THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume 15, Number 2/2014, pp
|
|
- Αἰκατερίνη Λύτρας
- 6 χρόνια πριν
- Προβολές:
Transcript
1 THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume 5, Number /0, pp. 07 DOUBLY STOCHASTIC MODELS WITH ASYMMETRIC GARCH ERRORS Muhmmd SHERAZ Uniersiy o Buchres, Fculy o Mhemics nd Compuer Science, Buchres, Romni E-mil: Muhmmd_sherz8@homil.com The mehods ddressing oliliy in compuionl innce nd economerics he been recenly repored in inncil lierure. Recenly Peiris e l. [8] he inroduced doubly sochsic oliliy models wih GARCH innoions. Rndom coeicien uoregressie sequences re specil cse o doubly sochsic ime series. In his pper, we consider doubly sochsic sionry ime series wih symmeric GARCH errors. Some generl properies o process, like rince nd kurosis re deried. Key words: GARCH processes, AGARCH-(I-(0,, doubly sochsic ime series, RCA(, RCA- MA(, Sign-RCA-MA(.. INTRODUCTION Recenly, here hs been growing deelopmen in he use o nonliner oliliy models in inncil lierure. Blck-Scholes opion pricing models hs some conrdicory ssumpions, such s consn oliliy nd normlly disribued log reurns. In mny inncil ime series, empiricl sudies reel some cs such s sock reurns nd oreign exchnge res h exhibi lepokurosis nd sochsic oliliy. Any disribuion cn be chrcerized by number o eures such s men, rince, skewness nd kurosis. The mesure o kurosis is considered s wheher he d re peked or l relie o Norml disribuion. The concep o sochsic oliliy or inncil ime series, he uoregressie condiionlly heeroscedsic (ARCH models, ws irs sudied by Engle [], nd is generlizion, he GARCH models by Bollersle []. The GARCH models ssume symmeric eecs on oliliy, h is good nd bd news he sme eec on oliliy, which is shorll o hese models. The symmeric GARCH (AGARCH by Engle nd Ng nd rious oher nonliner GARCH exensions he been proposed o cpure symmeric eecs [3, 5]. Rndom coeicien uoregressie (RCA ime series were inroduced by Nicholls nd Quinn [7] nd some o heir properies were sudied by Appdoo e l []. Thneswrn e l. [8] he lso sudied some RCA ime series nd oliliy modeling. In his pper, we derie he kurosis or rious clsses o doubly sochsic models wih symmeric GARCH innoions. Recenly Peiris e l. [8] he inroduced doubly sochsic oliliy models wih GARCH innoions. In Secion some rndom coeicien uoregressie ime series he been discussed. In Secion 3 some doubly sochsic models wih symmeric GARCH innoions re inroduced nd we derie ormul or kurosis in erms o model prmeers.. RANDOM COEFFICIENT AUTOREGRESSIVE TIME SERIES Rndom coeicien uoregressie sequences re specil cse o doubly sochsic ime series. Some rndom coeicien uoregressie ime series re s ollows: (, y φ+ b +, (
2 08 Muhmmd Sherz (, y φ+ b + +θ, ( ( y φ+ b + Φ s + +θ,, (3, i y > 0, where s 0, i y 0,, i y < 0. In ( 3 we he Rndom coeicien uoregressie (RCA(, Rndom coeicien uoregressie-moing erge (RCA-MA(, Sign-RCA-MA (, respeciely. The men, rince nd kurosis or he boe processes he been discussed in [0]. The wo necessry nd suicien condiions or second order sionriy o { y } re s ollows: b i.,, 0 b 0 N 0 0 ii. φ + b <. Here { b } nd { } re errors in he model, while φ, Φ nd ( E s, we cn clcule he kurosis. For more deils see [0]. A process o he ollowing orm ws considered in [9]: ( + + s re prmeers. Since E( s nd b b + + b,. ( Recenly Peiris e l [8] he sudied doubly sochsic model o he orm y ( φ+ b +,, b b + + b,. ( + + The momens or he model he been recenly clculed [8]. Here independen sequence o ribles wih men zero nd rince. i.,, ii. <, iii. φ +φ +φ <. N (5 is n ideniclly disribued In (5 he obsered rndom rible is modeled in wo seps. Firs, he disribuion o he obsered oucome is represened in sndrd wy nd second sep, b is reed s being isel rndom rible. THEOREM.. Consider (5 wih condiions i, ii nd iii hen we he ollowing resuls : (. E( b 0. E( b 3 ( E b 6 3 ( 3( ( ( 3 ( ( 6 3. E b
