evaluation of the weight distribution of a class of cyclic codes based on index 2 gauss sums the duals of cyclic codes with two zeros have been extensively studied and their weight distributions have recently been evaluated in some cases in this paper we determine the weight distribution of a certain new class of such codes by computations involving index 2 gauss sums

the weight distributions of the duals of cyclic codes with two zeros cyclic codes with two zeros and their dual codes have been a subject of study for many years however their weight distributions are known only for a few cases in this paper the weight distributions of the duals of the cyclic codes with two zeros are settled for a few more cases

slant joint antieigenvalues and antieigenvectors of operators in normal subalgebras abstract we will study the slant joint antieigenvalues and antieigenvectors of pairs of operators that belong to the same closed normal subalgebra of the algebra of bounded operators on a separable hilbert space this extends the slant antieigenvalue theory from single normal operators to pairs of normal operators our results may be viewed as extensions of the greub rheinboldt inequality from two positive operators to two normal operators

the weight distributions of cyclic codes and elliptic curves cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes have been studied for many years and find many applications the determination of the weight distributions of such codes is an open problem generally the weight distributions of cyclic codes are difficult to determine utilizing a class of elliptic curves this paper determines the weight distributions of dual codes of q ary cyclic codes with two zeros for a few more cases where q is an odd prime power

eigenvalues of the laplacian in two dimensions the eigenvalue problem for the laplace operator in two dimensions is classical in mathematics and physics nevertheless computational methods for estimating the eigenvalues are still of much current interest particularly in applications to acoustic and electromagnetic waveguides although our primary interest is with the computational methods there are a number of theoretical results on the behavior of the eigenvalues and eigenfunctions that are useful for understanding the methods and in addition are of interest in themselves these results are discussed first and then the various computational methods that have been used to estimate the eigenvalues are reviewed with particular emphasis on methods that give error bounds some of the more powerful techniques available are illustrated by applying them to a model problem

cyclic codes and sequences from generalized coulter matthews function in this paper we will study the exponential sum sigmaxisinfq x alphax pk 1 2 betax that is related to the generalized coulter matthews function x pk 1 2 with k gcd as applications we obtain the following the correlation distribution of a p ary m sequence and a decimated m sequence of degree pk 1 2 the weight distribution of the cyclic code whose dual has two zeros pi 1 and pi pk 1 2

symmetric anti eigenvalue and symmetric anti eigenvector the idea of symmetric anti eigenvalue and symmetric anti eigenvector of a bounded linear operator t on a hilbert space h is introduced the structure of symmetric anti eigenvectors of a self adjoint and certain classes of normal operators is found in terms of eigenvectors the kantorovich inequality for self adjoint operators and bounds for symmetric anti eigenvalues for certain classes of normal operators are also discussed

slant antieigenvalues and slant antieigenvectors of operators we will introduce a general notion of slant antieigenvalue and corresponding slant antieigenvector then we establish how that theory may be compared to and in some sense reduced to the standard antieigenvalue theory generally speaking our point of view is to accommodate such generalized antieigenvalue theories within the basic concepts and techniques of the original antieigenvalue theory

an extended operator trigonometry the operator trigonometry of symmetric positive definite spd matrices is extended to arbitrary invertible matrices a and to arbitrary invertible bounded operators a on a hilbert space some background and motivation for these results is provided

vibration of non homogeneous rectangular membranes with arbitrary interfaces abstract the study deals with the generalized solution of the title problem the free vibration problem of a rectangular membrane with partial domains each of uniform density and arbitrary interface is tackled previous studies by other researchers include straight parallel to the borders and oblique interfaces and bent ones the solution is found by means of a direct variational method with a series composed with a complete set of functions two alternative sets are explored trigonometric and power series such series are uniformly convergent to the exact solution the approach is straightforward and very efficient from the computational viewpoint a determinant factorization method is employed to automatically eliminate eventual spurious frequencies the well known analogy between plates and membranes does not hold in this problem and a demonstration is included diverse illustrations are worked out as the cases of an oblique straight line interface and an open curve line which divides the membrane in two domains each of different density are first presented also a rectangular membrane with an interior closed domain is stated and the numerical example of a circular interior zone is included comparison between the two alternatives and with other authors results show excellent agreement in all cases the computational cost is very low

