ΜΕΛΕΤΗ ΣΥΜΠΛΟΚΩΝ ΚΥΚΛΟΔΕΞΤΡΙΝΩΝ

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "ΜΕΛΕΤΗ ΣΥΜΠΛΟΚΩΝ ΚΥΚΛΟΔΕΞΤΡΙΝΩΝ"

Transcript

1 ΜΕΛΕΤΗ ΣΥΜΠΛΟΚΩΝ ΚΥΚΛΟΔΕΞΤΡΙΝΩΝ 1) File --> open --> /.../4cpa.cif 2) Περιοχή: Structure Navigator --> Crystal Structures --> 4cpa 3) Περιοχή: Display options --> More Info Space group:... ( * )Z:, Z : 4) Παρατηρήστε τη θερμική κίνηση του μοντέλου επιλέγοντας: Style Ellipsoid ή/και Colour Atomic displacement 5) Ανοίξτε το 4cpa.cif με έναν text editor (π.χ. wordpad) και σβήστε τη θέση (Β) με αριθμό κατάληψης 36% (θα αναγνωρίσετε τα άτομα από το όνομα τους που περιέχει το Β αλλά και από τον αριθμό κατάληψης τους που είναι 0.36). Αποθηκεύεστε το αρχείο με διαφορετικό όνομα π.χ. 4CPA_A.cif και ανοίξτε με mercury το νέο αυτό αρχείο. Τώρα θα πρέπει να βλέπετε ξεκάθαρα μόνο μία θέση guest. 4) ΔΙΑΜΟΡΦΩΣΗ ΜΟΡΙΟΥ ΞΕΝΙΣΤΗ (β-κυκλοδεξτρίνη) i) Ενδομοριακοί Υδρογονικοί δεσμοί; * For many discrete-molecule materials, the molecules pack together to form crystals in a relatively simple way determined by the Space Group. Such materials are said to have Z'=1 (Z-prime). Increasingly, crystallographers are beginning to find crystals in which the basic building block is not just one molecule, but several molecules taken together. Such materials are said to have Z'>1.

2 Ο22... Ο31 Απόσταση (Å) Γωνία ( ) ii) Conformational characteristics of the.-cd/ complex Residue n=1 n=2 n=3 n=4 n=5 n=6 n=7.. D (Å) Φ h ( ) d (Å) D K (Å) τ (º) ω(º) Conformation (Παράρτημα Ι i ) D = O4n O4(n+1) distances; Φ h = O4(n-1) O4n O4(n+1) angles; d = deviations of the O4n atoms from their least-squares plane; D k = KA O4nA; τ = tilt angles between the optimum O4n plane and the mean plane of the O4(n-1), C1n, C4n, O4n atoms; torsion angles ω = O5n-C5n-C6n-O6n; conformation of the primary hydroxyls iii) ΣΧΗΜΑΤΙΣΜΟΣ ΔΙΜΕΡΟΥΣ Περιοχή: Display options --> Packing

3 (Menu) Calculate --> Packing/Slicing --> a: b: c: Υδρογονικοί δεσμοί για σχηματισμό διμερούς συμπλόκων κατά τον άξονα b Απόσταση (Å) Γωνία ( ) Ο31... Ο3 7 5) ΔΙΑΜΟΡΦΩΣΗ ΞΕΝΙZOMENOY MOPIOY (4CPA) 5.1 Καρβοξύλιο (H-bonds με νερά έξω από cavity) 5.2 Etheric O 5.3 phenyl groups (pi-pi) - Shortest inter-phenyl carbon-carbon distance (SICD) = ( gia to C5A- C5A) [Hunter, 1990 rule 3.4<SICD<4.8] - centroids distance = offset(πυθαγορειο) = 1.68 (διαμετρος phenyl~2.78) 5.4 Cl (location: O2,O3 plane, H-bond entrapped water molecule)

4 6) ΑΛΛΗΛΕΠΙΔΡΑΣΕΙΣ ΞΕΝΙΣΤΗ ΞΕΝΙΖΟΜΕΝΟΥ CH-π interactions (ΠΑΡΑΡΤΗΜΑ ΙΙ ii ) ================= H:... C1:... C2:... ω =... θ =... Dpln=... Dlin =... Datm =... Region =...

