IRANIAN CONFERENCE ON APPLIED MATHEMATICS | Year:2013 | دوره:5 |Papers Count:123

ONE OF THE CRITICAL ISSUES IN SENSOR NETWORKS IS ENERGY CONSUMPTION. SINCE THE NODES HAVE THE EXTRA BURDEN OF COORDINATION, ENERGY RESOURCES IN SUCH NODES WILL DRAIN OUT MORE QUICKLY THAN IN OTHER NODES. TO MAXIMIZE THE LIFETIME OF NODES IN THE NETWORK, IT HAS BEEN PROPOSED THAT THE ROLE OF COORDINATORS BE ROTATED AMONG THE NODES IN THE NETWORK. BUT THIS ROTATION SHOULD BE IN SUCH A WAY THAT ENERGY CONVERSATION AND DATA GATHERING WERE SAFE AND CONTINUES. IN THIS PAPER WE MODEL COORDINATOR NODES AS A DOMINATING SET AND GIVE AN INTEGER PROGRAMMING BASED METHOD TO FIND THEM. FINALLY, WE PROVIDE AN ALGORITHM WHICH TRANSFERS ANY COORDINATOR NODES TO OTHER COORDINATOR NODES IN A SAFE AND CONTINUES WAY, WITHOUT ANY DISCONNECTION.

THE PRODUCTION POSSIBILITY SET IN DATA ENVELOPMENT ANALYSIS IS DEFINED BY THE INTERSECTION OF SOME HALF SPACES WHICH ARE CONSTRUCTED BY DEFINING HYPER PLANES. THESE DEFINING HYPER PLANES ARE INCLUDED MAXIMAL EFFICIENT FACES OF THE PRODUCTION POSSIBILITY SET. BECAUSE OF THE IMPORTANCE OF THE CHARACTERIZATIONS OF THE PRODUCTION POSSIBILITY SETS IN DATA ENVELOPMENT ANALYSIS WE SUGGEST A NEW METHOD TO IDENTIFY ALL MAXIMAL EFFICIENT FACES OF THE PRODUCTION POSSIBILITY SET.

IN THIS PAPER, WE PRESENT A HIGH ACCURATE SPECTRAL APPROXIMATION FOR SOLVING SHORTEST PATH PROBLEMS WITH BOUNDARY AND INTERIOR BARRIERS. FOR THIS PURPOSE, THE SHORTEST PATH PROBLEMS ARE MODELED AS VARIATIONAL PROBLEMS (VPS). THEN, THE LEGENDRE POLYNOMIALS ARE USED AS A BASIS FOR APPROXIMATING THE SOLUTION OF THESE PROBLEMS, AND BY USING CHEBYSHEV GAUSS LOBATTO (CGL) COLLOCATION POINTS TOGETHER WITH LEGENDRE GAUSS QUADRATURE RULE, THE VPS WILL BE CHANGED INTO NONLINEAR PROGRAMMING PROBLEMS (NLPS). THE RESULTING NLPS ARE SOLVED BY NLPSOLVE COMMAND IN MAPLE SOFTWARE. TWO NUMERICAL EXAMPLES ARE PROVIDED FOR SHOWING THE ROBUSTNESS OF THE PROPOSED METHOD WITH REGARD TO OTHER METHODS IN THE LITERATURE.

IN THIS PAPER, WE COMPUTE AN ERROR BOUND FOR THE NUMERICAL SOLUTION OF NONLINEAR FREDHOLM-HAMMERSTEIN INTEGRAL EQUATIONS. A COMBINATION OF CHEBYSHEV POLYNOMIALS AND BLOCK-PULSE FUNCTIONS AS HYBRID FUNCTIONS (HFS) IS CONSIDERED AND ITS UNIFORM CONVERGENCE IS ALSO INVESTIGATED. WE PROPOSE THAT THE AVAILABLE OPTIMAL VALUES OF N AND M CAN MINIMIZE THE RELATIVE ERRORS OF THE NUMERICAL SOLUTIONS. OUR NUMERICAL EXPERIMENTS SHOW THE SUPERIORITY AND ACCURACY OF THE HYBRID FUNCTIONS METHOD IN COMPARISON WITH THE BLOCK-PULSE FUNCTIONS AND CHEBYSHEV POLYNOMIALS METHODS.

IN THIS ARTICLE, WE INTRODUCE AN ITERATIVE METHOD FOR FINDING A COMMON ELEMENT OF SET OF FIXED POINTS OF THESE MAPPINGS AND THE SET OF SOLUTIONS OF A GENERALIZED EQUILIBRIUM PROBLEM IN A HILBERT SPACE. IN THIS PROPOSED ITERATION WE OBTAIN CONVERGENCE THEOREMS IN A HILBERT SPACE.

IN THIS ARTICLE, WE INVESTIGATE THE EXISTENCE A SOLUTION IN A CONVEX COMPLETE METRIC SPACE FOR THE FUNCTIONAL EQUATIONS AND THE SYSTEMS WHICH HAVE CERTAIN PROPERTIES. MOREOVER, BY CONSIDERING ONE ADDITIONAL CONDITION, WE SHOW THAT THE SOLUTION IS UNIQUE.

IN THE LAST FEW YEARS WE HAVE SEEN A VERY RAPID DEVELOPMENT ON SOLVING GENERALIZED GEOMETRIC PROGRAMMING (GGP) PROBLEMS, BUT SO FAR LESS WORKS HAS BEEN DEVOTED TO MOGP DUE TO THE INHERENT DIFFICULTY WHICH MAY ARISE IN SOLVING SUCH PROBLEMS. OUR AIM IN THIS PAPER IS TO CONSIDER THE PROBLEM OF MULTI-OBJECTIVE GEOMETRIC PROGRAMMING (MOGP) AND SOLVE THE PROBLEMS VIA TWO-LEVEL RELAXED LINEAR PROGRAMMING PROBLEMS AND THAT IS DUE TO SIMPLICITY WHICH OCCURS THROUGH LINEARIZATION I.ETRANSORMING A GP TO LP. IN THIS APPROACH EACH OF THE OBJECTIVE FUNCTIONS IN MULTI-OBJECTIVE GEOMETRIC PROGRAMMING IS INDIVIDUALLY LINEARIZED USING TWO-LEVEL LINEAR RELAXED BOUND METHOD, WHICH PROVIDES A LOWER BOUND FOR THE OPTIMAL VALUES. FINALLY OUR MOGP IS TRANSFORMED IN TO A MULTIOBJECTIVE LINEAR PROGRAMMING PROBLEM (MOLP) WHICH IS SOLVED BY REFERENCE POINT APPROACH.

IN THIS PAPER, A NEW OPERATIONAL METHOD BASED ON HYBRID FUNCTIONS OF LEGENDRE POLYNOMIALS AND BLOCK-PULSE-FUNCTIONS (BPFS) IS PROPOSED TO SOLVE AN ABEL INTEGRAL EQUATION. THE OPERATIONAL MATRIX OF FRACTIONAL INTEGRATION OF HYBRID FUNCTIONS IS OBTAINED. A NUMERICAL EXAMPLE SHOWS THE APPLICABILITY OF THE METHOD.

CALCULATIONS OF GREEN’S FUNCTION IN NANO RESEARCHES NEED TO SOLVE A SPECIAL CASE OF NONLINEAR MATRIX EQUATIONS, NUMERICALLY. THE SOLUTION OF INTEREST IN NANO APPLICATIONS IS A SPECIAL WEEKLY STABILIZING COMPLEX SYMMETRIC SOLUTION. IN THIS PAPER, WE PRESENT DOUBLING ALGORITHM METHOD FOR THIS PROPOSES. ALSO WE SHOW HOW THIS METHOD CAN BE USED TO FIND GOOD APPROXIMATE SOLUTIONS, EFFICIENTLY AND RELIABLY. IN A NUMERICAL EXAMPLE, DOUBLING ALGORITHM IS COMPARED WITH OTHER METHODS, NUMERICALLY.

IN THIS PAPER, A NEW MODEL FOR THE CLASS OF MULTI-OBJECTIVE TRANSPORTATION PROBLEMS IS INTRODUCED. THE MODEL IS DEVELOPED BY APPLYING THE CONCEPT OF DISPERSION AND DATA ENVELOPMENT ANALYSIS APPROACH TO LOCATION- TRANSPORTATION PROBLEM. THIS STUDY IS SIGNIFICANT FOR THE FOLLOWING REASONS. FIRSTLY, DISPERSION OF FACILITIES ALONG THE AREA NOT ONLY IMPROVES THE SERVICE LEVEL BUT ALSO REDUCES THE COMPETITION LEVEL BETWEEN FACILITIES. SECONDLY, EFFICIENCY OF LOCATED FACILITIES IS IDENTIFIED AS A SIGNIFICANT FACTOR WHICH IS NEGLECTED MOST OF THE TIME IN LOCATION PROBLEMS. BY ENTERING DATA ENVELOPMENT ANALYSIS IN OUR MODEL, A DIFFERENCE BETWEEN MORE EFFICIENT AND LESS EFFICIENT FACILITIES IS TAKEN INTO CONSIDERATION. ALL OF THESE POINTS INDICATE THAT THE PROPOSED MODEL IS MORE PRACTICAL AND REALISTIC IN COMPARISON WITH OTHER TRANSPORTATION MODELS. TO SOLVE THE PROPOSED MODEL, A MODIFIED VERSION OF THE FUZZY GOAL PROGRAMMING TECHNIQUE IN AN INTERACTIVE FRAMEWORK IS DEVELOPED. FINALLY, SOME COMPUTATIONAL RESULTS ARE ALSO REPORTED TO DEMONSTRATE THE VALIDITY OF THE MODEL.