antieigenvalues method of estimation and calculation abstract let t be a linear operator on a hilbert space h a method of estimation and calcu lation of inf re tx x tx x h x 1 as well as some other expressions containing two quadratic forms is proposed this method is based on the toeplitz hausdorff theorem on the convexity of the numerical range of any operator on h

five families of three weight ternary cyclic codes and their duals as a subclass of linear codes cyclic codes have applications in consumer electronics data storage systems and communication systems as they have efficient encoding and decoding algorithms in this paper five families of three weight ternary cyclic codes whose duals have two zeros are presented the weight distributions of the five families of cyclic codes are settled the duals of two families of the cyclic codes are optimal

weight distributions of some binary primitive cyclic codes let s and k be integers such that s is a divisor of 2 sup k 1 let g x be a divisor of x sup s 1 over f sub 2 and let spl pi x be a primitive polynomial of degree k over f sub 2 we consider the binary cyclic code c of length n 2 sup k 1 generated by x sup n 1 g x spl pi x for special cases we determine the weight distribution of c by using the weights of the cyclic code of length s generated by x sup s 1 g x

a family of five weight cyclic codes and their weight enumerators cyclic codes are a subclass of linear codes and have applications in consumer electronics data storage systems and communication systems as they have efficient encoding and decoding algorithms in this paper a family of p ary cyclic codes whose duals have three pairwise nonconjugate zeros is proposed the weight distribution of this family of cyclic codes is determined it turns out that the proposed cyclic codes have five nonzero weights

the weight enumerator of a class of cyclic codes cyclic codes with two zeros and their dual codes have been a subject of study for many years however their weight distributions are known only for a few cases in this paper the weight distributions of the duals of the cyclic codes with two zeros are settled for a few cases the weight distributions of punctured versions of these codes are also determined for several special cases

a general description for the weight distribution of some reducible cyclic codes a remarkably general result which provides the evaluation of a family of exponential sums was presented by moisio in 2000 in this work we use such a general result in order to determine the value distribution of a particular kind of exponential sum then motivated by some new ideas of ma we use this value distribution in order to formulate a general description for the weight distribution of a particular kind of reducible cyclic codes that has been recently studied as will be shown such a general description not only gives a unified explanation for these families of codes but also gives the weight distribution for other reducible cyclic codes that have not been studied so far in addition among the kind of codes studied here we will characterize those that are projective

the weight distribution of an extended class of reducible cyclic codes the weight distribution of a class of nonirreducible cyclic codes was given by ma et al 6 by imposing a special set of conditions on this class of codes it was recently shown that the resulting codes for this class can be obtained as elements in a family of codes introduced by vega in 7 now by using a different set of conditions the aim of this paper is to present an extended version for the class of codes studied by ma et al

antieigenvalues and total antieigenvalues of normal operators we will study antieigenvalues total antieigenvalues antieigenvectors and total antieigenvectors for normal operators this will generalize the earlier work of the author and karl gustafson on normal matrices on finite dimensional spaces we will also study antieigenvalues and total antieigenvalues of semigroups generated by accretive normal operators

optimal sets of frequency hopping sequences from linear cyclic codes in communication systems frequency hopping spread spectrum and direct sequence spread spectrum are two main spread coding technologies frequency hopping sequences are used in fh cdma systems in this paper an earlier idea of constructing optimal sets of frequency hopping sequences is further investigated new optimal parameters of sets of frequency hopping sequences are obtained with subcodes of the reed solomon codes optimal sets of frequency hopping sequences are constructed with a class of irreducible cyclic codes as a byproduct the weight distribution of a subclass of irreducible cyclic codes is determined

on the joint antieigenvalues of operators in normal subalgebras we will study the joint antieigenvalues of pairs of operators that belong to the same closed normal subalgebra of b h this extends antieigenvalue theory from single normal operators to pairs of commuting normal operators

optimal cyclic codes with generalized niho type zeros and the weight distribution in this paper we extend two earlier works further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions it is interesting to note that many cyclic codes in the family are optimal and have only a few non zero weights besides using similar ideas we carry out some subtle manipulation of certain exponential sums

free vibration of regular polygonal plates with simply supported edges the free vibration of regular polygonal plates with simply supported edges is studied by the dynamical analogy with membranes a regular polygonal membrane is formed on a rectangular membrane by fixing several segments with the reaction forces acting on all edges of an actual polygonal membrane regarded as unknown harmonic loads the stationary response of the membrane to these loads is expressed by the eigenfunctions of the extended rectangular membrane without internal supports the force distributions along the edges are expanded into fourier sine series with unknown coefficients and the homogeneous equations for the coefficients are derived by restraint conditions on the edges the natural frequencies and the mode shapes of the actual membrane are determined by calculating the eigenvalues and eigenvectors of the equations the method is applied to an equilateral triangular through a regular decagonal membrane the natural frequencies and mode shapes are calculated numerically and the effect of the shape of membrane is discussed the numerical values obtained for polygonal membranes are immediately converted into those of simply supported polygonal plates

niho type cross correlation functions via dickson polynomials and kloosterman sums suppose that n 2k is even we study the cross correlation function between two m sequences for niho type decimations d 2 sup k 1 s 1 we develop a new technique to study the value distribution of these cross correlation functions which makes use of dickson polynomials as a first application we derive here the distribution of the six valued cross correlation function for s 3 and odd k up to a term which depends on kloosterman sums in addition applying simpler methods we prove a theorem providing niho type decimations with four valued cross correlation functions and their distribution we conjecture that the latter result actually covers all such decimations

on the walsh transform of a class of functions from niho exponents in this paper a class of functions from niho exponents with four valued walsh transform is obtained for any prime by a uniform method and the distribution of the walsh transform values is also completely determined in particular this class of functions is proven to be bent for a special case although it is shown that the obtained bent functions are equivalent to the leander kholosha s class of bent functions a direct and much simpler proof for the bentness of this kind of niho functions is provided

exponential sums from half quadratic forms and their applications in this paper we consider a class of exponential sums from some half quadratic binomials the exponential sums are proven to be eleven valued with maximal magnitude 1 2 q sqrt q except for the trivial value q as applications first we investigate the autocorrelation and cross correlation distribution among the sequences in a sequence family second we determine the weight distributions of several classes of linear codes some of the dual codes have minimum distance four which are optimal with respect to the hamming bound our results extend the result by choi et al and show that some correlation values in it do not occur

on the weight distribution of cyclic codes with niho exponents recently there has been intensive research on the weight distributions of cyclic codes in this paper we compute the weight distributions of three classes of cyclic codes with niho exponents more specifically we obtain two classes of binary three weight and four weight cyclic codes and a class of nonbinary four weight cyclic codes the weight distributions follow from the determination of value distributions of certain exponential sums several examples are presented to show that some of our codes are optimal and some have the best known parameters

exact free vibration analysis for membrane assemblies with general classical boundary conditions abstract this paper proposes exact dynamic stiffness formulations for membranes and their assemblies under any arbitrary classical boundary conditions first by taking exact solutions in one direction satisfying all possible opposite edge supports we can derive exact general solutions of the helmholtz equation for membrane vibration then generic force and displacement boundary conditions in the other direction are expressed in terms of the general solutions finally the dynamic stiffness matrices of rectangular membrane elements are formulated which can be assembled directly and allows applications of arbitrary boundary conditions as an accurate and efficient modal solution technique the wittrick williams ww algorithm is applied onto the global dynamic stiffness matrix of the final structure the most important issue of the ww algorithm j 0 count has been resolved with the analytical expressions derived for all possible cases the proposed dynamic stiffness method dsm is then applied to several examples including individual membranes and their assemblies high accuracy and exactness of the proposed method within the whole frequency range is demonstrated by comparison with the finite element method besides interesting findings have been observed on repeated eigenvalues with distinct mode shapes corresponding to certain aspect ratio and tension ratio where physical and mathematical understanding has been provided

