Parashat Pinchas. Shabbat Tammuz 24, 5772, July 14, 2012 MATSATI.COM / Rightly Dividing The Word of God

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Parashat Pinchas. Shabbat Tammuz 24, 5772, July 14, 2012 MATSATI.COM / Rightly Dividing The Word of God"

Transcript

1 Parashat Pinchas פינחס פרשת / This Week s Reading השבועות הזה קוראים Numbers 25:10-30:1 :תורה 1 Kings 18:46-19:21 :הפטרה John :הברית :החדשה Triennial cycle: Bamidbar / Numbers 25:10-26:51 Shabbat Tammuz 24, 5772, July 14, 2012 MATSATI.COM / Rightly Dividing The Word of God matsati@matsati.com Our Tent, Our Bodies, and Sexual Sin In this week s reading from Parashat Pinchas (Bamidbar / Numbers 25:10-26:51) the Lord speaks to Moshe saying that Pinchas, the son of Eleazar, has turned away His wrath from the sons of Yisrael because he was zealous for the Lord. Pinchas Jealousy for the Lord is found in sefer Bamidbar / Numbers 25:7-9. Pinchas saw the sin of the sons of Yisrael and took action against a man ח ו י ב א אח ר א י ש-י ש ר א ל א ל-ה ק ב ה ו י ד ק ר א ת- ש נ יה ם א ת א י ש י ש ר א ל ו א ת-ה א ש ה א ל-ק ב ת ה ו ת ע צ ר of Yisrael 25:8 and he went after the man of Israel into the tent and pierced both of them through, the ה מ ג פ ה מ ע ל ב נ י י ש ר א ל : man of Israel and the woman, through the body. So the plague on the sons of Israel was checked. (NASB) 25:8. א ל- ק ב ת ה and א ל- ה ק ב ה While studying these Scriptures, it is interesting that in 25:8 the expressions are translated in the NASB as into the tent and through the body, respectively. This catches our attention since the same word used here is translated in two entirely differing ways being used in the same sentence. The first expression א ל- ה ק ב ה is translated as into the tent in the KJV and NASB, into the pavilion in the RV version, into the chamber in the JPS, and into the inner room in the RSV. The second expression א ל- ק ב ת ה is translated through her belly in the KJV, RV, and JPS bible versions. The word ק ב ת ה is from the root קבה meaning stomach or belly according to Brown-Drivers-Briggs Lexicon. This word is used elsewhere as a noun in the Hebrew Scriptures ג ו ז ה י ה י ה מ ש פ ט ה כ ה נ ים מ א ת ה ע ם מ א ת ז ב ח י ה ז ב ח א ם- ש ור א ם- such as in Devarim / Deuteronomy 18:3 Now this shall be the priests' due from the people, from those who offer a 18:3 ש ה ו נ ת ן ל כ ה ן ה ז ר ע ו ה ל ח י י ם ו ה ק ב ה : sacrifice, either an ox or a sheep, of which they shall give to the priest the shoulder and the two cheeks and the stomach. (NASB) is translated referring to the stomach of an ox or sheep. In ק ב ת ה Bamidbar 25:8 used as a noun is written in the feminine sense translated as through her belly (KJV) and is very interesting in regards to the sin the man and woman were committing. Specifically here in Parashat Pinchas the people are committing sexual sin with the women of Moab accompanied with idolatry. How do these scriptures on Pinchas actions against the man and woman, coupled with the Hebrew word translated as both tent and the belly, help us to understand sexual sin, and idolatry and the קבה importance of walking in the spirit today? Let s look a little closer at these Scriptures.

