legendre polynomial solutions of high order linear fredholm integro differential equations in this study a legendre collocation matrix method is presented to solve high order linear fredholm integro differential equations under the mixed conditions in terms of legendre polynomials the proposed method converts the equation and conditions to matrix equations by means of collocation points on the interval 1 1 which corresponding to systems of linear algebraic equations with legendre coefficients thus by solving the matrix equation legendre coefficients and polynomial approach are obtained also examples that illustrate the pertinent features of the method are presented and by using the error analysis the results are discussed

injective stabilization of additive functors ii co torsion and the auslander gruson jensen functor abstract the formalism of injective stabilization of additive functors is used to define a new notion of the torsion submodule of a module it applies to arbitrary modules over arbitrary rings for arbitrary modules over commutative domains it coincides with the classical torsion and for finitely presented modules over arbitrary rings it coincides with the bass torsion a formally dual approach based on projective stabilization gives rise to a new concept the cotorsion quotient module of a module this is done in complete generality the new concept is defined for any module over any ring unlike torsion cotorsion does not have classical prototypes general properties of these constructs are established it is shown that the auslander gruson jensen functor applied to the cotorsion functor returns the torsion functor as a consequence a ring is one sided absolutely pure if and only if each pure injective on the other side is cotorsion free if the injective envelope of the ring is finitely presented then the right adjoint of the auslander gruson jensen functor applied to the torsion functor returns the cotorsion functor this correspondence establishes a duality between torsion and cotorsion over such rings in particular this duality applies to artin algebras it is also shown that over any ring the character module of the torsion of a module is isomorphic to the cotorsion of the character module of the module under various finiteness conditions on the injective envelope of the ring the derived functors of torsion and cotorsion are computed

an approximation method for the solution of nonlinear integral equations a chebyshev collocation method has been presented to solve nonlinear integral equations in terms of chebyshev polynomials this method transforms the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown chebyshev coefficients finally some examples are presented to illustrate the method and results discussed

approximate solution to linear complex differential equation by a new approximate approach the purpose of this study is to give a taylor polynomial approximation for the solution of high order linear complex differential equations with variable coefficients and mixed conditions about any point for this purpose a matrix method is introduced this method is based on first taking the truncated taylor expansions of the functions in the complex differential equation and then substituting their matrix forms into the given equation hence the result matrix equation can be solved and the unknown taylor coefficients can be found approximately also examples that illustrate the pertinent features of the method are presented and the results are discussed

linkage of modules abstract it is shown that the notion of linkage of algebraic varieties introduced by peskine and szpiro can be generalized to finitely generated modules over non commutative noetherian semiperfect rings besides greater generality the module theoretic approach brings about new invariants of linkage and yields improved results and simpler proofs even in the traditional settings of commutative algebraic geometry and local algebra connections with auslander reiten sequences singularity theory derived categories local cohomology buchsbaum modules and maximal cohen macaulay approximations are discussed

on the complex oscillation of some linear differential equations we treat the linear differential equation f k a z f 0 wherek 2 is an integer anda z is a transcendental entire function of order a it is shown that any non trivial solution of the equation satisfies f a where f is the exponent of convergence of the zero sequence off under the conditionkn r 1 a t r a r efor ak 2kand an exceptional seteof finite linear measure the second order equationf ep1 z ep2 z q z f 0 wherep1 z p2 z are non constant polynomials andq z is an entire function is also studied

on rd optimized progressive image coding using jpeg among the many different modes of operations allowed in the current jpeg standard the sequential and progressive modes are the most widely used while the sequential jpeg mode yields essentially the same level of compression performance for most encoder implementations the performance of progressive jpeg depends highly upon the designed encoder structure this is due to the flexibility the standard leaves open in designing progressive jpeg encoders in this work a rate distortion rd optimized jpeg compliant progressive encoder is presented that produces a sequence of scans ordered in terms of decreasing importance our encoder outperforms an optimized sequential jpeg encoder in terms of compression efficiency substantially at low and high bit rates moreover unlike existing jpeg compliant encoders our encoder can achieve precise rate distortion control substantially better compression performance and precise rate control provided by our progressive jpeg compliant encoding algorithm are two highly desired features currently sought for the emerging jpeg 2000 standard