antieigenvalue techniques in statistics abstract in a number of his recent papers karl gustafson has outlined the similarities between the antieigenvalue theory he founded and several finite dimensional matrix optimization theorems for positive matrices arising in statistics in this paper we will show how the techniques that the author and karl gustafson have used for computation of antieigenvalues can also be applied to prove and generalize these matrix optimization theorems in statistics we will primarily focus on two techniques which we have used in antieigenvalue computations in recent years these two techniques are a two nonzero component property for certain class of functionals and converting the matrix optimization problems in statistics to a convex programing problem indeed these two techniques allow us to generalize some of the matrix optimization problems arising in statistics to strongly accretive operators on finite or infinite dimensional hilbert spaces

seven classes of three weight cyclic codes cyclic codes are a subclass of linear codes and have applications in consumer electronics data storage systems and communication systems as they have efficient encoding and decoding algorithms compared with linear block codes in this paper seven classes of three weight cyclic codes over gf p whose duals have two zeros are presented where p is an odd prime the weight distributions of the seven classes of cyclic codes are settled some of the cyclic codes are optimal in the sense that they meet certain bounds on linear codes the application of these cyclic codes in secret sharing is also considered

cyclic codes and sequences the generalized kasami case in this paper the large family of generalized kasami sequences has been studied in particular the cross correlation distribution among these sequences has been explicitly calculated meanwhile the weight distributions of two classes of cyclic codes could also be determined this paper generalizes the results from several previous papers

on the weight distributions of two classes of cyclic codes let q pm where p is an odd prime mges2 and 1lesklesm 1 let tr be the trace mapping from fq to fp and zetap e2pii p be a primitive pth root of unity in this paper we determine the value distribution of the following exponential sums sigmaxisinf qchi alphaxp k 1 betax2 alpha betaisinfq where chi x zetap tr x is the canonical additive character of fq as applications we have the following 1 we determine the weight distribution of the cyclic codes c1 and c2 over fpt with parity check polynomial h2 x h3 x and h1 x h2 x h3 x respectively where t is a divisor of d gcd m k and h1 x h2 x and h3 x are the minimal polynomials of pi 1 pi 2 and pi p k 1 over fpt respectively for a primitive element pi of fq 2 we determine the correlation distribution between two m sequences of period q 1 moreover we find a new class of p ary bent functions this paper extends the results in feng and luo 2008

exact vibration solutions for some irregularly shaped membranes and simply supported plates abstract a procedure is discussed for realizing some exact analytical eigenfunctions and corresponding eigenfrequencies for vibrating membranes with fixed rectilinear edges delineable on a grid of squares and their diagonals by the membrane plate analogy the corresponding eigenmodes and frequencies of simply supported vibrating plates of the same shapes may be obtained the fundamental modes of certain shapes with curved boundaries are also considered

operator trigonometry of statistics and econometrics a new and useful geometric point of view for the understanding and analysis of certain matrix methods as they are used in statistics and econometrics is presented applications to statistical efficiency parameter estimation and correlation theory are given in particular we show that worst case relative least squares efficiency although achieved by maximally inefficient regressors is also achieved by maximal covariance matrix turning vectors also we elaborate geometrically a commutator trace efficiency result of p bloomfield and g s watson biometrika 62 1975 121 well established lagrange multiplier methods for constrained optimizations are compared to use of an euler equation from the new geometric theory