2 פרשת פינחס ספר במדבר פרק כה פסוק ז -ט ז ו י ר א פ ינ ח ס ב ן-א ל ע ז ר ב ן- אה ר ן ה כ ה ן ו י ק ם מ ת ו ך ה ע ד ה ו י ק ח ר מ ח ב י ד ו: ח ו י ב א אח ר א י ש-י ש ר א ל א ל -ה ק ב ה ו י ד ק ר א ת- ש נ יה ם א ת א י ש י ש ר א ל ו א ת-ה א ש ה א ל-ק ב ת ה ו ת ע צ ר ה מ ג פ ה מ ע ל ב נ י י ש ר א ל : ט ו י ה י ו ה מ ת ים ב מ ג פ ה אר ב ע ה ו ע ש ר ים אל ף : Bamidbar / Numbers 25:7-9 25:7 When Phinehas the son of Eleazar, the son of Aaron the priest, saw it, he arose from the midst of the congregation and took a spear in his hand, 25:8 and he went after the man of Israel into the tent and pierced both of them through, the man of Israel and the woman, through the body. So the plague on the sons of Israel was checked. 25:9 Those who died by the plague were 24, 000. (NASB) In last week s study, Parashat Balak, Balak the king of Moab saw what Yisrael had done to the nations as they were making their way to the Promised Land. Balak formed an alliance with the people of Midian to rise up against Yisrael. Balak sought the help of Bilam to curse the people and offered money so that Bilam would help to prevent what will happen to him like what Yisrael was doing to the surrounding peoples. The Lord God did not allow Bilam to curse Yisrael. Since Bilam desired Balak s money, he devised a plan to cause Yisrael to sin. His plan was to use the Moabite women to cause Yisrael to sin at Peor (Bamidbar / Numbers 25:1-18) to engage with the women in physical fornication (harlotry) and worship their gods in spiritual fornication. Pinchas observing the sin of the people, and being on fire for the Mitzvot of the Lord, observed one man bringing a Moabite woman into the camp of the Lord. Pinchas entered into the tent of the Yisraelite and drove a spear through both the man and the woman that were engaged in the act of sexual sin. It is interesting here how the Moabites began with sinful deception and enticement to sexual sin which then progressed the to sinful worship in idolatry. In Bamidbar / Numbers 25:8 the expressions א ל- ה ק ב ה and א ל- ק ב ת ה translated as into the tent and through her belly respectively, reveal the nature of sexual sin in a very Hebraic way. According to the Scriptures, the Mishkhan (Tabernacle, Shemot / Exodus 36:8-39:43) is a large tent constructed to be a meeting place ( ה ל מ וע ד,א Tent of Meeting) for man to draw near to the Lord, seek the forgiveness of sins, and to know His will. In addition to this the Ketuvei Shelachim records the Apostle Paul saying our bodies are the dwelling place of God s Ruach HaKodesh (Holy Spirit, 1,(וישכן) Corinthians 3:16-20, 6:19-20). The body is also the way in which the Word of God yishkon dwelled / tabernacled amongst us according to John 1:14 14 Καὶ ὁ λόγος σὰρξ ἐγένετο καὶ ἐσκήνωσεν ἐν ἡμῖν, καὶ ἐθεασάμεθα τὴν δόξαν αὐτοῦ, δόξαν ὡς μονογενοῦς παρὰ πατρός, והדבר נהיה בשר וישכן בתוכנו ונחזה תפארתו כתפארת בן יחיד לאביו רב ἀληθείας. πλήρης χάριτος καὶ 1:14 And the Word became flesh, and dwelt among us, and we saw His glory, glory as of the only חסד ואמת begotten from the Father, full of grace and truth. (NASB) According to Bamidbar / Numbers 25:8 the word illustrates this same principle of tabernacling that the body can also function as a tent and קבה dwelling place for sexual sin. The most central place in our bodies is the belly and thus sexual sin is written to dwell in the belly. This is the understanding that the Apostle James had while writing on the sin of lust being conceived and giving birth according to James 1: The Greek text literally says epithumia sullabousa (ἐπιθυμία συλλαβοῦσα) meaning desire having conceived tiktei (τίκτει) gives birth. This illustration of birthing within the belly follows the Torah text on sexual sin being א ל- ק ב ת ה in the belly of the body. The body gives birth to sin in the belly that leads to fornication (or adultery) and then to idolatry. Once sexual sin is conceived, one s thoughts are consistently thinking upon committing the act of sex.

3 13 μηδεὶς πειραζόμενος λεγέτω ὅτι Ἀπὸ θεοῦ πειράζομαι: ὁ γὰρ θεὸς ἀπείραστός ἐστιν κακῶν, πειράζει δὲ αὐτὸς οὐδένα. 14 ἕκαστος δὲ πειράζεται ὑπὸ τῆς ἰδίας ἐπιθυμίας ἐξελκόμενος καὶ δελεαζόμενος: 15 εἶτα ἡ ἐπιθυμία συλλαβοῦσα τίκτει ἁμαρτίαν, ἡ δὲ ἁμαρτία ἀποτελεσθεῖσα ἀποκύει θάνατον. 16 Μὴ πλανᾶσθε, ἀδελφοί μου ἀγαπητοί. 17 πᾶσα δόσις ἀγαθὴ καὶ πᾶν δώρημα τέλειον ἄνωθέν ἐστιν, καταβαῖνον ἀπὸ τοῦ πατρὸς τῶν φώτων, παρ' ᾧ οὐκ ἔνι παραλλαγὴ ἢ τροπῆς ἀποσκίασμα. 18 βουληθεὶς ἀπεκύησεν ἡμᾶς λόγῳ ἀληθείας, εἰς τὸ εἶναι ἡμᾶς ἀπαρχήν τινα τῶν αὐτοῦ κτισμάτων. According to the Scriptures, idolatry seems to always be closely associated with sexual sin. The scriptures in Parashat Pinchas (Bamidbar 25:8) reveal that sexual sin is in fact a form of idolatry. When one continually dwells upon sexual immorality the person is committing all of one s faculties (both mental and physical abilities) being devoted to these thoughts. Sexual sin binds the will so that a person cannot focus or succeed in other matters; such a person yields his or her will to sin as a slave to lustful passion. Now you may have heard it said that when someone commits fornication or adultery such a person is unable to keep it in their pants. It is important to realize that our sex organs are not the issue; the real issue is in the mind. The battle that is waged is in the mind. Our sex organs carry out the desires of the mind. This is why James said in James 1: μηδεὶς πειραζόμενος λεγέτω ὅτι Ἀπὸ θεοῦ πειράζομαι: ὁ γὰρ θεὸς ἀπείραστός ἐστιν κακῶν, πειράζει δὲ αὐτὸς οὐδένα. 14 ἕκαστος δὲ πειράζεται ὑπὸ τῆς ἰδίας ἐπιθυμίας ἐξελκόμενος καὶ δελεαζόμενος: 15 εἶτα ἡ ἐπιθυμία συλλαβοῦσα τίκτει ἁμαρτίαν, ἡ δὲ ἁμαρτία ἀποτελεσθεῖσα ἀποκύει θάνατον. 1:13 Let no one say when he is tempted, I am being tempted by God ; for God cannot be tempted by evil, and He Himself does not tempt anyone. 1:14 But each one is tempted when he is carried away and enticed by his own lust. 1:15 Then when lust has conceived, it gives birth to sin; and when sin is accomplished, it brings forth death. 1:16 Do not be deceived, my beloved brethren. (NASB) James is saying here that the temptation comes from within by our own lusts by the statement when lust has conceived. When the mind conceives of the sin, it gives birth to sin, the giving birth that occurs in the belly ( ק ב ת ה.(א ל- The natural birthing process is a process that is designed by God for reproduction between a man and a woman. The reproduction (birthing) process begins in the belly. Therefore, it is not surprising that the belly is used as the reference point for sexual sin and lust. If temptation, lust, and sexual sin are found within the body, how do we keep ourselves from living in the lust of our flesh? Rav Shaul (the Apostle Paul) wrote in Galatians 5 saying πνεύματι περιπατεῖτε walk in the spirit. Two Greek words are juxtaposed together, pneumati from pneuma (πνεύμα) spirit and peripateite to walk thus meaning to walk in the spirit, we are not to not fulfill the desires of the flesh. 5:15-17 James 1: :13 Let no one say when he is tempted, I am being tempted by God ; for God cannot be tempted by evil, and He Himself does not tempt anyone. 1:14 But each one is tempted when he is carried away and enticed by his own lust. 1:15 Then when lust has conceived, it gives birth to sin; and when sin is accomplished, it brings forth death. 1:16 Do not be deceived, my beloved brethren. 1:17 Every good thing given and every perfect gift is from above, coming down from the Father of lights, with whom there is no variation or shifting shadow. 1:18 In the exercise of His will He brought us forth by the word of truth, so that we would be a kind of first fruits among His creatures. (NASB)