1 torsion of finite modules over semiperfect rings abstract we initiate the study of 1 torsion of finite modules over two sided noetherian semiperfect rings in particular we give a criterion for determining when the 1 torsion submodule contains minimal generators of the module we also provide an explicit construction for a projective cover of the submodule generated by the torsion elements in the top of the module some of the obtained results hold without the noetherian assumption we also give several applications to local algebra

oscillation results of certain higher order linear differential equations with periodic coefficients in the complex plane abstract 1 has given a characterization of homogeneous linear differential equations with certain analytic periodic coefficients which admits a solution with finite exponent of convergence however her method seems too general and in most cases too complicated for applications we give in this paper a direct approach to the problem and obtain several such characterizations which do not seem to follow from those of baesch in particular an explicit necessary and sufficient condition to the problem is given for certain third order equations the results again do not seem to follow from those of baesch our method is based on that of 8 which in turn depends on basic representations of solutions given by bank laine and langley

chebyshev polynomial solutions of systems of high order linear differential equations with variable coefficients a chebyshev collocation method has been presented for numerically solving systems of high order linear ordinary differential equations with variable coefficients using the chebyshev collocation points this method transforms the ode system and the given conditions to matrix equations with unknown chebyshev coefficients by means of the obtained matrix equations a new system of equations which corresponds to the system of linear algebraic equations is gained hence by finding the chebyshev coefficients easily the finite chebyshev series approach is obtained

scene adaptive coder an efficient single pass adaptive bandwidth compression technique using the discrete cosine transform is described the coding process involves a simple thresholding and normalization operation on the transform coefficients adaptivity is achieved by using a rate buffer for channel rate equalization the buffer status and input rate are monitored to generate a feedback normalization factor excellent results are demonstrated for coding of color images at 0 4 bits pixel corresponding to real time color television transmission over a 1 5 mbit s channel

a collocation method to find solutions of linear complex differential equations in circular domains in this study we introduce a collocation approach for solving high order linear complex differential equations in circular domain by using collocation points defined in a circular domain and bessel functions of the first kind this method transforms the linear complex differential equations into a matrix equation the matrix equation corresponds to a system of linear equations with the unknown bessel coefficients proposed method gives the analytic solution when the exact solutions are polynomials numerical examples are given to demonstrate the validity and applicability of the technique and the comparisons are made with existing results the results obtained from the examples demonstrate the efficiency and accuracy of the present work all of the numerical computations have been computed on computer using a code written in matlab

modified jpeg huffman coding it is a well observed characteristic that when a dct block is traversed in the zigzag order the ac coefficients generally decrease in size and the run length of zero coefficients increase in number this article presents a minor modification to the huffman coding of the jpeg baseline compression algorithm to exploit this redundancy for this purpose dct blocks are divided into bands so that each band can be coded using a separate code table three implementations are presented which all move the end of block marker up in the middle of dct block and use it to indicate the band boundaries experimental results are presented to compare reduction in the code size obtained by our methods with the jpeg sequential mode huffman coding and arithmetic coding methods the average code reduction to the total image code size of one of our methods is 4 our methods can also be used for progressive image transmission and hence experimental results are also given to compare them with two three and four band implementations of the jpeg spectral selection method

a taylor collocation method for the numerical solution of complex differential equations with mixed conditions in elliptic domains an approximate method for solving higher order linear complex differential equations in the elliptic domains is proposed the approach is based on a taylor collocation method which consists of the matrix representation of expressions in the differential equation and the collocation points defined in the elliptic domain illustrative examples are included to demonstrate the validity and applicability of the technique and performed on the computer using a program written in maple9

