International Journal of Mathematics Trends and Technology (IJMTT) Volume 37 Number 3 September 2016
|
|
- Shawn Golden
- 6 years ago
- Views:
Transcription
1 Inernaional Journal of ahemaics Trends and Technology (IJTT) Volume 37 Number 3 Sepember 6 Conveiy in he s Class of he Rough ahemaical Programming Problems T... Aeya, Kamilia l-bess, Deparmen of Physics and ngineering ahemaics, Faculy of ngineering, Tana Universiy, Tana, gyp Absrac Conve opimizaion is considered o be a reliable compuaional ool in engineering as i is used o solve many engineering problems in an efficien and fas mehod. The goal of his paper is o discuss, in deph, he conveiy in he s class of rough mahemaical programming and o presen some relaed resuls. Keywords conveiy, opimizaion, rough programming. I. INTRODUCTION Opimizaion (mahemaical programming) is a subfield of operaions research and i has a widely grown in he las hree decades. The goal of any opimizaion problem is o maimize (or minimize) one or more of obecive funcions under a deermined se of condiions. Opimizaion can be applied o many fields lie business, mining and engineering. Opimizaion is used in our daily life (e.g. moving from a place o anoher). The model of a simple mahemaical programming problem is: where g : U R is he crisp obecive funcion and U is he feasible se of he problem. U is he universe of he problem. Conve opimizaion problem involves maimizing concave funcions over conve ses. They can be convered ino a minimizaion problem of conve funcions by muliplying he obecive funcion by minus one. One of he advanages of conve opimizaion is ha i covers a broad range of pracical opimizaion problems. Also, here are some nonconve problems ha can be reformulaed ino conve problems. The oher advanage is ha if he decision se of he problem is conve, any local opimum is also a global opimum. There are some boos ha discuss conve opimizaion (e.g. Rocafellar [], Soer and Wizgall [3], Holmes [4], Bazaraa and Shey [5], eland and Temam [6], Ioffe and Tihomirov [7], Barbu and Precupanu [8] and Ponsein [9]). We assume ha he reader has a previous nowledge of conve opimizaion. In many acual opimizaion problems, he decision maer is no able o define he obecive funcion and/or he se of consrains precisely bu raher can define hem in a "rough sense". Rough se heory (RST), inroduced by Pawla [], provides a fleible mahemaical ool o he decision maer o solve such problems. Recenly, Youness [] combined rough se heory wih mahemaical programming. He described a new ype of mahemaical programming problems in which he feasible region is rough and called i RPP. He defined new conceps, namely, "conve rough se", "local rough opimal soluion" and "global rough opimal soluion". Osman e al. [] eended he previous wor and demonsraed ha he roughness may eis in he obecive funcion, he feasible se or boh of hem. They classified rough programming problems ino hree classes according o he place of roughness. They discussed he conveiy in he s class of he RPPs in which he decision se is rough and he obecive funcion is crisp. In heir discussion, hey showed ha he lower and/or upper approimaions of rough feasible se could be conve. They also inroduced new conceps such as: "Upper conve" and "Lower conve". In his paper, we eend he above menioned wors, and propose and prove some heorems relaed o he conveiy in he s class of RPPs. II. ROUGH ST THORY RST has been proven o be an ecellen mahemaical ool dealing wih vague or imprecise descripions of obecs. Therefore, many researchers applied RST o many domains such as paern recogniion, daa mining, arificial inelligence, image processing, machine learning and medical applicaions []. The rough se mehodology proposed by Pawla [], in 98, assumed ha any imprecise concep is characerized by a pair of precise conceps called he lower and he upper approimaions. RST is based on equivalence relaion ha pariions he universe ino classes of indiscernible obecs. RST epresses imprecision by employing a boundary region of a se. If he boundary region of a se is empy, hen he se is crisp (eac) oherwise he se is rough (ineac). RST uses equivalence relaion o group obecs wih similar characerisics ino indiscernibiliy classes and any vague se is characerized by a pair of precise ses called he lower and he upper approimaions. The lower approimaion includes all obecs ha surely belong o he concep of ineres, where he upper approimaion includes all obecs which possibly belong o ha imprecise concep. The main advanage of using RST in handling imprecise conceps is ha i does no need any addiional informaion. ISSN: hp:// Page 4
2 Inernaional Journal of ahemaics Trends and Technology (IJTT) Volume 37 Number 3 Sepember 6 Le U be a non-empy finie se of obecs, called he universe, and U U be an equivalence relaion on U. The ordered pair A=(U, ) is called an approimaion space generaed by on U. generaes a pariion U / { Y, Y,..., Y } m where Y, Y,..., Y are he equivalence classes of he m approimaion space A. Based on he equivalence relaion, he mapping [ ] : U U is given by [ ] { y U y }. Shorly, he subse [ ] U is he equivalence class conainin In RST, any subse U is defined in erms of he equivalence classes of he approimaion space A by is lower and upper approimaions (i.e. ( ) and ( ), respecively) as follows: ( ) { U [ ] } U I ( ) { [ ] } Therefore, ( ) ( ) The difference beween he upper and he lower approimaions is called he boundary of and is denoed by ( ) ( ) ( ). For simpliciy, le ( ), ( ). ( ) and III. TH ST CLASS OF RPPS [] Le A ( U, ) be an approimaion space generaed by an equivalence relaion on he universe U. Therefore, U / { Y, Y,..., Y } m is he pariioned universe generaed by on U where Y, Y,..., Y are he equivalence classes of he m approimaion space A. A RPP over he universe U aes he following form: () s.. where g : R is he crisp