3 3 Doubly sochsic models wih symmeric GARCH errors 09 + ( b 3 ( 3( ( 5. K 3 Proo. See deils in [8]. ( ( 6. φ +φ +φ ( ( E( b E( y ( ( ( φ 7. 3 ( φ E b 6φ E b φe b φ φ E( b ( E( b 3 ( φ E( b 6φ E( b φe( b ( y 8. K 3. DOUBLY STOCHASTIC MODELS WITH ASYMMETRIC GARCH ERRORS In his secion we discuss doubly sochsic oliliy models wih symmeric GARCH errors. The ollowing heorem proides he momens o doubly sochsic models wih AGARCH- (I-(0,. THEOREM. Consider he doubly sochsic oliliy process (5 wih AGARCH (I (0, errors o he ollowing orm hen we he resuls, nd 3 s ollows: ( (, y φ+ b y + ( b b + + b, + + z ( ω+α + r ( z ( αz ( φ +φ +φ. ( ze( z ( E( b E( E( y 3 ( φ E( b 6φ E( b φe( b φ. ( ( K, K is kurosis o he process. ( y ( y ( ( (( φ+ + Proo. E b y ( ( ( ( ( ( z E ( z ( αz φ E( b φ E( b E φ y + b y + + φ b y + φ y φ + E b + E z ( (
4 0 Muhmmd Sherz ( ( z ( αz ( φ +φ +φ ( (( φ+ + φ E( y + E( b E( y + 3zE( + 6φ E( b E( y E( b E( y 6E( b E( y E( E( b E( y E( ze( + 6zE( b E( y E( + 6zφ E( y E ( 3 ( φ E( b 6φ E( b φe( b 3zE( + 6 z ( E( b +φ E( E( y E( y 3 φ E( b 6φ E( b φe( b. E b y ( ( φ + + ( ( ( z ( αz ( φ +φ +φ ω+αr + E( y ( ( ( ( 3α α { } 3 ω+α r +α + α r z ( ( ( ( { } ( E ω+α r +α + α r E, 3α α α ( ω+αr +φ z αz φ +φ +φ 6 3 ( ( 3 ( ( ( z φ 6 φ φ 6 3 ( 3( ( ( ( y K. ( THEOREM. Consider he ollowing doubly sochsic ime series sisying condiions i, ii, iii s ollows: (, y φ+ b + +θ ( b b + + b, + + where is n ideniclly disribued independen sequence o ribles wih men zero nd rince nd we he ollowing condiions i, ii nd iii hen we he resuls, nd 3 s ollows: N 0 0 i.,, 0 0
5 5 Doubly sochsic models wih symmeric GARCH errors (. ii. <, iii. φ +φ +φ <. (. ( ( ( +θ ( ( φ +φ +φ ( E( y ( ( ( E( b 3 φ E( b 6φ E( b φe( b 3 + 6θ +θ + 6 +θ +φ ( ( K, K is kurosis o he process. ( y ( y ( ( Proo.. E φ+ b y + +θ ( φ ( + ( ( + ( +θ ( E b E E ( ( +θ ( ( φ +φ +φ ( ( b +θ E φ+ ( (( φ+ + +θ E( ( φ+ b y ( ( + +θ + φ+ b y + θ + φ+ b θ y E( φ+ b y + E( +θ E( + θ E( φ+ b E( E( y + E( φ+ b E( E( y. E b y 6 6 K ( y ( ( E( y ( ( ( E( b 3 φ E( b 6φ E( b φe( b 3 + 6θ +θ + 6 +θ +φ ( ( ( ( E( y ( ( ( E( b 3 φ E( b 6φ E( b φe( b ( +θ ( ( φ +φ +φ 3 + 6θ +θ + 6 +θ +φ. THEOREM Consider he doubly sochsic oliliy process wih AGARCH (I (0, errors o he ollowing orm hen we he resuls, nd 3 s ollows: (. (, y φ+ b y + +θ ( b b + + b, + + z ( ω+α + r z ( ω+α r ( +θ ( ( z ( α φ +φ +φ
6 Muhmmd Sherz 6 (. ( ( ( ( ( ( ( ( 3 φ E( b 6φ E( b φe( b 3 E + 6θ +θ + 6 +θ E b +φ E z z ( ( K, K is kurosis o he process. ( y ( y ( ( (( φ+ + +θ Proo.. E b y ( φ ( + ( ( + ( +θ ( ( E ( E( φ+ b +θ E b E E ( z z ( +θ ( ( z ( α φ +φ +φ ( (( φ+ + +θ E( ( φ+ b y ( ( + +θ + φ+ b y + θ + φ+ b θ y 3E( ( + 6θ +θ + 6 z ( +θ ( E( b +φ E( E( y 3 φ E( b 6φ E( b φe( b. E b y ( ( + ( ( ( ( ( 3α α 3 { } E ω+α r +α + α r ( ( z z ( ( ( ( z ( ω+αr +θ ω+αr E(, E( y α α φ +φ +φ ( ( ( ( ( 3α α { } 3 + 6θ +θ ω+α r +α + α r z z ( ( r ( ( αz ( φ +φ +φ 6 +θ ω+α φ φ φ + 3 ( ( 3 ( ( φ 6 φ φ6 3 ( 3( ( ( K, K is kurosis o he process ollows he deiniion. ( y ( y (
7 7 Doubly sochsic models wih symmeric GARCH errors 3 THEOREM. Consider he doubly sochsic oliliy process wih AGARCH(I (0, errors o he ollowing orm hen we he resuls, nd 3 s ollows: ( (, y φ+ b +Φ s y + +θ ( b b + + b, + + z ( ω+α + r z ( ω+α r ( +θ ( ( αz ( Φ +Φ +Φ φ +φ +φ. ( ( ( ( ( ( ( ( ( φ E( b 6φ E( b Φ 6Φ φ + E( b 3zE + 6θ +θ + 6 z +θ E b +φ +Φ E. ( ( ( K, K is kurosis o he process. ( y ( y ( ( (( φ+ +Φ + +θ ( E ( ( φ ( +Φ ( + ( ( + ( +θ ( E( b ( ( ( z +θ ω+αr E( y ( αz ( Φ +Φ +Φ φ +φ +φ Proo.. E b s y z +θ E b E E Φ φ+ ( (( φ+ +Φ + +θ ( ( + 6θ +θ + 6( +θ ( +φ +Φ ( φ E( b 6φ E( b Φ 6Φ ( φ + E( b 3 ( ( 6 6 ( ( φ E( b 6φ E( b Φ 6Φ φ + E( b. E b s y ( ( ( E E b E ( ( ( ( E + θ +θ + +θ E b +φ +Φ E ( z z ( ( + ( ( ( ( ( 3α α 3 { } E ω+α r +α + α r E ( ( αz z ( ω+α r ( +θ ( ( z ( α Φ +Φ +Φ φ +φ +φ