5 6) ΔΙΚΤΥΟ ΥΔΡΟΓΟΝΙΚΩΝ ΔΕΣΜΩΝ - ΝΕΡΑ

6 7) CRYSTAL PACKING

7 *i ΠΑΡΑΡΤΗΜΑ I Glucose is a highly complex chemical compound because it can exist is many isomeric forms and each isomer is subject to rotational isomerism. Within the cyclic form of glucose, rotation may occur around the O6-C6-C5-O5 torsion angle, termed the ω-angle, to form three rotamer conformations as shown in the diagram below. In referring to the orientations of the ω-angle and the O6-C6-C5- C4 angle, the three stable staered rotamer conformations are termed gauche-gauche (), gauche-trans () and trans-gauche (tg). For methyl α-d-glucopyranose at equilibrium the ratio of molecules in each rotamer conformation is reported as 57 : 38 : 5 : : tg. Kirschner, Karl N.; Woods, Robert J. (2001), "Solvent interactions determine carbohydrate conformation", Proc. Natl. Acad. Sci. USA 98 (19): This tendency for the ω-angle to prefer to adopt a gauche conformation is attributed to the gauche effect. (The term "gauche" refers to conformational isomers (conformers) where two vicinal (In chemistry vicinal (from Latin vicinus = neighbor) stands for any two functional groups bonded to two adjacent carbon atoms) groups are separated by a 60 torsion angle). Rotation around the C-5/C-6 bond is described by the angle ω. Three possible staered conformations possible; gauche-trans (), gauche-gauche (), trans-gauche(tg). Example Conformational characteristics of the α-cd/camphor complexes Residue n=1 n=2 n=3 n=4 n=5 n=6 R-αCD ω (º) Conformation a b 76.7 a 60.4 b 75.2 a 62.6 b 90.5 a b 80.8 c a b 80.3 a -52 b 64.8 c In stereochemistry, gauche interactions hinder bond rotation. For example, sighting along the C5-C6 bond, there are two possible relative potential energies. Τhe conformational families about the C 5 C 6 bond display a bias for gauche orientations. In general a gauche rotamer (, -HO(6) points outwards the CyD cavity) is less stable than an anti-rotamer ( - -HO(6) points inwards the CyD cavity).

8 ii ΠΑΡΑΡΤΗΜΑ ΙΙ CH/p Interactions as Demonstrated in the Crystal Structure of Host/Guest Compounds. A Database Study Hiroki Takahashi, Sei Tsuboyama, Yoji Umezawa, Kazumasa Honda and Motohiro Nishio Tetrahedron 56 (2000) CH/ interactions: O: centre of plane. C 1 and C 2 : nearest and second nearest sp 2 -carbons, respectively, to H. : dihedral angle defined by C 1 OC 2 and H C 1 C 2 planes. : angle HXC 1 D pln : H/ -plane distance (H/I) D atm : interatomic distance (H/C 1 ) D lin : distance between H and line C 1 C 2 (H/J) D max = Å Region 1 D pln < D max < 60 Region 2 D lin < D max < < < 130 Region 3 D atm < D max < < < 90 ( : HC 1 I)

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

Table S1 Selected bond lengths [Å] and angles [ ] for complexes 1 8. Complex 1. Complex 2. Complex 3. Complex 4. Complex 5.

Table S1 Selected bond lengths [Å] and angles [ ] for complexes 1 8. Complex 1. Complex 2. Complex 3. Complex 4. Complex 5. Table S1 Selected bond lengths [Å] and angles [ ] for complexes 1 8. Complex 1 Zn(1) O(1) 1.969(2) Zn(1) O(5) 1.989(3) Zn(1) O(6) 1.930(3) Zn(1) O(4) a 1.954(4) Zn(1) O(3) a 2.519(25) O(6) Zn(1) O(4) a

Διαβάστε περισσότερα

Solutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz

Solutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz Solutions to the Schrodinger equation atomic orbitals Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz ybridization Valence Bond Approach to bonding sp 3 (Ψ 2 s + Ψ 2 px + Ψ 2 py + Ψ 2 pz) sp 2 (Ψ 2 s + Ψ 2 px + Ψ 2 py)

Διαβάστε περισσότερα

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O Q1. (a) Explain the meaning of the terms mean bond enthalpy and standard enthalpy of formation. Mean bond enthalpy... Standard enthalpy of formation... (5) (b) Some mean bond enthalpies are given below.

