linear programming in linear time when the dimension is fixed it is demonstrated that the linear programming problem in d variables and n constraints can be solved in o n time when d is fixed this bound follows from a multidimensional search technique which is applicable for quadratic programming as well there is also developed an algorithm that is polynomial in both n and d provided d is bounded by a certain slowly growing function of n

applications of differential transform method to differential algebraic equations in this paper numerical solution of linear differential algebraic equations daes is considered by differential transform method two different problems have been solved by using the technique and solutions have been compared very well with those obtained by exact solutions differential transform method can easily be applied to daes and series solutions are obtained after the transformation here we have formulated series coefficients very simply for the considered problems

optimal shape analysis of a column structure under various loading conditions by using differential transform method dtm abstract the effects of loading on the optimal shape of an euler bernoulli column is investigated by considering four loading conditions which are mainly classified as eccentric compressive and follower type the governing equations obtained from the structural stability condition of the column are used as a constraint to determine the minimum value of the volume by applying hamilton principle in the preceding task the analysis is presented in step by step manner the calculations are carried out by using differential transform method dtm which is a seminumerical analytical solution technique that can be applied to various types of differential equations by using dtm the non linear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations the optimal distribution of cross sectional area along column length is obtained then the volume of such column is calculated and compared to that of the uniform column which is also stable under given loading the results obtained revealed out that dtm is a quite powerful solution technique for optimal shape analysis of a column structure

inverse obnoxious p median location problems on trees with edge length modifications under different norms abstract in this paper we consider an inverse obnoxious p median location problem with p 2 on trees in which the aim is to change the edge lengths at the minimum total cost so that a predetermined set of p vertices becomes an obnoxious p median location a novel combinatorial algorithm with o p 2 v t 2 log 2 v t time complexity is proposed for obtaining an optimal solution of the problem under the weighted manhattan norm moreover optimal solution algorithms with o p 2 v t time complexity are developed for the problem under the weighted chebyshev norm and the weighted bottleneck type hamming distance

the adomian decomposition method for computing eigenelements of sturm liouville two point boundary value problems we will consider the adomian decomposition method for computing the eigenelements of sturm liouville two point boundary value problem the method proved to be very successful and powerful in computing such elements numerical examples showed the competitive nature of the method comparison with the results of others will also be presented

lattice topological field theory in two dimensions the lattice definition of a two dimensional topological field theory tft is given generically and the exact solution is obtained explicitly in particular the set of all lattice topological field theories is shown to be in one to one correspondence with the set of all associative algebrasr and the physical hilbert space is identified with the centerz r of the associative algebrar perturbations of tft s are also considered in this approach showing that the form of topological perturbations is automatically determined and that all tft s are obtained from one tft by such perturbations several examples are presented including twistedn 2 minimal topological matter and the case wherer is a group ring

on an instance of the inverse shortest paths problem the inverse shortest paths problem in a graph is considered that is the problem of recovering the arc costs given some information about the shortest paths in the graph the problem is first motivated by some practical examples arising from applications an algorithm based on the goldfarb idnani method for convex quadratic programming is then proposed and analyzed for one of the instances of the problem preliminary numerical results are reported

application of differential transformation to eigenvalue problems using differential transformation to solve eigenvalue problems is introduced in this study first differential transformation is introduced briefly second taking differential transformation of the strum liouville problem a set of difference equations is derived doing some simple mathematics operations on these operations we can get any ith eigenvalue and eigenfunction at a time finally two eigenvalue problems are solved by the present method the calculated results are compared closely with the results obtained by another analytical method

the inverse convex ordered 1 median problem on trees under chebyshev norm and hamming distance abstract we investigate the inverse convex ordered 1 median problem on unweighted trees under the cost functions related to the chebyshev norm and the hamming distance by the special structure of the problem under chebyshev norm we deduce the so called maximum modification to modify the edge lengths of the tree additionally the cost function of the problem receives only finite values under the bottleneck hamming distance therefore we can find the optimal cost of the problem by applying binary search it is shown that both of the problems under chebyshev norm and under the bottleneck hamming distance can be solved in o n 2 log n time in all situations with or without essential topology changes here n is the number of vertices of the tree finally we prove that the problem under weighted sum hamming distance is np hard

flexural torsional coupled vibration analysis of axially loaded closed section composite timoshenko beam by using dtm abstract this study introduces the differential transform method dtm to analyse the free vibration response of an axially loaded closed section composite timoshenko beam which features material coupling between flapwise bending and torsional vibrations due to ply orientation the governing differential equations of motion are derived using hamilton s principle and solved by applying dtm the mode shapes are plotted the natural frequencies are calculated and the effects of the bending torsion coupling the axial force and the slenderness ratio on the natural frequencies are investigated using the computer package mathematica wherever possible comparisons are made with the studies in open literature

topological higher gauge theory from bf to bfcg theory we study generalizations of three and four dimensional bf theories in the context of higher gauge theory first we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of yetter mackaay and porter under certain conditions we can present their corresponding continuum counterparts in terms of classical lagrangians we then explain that two of these models are already familiar from the literature the ea model of three dimensional gravity coupled to topological matter and also a four dimensional model of bf theory coupled to topological matter

solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method in this paper we will give some results for developing the two dimensional differential transform tddt for double integrals then the tddt method will be developed for solving a class of two dimensional linear and nonlinear volterra integral equations we also give some examples to demonstrate the accuracy of the method

solutions of the system of differential equations by differential transform method in this study three dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time moreover as an application of two and three dimensional differential transform exact solutions of linear and non linear systems of partial differential equations have been investigated the results of the present method are compared very well with those obtained by decomposition method differential transform method can easily be applied to linear or non linear problems and reduces the size of computational work with this method exact solutions may be obtained without any need of cumbersome work and it is an useful tool for analytical and numerical solutions

some reverse location problems abstract the general location problem in a network is to find locations of facilities in a given network such that the total cost is minimum it is very often to have its reverse case in which the facilities have already been located on the network and the problem is how to improve the network within a given budget so that the improved network is as efficient as possible in this paper we present a strongly polynomial algorithm for a reverse location problem in tree networks the method can be extended to solve reverse two or more location problems

different applications for the differential transformation in the differential equations the differential transformation technique which is applied to solve eigenvalue problems and to solve partial differential equations p d e is proposed in this study first using the one dimensional differential transformation to construct the eigenvalues and the normalized eigenfunctions for the differential equation of the second and the fourth order second using the two dimensional differential transformation to solve p d e of the first and second order with constant coefficients in both cases a set of difference equations is derived and the calculated results are compared closely with the results obtained by other analytical methods

differential transform method for the system of two dimensional nonlinear volterra integro differential equations in this paper we develop the differential transform method dtm for solving a class of the system of two dimensional linear and nonlinear volterra integro differential equations of the second kind to this end we give some preliminary results of the differential transform and describe the method of this paper we also give some examples to demonstrate the accuracy of the presented method

on solving some eigenvalue problems by using a differential transformation this paper deals with eigenvalues and normalized eigenfunctions for a sturm liouville eigenvalue problem the technique we have used is based on applying a differential transform to our eigenvalue problem we have compared our results with some known analytical results

on second quantization of quantum groups we construct a deformation of the function algebra on the quantum group slq 2 into a trialgebra in the sense of crane and frenkel we show that this naturally acts on the trialgebraic deformation of the manin plane previously introduced by the authors alternatively one can view it as acting on the trialgebraic deformation of the fermionic manin plane we prove that the trialgebraic deformation of slq 2 defines a 2 c category a structure as needed for the superselection structure of massive two dimensional quantum field theories besides this we investigate another approach to trialgebra deformations of a bialgebra as a deformation of a fock space construction over the bialgebra

on the determination of approximate periodic solutions of some non linear ode abstract we propose a numerical symbolic method for the approximation of periodic solutions of a type of non linear ode the efficiency of our method is contrasted with the harmonic balance method and with another one which combines the differential transformation method with pade approximants on a non trivial example the relativistic oscillator it is shown that our method is computationally more reliable

application of the differential transformation method to a non linear conservative system this paper adopts the differential transformation method to solve the free vibrations of a conservative oscillator with inertia and static cubic non linearities the concept of differential transformation is briefly introduced and is then employed to derive a set of difference equations for the free vibration oscillator problem parametric studies on the effects of the time response are presented the results obtained from the differential transformation method are then compared with those from the runge kutta method in order to verify the accuracy of the proposed method it is shown that excellent agreement exists between the two sets of results

a new homotopy perturbation method for solving systems of partial differential equations abstract in this paper a new homotopy perturbation method nhpm is introduced for obtaining solutions of systems of non linear partial differential equations theoretical considerations are discussed to illustrate the capability and reliability of the method three examples are provided comparison of the results of applying nhpm with those of applying hpm reveal the effectiveness and convenience of the new technique

a numerical solution of second order linear partial differential equations by differential transform two dimensional differential transform provides an effective tool to numerically solve partial differential equations in this paper we propose a general numerical solution of second order linear partial differential equations using two dimensional differential transform numerical examples justify the proposed scheme

the 1 3 dimensional burgers equation and its comparative solutions in this paper we will carry out an analytic comparative study between the adomian decomposition method and the differential transformation method this is achieved by handling the 1 3 dimensional burgers equation two numerical simulations have also been carried out to validate and demonstrate efficiency of the two methods

structures and diagrammatics of four dimensional topological lattice field theories abstract crane and frenkel proposed a state sum invariant for triangulated 4 manifolds they sketched the definition of a hopf category that was to be used in their construction crane and yetter studied hopf categories and gave some examples using group cocycles that are associated to the drinfeld double of a finite group in this paper we define a state sum invariant of triangulated 4 manifolds using crane yetter cocycles as boltzmann weights our invariant is analogous to the 3 dimensional invariants defined by dijkgraaf and witten and the invariants that are defined via hopf algebras we present diagrammatic methods for the study of such invariants that illustrate connections between hopf categories and moves to triangulations