8 Muhmmd Sherz 8 ( ω + αr ( ( ( ( ( 3α α { } 3 + 6θ + θ ω + αr + α + α r z ( 6 z ( +θ ( φ +Φ ( + ( αz ( Φ +Φ +Φ φ +φ +φ ( ( + + 3( + +( φ 3 3 6( φ +Φ 6 Φ φ Φ ( ( K, K is kurosis o he process ollows he deiniion. ( y ( y (. CONCLUSIONS In his pper, he kurosis o doubly sochsic models wih AGARCH-(I-(0, innoions re deried. Sisicl inerences or hese doubly sochsic models wih symmeric GARCH errors nd se spce modeling cn be iewed s specil cse or nonliner ime series. REFERENCES. APPADOO, S.S., GHAHRAMANI, M., THAVANESWARAN, A., Momen properies o someime series models, The Mhemicl Scienis, 30, pp , BOLLERSLEV, T., Generlized uoregressie condiionl heeroscedsiciy, Journl o Economerics, 3, pp , 986. CHRISTIAN, F., JEAN, Z.M., GARCH models, Jhon Wiley nd Sons, 00.. ENGLE, R.F., Auoregressie condiionl heeroscedsiciy wih esimes o he rince o U.K.inlion, Econonomeric, 50, pp , GEORGE, L., Compuionl innce: Numericl mehods or pricing inncil insrumens, Buerworh-Heinemnn, Elseie, JURGEN, F., WOLFGANG, H.K., CHRISTIAN, H.M., Sisics o Finncil Mrkes: An Inroducion, Springer, NICHOLLS, D., QUINN, B.G., Rndom Coeicien Auoregressie Models, An Inroducion: Lecor Noes in Sisics, Springer, New York, PEIRIS, S., THAVANESWARAN,A., APPADOO,S.S., Doubly sochsic models wih GARCH models, Applied Mhemics Leers,, pp , SHIRYAEV, A.N., Probbiliy, nd ed.,springer-verlg, New York Inc, THAVANESWARAN, A., APPADOO, S.S., BECTOR,C.R, Recen deelopmens in oliliy modeling nd pplicions, Journl o Applied Mhemics nd decision sciences, Aricle ID8630, pp. Receied Ocober 3, 0
Appendix. The solution begins with Eq. (2.15) from the text, which we repeat here for 1, (A.1)
Aenix Aenix A: The equaion o he sock rice. The soluion egins wih Eq..5 rom he ex, which we reea here or convenience as Eq.A.: [ [ E E X, A. c α where X u ε, α γ, an c α y AR. Take execaions o Eq. A. as
RCA models with correlated errors
Applied Mathematics Letters 19 (006) 84 89 www.elsevier.com/locate/aml RCA models with correlated errors S.S. Appadoo a,a.thavaneswaran a,,jagbir Singh b a Department of Statistics, The University of Manitoba,
Χρονοσειρές Μάθημα 3
Χρονοσειρές Μάθημα 3 Ασυσχέτιστες (λευκός θόρυβος) και ανεξάρτητες (iid) παρατηρήσεις Chafield C., The Analysis of Time Series, An Inroducion, 6 h ediion,. 38 (Chaer 3): Some auhors refer o make he weaker
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
Fourier Transform. Fourier Transform
ECE 307 Z. Aliyziioglu Eleril & Compuer Engineering Dep. Cl Poly Pomon The Fourier rnsform (FT is he exension of he Fourier series o nonperiodi signls. The Fourier rnsform of signl exis if sisfies he following
Homomorphism of Intuitionistic Fuzzy Groups
International Mathematical Forum, Vol. 6, 20, no. 64, 369-378 Homomorphism o Intuitionistic Fuzz Groups P. K. Sharma Department o Mathematics, D..V. College Jalandhar Cit, Punjab, India pksharma@davjalandhar.com
[ ) so that the function obtained (denoted, as before, by
Ukrinin Mhemicl Journl, Vol. 56, No. 9, 4 APPROXIMATION OF FUNTIONS DEFINED ON THE REAL AXIS BY OPERATORS GENERATED BY -METHODS OF SUMMATION OF THEIR FOURIER INTEGRALS Yu. I. Khrkeych nd T. V. Zhyhllo
Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών. Εθνικό Μετσόβιο Πολυτεχνείο. Thales Workshop, 1-3 July 2015.
Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών Εθνικό Μετσόβιο Πολυτεχνείο Thles Worksho, 1-3 July 015 The isomorhism function from S3(L(,1)) to the free module Boštjn Gbrovšek Άδεια Χρήσης Το παρόν
APPENDIX A DERIVATION OF JOINT FAILURE DENSITIES
APPENDIX A DERIVAION OF JOIN FAILRE DENSIIES I his Appedi we prese he derivaio o he eample ailre models as show i Chaper 3. Assme ha he ime ad se o ailre are relaed by he cio g ad he sochasic are o his
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
On Strong Product of Two Fuzzy Graphs
Inernaional Journal of Scienific and Research Publicaions, Volume 4, Issue 10, Ocober 014 1 ISSN 50-3153 On Srong Produc of Two Fuzzy Graphs Dr. K. Radha* Mr.S. Arumugam** * P.G & Research Deparmen of
ΕΡΓΑΣΙΑ ΜΑΘΗΜΑΤΟΣ: ΘΕΩΡΙΑ ΒΕΛΤΙΣΤΟΥ ΕΛΕΓΧΟΥ ΦΙΛΤΡΟ KALMAN ΜΩΥΣΗΣ ΛΑΖΑΡΟΣ
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ ΜΕΤΑΠΤΥΧΙΑΚΟ ΠΡΟΓΡΑΜΜΑ ΣΠΟΥΔΩΝ ΘΕΩΡΗΤΙΚΗ ΠΛΗΡΟΦΟΡΙΚΗ ΚΑΙ ΘΕΩΡΙΑ ΣΥΣΤΗΜΑΤΩΝ & ΕΛΕΓΧΟΥ ΕΡΓΑΣΙΑ ΜΑΘΗΜΑΤΟΣ: ΘΕΩΡΙΑ ΒΕΛΤΙΣΤΟΥ ΕΛΕΓΧΟΥ ΦΙΛΤΡΟ KALMAN ΜΩΥΣΗΣ
9.1 Introduction 9.2 Lags in the Error Term: Autocorrelation 9.3 Estimating an AR(1) Error Model 9.4 Testing for Autocorrelation 9.
9.1 Inroducion 9.2 Lags in he Error Term: Auocorrelaion 9.3 Esimaing an AR(1) Error Model 9.4 Tesing for Auocorrelaion 9.5 An Inroducion o Forecasing: Auoregressive Models 9.6 Finie Disribued Lags 9.7
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
SCITECH Volume 13, Issue 2 RESEARCH ORGANISATION Published online: March 29, 2018
Journal of rogressive Research in Mathematics(JRM) ISSN: 2395-028 SCITECH Volume 3, Issue 2 RESEARCH ORGANISATION ublished online: March 29, 208 Journal of rogressive Research in Mathematics www.scitecresearch.com/journals
Anti-aliasing Prefilter (6B) Young Won Lim 6/8/12
ni-aliasing Prefiler (6B) Copyrigh (c) Young W. Lim. Permission is graned o copy, disribue and/or modify his documen under he erms of he GNU Free Documenaion License, Version. or any laer version published
( ) ( t) ( 0) ( ) dw w. = = β. Then the solution of (1.1) is easily found to. wt = t+ t. We generalize this to the following nonlinear differential
Periodic oluion of van der Pol differenial equaion. by A. Arimoo Deparmen of Mahemaic Muahi Iniue of Technology Tokyo Japan in Seminar a Kiami Iniue of Technology January 8 9. Inroducion Le u conider a
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,
A summation formula ramified with hypergeometric function and involving recurrence relation
South Asian Journal of Mathematics 017, Vol. 7 ( 1): 1 4 www.sajm-online.com ISSN 51-151 RESEARCH ARTICLE A summation formula ramified with hypergeometric function and involving recurrence relation Salahuddin
Riemann Hypothesis: a GGC representation
Riemann Hypohesis: a GGC represenaion Nicholas G. Polson Universiy of Chicago Augus 8, 8 Absrac A GGC Generalized Gamma Convoluion represenaion for Riemann s reciprocal ξ-funcion is consruced. This provides
Oscillatory integrals
Oscilltory integrls Jordn Bell jordn.bell@gmil.com Deprtment of Mthemtics, University of Toronto August, 0 Oscilltory integrls Suppose tht Φ C R d ), ψ DR d ), nd tht Φ is rel-vlued. I : 0, ) C by Iλ)
Coefficient Inequalities for a New Subclass of K-uniformly Convex Functions
International Journal of Computational Science and Mathematics. ISSN 0974-89 Volume, Number (00), pp. 67--75 International Research Publication House http://www.irphouse.com Coefficient Inequalities for
The Euler Equations! λ 1. λ 2. λ 3. ρ ρu. E = e + u 2 /2. E + p ρ. = de /dt. = dh / dt; h = h( T ); c p. / c v. ; γ = c p. p = ( γ 1)ρe. c v.
hp://www.nd.ed/~gryggva/cfd-corse/ The Eler Eqaions The Eler Eqaions The Eler eqaions for D flow: + + p = x E E + p where Define E = e + / H = h + /; h = e + p/ Gréar Tryggvason Spring 3 Ideal Gas: p =
A Bonus-Malus System as a Markov Set-Chain. Małgorzata Niemiec Warsaw School of Economics Institute of Econometrics
A Bonus-Malus System as a Markov Set-Chain Małgorzata Niemiec Warsaw School of Economics Institute of Econometrics Contents 1. Markov set-chain 2. Model of bonus-malus system 3. Example 4. Conclusions
Homomorphism in Intuitionistic Fuzzy Automata
International Journal of Fuzzy Mathematics Systems. ISSN 2248-9940 Volume 3, Number 1 (2013), pp. 39-45 Research India Publications http://www.ripublication.com/ijfms.htm Homomorphism in Intuitionistic
Bayesian modeling of inseparable space-time variation in disease risk
Bayesian modeling of inseparable space-time variation in disease risk Leonhard Knorr-Held Laina Mercer Department of Statistics UW May, 013 Motivation Ohio Lung Cancer Example Lung Cancer Mortality Rates
Bayesian statistics. DS GA 1002 Probability and Statistics for Data Science.
