DIMENSIONS FOR HOT ROLLED STEEL BEAM, COLUMN, CHANNEL AND ANGLE SECTIONS
|
|
|
- Μέγαιρα Κοσμόπουλος
- 7 χρόνια πριν
- Προβολές:
Transcript
1 Indian Standard (Reaffirmed 1999) Edition 4.1 ( ) DIENSIONS FOR HOT ROLLED STEEL BEA, COLUN, CHANNEL AND ANGLE SECTIONS ( Third Revision ) (Incorporating Amendment No. 1) UDC : 00.7 BIS 2002 B U R E A U O F I N D I A N S T A N D A R D S ANAK BHAVAN, 9 BAHADUR SHAH ZAFAR ARG NEW DELHI Price Group 7
2 Structural Sections Committee, SDC FOREWORD This Indian Standard (Third Revision) was adopted by the Bureau of Indian Standards on April 199, after the draft finalized by the Structural Sections Committee had been approved by the Structural and etals Division Council. Under the steel economy programme, a rational, efficient and economical series of Indian Standards on beam sections, channel sections and angle sections was evolved in 197 and IS 0 : 197 was published covering junior, light weight, medium weight, wide flange and heavy weight beam sections; junior, light weight and medium weight channel sections and equal and unequal leg angle sections. This standard was revised in 194. In the second revision of this standard, parts relating to medium weight beam sections B series, column sections SC series, channel sections C and CP series and equal and unequal leg angles were revised and published as Parts 1, 2, 3, and of IS 0, respectively. Sections not covered in these parts, however continued in IS 0 : 194. In the present revision, the Committee felt it convenient to merge all the five parts into one standard. The sections which were retained in IS 0 : 194 subsequent to its second revision in five parts are included in this standard with a view that these sections although not being rolled in the country at present may in future be rolled owing to their efficiency and resultant economy in the use of steel. However, the designers are advised to check from JPC/producers regarding availability of such sections. Following additional modifications have been affected in this revision: a) edium weight beam sections B 100 having the flange width and web thickness of 70 mm and 4. mm, respectively, has been modified to 0 mm flange width and 4.7 mm web thickness; b) Two sections, namely, BFB 10 and RSJ 200 which are mainly used in railway electrification have been included as SC 10 and WB 200, respectively; c) Additional equal leg angles 0 0 4, (in place of ), and have been included in the supplimentary list; d) Amendments issued so far to the various parts of the standard and to IS 0 : 194 have been incorporated; and e) ass, area and other sectional properties have been expressed in three significant places. This edition 4.1 incorporates Amendment No. 1 (July 1992). Side bar indicates modification of the text as the result of incorporation of the amendment.
3 Indian Standard DIENSIONS FOR HOT ROLLED STEEL BEA, COLUN, CHANNEL AND ANGLE SECTIONS ( Third Revision ) 1 SCOPE This standard covers the nominal dimensions, mass and sectional properties of hot rolled sloping flange beam and column sections, sloping and parallel flange channel sections and equal and unequal leg angle sections. 2 REFERENCES The Indian Standard IS 12 : 19 Rolled and cutting tolerances for hot rolled steel products ( fourth revision ) is a necessary adjunct to this standard. SECTION 1 GENERAL 3 TERINOLOGY 3.1 Y-Y Axis A line parallel to the axis of the web of the section (in the case of beams and channels) or parallel to the axis of the longer flange (in the case of unequal angles) or either flange (in the case of equal angles) and passing through the centre of gravity of the profile of the section. 3.2 X-X Axis A line passing through the centre of gravity of the profile of the section, and at right angles to the Y-Y axis. 3.3 U-U and V-V Axes Lines passing through the centre of gravity of the profile of the section, representing the principal axes of angle sections. 4 SYBOLS 4.1 Letter symbols used in this standard have been indicated appropriately in Sections 2 to. ore explicit definitions for certain symbols, used in the figures and tables of Sections 2 to are given in and Symbols for A, B = the longer and the shorter leg length of angle section, respectively; B D R 1 R 2 t T = flange width of beam, column or channel sections; = depth of beam, column or channel section; = radius at fillet or root; = radius at toe; = thickness of web of beam, column or channel section; thickness of leg of angle section; and = thickness of flange of beam, column or channel section Symbols for a = sectional area, C ( with subscripts x, y, u or v ) = distance of centre of gravity, C x = A e x, C y = B e y, e x = distance of extreme fibre from X-X axis, e y = distance of extreme fibre from Y-Y axis, I x = moment of inertia about X-X axis, I y = moment of inertia about Y-Y axis, I u = moment of inertia ( ax ) about U-U axis, I v = moment of inertia ( in ) about V-V axis, = mass of the section per metre length, I x Z x = ---- = e x I y e y Z y = ---- = I x modulus of section about X-X axis, modulus of section about Y-Y axis, radius of gyration about X-X r x = ---- = a axis, 1