Διαβάστε περισσότερα

Electronic Supplementary Information:

Electronic Supplementary Information: Electronic Supplementary Information: 2 6 5 7 2 N S 3 9 6 7 5 2 S N 3 9 Scheme S. Atom numbering for thione and thiol tautomers of thioacetamide 3 0.6 0. absorbance 0.2 0.0 0.5 0.0 0.05 0.00 N 2 Ar km/mol

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

Supporting Information

Supporting Information Supporting Information rigin of the Regio- and Stereoselectivity of Allylic Substitution of rganocopper Reagents Naohiko Yoshikai, Song-Lin Zhang, and Eiichi Nakamura* Department of Chemistry, The University

Διαβάστε περισσότερα

Carbohydrates in the gas phase: conformational preference of D-ribose and 2-deoxy-D-ribose

Carbohydrates in the gas phase: conformational preference of D-ribose and 2-deoxy-D-ribose New J. Chem ELECTRONIC SUPPLEMENTARY INFORMATION Carbohydrates in the gas phase: conformational preference of D-ribose and 2-deoxy-D-ribose Luis Miguel Azofra,*, María Mar Quesada-Moreno, Ibon Alkorta,

Διαβάστε περισσότερα

Multifunctinality and Crystal Dynamics of Highly Stable Porous Metal-Organic Framework [Zn 4 O(NTB) 2 ]

Multifunctinality and Crystal Dynamics of Highly Stable Porous Metal-Organic Framework [Zn 4 O(NTB) 2 ] Supporting Information Multifunctinality and Crystal Dynamics of Highly Stable Porous Metal-Organic Framework [Zn 4 O(NTB) 2 ] Eun Young Lee, Seung Yeon Jang, and Myunghyun Paik Suh* School of Chemistry,

Διαβάστε περισσότερα

College of Life Science, Dalian Nationalities University, Dalian , PR China.

College of Life Science, Dalian Nationalities University, Dalian , PR China. Electronic Supplementary Material (ESI) for New Journal of Chemistry. This journal is The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2018 Postsynthetic modification

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

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

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

Nitric oxide (NO) reactivity studies on mononuclear Iron(II) complexes supported by a tetradentate Schiff base Ligand

Nitric oxide (NO) reactivity studies on mononuclear Iron(II) complexes supported by a tetradentate Schiff base Ligand Electronic Supplementary Material (ESI) for RSC Advances. This journal is The Royal Society of Chemistry 2016 Nitric oxide (NO) reactivity studies on mononuclear Iron(II) complexes supported by a tetradentate

Διαβάστε περισσότερα

Enantioselective Synthesis of the Anti-inflammatory Agent ( )-Acanthoic Acid

Enantioselective Synthesis of the Anti-inflammatory Agent ( )-Acanthoic Acid Enantioselective Synthesis of the Anti-inflammatory Agent ( )-Acanthoic Acid Taotao Ling, a Chinmay Chowdhury, a Bryan A. Kramer, a Binh G. Vong, a Michael A. Palladino b and Emmanuel A. Theodorakis a

Διαβάστε περισσότερα

Supporting Information

Supporting Information SUPPORTING INFORMATION FOR: Trialkylstibine complexes of boron, aluminium, gallium and indium trihalides: synthesis, properties and bonding Victoria K. Greenacre, William Levason and Gillian Reid Chemistry,

Διαβάστε περισσότερα

Patrycja Miszczyk, Dorota Wieczorek, Joanna Gałęzowska, Błażej Dziuk, Joanna Wietrzyk and Ewa Chmielewska. 1. Spectroscopic Data.

Patrycja Miszczyk, Dorota Wieczorek, Joanna Gałęzowska, Błażej Dziuk, Joanna Wietrzyk and Ewa Chmielewska. 1. Spectroscopic Data. ; doi:10.3390/molecules22020254 S1 of S23 Supplementary Materials: Reaction of 3-Amino-1,2,4-Triazole with Diethyl Phosphite and Triethyl Orthoformate: Acid-Base Properties and Antiosteoporotic Activities

Διαβάστε περισσότερα

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3) Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)

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

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

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

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

IV. ANHANG 179. Anhang 178

IV. ANHANG 179. Anhang 178 Anhang 178 IV. ANHANG 179 1. Röntgenstrukturanalysen (Tabellen) 179 1.1. Diastereomer A (Diplomarbeit) 179 1.2. Diastereomer B (Diplomarbeit) 186 1.3. Aldoladdukt 5A 193 1.4. Aldoladdukt 13A 200 1.5. Aldoladdukt