Bayesian statistics DS GA 1002 Probability and Statistics for Data Science http://www.cims.nyu.edu/~cfgranda/pages/dsga1002_fall17 Carlos Fernandez-Granda Frequentist vs Bayesian statistics In frequentist
( ) ( ) ( ) Fourier series. ; m is an integer. r(t) is periodic (T>0), r(t+t) = r(t), t Fundamental period T 0 = smallest T. Fundamental frequency ω
Fourier series e jm when m d when m ; m is an ineger. jm jm jm jm e d e e e jm jm jm jm r( is periodi (>, r(+ r(, Fundamenal period smalles Fundamenal frequeny r ( + r ( is periodi hen M M e j M, e j,
Using Seasonal Time Series Models to Forecast Electrical Power Consumption in Fallujah City
0 / Using esonl ime eries Models o Forecs Elecricl Power Consumpion in Fllujh Ciy.... ( ) / (00005). ARIMA (,, ) (0,, ) : 0. 0 Absrc his reserch del wih using sesonl ime series models o sudy nd nlysis
Solutions 3. February 2, Apply composite Simpson s rule with m = 1, 2, 4 panels to approximate the integrals:
s Februry 2, 216 1 Exercise 5.2. Apply composite Simpson s rule with m = 1, 2, 4 pnels to pproximte the integrls: () x 2 dx = 1 π/2, (b) cos(x) dx = 1, (c) e x dx = e 1, nd report the errors. () f(x) =
I Feel Pretty VOIX. MARIA et Trois Filles - N 12. BERNSTEIN Leonard Adaptation F. Pissaloux. ι œ. % α α α œ % α α α œ. œ œ œ. œ œ œ œ. œ œ. œ œ ƒ.
VOX Feel Pretty MARA et Trois Filles - N 12 BERNSTEN Leonrd Adpttion F. Pissloux Violons Contrebsse A 2 7 2 7 Allegro qd 69 1 2 4 5 6 7 8 9 B 10 11 12 1 14 15 16 17 18 19 20 21 22 2 24 C 25 26 27 28 29
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
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
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
TRM +4!5"2# 6!#!-!2&'!5$27!842//22&'9&2:1*;832<
TRM!"#$%& ' *,-./ *!#!!%!&!3,&!$-!$./!!"#$%&'*" 4!5"# 6!#!-!&'!5$7!84//&'9&:*;83< #:4
If ABC is any oblique triangle with sides a, b, and c, the following equations are valid. 2bc. (a) a 2 b 2 c 2 2bc cos A or cos A b2 c 2 a 2.
etion 6. Lw of osines 59 etion 6. Lw of osines If is ny oblique tringle with sides, b, nd, the following equtions re vlid. () b b os or os b b (b) b os or os b () b b os or os b b You should be ble to
Reservoir modeling. Reservoir modelling Linear reservoirs. The linear reservoir, no input. Starting up reservoir modeling
Reservoir modeling Reservoir modelling Linear reservoirs Paul Torfs Basic equaion for one reservoir:) change in sorage = sum of inflows minus ouflows = Q in,n Q ou,n n n jus an ordinary differenial equaion
The Metric Characterization ofthegeneralized FermatPoints
Global Journal of Science Fronier Research Mahemaics and Decision Sciences Volume Issue 0 Version 0 Year 0 Type : Double Blind Peer Reviewed Inernaional Research Journal Publisher: Global Journals Inc
& Risk Management , A.T.E.I.
Μεταβλητότητα & Risk Managemen Οικονοµικό Επιµελητήριο της Ελλάδας Επιµορφωτικά Σεµινάρια Σταύρος. Ντεγιαννάκης, Οικονοµικό Πανεπιστήµιο Αθηνών Χρήστος Φλώρος, A.T.E.I. Κρήτης Volailiy - Μεταβλητότητα
Multi-dimensional Central Limit Theorem
Mult-dmensonal Central Lmt heorem Outlne () () () t as () + () + + () () () Consder a sequence of ndependent random proceses t, t, dentcal to some ( t). Assume t 0. Defne the sum process t t t t () t tme
Commutative Monoids in Intuitionistic Fuzzy Sets
Commutative Monoids in Intuitionistic Fuzzy Sets S K Mala #1, Dr. MM Shanmugapriya *2 1 PhD Scholar in Mathematics, Karpagam University, Coimbatore, Tamilnadu- 641021 Assistant Professor of Mathematics,
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
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
Η ΨΥΧΙΑΤΡΙΚΗ - ΨΥΧΟΛΟΓΙΚΗ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΗ ΣΤΗΝ ΠΟΙΝΙΚΗ ΔΙΚΗ
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΝΟΜΙΚΗ ΣΧΟΛΗ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΤΟΜΕΑΣ ΙΣΤΟΡΙΑΣ ΦΙΛΟΣΟΦΙΑΣ ΚΑΙ ΚΟΙΝΩΝΙΟΛΟΓΙΑΣ ΤΟΥ ΔΙΚΑΙΟΥ Διπλωματική εργασία στο μάθημα «ΚΟΙΝΩΝΙΟΛΟΓΙΑ ΤΟΥ ΔΙΚΑΙΟΥ»