obecive funcion. U is he se of consrains of he problem, ha is roughly defined in he universe U by and where: { U [ ] } U { ([ ] ) }, Definiion 3.: In problem (), he opimal value g of he obecive funcion is defined by is lower and upper bounds g and g g where ma{, } ma{, } ma min g ( ) Y Y g, respecively, such ha: Definiion 3.: In problem (), a poin is a surely-feasible soluion, if and only if. Definiion 3.3: In problem (), a poin is a possibly-feasible soluion, if and only if. Definiion 3.4: In problem (), a poin is a surely-no feasible soluion, if and only if. Definiion 3.5: In problem (), a poin is a g( ) surely-opimal soluion, if and only if Definiion 3.6: In problem (), a poin is a g( ) possibly-opimal soluion, if and only if Definiion 3.7: In problem (), a poin is a surely-no opimal soluion, if and only if g( ) Definiion 3.8: In problem (), here are four opimal ses covering all possible degrees of feasibiliy and opimaliy, as follows: The se of all surely-feasible, surely-opimal soluions is denoed by FO s s, and i is defined by: FO { () } s s g The se of all surely-feasible, possiblyopimal soluions is denoed by FO s p, and i FO { ( ) } s p g The se of all possibly-feasible, surelyopimal soluions is denoed by FO p s, and i FO { ( ) } p s g The se of all possibly-feasible, possiblyopimal soluions is denoed by FO p p, and i F O { ( ) } p p g IV. CONVXITY IN ST CLASS OF RPPS Conve ses and concave funcions have many aracive properies in mahemaical programming. For eample, any local maimum poin of a concave funcion over a conve se is also a global maimum poin. In his secion, we presen some significan ISSN: hp:// Page 5
3 Inernaional Journal of ahemaics Trends and Technology (IJTT) Volume 37 Number 3 Sepember 6 properies of RPPs ha have conve rough se and concave crisp funcion. Definiion 4.: A rough se is U - conve, if is upper approimaion is conve []. Definiion 4.: A rough se is L - conve, if is lower approimaion is conve []. Definiion 4.3: A rough se is conve, if is upper and lower approimaions (i.e. and ) are conve []. Definiion 4.4: A funcion g ( ) is concave on a conve se S, if g( ( ) ) g( ) ( ) g( ) for each, S and for each (,) []. Definiion 4.5: A funcion g ( ) is sricly concave on a nonempy conve se S, if g( ( ) ) g( ) ( ) g( ) for each, S and for each (,) []. Definiion 4.6: A funcion g ( ) is quasiconcave on a conve se S, if g( ( ) ) min{ g( ), g( )} for each, S and for each (,) []. Definiion 4.7: A funcion g ( ) is sricly quasiconcave on a nonempy conve se S, if for each, S wih g( ) g( ), we have g( ( ) ) min{ g( ), g( )} for each (,) []. Definiion 4.8: A funcion g ( ) is srongly quasiconcave on a nonempy conve se S, if for each, S wih, we have g( ( ) ) min{ g( ), g( )} for each (,) []. Theorem 4.: In problem (), if is a nonempy conve se and is a local opimal soluion hen: ) If g ( ) is a sricly quasiconcave funcion, hen is a surely-global opimal soluion. ) If g ( ) is a srongly quasiconcave funcion, hen is he unique surely-global opimal soluion. 3) If g ( ) is a srongly quasiconcave funcion Proof: and, hen is he unique global opimal soluion (i.e. F O F O F O F O {} ). ) Suppose, on he conrary, ha here is an ˆ wih g( ˆ ) g( ). By conveiy of, ˆ ( ), (,). Since is a local maimum by assumpion, hen g( ) g( ˆ ( ) ), (, ) for some (,). Bu since g ( ) is sricly quasiconcave and g( ˆ ) g( ), hen g( ˆ ( ) ) g( ), (,). This conradicion shows ha ˆ does no eis. ) Since is a local opimal soluion, hen here is an - neighborhood N ) around where g( ) g( ) for N ( ). Assume by conradicion o he conclusion of he heory ha here is a poin ˆ such ha ˆ and g( ˆ ) g( ). By srong quasiconcaviy, i follows ha g( ˆ ( ) ) min{ g( ˆ), g( )} g( ), (,). Bu for small enough, ˆ ( ) N ( ) and hence local opimaliy of is violaed. 3) If g ( ) is a srongly quasiconcave funcion g g Thus, and, hen is a unique surely and possibly opimal soluion. Hence, F O F O F O F O {}. ( ) Theorem 4.: In problem (), if is a nonempy conve se and is a local opimal soluion hen: ) If g ( ) is a concave funcion, hen is a surely-global opimal soluion. ) If g ( ) is a sricly concave funcion, hen is he unique surely-global opimal soluion. 3) If g ( ) is a sricly concave funcion and, hen is he unique global opimal soluion (i.e. F O F O F O F O {} ). Proof: I is similar o he above proof. Theorem 4.3: In problem (), if is a nonempy U - conve se and g ( ) is a concave funcion on, hen he poin is a surely-opimal soluion o his problem if and only if g ( ) has a subgradien a such ha ( ) for all. ( ISSN: hp:// Page 6
4 Inernaional Journal of ahemaics Trends and Technology (IJTT) Volume 37 Number 3 Sepember 6 Proof: Assume ha ( ), where. is a subgradien of g a. By concaviy of g, g( ) g( ) ( ) g( ), and herefore is a surely-opimal soluion o he problem. To show he converse, assume ha is a surelyopimal soluion o he problem, and form he following wo ses in U : S {(, y) U, y g( ) g( )} S y y {(, ), } I is easy o prove ha boh S and S are conve ses. Also S S because oherwise here would be a poin ( y, ) where, y g( ) g( ) conradicing he assumpion ha is an opimal soluion of he problem. Since S S, hen here is a hyperplane ha separaes S and S. Thus, here is a nonzero vecor (, ) and a scalar such ha: ( ) y, U, y g( ) g( ) () ( ) y,, y () If we le and y in (), hen. Ne, leing and y in () maes. Since his is rue for, hen and. Briefly, we conclude ha and. If, hen from () ( ), U. If we le, hen ( ) and hus. Since (, ) (,), hen. Dividing () and () by and denoing / by, we obain he following inequaliies: ( ) y, U, y g( ) g( ) (3) ( ) y,, y (4) By leing y in (4), we obain ( ),. From (3), i is clear ha g( ) g( ) ( ), U. Thus, ( ), is a subgradien of g a such ha. Theorem 4.4: In problem (), if is a nonempy U - conve se and g ( ) is a concave funcion on where is open, hen he poin surely-opimal soluion o his problem