4 14 ὁ γὰρ πᾶς νόμος ἐν ἑνὶ λόγῳ πεπλήρωται, ἐν τῷ Ἀγαπήσεις τὸν πλησίον σου ὡς σεαυτόν. 15 εἰ δὲ ἀλλήλους δάκνετε καὶ κατεσθίετε, βλέπετε μὴ ὑπ' ἀλλήλων ἀναλωθῆτε. 16 Λέγω δέ, πνεύματι περιπατεῖτε καὶ ἐπιθυμίαν σαρκὸς οὐ μὴ τελέσητε. 17 ἡ γὰρ σὰρξ ἐπιθυμεῖ κατὰ τοῦ πνεύματος, τὸ δὲ πνεῦμα κατὰ τῆς σαρκός: ταῦτα γὰρ ἀλλήλοις ἀντίκειται, ἵνα μὴ ἃ ἐὰν θέλητε ταῦτα ποιῆτε. 18 εἰ δὲ πνεύματι ἄγεσθε, οὐκ ἐστὲ ὑπὸ νόμον. 19 φανερὰ δέ ἐστιν τὰ ἔργα τῆς σαρκός, ἅτινά ἐστιν πορνεία, ἀκαθαρσία, ἀσέλγεια, 20 εἰδωλολατρία, φαρμακεία, ἔχθραι, ἔρις, ζῆλος, θυμοί, ἐριθείαι, διχοστασίαι, αἱρέσεις, 21 φθόνοι, μέθαι, κῶμοι, καὶ τὰ ὅμοια τούτοις, ἃ προλέγω ὑμῖν καθὼς προεῖπον ὅτι οἱ τὰ τοιαῦτα πράσσοντες βασιλείαν θεοῦ οὐ κληρονομήσουσιν. 22 Ὁ δὲ καρπὸς τοῦ πνεύματός ἐστιν ἀγάπη, χαρά, εἰρήνη, μακροθυμία, χρηστότης, ἀγαθωσύνη, πίστις, 23 πραΰτης, ἐγκράτεια: κατὰ τῶν τοιούτων οὐκ ἔστιν νόμος. 24 οἱ δὲ τοῦ Χριστοῦ [Ἰησοῦ] τὴν σάρκα ἐσταύρωσαν σὺν τοῖς παθήμασιν καὶ ταῖς ἐπιθυμίαις. 25 εἰ ζῶμεν πνεύματι, πνεύματι καὶ στοιχῶμεν. 26 μὴ γινώμεθα κενόδοξοι, ἀλλήλους προκαλούμενοι, ἀλλήλοις φθονοῦντες. Galatians 5: :14 For the whole Law is fulfilled in one word, in the statement You shall love your neighbor as yourself. 5:15 But if you bite and devour one another, take care that you are not consumed by one another. 5:16 But I say, walk by the Spirit, and you will not carry out the desire of the flesh. 5:17 For the flesh sets its desire against the Spirit, and the Spirit against the flesh; for these are in opposition to one another, so that you may not do the things that you please. 5:18 But if you are led by the Spirit, you are not under the Law. 5:19 Now the deeds of the flesh are evident, which are: immorality, impurity, sensuality, 5:20 idolatry, sorcery, enmities, strife, jealousy, outbursts of anger, disputes, dissensions, factions, 5:21 envying, drunkenness, carousing, and things like these, of which I forewarn you, just as I have forewarned you, that those who practice such things will not inherit the kingdom of God. 5:22 But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, 5:23 gentleness, self-control; against such things there is no law. 5:24 Now those who belong to Christ Jesus have crucified the flesh with its passions and desires. 5:25 If we live by the Spirit, let us also walk by the Spirit. (NASB) ספר אל-הגלטיים פרק ה פסוק טו-טז טו אבל אם תנשכו ותאכלו איש את אחיו ראו פן תכלו איש על ידי רעהו והנני אמר התהלכו ברוח ולא תמלאו את תאות הבשר טז כי הבשר מתאוה הפך מן הרוח והרוח הפך מן הבשר ושניהם מתקוממים זה לזה עד שלא תוכלו לעשות את אשר תחפצו התהלכו ברוח ( spirit The Hebrew translation of the Greek text says those who walk like men of the then they will not fulfill the lust of the flesh. What does it mean to walk,(ולא תמלאו את תאות הבשר in the spirit? How do we know when we are walking in the spirit and when we are not? Paul wrote again in Ephesians 5:15-17 saying 15 Βλέπετε οὖν ἀκριβῶς πῶς περιπατεῖτε, μὴ ὡς ἄσοφοι ἀλλ' ὡς σοφοί, 16 ἐξαγοραζόμενοι τὸν καιρόν, ὅτι αἱ ἡμέραι πονηραί εἰσιν. 17 διὰ τοῦτο μὴ γίνεσθε ἄφρονες, ἀλλὰ συνίετε τί τὸ θέλημα τοῦ κυρίου. 5:15 Therefore be careful how you walk, not as unwise men but as wise, 5:16 making the most of your time, because the days are evil. 5:17 So then do not be foolish, but understand what the will of the Lord is. (NASB) This sounds a lot like what Solomon wrote in Mishley / Proverbs 6:32 : ל לא-י ב וז ו ל ג נ ב כ י י ג נ וב ל מ ל א נ פ ש ו כ י י ר ע ב 6:32 The one who commits adultery with a woman is lacking sense; He who would destroy himself does it. (NASB) thus the person involved in sexual sin is unwise and looking to destroy his or her self by doing so. Paul says that we are to be walking in the spirit; essentially we need to be using our time each day during the week studying the Holy Scriptures. We need to fill our time with activities that are centered on God, his Ruach HaKodesh (Holy Spirit) and on Yeshua God s Son. By doing this, we become busy not giving opportunity for

5 the flesh to sin or carry out its desires. Paul noted the fruits of the flesh in Galatians 5:19 saying 19 φανερὰ δέ ἐστιν τὰ ἔργα τῆς σαρκός, ἅτινά ἐστιν πορνεία, ἀκαθαρσία, ἀσέλγεια, 20 εἰδωλολατρία, φαρμακεία, ἔχθραι, ἔρις, ζῆλος, θυμοί, ἐριθείαι, διχοστασίαι, αἱρέσεις, 21 φθόνοι, μέθαι, κῶμοι, καὶ τὰ ὅμοια τούτοις, ἃ προλέγω ὑμῖν καθὼς προεῖπον ὅτι οἱ τὰ τοιαῦτα πράσσοντες βασιλείαν θεοῦ οὐ κληρονομήσουσιν. 22 Ὁ δὲ καρπὸς τοῦ πνεύματός ἐστιν ἀγάπη, χαρά, εἰρήνη, μακροθυμία, χρηστότης, ἀγαθωσύνη, πίστις, 23 πραΰτης, ἐγκράτεια: κατὰ τῶν τοιούτων οὐκ ἔστιν νόμος. 5:19 Now the deeds of the flesh are evident, which are: immorality, impurity, sensuality, 5:20 idolatry, sorcery, enmities, strife, jealousy, outbursts of anger, disputes, dissensions, factions, 5:21 envying, drunkenness, carousing, and things like these, of which I forewarn you, just as I have forewarned you, that those who practice such things will not inherit the kingdom of God. And similarly, walking by the spirit produces the fruit of the spirit which are 5:22 But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, 5:23 gentleness, self-control; against such things there is no law. Based upon my own experience an idle mind gravitates towards sin. When we are walking by the Ruach HaKodesh (Holy Spirit), using our time according to God s will, the flesh does not have opportunity for a chance to sin. Scripture says that 7 διότι τὸ φρόνημα τῆς σαρκὸς ἔχθρα εἰς θεόν, τῷ γὰρ νόμῳ τοῦ θεοῦ οὐχ ὑποτάσσεται, οὐδὲ γὰρ δύναται: 8 οἱ δὲ ἐν σαρκὶ ὄντες θεῷ ἀρέσαι οὐ δύνανται. because the mind set on the flesh is hostile toward God; for it does not subject itself to the law of God, for it is not even able to do so and those who are in the flesh cannot please God. (Romans 8:7-8, NASB) therefore, the Scriptures are clear, the way we keep ourselves from sin, and specifically sexual sin is by walking in the Ruach HaKodesh to seek God s will in the use of our time and then focusing our minds on using our time to study God s Word. This takes a daily determination to set ourselves on a path that is centered in God s will. As mentioned in last week s study, the Scriptures are given to us to teach us about God s plan for salvation, how to draw near to the Lord and how we should be living as the children of God. The very reason God gives us His Word is to educate us, this is why it is so important to study God's word. The Hebrew word for educate, train, guide, and schooling is חנוך (chinukh) it is also interesting that the word for dedication shares the same Hebrew root חנכה (Chanukah). So to educate, train, and study the Word of God appears to be synonymous with the dedication of our lives to the Lord according to the Hebrew language. This is exactly what we are supposed to do, to set our lives in a direction that is dedicated wholly to the Lord. Our being educated by the scriptures is foundational to our living and remaining in the Messiah Yeshua. All those who follow Yeshua are called תלמידים (talmidim, students) whose Hebrew root comes from the word למד (lamad) meaning to learn and is the Hebrew word translated as disciple in the Hebrew NT. The very nature of our being the disciples of Yeshua is to learn, study, and be schooled in God s Word. There is much depth in meaning and understanding of who we are in Christ which only comes by our If we are honest about it we have committed each one of these sins in our heart at some point in our lifetime. Oh what a wretched man that I am! I completely understand how the Apostle Paul felt in Romans chapter 7. How great is our need for a Savior, for Yeshua (Jesus)! actually taking the time to study God's Word. The very act of studying God s Word is to walk in the spirit as Paul is describing in the Scriptures. The scriptures say "Your Word is my shield and protection," and that literally is the case for protection from deception. In addition to this, studying, educating, and training ourselves in God's Word is characteristic of who we are in Yeshua the Messiah! If you want to be uncharacteristic as a believer and remain completely defeated in your walk before the Lord, stop studying the Word of God, stop reading your bible, and stop believing that the Scriptures are relevant for your life today.

6 Yeshua gave a parable to the people in Mark 7:14-16 saying 14 Καὶ προσκαλεσάμενος πάλιν τὸν ὄχλον ἔλεγεν αὐτοῖς, Ἀκούσατέ μου πάντες καὶ σύνετε. 15 οὐδέν ἐστιν ἔξωθεν τοῦ ἀνθρώπου εἰσπορευόμενον εἰς αὐτὸν ὃ δύναται κοινῶσαι αὐτόν: ἀλλὰ τὰ ἐκ τοῦ ἀνθρώπου ἐκπορευόμενά ἐστιν τὰ κοινοῦντα τὸν ἄνθρωπον. 16 Καὶ 17 ὅτε εἰσῆλθεν εἰς οἶκον ἀπὸ τοῦ ὄχλου, ἐπηρώτων αὐτὸν οἱ μαθηταὶ αὐτοῦ τὴν παραβολήν. 7:14 After He called the crowd to Him again, He began saying to them, Listen to Me, all of you, and understand: 7:15 there is nothing outside the man which can defile him if it goes into him; but the things which proceed out of the man are what defile the man. 7:16 If anyone has ears to hear, let him hear. (NASB) The talmudim (disciples) did not understand Yeshua and asked the meaning of this very short parable saying 17 ὅτε εἰσῆλθεν εἰς οἶκον ἀπὸ τοῦ ὄχλου, ἐπηρώτων αὐτὸν οἱ μαθηταὶ αὐτοῦ τὴν παραβολήν. 18 καὶ λέγει αὐτοῖς, Οὕτως καὶ ὑμεῖς ἀσύνετοί ἐστε; οὐ νοεῖτε ὅτι πᾶν τὸ ἔξωθεν εἰσπορευόμενον εἰς τὸν ἄνθρωπον οὐ δύναται αὐτὸν κοινῶσαι, 19 ὅτι οὐκ εἰσπορεύεται αὐτοῦ εἰς τὴν καρδίαν ἀλλ' εἰς τὴν κοιλίαν, καὶ εἰς τὸν ἀφεδρῶνα ἐκπορεύεται; καθαρίζων πάντα τὰ βρώματα. 20 ἔλεγεν δὲ ὅτι Τὸ ἐκ τοῦ ἀνθρώπου ἐκπορευόμενον ἐκεῖνο κοινοῖ τὸν ἄνθρωπον: 21 ἔσωθεν γὰρ ἐκ τῆς καρδίας τῶν ἀνθρώπων οἱ διαλογισμοὶ οἱ κακοὶ ἐκπορεύονται, πορνεῖαι, κλοπαί, φόνοι, 22 μοιχεῖαι, πλεονεξίαι, πονηρίαι, δόλος, ἀσέλγεια, ὀφθαλμὸς πονηρός, βλασφημία, ὑπερηφανία, ἀφροσύνη: 23 πάντα ταῦτα τὰ πονηρὰ ἔσωθεν ἐκπορεύεται καὶ κοινοῖ τὸν ἄνθρωπον. 7:17 When he had left the crowd and entered the house, His disciples questioned Him about the parable. 7:18 And He said to them, Are you so lacking in understanding also? Do you not understand that whatever goes into the man from outside cannot defile him, 7:19 because it does not go into his heart, but into his stomach, and is eliminated? 7:20 And He was saying, That which proceeds out of the man, that is what defiles the man. 7:21 For from within, out of the heart of men, proceed the evil thoughts, fornications, thefts, murders, adulteries, 7:22 deeds of coveting and wickedness, as well as deceit, sensuality, envy, slander, pride and foolishness. 7:23 All these evil things proceed from within and defile the man. (NASB) Here, Yeshua (Jesus) raises the bar and speaks of the thing that truly defiles a man is what comes from within and from out of the heart of men. If we go through that list in 7:21-22, and if we are truly honest about what we read, we are all guilty of each one of א ל- these things. Each of these begins as it is written in sefer Bamidbar / Numbers in the expressions through her belly which reveal the nature of sin, it begins from א ל- ק ב ת ה in the tent and ה ק ב ה within and from out of our hearts just as Yeshua said in Mark 7: Each of these sins is epithumia sullabousa tikei (ἐπιθυμία συλλαβοῦσα τίκτει) the desire having given birth from within the heart and mind once it is conceived. The illustration that Yeshua gave is not only very Hebraic but also very Torah based. Not only is Yeshua raising the bar from the traditional understanding of Judaism in his day, he is using this illustration to show the very depth of sins wickedness which proceeds from the heart that leads to certain death. This is why it is so important to study God s Word and to walk according to the spirit daily! Do you want victory from sin in your life today? If you want victory from sin, if you want to begin living according to the spirit as the Apostle Paul wrote, you can begin by placing your faith in Yeshua the Messiah today, right this moment. Begin to walk in God s ways by taking the first steps of faith. The first step begins by faith in God and in His Messiah, Yeshua, God s only begotten Son. Also, for those who already believe in Yeshua, if you want to begin new, come say the following prayer with me. Let s pray! Heavenly Father, Your Word is truly a light unto our feet! Lord, I recognize the depth and wickedness of sin within my heart. Please have mercy upon me. I take the first steps in faith, that You sent Your Son