IN THIS PAPER A MATRIX METHOD FOR APPROXIMATE SOLUTION OF INFINITE BOUNDARY INTEGRAL EQUATIONS (IBIE) OF THE SECOND KIND WITH DEGENERATE KERNEL IS PRESENTED. THE SOLUTION INVOLVES A TRUNCATED LAGUERRE SERIES APPROXIMATION. THE METHOD IS BASED ON FIRST TAKING THE TRUNCATED LAGUERRE SERIES EXPANSIONS OF THE FUNCTIONS IN THE EQUATION AND THEN SUBSTITUTING THEIR MATRIX FORMS INTO THE EQUATION. THEREBY THE EQUATION REDUCES TO A MATRIX EQUATION, WHICH CORRESPONDS TO A LINEAR SYSTEM OF ALGEBRAIC EQUATIONS WITH UNKNOWN LAGUERRE COEFFICIENTS. EXAMPLES ARE CONSIDERED TO VERIFY THE EFFECTIVENESS OF THE PROPOSED DERIVATIONS.

MANY PHYSICAL PROBLEMS MAY BE MODELED BY PDES CONTACTING PARAMETERS AS THE COEFFICIENTS AND STUDY SUCH PDES HAS A GREAT INTEREST IN BOTH THEORY AND APPLICATION. IN THIS PAPER WE USE COMPUTER ALGEBRA TOOLS TO ANALYZE A PARAMETRIC LINEAR PDE SYSTEM TO GAIN A COMPLETE PARTITION ON THE SPACE OF PARAMETERS, FROM WHICH THE SOLUTIONS OF THE PDE SYSTEM WILL BE DETERMINED BY SOLVING A SYSTEM OF NON-DIFFERENTIAL POLYNOMIAL EQUATIONS.

THE DEAD WATER THEORY IS ONE OF SUBJECTS THAT CONTAIN NONLINEAR VOLTERRA-HAMMERSTIEN INTEGRAL EQUATIONS. THE MAIN FOCUS OF THIS PAPER IS TO PRESENT A BRIEF PROOF OF SOLUTION EXISTENCE FOR THIS EQUATIONS IN TWO VARIABLES AND PROPOSE A NUMERICAL SOLUTION METHOD FOR THEM BASED ON EXTENSION METHOD.

THIS PAPER PRESENTS A NEW MULTI-LAYER NEURAL NETWORK WHICH IS BASED ON ORTHOGONAL FUNCTIONS. THE GOAL OF THIS WORK IS TO DETERMINE THE APPROXIMATION COEFFICIENTS USING NEURAL NETWORKS. SOME TEST CASES ARE INVESTIGATED AND THE RESULTS SHOW THAT THE NEURAL NETWORKS HAVE A GOOD PERFORMANCE AND ACCEPTABLE IN CONVERGENCE TIME AND APPROXIMATION ERROR.

IN THE CURRENT WORK A NUMERICAL ANALYSIS BASED ON THE COLLOCATION METHOD IS PERFORMED TO FIND THE NUMERICAL SOLUTION OF THE FRACTIONAL HEAT LIKE EQUATION WITH VARIABLE COEFFICIENT. THE FRACTIONAL DERIVATIVE IS DESCRIBED BASED ON THE CAPUTO SENSE. THE APPROXIMATE SOLUTION IS EXPANDED AS THE ELEMENTS OF SHIFTED LEGENDRE POLYNOMIALS IN TIME AND THE ALSO SHIFTED SINC FUNCTIONS IN SPACE WITH UNKNOWN COEFFICIENT. THE PROPERTIES OF THE PROPOSED SOLUTION ARE USED TO REDUCE THE FRACTIONAL DIFFERENTIAL PROBLEM TO THE SOLUTION OF A SYSTEM OF A LINEAR ALGEBRAIC EQUATION. FINALLY, THE PRESENTED APPROACH IS USED TO SOLVE AN EXAMPLE OF THE GOVERNING PROBLEM. THE COMPUTED RESULTS DEMONSTRATE THE RELIABILITY, ACCURACY AND EFFICIENCY OF THIS METHOD.

IN THIS PAPER INFECTIOUS DISEASE MODELS WITH TIME-VARYING PARAMETERS AND GENERAL NONLINEAR INCIDENCE RATES ARE ANALYZED. THE FUNCTIONAL FORM OF THE NONLINEAR INCIDENCE RATE IS ASSUMED TO CHANGE IN TIME, DUE TO, FOR EXAMPLE, ENVIRONMENTAL FACTORS OR A CHANGE IN POPULATION BEHAVIOR. WE PRESENTS CONTINUOUS TIME LINEAR VACCINATION-BASED CONTROL STRATEGY FOR A SEIR DISEASE MODEL. A CONTROL STRATEGY WITH VACCINE FAILURE IS APPLIED TO CONTROL PRESENTED MODEL. THE CONTROL OBJECTIVE IS THE ASYMPTOTICALLY TRACKING OF THE REMOVED-BY-IMMUNITY POPULATION TO THE TOTAL POPULATION WHILE ACHIEVING SIMULTANEOUSLY THE REMAINING POPULATION TO ASYMPTOTICALLY TEND TO ZERO. THE VACCINATION STRATEGY IS BASED ON A CONTINUOUS-TIME NONLINEAR CONTROL LAW VIA AN EXACT FEEDBACK INPUT-OUTPUT LINEARIZATION APPROACH. ALSO THIS PAPER APPLIES THE SLIDING MODE CONTROL TO A SEIR EPIDEMIC WHILE AN SLIDING CONTROL SYSTEM IS DESIGNED. WITH THIS CONTROLLER, ALL THE POPULATION TENDS TO BE IMMUNE WHILE THE SUSCEPTIBLE, INFECTIVE AND INFECTIOUS TEND TO ZERO.

IN THIS PAPER, WE EXAMINED THE GLOBAL COLLOCATION METHOD USING STANDARD TYPES OF RADIAL BASIS FUNCTION FOR NUMERICAL SOLUTION OF THE MODIFIED EQUAL WIDTH (MEW) EQUATION. THE PROPAGATION OF SINGLE SOLITONS AND THE INTERACTION OF TWO SOLITARY WAVES ARE USED TO VALIDATE THE METHOD WHICH IS FOUND TO BE ACCURATE AND EFFICIENT.

PRICING THE AMERICAN PUT OPTION IS THE OBJECTIVE OF THIS PAPER. FOR THIS PURPOSE, FIRST THE MODELING OF AMERICAN OPTION UNDER THE CONSTANT ELASTICITY OF VARIANCE (CEV) MODEL IS DESCRIBED, THEN THE LINEAR COMPLEMENTARITY FORMULATION IS GIVEN. IN THE SEQUEL, THE PROJECTED SUCCESSIVE OVERRELAXATION (PSOR) ALGORITHM IS EMPLOYED TO HANDLE THE NUMERICAL RESULT.

A DESIGN PROBLEM OF LINEAR ANTENNA ARRAYS AND ARRAY PATTERN SYNTHESIS PROBLEMS CAN BE EXPRESSED AS CONVEX OPTIMIZATION PROBLEMS, WHICH CAN BE SOLVED. THESE PROBLEMS ARE MODELED AS A SIMPLE OPTIMIZATION PROBLEM. THE SYNTHESIS PROBLEMS INVOLVE ARRAYS WITH ARBITRARY GEOMETRY AND ELEMENT DIRECTION, CONSTRAINTS ON FAR-AND NEAR-FIELD PATTERNS OVER NARROW OR BROAD FREQUENCY BANDWIDTH, AND SOME IMPORTANT ROBUSTNESS CONSTRAINS. WE SHOW BY USING NUMERICAL METHODS AND MATHEMATICAL FRAMEWORK AN OPTIMUM A SET OF WEIGHTS OF ANTENNA ELEMENT THAT PROVIDE A RADIATION PATTERN WITH MAXIMAL LEVEL REDUCTION WITH CVX PROGRAMMING.

THE PRESENT STUDY UTILIZES HOMOTOPY PERTURBATION ELZAKI TRANSFORM METHOD TO OBTAIN SOLUTIONS OF THE INITIAL VALUE PROBLEM OF HYPERBOLIC TYPE WHICH IS CALLED TELEGRAPH EQUATION. FINALLY, ONE EXAMPLE IS PROVIDED TO SHOW THE EFFICIENCY OF THE METHOD, ALL OBTAINED NUMERICAL RESULTS ARE COMPARED WITH THE SINC SOLUTIONS.

MANY MODELS IN PHYSICS, CHEMISTRY, ENGINEERING, ETC, ARE DESCRIBED BY SPDES. SINCE THE EXACT SOLUTION OF THESE EQUATIONS ARE RARELY KNOWN, THE NUMERICAL ANALYSIS OF SPDES HAS BEEN RECENTLY THE SUBJECT OF MANY ARTICLES. THE MAIN PURPOSE OF THIS ARTICLE IS TO CONSIDER THE PATHWISE NUMERICAL APPROXIMATION OF NONLINEAR PARABOLIC SPDES SUCH THAT THE DRIFT TERM IS A LOCALLY-LIPSCHITZ FUNCTION. WE CONSIDER AS A FORCING TERM AN INFINITE-DIMENSIONAL STOCHASTIC PROCESS EXPANDED IN THE EIGENFUNCTIONS OF THE LINEAR OPERATOR A PRESENT IN THE SPDE.