if and only if here is a zero subgradien of g ( ) a. is a Proof: By he previous heorem, is a surely- opimal soluion if and only if ( ), where is a subgradien of g a. Since posiive. is open, hen. Hence, for some. This means ha Theorem 4.5: In problem (), if is a nonempy U - conve se and g ( ) is a differeniable concave funcion on, hen he poin is a surelyopimal soluion o his problem if and only if g ( )( ),. Furhermore, if is open hen he poin is a surely-opimal soluion o his problem if and only if g ( ). Proof: I is sraighforward. Theorem 4.6: Consider he problem: min g ( ) subec o, where (he upper approimaion of he rough se ) is a nonempy conve se and g ( ) is a concave funcion on. If is a local opimal soluion hen ( ) for all subgradien of g a. where is a Proof: Assume ha is a local opimal soluion. Then here is an - neighborhood N ( ) where g( ) g( ), N ( ). Le, and noice ha here is ( ) N ( ) for, o. Thus, g( ( )) g( ). Le be a subgradien of g a and by concaviy of g, we have g( ) g( ( )) ( ). The above wo inequaliies imply ha ( ), and dividing by, we ge he required resul. Theorem 4.7: Consider he problem: min g ( ) subec o, where (he upper approimaion of he rough se ) is a conve se and g ( ) is a differeniable concave funcion on. If is a local opimal soluion hen g ( ), where is a subgradien of g a. Proof: I is sraighforward. Theorem 4.8: Consider he problem: min g ( ) subec o, where (he upper ISSN: hp:// Page 7
5 Inernaional Journal of ahemaics Trends and Technology (IJTT) Volume 37 Number 3 Sepember 6 approimaion of he rough se ) is a nonempy compac polyhedral se and g ( ) is a concave funcion on. Then, here is an opimal soluion o he problem, where is an ereme poin of. Proof: Since minimum a is compac, g assumes a. If is an ereme poin of, hen he resul is acquired. Oherwise, where,, and is an ereme poin of for,,...,. By he concaviy of g, we have g ( ) g ( ) g ( ) Bu since g( ) g( ), for,,...,, he above inequaliy implies ha g( ) g( ) for,,...,. Hence, he ereme poins,,..., are opimal soluions o he problem and he proof is complee. Theorem 4.9: Consider he problem: min g ( ) subec o, where (he upper approimaion of he rough se ) is a nonempy compac polyhedral se and g ( ) is a quasiconcave funcion on. Then, here is an opimal soluion o he problem, where is an ereme poin of. Proof: Since g is a funcion on and hence ges a minimum a. If here is an ereme poin whose obecive is equal o g ( ), hen he resul is acquired. Oherwise, le,,..., be ereme poins of, and suppose ha g( ) g( ) for,,...,. can be represened as,,,,...,. where Since g( ) g( ) for each, hen g( ) min g( ) () Now consider he se Noice ha conve se. Hence, for,,..., { g( ) }. and belongs o is a. By quasiconcaviy of g, g ( ), which conradics (). This conradicion shows ha g( ) g( ) for some ereme poin and he resul is obained. V. CONCLUSIONS In his paper, we provided some essenials of conve ses, conve funcions, and conve opimizaion problems in a rough environmen. RFRNCS [] Z. Pawla, Rough ses, Inernaional Journal of Compuer and Informaion Sciences,, , 98. [] R. T. Rocafellar, Conve Analysis, Princeon Universiy Press, 97. [3] J. Soer and C. Wizgall, Conveiy and Opimizaion in Finie Dimensions I, Springer-Verlag, 97. [4] Holmes, R. B., A Course on Opimizaion and Bes Approimaion, Springer-Verlag, Berlin and New Yor, 97. [5] Bazaraa,. S., and Shey, C.., Foundaions of Opimizaion, Springer-Verlag, Berlin and New Yor, 976. [6] eland, I., and Temam, R., Conve Analysis and Variaional Problems, Norh Holland Publisher, Amserdam, 976. [7] Ioffe, A. D., and Tihomirov, Y.., Theory of ernal Problems, Norh Holland Publisher, Amserdam, 979. [8] Barbu, V., and Precupanu, T., Conveiy and Opimizaion in Banach Spaces, Sihoff and Noordhoff, Alphen aan de Rin, 978. [9] Ponsein, J., "Approaches o he Theory of Opimizaion," Cambridge Universiy, Press, London and New Yor, 98. [].A. Youness, Characerizing soluions of rough programming problems, uropean Journal of Operaional Research, vol.68, no.3, pp.9-9, 6. [].S. Osman,.F. Lashein,.A. Youness, T... Aeya, ahemaical programming in rough environmen, Opimizaion, vol.6, no.5, pp.63-6,. [] ohar S. Bazaraaa, Hanif D. Sherali, C.. Shey, Nonlinear Programming: Theory and Algorihms, John Wiley and Sons Inc., 3 rd ed.; 6. ISSN: hp:// Page 8
The Asymptotic Behavior of Nonoscillatory Solutions of Some Nonlinear Dynamic Equations on Time Scales
Advances in Dynamical Sysems and Applicaions. ISSN 0973-5321 Volume 1 Number 1 (2006, pp. 103 112 c Research India Publicaions hp://www.ripublicaion.com/adsa.hm The Asympoic Behavior of Nonoscillaory Soluions
More informationSOME PROPERTIES OF GENERALIZED STRONGLY HARMONIC CONVEX FUNCTIONS MUHAMMAD ASLAM NOOR, KHALIDA INAYAT NOOR, SABAH IFTIKHAR AND FARHAT SAFDAR
Inernaional Journal o Analysis and Applicaions Volume 16, Number 3 2018, 427-436 URL: hps://doi.org/10.28924/2291-8639 DOI: 10.28924/2291-8639-16-2018-427 SOME PROPERTIES OF GENERALIZED STRONGLY HARMONIC
More informationChapter 4. Truncation Errors
Chaper 4. Truncaion Errors and he Taylor Series Truncaion Errors and he Taylor Series Non-elemenary funcions such as rigonomeric, eponenial, and ohers are epressed in an approimae fashion using Taylor
More informationLecture 20: Riccati Equations and Least Squares Feedback Control
34-5 LINEAR SYSTEMS Lecure : Riccai Equaions and Leas Squares Feedback Conrol 5.6.4 Sae Feedback via Riccai Equaions A recursive approach in generaing he marix-valued funcion W ( ) equaion for i for he
More informationImproved Approximate Solutions for Nonlinear Evolutions Equations in Mathematical Physics Using the Reduced Differential Transform Method
Journal of Applied Mahemaics & Bioinformaics, vol., no., 01, 1-14 ISSN: 179-660 (prin), 179-699 (online) Scienpress Ld, 01 Improved Approimae Soluions for Nonlinear Evoluions Equaions in Mahemaical Physics