linear differential equations with entire coefficients of p q order in the complex plane in this paper we firstly investigate the complex high order linear differential equations in which the coefficients are entire functions of p q order and obtain some results which improve and generalize some previous results in cao 2009 3 chen and yang 2000 4 heittokangas et al 2006 12 kinnunen 1998 17 tu and yi 2008 20

on the meromorphic solutions of linear differential equations on the complex plane abstract in this paper we investigate the iterated order iterated type and iterated convergence exponent of zeros of meromorphic solutions of the equations f k a k 1 z f k 1 a 1 z f a 0 z f 0 f k a k 1 z f k 1 a 1 z f a 0 z f f z where a 0 0 a 1 a k 1 and f 0 are meromorphic on the complex plane we improve and extend many results due to z x chen z x chen and c c yang l kinnunen b belaidi j tu and c f yi t b cao and h x yi and others the fixed points of solutions are also considered in this paper some errors in earlier papers of the present authors and others are pointed out

the auslander gruson jensen recollement abstract for any ring r the auslander gruson jensen functor d a fp r mod ab mod r ab op is the exact functor which sends a representable functor x to the tensor functor x we show that this functor admits a fully faithful right adjoint d r and a fully faithful left adjoint d l that is we show that d a is part of a recollement of abelian categories in particular this shows that d a is a localisation and a colocalisation which gives an equivalence of categories fp r mod ab f d a f 0 mod r ab op we show that f d a f 0 is the serre subcategory of fp r mod ab consisting of finitely presented functors which arise from a pure exact sequence as an application of our main result we show that the 0 th right pure derived functor of a finitely presented functor r mod ab is also finitely presented

free vibration of a strong non linear system described with complex functions abstract in this paper two approximate analytical methods for solving strong non linear differential equations with complex functions are developed besides the adopted elliptic krylov bogolubov procedure an alternative analytical method based on the variation of the parameters as well as the elliptic krylov bogolubov is introduced the difference is that the alternative method considers two approximate first order differential equations the suggested procedures are compared and tested for the system with strong cubic non linearity and a small non linearity of van der pol type comparing the approximate analytical solutions with exact numerical solution it is concluded that the difference is negligible

taylor polynomial solution of high order nonlinear volterra fredholm integro differential equations in this paper a taylor method is developed to find an approximate solution for high order nonlinear volterra fredholm integro differential equation numerical examples presented to illustrate the accuracy of the method

approximate solution of complex differential equations for a rectangular domain with taylor collocation method in this study taylor collocation method is investigated for the approximate computation of high order linear complex differential equations using the collocation points on any rectangular domain in the complex plane the method transforms the given complex differential equation and the mixed conditions to matrix equation with unknown taylor coefficients by means of the obtained matrix equations the taylor coefficients can be easily computed hence the finite taylor series approach is obtained also examples are presented and the results are discussed

injective stabilization of additive functors i preliminaries abstract this paper is the first one in a series of three dealing with the concept of injective stabilization of the tensor product and its applications its primary goal is to collect known facts and establish a basic operational calculus that will be used in the subsequent parts this is done in greater generality than is necessary for the stated goal several results of independent interest are also established they include among other things connections with satellites an explicit construction of the stabilization of a finitely presented functor various exactness properties of the injectively stable functors a construction from a functor and a short exact sequence of a doubly infinite exact sequence by splicing the injective stabilization of the functor and its derived functors when specialized to the tensor product with a finitely presented module the injective stabilization with coefficients in the ring is isomorphic to the 1 torsion functor the auslander reiten formula is extended to a more general formula which holds for arbitrary i e not necessarily finite modules over arbitrary associative rings with identity weakening of the assumptions in the theorems of eilenberg and watts leads to characterizations of the requisite zeroth derived functors the subsequent papers provide applications of the developed techniques part ii deals with new notions of torsion module and cotorsion module of a module this is done for arbitrary modules over arbitrary rings part iii introduces a new concept called the asymptotic stabilization of the tensor product the result is closely related to different variants of stable homology these are generalizations of tate homology to arbitrary rings a comparison transformation from vogel homology to the asymptotic stabilization of the tensor product is constructed and shown to be epic