an analysis and comparison of conservative upwind difference schemes for ideal and non ideal gases in a recent paper p glaister conservative upwind difference schemes for the euler equations comput math appl 45 2003 1673 1682 a number of numerical schemes were presented for the euler equations governing compressible flows of an ideal gas the principal one of which is based on a conservative linearisation approach this scheme was subsequently extended to encompass compressible flows of real gases where the equation of state allows for non ideal gases p glaister conservative upwind difference schemes for compressible flows of a real gas comput math appl 48 2004 469 480 these schemes use different parameter vectors in their construction and consequently the scheme in p glaister conservative upwind difference schemes for compressible flows of a real gas comput math appl 48 2004 469 480 when applied to the special case of an ideal gas is not identical to the principal ideal gas scheme in p glaister conservative upwind difference schemes for the euler equations comput math appl 45 2003 1673 1682 in this paper it is shown how these schemes are related followed by a numerical comparison when each is applied to two standard test problems

on the unsolvability of inverse eigenvalues problems almost everywhere abstract using sard s theorem we show that the inverse eigenvalue problems are unsolvable almost everywhere if too many of the eigenvalues are equal

new eigenvalue estimates for complex matrices abstract in a recent work 1 we have proved that all the eigenvalues j of a complex matrix a of order n lie in a disk with center at tr a n and radius n 1 n k 1 n k 2 tr a 2 n 1 2 in this paper we prove that the eigenvalues of a are contained in a rectangle with vertices on the boundary circle of the mentioned disk improving in this way the result in 1 we recall some inequalities which alloww us to bound the radius of the disk and the rectangle the bounds can be computed without knowing the eigenvalues of a

localization of eigenvalues in elliptic regions abstract we prove that the eigenvalues j of an n by n complex matrix a with its characteristic polynomial having real coefficients lie in the elliptic region defined by 2 tr a n 2 2 y 2 2 2 where n 1 n n 1 n re k 2 re te a 2 n 1 2 and n 1 n k 1 n im k 2 1 2 this region is intersected with the strip y 1 2 k 1 u im k 2 1 2 to obtain an improved eigenvalue localization region we also give bounds for the semiaxes which can be computed without knowing the eigenvalues of a when a has r n nonzero eigenvalues we obtain a smaller elliptic region containing such nonzero eigenvalues

new conditions for the additive inverse eigenvalue problem for matrices abstract this paper deals with the following inverse eigenvalue problem given an n by n real symmetric matrix a and a set of real numbers i 1 n find a diagonal matrix d such that a d has eigenvalues i for the solvability of this problem a number of necessary conditions and sufficient conditions are known in this work new necessary conditions are derived while some sufficient conditions are optimized in particular one sufficient condition due to morel is obtained by optimizing a sufficient condition discovered by laborde

furuta s inequality and its application to ando s theorem abstract as a continuation of preceding notes we discuss furuta s inequality under the chaotic order defined by log a log b for positive invertible operators a and b which is applied to a generalization of ando s theorem consequently we obtain furuta s inequality under the chaotic order

genuinely multidimensional upwinding for the 2d shallow water equations a multidimensional upwinding technique is applied to the simulation of 2d shallow water flows it is adapted from fluctuation splitting methods recently proposed for the solution of the euler system of equations on unstructured triangular grids the basis of the numerical method is stated and the particular adaptation to the shallow water system is described numerical results of interest to hydraulic engineers are presented despite the complexities advantages related to the use of a discretisation based on triangles would seem to make the schemes competitive with those currently in use

conservative upwind difference schemes for the euler equations for real gas flows in a duct in a recent paper p glaister conservative upwind difference schemes for compressible flows in a duct comput math appl 56 2008 1787 1796 numerical schemes based on a conservative linearisation are presented for the euler equations governing compressible flows of an ideal gas in a duct of variable cross section and in p glaister conservative upwind difference schemes for compressible flows of a real gas comput math appl 48 2004 469 480 schemes based on this philosophy are presented for real gas flows with slab symmetry in this paper we seek to extend these ideas to encompass compressible flows of real gases in a duct this will incorporate the handling of additional terms arising out of the variable geometry and the non ideal nature of the gas

accurate flux vector splitting for shocks and shear layers a multidimensional upwinding technique is applied to the simulation of 2d shallow water flows it is adapted from fluctuation splitting methods recently proposed for the solution of the euler system of equations on unstructured triangular grids the basis of the numerical method is state and the particular adaptation to the shallow water system is described numerical results of interest to hydraulic engineers are presented despite the complexities advantages related to the use of a discretisation based on triangles would seem to make the schemes competitive with those currently in use 16 refs 23 figs

conservative upwind difference schemes for the shallow water equations abstract a study of a number of current numerical schemes for the shallow water equations leads to the establishment of relationships between these schemes further analysis then suggests new formulations of the schemes as well as an alternative scheme having the same key properties