IN THIS WORK, BASED ON THE LEAST-SQUARE MINIMAL RESIDUAL (LSMR) ALGORITHM, WE PROPOSE A MATRIX ITERATIVE METHOD FOR COMPUTING COMMON SYMMETRIC SOLUTION OR COMMON SYMMETRIC LEAST SQUARES SOLUTION THE PAIR OF MATRIX EQUATIONS A´B=E AND C´D=F. NUMERICAL EXPERIMENT ILLUSTRATING THE EFFICIENCY OF THE NEW METHOD IS PRESENTED. A COMPARISON WITH THE WELL-KNOWN YXP_M AND LSQR_M METHODS IS ALSO INCLUDED.

IN THIS PAPER, A TWO LEVEL DIFFERENCE SCHEME IS PROPOSED FOR SOLVING THE TELEGRAPH EQUATION UTT+2AUT+B2U=UXX+F (X,T), A £X£B, T³0, WHERE A=P(T) IS A POSITIVE FUNCTION OF T AND B IS A POSITIVE CONSTANT. THIS METHOD BASED ON THE QUARTIC SPLINE INTERPOLATION IN SPACE DIRECTION AND GENERALIZED TRAPEZOIDAL FORMULA IN TIME DIRECTION. STABILITY ANALYSIS OF THE SCHEME IS CARRIED OUT. NUMERICAL EXAMPLES ARE USED TO ILLUSTRATE THE EFFICIENCY OF THE NEW DIFFERENCE SCHEME.

IT IS ATTEMPTED TO INTRODUCE A NEW METHOD WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS. THIS FAMILY USES FOUR FUNCTION EVALUATIONS PER CYCLE AND IS DERIVATIVE FREE WITH ORDER OF CONVERGENCE 12. ITS CONSTRUCTION AND ERROR ANALYSIS WILL BE PRESENTED IN DETAILS ALONG WITH NUMERICAL IMPLEMENTATIONS AND COMPARISONS WITH SOME EXISTING METHOD IN THIS CLASS.

IN THIS PAPER, THE GENERALIZED SUCCESSIVE OVER RELAXATION (GSOR) ITERATIVE METHOD IS UTILIZED TO SOLVE A BROAD CLASS OF COMPLEX SYMMETRIC LINEAR SYSTEMS. WE THEN INVESTIGATE ITS CONVERGENCE PROPERTIES. FINALLY WE GIVE SOME NUMERICAL EXPERIMENTS TO VALIDATE THE THEORETICAL RESULTS AND COMPARE WITH THE MODIFIED HERMITIAN AND SKEW-HERMITIAN SPLITTING (MHSS) ITERATION.

IN THIS PAPER WE APPLY THE INVASIVE WEED OPTIMIZATION ALGORITHM (IWO) FOR SOLVING BI-LEVEL LINEAR PROGRAMMING PROBLEMS (BLPPS). THE PERFORMANCE OF THE PROPOSED METHOD IS ASCERTAINED BY COMPARING THE RESULTS WITH PARTICLE SWARM OPTIMIZATION (PSO). THE RESULT ILLUSTRATE THAT THE IWO ALGORITHM HAS GOOD PERFORMANCE FOR SOLVING BLPPS.

THIS PAPER DESCRIBES A NUMERICAL METHOD FOR SOLVING NONLINEAR MIXED VOLTERRA-FREDHOLM TYPE INTEGRAL EQUATIONS OF THE SECOND KIND. THE PROPOSED METHOD UTILIZES RADIAL BASIS FUNCTIONS (RBFS) WITH POLYNOMIAL PRECISION AS A BASIS IN THE DISCRETE COLLOCATION METHOD. THE RBF TECHNIQUE IS AN EFFECTIVE SCHEME FOR THE APPROXIMATION OF AN UNKNOWN FUNCTION USING A SET OF DISORDERED DATA. THE COMPUTATIONAL METHOD DEVELOPED IN THE CURRENT PAPER DOES NOT REQUIRE ANY BACKGROUND MESH OR CELL STRUCTURES, SO IT IS MESHLESS METHOD. THIS SCHEME REDUCES THE SOLUTION OF THE NONLINEAR MIXED VOLTERRA- FREDHOLM INTEGRAL EQUATION TO THE SOLUTION OF A NONLINEAR SYSTEM OF ALGEBRAIC EQUATIONS. THE PROPOSED METHOD IS EASY TO IMPLEMENT ON COMPUTER AND IS MORE FLEXIBLE FOR MOST CLASSES OF INTEGRAL EQUATIONS. THE VALIDITY AND EFFICIENCY OF THE NEW TECHNIQUE ARE DEMONSTRATED THROUGH A NUMERICAL EXAMPLE.

WE USUALLY REQUIRE DETERMINANTS, INVERSES, AND BOUNDS FOR INVERSES OF BAND MATRICES. IN THIS PAPER WE INVESTIGATE THE MONOTONICITY OF BAND MATRICES WHICH WILL BE NEEDED IN THE PROVING THE CONVERGENCE ANALYSIS OF FINITE DIFFERENCE, SPLINE AND NON-POLYNOMIAL SPLINE METHODS.

IN THIS PAPER, THE CONCEPTS OF STATE ALTERNATING REGULAR TREE GRAMMAR (SARTG) AND EXTENDED ALTERNATING REGULAR TREE GRAMMAR (EARTG) ARE DEFINED AND THE EQUIVALENCE BETWEEN THEM IS SHOWN. ALSO, THEOREMS CONCERNING THE RELATIONS BETWEEN VARIOUS TYPES OF ALTERNATING REGULAR TREE GRAMMARS ARE PROVED.

IN THIS PAPER, AN EFFECTIVE METHOD IS PROPOSED TO DETERMINE THE NUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATIONS. THIS METHOD IS BASED ON A NEW SET OF ORTHOGONAL HYBRID FUNCTIONS (HFS) INCLUDED SAMPLE-AND-HOLD FUNCTIONS (SHFS) AND TRIANGULAR FUNCTIONS (TFS). THE HFS ARE UTILIZED AS BASIS TO REDUCE THE SOLUTION OF INTEGRO-DIFFERENTIAL EQUATIONS TO THE SOLUTION OF ALGEBRAIC EQUATIONS. A NUMERICAL EXAMPLE IS PROVIDED TO ILLUSTRATE THE ACCURACY AND COMPUTATIONAL EFFICIENCY OF THE PROPOSED METHOD.

THE PURPOSE OF THIS STUDY WAS TO INVESTIGATE PHYSIOLOGICAL AND ANTHROPOMETRIC CHARACTERISTICS OF IRANIAN ADOLESCENT GIRL VOLLEYBALL PLAYERS AND TO PROVIDE PHYSIOLOGICAL AND ANTHROPOMETRIC PATTERN BY USING DATA ENVELOPMENT ANALYSIS (DEA). IN ORDER TO DO THIS, 172 IRANIAN ADOLESCENT GIRL VOLLEYBALL PLAYERS BEING 15.34 ±1.5 YEARS OLD WERE SELECTED FROM DIFFERENT PROVINCES TO PARTICIPATE IN THIS RESEARCH .THEN .PARTICIPANTS’ PHYSIOLOGICAL VARIANTS AND ANTHROPOMETRICAL VARIABLES WERE MEASURED. THE MEAN AND STANDARD DEVIATION OF EACH ITEM OF MEASUREMENT WERE CALCULATED. IN ADDITION, DEA OF THIS PATTERN WAS DETERMINED BY MATHEMATICAL ANALYSIS. THE RESULTS OF THIS STUDY ARE SHOWED ANTHROPOMETRIC AND PHYSIOLOGICAL CHARACTERISTICS OF IRANIAN ADOLESCENT GIRL VOLLEYBALL PLAYERS, AND ACCORDING TO THIS PRESENT PATTERN, VOLLEYBALL COACHES CAN USE FOR IDENTIFYING, TRAINING AND PLANNING OF EXERCISE PROGRAMS TALENT PLAYERS.

THE REDUCED DIFFERENTIAL TRANSFORM METHOD IS ONE OF THE APPROXIMATE METHODS WHICH CAN BE EASILY APPLIED TO MANY LINEAR AND NONLINEAR PROBLEMS AND IS CAPABLE OF REDUCING THE SIZE OF COMPUTATIONAL WORK. EXACT SOLUTIONS CAN ALSO BE ACHIEVED BY THE KNOWN FORMS OF THE SERIES SOLUTIONS. THE METHOD CAN EASILY BE APPLIED TO MANY LINEAR AND NON-LINEAR PROBLEMS AND IS CAPABLE OF REDUCING THE SIZE OF COMPUTATIONAL WORK. EXACT SOLUTIONS CAN ALSO BE ACHIEVED BY THE KNOWN FORMS OF THE SERIES SOLUTIONS. SEVERAL ILLUSTRATIVE EXAMPLES ARE GIVEN TO DEMONSTRATE THE EFFECTIVENESS OF THE PRESENT METHOD.

EFFICIENCY ON THE ORDER OF 25% IS NOW ACHIEVABLE ON SILICON CRYSTALLINE SOLAR CELLS. QUANTUM DOT SOLAR CELLS INCREASE THE CELL’S EFFICIENCY GREATLY. BOSE–EINSTEIN EQUATIONS IN EFFICIENCY OF SOLAR CELLS ARE APPEARED. THESE EQUATIONS CAN’T BE SOLVED IN THE FORM OF CONVENTIONAL BUT SHOULD BE SOLVED BY NUMERICAL METHODS. IN THIS STUDY, A COMBINATION OF DESCRIPTIVE AND EMPIRICAL APPROACHES TO BOTH LIBRARY AND ARCHIVAL DATA COLLECTION, RESEARCH AND FIELD TESTS HAVE BEEN. FIRST, THE DOCUMENT LIBRARY AND INTERNET REFERENCES KEYWORDS USED THROUGHOUT THIS STUDY WERE REPEATED SEARCH JOURNALS AND ARTICLES RELATED TO THIS RESEARCH HAS BEEN SOME OF THE KEY FACTORS AND PRINCIPLES DERIVED FROM THESE SOURCES AND TO ANALYZE THEM THIS RESEARCH HAVE BEEN CONDUCTED USING MATLAB. THE RESULTS SHOW THAT ROOTS OF THE DENOMINATOR OF THE INTEGRAND SHOULD NOT BE INCLUDED IN CALCULATING THE BOSE–EINSTEIN INTEGRAL BECAUSE IN THIS CASE THE FUNCTION WILL DIVERGE. IN QUANTUM COMPUTING NUMBERS ARE WITHIN IN FEMTO AND THE ACCEPTABLE ERROR WOULD BE MUCH SMALLER.