4 radius of gyration about Y-Y r y = ---- = a axis, I radius of gyration about U-U r u = ---- u = a axis, radius of gyration about V-V r v = ---- = a axis, α I y I v = angle between U-U and X-X axes of angle section; slope of flange in the case of beam, column or channel. CLASSIFICATION.1 Beam, column, channel and angle sections are classified as follows:.1.1 Beams a) Indian Standard junior beams (ISJB) b) Indian Standard light weight beams (ISLB) c) Indian Standard medium weight beams (ISB) d) Indian Standard wide flange beams (ISWB).1.2 Columns/Heavy Weight Beams a) Indian Standard column sections (ISSC) b) Indian Standard heavy weight beam (ISHB).1.3 Channels a) Indian Standard junior channels (ISJC) b) Indian Standard light weight channels (ISLC) c) Indian Standard medium weight channels (ISC) d) Indian Standard medium weight parallel flange channels (ISCP). Angles a) Indian Standard equal leg angles (ISA) b) Indian Standard unequal leg angles (ISA).2 The following abbreviated reference symbols have been used in designating the Indian Standard sections mentioned in.1: Section Beams Columns/heavy beams Channels Classification Abbreviated Reference Symbol ISJB ISLB ISB ISWB ISSC ISHB ISJC ISLC ISC ISCP JB LB B WB SC HB JC LC C CP Angles ISA DESIGNATION.1 Beam, columns and channel sections shall be designated by the respective abbreviated reference symbols followed by the depth of the section, for example: a) B 200 for a medium weight beam of depth 200 mm, b) SC 200 for a column section of depth 200 mm, c) C 200 for medium weight channel of depth 200 mm, and d) CP 200 for a medium weight parallel flange channel of depth 200 mm..2 Equal and unequal leg angles shall be designated by the abbreviated reference symbols () followed by the dimensions A, B and t. For example, represents unequal leg angle of dimensions 200 mm, 100 mm and thickness 10 mm. 7 DIENSIONS, ASS AND TOLERANCES 7.1 Nominal dimensions and mass of beam, column, channel and equal and unequal angles shall conform to the values given in Sections 2, 3, 4, and, respectively of the standard. 7.2 Dimensional and mass tolerances of the various sections shall conform to the appropriate values stipulated in IS 12 : 19. SECTIONAL PROPERTIES properties of the beams, columns, channel and equal and unequal leg angles are given in Sections 2 to for information. 2
5 Table 2.1 SECTION 2 BEA SECTIONS Nominal, ass and of Indian Standard edium Flange Beams 3 ass D B t T Flange R 1 R 2 I x I y r x r y Z x Z y Slope, ax kg/m cm 2 mm mm mm mm α, deg mm mm cm 4 cm 4 cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) B B B B B B B B
6 ass Table 2.1 ( Concluded ) D B t T Flange R 1 R 2 I x I y r x r y Z x Z y Slope, ax kg/m cm 2 mm mm mm mm α, deg mm mm cm 4 cm 4 cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) B B B B B B A
7 Table 2.2 Nominal, ass and of Indian Standard Junior and Light Weight Beams (Figure same as given in Table 2.1) 4 ass D B t T Flange R 1 R 2 I x I y r x r y Z x Z y Slope, ax kg/m cm 2 mm mm mm mm α, deg mm mm cm 4 cm 4 cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) Junior Beams JB JB JB JB Light Weight Beams LB LB LB(P) LB LB LB LB(P) LB LB(P) LB LB LB LB LB(P) LB LB LB LB LB LB LB NOTE (P) Stands for provisional section.
8 ass Table 2.2 ( Concluded ) D B t T Flange R 1 R 2 I x I y r x r y Z x Z y Slope, ax kg/m cm 2 mm mm mm mm α, deg mm mm cm 4 cm 4 cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) 4A Wide Flange Beams WB WB WB WB 200* WB WB WB WB WB WB WB WB WB WB WB 200* (RSJ Section) is mainly used for railway electrification.
9 Table 3.1 SECTION 3 COLUN/HEAVY WEIGHT BEA SECTIONS Nominal, ass and of Indian Standard Columns and Heavy Weight Beams ass D B t T Flange R 1 R 2 I x I y r x r y Z x Z y Slope, α kg/m cm 2 mm mm mm mm deg mm mm cm 4 cm 4 cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) Column Sections SC SC SC SC 10* SC SC SC SC SC SC 10* (BFB Section) is mainly used for railway electrification.
