on computing of arbitrary positive integer powers of odd order anti tridiagonal matrices with zeros in main skew diagonal and elements 1 1 1 1 1 1 1 1 in neighbouring diagonals in this paper we derive the general expression of the lth power email protected n for one type of anti tridiagonal matrices of odd order

on possibility distribution abstract in this paper the concept of possibility is further considered fuzzy optimal value of the linear programming with fuzzy numbers is given and the continuity theorems of optimal value in parametric linear programming are proposed

obstructions to embeddability into hyperquadrics and explicit examples we give series of explicit examples of levi nondegenerate real analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension for this we construct invariants attached to a given hypersurface that serve as obstructions to embeddability we further study the embeddability problem for real analytic submanifolds of higher codimension and answer a question by forstneric

on anti pentadiagonal persymmetric hankel matrices with perturbed corners in this paper we express the eigenvalues of real anti pentadiagonal persymmetric hankel matrices with perturbed corners as the zeros of explicit rational functions from these prescribed eigenvalues we give an orthogonal diagonalization for these matrices and a formula to compute its integer powers in particular an explicit expression not depending on any unknown parameter for the determinant and the inverse of complex anti pentadiagonal persymmetric hankel matrices with perturbed corners is provided

on computing of arbitrary positive powers for one type of anti tridiagonal matrices of even order abstract in this paper the general expression of the lth power l n where n is the set of positive integers for one type of anti tridiagonal matrices of even order is derived

numerical solution of a secular equation a method is proposed for the solution of a secular equation arising in modified symmetric eigenvalue problems and in several other areas this equation has singularities which make the application of standard root finding methods difficult in order to solve the equation a class of transformations of variables is considered which transform the equation into one for which newton s method converges from any point in a certain given interval in addition the form of the transformed equation suggests a convergence accelerating modification of newton s method the same ideas are applied to the secant method and numerical results are presented

a normal form for a real 2 codimensional submanifold in cn 1 near a cr singularity abstract we construct a formal normal form for a class of real submanifolds m c n 1 of codimension 2 near a cr singularity approximating the sphere our result gives a generalization of huang yin s normal form in c 2 to the higher dimensional analog case

on computing of arbitrary positive powers for anti tridiagonal matrices of even order abstract in this paper the general expression of the lth power l n for one type of anti tridiagonal matrices is derived expressions of eigenvectors and jordan s form of the matrix and of the transforming matrix and its inverse are given

convergent normal form and canonical connection for hypersurfaces of finite type in c2 abstract we study the holomorphic equivalence problem for finite type hypersurfaces in c 2 we discover a geometric condition which is sufficient for the existence of a natural convergent normal form for a finite type hypersurface we also provide an explicit construction of such a normal form as an application we construct a canonical connection for a large class of finite type hypersurfaces to the best of our knowledge this gives the first construction of an invariant connection for levi degenerate hypersurfaces in c 2

the statistical convergence for sequences of fuzzy number valued functions based on the concept of statistical convergence of sequences of fuzzy numbers the statistical convergence uniformly statistical convergence and equi statistical convergence of sequences of fuzzy number valued functions are defined and investigated in this paper the relationship among statistical convergence uniformly statistical convergence equi statistical convergence of sequences of fuzzy number valued functions and their representations of sequences of level cuts are discussed in addition the egorov and lebesgue theorems for the statistical convergence of sequences of fuzzy number valued functions are obtained in a finite measure set finally the statistical convergence in measure for sequences of fuzzy number valued functions is investigated and it is proved that the outer and inner statistical convergence in measure are equivalent in a finite measure set for a sequence of fuzzy number valued functions

integer powers of real odd order skew persymmetric anti tridiagonal matrices with constant anti diagonals antitridiag n a c a a r 0 c r in this paper we give the eigenvalue decomposition for real odd order skew persymmetric anti tridiagonal matrices with constant anti diagonals and derive the general expression for integer powers of such matrices

finite type hypersurfaces with divergent normal form we consider the convergence problem for normal forms on finite type hypersurfaces in dimension two constructed in kola math res lett 12 897 910 2005 two families of examples of hypersurfaces with divergent normal form are given the results also show that the divergence phenomenon cannot be avoided by a modification of the normal form construction