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

SUPPLEMENTARY MATERIAL

SUPPLEMENTARY MATERIAL 10.1071/CH16014_AC The Authors 2016 Australian Journal of Chemistry 2016, 69(9), 1049-1053 SUPPLEMENTARY MATERIAL A Green Approach for the Synthesis of Novel 7,11-Dihydro-6H-chromeno[3,4- e]isoxazolo[5,4-b]pyridin-6-one

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

Homework 8 Model Solution Section

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

Διαβάστε περισσότερα

Spherical Coordinates

Spherical Coordinates Spherical Coordinates MATH 311, Calculus III J. Robert Buchanan Department of Mathematics Fall 2011 Spherical Coordinates Another means of locating points in three-dimensional space is known as the spherical

Διαβάστε περισσότερα

Stereochemistry and mechanistic insight in the [2 k +2 i +2 i ] annulations of ketenes and imines

Stereochemistry and mechanistic insight in the [2 k +2 i +2 i ] annulations of ketenes and imines Stereochemistry and mechanistic insight in the [2 k +2 i +2 i ] annulations of ketenes and imines Zhanhui Yang, Wei He, Baoxiang Cheng and Jiaxi Xu* State Key Laboratory of Chemical Resource Engineering,

Διαβάστε περισσότερα

Electronic Supplementary Information (ESI)

Electronic Supplementary Information (ESI) Electronic Supplementary Material (ESI) for RSC Advances. This journal is The Royal Society of Chemistry 2016 Electronic Supplementary Information (ESI) Cyclopentadienyl iron dicarbonyl (CpFe(CO) 2 ) derivatives

Διαβάστε περισσότερα

Supporting information. An unusual bifunctional Tb-MOF for highly sensing of Ba 2+ ions and remarkable selectivities of CO 2 /N 2 and CO 2 /CH 4

Supporting information. An unusual bifunctional Tb-MOF for highly sensing of Ba 2+ ions and remarkable selectivities of CO 2 /N 2 and CO 2 /CH 4 Electronic Supplementary Material (ESI) for Journal of Materials Chemistry A. This journal is The Royal Society of Chemistry 2015 Supporting information An unusual bifunctional Tb-MOF for highly sensing

Διαβάστε περισσότερα

Pyrrolo[2,3-d:5,4-d']bisthiazoles: Alternate Synthetic Routes and a Comparative Study to Analogous Fused-ring Bithiophenes

Pyrrolo[2,3-d:5,4-d']bisthiazoles: Alternate Synthetic Routes and a Comparative Study to Analogous Fused-ring Bithiophenes SUPPORTING INFORMATION Pyrrolo[2,3-d:5,4-d']bisthiazoles: Alternate Synthetic Routes and a Comparative Study to Analogous Fused-ring Bithiophenes Eric J. Uzelac, Casey B. McCausland, and Seth C. Rasmussen*

Διαβάστε περισσότερα

Butadiene as a Ligand in Open Sandwich Compounds

Butadiene as a Ligand in Open Sandwich Compounds Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2018 Butadiene as a Ligand in Open Sandwich Compounds Qunchao Fan, a Jia Fu, a Huidong

Διαβάστε περισσότερα

Supporting Information. Generation Response. Physics & Chemistry of CAS, 40-1 South Beijing Road, Urumqi , China. China , USA

Supporting Information. Generation Response. Physics & Chemistry of CAS, 40-1 South Beijing Road, Urumqi , China. China , USA Supporting Information Pb 3 B 6 O 11 F 2 : A First Noncentrocentric Lead Fluoroborate with Large Second Harmonic Generation Response Hongyi Li, a Hongping Wu, a * Xin Su, a Hongwei Yu, a,b Shilie Pan,

Διαβάστε περισσότερα

Zebra reaction or the recipe for heterodimeric zinc complexes synthesis

Zebra reaction or the recipe for heterodimeric zinc complexes synthesis Electronic Supplementary Material (ESI) for Dalton Transactions. This journal is The Royal Society of Chemistry 05 Supporting Information Zebra reaction or the recipe for heterodimeric zinc complexes synthesis

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

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

Πρόβλημα 1: Αναζήτηση Ελάχιστης/Μέγιστης Τιμής

Πρόβλημα 1: Αναζήτηση Ελάχιστης/Μέγιστης Τιμής Πρόβλημα 1: Αναζήτηση Ελάχιστης/Μέγιστης Τιμής Να γραφεί πρόγραμμα το οποίο δέχεται ως είσοδο μια ακολουθία S από n (n 40) ακέραιους αριθμούς και επιστρέφει ως έξοδο δύο ακολουθίες από θετικούς ακέραιους

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

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

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

Διαβάστε περισσότερα

ELECTRONIC SUPPLEMENTARY MATERIAL-RSC Adv.