10 A ass Table 3.1 ( Concluded ) D B t T Flange R 1 R 2 I x I y r x r y Z x Z y Slope, α kg/m cm 2 mm mm mm mm deg mm mm cm 4 cm 4 cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) Heavy Weight Beams/Columns HB HB 10* HB 10* HB HB 200* HB HB 22* HB HB 20* HB HB 300* HB HB 30* HB HB 400* HB HB40* NOTE HB sections are also used as column sections. *These heavier sections in each size are obtained from the same set of rolls as the lighter sections by spreading of the rolls. The width of flanges of these sections gets increased by an amount equal to the difference between the thicknesses of the webs. Therefore, while ordering these heavier sections, mass should be mentioned.
11 Table 4.1 SECTION 4 CHANNEL SECTIONS, ass and of Sloping Flange Channels ass D B t T Flange R 1 R 2 C y I x I y r x r y Z x Z y Slope, α kg/m cm 2 mm mm mm mm deg mm mm mm cm 4 cm 4 cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) edium Weight Channels C C C C 12* C C 10* C C 17* *The heavier sections in each size intended for use in wagon industry are to be obtained from same set of rolls as the corresponding lightest section in that size group, by raising the rolls.
12 A ass Table 4.1 ( Concluded ) D B t T Flange R 1 R 2 C y I x I y r x r y Z x Z y Slope, α kg/m cm 2 mm mm mm mm deg mm mm mm cm 4 cm 4 cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) C C 200* C C 22* C C 20* C 20* C C 300* C 300* C C *The heavier sections in each size intended for use in wagon industry are to be obtained from same set of rolls as the corresponding lightest section in that size group, by raising the rolls. Junior Channels JC JC JC JC JC Light Weight Channels LC LC LC LC (P) LC LC (P) LC LC LC (P) LC LC LC LC (P) LC LC NOTE (P) stands for provisional section.
13 Table 4.2, ass and of Parallel Flange Channels 7 ass D B t T R 1 R 2 C y I x I y r x r y Z x Z y kg/m cm 2 mm mm mm mm mm mm mm cm 4 cm 4 cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) CP CP CP CP 12* CP CP 10* *The heavier sections in each size intended for use in wagon industry are to be obtained from the same set of rolls as the corresponding lightest section in that size group, by raising the rolls.
14 7A ass Table 4.2 ( Concluded ) D B t T R 1 R 2 C y I x I y r x r y Z x Z y kg/m cm 2 mm mm mm mm mm mm mm cm 4 cm 4 cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) CP CP 17* CP CP 200* CP CP 22* CP CP 20* CP 20* CP CP 300* CP 300* CP CP *The heavier sections in each size intended for use in wagon industry are to be obtained from the same set of rolls as the corresponding lightest section in that size group, by raising the rolls.
15 Table.1 SECTION EQUAL LEG ANGLES Nominal, ass and of Indian Standard Equal Leg Angles ass area, a AB t R 1 R 2 C x C y I x I y I u ( ax ) I v ( in ) r x r y r u ( ax ) r v ( in ) Z x Z y Kg/m Cm 2 mmmm mm mm mm cm cm cm 4 cm 4 cm 4 cm 4 cm cm cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) (1) (19) Should be resonably square
16 A ass area, a Table.1 ( Continued ) AB t R 1 R 2 C x C y I x I y I u ( ax ) I v ( in ) r x r y r u ( ax ) r v ( in ) Z x Z y Kg/m Cm 2 mmmm mm mm mm cm cm cm 4 cm 4 cm 4 cm 4 cm cm cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) (1) (19) Should be resonably square
17 Table.1 ( Concluded ) 9 ass area, a AB t R 1 R 2 C x C y I x I y I u ( ax ) I v ( in ) r x r y r u ( ax ) r v ( in ) Z x Z y Kg/m Cm 2 mmmm mm mm mm cm cm cm 4 cm 4 cm 4 cm 4 cm cm cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) (1) (19)
18 10 Table.2 Supplementary List of Indian Standard Equal Leg Angles Nominal, ass and ass AB t R 1 R 2 C x C y I x I y I u I v r x r y r u r v Z x Z y ( ax ) ( in ) ( ax ) ( in ) Kg/m Cm 2 mmmm mm mm mm cm cm cm 4 cm 4 cm 4 cm 4 cm cm cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) (1) (19) Should be reasonably Square
19 Table.1 SECTION UNEQUAL LEG ANGLES Nominal, ass and of Indian Standard Unequal Leg Angles 11 ass area, a AB t R 1 R 2 C x C y Tan α I x I y I u I v r x r y r u r v Z x Z y ( ax ) ( in ) ( ax ) ( in ) Kg/m cm 2 mmmm mm mm mm cm cm cm 4 cm 4 cm 4 cm 4 cm cm cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) (1) (19) (20) Should be reasonably square
20 11A ass area, a Table.1 ( Continued ) AB t R 1 R 2 C x C y Tan α I x I y I u I v r x r y r u r v Z x Z y ( ax ) ( in ) ( ax ) ( in ) Kg/m cm 2 mmmm mm mm mm cm cm cm 4 cm 4 cm 4 cm 4 cm cm cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) (1) (19) (20) Should be reasonably square