the inverse fermat weber problem abstract given n points in the plane with nonnegative weights the inverse fermat weber problem consists in changing the weights at minimum cost such that a prespecified point in the plane becomes the euclidean 1 median the cost is proportional to the increase or decrease of the corresponding weight in case that the prespecified point does not coincide with one of the given n points the inverse fermat weber problem can be formulated as linear program we derive a purely combinatorial algorithm which solves the inverse fermat weber problem with unit cost using o n greedy like iterations where each of them can be done in constant time if the points are sorted according to their slopes if the prespecified point coincides with one of the given n points it is shown that the corresponding inverse problem can be written as convex problem and hence is solvable in polynomial time to any fixed precision

differential transformation technique for steady nonlinear heat conduction problems in this paper the differential transformation method is applied to solve steady nonlinear heat conduction problems the proposed approach provides a new iterative procedure to find the spectrum of the analytic solutions therefore approximate solutions can be obtained in the form of taylor s series expansion throughout the range of interest

solving partial differential equations by two dimensional differential transform method using two dimensional differential transform to solve partial differential equations pde is proposed in this study first the theory of two dimensional differential transform is introduced second taking two dimensional differential transform of a pde problem a set of difference equations is derived doing some simple mathematical operations on these equations we can get a closed form series solution or an approximate solution quickly finally three pde problems with constant and variable coefficients are solved by the present method the calculated results are compared very well with those obtained by other analytical or approximate methods

2 groups trialgebras and their hopf categories of representations a strict 2 group is a 2 category with one object in which all morphisms and all 2 morphisms have inverses 2 groups have been studied in the context of homotopy theory higher gauge theory and topological quantum field theory tqft in the present article we develop the notions of trialgebra and cotrialgebra generalizations of hopf algebras with two multiplications and one comultiplication or vice versa and the notion of hopf categories generalizations of monoidal categories with an additional functorial comultiplication we show that each strict 2 group has a group algebra which is a cocommutative trialgebra and that each strict finite 2 group has a function algebra which is a commutative cotrialgebra each such commutative cotrialgebra gives rise to a symmetric hopf category of corepresentations in the semisimple case this hopf category is a 2 vector space according to kapranov and voevodsky we also show that strict compact topological 2 groups are characterized by their c cotrialgebras of complex valued functions generalizing the gel fand representation and that commutative cotrialgebras are characterized by their symmetric hopf categories of corepresentations generalizing tannaka krei n reconstruction technically all these results are obtained using ideas from functorial semantics by studying models of the essentially algebraic theory of categories in various base categories of familiar algebraic structures and the functors that describe the relationships between them

differential transformation technique for solving higher order initial value problems in this paper the differential transformation method is applied to solve the higher order initial value problems hoivps the differential transformation method of fixed grid size is used to approximate solutions hoivps the higher order of taylor s series be applied thus there exist a trade off between the selection of the order of taylor s series and the grid size the proposed method provides the taylor s series between any adjacent grid points numerical examples are used to illustrate the preciseness and effectiveness of the proposed the method

numerical solutions of linear time varying descriptor systems via hybrid functions state analysis of linear time varying descriptor systems via hybrid functions are proposed in this paper based upon some useful properties of hybrid functions a special product matrix and a related coefficient matrix are applied to solve the descriptor systems the unknown coefficient matrix will be in generalized lyapunov equation form which is solved via the kronecker product method the advantages of hybrid functions are not only the values of n and m are adjustable but also it can yield more accurate numerical solutions than orthogonal functions and orthogonal polynomials to the problems of solving the descriptor systems we propose that the available optimal values of n and m can minimize the relative errors in the numerical solutions the high accuracy and the wide applicability of hybrid function approach will be demonstrated with numerical examples

free vibration analysis of circular plates by differential transformation method this study analyses the free vibrations of circular thin plates for simply supported clamped and free boundary conditions the solution method used is differential transform method dtm which is a semi numerical analytical solution technique that can be applied to various types of differential equations by using dtm the governing differential equations are reduced to recurrence relations and its related boundary regularity conditions are transformed into a set of algebraic equations the frequency equations are obtained for the possible combinations of the outer edge boundary conditions and the regularity conditions at the center of the circular plate numerical results for the dimensionless natural frequencies are presented and then compared to the bessel function solution and the numerical solutions that appear in literature it is observed that dtm is a robust and powerful tool for eigenvalue analysis of circular thin plates

an efficient method for computing eigenelements of sturm liouville fourth order boundary value problems in this paper an efficient method based on the adomian decomposition for computing the eigenelements of fourth order sturm liouville boundary value problems is developed numerical examples show that the method proposed is easy to implement and produces accurate results

vibration analysis of continuous systems by differential transformation this paper demonstrates the application of the technique of differential transformation to free vibration of continuous systems the specific problem chosen for this purpose is that of thin beams the transformation technique is employed for deriving frequency equations and mode functions the frequencies and mode shapes obtained from the differential transformation solutions are compared with the exact analytical solutions it is shown that the solutions obtained from the technique have a very high degree of accuracy