ELECTRONIC SUPPLEMENTARY MATERIAL-RSC Adv. Electronic Supplementary Material (ESI) for RSC Advances. This journal is The Royal Society of Chemistry 2016 ELECTRONIC SUPPLEMENTARY MATERIAL-RSC Adv. Studies of molecular structure, hydrogen bonding

Διαβάστε περισσότερα

Supporting Information. Partial thioamide scan on the lipopeptaibiotic trichogin GA IV. Effects on

Supporting Information. Partial thioamide scan on the lipopeptaibiotic trichogin GA IV. Effects on Supporting Information for Partial thioamide scan on the lipopeptaibiotic trichogin GA IV. Effects on folding and bioactivity Marta De Zotti 1, Barbara Biondi 1, Cristina Peggion 1, Matteo De Poli 1, Haleh

Διαβάστε περισσότερα

Cycloaddition of Homochiral Dihydroimidazoles: A 1,3-Dipolar Cycloaddition Route to Optically Active Pyrrolo[1,2-a]imidazoles

Cycloaddition of Homochiral Dihydroimidazoles: A 1,3-Dipolar Cycloaddition Route to Optically Active Pyrrolo[1,2-a]imidazoles X-Ray crystallographic data tables for paper: Supplementary Material (ESI) for Organic & Biomolecular Chemistry Cycloaddition of Homochiral Dihydroimidazoles: A 1,3-Dipolar Cycloaddition Route to Optically

Διαβάστε περισσότερα

On a four-dimensional hyperbolic manifold with finite volume

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

Διαβάστε περισσότερα

Section 8.2 Graphs of Polar Equations

Section 8.2 Graphs of Polar Equations Section 8. Graphs of Polar Equations Graphing Polar Equations The graph of a polar equation r = f(θ), or more generally F(r,θ) = 0, consists of all points P that have at least one polar representation

Διαβάστε περισσότερα

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.

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

Διαβάστε περισσότερα

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

Reminders: linear functions

Reminders: linear functions Reminders: linear functions Let U and V be vector spaces over the same field F. Definition A function f : U V is linear if for every u 1, u 2 U, f (u 1 + u 2 ) = f (u 1 ) + f (u 2 ), and for every u U

Διαβάστε περισσότερα

Εγχειρίδια Μαθηµατικών και Χταποδάκι στα Κάρβουνα

Εγχειρίδια Μαθηµατικών και Χταποδάκι στα Κάρβουνα [ 1 ] Πανεπιστήµιο Κύπρου Εγχειρίδια Μαθηµατικών και Χταποδάκι στα Κάρβουνα Νίκος Στυλιανόπουλος, Πανεπιστήµιο Κύπρου Λευκωσία, εκέµβριος 2009 [ 2 ] Πανεπιστήµιο Κύπρου Πόσο σηµαντική είναι η απόδειξη

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Όλοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα μικρότεροι του 10000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Αν κάπου κάνετε κάποιες υποθέσεις

Διαβάστε περισσότερα

Supplementary materials. Mode Analysis. Matthias M. N. Wolf, Christian Schumann, Ruth Groß, Tatiana Domratcheva 1 and Rolf. Diller

Supplementary materials. Mode Analysis. Matthias M. N. Wolf, Christian Schumann, Ruth Groß, Tatiana Domratcheva 1 and Rolf. Diller Supplementary materials Ultrafast Infrared Spectroscopy of Riboflavin: Dynamics, Electronic Structure, and Vibrational Mode Analysis Matthias M. N. Wolf, Christian Schumann, Ruth Groß, Tatiana Domratcheva

Διαβάστε περισσότερα

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS

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

Διαβάστε περισσότερα

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ

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

Διαβάστε περισσότερα

Review: Molecules = + + = + + Start with the full Hamiltonian. Use the Born-Oppenheimer approximation