IN THIS WORK AN EFFICIENT NUMERICAL TECHNIQUE IS INTRODUCED AND APPLIED TO APPROXIMATE THE NUMERICAL SOLUTION OF A TIME FRACTIONAL HEAT LIKE EQUATION WITH VARIABLE COEFFICIENT. THE FRACTIONAL DERIVATIVE IS DESCRIBED BASED ON THE CAPUTO SENSE. FIRSTLY AN ESPECIAL FINITE DIFFERENCE SCHEME IS USED TO DISCRETIZE TIME FRACTIONAL DERIVATIVE, THEN A RADIAL BASIS FUNCTION APPROXIMATION METHOD IS EMPLOYED TO DEAL WITH SPATIAL DERIVATIVE TERMS. THE STABILITY AND CONVERGENCE OF THIS MESHLESS APPROACH ARE DISCUSSED. FINALLY NUMERICAL EXAMPLES ARE GIVEN TO DEMONSTRATE THE RELIABILITY, ACCURACY OF THE PRESENTED METHOD.

RATIONALIZED HAAR FUNCTIONS ARE USED TO APPROXIMATE THE SOLUTION OF NONLINEAR VOLTERRA INTEGRAL EQUATIONS. THE PROPERTIES OF RATIONALIZED HAAR FUNCTIONS ARE FIRST PRESENTED, AND THE OPERATIONAL MATRIX OF INTEGRATION TOGETHER WITH THE PRODUCT OPERATIONAL MATRIX ARE UTILIZED TO REDUCE THE COMPUTATION OF INTEGRAL EQUATIONS INTO SOME ALGEBRAIC EQUATIONS. THE METHOD IS COMPUTATIONALLY ATTRACTIVE, AND APPLICATIONS ARE DEMONSTRATED THROUGH ILLUSTRATIVE EXAMPLES.

SPECIAL KIND OF SECRET SHARING SCHEMES ARE VISUAL CRYPTOGRAPHY SCHEMES (VCS). IN A BIPARTITE SECRET SHARING SCHEME, THE SET OF PARTICIPANTS IS DIVIDED INTO TWO PARTS, AND ALL PARTICIPANTS IN EACH PART PLAY AN EQUIVALENT ROLE. IN THIS PAPER WE STUDY AN INTERESTING CLASS OF BIPARTITE ACCESS STRUCTURES: THE KING AND N PAWNS ACCESS STRUCTURES (FORMULA) THE KING AND ANY ONE PAWN MAY RECONSTRUCT THE SECRET, AS MAY THE SET OF ALL PAWNS. WE PRESENT S1 AND S2 VISUAL CRYPTOGRAPHY SCHEMES FOR THIS CLASS OF ACCESS STRUCTURE. FINALLY WE COMPUTE THE INFORMATION RATE OF OUR SCHEMES AND PRESENT ONE S SCHEME SUCH THAT IT HAS SUITABLE WEIGHTED AVERAGE OF S1 AND S2.

IN THIS PAPER, WE INTRODUCE THE NOTION OF K-RANK NUMERICAL RANGE OF RECTANGULAR COMPLEX MATRICES. SOME ALGEBRAIC AND GEOMETRICAL PROPERTIES ARE INVESTIGATED. WE ALSO, FOR E, WE INTRODUCE THE NOTION OF BIRKHOFF-JAMES APPROXIMATE ORTHOGONALITY SETS FOR E-HIGHER RANK NUMERICAL RANGES OF RECTANGULAR MATRICES. THE PROPOSED DEFINITION YIELDS A NATURAL GENERALIZATION OF STANDARD HIGHER RANK NUMERICAL RANGE.

IN THIS PAPER WE STUDY MINIMIZING THE RATIO OF TWO INDEFINITE QUADRATIC FUNCTIONS SUBJECT TO A STRICTLY CONVEX QUADRATIC CONSTRAINT. USING THE DINKELBACH IDEA, A GENERALIZED NEWTON METHOD IS DEVELOPED TO SOLVE THE PROBLEM. IT REQUIRES SOLVING A NONCONVEX QUADRATIC OPTIMIZATION PROBLEM AT EACH ITERATION. TO SOLVE THE QUADRATIC MINIMIZATION PROBLEMS A DIAGONALIZATION SCHEME IS PROPOSED. OUR PRELIMINARY NUMERICAL EXPERIMENTS SHOW THAT THE NEW SCHEME IS EXTREMELY FASTER IN COMPARISON TO THE KNOWN SEMIDEFINITE OPTIMIZATION (SDO) APPROACH ON FINDING THE GLOBAL OPTIMAL SOLUTION.

THE MOTIVATION OF THIS WORK IS TO REGISTER MR (MAGNET-RESONANCE) BRAIN TUMOR IMAGES WITH A BRAIN ATLAS. SUCH A REGISTRATION METHOD CAN MAKE POSSIBLE THE POOLING OF DATA FROM DIFFERENT BRAIN TUMOR PATIENTS INTO A COMMON STEREOTAXIC SPACE. THE SHAPE, SIZE AND LOCATION OF THE INITIAL SEED ARE CRITICAL FOR ACHIEVING TOPOLOGICAL EQUIVALENCE BETWEEN THE ATLAS AND PATIENTS IMAGES. WE FOCUS ON THE AUTOMATIC ESTIMATION OF THESE PARAMETERS, PERTAINING TO TUMOR SIMULATION AND PROPOSE AN OBJECTIVE FUNCTION REFLECTING FEATURE-BASED SIMILARITY AND ELASTIC STRETCHING ENERGY AND OPTIMIZE IT WITH APPSPACK (ASYNCHRONOUS PARALLEL PATTERN SEARCH), FOR ACHIEVING SIGNIFICANT REDUCTION OF THE COMPUTATIONAL COST.

AN EFFECTIVE METHOD BASED ON TRIANGULAR FUNCTIONS IS PROPOSED FOR THE SOLUTIONS OF 2D VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS. THE MAIN ADVANTAGE OF THIS METHOD IS ITS EFFICIENCY AND SIMPLE APPLICABILITY. A NUMERICAL EXAMPLE IS PRESENTED TO SHOW THAT THE ACCURACY OF THE METHOD.

CONTROL THEORY IS A MATHEMATICAL DESCRIPTION OF HOW TO ACT OPTIMALLY TO GAIN FUTURE REWARDS. IN THIS PAPER WE GIVE AN INTRODUCTION TO DETERMINISTIC AND STOCHASTIC CONTROL THEORY, PARTIAL OBSERVABILITY, LEARNING AND THE COMBINED PROBLEM OF INFERENCE AND CONTROL. SUBSEQUENTLY, WE DISCUSS A CLASS OF LINEAR QUADRATIC STOCHASTIC CONTROL PROBLEMS THAT CAN BE EFFICIENTLY SOLVED. WE ILLUSTRATE THE THEORY WITH AN EXAMPLE.

IN THIS PAPER, WE INTRODUCE A NEW APPROACH TO FIND THE BEST AORTO-CORONARIC BYPASS CONFIGURATION. OUR APPROACH MAINLY IS BASED ON THE DEFINITION OF A MEASURE ON A PRODUCT SPACE, THEN BY USING MEASURE THEORY APPROACH (EMBEDDING METHOD), THE PROBLEM OF OPTIMAL DESIGN OF BYPASS CONFIGURATION IS METAMORPHOSED TO A LINEAR PROGRAMMING PROBLEM, WHERE THE NEW PROBLEM CAN BE SOLVED EASILY BY SIMPLEX METHOD. SINCE THE ORIGINAL AND NEW PROBLEMS ARE ISOMORPHIC, SO WE CAN FIND THE OPTIMAL SHAPE OF BYPASS CONFIGURATION. AN ILLUSTRATIVE EXAMPLE DEMONSTRATES THE EFFECTIVENESS OF THE PROPOSED METHOD.

THIS PAPER DEVELOPS A NEW ANALYTICAL SOLUTION FOR KALECKIAN-TYPE MODEL OF BUSINESS CYCLE VIA HOMOTOPY ANALYSIS METHOD. THIS MODEL IS REPRESENTED BY NONLINEAR DELAY DIFFERENTIAL EQUATION. THE PRESENT METHOD RESULTS FOR THE MODEL ARE COMPARED WITH THE DIRECT NUMERICAL AND EXISTING LITERATURE RESULTS AND FOUND TO BE ACCURATE. THE FACT THAT HAM SOLVES NONLINEAR PROBLEMS WITHOUT USING ADOMIAN’S POLYNOMIALS CAN BE CONSIDERED AS A CLEAR ADVANTAGE OF THIS TECHNIQUE OVER THE DECOMPOSITION METHOD. MOREOVER, THE RESULTS OF THE UNDERLYING EQUATION SHOW THAT THE BUSINESS CYCLE IS STABLE.