d dt S = (t)si d dt R = (t)i d dt I = (t)si (t)i
d d S = ()SI d d I = ()SI ()I d d R = ()I d d S = ()SI μs + fi + hr d d I = + ()SI (μ + + f + ())I d d R = ()I (μ + h)r d d P(S,I,) = ()(S +1)(I 1)P(S +1, I 1, ) +()(I +1)P(S,I +1, ) (()SI + ()I)P(S,I,)
Lecture 12 Modulation and Sampling
EE 2 spring 2-22 Handou #25 Lecure 2 Modulaion and Sampling The Fourier ransform of he produc of wo signals Modulaion of a signal wih a sinusoid Sampling wih an impulse rain The sampling heorem 2 Convoluion
INTEGRAL INEQUALITY REGARDING r-convex AND
J Koren Mth Soc 47, No, pp 373 383 DOI 434/JKMS47373 INTEGRAL INEQUALITY REGARDING r-convex AND r-concave FUNCTIONS WdAllh T Sulimn Astrct New integrl inequlities concerning r-conve nd r-concve functions
Ηλεκτρονικοί Υπολογιστές IV
ΠΑΝΕΠΙΣΤΗΜΙΟ ΙΩΑΝΝΙΝΩΝ ΑΝΟΙΚΤΑ ΑΚΑΔΗΜΑΪΚΑ ΜΑΘΗΜΑΤΑ Ηλεκτρονικοί Υπολογιστές IV Μοντέλα χρονολογικών σειρών Διδάσκων: Επίκουρος Καθηγητής Αθανάσιος Σταυρακούδης Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό
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 :
Necessary and sufficient conditions for oscillation of first order nonlinear neutral differential equations
J. Mah. Anal. Appl. 321 (2006) 553 568 www.elsevier.com/locae/jmaa Necessary sufficien condiions for oscillaion of firs order nonlinear neural differenial equaions X.H. ang a,, Xiaoyan Lin b a School of
Αστάθεια (volatility)
Αστάθεια volly N Χρονοσειρά πρώτων διαφορών ή σχετικών μεταβολών { } Μεταβλητότητα ή αστάθεια σε κάθε χρονική στιγμή σ ή σ y y y y y Ηαστάθειαs δίνεται με αναφορά σε κάποια περίοδο T vol : - στιγμιαία
J. of Math. (PRC) u(t k ) = I k (u(t k )), k = 1, 2,, (1.6) , [3, 4] (1.1), (1.2), (1.3), [6 8]
Vol 36 ( 216 ) No 3 J of Mah (PR) 1, 2, 3 (1, 4335) (2, 4365) (3, 431) :,,,, : ; ; ; MR(21) : 35A1; 35A2 : O17529 : A : 255-7797(216)3-591-7 1 d d [x() g(, x )] = f(, x ),, (11) x = ϕ(), [ r, ], (12) x(
Predictability and Model Selection in the Context of ARCH Models
Predicabiliy and Model Selecion in he Conex of ARCH Models Savros Degiannakis and Evdokia Xekalaki Deparmen of Saisics Ahens Universiy of Economics and Business 76 Paission Sree 434 Ahens Greece echnical
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
Estimation for ARMA Processes with Stable Noise. Matt Calder & Richard A. Davis Colorado State University
Estimation for ARMA Processes with Stable Noise Matt Calder & Richard A. Davis Colorado State University rdavis@stat.colostate.edu 1 ARMA processes with stable noise Review of M-estimation Examples of
Multi-dimensional Central Limit Theorem
Mult-dmensonal Central Lmt heorem Outlne () () () t as () + () + + () () () Consder a sequence of ndependent random proceses t, t, dentcal to some ( t). Assume t 0. Defne the sum process t t t t () t ();
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
AMS 212B Perturbation Methods Lecture 14 Copyright by Hongyun Wang, UCSC. Example: Eigenvalue problem with a turning point inside the interval
AMS B Perturbtion Methods Lecture 4 Copyright by Hongyun Wng, UCSC Emple: Eigenvlue problem with turning point inside the intervl y + λ y y = =, y( ) = The ODE for y() hs the form y () + λ f() y() = with
Oscillation Criteria for Nonlinear Damped Dynamic Equations on Time Scales
Oscillaion Crieria for Nonlinear Damped Dynamic Equaions on ime Scales Lynn Erbe, aher S Hassan, and Allan Peerson Absrac We presen new oscillaion crieria for he second order nonlinear damped delay dynamic
ON NEGATIVE MOMENTS OF CERTAIN DISCRETE DISTRIBUTIONS
Pa J Statist 2009 Vol 25(2), 135-140 ON NEGTIVE MOMENTS OF CERTIN DISCRETE DISTRIBUTIONS Masood nwar 1 and Munir hmad 2 1 Department of Maematics, COMSTS Institute of Information Technology, Islamabad,
Figure A.2: MPC and MPCP Age Profiles (estimating ρ, ρ = 2, φ = 0.03)..