7 to make and everlasting covenant in His blood upon the cross. Please have mercy on me Lord; please forgive me of my sins because of what Yeshua (Jesus) has done on my behalf. I believe Yeshua died for my sins and that He is the promised Messiah! Cleanse me from all sin Lord in Yeshua s name. Help me set my feet on the path of righteousness and walk in the spirit by the help of Your Ruach HaKodesh (Holy Spirit). I want to be Your disciple and Your dwelling place, I want to be filled with all of You Lord. I am tired of being filled with wickedness in my heart. Lord, beginning today I want to sanctify your Name, Your Word, Your Son, and all that You are in my body for Your glory. Help me to begin living according to Your will. I no longer want to defile this body, the holy place of God. Sanctify me in Your Word and in Your Son Yeshua. Thank You Lord for everything You have done for me. In all things, I give You the glory, the honor, and the praise forever and ever. In Yeshua s (Jesus ) Name I pray! Amen What to pray: Ask the Lord to increase your faith and joy that is found in Him. Ask the Lord to help you to set your feet on the path of righteousness, the straight and narrow path. Thank the Lord for lifting the burden of sin and revealing His truth in this day and age of unbelief. Be Blessed in Yeshua, Christ our Messiah! * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * הללויה לאדוננו מורנו ורבינו ישוע מלך המשיח לעולם ועד : Hallelujah for our Lord, our Teacher, our Rabbi, Yeshua King Messiah forever and ever

αὐτόν φέρω αὐτόν τὸ φῶς τὸ φῶς αὐτόν τὸ φῶς ὁ λόγος ὁ κόσμος δι αὐτοῦ ἐγένετο, καὶ ὁ κόσμος αὐτὸν οὐκ ἔγνω αὐτόν

αὐτόν φέρω αὐτόν τὸ φῶς τὸ φῶς αὐτόν τὸ φῶς ὁ λόγος ὁ κόσμος δι αὐτοῦ ἐγένετο, καὶ ὁ κόσμος αὐτὸν οὐκ ἔγνω αὐτόν ἐγένετο ἄνθρωπος, ἀπεσταλμένος παρὰ θεοῦ, ὄνομα αὐτῷ Ἰωάννης οὗτος ἦλθεν εἰς μαρτυρίαν ἵνα μαρτυρήσῃ περὶ τοῦ φωτός, ἵνα πάντες πιστεύσωσιν δι αὐτοῦ. οὐκ ἦν ἐκεῖνος τὸ φῶς, ἀλλ ἵνα μαρτυρήσῃ περὶ τοῦ φωτός.

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

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

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

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

1 John 5. LGNT - September 6, 2019 Page 1. Book Chapter Verse. Word # 1 John Greek. # of words. Numeric value. Interlinear English.

1 John 5. LGNT - September 6, 2019 Page 1. Book Chapter Verse. Word # 1 John Greek. # of words. Numeric value. Interlinear English. Book Chapter Verse Interlinear English Word # 1 John Greek # of letters # of words Numeric value 230501 everyone 01709 ΠΑΣ 3 281 230501 01710 Ο 1 70 230501 believing 01711 ΠΙΣΤΕΥΩΝ 8 1845 230501 that 01712

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 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

ΦωτίστεΤονΚόσμο. ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ Νοεμβρίου Δεκεμβρίου 2017

ΦωτίστεΤονΚόσμο. ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ Νοεμβρίου Δεκεμβρίου 2017 ΦωτίστεΤονΚόσμο ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ 2017 24 Νοεμβρίου -- 25 Δεκεμβρίου 2017 ΘΕΜΑ «Καθώς ακολουθούμε το παράδειγμα του Σωτήρος και ζούμε όπως ζούσε Εκείνος και όπως δίδασκε, αυτό το φως θα καίει μέσα

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

LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014

LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014 LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26 18 November 2014 But Weekend I love The song I sing I smile I laugh Greek (thing) Greek(people) Greek (man) αλλά (το) Σαββατοκύριακο αγαπώ (το) τραγούδι τραγουδώ

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

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

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

Section 8.3 Trigonometric Equations

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

Διαβάστε περισσότερα

14 Lesson 2: The Omega Verb - Present Tense

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

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

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

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

Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951)

Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951) 1 Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951) Αναγνώσματα από το βιβλίο Η Απόλαυση της Μουσικής (Machlis, Forney), για τους μαθητές που θα μελετήσουν το έργο: «Ο Σαίνμπεργκ

Διαβάστε περισσότερα

Calling and Training Disciples: How to Pray complex: Lord s Prayer 1

Calling and Training Disciples: How to Pray complex: Lord s Prayer 1 Calling and Training Disciples: How to Pray complex: Lord s Prayer 1 Matt Mark Luke Greek Reconstruction Hebrew Reconstruction 1 ו י ה י בּ ה י'ת' 1 11:1 καὶ ἐγένετο ἐν τῷ εἶναι αὐτὸν καὶ ἐγένετο ἐν τῷ

Διαβάστε περισσότερα

ΑΓΓΛΙΚΑ ΙΙΙ. Ενότητα 12b: The Little Prince. Ζωή Κανταρίδου Τμήμα Εφαρμοσμένης Πληροφορικής

ΑΓΓΛΙΚΑ ΙΙΙ. Ενότητα 12b: The Little Prince. Ζωή Κανταρίδου Τμήμα Εφαρμοσμένης Πληροφορικής Ενότητα 12b: The Little Prince Τμήμα Εφαρμοσμένης Πληροφορικής Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative Commons. Για εκπαιδευτικό υλικό, όπως εικόνες, που υπόκειται

Διαβάστε περισσότερα

Living and Nonliving Created by: Maria Okraska

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

Διαβάστε περισσότερα

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

Relationships & Reconciliation. Engaging the World Series The Lord s Prayer

Relationships & Reconciliation. Engaging the World Series The Lord s Prayer Relationships & Reconciliation Engaging the World Series The Lord s Prayer ZGM Vision Every Life for Jesus 11 Jan 2015 ZGM Mission We are a Spirit-led Community That Exalts Christ, By Equipping Disciples

Διαβάστε περισσότερα

LESSON 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28. 2 December 2014

LESSON 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28. 2 December 2014 LESSON 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28 2 December 2014 Place/Seat Right (noun) I am right I am not right It matters It does not matter The same (singular) The same (Plural) Η θέση Το δίκιο Έχω

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

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

FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17

FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17 FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17 Name: Surname: Date: Class: 1. Write these words in the correct order. /Γράψε αυτέσ τισ λέξεισ ςτη ςωςτή ςειρά. 1) playing / his / not /

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

ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ

ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ ΜΑΘΗΜΑΤΑ ΥΠΕΥΘΥΝΟΤΗΤΑΣ/ LESSONS ABOUT RESPONSIBILITY Μάθημα 1: Νιώθω υπερήφανος όταν.../ I feel proud when.