More informationGENERALIZATION OF THE FORMULA OF FAA DI BRUNO FOR A COMPOSITE FUNCTION WITH A VECTOR ARGUMENT
Inerna J Mah & Mah Sci Vol 4, No 7 000) 48 49 S0670000970 Hindawi Publishing Corp GENERALIZATION OF THE FORMULA OF FAA DI BRUNO FOR A COMPOSITE FUNCTION WITH A VECTOR ARGUMENT RUMEN L MISHKOV Received
More informationCorrespondence should be addressed to Nguyen Buong,
Hindawi Publishing Corporaion Fixed Poin Theory and Applicaions Volume 011, Aricle ID 76859, 10 pages doi:101155/011/76859 Research Aricle An Implici Ieraion Mehod for Variaional Inequaliies over he Se
More informationSupplement for Stochastic Convex Optimization: Faster Local Growth Implies Faster Global Convergence
Supplemen for Sochasic Convex Opimizaion: Faser Local Growh Implies Faser Global Convergence Yi Xu Qihang Lin ianbao Yang Proof of heorem heorem Suppose Assumpion holds and F (w) obeys he LGC (6) Given
More informationOscillation of an Euler Cauchy Dynamic Equation S. Huff, G. Olumolode, N. Pennington, and A. Peterson
PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS May 4 7, 00, Wilmingon, NC, USA pp 0 Oscillaion of an Euler Cauchy Dynamic Equaion S Huff, G Olumolode,
More informationHaar Wavelet Operational Matrix Method for Solving Fractional Partial Differential Equations
Copyrigh 22 Tech Science Press CMES, vol.88, no.3, pp.229-243, 22 Haar Wavele Operaional Mari Mehod for Solving Fracional Parial Differenial Equaions Mingu Yi and Yiming Chen Absrac: In his paper, Haar
More informationCourse Notes for EE227C (Spring 2018): Convex Optimization and Approximation
Course Noes for EE7C Spring 018: Convex Opimizaion and Approximaion Insrucor: Moriz Hard Email: hard+ee7c@berkeley.edu Graduae Insrucor: Max Simchowiz Email: msimchow+ee7c@berkeley.edu Ocober 15, 018 3
More informationarxiv: v1 [math.pr] 19 Feb 2011
A NOTE ON FELLER SEMIGROUPS AND RESOLVENTS VADIM KOSTRYKIN, JÜRGEN POTTHOFF, AND ROBERT SCHRADER ABSTRACT. Various equivalen condiions for a semigroup or a resolven generaed by a Markov process o be of
More informationVariational Iteration Method for Solving System of Fractional Order Ordinary Differential Equations
IOSR Journal of Mahemaics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 1, Issue 6 Ver. II (Nov - Dec. 214), PP 48-54 Variaional Ieraion Mehod for Solving Sysem of Fracional Order Ordinary Differenial
More informationSome New Uniqueness Results of Solutions to Nonlinear Fractional Integro-Differential Equations
Annals of Pure and Applied Mahemaics Vol. 6, No. 2, 28, 345-352 ISSN: 2279-87X (P), 2279-888(online) Published on 22 February 28 www.researchmahsci.org DOI: hp://dx.doi.org/.22457/apam.v6n2a Annals of
More informationApplying Genetic Algorithms for Inventory Lot-Sizing Problem with Supplier Selection under Storage Capacity Constraints
IJCSI Inernaional Journal of Compuer Science Issues, Vol 9, Issue 1, No 1, January 2012 wwwijcsiorg 18 Applying Geneic Algorihms for Invenory Lo-Sizing Problem wih Supplier Selecion under Sorage Capaciy
More informationRoughness in ordered Semigroups. Muhammad Shabir and Shumaila Irshad
World Applied Sciences Journal 22 (Special Issue of Applied Mah): 84-105, 2013 ISSN 1818-4952 IDOSI Publicaions, 2013 DOI: 105829/idosiwasj22am102013 Roughness in ordered Semigroups Muhammad Shabir and
More informationApplication of a Stochastic-Fuzzy Approach to Modeling Optimal Discrete Time Dynamical Systems by Using Large Scale Data Processing
Applicaion of a Sochasic-Fuzzy Approach o Modeling Opimal Discree Time Dynamical Sysems by Using Large Scale Daa Processing AA WALASZE-BABISZEWSA Deparmen of Compuer Engineering Opole Universiy of Technology
More information3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon
3..3 INRODUCION O DYNAMIC OPIMIZAION: DISCREE IME PROBLEMS A. he Hamilonian and Firs-Order Condiions in a Finie ime Horizon Define a new funcion, he Hamilonian funcion, H. H he change in he oal value of
More informationEssential Maps and Coincidence Principles for General Classes of Maps
Filoma 31:11 (2017), 3553 3558 hps://doi.org/10.2298/fil1711553o Published by Faculy of Sciences Mahemaics, Universiy of Niš, Serbia Available a: hp://www.pmf.ni.ac.rs/filoma Essenial Maps Coincidence
More informationApplication of He s Variational Iteration Method for Solving Seventh Order Sawada-Kotera Equations
Applied Mahemaical Sciences, Vol. 2, 28, no. 1, 471-477 Applicaion of He s Variaional Ieraion Mehod for Solving Sevenh Order Sawada-Koera Equaions Hossein Jafari a,1, Allahbakhsh Yazdani a, Javad Vahidi
More informationAnn. Funct. Anal. 2 (2011), no. 2, A nnals of F unctional A nalysis ISSN: (electronic) URL:
Ann. Func. Anal. 2 2011, no. 2, 34 41 A nnals of F uncional A nalysis ISSN: 2008-8752 elecronic URL: www.emis.de/journals/afa/ CLASSIFICAION OF POSIIVE SOLUIONS OF NONLINEAR SYSEMS OF VOLERRA INEGRAL EQUAIONS
More informationA Primal-Dual Type Algorithm with the O(1/t) Convergence Rate for Large Scale Constrained Convex Programs
PROC. IEEE CONFERENCE ON DECISION AND CONTROL, 06 A Primal-Dual Type Algorihm wih he O(/) Convergence Rae for Large Scale Consrained Convex Programs Hao Yu and Michael J. Neely Absrac This paper considers
More informationAPPLICATION OF CHEBYSHEV APPROXIMATION IN THE PROCESS OF VARIATIONAL ITERATION METHOD FOR SOLVING DIFFERENTIAL- ALGEBRAIC EQUATIONS
Mahemaical and Compuaional Applicaions, Vol., No. 4, pp. 99-978,. Associaion for Scienific Research APPLICATION OF CHEBYSHEV APPROXIMATION IN THE PROCESS OF VARIATIONAL ITERATION METHOD FOR SOLVING DIFFERENTIAL-
More informationTO our knowledge, most exciting results on the existence
IAENG Inernaional Journal of Applied Mahemaics, 42:, IJAM_42 2 Exisence and Uniqueness of a Periodic Soluion for hird-order Delay Differenial Equaion wih wo Deviaing Argumens A. M. A. Abou-El-Ela, A. I.
More informationSUFFICIENT CONDITIONS FOR EXISTENCE SOLUTION OF LINEAR TWO-POINT BOUNDARY PROBLEM IN MINIMIZATION OF QUADRATIC FUNCTIONAL
HE PUBLISHING HOUSE PROCEEDINGS OF HE ROMANIAN ACADEMY, Series A, OF HE ROMANIAN ACADEMY Volume, Number 4/200, pp 287 293 SUFFICIEN CONDIIONS FOR EXISENCE SOLUION OF LINEAR WO-POIN BOUNDARY PROBLEM IN
More informationInequality measures for intersecting Lorenz curves: an alternative weak ordering
h Inernaional Scienific Conference Financial managemen of Firms and Financial Insiuions Osrava VŠB-TU of Osrava, Faculy of Economics, Deparmen of Finance 7 h 8 h Sepember 25 Absrac Inequaliy measures for
More information11!Hí MATHEMATICS : ERDŐS AND ULAM PROC. N. A. S. of decomposiion, properly speaking) conradics he possibiliy of defining a counably addiive real-valu
ON EQUATIONS WITH SETS AS UNKNOWNS BY PAUL ERDŐS AND S. ULAM DEPARTMENT OF MATHEMATICS, UNIVERSITY OF COLORADO, BOULDER Communicaed May 27, 1968 We shall presen here a number of resuls in se heory concerning
More informationHomotopy Perturbation Method for Solving Some Initial Boundary Value Problems with Non Local Conditions
Proceedings of he World Congress on Engineering and Compuer Science 23 Vol I WCECS 23, 23-25 Ocober, 23, San Francisco, USA Homoopy Perurbaion Mehod for Solving Some Iniial Boundary Value Problems wih
More informationAn introduction to the theory of SDDP algorithm
An inroducion o he heory of SDDP algorihm V. Leclère (ENPC) Augus 1, 2014 V. Leclère Inroducion o SDDP Augus 1, 2014 1 / 21 Inroducion Large scale sochasic problem are hard o solve. Two ways of aacking
More informationOptimality Conditions for Unconstrained Problems
62 CHAPTER 6 Opimaliy Condiions for Unconsrained Problems 1 Unconsrained Opimizaion 11 Exisence Consider he problem of minimizing he funcion f : R n R where f is coninuous on all of R n : P min f(x) x
More informationCHARACTERIZATION OF REARRANGEMENT INVARIANT SPACES WITH FIXED POINTS FOR THE HARDY LITTLEWOOD MAXIMAL OPERATOR
Annales Academiæ Scieniarum Fennicæ Mahemaica Volumen 31, 2006, 39 46 CHARACTERIZATION OF REARRANGEMENT INVARIANT SPACES WITH FIXED POINTS FOR THE HARDY LITTLEWOOD MAXIMAL OPERATOR Joaquim Marín and Javier
More informationMonotonic Solutions of a Class of Quadratic Singular Integral Equations of Volterra type
In. J. Conemp. Mah. Sci., Vol. 2, 27, no. 2, 89-2 Monoonic Soluions of a Class of Quadraic Singular Inegral Equaions of Volerra ype Mahmoud M. El Borai Deparmen of Mahemaics, Faculy of Science, Alexandria
More information4.2 The Fourier Transform
4.2. THE FOURIER TRANSFORM 57 4.2 The Fourier Transform 4.2.1 Inroducion One way o look a Fourier series is ha i is a ransformaion from he ime domain o he frequency domain. Given a signal f (), finding
More informationInternational Journal of Scientific & Engineering Research, Volume 4, Issue 10, October ISSN
Inernaional Journal of Scienific & Engineering Research, Volume 4, Issue 10, Ocober-2013 900 FUZZY MEAN RESIDUAL LIFE ORDERING OF FUZZY RANDOM VARIABLES J. EARNEST LAZARUS PIRIYAKUMAR 1, A. YAMUNA 2 1.
More informationChapter 2. First Order Scalar Equations
Chaper. Firs Order Scalar Equaions We sar our sudy of differenial equaions in he same way he pioneers in his field did. We show paricular echniques o solve paricular ypes of firs order differenial equaions.
More information1 Review of Zero-Sum Games
COS 5: heoreical Machine Learning Lecurer: Rob Schapire Lecure #23 Scribe: Eugene Brevdo April 30, 2008 Review of Zero-Sum Games Las ime we inroduced a mahemaical model for wo player zero-sum games. Any
More information4. Advanced Stability Theory
Applied Nonlinear Conrol Nguyen an ien - 4 4 Advanced Sabiliy heory he objecive of his chaper is o presen sabiliy analysis for non-auonomous sysems 41 Conceps of Sabiliy for Non-Auonomous Sysems Equilibrium
More informationMixing times and hitting times: lecture notes
Miing imes and hiing imes: lecure noes Yuval Peres Perla Sousi 1 Inroducion Miing imes and hiing imes are among he mos fundamenal noions associaed wih a finie Markov chain. A variey of ools have been developed
More informationSTATE-SPACE MODELLING. A mass balance across the tank gives:
B. Lennox and N.F. Thornhill, 9, Sae Space Modelling, IChemE Process Managemen and Conrol Subjec Group Newsleer STE-SPACE MODELLING Inroducion: Over he pas decade or so here has been an ever increasing
More informationON THE DEGREES OF RATIONAL KNOTS
ON THE DEGREES OF RATIONAL KNOTS DONOVAN MCFERON, ALEXANDRA ZUSER Absrac. In his paper, we explore he issue of minimizing he degrees on raional knos. We se a bound on hese degrees using Bézou s heorem,
More informationA NOTE ON THE STRUCTURE OF BILATTICES. A. Avron. School of Mathematical Sciences. Sackler Faculty of Exact Sciences. Tel Aviv University
A NOTE ON THE STRUCTURE OF BILATTICES A. Avron School of Mahemaical Sciences Sacler Faculy of Exac Sciences Tel Aviv Universiy Tel Aviv 69978, Israel The noion of a bilaice was rs inroduced by Ginsburg
More information2. Nonlinear Conservation Law Equations
. Nonlinear Conservaion Law Equaions One of he clear lessons learned over recen years in sudying nonlinear parial differenial equaions is ha i is generally no wise o ry o aack a general class of nonlinear
More informationTechnical Report Doc ID: TR March-2013 (Last revision: 23-February-2016) On formulating quadratic functions in optimization models.