21 Table.1 ( Concluded ) ass area, a AB t R 1 R 2 C x C y Tan α I x I y I u I v r x r y r u r v Z x Z y ( ax ) ( in ) ( ax ) ( in ) Kg/m cm 2 mmmm mm mm mm cm cm cm 4 cm 4 cm 4 cm 4 cm cm cm cm cm 3 cm (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) (1) (19) (20)
22 13 Table.2 Supplementary List of Indian Standard Unequal Leg Angles Nominal, ass and ass AB t R 1 R 2 C x C y Tan α I x I y I u I v r x r y r u r v Z x Z y ( ax ) ( in ) ( ax ) ( in ) Kg/m cm 2 mmmm mm mm mm cm cm cm 4 cm 4 cm 4 cm 4 cm cm cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) (1) (19) (20) Should be reasonably square
23 ass Table.2 ( Concluded ) AB t R 1 R 2 C x C y Tan α I x I y I u I v r x r y r u r v Z x Z y ( ax ) ( in ) ( ax ) ( in ) Kg/m cm 2 mmmm mm mm mm cm cm cm 4 cm 4 cm 4 cm 4 cm cm cm cm cm 3 cm 3 (1) (2) (3) (4) () () (7) () (9) (10) (11) (12) (13) (14) (1) (1) (17) (1) (19) (20) A
24 Bureau of Indian Standards BIS is a statutory institution established under the Bureau of Indian Standards Act, 19 to promote harmonious development of the activities of standardization, marking and quality certification of goods and attending to connected matters in the country. Copyright BIS has the copyright of all its publications. No part of these publications may be reproduced in any form without the prior permission in writing of BIS. This does not preclude the free use, in the course of implementing the standard, of necessary details, such as symbols and sizes, type or grade designations. Enquiries relating to copyright be addressed to the Director (Publications), BIS. Review of Indian Standards Amendments are issued to standards as the need arises on the basis of comments. Standards are also reviewed periodically; a standard along with amendments is reaffirmed when such review indicates that no changes are needed; if the review indicates that changes are needed, it is taken up for revision. Users of Indian Standards should ascertain that they are in possession of the latest amendments or edition by referring to the latest issue of BIS Catalogue and Standards : onthly Additions. This Indian Standard has been developed from Doc : No. SDC ( 31 ) and amended by CED Amendments Issued Since Publication Amend No. Date of Issue Amd. No. 1 July 1992 Headquarters: BUREAU OF INDIAN STANDARDS anak Bhavan, 9 Bahadur Shah Zafar arg, New Delhi Telephones: , , Regional Offices: Central Eastern : anak Bhavan, 9 Bahadur Shah Zafar arg NEW DELHI : 1/14 C. I. T. Scheme VII, V. I. P. Road, Kankurgachi KOLKATA Telegrams: anaksanstha (Common to all offices) Telephone , , Northern : SCO 33-33, Sector 34-A, CHANDIGARH Southern : C. I. T. Campus, IV Cross Road, CHENNAI , , Western : anakalaya, E9 IDC, arol, Andheri (East) UBAI , , Branches : AHEDABAD. BANGALORE. BHOPAL. BHUBANESHWAR. COIBATORE. FARIDABAD. GHAZIABAD. GUWAHATI. HYDERABAD. JAIPUR. KANPUR. LUCKNOW. NAGPUR. NALAGARH. PATNA. PUNE. RAJKOT. THIRUVANANTHAPURA. VISHAKHAPATNA.
Cross sectional area, square inches or square millimeters
Symbols A E Cross sectional area, square inches or square millimeters of Elasticity, 29,000 kips per square inch or 200 000 Newtons per square millimeter (N/mm 2 ) I Moment of inertia (X & Y axis), inches
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.
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) =
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)
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
Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------
Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin
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
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,
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
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.
Math 6 SL Probability Distributions Practice Test Mark Scheme
Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry
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
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
«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ»
I ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΗ ΝΟΜΙΚΩΝ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΠΟΛΙΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ «ΔΙΟΙΚΗΣΗ ΚΑΙ ΟΙΚΟΝΟΜΙΑ» ΚΑΤΕΥΘΥΝΣΗ: ΟΙΚΟΝΟΜΙΚΗ
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
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
Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author.
Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author. 2012, Γεράσιμος Χρ. Σιάσος / Gerasimos Siasos, All rights reserved. Στοιχεία επικοινωνίας συγγραφέα / Author
ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ
ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΝΟΜΙΚΟ ΚΑΙ ΘΕΣΜΙΚΟ ΦΟΡΟΛΟΓΙΚΟ ΠΛΑΙΣΙΟ ΚΤΗΣΗΣ ΚΑΙ ΕΚΜΕΤΑΛΛΕΥΣΗΣ ΠΛΟΙΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που υποβλήθηκε στο
Second Order Partial Differential Equations
Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y
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
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
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
Review Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. 1) sin - 11π 1 1) + - + - - ) sin 11π 1 ) ( -
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
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
Technical Data for Profiles. α ( C) = 250 N/mm 2 (36,000 lb./in. 2 ) = 200 N/mm 2 (29,000 lb./in 2 ) A 5 = 10% A 10 = 8%
91 500 201 0/11 Aluminum raming Linear Motion and Assembly Technologies 1 Section : Engineering Data and Speciications Technical Data or Proiles Metric U.S. Equivalent Material designation according to
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
ΕΘΝΙΚΗ ΣΧΟΛΗ ΔΗΜΟΣΙΑΣ ΔΙΟΙΚΗΣΗΣ ΙΓ' ΕΚΠΑΙΔΕΥΤΙΚΗ ΣΕΙΡΑ
ΕΘΝΙΚΗ ΣΧΟΛΗ ΔΗΜΟΣΙΑΣ ΔΙΟΙΚΗΣΗΣ ΙΓ' ΕΚΠΑΙΔΕΥΤΙΚΗ ΣΕΙΡΑ ΤΜΗΜΑ ΤΟΠΙΚΗΣ ΑΥΤΟΔΙΟΙΚΗΣΗΣ ΚΑΙ ΠΕΡΙΦΕΡΕΙΑΚΗΣ ΑΝΑΠΤΥΞΗΣ ΤΕΛΙΚΗ ΕΡΓΑΣΙΑ: ΠΕΡΙΒΑΛΛΟΝ ΚΑΙ ΑΝΑΠΤΥΞΗ: ΠΡΟΣΕΓΓΙΣΗ ΜΕΣΩ ΔΕΙΚΤΩΝ Επιβλέπων: Αθ.Δελαπάσχος
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
Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων. Εξάμηνο 7 ο
Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων Εξάμηνο 7 ο Procedures and Functions Stored procedures and functions are named blocks of code that enable you to group and organize a series of SQL and PL/SQL
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
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 :
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
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
ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ
ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΘΕΜΑ :ΤΥΠΟΙ ΑΕΡΟΣΥΜΠΙΕΣΤΩΝ ΚΑΙ ΤΡΟΠΟΙ ΛΕΙΤΟΥΡΓΙΑΣ ΣΠΟΥ ΑΣΤΡΙΑ: ΕΥΘΥΜΙΑ ΟΥ ΣΩΣΑΝΝΑ ΕΠΙΒΛΕΠΩΝ ΚΑΘΗΓΗΤΗΣ : ΓΟΥΛΟΠΟΥΛΟΣ ΑΘΑΝΑΣΙΟΣ 1 ΑΚΑ
Trigonometry 1.TRIGONOMETRIC RATIOS
Trigonometry.TRIGONOMETRIC RATIOS. If a ray OP makes an angle with the positive direction of X-axis then y x i) Sin ii) cos r r iii) tan x y (x 0) iv) cot y x (y 0) y P v) sec x r (x 0) vi) cosec y r (y
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
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
Volume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is
Volume of a Cuboid The formula for the volume of a cuboid is Volume = length x breadth x height V = l x b x h Example Work out the volume of this cuboid 10 cm 15 cm V = l x b x h V = 15 x 6 x 10 V = 900cm³
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,
Capacitors - Capacitance, Charge and Potential Difference
Capacitors - Capacitance, Charge and Potential Difference Capacitors store electric charge. This ability to store electric charge is known as capacitance. A simple capacitor consists of 2 parallel metal
2. THEORY OF EQUATIONS. PREVIOUS EAMCET Bits.
EAMCET-. THEORY OF EQUATIONS PREVIOUS EAMCET Bits. Each of the roots of the equation x 6x + 6x 5= are increased by k so that the new transformed equation does not contain term. Then k =... - 4. - Sol.