THIS PAPER CONTAINS BASIC INFORMATION ABOUT A SPECIAL AND POPULAR INSURANCE CONTRACT WHAT IS CALLED “GUARANTEED MINIMUM WITHDRAWAL BENEFIT” (GMWB). AFTER INTRODUCING THE MENTIONED CONTRACT AS A FINANCIAL DERIVATIVE, PRICING OF THIS CONTRACT WILL BE STATED BY LINKING THIS DERIVATIVE TO OTHER FINANCIAL MATHEMATICS DEFINITION SUCH AS DISCRETE TIME ASSUMPTION AND CALL OPTION WHAT IS RELATED TO DIFFERENTIAL EQUATION OF STOCK PRICE USING BROWNIAN MOTION AS THE STOCHASTIC TERM. IN ADDITION, COMPARING BETWEEN CONSEQUENCES OF DISCRETE TIME ASSUMPTION AND CONTINUOUS TIME ASSUMPTION WILL BE STUDIED.

A NUMERICAL TECHNIQUE FOR SOLVING INHOMOGENEOUS NONLINEAR KLEIN-GORDON EQUATION IS DEVELOPED. THE APPROACH IS BASED ON A COMPACTLY SUPPORTED TRIGONOMETRIC WAVELET WHICH IS CONSTRUCTED FOR HERMITE INTERPOLATION. THE METHOD CONSISTS OF EXPANDING THE REQUIRED APPROXIMATE SOLUTION AS THE ELEMENTS OF TRIGONOMETRIC WAVELET. USING THE OPERATIONAL MATRIX OF DERIVATIVE, WE REDUCE THE PROBLEM TO A SET OF ALGEBRAIC EQUATIONS. ILLUSTRATIVE EXAMPLES ARE INCLUDED TO DEMONSTRATE THE VALIDITY AND APPLICABILITY OF THIS APPROACH. THE METHOD IS EASY TO IMPLEMENT AND PRODUCES ACCURATE RESULTS.

IN THIS STUDY, WE PRESENT A NEW FIXED POINT METHOD FOR L1-NORM REGULARIZATION PROBLEMS ARISING FROM SPARSE SOLUTION RECOVERY IN COMPRESSIVE SENSING. THE PROBLEM IS REFORMULATE AS AN EQUIVALENT NON-SMOOTH EQUATION, THEN THE COMBINATION OF BOTH AN EFFECTIVE TRUST-REGION AND A FIXED POINT STRATEGY ARE USED TO SOLVE IT. MODIFY THE SHRINKAGE PARAMETER BASED ON DOGLEG TECHNIQUE SHOW THAT THE NEW ALGORITHM IS MORE EFFICIENT AND ROBUSTNESS. THE PROPOSED APPROACH IS GLOBAL CONVERGENCE AND THE RATE OF CONVERGENCE IS Q-LINEAR.

THIS PAPER INTRODUCES A NEW APPROACH FOR SOLVING TRAVELING SALESMAN PROBLEM. THIS METHOD OFFERS SIGNIFICANT ADVANTAGES OVER SIMILAR METHODS, IN THE PROCESS, FIRST WE DEFINE THE DISTANCE MATRIX, THEN BY USING DETERMINANT REPRESENTATION WE OBTAIN A REDUCED MATRIX WHICH HAS AT LEAST ONE 1 IN EACH ROW AND EACH COLUMN. THEN BY USING THE NEW METHOD, WE OBTAIN AN OPTIMAL SOLUTION FOR TRAVELING SALESMAN PROBLEM BY ASSIGNING ONES TO EACH ROW AND EACH COLUMN. THE NEW METHOD IS BASED ON CREATING SOME ONES IN THE DISTANCE MATRIX AND THEN TRY TO FIND A COMPLETE SOLUTION TO THERE ONES.THE PROPOSED METHOD IS A SYSTEMATIC PROCEDURE, EASY TO APPLY AND CAN BE UTILIZED FOR ALL TYPES OF TRAVELING SALESMAN PROBLEM WITH MAXIMIZE OR MINIMIZE OBJECTIVE FUNCTIONS.AT THE END, THIS METHOD IS ILLUSTRATED WITH SOME NUMERICAL EXAMPLES.

IN THIS PAPER, BY USING THE LEGGETT-WILLIAMS FIXED POINT THEOREM IN A CONE, WE PROVE THE EXISTENCE OF THREE POSITIVE SOLUTIONS FOR NONLINEAR SINGULAR BOUNDARY VALUE PROBLEMS.

IN THIS PAPER, WE INTRODUCE THE MAPPINGS WHICH HAVE A UNIQUE EIGENVECTOR. ALSO, THE ORDERED PAIRS OF SELF-MAPPINGS ARE INTRODUCED WHICH HAVE A UNIQUE COMMON EIGENVECTOR.

IN THIS STUDY, WE INTRODUCE TWO EFFECTIVE NONMONOTONE TRUST-REGION ALGORITHMS FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS SPECIFYING RADIUSES MORE PRACTICALLY THAN THE TRADITIONAL NONMONOTONE TRUST-REGION STRUCTURE. THE TRADITIONAL NONMONOTONE TRUST-REGION FRAMEWORK EMPLOYS A NONMONOTONE RATIO AS A MEASURE BOTH TO ACCEPT NEW POINT AND TO UPDATE THE TRUST REGION RADIUS. ALTHOUGH THIS IDEA IS EFFICIENT FOR HIGHLY NONLINEAR PROBLEMS, IT INCREASE THE TRUST-REGION RADIUS MORE THAN WHAT IS NEEDED, ESPECIALLY FOR COMMON PRACTICAL PROBLEMS. THE INTRODUCED FRAMEWORKS SUGGEST TAKING ADVANTAGE OF NONMONOTONE RATIOS JUST AS AN ACCEPTANCE CRITERION FOR A NEW TRIAL STEP, WHILE IT IS ADVISED TO EXPLOIT THE TRADITIONAL MONOTONE RATIO OR A HYBRID OF MONOTONE AND NONMONOTONE RATIOS FOR UPDATING THE TRUST-REGION RADIUS.

IN THIS PAPER, PROBLEMS WHICH ARE FORMULATED AS PROBLEMS OF NONSMOOTH, NONCONVEX OPTIMIZATION WITH A LOCALLY LIPSCHITZ OBJECTIVE FUNCTIONS ARE CONSIDERED. ALSO, WE PRESENT A SIMPLE AND EFFICIENT DESCENT ALGORITHM FOR SOLVING THEM. DESCENT DIRECTIONS IN THIS ALGORITHM ARE COMPUTED BY CONJUGATE GRADIENT METHOD USING THE GENERALIZED GRADIENT. WE COMPARE THE PROPOSED ALGORITHM WITH APPROXIMATE SUBGRADIENT ALGORITHM USING THE RESULTS OF NUMERICAL EXPERIMENTS. THESE RESULTS HAVE BEEN PRESENTED WHICH DEMONSTRATE THE EFFECTIVENESS OF THE PROPOSED ALGORITHM OVER THE APPROXIMATE SUBGRADIENT METHOD.

IN THIS PAPER SINC-GALERKIN METHOD (SGM) IS APPLIED FOR STURM-LIOUVILLE PROBLEM. TO SHOW THE ACCURACY OF THE METHOD TABLES ARE GIVEN AT THE END OF PAPER FOR DIFFERENT EIGENVALUE OF PARAMETER L. IN THIS TABLES THE ABSOLUTE ERROR IS CALCULATED.

WE COMPUTE THE XPLICIT COEFFICIENTS OF A CONTINUED FORM OF INTERPOLATING FOR ONE AND TWO ORTHO-TRIPLE VIA B-NETS. THUS THE COMPUTATION OF MUITIPLE INTEGRALS CAN BE CONVERTED INTO THE SUM OF THE COEFFICIENTS IN TERMS OF THE B-NET OVER TRIANGULAR DOMAIN MUCH EFFECTIVELY AND CONVENIENTIY. BASED ON A NEW SYMMETRICAL ALGORITHM OF PATTIAL INVERSE DIFFERENCES, A NOVEL CONTINUED FRACTIONS INTER- POLATION SCHEME IS PRESENTED OVER ARBITRARY ORTHO- TRIPLES IN R2, WHICH IS A BIVARIATE OSCULATORY INTERPOLATION FORMULA WITH ONE- ORTHER PARTIAL DERIVATIVES AT ALL CORNER POINTS IN THE ORTHO-TRIPLES. FURTHERMORE, ITS CHARACTERIZATION THEOREM IS PRESENTED BY THREE- TERM RECURRENCE RELATION. THE NEW SCHEME HAS ADVANTAGEOUS WHICH WE SHOW THROAQH SEVERAL NUMERICUL EXAMPLES.

IN THIS PAPER, WE HAVE USED NEWTON MODIFIED METHODS FOR SOLVING SYSTEMS OF NONLINEAR EQUATION. WE INTRODUCED TWO ITERATIVE METHODS OF NEWTON SUCH AS TWO AND FOURTH ORDER OF CONVERGENCE. SEVERAL NUMERICAL EXAMPLES ARE GIVEN TO ILLUSTRATE THE EFFICIENCY AND PERFORMANCE OF THE ITERATIVE METHODS.