Review: Molecules = + + = + + Start with the full Hamiltonian. Use the Born-Oppenheimer approximation Review: Molecules Start with the full amiltonian Ze e = + + ZZe A A B i A i me A ma ia, 4πε 0riA i< j4πε 0rij A< B4πε 0rAB Use the Born-Oppenheimer approximation elec Ze e = + + A A B i i me ia, 4πε 0riA

Διαβάστε περισσότερα

Supporting Information To. Microhydration of caesium compounds: Journal of Molecular Modeling

Supporting Information To. Microhydration of caesium compounds: Journal of Molecular Modeling Supporting Information To Microhydration of caesium compounds: Cs, CsOH, CsI and Cs 2 I 2 complexes with one to three H 2 O molecules of nuclear safety interest Journal of Molecular Modeling Mária Sudolská

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

UDZ Swirl diffuser. Product facts. Quick-selection. Swirl diffuser UDZ. Product code example:

UDZ Swirl diffuser. Product facts. Quick-selection. Swirl diffuser UDZ. Product code example: UDZ Swirl diffuser Swirl diffuser UDZ, which is intended for installation in a ventilation duct, can be used in premises with a large volume, for example factory premises, storage areas, superstores, halls,

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

6.1. Dirac Equation. Hamiltonian. Dirac Eq.

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

Διαβάστε περισσότερα

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

D Alembert s Solution to the Wave Equation

D Alembert s Solution to the Wave Equation D Alembert s Solution to the Wave Equation MATH 467 Partial Differential Equations J. Robert Buchanan Department of Mathematics Fall 2018 Objectives In this lesson we will learn: a change of variable technique

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

Supporting Information

Supporting Information Supporting Information Aluminum Complexes of N 2 O 2 3 Formazanate Ligands Supported by Phosphine Oxide Donors Ryan R. Maar, Amir Rabiee Kenaree, Ruizhong Zhang, Yichen Tao, Benjamin D. Katzman, Viktor

Διαβάστε περισσότερα

CHAPTER 101 FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD

CHAPTER 101 FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD CHAPTER FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD EXERCISE 36 Page 66. Determine the Fourier series for the periodic function: f(x), when x +, when x which is periodic outside this rge of period.

Διαβάστε περισσότερα

Nickel and Platinum PCP Pincer Complexes Incorporating an Acyclic Diaminoalkyl Central Moiety Connecting Imidazole or Pyrazole Rings

Nickel and Platinum PCP Pincer Complexes Incorporating an Acyclic Diaminoalkyl Central Moiety Connecting Imidazole or Pyrazole Rings ickel and Platinum PCP Pincer Complexes Incorporating an Acyclic Diaminoalkyl Central Moiety Connecting Imidazole or Pyrazole Rings Braulio M. Puerta Lombardi, Rudy M. Braun, Chris Gendy, Chia Yun Chang,

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1. Exercises 0 More exercises are available in Elementary Differential Equations. If you have a problem to solve any of them, feel free to come to office hour. Problem Find a fundamental matrix of the given

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

Electronic Supplementary Information (ESI)

Electronic Supplementary Information (ESI) Electronic Supplementary Material (ESI) for Dalton Transactions. This journal is The Royal Society of Chemistry 2016 Electronic Supplementary Information (ESI) CPh 3 as a functional group in P-heterocyclic

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

C H Activation of Cp* Ligand Coordinated to Ruthenium. Center: Synthesis and Reactivity of a Thiolate-Bridged

C H Activation of Cp* Ligand Coordinated to Ruthenium. Center: Synthesis and Reactivity of a Thiolate-Bridged Supporting Information C H Activation of Cp* Ligand Coordinated to Ruthenium Center: Synthesis and Reactivity of a Thiolate-Bridged Diruthenium Complex Featuring Fulvene-like Cp* Ligand Xiaoxiao Ji, Dawei

Διαβάστε περισσότερα

Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας

Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας ΤΕΙ ΚΑΒΑΛΑΣ ΠΑΡΑΡΤΗΜΑ ΔΡΑΜΑΣ ΤΜΗΜΑ ΑΡΧΙΤΕΚΤΟΝΙΚΗΤΟΠΙΟΥ Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας

Διαβάστε περισσότερα

k A = [k, k]( )[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +

k A = [k, k]( )[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R + Chapter 3. Fuzzy Arithmetic 3- Fuzzy arithmetic: ~Addition(+) and subtraction (-): Let A = [a and B = [b, b in R If x [a and y [b, b than x+y [a +b +b Symbolically,we write A(+)B = [a (+)[b, b = [a +b

