβάστε περισσότερα

Business English. Ενότητα # 2: Management. Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων

Business English. Ενότητα # 2: Management. Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα Business English Ενότητα # 2: Management Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων Άδειες Χρήσης Το παρόν εκπαιδευτικό

Διαβάστε περισσότερα

Μελέτη των μεταβολών των χρήσεων γης στο Ζαγόρι Ιωαννίνων 0

Μελέτη των μεταβολών των χρήσεων γης στο Ζαγόρι Ιωαννίνων 0 Μελέτη των μεταβολών των χρήσεων γης στο Ζαγόρι Ιωαννίνων 0 ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΔΙΕΠΙΣΤΗΜΟΝΙΚΟ - ΔΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ (Δ.Π.Μ.Σ.) "ΠΕΡΙΒΑΛΛΟΝ ΚΑΙ ΑΝΑΠΤΥΞΗ" 2 η ΚΑΤΕΥΘΥΝΣΗ

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙ ΕΥΤΙΚΟ Ι ΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙ ΕΥΤΙΚΟ Ι ΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙ ΕΥΤΙΚΟ Ι ΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Το franchising ( δικαιόχρηση ) ως µέθοδος ανάπτυξης των επιχειρήσεων λιανικού εµπορίου

Διαβάστε περισσότερα

Επίλυση Προβλήματος σε Προγραμματιστικό Περιβάλλον από Παιδιά Προσχολικής Ηλικίας

Επίλυση Προβλήματος σε Προγραμματιστικό Περιβάλλον από Παιδιά Προσχολικής Ηλικίας Επίλυση Προβλήματος σε Προγραμματιστικό Περιβάλλον από Παιδιά Προσχολικής Ηλικίας Γ. Φεσάκης, Ε. Γουλή, Ε. Μαυρουδή Τμήμα Επιστημών Προσχολικής Αγωγής και Εκπαιδευτικού Σχεδιασμού, Πανεπιστήμιο Αιγαίου

Διαβάστε περισσότερα

WEEK 21. The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1

WEEK 21. The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1 WEEK 21 The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1 I. The Feast of Firstfruits signifies the resurrected Christ as the firstfruits for our enjoyment as

Διαβάστε περισσότερα

2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, EVALUATION REPORT

2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, EVALUATION REPORT 2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, 26-6-2016 Can anyone hear me? The participation of juveniles in juvenile justice. EVALUATION REPORT 80 professionals

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

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ. Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action

Διαβάστε περισσότερα

ΕΘΝΙΚΗ ΣΧΟΛΗ ΗΜΟΣΙΑΣ ΙΟΙΚΗΣΗΣ

ΕΘΝΙΚΗ ΣΧΟΛΗ ΗΜΟΣΙΑΣ ΙΟΙΚΗΣΗΣ Ε ΕΘΝΙΚΗ ΣΧΟΛΗ ΗΜΟΣΙΑΣ ΙΟΙΚΗΣΗΣ ΙE ΕΚΠΑΙ ΕΥΤΙΚΗ ΣΕΙΡΑ ΤΜΗΜΑ ΓΕΝΙΚΗΣ ΙΟΙΚΗΣΗΣ ΤΕΛΙΚΗ ΕΡΓΑΣΙΑ Θέµα: Εκπαίδευση: Μέσο ανάπτυξης του ανθρώπινου παράγοντα και εργαλείο διοικητικής µεταρρύθµισης Επιβλέπουσα:

Διαβάστε περισσότερα

Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο

Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο Δρ. Παναγιώτης Πεντάρης - University of Greenwich - Association for the Study of Death and Society (ASDS) Περιεχόµενα Εννοιολογικές

Διαβάστε περισσότερα

ΓΗΠΛΧΜΑΣΗΚΖ ΔΡΓΑΗΑ ΑΡΥΗΣΔΚΣΟΝΗΚΖ ΣΧΝ ΓΔΦΤΡΧΝ ΑΠΟ ΑΠΟΦΖ ΜΟΡΦΟΛΟΓΗΑ ΚΑΗ ΑΗΘΖΣΗΚΖ

ΓΗΠΛΧΜΑΣΗΚΖ ΔΡΓΑΗΑ ΑΡΥΗΣΔΚΣΟΝΗΚΖ ΣΧΝ ΓΔΦΤΡΧΝ ΑΠΟ ΑΠΟΦΖ ΜΟΡΦΟΛΟΓΗΑ ΚΑΗ ΑΗΘΖΣΗΚΖ ΔΘΝΗΚΟ ΜΔΣΟΒΗΟ ΠΟΛΤΣΔΥΝΔΗΟ ΥΟΛΖ ΠΟΛΗΣΗΚΧΝ ΜΖΥΑΝΗΚΧΝ ΣΟΜΔΑ ΓΟΜΟΣΑΣΗΚΖ ΓΗΠΛΧΜΑΣΗΚΖ ΔΡΓΑΗΑ ΑΡΥΗΣΔΚΣΟΝΗΚΖ ΣΧΝ ΓΔΦΤΡΧΝ ΑΠΟ ΑΠΟΦΖ ΜΟΡΦΟΛΟΓΗΑ ΚΑΗ ΑΗΘΖΣΗΚΖ ΔΤΘΤΜΗΑ ΝΗΚ. ΚΟΤΚΗΟΤ 01104766 ΔΠΗΒΛΔΠΧΝ:ΑΝ.ΚΑΘΖΓΖΣΖ ΗΧΑΝΝΖ

Διαβάστε περισσότερα