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

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

Διαβάστε περισσότερα

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

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

1 JOHN 4:1--5:12 The New Testament Eyewitnesses The Son

1 JOHN 4:1--5:12 The New Testament Eyewitnesses The Son 70 The Spirit Agreement that Jesus is the Son is the Revelation of the Spirit Apostles which is the Apostolic witness Children Thus those who believe the Apostles are children Witnesses to The Love of

Διαβάστε περισσότερα

7 Present PERFECT Simple. 8 Present PERFECT Continuous. 9 Past PERFECT Simple. 10 Past PERFECT Continuous. 11 Future PERFECT Simple

7 Present PERFECT Simple. 8 Present PERFECT Continuous. 9 Past PERFECT Simple. 10 Past PERFECT Continuous. 11 Future PERFECT Simple A/ Ονόματα και ένα παράδειγμα 1 Present Simple 7 Present PERFECT Simple 2 Present Continuous 8 Present PERFECT Continuous 3 Past Simple (+ used to) 9 Past PERFECT Simple she eats she is eating she ate

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

13:31 38 Intro to farewell discourse. Jesus is going

13:31 38 Intro to farewell discourse. Jesus is going South Central Gospel Partnership Day Conference THESE THINGS I HAVE SAID TO YOU John 14-16 If running a discipleship group/course, what topics would you want to cover? Purpose clauses in John 14-16 ταῦτα

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

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

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

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

BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN. Fairly true If I decide to learn something hard, I can.

BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN. Fairly true If I decide to learn something hard, I can. BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN Name GRADE Science Teacher A. What do I think about School? bit I try hard to do well in school. I look forward to coming to school.

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

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

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

Please be sure that your kid memorized the song. Students homework -Pg.2: Read the song and the translation 3 times.

Please be sure that your kid memorized the song. Students homework -Pg.2: Read the song and the translation 3 times. 1 Name: Ms. Mesimeri Homework Δευτέρα Section: Τράβα μπρος Trava embros Parents homework -Print this homework packet. During the next two weeks we will mainly deal with the song «Trava ebros. Students

Διαβάστε περισσότερα

«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE

«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE «ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE We would like to invite you to participate in GAMIAN- Europe research project. You should only participate if you want to and choosing

Διαβάστε περισσότερα

ΘΕΙΑΣ ΑΝΑΛΗΨΕΩΣ. Greek Orthodox Church. Ελληνική Ορθόδοξη Εκκλησία. Ecumenical Patriarchate Greek Orthodox Metropolis of New Jersey ASCENSION

ΘΕΙΑΣ ΑΝΑΛΗΨΕΩΣ. Greek Orthodox Church. Ελληνική Ορθόδοξη Εκκλησία. Ecumenical Patriarchate Greek Orthodox Metropolis of New Jersey ASCENSION Ecumenical Patriarchate Greek Orthodox Metropolis of New Jersey ASCENSION Greek Orthodox Church FAIRVIEW - NEW JERSEY Weekly Bulletin Sunday June 1 st, 2014 Fathers of the 1st Ecumenical Council Οικουμενικόν

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

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

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

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

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

If You Build It, They May Come Parable of the Tower Builder

If You Build It, They May Come Parable of the Tower Builder If You Build It, They May Come Parable of the Mark Vitalis Hoffman www.crossmarks.com Τίς γὰρ ἐξ ὑµῶν θέλων πύργον οἰκοδοµῆσαι οὐχὶ πρῶτον καθίσας ψηφίζει τὴν δαπάνην, εἰ ἔχει εἰς ἀπαρτισµόν; doesn't first

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

Matthew Mark Luke Luke Greek Reconstruction Hebrew Reconstruction. καὶ εὐαγγελιζόμενος τὴν βασιλείαν τοῦ θεοῦ

Matthew Mark Luke Luke Greek Reconstruction Hebrew Reconstruction. καὶ εὐαγγελιζόμενος τὴν βασιλείαν τοῦ θεοῦ Calling and Training Disciples: "Mission of the Twelve" complex: Sending the Twelve: Commissioning 1 1 9:35 καὶ περιῆγεν 6:6b καὶ περιῆγεν [8:1 καὶ ἐγένετο ἐν τῷ καθεξῆς καὶ αὐτὸς διώδευεν And / was going

Διαβάστε περισσότερα

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ ΕΛΛΗΝΙΔΕΣ ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΚΔΟΣΗ ΤΗΣ ΣΟΡΟΠΤΙΜΙΣΤΙΚΗΣ ΕΝΩΣΗΣ ΕΛΛΑΔΟΣ - ΤΕΥΧΟΣ Νο 110 - Δ ΤΡΙΜΗΝΟ 2014 Το πρώτο βραβείο κέρδισε η Ελλάδα για την φωτογραφία Blue + Yellow = Green στον διαγωνισμό 2014 του