Διαβάστε περισσότερα

Chapter 6: Systems of Linear Differential. be continuous functions on the interval

Chapter 6: Systems of Linear Differential. be continuous functions on the interval Chapter 6: Systems of Linear Differential Equations Let a (t), a 2 (t),..., a nn (t), b (t), b 2 (t),..., b n (t) be continuous functions on the interval I. The system of n first-order differential equations

Διαβάστε περισσότερα

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds! MTH U341 urface Integrals, tokes theorem, the divergence theorem To be turned in Wed., Dec. 1. 1. Let be the sphere of radius a, x 2 + y 2 + z 2 a 2. a. Use spherical coordinates (with ρ a) to parametrize.

Διαβάστε περισσότερα

Isotopic and Geochemical Study of Travertine and Hot Springs Occurring Along the Yumoto Fault at North Coast of the Oga Peninsula, Akita Prefecture

Isotopic and Geochemical Study of Travertine and Hot Springs Occurring Along the Yumoto Fault at North Coast of the Oga Peninsula, Akita Prefecture J. Hot Spring Sci. /2 **2 * + + + + + +3 ++ * * + 3 Isotopic and Geochemical Study of Travertine and Hot Springs Occurring Along the Yumoto Fault at North Coast of the Oga Peninsula Akita Prefecture +

Διαβάστε περισσότερα

[ Co( aipamp apamp) ( amp) Cl] [ ZnCl 4 ]

[ Co( aipamp apamp) ( amp) Cl] [ ZnCl 4 ] 2004 62 23, 2334 2342 ACTA CHIMICA SINICA Vol 62, 2004 No 23, 2334 2342 [ Co( aipamp apamp) ( amp) Cl] [ ZnCl 4 ] a b Ξ, a a a a a Ξ ( a 550025) ( b 210000) X [ Co (aipamp) (amp) Cl ][ ZnCl 4 ] (aipamp

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

Electronic supplementary information (ESI) Bodipy functionalized ortho-carborane dyads for low-energy photosensitization

Electronic supplementary information (ESI) Bodipy functionalized ortho-carborane dyads for low-energy photosensitization Electronic Supplementary Material (ESI) for Dalton Transactions. This journal is The Royal Society of Chemistry 2014 Electronic supplementary information (ESI) Bodipy functionalized ortho-carborane dyads

Διαβάστε περισσότερα

Tunable Ligand Emission of Napthylsalophen Triple-Decker Dinuclear Lanthanide (III) Sandwich Complexes

Tunable Ligand Emission of Napthylsalophen Triple-Decker Dinuclear Lanthanide (III) Sandwich Complexes Electronic Supplementary Material (ESI) for Dalton Transactions. This journal is The Royal Society of Chemistry 2017 Supplemental Information Tunable Ligand Emission of Napthylsalophen Triple-Decker Dinuclear

Διαβάστε περισσότερα

Supplementary Information

Supplementary Information 9.4 6.60. 8.6 8.8 9.29 20.04 29.6 0.07 6. 40.92 4.64 06.0 6.29 6.0-0.00 Supplementary Information Conformational Analysis, Experimental and GIA-DFT C NMR Chemical Shift Calculation on 2 -Hydroxy-,4,-trimethoxy-chalcone

Διαβάστε περισσότερα

Triclinic, P1 a = (2) Å b = (3) Å c = (4) Å = (1) = (1) = (1) Data collection.

Triclinic, P1 a = (2) Å b = (3) Å c = (4) Å = (1) = (1) = (1) Data collection. organic compounds Acta Crystallographica Section E Structure Reports Online ISSN 1600-5368 Benzyl N 0 -(4,6-dimethoxy-2-methyl-3- phenyl-1h-indol-7-ylmethylene)- hydrazinecarbodithioate Hamid Khaldei,

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

Supporting Information

Supporting Information Supporting Information Wiley-VCH 27 69451 Weinheim, Germany Supplementary Figure 1. Synthetic results as detected by XRD (Cu-Kα). Simulation pattern of MCM-68 Relative Intensity / a.u. YNU-2P Conventional

Διαβάστε περισσότερα

Supporting Information

Supporting Information Supporting Information for Pyrene nucleobase conjugates: synthesis, oligonucleotide binding and confocal bioimaging studies Artur Jabłoński 1, Yannic Fritz 2, Hans-Achim Wagenknecht 2, Rafał Czerwieniec