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SUPPOSE THAT THE COEFFICIENT OF OBJECTIVE FUNCTION, THE COEFFICIENT MATRIX AND THE RIGHT-HAND SIDE CONSTRAINTS ARE NOT DETERMINED EXACTLY, BUT ARE ONLY KNOWN TO LIE WITHIN SOME REAL INTERVALS. SUCH A DECISION PROBLEM WHICH REPRESENTS A FAMILY OF LINEAR PROGRAMMING PROBLEMS IS CALLED AN INTERVAL LINEAR PROGRAMMING PROBLEM. IN THIS PAPER WE PROPOSE A NEW CONCEPT OF SOLVING THE LINEAR PROGRAMMING PROBLEMS WITH INTERVAL COEFFICIENTS. OUR PROPOSAL IS BASED ON THE NOTION OF THE RANGE OF THE UNIQUELY DETERMINED OPTIMAL VALUE OF EACH LINEAR PROGRAMMING PROBLEM IN THE FAMILY OVER THE INTERVAL DATA. WE DRIVE FORMULAE FOR COMPUTING THIS RANGE AS THE CORNERSTONE OF OUR APPROACH WHICH WILL ALLOW THE DECISION MAKER TO HAVE A GENERAL VIEW OF THE PROBLEM AND TO CHOOSE THE FINAL SOLUTION IN A WAY THAT BEST SUITS HIS PREFERENCES.

THIS APPROACH CONSIDERS SEVERAL ESTIMATORS FOR ESTIMATING THE RIDGE PARAMETER IN THE STUDY OF PARTIAL LINEAR MODELS. A SIMULATION STUDY HAS BEEN CONDUCTED TO COMPARE THE PERFORMANCE OF THE ESTIMATORS. BASED ON THE SIMULATION STUDY WE FOUND THAT, INCREASING THE CORRELATION BETWEEN THE INDEPENDENT VARIABLES HAS POSITIVE EFFECT ON THE MSE (SIGNAL-TO-NOISE-RATIO). HOWEVER, INCREASING THE VALUE OF SIGNAL TO NOISE (R2) HAS NEGATIVE EFFECT ON MSE. WHEN THE SAMPLE SIZE INCREASES THE MSE DECREASES EVEN WHEN THE CORRELATION BETWEEN THE INDEPENDENT ARIABLES IS LARGE.

IN THIS PAPER, HOMOTOPY PERTURBATION METHOD IS APPLIED TO SOLVE NON-LINEAR TWO-DIMENSIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER. EXAMPLES ARE PRESENTED TO ILLUSTRATE THE ABILITY OF THE METHOD. THE RESULTS REVEAL THAT THE PROPOSED METHOD, VERY EFFECTIVE AND SIMPLE.

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OPTIMAL HOMOTOPY ANALYSIS METHOD IS A POWERFUL TOOL FOR NONLINEAR DIFFERENTIAL EQUATIONS. IN THIS METHOD, THE CONVERGENCE OF THE SERIES SOLUTIONS IS CONTROLLED BY ONE OR MORE PARAMETERS WHICH CAN BE DETERMINED BY MINIMIZING A CERTAIN FUNCTION. THERE ARE SEVERAL APPROACHES TO DETERMINE THE OPTIMAL VALUES OF THESE PARAMETERS, WHICH CAN BE DIVIDED INTO TWO CATEGORIES, I.E. GLOBAL OPTIMIZATION APPROACH AND STEP-BY-STEP OPTIMIZATION APPROACH. IN THE GLOBAL OPTIMIZATION APPROACH, ALL THE PARAMETERS ARE OPTIMIZED SIMULTANEOUSLY AT THE LAST ORDER OF APPROXIMATION. HOWEVER, THIS PROCESS LEADS TO A SYSTEM OF COUPLED, NONLINEAR ALGEBRAIC EQUATIONS IN MULTIPLE VARIABLES WHICH ARE VERY DIFFICULT TO SOLVE. IN THE STEP-BY-STEP APPROACH, THE OPTIMAL VALUES OF THESE PARAMETERS ARE DETERMINED SEQUENTIALLY, THAT IS, THEY ARE DETERMINED ONE BY ONE AT DIFFERENT ORDERS OF APPROXIMATION. IN THIS WAY, THE COMPUTATIONAL EFFICIENCY IS SIGNIFICANTLY IMPROVED, ESPECIALLY WHEN HIGH ORDER OF APPROXIMATION IS NEEDED. IN THIS PAPER, FIRST DESCRIBED HAM AND THEN DESCRIBED OPTIMAL HAM AND EXPLAINED BASIC IDEAS.

IN THIS PAPER, THE CLASSICAL LIE THEORY IS APPLIED TO STUDY BBM EQUATION TO OBTAIN ITS SYMMETRIES, INVARIANT SOLUTIONS, SYMMETRY REDUCTION AND DIFFERENTIAL INVARIANTS. BY WITNESSING THE ADJOINT REPRESENTATION OF MENTIONED SYMMETRY GROUPS ON THEIR LIE ALGEBRAS, WE FIND THE PRELIMINARY CLASSIFICATION (OPTIMAL SYSTEM) OF IT'S GROUP-INVARIANT SOLUTIONS WHICH PROVIDES NEW EXACT SOLUTIONS.

IN THIS PAPER, WE USE A COMBINATION OF BERNSTEIN AND BLOCK-PULSE FUNCTIONS ON THE INTERVAL [0, 1], THAT IS CALLED HYBRID FUNCTIONS, TO ESTIMATE THE SOLUTION OF LINEAR AND NONLINEAR FREDHOLM INTEGRAL EQUATIONS. FIRST, WE PRESENT SOME PROPERTIES OF THESE FUNCTIONS THEN WE USE THEM FOR CONVERTING THE FREDHOLM INTEGRAL EQUATIONS TO A SYSTEM OF EQUATIONS. AN ILLUSTRATIVE EXAMPLE IS INCLUDED TO DEMONSTRATE THE VALIDITY AND APPLICABILITY OF THIS TECHNIQUE.

GIVEN TWO ARITHMETIC SEQUENCES WITH POSITIVE INTEGER COMMON DIFFERENCES, WE GIVE A NECESSARY AND SUFFICIENT CONDITION TO HAVE COMMON TERMS. ALSO WE PRESENT A METHOD TO FIND THEM. SOME ILLUSTRATING EXAMPLES ARE INCLUDED.

IN THIS WORK A NUMERICAL METHOD FOR FINDING THE OPTIMAL CONTROL OF A TIME-DELAY SYSTEM VIA A WAVELETS APPROACH IS DISCUSSED. WE HAVE CHOSEN CAS WAVELET FUNCTIONS AS A FAMILY OF ORTHOGONAL BASIS FUNCTIONS FOR OUR PURPOSE. THE PROPERTIES OF THE CAS WAVELETS ARE PRESENTED. THE OPERATIONAL MATRICES OF INTEGRATION, DELAY AND PRODUCT ARE GIVEN. THESE MATRICES ARE THEN UTILIZED TO REDUCE THE SOLUTION OF OPTIMAL CONTROL TO THE SOLUTION OF NONLINEAR PROGRAMMING PROBLEM. AN ILLUSTRATIVE EXAMPLE IS INCLUDED TO DEMONSTRATE THE VALIDITY AND APPLICABILITY OF THE TECHNIQUE.

IN THIS PAPER, THE VARIATINAL ITERATION METHOD IS PROPOSED TO SOLVE FREDHOLM’S NTH-ORDER INTEGRO- DIFFERENTIAL EQUATIONS THE INITIAL APPROXIMATION IS SELECTED WISELY WHICH SATISFIES THE INITIAL CONDITIONS. THE RESULTS REVEAL THAT THIS METHOD IS VERY EFFECTIVE AND CONVENIENT IN COMPARISON WITH OTHER METHODS.

IN THIS PAPER WE FIND AND STUDY TWO CLASSES OF 7TH ORDER COMPLETE HYPERELLIPTIC INTEGRALS OF THE FIRST KIND AND SHOW THAT THE THESE CLASSES ARE CHEBYSHEV AND EXACT BOUNDS FOR THEIR NUMBER OF ZEROS ARE TWO.

IN THIS PAPER, WE PROPOSE AN EFFECTIVE SMOOTHING METHOD TO SOLVE THE NP-HARD ABSOLUTE VALUE EQUATION, WHEN THE SOLUTION IS UNIQUE. TO DO SO, WE UNIFORMLY APPROXIMATE THE ABSOLUTE VALUE FUNCTION IN SUCH A WAY THAT THE NONSMOOTH ABSOLUTE VALUE EQUATION CAN BE FORMULATED AS A SMOOTH NONLINEAR EQUATION. BY SOLVING A PARAMETRIC SMOOTH NONLINEAR EQUATION USING NEWTON METHOD, FOR A DECREASING SEQUENCE OF PARAMETERS, WE CAN GET THE SOLUTION OF THE ABSOLUTE VALUE EQUATION. NUMERICAL RESULTS INDICATE EFFECTIVENESS AND ROBUSTNESS OF THE METHOD TO SOLVE ABSOLUTE VALUE EQUATIONS.

THIS ARTICLE CONSIDER AN INVERSE EIGENVALUE PROBLEM FOR NONNEGATIVE BISYMMETRIC MATRICES OF ORDER TWO TO FOUR. WE FIRST DISCUSS THE SPECIFIED STRUCTURE OF BISYMMETRIC MATRICES, THEN FOR A GIVEN SET OF REAL NUMBERS WITH SPECIAL CONDITION, WE CONSTRUCT A NONNEGATIVE BISYMMETRIC MATRIX SUCH THAT THE GIVEN SET IS ITS SPECTRUM.

THIS PAPER INTRODUCES A MESH GENERATING ALGORITHM FOR SOLVING THE TRAFFIC FLOW EQUATION AS A CONSERVATION LAW EQUATION. THE IDEA BEHIND THE NEW METHOD IS TO USE THE CHARACTERISTIC CURVES AND MOVING NON-OSCILLATORY FINITE VOLUME METHOD. IN ADDITION, WHEN CHARACTERISTIC CURVES INTERSECT THE PROPOSED SCHEME USES SHOCK SPEED EQUATION IN ORDER TO IMPROVE COMPUTATIONAL EFFICIENCY. WE ALSO COMPARE THE OBTAINED RESULTS WITH THE CORRESPONDING SOLUTIONS COMPUTED BY THE MOVING MESH METHOD.