ΠΡΕΣΒΕΙΑ ΤΗΣ ΕΛΛΑΔΟΣ ΓΡΑΦΕΙΟ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΕΜΠΟΡΙΚΩΝ ΥΠΟΘΕΣΕΩΝ ΑΔΙΑΒΑΘΜΗΤΟ ΚΑΝΟΝΙΚΟ
ΠΡΕΣΒΕΙΑ ΤΗΣ ΕΛΛΑΔΟΣ ΓΡΑΦΕΙΟ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΕΜΠΟΡΙΚΩΝ ΥΠΟΘΕΣΕΩΝ 18, Aisha El Taymoureya, Garden City, Cairo - Egypt Tel.: +202 27952036-27948482, Fax: +202 27940684 E-mail: ecocom-cairo@mfa.gr www.agora.mfa.gr/eg50
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
Matrices and Determinants
Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z
Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1
Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test
Πνεσμαηικά Γικαιώμαηα 2006 Ίδρσμα ECDL (ECDL Foundation - www.ecdl.org)
Έθδνζε 1.5 PEOPLECERT Hellas A.E - Φορέας Πιζηοποίηζης Ανθρώπινοσ Γσναμικού Κνξαή 3, 105 64 Αζήλα, Τει.: 210 372 9100, Fax: 210 372 9101, e-mail: info@peoplecert.org, www.peoplecert.org Πνεσμαηικά Γικαιώμαηα
Chapter 7 Transformations of Stress and Strain
Chapter 7 Transformations of Stress and Strain INTRODUCTION Transformation of Plane Stress Mohr s Circle for Plane Stress Application of Mohr s Circle to 3D Analsis 90 60 60 0 0 50 90 Introduction 7-1
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
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
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
Πτυχιακή Εργασία. Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους
ΑΛΕΞΑΝΔΡΕΙΟ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΣΧΟΛΗ ΤΕΧΝΟΛΟΓΙΑΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΜΗΜΑ ΔΙΑΤΡΟΦΗΣ ΚΑΙ ΔΙΑΙΤΟΛΟΓΙΑΣ Πτυχιακή Εργασία Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους Εκπόνηση:
ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ
ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ Γηπισκαηηθή Δξγαζία ηνπ Φνηηεηή ηνπ ηκήκαηνο Ζιεθηξνιόγσλ Μεραληθώλ θαη Σερλνινγίαο Ζιεθηξνληθώλ
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
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
ΕΦΗΜΕΡΙΣ ΤΗΣ ΚΥΒΕΡΝΗΣΕΩΣ
34769 ΕΦΗΜΕΡΙΣ ΤΗΣ ΚΥΒΕΡΝΗΣΕΩΣ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΔΗΜΟΚΡΑΤΙΑΣ ΤΕΥΧΟΣ ΔΕΥΤΕΡΟ Αρ. Φύλλου 2876 29 Δεκεμβρίου 2015 ΠΕΡΙΕΧΟΜΕΝΑ ΑΠΟΦΑΣΕΙΣ Καθορισμός των μειζόνων κατηγοριών δαπανών του Κρατικού Προϋπολογισμού Διαδικασία
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
SCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions
SCHOOL OF MATHEMATICAL SCIENCES GLMA Linear Mathematics 00- Examination Solutions. (a) i. ( + 5i)( i) = (6 + 5) + (5 )i = + i. Real part is, imaginary part is. (b) ii. + 5i i ( + 5i)( + i) = ( i)( + i)
[1] P Q. Fig. 3.1
![[1] P Q. Fig. 3.1](/thumbs/79/80362156.jpg "[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
Assalamu `alaikum wr. wb.
LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump
ΣΧΕΔΙΑΣΜΟΣ ΚΑΙ ΕΝΙΣΧΥΣΗ ΤΩΝ ΚΟΜΒΩΝ ΟΠΛΙΣΜΕΝΟΥ ΣΚΥΡΟΔΕΜΑΤΟΣ ΜΕ ΒΑΣΗ ΤΟΥΣ ΕΥΡΩΚΩΔΙΚΕΣ
Σχολή Μηχανικής και Τεχνολογίας Πτυχιακή εργασία ΣΧΕΔΙΑΣΜΟΣ ΚΑΙ ΕΝΙΣΧΥΣΗ ΤΩΝ ΚΟΜΒΩΝ ΟΠΛΙΣΜΕΝΟΥ ΣΚΥΡΟΔΕΜΑΤΟΣ ΜΕ ΒΑΣΗ ΤΟΥΣ ΕΥΡΩΚΩΔΙΚΕΣ Σωτήρης Παύλου Λεμεσός, Μάιος 2018 i ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ
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
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
Modern Greek Extension
Centre Number 2017 HIGHER SCHOOL CERTIFICATE EXAMINATION Student Number Modern Greek Extension Written Examination General Instructions Reading time 10 minutes Working time 1 hour and 50 minutes Write
CRASH COURSE IN PRECALCULUS
CRASH COURSE IN PRECALCULUS Shiah-Sen Wang The graphs are prepared by Chien-Lun Lai Based on : Precalculus: Mathematics for Calculus by J. Stuwart, L. Redin & S. Watson, 6th edition, 01, Brooks/Cole Chapter
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
Notes on the Open Economy
Notes on the Open Econom Ben J. Heijdra Universit of Groningen April 24 Introduction In this note we stud the two-countr model of Table.4 in more detail. restated here for convenience. The model is Table.4.
«Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων. Η μεταξύ τους σχέση και εξέλιξη.»
ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΑΓΡΟΝΟΜΩΝ ΚΑΙ ΤΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΓΕΩΓΡΑΦΙΑΣ ΚΑΙ ΠΕΡΙΦΕΡΕΙΑΚΟΥ ΣΧΕΔΙΑΣΜΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ: «Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων.
Correction Table for an Alcoholometer Calibrated at 20 o C
An alcoholometer is a device that measures the concentration of ethanol in a water-ethanol mixture (often in units of %abv percent alcohol by volume). The depth to which an alcoholometer sinks in a water-ethanol
HSS Hollow. Structural Sections LRFD COLUMN LOAD TABLES HSS: TECHNICAL BROCHURE
HSS Hollow Structural Sections LRFD COLUMN LOAD TABLES HSS: TECHNICAL BROCHURE Steel Tube Institute Waukegan Road, Suite Glenview, IL TEL:.1.1 FA:..1 HSS Manufacturing Methods The transformation of steel
Aluminum Electrolytic Capacitors
Aluminum Electrolytic Capacitors Snap-In, Mini., 105 C, High Ripple APS TS-NH ECE-S (G) Series: TS-NH Features Long life: 105 C 2,000 hours; high ripple current handling ability Wide CV value range (47
Trigonometric Formula Sheet
Trigonometric Formula Sheet Definition of the Trig Functions Right Triangle Definition Assume that: 0 < θ < or 0 < θ < 90 Unit Circle Definition Assume θ can be any angle. y x, y hypotenuse opposite θ
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
Aluminum Electrolytic Capacitors (Large Can Type)
Aluminum Electrolytic Capacitors (Large Can Type) Snap-In, 85 C TS-U ECE-S (U) Series: TS-U Features General purpose Wide CV value range (33 ~ 47,000 µf/16 4V) Various case sizes Top vent construction
Μελέτη των μεταβολών των χρήσεων γης στο Ζαγόρι Ιωαννίνων 0
Μελέτη των μεταβολών των χρήσεων γης στο Ζαγόρι Ιωαννίνων 0 ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΔΙΕΠΙΣΤΗΜΟΝΙΚΟ - ΔΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ (Δ.Π.Μ.Σ.) "ΠΕΡΙΒΑΛΛΟΝ ΚΑΙ ΑΝΑΠΤΥΞΗ" 2 η ΚΑΤΕΥΘΥΝΣΗ
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙ ΕΥΤΙΚΟ Ι ΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙ ΕΥΤΙΚΟ Ι ΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Το franchising ( δικαιόχρηση ) ως µέθοδος ανάπτυξης των επιχειρήσεων λιανικού εµπορίου
2007 Classical Greek. Intermediate 2 Translation. Finalised Marking Instructions
2007 Classical Greek Intermediate 2 Translation Finalised Marking Instructions Scottish Qualifications Authority 2007 The information in this publication may be reproduced to support SQA qualifications
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΛΟΓΙΣΤΙΚΗ ΚΑΙ ΦΟΡΟΛΟΓΙΑ Ο.Ε. ΕΙΣΗΓΗΤΡΙΑ ΚΑΘΗΓΗΤΡΙΑ: κ. ΟΥΡΑΝΟΥ ΕΡΜΙΟΝΗ ΣΠΟΥΔΑΣΤΡΙΕΣ: ΔΕΜΕΤΖΟΥ ΑΓΛΑΪΑ
Προς όλα τα μέλη του Συνδέσμου Τεχνική Εγκύκλιος Αρ. 36
Προς όλα τα μέλη του Συνδέσμου Τεχνική Εγκύκλιος Αρ. 36 23 Μαΐου 2008 Θέμα: Αναθεωρημένο υπόδειγμα ψηφίσματος προς κατάθεση στον Έφορο Εταιρειών για τη μετατροπή μετοχικού κεφαλαίου σε Ευρώ την 1 Ιανουαρίου
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
Congruence Classes of Invertible Matrices of Order 3 over F 2
International Journal of Algebra, Vol. 8, 24, no. 5, 239-246 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.2988/ija.24.422 Congruence Classes of Invertible Matrices of Order 3 over F 2 Ligong An and
ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 11/3/2006
ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 11/3/26 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα μικρότεροι το 1 εκτός αν ορίζεται διαφορετικά στη διατύπωση
PARTIAL NOTES for 6.1 Trigonometric Identities
PARTIAL NOTES for 6.1 Trigonometric Identities tanθ = sinθ cosθ cotθ = cosθ sinθ BASIC IDENTITIES cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ PYTHAGOREAN IDENTITIES sin θ + cos θ =1 tan θ +1= sec θ 1 + cot