Technical Repor Doc ID: TR--203 06-March-203 (Las revision: 23-Februar-206) On formulaing quadraic funcions in opimizaion models. Auhor: Erling D. Andersen Convex quadraic consrains quie frequenl appear
More informationNumerical Solution of Fractional Variational Problems Using Direct Haar Wavelet Method
ISSN: 39-8753 Engineering and echnology (An ISO 397: 7 Cerified Organizaion) Vol. 3, Issue 5, May 4 Numerical Soluion of Fracional Variaional Problems Using Direc Haar Wavele Mehod Osama H. M., Fadhel
More informationarxiv: v1 [math.fa] 9 Dec 2018
AN INVERSE FUNCTION THEOREM CONVERSE arxiv:1812.03561v1 [mah.fa] 9 Dec 2018 JIMMIE LAWSON Absrac. We esablish he following converse of he well-known inverse funcion heorem. Le g : U V and f : V U be inverse
More informationANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 6 SECTION 6.1: LIFE CYCLE CONSUMPTION AND WEALTH T 1. . Let ct. ) is a strictly concave function of c
John Riley December 00 S O EVEN NUMBERED EXERCISES IN CHAPER 6 SECION 6: LIFE CYCLE CONSUMPION AND WEALH Eercise 6-: Opimal saving wih more han one commodiy A consumer has a period uiliy funcion δ u (
More informationSPECTRAL EVOLUTION OF A ONE PARAMETER EXTENSION OF A REAL SYMMETRIC TOEPLITZ MATRIX* William F. Trench. SIAM J. Matrix Anal. Appl. 11 (1990),
SPECTRAL EVOLUTION OF A ONE PARAMETER EXTENSION OF A REAL SYMMETRIC TOEPLITZ MATRIX* William F Trench SIAM J Marix Anal Appl 11 (1990), 601-611 Absrac Le T n = ( i j ) n i,j=1 (n 3) be a real symmeric
More informationMathematical Theory and Modeling ISSN (Paper) ISSN (Online) Vol 3, No.3, 2013
Mahemaical Theory and Modeling ISSN -580 (Paper) ISSN 5-05 (Online) Vol, No., 0 www.iise.org The ffec of Inverse Transformaion on he Uni Mean and Consan Variance Assumpions of a Muliplicaive rror Model
More informationAn Excursion into Set Theory using a Constructivist Approach
An Excursion ino Se Theory using a Consrucivis Approach Miderm Repor Nihil Pail under supervision of Ksenija Simic Fall 2005 Absrac Consrucive logic is an alernaive o he heory of classical logic ha draws
More informationRANDOM LAGRANGE MULTIPLIERS AND TRANSVERSALITY
ECO 504 Spring 2006 Chris Sims RANDOM LAGRANGE MULTIPLIERS AND TRANSVERSALITY 1. INTRODUCTION Lagrange muliplier mehods are sandard fare in elemenary calculus courses, and hey play a cenral role in economic
More informationThis document was generated at 1:04 PM, 09/10/13 Copyright 2013 Richard T. Woodward. 4. End points and transversality conditions AGEC
his documen was generaed a 1:4 PM, 9/1/13 Copyrigh 213 Richard. Woodward 4. End poins and ransversaliy condiions AGEC 637-213 F z d Recall from Lecure 3 ha a ypical opimal conrol problem is o maimize (,,
More informationThe Stacked Semi-Groups and Fuzzy Stacked Systems on Transportation Models
Inernaional Journal of Scienific and Research Publicaions, Volume 4, Issue 8, Augus 2014 1 The Sacked Semi-Groups and Fuzzy Sacked Sysems on Transporaion Models Aymen. A. Ahmed Imam *, Mohammed Ali Bshir
More informationFractional Method of Characteristics for Fractional Partial Differential Equations
Fracional Mehod of Characerisics for Fracional Parial Differenial Equaions Guo-cheng Wu* Modern Teile Insiue, Donghua Universiy, 188 Yan-an ilu Road, Shanghai 51, PR China Absrac The mehod of characerisics
More informationStochastic Model for Cancer Cell Growth through Single Forward Mutation
Journal of Modern Applied Saisical Mehods Volume 16 Issue 1 Aricle 31 5-1-2017 Sochasic Model for Cancer Cell Growh hrough Single Forward Muaion Jayabharahiraj Jayabalan Pondicherry Universiy, jayabharahi8@gmail.com
More informationCHAPTER 2: Mathematics for Microeconomics
CHAPTER : Mahemaics for Microeconomics The problems in his chaper are primarily mahemaical. They are inended o give sudens some pracice wih he conceps inroduced in Chaper, bu he problems in hemselves offer
More informationSolutions from Chapter 9.1 and 9.2
Soluions from Chaper 9 and 92 Secion 9 Problem # This basically boils down o an exercise in he chain rule from calculus We are looking for soluions of he form: u( x) = f( k x c) where k x R 3 and k is
More informationCharacterization of Gamma Hemirings by Generalized Fuzzy Gamma Ideals
Available a hp://pvamu.edu/aam Appl. Appl. Mah. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 495-520 Applicaions and Applied Mahemaics: An Inernaional Journal (AAM) Characerizaion of Gamma Hemirings
More informationA Forward-Backward Splitting Method with Component-wise Lazy Evaluation for Online Structured Convex Optimization
A Forward-Backward Spliing Mehod wih Componen-wise Lazy Evaluaion for Online Srucured Convex Opimizaion Yukihiro Togari and Nobuo Yamashia March 28, 2016 Absrac: We consider large-scale opimizaion problems
More informationMath 315: Linear Algebra Solutions to Assignment 6
Mah 35: Linear Algebra s o Assignmen 6 # Which of he following ses of vecors are bases for R 2? {2,, 3, }, {4,, 7, 8}, {,,, 3}, {3, 9, 4, 2}. Explain your answer. To generae he whole R 2, wo linearly independen
More informationCHAPTER 2 Signals And Spectra
CHAPER Signals And Specra Properies of Signals and Noise In communicaion sysems he received waveform is usually caegorized ino he desired par conaining he informaion, and he undesired par. he desired par
More informationA Specification Test for Linear Dynamic Stochastic General Equilibrium Models
Journal of Saisical and Economeric Mehods, vol.1, no.2, 2012, 65-70 ISSN: 2241-0384 (prin), 2241-0376 (online) Scienpress Ld, 2012 A Specificaion Tes for Linear Dynamic Sochasic General Equilibrium Models