Διαβάστε περισσότερα

I am. Present indicative

I am. Present indicative εἰμί eimi Present indicative εἰμί εἶ ἐστί(ν) ἐσμέν ἐστέ εἰσί(ν) John 3:28 εἰμὶ ἐγὼ ὁ χριστός eimi ego ho christos John 3:28 εἰμὶ ἐγὼ ὁ χριστός eimi ego ho christos the Christ John 1:19 Σὺτίςεἶ; Su tis

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

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 9: Inversion Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons εκτός

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

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

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

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

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

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

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

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

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

2 Thessalonians 3. Greek

2 Thessalonians 3. Greek Book Chapter Verse Interlinear English Word # in 2 Thess Greek # of letters # of words Numeric value 140301 00548 ΤΟ 2 370 140301 finally 00549 ΛΟΙΠΟΝ 6 310 140301 pray 00550 ΠΡΟΣΕΥΧΕΣΘΕ 11 1674 140301

Διαβάστε περισσότερα

Srednicki Chapter 55

Srednicki Chapter 55 Srednicki Chapter 55 QFT Problems & Solutions A. George August 3, 03 Srednicki 55.. Use equations 55.3-55.0 and A i, A j ] = Π i, Π j ] = 0 (at equal times) to verify equations 55.-55.3. This is our third

Διαβάστε περισσότερα

Notes are available 1

Notes are available 1 Notes are available 1 Galatians 2:15 4.12 2 3:15, 3:19 interpretational contradiction LAW cannot be and was added Promise 3 Gal.3:19 4 Mt 6:27 Which of you by taking thought can add one cubit unto

Διαβάστε περισσότερα

Ephesians. Wayne Stewart

Ephesians. Wayne Stewart Ephesians Wayne Stewart 1 Shadows of a ministry independent of Jerusalem and the 12 Taken from CH Welch 2 Acts 28:25 25 (AV) And when they agreed not among themselves, they departed, after that Paul had

Διαβάστε περισσότερα

εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016

εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016 εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016 Conditional Relative Clauses relative clauses referring to an indefinite person or thing (whoever, whatever, anyone,

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

LESSON 9 (ΜΑΘΗΜΑ ΕΝΝΙΑ) REF: 202/053/29-ADV. 14 January 2014

LESSON 9 (ΜΑΘΗΜΑ ΕΝΝΙΑ) REF: 202/053/29-ADV. 14 January 2014 LESSON 9 (ΜΑΘΗΜΑ ΕΝΝΙΑ) REF: 202/053/29-ADV 14 January 2014 Nobody/No-one Κανένας/καμία/κανένα What s the matter?/what s happening? Τι συμβαίνει; (simvenee) All right/ok εντάξει Moment η στιγμή (stigmee)

Διαβάστε περισσότερα

Final Test Grammar. Term C'

Final Test Grammar. Term C' Final Test Grammar Term C' Book: Starting Steps 1 & Extra and Friends Vocabulary and Grammar Practice Class: Junior AB Name: /43 Date: E xercise 1 L ook at the example and do the same. ( Κξίηα ηξ παοάδειγμα

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

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

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

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

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

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

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

Uniform Convergence of Fourier Series Michael Taylor

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

Διαβάστε περισσότερα

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

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

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

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

Στο εστιατόριο «ToDokimasesPrinToBgaleisStonKosmo?» έξω από τους δακτυλίους του Κρόνου, οι παραγγελίες γίνονται ηλεκτρονικά.

Στο εστιατόριο «ToDokimasesPrinToBgaleisStonKosmo?» έξω από τους δακτυλίους του Κρόνου, οι παραγγελίες γίνονται ηλεκτρονικά. Διαστημικό εστιατόριο του (Μ)ΑστροΈκτορα Στο εστιατόριο «ToDokimasesPrinToBgaleisStonKosmo?» έξω από τους δακτυλίους του Κρόνου, οι παραγγελίες γίνονται ηλεκτρονικά. Μόλις μια παρέα πελατών κάτσει σε ένα

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

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

Sample Pages of John in Greek Σελίδες δειγμάτων John στα ελληνικά KEY WORDS AND PHRASES IN JOHN ΛΈΞΕΙΣ ΚΛΕΙΔΊ ΚΑΙ ΦΡΑΣΕΙΣ ΣΕ JOHN

Sample Pages of John in Greek Σελίδες δειγμάτων John στα ελληνικά KEY WORDS AND PHRASES IN JOHN ΛΈΞΕΙΣ ΚΛΕΙΔΊ ΚΑΙ ΦΡΑΣΕΙΣ ΣΕ JOHN Sample Pages of John in Greek Σελίδες δειγμάτων John στα ελληνικά KEY WORDS AND PHRASES IN JOHN ΛΈΞΕΙΣ ΚΛΕΙΔΊ ΚΑΙ ΦΡΑΣΕΙΣ ΣΕ JOHN BELIEVE (80 VERSES) ΘΕΩΡΗΣΤΕ (80 ΣΤΙΧΟΙ) 1:7 4:39 6:30 8:24 10:38 12:37

Διαβάστε περισσότερα

Matthew Mark Luke Greek Reconstruction Hebrew Reconstruction

Matthew Mark Luke Greek Reconstruction Hebrew Reconstruction Passover: Preparations for Eating Passover Lamb (Matt. 26:17-19; Mark 14:12-16; Luke 22:7-13) 1 1 ו יּ ב א י(ם 1 26:17 τῇ δὲ πρώτῃ 14:12 καὶ τῇ πρώτῃ ἡμέρᾳ 22:7 ἦλθεν δὲ ἡ ἡμέρα ἦλθεν δὲ ἡ ἡμέρα on the

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

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Centre No. Candidate No. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Materials required for examination Nil Paper Reference

Διαβάστε περισσότερα