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
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
Technical Information T-9100 SI. Suva. refrigerants. Thermodynamic Properties of. Suva Refrigerant [R-410A (50/50)]
![Technical Information T-9100 SI. Suva. refrigerants. Thermodynamic Properties of. Suva Refrigerant [R-410A (50/50)]](/thumbs/89/98928029.jpg "Technical Information T-9100 SI. Suva. refrigerants. Thermodynamic Properties of. Suva Refrigerant [R-410A (50/50)]")
d Suva refrigerants Technical Information T-9100SI Thermodynamic Properties of Suva 9100 Refrigerant [R-410A (50/50)] Thermodynamic Properties of Suva 9100 Refrigerant SI Units New tables of the thermodynamic
GAUGE BLOCKS. Grade 0 Tolerance for the variation in length. Limit deviation of length. ± 0.25μm. 0.14μm ±0.80μm. ± 1.90μm. ± 0.40μm. ± 1.
GAUGE BLOCKS Accuracy according to ISO650 Nominal length (mm) Limit deviation of length Grade 0 Tolerance for the variation in length Grade Grade Grade Grade 2 Limit deviations of Tolerance for the Limit
ST5224: Advanced Statistical Theory II
ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known
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
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
Lecture 26: Circular domains
Introductory lecture notes on Partial Differential Equations - c Anthony Peirce. Not to be copied, used, or revised without eplicit written permission from the copyright owner. 1 Lecture 6: Circular domains
GREECE BULGARIA 6 th JOINT MONITORING
GREECE BULGARIA 6 th JOINT MONITORING COMMITTEE BANSKO 26-5-2015 LEGISLATIVE FRAMEWORK Regulation 1083/2006 (general provisions for ERDF). Regulation 1080/2006 (ERDF) Regulation 1028/2006 (Implementing
Cambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Examinations Cambridge International General Certificate of Secondary Education *4358398658* GREEK 0543/04 Paper 4 Writing May/June 2015 1 hour Candidates answer on the Question
Appendix to On the stability of a compressible axisymmetric rotating flow in a pipe. By Z. Rusak & J. H. Lee
Appendi to On the stability of a compressible aisymmetric rotating flow in a pipe By Z. Rusak & J. H. Lee Journal of Fluid Mechanics, vol. 5 4, pp. 5 4 This material has not been copy-edited or typeset
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
k A = [k, k]( )[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +
[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +](/thumbs/73/69566903.jpg "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
Προσωπική Aνάπτυξη. Ενότητα 2: Διαπραγμάτευση. Juan Carlos Martínez Director of Projects Development Department
Προσωπική Aνάπτυξη Ενότητα 2: Διαπραγμάτευση Juan Carlos Martínez Director of Projects Development Department Unit Scope Σε αυτή την ενότητα θα μελετήσουμε τα βασικά των καταστάσεων διαπραγμάτευσης winwin,
Mock Exam 7. 1 Hong Kong Educational Publishing Company. Section A 1. Reference: HKDSE Math M Q2 (a) (1 + kx) n 1M + 1A = (1) =
Mock Eam 7 Mock Eam 7 Section A. Reference: HKDSE Math M 0 Q (a) ( + k) n nn ( )( k) + nk ( ) + + nn ( ) k + nk + + + A nk... () nn ( ) k... () From (), k...() n Substituting () into (), nn ( ) n 76n 76n
Written Examination. Antennas and Propagation (AA ) April 26, 2017.
Written Examination Antennas and Propagation (AA. 6-7) April 6, 7. Problem ( points) Let us consider a wire antenna as in Fig. characterized by a z-oriented linear filamentary current I(z) = I cos(kz)ẑ
1) Abstract (To be organized as: background, aim, workpackages, expected results) (300 words max) Το όριο λέξεων θα είναι ελαστικό.
UΓενικές Επισημάνσεις 1. Παρακάτω θα βρείτε απαντήσεις του Υπουργείου, σχετικά με τη συμπλήρωση της ηλεκτρονικής φόρμας. Διευκρινίζεται ότι στα περισσότερα θέματα οι απαντήσεις ήταν προφορικές (τηλεφωνικά),