More informationExistence of positive solution for a third-order three-point BVP with sign-changing Green s function
Elecronic Journal of Qualiaive Theory of Differenial Equaions 13, No. 3, 1-11; hp://www.mah.u-szeged.hu/ejqde/ Exisence of posiive soluion for a hird-order hree-poin BVP wih sign-changing Green s funcion
More informationSPLICING OF TIME OPTIMAL CONTROLS
Dynamic Sysems and Applicaions 21 (212) 169-186 SPLICING OF TIME OPTIMAL CONTROLS H. O. FATTORINI Deparmen of Mahemaics, Universiy of California Los Angeles, California 995-1555, USA ABSTRACT. Two conrols
More informationA Hop Constrained Min-Sum Arborescence with Outage Costs
A Hop Consrained Min-Sum Arborescence wih Ouage Coss Rakesh Kawara Minnesoa Sae Universiy, Mankao, MN 56001 Email: Kawara@mnsu.edu Absrac The hop consrained min-sum arborescence wih ouage coss problem
More informationExistence Theory of Second Order Random Differential Equations
Global Journal of Mahemaical Sciences: Theory and Pracical. ISSN 974-32 Volume 4, Number 3 (22), pp. 33-3 Inernaional Research Publicaion House hp://www.irphouse.com Exisence Theory of Second Order Random
More informationThe Optimal Stopping Time for Selling an Asset When It Is Uncertain Whether the Price Process Is Increasing or Decreasing When the Horizon Is Infinite
American Journal of Operaions Research, 08, 8, 8-9 hp://wwwscirporg/journal/ajor ISSN Online: 60-8849 ISSN Prin: 60-8830 The Opimal Sopping Time for Selling an Asse When I Is Uncerain Wheher he Price Process
More informationL-fuzzy valued measure and integral
USFLAT-LFA 2011 July 2011 Aix-les-Bains, France L-fuzzy valued measure and inegral Vecislavs Ruza, 1 Svelana Asmuss 1,2 1 Universiy of Lavia, Deparmen of ahemaics 2 Insiue of ahemaics and Compuer Science
More informationVehicle Arrival Models : Headway
Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where
More informationCash Flow Valuation Mode Lin Discrete Time
IOSR Journal of Mahemaics (IOSR-JM) e-issn: 2278-5728,p-ISSN: 2319-765X, 6, Issue 6 (May. - Jun. 2013), PP 35-41 Cash Flow Valuaion Mode Lin Discree Time Olayiwola. M. A. and Oni, N. O. Deparmen of Mahemaics
More informationIntuitionistic Fuzzy 2-norm
In. Journal of Mah. Analysis, Vol. 5, 2011, no. 14, 651-659 Inuiionisic Fuzzy 2-norm B. Surender Reddy Deparmen of Mahemaics, PGCS, Saifabad, Osmania Universiy Hyderabad - 500004, A.P., India bsrmahou@yahoo.com
More informationBBP-type formulas, in general bases, for arctangents of real numbers
Noes on Number Theory and Discree Mahemaics Vol. 19, 13, No. 3, 33 54 BBP-ype formulas, in general bases, for arcangens of real numbers Kunle Adegoke 1 and Olawanle Layeni 2 1 Deparmen of Physics, Obafemi
More informationUndetermined coefficients for local fractional differential equations
Available online a www.isr-publicaions.com/jmcs J. Mah. Compuer Sci. 16 (2016), 140 146 Research Aricle Undeermined coefficiens for local fracional differenial equaions Roshdi Khalil a,, Mohammed Al Horani
More informationThe Contradiction within Equations of Motion with Constant Acceleration
The Conradicion wihin Equaions of Moion wih Consan Acceleraion Louai Hassan Elzein Basheir (Daed: July 7, 0 This paper is prepared o demonsrae he violaion of rules of mahemaics in he algebraic derivaion
More informationSolution of Integro-Differential Equations by Using ELzaki Transform
Global Journal of Mahemaical Sciences: Theory and Pracical. Volume, Number (), pp. - Inernaional Research Publicaion House hp://www.irphouse.com Soluion of Inegro-Differenial Equaions by Using ELzaki Transform
More informationLecture Notes 2. The Hilbert Space Approach to Time Series
Time Series Seven N. Durlauf Universiy of Wisconsin. Basic ideas Lecure Noes. The Hilber Space Approach o Time Series The Hilber space framework provides a very powerful language for discussing he relaionship
More informationAn Introduction to Malliavin calculus and its applications
An Inroducion o Malliavin calculus and is applicaions Lecure 5: Smoohness of he densiy and Hörmander s heorem David Nualar Deparmen of Mahemaics Kansas Universiy Universiy of Wyoming Summer School 214
More informationLinear Response Theory: The connection between QFT and experiments
Phys540.nb 39 3 Linear Response Theory: The connecion beween QFT and experimens 3.1. Basic conceps and ideas Q: How do we measure he conduciviy of a meal? A: we firs inroduce a weak elecric field E, and
More informationFinal Spring 2007
.615 Final Spring 7 Overview The purpose of he final exam is o calculae he MHD β limi in a high-bea oroidal okamak agains he dangerous n = 1 exernal ballooning-kink mode. Effecively, his corresponds o
More informationPhysics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle
Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,
More informationParticle Swarm Optimization Combining Diversification and Intensification for Nonlinear Integer Programming Problems
Paricle Swarm Opimizaion Combining Diversificaion and Inensificaion for Nonlinear Ineger Programming Problems Takeshi Masui, Masaoshi Sakawa, Kosuke Kao and Koichi Masumoo Hiroshima Universiy 1-4-1, Kagamiyama,
More information10. State Space Methods
. Sae Space Mehods. Inroducion Sae space modelling was briefly inroduced in chaper. Here more coverage is provided of sae space mehods before some of heir uses in conrol sysem design are covered in he
More informationBOUNDEDNESS OF MAXIMAL FUNCTIONS ON NON-DOUBLING MANIFOLDS WITH ENDS
BOUNDEDNESS OF MAXIMAL FUNCTIONS ON NON-DOUBLING MANIFOLDS WITH ENDS XUAN THINH DUONG, JI LI, AND ADAM SIKORA Absrac Le M be a manifold wih ends consruced in [2] and be he Laplace-Belrami operaor on M
More informationA New Kind of Fuzzy Sublattice (Ideal, Filter) of A Lattice
nernaional Journal of Fuzzy Sysems Vol 3 No March 2 55 A New Kind of Fuzzy Sublaice (deal Filer) of A Laice B Davvaz O Kazanci Absrac Our aim in his paper is o inroduce sudy a new sor of fuzzy sublaice
More informationAppendix to Online l 1 -Dictionary Learning with Application to Novel Document Detection
Appendix o Online l -Dicionary Learning wih Applicaion o Novel Documen Deecion Shiva Prasad Kasiviswanahan Huahua Wang Arindam Banerjee Prem Melville A Background abou ADMM In his secion, we give a brief
More informationOn Gronwall s Type Integral Inequalities with Singular Kernels
Filoma 31:4 (217), 141 149 DOI 1.2298/FIL17441A Published by Faculy of Sciences and Mahemaics, Universiy of Niš, Serbia Available a: hp://www.pmf.ni.ac.rs/filoma On Gronwall s Type Inegral Inequaliies
More informationSOME MORE APPLICATIONS OF THE HAHN-BANACH THEOREM
SOME MORE APPLICATIONS OF THE HAHN-BANACH THEOREM FRANCISCO JAVIER GARCÍA-PACHECO, DANIELE PUGLISI, AND GUSTI VAN ZYL Absrac We give a new proof of he fac ha equivalen norms on subspaces can be exended
More informationRandom Walk with Anti-Correlated Steps
Random Walk wih Ani-Correlaed Seps John Noga Dirk Wagner 2 Absrac We conjecure he expeced value of random walks wih ani-correlaed seps o be exacly. We suppor his conjecure wih 2 plausibiliy argumens and
More informationHeat kernel and Harnack inequality on Riemannian manifolds
Hea kernel and Harnack inequaliy on Riemannian manifolds Alexander Grigor yan UHK 11/02/2014 onens 1 Laplace operaor and hea kernel 1 2 Uniform Faber-Krahn inequaliy 3 3 Gaussian upper bounds 4 4 ean-value
More informationOn Measuring Pro-Poor Growth. 1. On Various Ways of Measuring Pro-Poor Growth: A Short Review of the Literature
On Measuring Pro-Poor Growh 1. On Various Ways of Measuring Pro-Poor Growh: A Shor eview of he Lieraure During he pas en years or so here have been various suggesions concerning he way one should check
More information1.1. Example: Polynomial Curve Fitting 4 1. INTRODUCTION
4. INTRODUCTION Figure.2 Plo of a raining daa se of N = poins, shown as blue circles, each comprising an observaion of he inpu variable along wih he corresponding arge variable. The green curve shows he
More informationOn the Solutions of First and Second Order Nonlinear Initial Value Problems
Proceedings of he World Congress on Engineering 13 Vol I, WCE 13, July 3-5, 13, London, U.K. On he Soluions of Firs and Second Order Nonlinear Iniial Value Problems Sia Charkri Absrac In his paper, we
More informationThe Application of Optimal Homotopy Asymptotic Method for One-Dimensional Heat and Advection- Diffusion Equations
Inf. Sci. Le., No., 57-61 13) 57 Informaion Sciences Leers An Inernaional Journal hp://d.doi.org/1.1785/isl/ The Applicaion of Opimal Homoopy Asympoic Mehod for One-Dimensional Hea and Advecion- Diffusion
More information23.5. Half-Range Series. Introduction. Prerequisites. Learning Outcomes
Half-Range Series 2.5 Inroducion In his Secion we address he following problem: Can we find a Fourier series expansion of a funcion defined over a finie inerval? Of course we recognise ha such a funcion
More informationPositive continuous solution of a quadratic integral equation of fractional orders
Mah. Sci. Le., No., 9-7 (3) 9 Mahemaical Sciences Leers An Inernaional Journal @ 3 NSP Naural Sciences Publishing Cor. Posiive coninuous soluion of a quadraic inegral equaion of fracional orders A. M.
More informationarxiv: v1 [math.ca] 15 Nov 2016
arxiv:6.599v [mah.ca] 5 Nov 26 Counerexamples on Jumarie s hree basic fracional calculus formulae for non-differeniable coninuous funcions Cheng-shi Liu Deparmen of Mahemaics Norheas Peroleum Universiy
More information12: AUTOREGRESSIVE AND MOVING AVERAGE PROCESSES IN DISCRETE TIME. Σ j =
1: AUTOREGRESSIVE AND MOVING AVERAGE PROCESSES IN DISCRETE TIME Moving Averages Recall ha a whie noise process is a series { } = having variance σ. The whie noise process has specral densiy f (λ) = of
More informationRobotics I. April 11, The kinematics of a 3R spatial robot is specified by the Denavit-Hartenberg parameters in Tab. 1.
Roboics I April 11, 017 Exercise 1 he kinemaics of a 3R spaial robo is specified by he Denavi-Harenberg parameers in ab 1 i α i d i a i θ i 1 π/ L 1 0 1 0 0 L 3 0 0 L 3 3 able 1: able of DH parameers of
More informationMean-square Stability Control for Networked Systems with Stochastic Time Delay
JOURNAL OF SIMULAION VOL. 5 NO. May 7 Mean-square Sabiliy Conrol for Newored Sysems wih Sochasic ime Delay YAO Hejun YUAN Fushun School of Mahemaics and Saisics Anyang Normal Universiy Anyang Henan. 455
More informationProduct of Fuzzy Metric Spaces and Fixed Point Theorems
In. J. Conemp. Mah. Sciences, Vol. 3, 2008, no. 15, 703-712 Produc of Fuzzy Meric Spaces and Fixed Poin Theorems Mohd. Rafi Segi Rahma School of Applied Mahemaics The Universiy of Noingham Malaysia Campus
More informationCONTRIBUTION TO IMPULSIVE EQUATIONS
European Scienific Journal Sepember 214 /SPECIAL/ ediion Vol.3 ISSN: 1857 7881 (Prin) e - ISSN 1857-7431 CONTRIBUTION TO IMPULSIVE EQUATIONS Berrabah Faima Zohra, MA Universiy of sidi bel abbes/ Algeria
More information