IN THIS PAPER THE ASYMPTOTIC EXPANSION OF MELNIKOV FUNCTION OF FIRST-ORDER ABOUT A HETEROCLINIC LOOP CONNECTING A CUSP OF ORDER TWO AND A HYPERBOLIC SADDLE FOR A PLANAR NEAR- HAMILTONIAN SYSTEM IS GIVEN. WE FIND THAT AT MOST THREE LIMIT CYCLES CAN BE BIFURCATED FROM THE PERIOD ANNULUS, ALSO WE GIVE DIFFERENT DISTRIBUTION OF BIFURCATED LIMIT CYCLES.

IN THIS PAPER, WE FIND GENERAL SOLUTIONS OF NON-LIE SYMMETRIES EQUATION OF THE FORM X= (F (T,X)+G (T,X)X)EX THROUGH L-SYMMETRY METHOD.L -SYMMETRY LET US REDUCE THE ORDER OF THIS EQUATION.

PROJECT CONTROL PROBLEM CONSISTS OF MONITORING THE PROJECT PROGRESS AT SOME CONTROL POINTS, FINDING POSSIBLE DEVIATIONS FROM THE BASE SCHEDULE AND IF NECESSARY, MAKING SOME ADJUSTMENTS TO THE DEVIATED SCHEDULE SUBJECT TO THE BUDGETS, THE EXISTING RECOVERING POLICIES AND THE OTHER ENVIRONMENTAL AND TECHNICAL POSSIBILITIES IN ORDER TO BRING THE SCHEDULE BACK ON THE RIGHT TRACK. IN THIS STUDY AND FOR THE FIRST TIME WE ADOPT THE MAXIMUM COVERING LOCATION MODEL TO FIND THE TIMINGS OF CONTROL POINTS SUCH THAT THE MAXIMUM CONTROL COVERAGE IS ACHIEVED, I.E. WITHIN THE GIVEN CONSTRAINTS ACHIEVING A SCHEDULE WHICH IS GLOBALLY AS CLOSE TO THE BASE SCHEDULE AS POSSIBLE. A NUMERICAL EXAMPLE ILLUSTRATES THE PROPOSED SOLUTION PROCEDURE.

IN THIS PAPER WE GIVE A GENERALIZATION ON MEASURE THEORY METHOD FOR SOLVING OPTIMAL CONTROL PROBLEMS AND OTHER NONLINEAR PROBLEMS THAT INTRODUCED BY J.E. RUBIO [3].

IN 2001, LEVINE AND HIS COWORKERS PRESENTED A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS AT THE LEVEL OF THE CELL. THIS IS THE FIRST MODEL THAT ENDOTHELIAL CELL MOVEMENT IN A ' MOTHER CAPILLARY' IS TIED TO ENDOTHELIAL CELL MOVEMENT AND PROLIFERATION IN THE DEVELOPING ' DAUGHTER CAPILLARY.IN THIS PAPER, ADAPTIVE MOVING MESH METHOD IS DESCRIBED BRIEFLY WHICH IN THIS METHOD, TO RAISE ACCURACY AND EFFICIENCY, INSTEAD OF USING A UNIFORM GRID BY A MONITOR FUNCTION NODES ARE CONCENTRATED IN AREAS WHERE GREATER ACCURACY IS REQUIRED. THE REST OF THE PAPER THE ADAPTIVE MOVING MESH METHOD IS USED FOR THE NUMERICAL SOLUTION OF THE ABOVE MODEL OF CAPILLARY FORMATION IN TUMOR ANGIOGENESIS.

IN THIS PAPER, BY USING THE FIXED POINT THEOREM, WE PROVE THE EXISTENCE OF POSITIVE SOLUTIONS FOR A SYSTEM OF M-POINT FRACTIONAL BOUNDARY VALUE PROBLEM.

THE PURPOSE OF THIS WORK IS TO PROVIDE THE RELIABLE SOLUTION FOR THE NONLINEAR VOLTERRA INTEGRO DIFFERENTIAL EQUATIONS OF THE SECOND KIND WITH SEPARABLE KERNEL BY USING THE COMBINE TAYLOR SERIES AND HOMOTOPY PERTURBATION METHOD. THE COMBINED ALGORITHM IS CAPABLE OF HANDLING NONLINEAR VOLTERRA INTEGRO DIFFERENTIAL EQUATION. COMPARSIONS OF THE RESULTS OF APPLYING NEW TECHNIQUE AND CLASSICAL HPM REVEAL THE NEW TECHNIQUE IS VERY EFFICTIVE AND CONVENIENT. MOREOVER, ONE PARTICULAR EXAMPLE IS DISCUSSED TO SHOW THE RELIABILITY AND THE PERFORMANCE OF THE COMBINE TAYLOR SERIES AND HOMOTOPY PERTURBATION METHOD.

IN THIS PAPER, WE WILL PRESENT A NEW ALGORITHM FOR SOLVING ITO STOCHASTIC DIFFERENTIAL EQUATIONS (SDES) IN CONTINUOUS PIECEWISE POLYNOMIAL SPACE. IN THIS APPROACH, WE WILL EMPLOY PIECEWISE COLLOCATION METHOD FOR DRIFT AND DIFFUSION TERMS OF THE GIVEN EQUATION. CONVERGENCE ORDER OF THE METHOD IS INVESTIGATED AND SOME NUMERICAL EXAMPLES ARE CONSIDERED TO DEMONSTRATE THE EFFICIENCY AND ROBUSTNESS OF THE METHOD.

IN THIS PAPER, WE STATE AND PROVE A NEW FORMULA EXPRESSING EXPLICITLY THE RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OF THE TRIANGULAR FUNCTIONS (TFS) WITH ANY FRACTIONAL-ORDER, IN TERMS OF TFS THEMSELVES AND USE IT TO CONSTRUCT A NEW AND GENERAL FORMULATION FOR THE TRIANGULAR FUNCTION (TF) OPERATIONAL MATRIX OF FRACTIONAL INTEGRAL (TF-OMFI). ALSO, BY USING THE TF-OMFI AND A SPECTRAL TAU METHOD, WE DEVELOP A DIRECT SOLUTION TECHNIQUE FOR SOLVING A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION.

IN THIS PAPER, AN ALGORITHM BASED ON THE REGULARIZATION AND ADOMIAN DECOMPOSITION METHODS, FOR HANDLING THE ILL-POSED TWO-DIMENSIONAL FREDHOLM EQUATIONS, IS INTRODUCED. THE APPLICATION OF THE PROPOSED ALGORITHM IS BASED ON THE TRANSFORMING THE FIRST KIND EQUATION TO A SECOND KIND EQUATION BY THE REGULARIZATION METHOD. THEN, BY CONVERTING THE FIRST KIND TO A SECOND KIND, THE ADOMIAN METHOD IS EMPLOYED TO HANDLE THE RESULTING FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND. THE EFFICIENCY OF THE APPROACH WILL BE SHOWN BY APPLYING THE PROCEDURE ON SOME EXAMPLES. THE MATHEMATICA PROGRAM BASED ON THE PROCEDURES IN THIS PAPER IS DESIGNED.

IN THIS ARTICLE, WE USE A GENERALIZATION OF THE EULER-MACLAURIN SUMMATION FORMULA FOR SOLVING WEAKLY SINGULAR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND. SINCE THE CLASSICAL EULER-MACLAURIN SUMMATION FORMULA MAY NOT BE APPLIED FOR APPROXIMATING SINGULAR INTEGRALS, THEN WE CANNOT USE THIS FORMULA FOR OBTAINING THE NUMERICAL SOLUTION OF WEAKLY SINGULAR FREDHOLM INTEGRAL EQUATIONS. BY THIS IDEA, THE BASIC EQUATIONS WILL BE CHANGED INTO THE ASSOCIATED SYSTEMS OF ALGEBRAIC EQUATIONS. SOME NUMERICAL EXAMPLES ARE GIVEN TO SHOW THE EFFECTIVENESS OF THE METHOD.

WE PROVIDE A SUMMARY OF TWO IMPORTANT WORKS ON COMPOUND QUADRATURE RULES. THE RULES CAN TREAT WEAKLY SINGULAR INTEGRALS WITH ANY KIND OF INTEGRABLE SINGULARITIES. THE RULES OWE THEIR ADVANTAGES OF SIMPLICITY AND EFFICIENCY MAINLY TO CHOOSE OF APPROPRIATE GRADED MESHES.

IN THIS PAPER, WE EXAMINED THE GLOBAL COLLOCATION METHOD USING SINC BASIS FUNCTIONS FOR NUMERICAL SOLUTION OF THE MODIFIED REGULARIZED LONG WAVE (MRLW) EQUATION. THE PROPAGATION OF SINGLE SOLITONS AND THE INTERACTION OF TWO SOLITARY WAVES ARE USED TO VALIDATE THE METHOD WHICH IS FOUND TO BE ACCURATE AND EFFICIENT.