Supplemental Material (not for publication) Persistent vs. Permanent Income Shocks in the Buffer-Stock Model Jeppe Druedahl Thomas H. Jørgensen May, A Additional Figures and Tables Figure A.: Wealth and
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
Key Formulas From Larson/Farber Elementary Statistics: Picturing the World, Second Edition 2002 Prentice Hall
64_INS.qxd /6/0 :56 AM Page Key Formulas From Larson/Farber Elemenary Saisics: Picuring he World, Second Ediion 00 Prenice Hall CHAPTER Class Widh = round up o nex convenien number Maximum daa enry - Minimum
ΑΓΓΛΙΚΑ IV. Ενότητα 6: Analysis of Greece: Your Strategic Partner in Southeast Europe. Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών
Ενότητα 6: Analysis of Greece: Your Strategic Partner in Southeast Europe Ιφιγένεια Μαχίλη Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative Commons. Για εκπαιδευτικό υλικό,
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
Problem 7.19 Ignoring reflection at the air soil boundary, if the amplitude of a 3-GHz incident wave is 10 V/m at the surface of a wet soil medium, at what depth will it be down to 1 mv/m? Wet soil is
ΖητΗματα υποδοχης και προσληψης του Franz Kafka στην ΕλλΑδα
ΖητΗματα υποδοχης και προσληψης του Franz Kafka στην ΕλλΑδα Ζητήματα υποδοχής και πρόσληψης του Franz Kafka στην Ελλάδα Μιχ. Γ. Μπακογιάννης Aspects of Kafka s reception in Modern Greek Literature: The
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
Solutions_3. 1 Exercise Exercise January 26, 2017
s_3 Jnury 26, 217 1 Exercise 5.2.3 Apply composite Simpson s rule with m = 1, 2, 4 pnels to pproximte the integrls: () x 2 dx = 1 π/2 3, (b) cos(x) dx = 1, (c) e x dx = e 1, nd report the errors. () f(x)
Abstract Storage Devices
Abstract Storage Devices Robert König Ueli Maurer Stefano Tessaro SOFSEM 2009 January 27, 2009 Outline 1. Motivation: Storage Devices 2. Abstract Storage Devices (ASD s) 3. Reducibility 4. Factoring ASD
Lecture 7: Overdispersion in Poisson regression
Lecture 7: Overdispersion in Poisson regression Claudia Czado TU München c (Claudia Czado, TU Munich) ZFS/IMS Göttingen 2004 0 Overview Introduction Modeling overdispersion through mixing Score test for
Εμπειρική εκτίμηση συνάρτησης προσφοράς πρόβειου κρέατος στα πλαίσια των μεταρρυθμίσεων της ΚΑΠ
Εμπειρική εκτίμηση συνάρτησης προσφοράς πρόβειου κρέατος στα πλαίσια των μεταρρυθμίσεων της ΚΑΠ Αντώνιος Ρεζίτης 1, Κωνσταντίνος Σταυρόπουλος Παρουσιάστηκε στο 10 ο Πανελλήνιο Συνέδριο Αγροτικής Οικονομίας
Jordan Form of a Square Matrix
Jordan Form of a Square Matrix Josh Engwer Texas Tech University josh.engwer@ttu.edu June 3 KEY CONCEPTS & DEFINITIONS: R Set of all real numbers C Set of all complex numbers = {a + bi : a b R and i =
ω = radians per sec, t = 3 sec
Secion. Linear and Angular Speed 7. From exercise, =. A= r A = ( 00 ) (. ) = 7,00 in 7. Since 7 is in quadran IV, he reference 7 8 7 angle is = =. In quadran IV, he cosine is posiive. Thus, 7 cos = cos
Vol. 40 No Journal of Jiangxi Normal University Natural Science Jul. 2016
4 4 Vol 4 No 4 26 7 Journal of Jiangxi Normal Universiy Naural Science Jul 26-5862 26 4-349-5 3 2 6 2 67 3 3 O 77 9 A DOI 6357 /j cnki issn-5862 26 4 4 C q x' x /q G s = { α 2 - s -9 2 β 2 2 s α 2 - s
Low ESR Tantalum Capacitors (TCR Series)
Low SR Tnlum pciors (TR Series) Pr Numer Srucure Feures: RoHS omplin nd Hlogen Free Lower SR hn sndrd Tnlum xcellen frequency chrcerisics nd impednce Lser mrking for esy idenificion Volge rnge: 4V o 50V
þÿ ÀÌ Ä º± µä À ¹ ¼ ½
Neapolis University HEPHAESTUS Repository School of Economic Sciences and Business http://hephaestus.nup.ac.cy Master Degree Thesis 2016 þÿ ÀÌ Ä º± µä À ¹ ¼ ½ þÿµºà±¹ µåä¹ºì ¹ ¹º ĹºÌ ÃÍÃÄ ¼± þÿãä ½ º±Ä±½µ¼
Το απόθεμα των σπόρων στο έδαφος σε λιβαδικά οικοσυστήματα του όρους Ψηλορείτη Κρήτης
Το απόθεμα των σπόρων στο έδαφος σε λιβαδικά οικοσυστήματα του όρους Ψηλορείτη Κρήτης Το απόθεμα των σπόρων στο έδαφος σε λιβαδικά οικοσυστήματα του όρους Ψηλορείτη Κρήτης Γ. Καζάκης 1 και Β. Π. Παπαναστάσης
THEORETICAL PROPERTIES OF THE WEIGHTED FELLER-PARETO AND RELATED DISTRIBUTIONS
ASIAN JOURNAL OF MATHEMATICS AND APPLICATIONS Volume 204 Aricle ID ama073 2 pages ISSN 2307-7743 hp://scienceasia.asia THEORETICAL PROPERTIES OF THE WEIGHTED FELLER-PARETO AND RELATED DISTRIBUTIONS OLUSEYI
Ελαφρές κυψελωτές πλάκες - ένα νέο προϊόν για την επιπλοποιία και ξυλουργική. ΒΑΣΙΛΕΙΟΥ ΒΑΣΙΛΕΙΟΣ και ΜΠΑΡΜΠΟΥΤΗΣ ΙΩΑΝΝΗΣ
Ελαφρές κυψελωτές πλάκες - ένα νέο προϊόν για την επιπλοποιία και ξυλουργική ΒΑΣΙΛΕΙΟΥ ΒΑΣΙΛΕΙΟΣ και ΜΠΑΡΜΠΟΥΤΗΣ ΙΩΑΝΝΗΣ Αριστοτέλειο Πανεπιστήµιο Θεσσαλονίκης Σχολή ασολογίας και Φυσικού Περιβάλλοντος,
Buried Markov Model Pairwise
Buried Markov Model 1 2 2 HMM Buried Markov Model J. Bilmes Buried Markov Model Pairwise 0.6 0.6 1.3 Structuring Model for Speech Recognition using Buried Markov Model Takayuki Yamamoto, 1 Tetsuya Takiguchi
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
Fractional Colorings and Zykov Products of graphs
Fractional Colorings and Zykov Products of graphs Who? Nichole Schimanski When? July 27, 2011 Graphs A graph, G, consists of a vertex set, V (G), and an edge set, E(G). V (G) is any finite set E(G) is
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
( )( ) La Salle College Form Six Mock Examination 2013 Mathematics Compulsory Part Paper 2 Solution
L Slle ollege Form Si Mock Emintion 0 Mthemtics ompulsor Prt Pper Solution 6 D 6 D 6 6 D D 7 D 7 7 7 8 8 8 8 D 9 9 D 9 D 9 D 5 0 5 0 5 0 5 0 D 5. = + + = + = = = + = =. D The selling price = $ ( 5 + 00)
Vidyamandir Classes. Solutions to Revision Test Series - 2/ ACEG / IITJEE (Mathematics) = 2 centre = r. a
Per -.(D).() Vdymndr lsses Solutons to evson est Seres - / EG / JEE - (Mthemtcs) Let nd re dmetrcl ends of crcle Let nd D re dmetrcl ends of crcle Hence mnmum dstnce s. y + 4 + 4 6 Let verte (h, k) then
The Early Universe Big Bang Cosmology: Einstein Universe Friedmann-Lemaître Universe Einstein-deSitter Universe
Seminr The Erly Universe Big Bng Cosmology: Einsein Universe Friemnn-Lemîre Universe Einsein-eSier Universe by Oliver Schmi Ouline The observe universe Meric of he universe Curvure Einsein Equion Cosmologicl
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.