Διαβάστε περισσότερα

1. Πόσοι αριθμοί μικρότεροι του διαιρούνται με όλους τους μονοψήφιους αριθμούς;

1. Πόσοι αριθμοί μικρότεροι του διαιρούνται με όλους τους μονοψήφιους αριθμούς; ΚΥΠΡΙΚΗ ΜΘΗΜΤΙΚΗ ΤΙΡΙ ΠΡΧΙΚΟΣ ΙΩΝΙΣΜΟΣ 7//2009 ΩΡ 0:00-2:00 ΟΗΙΣ. Να λύσετε όλα τα θέματα. Κάθε θέμα βαθμολογείται με 0 μονάδες. 2. Να γράφετε με μπλε ή μαύρο μελάνι (επιτρέπεται η χρήση μολυβιού για τα

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

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

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

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

Διαβάστε περισσότερα

Section 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

Nuclear Physics 5. Name: Date: 8 (1)

Nuclear Physics 5. Name: Date: 8 (1) Name: Date: Nuclear Physics 5. A sample of radioactive carbon-4 decays into a stable isotope of nitrogen. As the carbon-4 decays, the rate at which the amount of nitrogen is produced A. decreases linearly

Διαβάστε περισσότερα

Solutions to Exercise Sheet 5

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

Διαβάστε περισσότερα

Experimental. Crystal data. C 23 H 27 ClN 2 O M r = Triclinic, P1 a = (3) Å b = (6) Å c = (7) Å = (4) = 80.

Experimental. Crystal data. C 23 H 27 ClN 2 O M r = Triclinic, P1 a = (3) Å b = (6) Å c = (7) Å = (4) = 80. organic compounds Acta Crystallographica Section E Structure Reports Online ISSN 1600-5368 8-{(E)-[(4-Chlorophenyl)imino]methyl}- 1,1,7,7-tetramethyl-1,2,3,5,6,7-hexahydropyrido[3,2,1-ij]quinolin-9-ol

Διαβάστε περισσότερα

( y) Partial Differential Equations

( y) Partial Differential Equations Partial Dierential Equations Linear P.D.Es. contains no owers roducts o the deendent variables / an o its derivatives can occasionall be solved. Consider eamle ( ) a (sometimes written as a ) we can integrate

Διαβάστε περισσότερα

Σχέσεις, Ιδιότητες, Κλειστότητες

Σχέσεις, Ιδιότητες, Κλειστότητες Σχέσεις, Ιδιότητες, Κλειστότητες Ορέστης Τελέλης telelis@unipi.gr Τµήµα Ψηφιακών Συστηµάτων, Πανεπιστήµιο Πειραιώς Ο. Τελέλης Πανεπιστήµιο Πειραιώς Σχέσεις 1 / 26 Εισαγωγή & Ορισµοί ιµελής Σχέση R από

Διαβάστε περισσότερα

Supplementary Information for

Supplementary Information for Supplentary Information for Aggregation induced blue-shifted ission molecular picture from QM/MM study Qunyan Wu, a Tian Zhang, a Qian Peng,* b Dong Wang, a and Zhigang Shuai* a a Key Loratory of Organic

Διαβάστε περισσότερα

Electronic Supplementary Information

Electronic Supplementary Information Electronic Supplementary Information The preferred all-gauche conformations in 3-fluoro-1,2-propanediol Laize A. F. Andrade, a Josué M. Silla, a Claudimar J. Duarte, b Roberto Rittner, b Matheus P. Freitas*,a

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΑ & ΕΠΙΣΤΗΜΗ ΤΩΝ ΥΛΙΚΩΝ

ΤΕΧΝΟΛΟΓΙΑ & ΕΠΙΣΤΗΜΗ ΤΩΝ ΥΛΙΚΩΝ Τμήμα Τεχνολόγων Περιβάλλοντος Κατεύθυνσης Συντήρησης Πολιτισμικής Κληρονομιάς ΤΕΧΝΟΛΟΓΙΑ & ΕΠΙΣΤΗΜΗ ΤΩΝ ΥΛΙΚΩΝ 6 η Ενότητα ΣΤΕΡΕΑ ΚΑΤΑΣΤΑΣΗ Δημήτριος Λαμπάκης Τύποι Στερεών Βασική Ερώτηση: Πως τα άτομα

Διαβάστε περισσότερα

Calculating the propagation delay of coaxial cable

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

Διαβάστε περισσότερα