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IN THIS PAPER, WE PRESENT A NEW METHOD OF EIGENVALUE ASSIGNMENT FOR DESCRIPTOR SYSTEMS, USING INVERSE EIGENVALUE PROBLEM. IN THIS METHOD, FIRST WE DEFINE THE INPUT AS A MULTIPLE OF THE OUTPUT DERIVATIVE FEEDBACK AND CHANGE THE DESCRIPTOR SYSTEM TO THE STANDARD SYSTEM WITH OUTPUT FEEDBACK, THEN ACCORDING TO THE EXISTS THEOREMS IN INVERSE EIGENVALUE PROBLEM, OUTPUT FEEDBACK MATRIX K IS CALCULATED SUCH THAT EIGENVALUES OF CLOSE-LOOP SYSTEM ARE ARBITRARY AND PRESCRIBED. A SIMPLE ALGORITHM AND A EXAMPLE IS GIVEN TO ILLUSTRATE THE RESULTS.

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THE AIM OF THIS PAPER TO EMPHASIZE ON THE IMPORTANCE OF MEMORY MANAGEMENT ISSUES IN MATLAB'S IMPLEMENTATION OF MATRIX-MATRIX MULTIPLICATION OVER MAX-PLUS ALGEBRA. THINKING IN THE SCALAR LEVEL, THE SIMPLEST WAY TO IMPLEMENT THE MATRIX MULTIPLICATION UPDATE IS TO UTILIZE 3 NESTED LOOPS. WE DEVELOP COLUMN-ORIENTED CODES FOR MATRIX-MATRIX MULTIPLICATION OVER (MAX, +). WE SHOW HOW VECTORIZATION SPEEDS-UP MATRIX-MATRIX MULTIPLICATION OVER MAX-PLUS ALGEBRA.

IN THIS PAPER, WE STUDY THE EXISTENCE OF SIGN-CHANGING SOLUTIONS FOR A BREZIS-NIRENBERG TYPE PROBLEM INVOLVING HARDY POTENTIAL AND SINGULAR COEFFICIENTS. WE USE THE LINKING THEOREM TO PROVE OUR MAIN RESULT.

IN THIS PAPER A NEW METHOD IS SUGGESTED FOR SOLVING MULTI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEM. THE PROPOSED METHOD IS BASED UPON TRANSFORMING TO MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM BY USING V.JOSHI, E.SINGH, N.GUPTA, PRIMAL-DUAL APPROACH TO SOLVE LINEAR FRACTIONAL PROGRAMMING PROBLEM, JOURNAL OF THE APPLIED MATHEMATICS, STATISTICS AND INFORMATICS (JAMSI), 4 (2008), NO.1. IN THE END, THE PROPOSED METHOD HAVE BEEN UTILIZED FOR EXAMPLES.

IN THIS PAPER, WE INTRODUCE F-TRANSFORM BASED ON FUZZY APPROXIMATION MODELS. WE SHOW HOW THE F-TRANSFORM TECHNIQUE CAN BE GENERALIZED TO THE HIGHER DEGREE. A DETAILED CHARACTERIZATION OF THE F2-TRANSFORM WITH SECOND ORDER POLYNOMIALS AS COMPONENTS IS GIVEN.

IN THIS PAPER, WE PROPOSE A NEW TWO-PARAMETER CLASS OF ITERATIVE METHODS TO SOLVE A NONLINEAR EQUATION. IT IS PROVED THAT ANY METHOD IN THIS CLASS IS CUBICALLY CONVERGENT IF AND ONLY IF THE PARAMETERS SUM UP TO ONE. SOME OF EXISTING THIRD-ORDER METHODS, BY SUITABLE SELECTION OF PARAMETERS, CAN BE PUT IN THIS CLASS. EVERY ITERATION OF THE CLASS REQUIRES ON EVALUATION OF THE FUNCTION, THREE OF THE FIRST DERIVATIVE, AND NONE OF THE SECOND DERIVATIVE. HENCE, ITS EFFICIENCY INDEX IS 31/4=1.316 THAT IS WORSE THAN ALL OTHER CUBICALLY CONVERGENT METHODS CONSIDERED. HOWEVER, NUMERICAL EXPERIMENTS SHOW THAT A SPECIAL METHOD IN OUR CLASS IS COMPARABLE TO THOSE IN TERMS OF ITERATIONS NUMBER.

MANY OF THE PROPOSED APPROACHES FOR NONLINEAR SYSTEMS CONTROL ARE DEVELOPED UNDER THE ASSUMPTION THAT ALL INVOLVED PARAMETERS ARE KNOWN. HOWEVER, THE SYSTEM UNCERTAINTIES ARE ALWAYS UNAVOIDABLE AND SOME SYSTEM PARAMETERS CANNOT BE EXACTLY KNOWN IN THE MOST PART OF THE CASES. IN THIS PAPER, ADAPTIVE CONTROL (AC) SCHEME IS PROPOSED TO SYSTEM IS ABLE TO ACHIEVE THE CONTROL OBJECTIVE REGARDLESS THE PARAMETRIC UNCERTAINTIES OF THE MODEL AND THE LACK OF A PRIORI KNOWLEDGE ON THE SYSTEM. ALSO, IS APPLIED THE ADAPTIVE SLIDING MODE CONTROL (ASMC) FOR SYNCHRONIZATION OF CHAOS IN HEART OSCILLATORS AND ROSSLER SYSTEM IN PRESENCE OF UNKNOWN PARAMETERS. FIRST, SUPPOSE THAT THERE ARE NO PARAMETER UNCERTAINTIES IN THE SYSTEM MODEL. THEN, THIS CONDITION IS REMOVED WHILE AN ADAPTIVE SLIDING MODE CONTROL SYSTEM IS DESIGNED. THE ADVANTAGES OF OBTAINING SUCH A MOTION ARE TWOFOLD: FIRSTLY THE SYSTEM BEHAVES AS A SYSTEM OF REDUCED ORDER WITH RESPECT TO THE ORIGINAL PLANT, AND SECONDLY THE MOVEMENT ON THE SLIDING SURFACE OF THE SYSTEM IS INSENSITIVE TO A PARTICULAR KIND OF PERTURBATION AND MODEL UNCERTAINTIES.

THE AIM OF THIS PAPER IS TO APPROXIMATE THE SOLUTION OF A CLASS OF INTEGRAL EQUATIONS OF THE THIRD KIND ON UNBOUNDED DOMAIN BY MEANS OF COLLOCATION METHOD BASED ON THE GENERALIZED LAGUERRE POLYNOMIALS….

THIS PAPER STUDIES THE MODIFIED SINC-GALERKIN METHOD FOR FINDING NUMERICAL SOLUTION OF THOMAS-FERMI PROBLEM. FIRST THE PROPERTIES OF THE SINC BASIS FUNCTION ARE PRESENTED THEN THE BASIC SINC-GALERKIN METHOD IS STUDIED. THE NUMERICAL RESULTS SHOW THE ACCURACY AND EFFICIENCY OF THE METHOD.

IN THIS PAPER, WE PROPOSE A METHOD FOR THE SOLUTION OF A MULTI-OBJECTIVE OPTIMAL CONTROL PROBLEM (MOOCP) IN A LINEAR DISTRIBUTED-PARAMETER SYSTEM GOVERNED BY A WAVE EQUATION. THE CONTROL PROBLEM OF THIS DISTRIBUTED-PARAMETER SYSTEM IS REDUCED TO AN APPROXIMATE MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM. THEN THE FUZZY GOAL PROGRAMMING TECHNIQUE TOGETHER WITH SIMPLEX METHOD OF LINEAR PROGRAMMING (LP) PROBLEMS IS USED TO FIND A PARETO OPTIMAL SOLUTION WITH THE BEST SATISFACTION PERFORMANCE. AN ILLUSTRATIVE NUMERICAL EXAMPLE IS WORKED OUT TO INDICATE THE EFFICIENCY OF THE PROPOSED METHOD.

WE CONSIDER THE CONCEPT OF THE SO-CALLED CARTAN EQUIVALENCE PROBLEM AND INTRODUCE THOSE FUNDAMENTAL RESULTS IN WHICH ITS ASSOCIATED POWERFUL ALGORITHM RELIES ON THEM. IN PARTICULAR AND FOR ILLUSTRATING BETTER THE CONCEPT, WE CONSIDER THE EQUIVALENCE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS AND SHOW THAT IN WHAT CIRCUMSTANCES SUCH ODES CAN BE EQUIVALENT TO THE SIMPLEST ONE Y”=0.

IN THIS PAPER, WE ILLUSTRATE THE SOLUTION OF THE INVERSE PROBLEM OF ESTIMATING THE TEMPERATURE-DEPENDENT HEAT SOURCE. INVERSE PROBLEMS OF ESTIMATING TEMPERATURE-DEPENDENT PROPERTIES AND HAVE BEEN GENERALLY SOLVED BY THE CONJUGATE GRADIENT METHOD WITH ADJOINT PROBLEM. ONE-DIMENSIONAL FORMULATION OF HEAT CONDUCTION PROBLEM IN A SLAB WAS USED. AN UNKNOWN HEAT SOURCE ARE ESTIMATED USING CONJUGATE GRADIENT METHOD. FINALLY, THE RESULTS OBTAINED FROM INVERSE METHOD COVER THE EXACT VALUES PROPERLY.

A NUMERICAL TECHNIQUE BASED ON FOURIER SERIES FOR FINDING OPTIMAL CONTROL OF NONLINEAR SYSTEM WITH QUADRATIC PERFORMANCE INDEX IS PRESENTED. AN OPERATIONAL MATRIX OF INTEGRATION AND PRODUCT MATRIX ARE INTRODUCED AND ARE USED TO REDUCE THE NONLINEAR DIFFERENTIAL EQUATION TO THE SOLUTION OF NONLINEAR ALGEBRAIC EQUATIONS. TWO EXAMPLES ARE CONSIDERED AND THE RESULT SHOW THE ACCURACY OF THE METHOD.