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
DETERMINATION OF DYNAMIC CHARACTERISTICS OF A 2DOF SYSTEM. by Zoran VARGA, Ms.C.E.
DETERMINATION OF DYNAMIC CHARACTERISTICS OF A 2DOF SYSTEM by Zoran VARGA, Ms.C.E. Euro-Apex B.V. 1990-2012 All Rights Reserved. The 2 DOF System Symbols m 1 =3m [kg] m 2 =8m m=10 [kg] l=2 [m] E=210000
MA6451-PROBABILITY & RANDOM PROCESS. UNIT-IV-CORRELATION AND SPECTRAL DENSITIES By K.VIJAYALAKSHMI Dept. of Applied mathematics
M645-POBBILIY & NDOM POCESS UNI-IV-COELION ND SPECL DENSIIES By K.VIJYLKSHMI Dp. of pplid mhmics COELION ND SPECL DENSIIES Dfiniion: uo Corrlion h uo Corrlion of rndom procss {x}is dfind by xx xx im vrg
Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1
Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the
Applying Markov Decision Processes to Role-playing Game
1,a) 1 1 1 1 2011 8 25, 2012 3 2 MDPRPG RPG MDP RPG MDP RPG MDP RPG MDP RPG Applying Markov Decision Processes to Role-playing Game Yasunari Maeda 1,a) Fumitaro Goto 1 Hiroshi Masui 1 Fumito Masui 1 Masakiyo
Homomorphism and Cartesian Product on Fuzzy Translation and Fuzzy Multiplication of PS-algebras
Annals of Pure and Applied athematics Vol. 8, No. 1, 2014, 93-104 ISSN: 2279-087X (P), 2279-0888(online) Published on 11 November 2014 www.researchmathsci.org Annals of Homomorphism and Cartesian Product
ΤΟ ΜΟΝΤΕΛΟ Οι Υποθέσεις Η Απλή Περίπτωση για λi = μi 25 = Η Γενική Περίπτωση για λi μi..35
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΗ ΘΕΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΤΟΜΕΑΣ ΣΤΑΤΙΣΤΙΚΗΣ ΚΑΙ ΕΠΙΧΕΙΡΗΣΙΑΚΗΣ ΕΡΕΥΝΑΣ ΑΝΑΛΥΣΗ ΤΩΝ ΣΥΣΧΕΤΙΣΕΩΝ ΧΡΕΟΚΟΠΙΑΣ ΚΑΙ ΤΩΝ
HW 3 Solutions 1. a) I use the auto.arima R function to search over models using AIC and decide on an ARMA(3,1)
HW 3 Solutions a) I use the autoarima R function to search over models using AIC and decide on an ARMA3,) b) I compare the ARMA3,) to ARMA,0) ARMA3,) does better in all three criteria c) The plot of the
«Βιοδοκιμές αποτελεσματικότητας ουσιών φυτικής προέλευσης επί του δορυφόρου της πατάτας Leptinotarsa decemlineata (Say) (Coleoptera: Chrysomelidae)»
ΓΕΩΠΟΝΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ ΣΧΟΛΗ ΑΓΡΟΤΙΚΗΣ ΠΑΡΑΓΩΓΗΣ ΥΠΟΔΟΜΩΝ ΚΑΙ ΠΕΡΙΒΑΛΛΟΝΤΟΣ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΦΥΤΙΚΗΣ ΠΑΡΑΓΩΓΗΣ Εργαστήριο Γεωργικής Ζωολογίας & Εντομολογίας Αθήνα 2015 «Βιοδοκιμές αποτελεσματικότητας
GÖKHAN ÇUVALCIOĞLU, KRASSIMIR T. ATANASSOV, AND SINEM TARSUSLU(YILMAZ)
IFSCOM016 1 Proceeding Book No. 1 pp. 155-161 (016) ISBN: 978-975-6900-54-3 SOME RESULTS ON S α,β AND T α,β INTUITIONISTIC FUZZY MODAL OPERATORS GÖKHAN ÇUVALCIOĞLU, KRASSIMIR T. ATANASSOV, AND SINEM TARSUSLU(YILMAZ)
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
Space-Time Symmetries
Chapter Space-Time Symmetries In classical fiel theory any continuous symmetry of the action generates a conserve current by Noether's proceure. If the Lagrangian is not invariant but only shifts by a