powers of complex persymmetric or skew persymmetric anti tridiagonal matrices with constant anti diagonals in this paper we derive a general expression for the entries of the powers of any complex persymmetric or skew persymmetric anti tridiagonal matrix with constant anti diagonals in terms of the chebyshev polynomials of the second kind

possibilistic linear programming with triangular fuzzy numbers abstract we consider a mathematical programming problem where all the parameters may be fuzzy variables specified by their possibility distribution and we define the possibility distribution of the objective function the ideas are illustrated on possibilistic linear programming

integer powers of real even order anti tridiagonal hankel matrices of the form antitridiagn a c a in this paper we give the eigenvalue decomposition for one type of real even order anti tridiagonal hankel matrices and derive the general expression for integer powers of such matrices

real hypersurfaces orders of contact and applications a fundamental problem in the modem theory of several complex variables concerns the boundary behavior of the cauchy riemann equations suppose that d is an open domain in cn and that its boundary m is a smooth real submanifold of cn how does the geometry of m influence the function theory on d one approach to this question is the a neumann problem 6 there one studies the inhomogeneous cauchy riemann equations au a where a is a 0 q form with distribution coefficients on the closed domain d u m satisfying the necessary compatibility condition a a 0 the a neumann problem constructs a particular solution u which is orthogonal to the null space of the complex laplacian kohn 10a has solved this problem and has shown that good local regularity properties for u in terms of a follow from so called subelliptic estimates it is natural to seek geometric conditions on m that are necessary and sufficient for these estimates in this paper we will be concerned with a certain geometric condition on m that we feel is the right one for subellipticity although the motivation for the questions discussed here comes from partial differential equations the techniques come from algebraic geometry to see why we state theorems of kohn greiner and catlin concerning subellipticity kohn 1oa has discovered a sufficient condition for a subelliptic estimate near a fixed point p in m in case d is pseudoconvex and is contained in c2 this condition is equivalent to the finiteness of order of tangency of every complex analytic one dimensional manifold with m at p greiner 13 established the necessity of this condition in

powers of real persymmetric anti tridiagonal matrices with constant anti diagonals in this paper we present an eigenvalue decomposition with an orthogonal eigenvector matrix for any real persymmetric anti tridiagonal matrix with constant anti diagonals furthermore we derive a general expression for the entries of the powers of these anti tridiagonal matrices in terms of the chebyshev polynomials of the second kind

integer powers of anti tridiagonal matrices of the form antitridiag n a 0 b a b r in this paper we use chebyshev polynomials to derive a general expression for integer powers of real anti tridiagonal matrices with constant anti diagonals and null northeast to southwest diagonal

forward stable eigenvalue decomposition of rank one modifications of diagonal matrices abstract we present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank one modification of a diagonal matrix the algorithm computes each eigenvalue and all components of the corresponding eigenvector with high relative accuracy in o n operations the algorithm is based on a shift and invert approach only a single element of the inverse of the shifted matrix eventually needs to be computed with double the working precision each eigenvalue and the corresponding eigenvector can be computed separately which makes the algorithm adaptable for parallel computing our results extend to the complex hermitian case the algorithm is similar to the algorithm for solving the eigenvalue problem for real symmetric arrowhead matrices from n jakovcevic stor et al 2015 16

nonnegative and positive definiteness of matrices modified by two matrices of rank one abstract necessary and sufficient conditions are given for the nonnegative and positive definiteness of matrices of the form a a 1 a 1 a 2 a 2 and a a 1 a 1 a 2 a 2 where a is a hermitian matrix and a 1 a 2 are complex vectors they are derived using some auxiliary results which seem to be of independent interest as well some particular cases of these conditions are also discussed especially in the context of related results known in the literature

a bishop surface with a vanishing bishop invariant we give a solution to the equivalence problem for bishop surfaces with the bishop invariant 0 as a consequence we answer in the negative a problem that moser asked in 1985 after his work with webster in 1983 and his own work in 1985 this will be done in two major steps we first derive the formal normal form for such surfaces we then show that two real analytic bishop surfaces with 0 are holomorphically equivalent if and only if they have the same formal normal form up to a trivial rotation our normal form is constructed by an induction procedure through a completely new weighting system from what is used in the literature our convergence proof is done through a new hyperbolic geometry associated with the surface