conservative upwind difference schemes for compressible flows in a duct numerical results are presented and compared for four conservative upwind difference schemes for the euler equations representing the compressible flow of a gas in a duct of variable cross section the schemes are applied to a problem involving the interaction and reflection of a converging cylindrical shock the schemes vary in their treatment of the flux balance including treating part of it as a source as well as in the averaging of flow variables and whether the source term arising out of the geometry of the problem is handled using upwinding or treated as a point source the schemes are shown to give similar results while being different in construction and implementation and each having different approximate jacobians and treatment of the source

conservative upwind difference schemes for compressible flows of a real gas in a recent paper 1 numerical schemes based on a conservative linearisation arepresented for the euler equations governing compressible flows of an ideal gas and the subsequent study of these schemes establishes relationships between them through the use of a source term in this paper we seek to extend these ideas to encompass compressible flows of real gases where the equation of state allows for nonideal gases

on the solvability of polynomial systems arising in control we consider a compactification of a general system of polynomial equations in weighted projective space and give some sufficient conditions about the solvability of a polynomial system over c and r we also prove that for generic linear subspaces the inverse eigenvalue problem with perturbations in the linear subspace always has n solutions

on some operator inequalities a real valued continuous function f 2 defined on a finite or infinite interval of the real line is said to be operator monotone if for any pair of bounded selfadjoint operators a b on an infinite dimensional hilbert space a b implies f a f b here f a and f b are defined according to the usual functional calculus and refers to the order relation induced by the cone of positive semi definite operators operator monotony is quite a restrictive condition in fact for p 0 the function f 2 2 p is operator monotone on the half line 0 c if and only if 0 1 the function f 2 2 p possesses some property akin to operator monotony in this direction furuta i 3 recently observed that if r 0 p 0 q 1 satisfies 1 2r q p 2r then a b 0 implies a tp 2 q arbpa r l if p 2r and q 2 the requirement is automatically satisfied hence a p ap 2bpap 2 i 2 whenever a b 0 when a is invertible this means that

sufficient conditions for the solubility of inverse eigenvalue problems abstract we define an inverse eigenvalue problem which contains as special cases the classical additive and multiplicative inverse eigenvalue problems using some results on the distance of eigenvalues from matrix diagonal elements and brouwer s fixed point theorem we give sufficient conditions for the solubility of the problem

a comparison of conservative upwind difference schemes for the euler equations numerical results are presented and compared for three conservative upwind difference schemes for the euler equations when applied to two standard test problems this includes consideration of the effect of treating part of the flux balance as a source and a comparison of different averaging of the flow variables two of the schemes are also shown to be equivalent in their implementation while being different in construction and having different approximate jacobians

a decreasing sequence of eigenvalue localization regions abstract we construct a decreasing sequence of rectangles rp in such a way that all the eigenvalues of a complex matrix a are contained in each rectangle when a is a matrix with real spectrum or a normal matrix each rp can be obtained without knowing the eigenvalues of a

operator monotone functions which are defined implicitly and operator inequalities the function t 0 1 is operator monotone on 0 t this is known as the lowner heinz inequality however not too many examples of concrete operator monotone functions are known so far we will systematically seek operator monotone functions which are defined implicitly this investigation is new and our method seems to be powerful we will actually find a family of operator monotone functions which includes t 0 1 moreover by constructing one parameter families of operator monotone functions we will get many operator inequalities especially we will extend the furuta inequality and the exponential inequality of ando

an algorithm for symmetric generalized inverse eigenvalue problems abstract using qr like decomposition with column pivoting and least squares techniques we propose a new and efficient algorithm for solving symmetric generalized inverse eigenvalue problems and give its locally quadratic convergence analysis we also present some numerical experiments which illustrate the behaviour of our algorithm

conservative upwind difference schemes for the euler equations abstract in a recent paper 1 a number of numerical schemes for the shallow water equations based on a conservative linearization are analyzed in particular it is established that the schemes are related through the use of a source term in this paper this technique is applied to the euler equations and further analysis suggests a new formulation of an existing scheme having the same key properties

a new majorization between functions polynomials and operator inequalities let p be the set of all non negative operator monotone functions defined on 0 and put p 1 h h 1 p then p p 1 p 1 and p 1 p 1 p 1 for a function h t and a strictly increasing function h we write

an analysis of arithmetic averaging in a riemann solver for the one dimensional euler equations abstract an analysis of various arithmetic averaging procedures is undertaken for an approximate riemann solver for the one dimensional euler equations governing the compressible flow of an ideal gas this study draws on earlier work for both the reduced set of equations governing shallow water flows and the full euler equations and is ultimately intended for use with the equations governing two dimensional steady and unsteady compressible flows

mixed matrix operator inequalities we will show that if 0 a b c and s s t t 1 then a s bs t ct implies that ar 2 s bss t cst ar 2 ar 2 s bts t ctt ar 2 s r t r fort 1 t s 0 r 0 and a1 r ar 2 s bts t ctt ar 2 1 r t r fort 1 r 0 these are the extensions of inequalities shown by t furuta proc amer math soc 101 1987 85 111 1991 511 moreover we will give an inequality say mixed inequality which includes the above inequalities and the inequality due to hansen pedersen math ann 258 1982 229

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached