infinitely divisible nonnegative matrices m matrices and the embedding problem for finite state stationary markov chains abstract this paper explicitly details the relation between m matrices nonnegative roots of nonnegative matrices and the embedding problem for finite state stationary markov chains the set of nonsingular nonnegative matrices with arbitrary nonnegative roots is shown to be the closure of the set of matrices with matrix roots in im the methods presented here employ nothing beyond basic matrix analysis however it answers a question regarding m matrices posed over 30 years ago and as an application a new characterization of the set of all embeddable stochastic matrices is obtained as a corollary

graph theoretic methods for matrix completion problems abstract a pattern is a list of positions in an n n real matrix a matrix completion problem for the class of matrices asks whether every partial matrix whose specified entries are exactly the positions of the pattern can be completed to a matrix we survey the current state of research on matrix completion problems for many subclasses of p 0 matrices including positive definite matrices m matrices inverse m matrices p matrices and matrices defined by various sign symmetry and positivity conditions on p 0 and p matrices graph theoretic techniques used to study completion problems are discussed several new results are also presented including the solution to the m 0 matrix completion problem and the sign symmetric p 0 matrix completion problem

inverse no matrices abstract results similar to those of thomas l markham concerning inverse m matrices are shown to hold for inverse n o matrices a more general result and an alternate method of proof using schur complements are given for one of markham s theorems conditions are given to transform a nonpositive matrix to an n o amtrix by multiplication by householder transformations also an lu factorization of an inverse n o matrix is given

reasoning with the finitely many valued łukasiewicz fuzzy description logic sroiq fuzzy description logics are a formalism for the representation of structured knowledge affected by imprecision or vagueness they have become popular as a language for fuzzy ontology representation to date most of the work in this direction has focused on the so called zadeh family of fuzzy operators or fuzzy logic which has several limitations in this paper we generalize existing proposals and show how to reason with a fuzzy extension of the logic sroiq the logic behind the language owl 2 under finitely many valued lukasiewicz fuzzy logic we show for the first time that it is decidable over a finite set of truth values by presenting a reasoning preserving procedure to obtain a non fuzzy representation for the logic this reduction makes it possible to reuse current representation languages as well as currently available reasoners for ontologies

sign patterns of inverse nonnegative matrices abstract we determine here the 0 sign patterns which occur among the inverses of nonsingular entrywise nonnegative matrices these results complete a sequence of work which began with the characterization of all possible sign patterns which occur among inverses of positive matrices and the characterization in this general case is more involved to state than the earlier ones

closure properties of certain positivity classes of matrices under various algebraic operations abstract we present a table indicating whether or not each of five positivity classes of matrices positive definite hermitian matrices m matrices inverse m matrices totally positive matrices and inverse totally positive matrices is closed under each of seven algebraic operations conventional multiplication addition powers extraction of roots hadamard multiplication the hadamard product of one element and the inverse of another and lu factorization three of these 35 facts seem not to have been previously known and key examples and references are given

on the failure of the finite model property in some fuzzy description logics fuzzy description logics dls are a family of logics which allow the representation of and the reasoning with structured knowledge affected by vagueness although most of the not very expressive crisp dls such as alc enjoy the finite model property fmp this is not the case once we move into the fuzzy case in this paper we show that if we allow arbitrary knowledge bases then the fuzzy dls alc under lukasiewicz and product fuzzy logics do not verify the fmp even if we restrict to witnessed models in other words finite satisfiability and witnessed satisfiability are different for arbitrary knowledge bases the aim of this paper is to point out the failure of fmp because it affects several algorithms published in the literature for reasoning under fuzzy dls

classes of products of m matrices and inverse m matrices abstract suppose a is an n n matrix with real entries we are concerned with the following question when is a a product of m matrices and inverses of m matrices first some general results are elaborated then four special classes of matrices are investigated for two of these classes our considerations involve the determination when a is a product of m matrices from these classes the role of the exponential function for these classes is noted and a conjecture is posed for a commuting class of m matrices

higher order mixed moment approximations for the fokker planck equation in one space dimension we study mixed moment models full zeroth moment half higher moments for a fokker planck equation in one space dimension mixed moment minimum entropy models are known to overcome the zero net flux problem of full moment minimum entropy m n models a realizability theory for these mixed moments of arbitrary order is derived as well as a new closure which we refer to as kershaw closure they provide nonnegative distribution functions combined with an analytical closure numerical tests are performed with standard first order finite volume schemes and compared with a finite difference fokker planck scheme

on the inverse of a special schur complement abstract the inverse of a schur complement is a very useful tool in many algorithms for the computation of the matrix inversion in this paper we study the inverse of a special schur complement cd 1 b we proved that always exist some x and y such that xdy is a inverse of cd 1 b furthermore using minimal rank properties we give some explicit expressions for x y and the inverse of cd 1 b numerical examples also given

inverse m matrices ii this is an update of the 1981 survey by the first author in the meantime a considerable amount has been learned about the very special structure of the important class of inverse m matrices developments since the earlier survey are emphasized but we have tried to be somewhat complete and some results have not previously been published some proofs are given where appropriate and references are given for others after some elementary preliminaries results are grouped by certain natural categories

a realizability preserving discontinuous galerkin method for the m1 model of radiative transfer the m 1 model for radiative transfer coupled to a material energy equation in planar geometry is studied in this paper for this model to be well posed its moment variables must fulfill certain realizability conditions our main focus is the design and implementation of an explicit runge kutta discontinuous galerkin method which under a more restrictive cfl condition guarantees the realizability of the moment variables and the positivity of the material temperature an analytical proof for our realizability preserving scheme which also includes a slope limiting technique is provided and confirmed by various numerical examples among other things we present accuracy tests showing convergence up to fourth order compare our results with an analytical solution in a riemann problem and consider a marshak wave problem

the degree of an exact order matrix the classes of exact order k matrices for any positive integer k were defined and studied by mohan parthasarathy and sridhar mohan s r t parthasarathy r sridhar 1994 the linear complementarity problem with exact order matrices math oper res 19 618 644 here we prove results on the linear complementarity problem lcpq m for m belonging to the class of exact order k k 3 using the concepts of degree theory our main result in this paper consists in proving that a matrix m rn n of exact order k for any positive integer n k 3 belongs to the class q if and only if the degree of m is either 1 or 1 also a complete characterization of exact order 2 matrices is presented in terms of their inverse structure

partial moment entropy approximation to radiative heat transfer we extend the half moment entropy closure for the radiative heat transfer equations presented in dubroca and klar b dubroca a klar half moment closure for radiative transfer equations j comput phys 180 2002 584 596 and turpault et al r turpault m frank b dubroca a klar multigroup half space moment approximations to the radiative heat transfer equations j comput phys 198 2004 363 371 to multi d to that end we consider a partial moment system with general partitions of the unit sphere closed by an entropy minimization principle we give physical and mathematical reasons for this choice of model and study its properties several numerical examples in different physical regimes are presented

the symmetric m matrix and symmetric inverse m matrix completion problems abstract the symmetric m matrix and symmetric m 0 matrix completion problems are solved and results of johnson and smith linear algebra appl 290 1999 193 are extended to solve the symmetric inverse m matrix completion problem 1 a pattern i e a list of positions in an n n matrix has symmetric m completion i e every partial symmetric m matrix specifying the pattern can be completed to a symmetric m matrix if and only if the principal subpattern r determined by its diagonal is permutation similar to a pattern that is block diagonal with each diagonal block complete or in graph theoretic terms if and only if each component of the graph of r is a clique 2 a pattern has symmetric m 0 completion if and only if the pattern is permutation similar to a pattern that is block diagonal with each diagonal block either complete or omitting all diagonal positions or in graph theoretic terms if and only if every principal subpattern corresponding to a component of the graph of the pattern either omits all diagonal positions or includes all positions 3 a pattern has symmetric inverse m completion if and only if its graph is block clique and no diagonal position is omitted that corresponds to a vertex in a graph block of order 2 the techniques used are also applied to matrix completion problems for other classes of symmetric matrices

on inverse m matrices abstract we generalize a previous result of lewin and neumann and present a characterization of inverse m matrices the approach is mainly graph theoretical

kershaw closures for linear transport equations in slab geometry ii this paper provides a generalization of the realizability preserving discontinuous galerkin scheme given in 3 to general full moment models that can be closed analytically it is applied to the class of kershaw closures which are able to provide a cheap closure of the moment problem this results in an efficient algorithm for the underlying linear transport equation the efficiency of high order methods is demonstrated using numerical convergence tests and non smooth benchmark problems

inverse transport calculations in optical imaging with subspace optimization algorithms inverse boundary value problems for the radiative transport equation play an important role in optics based medical imaging techniques such as diffuse optical tomography dot and fluorescence optical tomography fot despite the rapid progress in the mathematical theory and numerical computation of these inverse problems in recent years developing robust and efficient reconstruction algorithms remains a challenging task and an active research topic we propose here a robust reconstruction method that is based on subspace minimization techniques the method splits the unknown transport solution or a functional of it into low frequency and high frequency components and uses singular value decomposition to analytically recover part of low frequency information minimization is then applied to recover part of the high frequency components of the unknowns we present some numerical simulations with synthetic data to demonstrate the performance of the proposed algorithm

completions of inverse m matrix patterns abstract a list of positions in an n n real matrix that includes all diagonal positions a pattern is said to have inverse m completion if every partial inverse m matrix that specifies exactly these positions can be completed to an inverse m matrix johnson and smith c r johnson r l smith linear algebra and its applications 241 243 1996 655 667 characterize the positionally symmetric patterns that have inverse m completion as those patterns whose graphs are block clique in this paper the restriction of positional symmetry is removed a pattern has inverse m completion if and only if the digraph g of the pattern has the properties a the induced subdigraph of a cycle is a clique and b if g contains both arc i j and a path of length 1 between i and j then the induced subdigraph of the path is a clique furthermore any irreducible pattern with inverse m completion is positionally symmetric and has a block clique digraph any pattern is permutation similar to a block lower triangular pattern with irreducible diagonal blocks and such a pattern has inverse m completion if and only if i the pattern digraph of each diagonal block is block clique ii each subdiagonal block contains at most one position and iii the pattern digraph of the block structure has no alternate path to a single arc

on copositive matrices abstract a criterion for copositive matrices is given and for n 3 the set of all copositive matrices is determined in terms of matrix elements copositive matrices are applied to the problem of excluding periodic solutions of certain algebraic differential equations

some properties of schur complements and diagonal schur complements of diagonally dominant matrices in this paper we prove that the diagonal schur complement of a strictly doubly diagonally dominant matrix is strictly doubly diagonally dominant matrix the same holds for the diagonal schur complement of a strictly generalized doubly diagonally dominant matrix and a nonsingular h matrix we point out that under certain assumptions the diagonal schur complement of a strictly doubly doubly product diagonally dominant matrix is also strictly doubly doubly product diagonally dominant further we provide the distribution of the real parts of eigenvalues of a diagonal schur complement of h matrix we also show that the schur complement of a diagonally dominant matrix is not always diagonally dominant by a numerical example and then obtain a sufficient condition to ensure that the schur complement of a diagonally dominant matrix is diagonally dominant

looking for nonnegative solutions of a leontief dynamic model let a be an n n nonnegative real matrix we know that a is monotone if it has a nonnegative inverse moreover if a has an appropriate generalized inverse then we can obtain nonnegative solutions for the linear system ax b where b 0 in this paper using properties about nonnegatives matrices we present sufficient conditions in order that the leontief price model i f p k 1 1 r k fp k gp0 k 1 a0 where f i at 1bt and g i at 1 have nonnegative solutions

on schur complement of block diagonally dominant matrices abstract it is well known that the schur complements of strictly diagonally dominant matrices are strictly diagonally dominant d carlson t markham schur complements of diagonally dominant matrices czech math j 29 104 1979 246 251 the same is true of generalized strictly diagonally dominant matrices jianzhou liu yungqing huang some properties on schur complements of h matrix and diagonally dominant matrices linear algebra appl 389 2004 365 380 in this paper this result is extended to the block strictly diagonally dominant matrices and the generalized block strictly diagonally dominant matrices that is it is shown that the schur complement of a block strictly diagonally dominant matrix is a block strictly diagonally dominant matrix and so is the schur complement of a generalized block strictly diagonally dominant matrix

inverse m matrix completions of patterns omitting some diagonal positions abstract let n 1 n which subsets q of n n have the property that whenever a ij for i j q form a partial inverse m matrix i e a ij 0 and if l l q then the inverse of a ij i j l is an m matrix a ij can be defined for i j q so that the inverse of a a ij is an m matrix in terms of a digraph g with vertex set n and arcs i j q with i j our results say 1 it is necessary that the induced subdigraph of any alternate path to an arc be a clique 2 a cycle need not be contained in a clique if i i q for at least one vertex i of 3 when n 4 it is necessary and sufficient that condition 1 is true and every simple cycle has a vertex i with i i q and 4 the general question can be reduced to the case in which g is strongly connected much as it has been when q contains i i for every i n

nonnegative matrices with power invariant zero patterns abstract if a is a nonsingular m matrix the elements of the sequence a k all have the same zero pattern using the drazin inverse we show that a similar zero pattern invariance property holds for a class of matrices which is larger than the generalized m matrices

fuzzy description logics with general t norms and datatypes fuzzy description logics dls are a family of logics which allow the representation of and the reasoning within structured knowledge affected by vagueness although a relatively important amount of work has been carried out in the last years current fuzzy dls still present several limitations in this work we face two problems the common restriction to zadeh and lukasiewicz fuzzy logics and the inability to deal with datatypes different from fuzzy sets in particular we propose a semantics based on the use of a general left continuous t norm and an involutive negation specially focused on product logic and furthermore we show how to handle functional concrete roles relating individuals of the domain and strings real or integer numbers

on the inverse mean first passage matrix problem and the inverse m matrix problem abstract the inverse mean first passage time problem is given a positive matrix m r n n then when does there exist an n state discrete time homogeneous ergodic markov chain c whose mean first passage matrix is m the inverse m matrix problem is given a nonnegative matrix a then when is a an inverse of an m matrix the main thrust of this paper is to show that the existence of a solution to one of the problems can be characterized by the existence of a solution to the other in so doing we extend earlier results of tetali and fiedler

generalized ultrametric matrices a class of inverse m matrices abstract recently marti nez michon and san marti n introduced the new class of symmetric strictly ultrametric matrices they proved that the inverse of a strictly ultrametric matrix is a strictly row and strictly column diagonally dominant stieltjes matrix here we generalize their result by introducing a class of nonsymmetric matrices calledgeneralized ultrametric matrices we give a necessary and sufficient condition for the regularity of these matrices and prove that the inverse of a nonsingular generalized ultrametric matrix is a row and column diagonally dominant m matrix we establish that a nonnegative matrix is a generalized ultrametric matrix if and only if the matrix is a certain sum of at most rank two matrices moreover we give a characterization of generalized ultrametric matrices based on weighted trees the entries of generalized ultrametric matrices then arise as certain distances between the leaves and the root of the tree

characterizations of inverse m matrices with special zero patterns in this paper we provide some characterizations of inverse m matrices with special zero patterns in particular we give necessary and sufficient conditions for k diagonal matrices and symmetric k diagonal matrices to be inverse m matrices in addition results for triadic matrices tridiagonal matrices and symmetric 5 diagonal matrices are presented as corollaries

on the un decidability of fuzzy description logics under łukasiewicz t norm recently there have been some unexpected results concerning fuzzy description logics fdls with general concept inclusions gcis they show that unlike the classical case the dl alc with gcis does not have the finite model property under lukasiewicz logic or product logic the proposed reasoning algorithms are neither correct nor complete and specifically knowledge base satisfiability is an undecidable problem for product logic in this work we show that knowledge base satisfiability is also an undecidable problem for lukasiewicz logic we additionally provide a decision algorithm for acyclic alc knowledge bases under lukasiewicz logic via a mixed integer linear programming milp based procedure note however that the decidability of this problem is already known while similar milp based algorithms have been proposed in the literature for acyclic alc knowledge bases under lukasiewicz logic none of them exhibit formal proofs of their correctness and completeness which is the additional contribution here

matrices with a transitive graph and inverse m matrices abstract the relationship between inverse m matrices and matrices whose graph is transitive is studied the results are applied to obtain a new proof of the characterization due to m lewin and m neumann of 0 1 inverse m matrices

criteria for sign regularity of sets of matrices abstract we consider matrix intervals with respect to a certain checkerboard partial ordering we show that every real matrix contained in a matrix interval is sign regular if two special matrices taken from that matrix interval are sign regular

inverse m matrices abstract this is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of m matrices and is aimed at an audience conversant with basic ideas of matrix theory a theme is the parallels anddifferences between the class of m matrices and the class of inverse m matrices among the primary tools used are diagonal multiplications the neumann expansion and the form of the inverse of a partitioned matrix some of the results seem not to have appeared before and several unsolved problems are mentioned

half moment closure for radiative transfer equations in this paper a moment method for radiative transfer equations is considered which has been developed and investigated using different approaches problems appearing for this moment system for boundary value problems using maxwell type boundary conditions are described a new method based on the consideration of positive and negative half fluxes is developed and shown to overcome the above problems moreover a numerical scheme and numerical results for the new moment system are presented

first order continuous and discontinuous galerkin moment models for a linear kinetic equation model derivation and realizability theory abstract we provide two new classes of moment models for linear kinetic equations in slab and three dimensional geometry they are based on classical finite elements and low order discontinuous galerkin approximations on the unit sphere we investigate their realizability conditions and other basic properties numerical tests show that these models are more efficient than classical full moment models in a space homogeneous test when the analytical solution is not smooth

making fuzzy description logic more general a version of fuzzy description logic based on the basic continuous t norm based fuzzy predicate logic bl is presented problems of satisfiability validity and subsumption of concepts are discussed and reduced to problems of fuzzy propositional logic known to be decidable for any continuous t norm for lukasiewicz t norm some stronger results are obtained

adaptive computation for boundary control of radiative heat transfer in glass this paper is concerned with an optimal boundary control of the cooling down process of glass an important step in glass manufacturing since the computation of the complete radiative heat transfer equations is too complex for optimization purposes we use simplified approximations of spherical harmonics including a practically relevant frequency bands model the optimal control problem is considered as a constrained optimization problem a first order optimality system is derived and decoupled with the help of a gradient method based on the solution to the adjoint equations the arising partial differential algebraic equations of mixed parabolic elliptic type are numerically solved by a self adaptive method of lines approach of rothe type adaptive finite elements in space and one step methods of rosenbrock type with variable step sizes in time are applied we present numerical results for a two dimensional glass cooling problem

on maximum principles for monotone matrices abstract for monotone matrices and h matrices maximum principles are defined and necessary and sufficient conditions are derived for these principles to hold

the role of crisp elements in fuzzy ontologies the case of fuzzy owl 2 el in the last years fuzzy ontologies and fuzzy description logics dls have been applied successfully to several real world domains some recent results on fuzzy dls show an increase in the theoretical complexity even for not expressive languages however it still may be possible to obtain reasoning algorithms performing well in practice this paper studies some cases where reasoning with a fuzzy ontology can be reduced to reasoning with a tractable classical language an owl 2 profile then building on the assumption that not all concepts and roles in fuzzy ontologies are indeed fuzzy we show that reasoning algorithms can be optimized by taking into account the existence of possible crisp concepts and roles we also prove the usefulness on crisp representation reasoning algorithms over an empirical evaluation over fuzzy owl 2 el ontologies and discuss some preliminary techniques to learn which elements should be considered to be crisp or noncrisp

the schur complements of generalized doubly diagonally dominant matrices as is known the schur complements of diagonally dominant matrices are diagonally dominant the same is true of doubly diagonally dominant matrices the purpose of this paper is to extend the results to the generalized doubly diagonally dominant matrices a proper subset of h matrices that is we show that the schur complement of a generalized doubly diagonally dominant matrix is a generalized doubly diagonally dominant matrix

the quasi principal rank characteristic sequence abstract a minor of a matrix is quasi principal if it is a principal or an almost principal minor the quasi principal rank characteristic sequence qpr sequence of an n n symmetric matrix is introduced which is defined as q 1 q 2 q n where q k is a s or n according as all some but not all or none of its quasi principal minors of order k are nonzero this sequence extends the principal rank characteristic sequences in the literature which only depend on the principal minors of the matrix a necessary condition for the attainability of a qpr sequence is established using probabilistic techniques a complete characterization of the qpr sequences that are attainable by symmetric matrices over fields of characteristic 0 is given

radiation transport modeling using extended quadrature method of moments abstract the radiative transfer equation describes the propagation of radiation through a material medium while it provides a highly accurate description of the radiation field the large phase space on which the equation is defined makes it numerically challenging as a consequence significant effort has gone into the development of accurate approximation methods recently an extended quadrature method of moments eqmom has been developed to solve univariate population balance equations which also have a large phase space and thus face similar computational challenges the distinct advantage of the eqmom approach over other moment methods is that it generates moment equations that are consistent with a positive phase space density and has a moment inversion algorithm that is fast and efficient the goal of the current paper is to present the eqmom method in the context of radiation transport to discuss advantages and disadvantages and to demonstrate its performance on a set of standard one dimensional benchmark problems that encompass optically thin thick and transition regimes special attention is given in the implementation to the issue of realizability that is consistency with a positive phase space density numerical results in one dimension are promising and lay the foundation for extending the same framework to multiple dimensions

high order entropy based closures for linear transport in slab geometry ii a computational study of the optimization problem we present a numerical algorithm to implement entropy based m n moment models in the context of a simple linear kinetic equation for particles moving through a material slab the closure for these models as is the case for all entropy based models is derived through the solution of a constrained convex optimization problem the algorithm has two components the first component is a discretization of the moment equations which preserves the set of realizable moments thereby ensuring that the optimization problem has a solution in exact arithmetic the discretization is a second order kinetic scheme which uses muscl type limiting in space and a strong stability preserving runge kutta time integrator the second component of the algorithm is a newton based solver for the dual optimization problem which uses an adaptive quadrature to evaluate integrals in the dual objective and its derivatives the accuracy of the numerical solution to the dual problem plays a key role in the time step restric

inequalities for m matrices and inverse m matrices in this paper we establish some determinantal inequalities concerning m matrices and inverse m matrices the main results are as follows 1 if a aij is either an n n m matrix or inverse m matrix then for any permutation i1 i2 in of 1 2 n a deta i 1naii s 2n1 ai1i2 ais 1isaisi1 ai1i1ai2i2 aisis b deta i 1naii if and only if a is essentially triangular 2 if a aij is an n n m matrix b bij is an n n inverse m matrix a b denotes the hadamard product of a and b then a b is an m matrix and for any permutation i1 i2 in of 1 2 n det a b det ab s 2naisisdeta i1 i2 is 1 deta i1 is 1 is bisisdetb i1 i2 is 1 detb i1 is 1 is 1

the dominant degree and disc theorem for the schur complement of matrix the theory of schur complement plays an important role in many fields such as control theory and computational mathematics in this paper we obtain some estimates for the diagonally c diagonally and product c diagonally dominant degree on the schur complement of matrices which improve some relative results as application we present some bounds for the eigenvalues of schur complement by the entries of the original matrix instead of those of the schur complement particularly we obtain that the eigenvalues of the schur complements are located in the gerschgorin circles of the original matrices under certain conditions

on perron complements of inverse n0 matrices abstract in this paper we show that the perron complements of irreducible n 0 matrices are n 0 matrices we also demonstrate the perron complements of irreducible inverse n 0 matrices are inverse n 0 matrices with a little restriction in addition we give some related inequalities about inverse n 0 matrices

principal pivot transforms properties and applications the principal pivot transform ppt is a transformation of the matrix of a linear system tantamount to exchanging unknowns with the corresponding entries of the right hand side of the system the notion of the ppt is encountered in mathematical programming statistics and numerical analysis among other areas the purpose of this paper is to draw attention to the main properties and uses of ppts make some new observations and motivate further applications of ppts in matrix theory special consideration is given to ppts of matrices whose principal minors are positive 2000 elsevier science inc all rights reserved

optimising fuzzy description logic reasoners with general concept inclusion absorption general concept inclusion gci absorption algorithms have shown to play an important role in classical description logic dl reasoners they allow to transform gcis into simpler forms to which we may apply specialised inference rules returning important performance gains in this work we develop the first absorption algorithm for fuzzy dls implement it in the fuzzydl reasoner and evaluate it extensively over both classical and fuzzy ontologies the results show that our algorithm improves the performance of the reasoner significantly

the limits of decidability in fuzzy description logics with general concept inclusions fuzzy description logics dls can be used to represent and reason with vague knowledge this family of logical formalisms is very diverse each member being characterized by a specific choice of constructors axioms and triangular norms which are used to specify the semantics unfortunately it has recently been shown that the consistency problem in many fuzzy dls with general concept inclusion axioms is undecidable in this paper we present a proof framework that allows us to extend these results to cover large classes of fuzzy dls on the other hand we also provide matching decidability results for most of the remaining logics as a result we obtain a near universal classification of fuzzy dls according to the decidability of their consistency problem

notes on completely positive matrices abstract let a be a n n symmetric matrix and in the closure of inverse m matrices then a can be factored as a bb t for some nonnegative lower triangular n n matrix b and cp rank a n if a is a positive semidefinite 0 1 matrix then a is completely positive and cp rank a rank a if a is a nonnegative symmetric h matrix then a is completely positive and cp rank a n n 1 2 n n where is the number of connected components of the graph g a

multigroup half space moment approximations to the radiative heat transfer equations the half space moment approximation to the radiative heat transfer equations developed in j comp phys 180 2002 584 for frequency independent absorption and scattering is extended to frequency dependent coefficients using averaging over frequency groups we compare numerical results obtained with this new model to known approximations in different physical regimes

geometric aspects of the symmetric inverse m matrix problem abstract we investigate the symmetric inverse m matrix problem from a geometric perspective the central question in this geometric context is which conditions on the k dimensional facets of an n simplex s guarantee that s has no obtuse dihedral angles the simplest of such conditions is that if all triangular facets of s are equilateral then s is regular and thus nonobtuse first we study the properties of an n simplex s whose k facets are all nonobtuse and generalize some classical results by fiedler 14 we prove that if all n 1 facets of an n simplex s are nonobtuse each makes at most one obtuse dihedral angle with another facet this helps to identify a special type of tetrahedron which we will call sub orthocentric with the property that if all tetrahedral facets of s are sub orthocentric then s is nonobtuse rephrased in the language of linear algebra this constitutes a purely geometric proof of the fact that each symmetric ultrametric matrix 28 is the inverse of a weakly diagonally dominant m matrix the geometric proof provides valuable insights that supplement the discrete measure theoretic 24 and the linear algebraic 25 proof the review papers 20 21 support our believe that the linear algebraic perspective on the inverse m matrix problem dominates the literature the geometric perspective however connects sign properties of entries of inverses of a symmetric positive definite matrix to the dihedral angle properties of an underlying simplex and enables an explicit visualization of how these angles and signs can be manipulated this will serve to formulate purely geometric conditions on the k facets of an n simplex s that may render s nonobtuse also for k 3 for this we generalize the class of sub orthocentric tetrahedra that gives rise to the class of ultrametric matrices to sub orthocentric simplices that define symmetric positive definite matrices a with special types of k k principal submatrices for k 3 each sub orthocentric simplices is nonobtuse and we conjecture that any simplex with sub orthocentric facets only is sub orthocentric itself along the way several additional new concepts will be introduced such as vertex gramians simplicial matrix classes the dual hull and the sub orthocentric set of a nonobtuse simplex and nonblocking matrices these concepts may also be of use in a different linear algebraic setting in particular in the context if completely positive matrices for which we will prove some auxiliary results as well

positive path product and inverse m matrices it is known that an inverse m matrix is strict path product but not necessarily vice versa for n 3 it is shown that any square positive matrix may be made strict path product by predictable additions to the diagonal and that any normalized strict path product matrix may be made inverse m by additions to the diagonal that are bounded in terms of the size of the matrix the latter has implications for pairs of inverse m matrices whose hadamard product is inverse m a determinantal inequality relating principal minors and certain associated almost principal minors is derived for normalized inverse m matrices

asymptotic preserving well balanced schemes for radiative transfer and the rosseland approximation we are concerned with efficient numerical simulation of the radiative transfer equations to this end we follow the well balanced approach s canvas and reformulate the relaxation term as a nonconservative product regularized by steady state curves while keeping the velocity variable continuous these steady state equations are of fredholm type the resulting upwind schemes are proved to be stable under a reasonable parabolic cfl condition of the type t o x2 among other desirable properties some numerical results demonstrate the realizability and the efficiency of this process

kershaw closures for linear transport equations in slab geometry i model derivation abstract this paper provides a new class of moment models for linear kinetic equations in slab geometry these models can be evaluated cheaply while preserving the important realizability property that is the fact that the underlying closure is non negative several comparisons with the expensive state of the art minimum entropy models are made showing the similarity in approximation quality of the two classes

copositive matrices and definiteness of quadratic forms subject to homogeneous linear inequality constraints abstract a symmetric matrix c is called copositive if the quadratic form x cx is nonnegative for all nonnegative values of the variables x 1 x 2 x n x a known sufficient condition for a quadratic form x qx to be positive unless x 0 subject to the linear inequality constraints ax 0 is that there should exist a copositive matrix c such that q a ca is positive definite the main result of this paper establishes the necessity of this condition for x qx to be merely nonnegative subject to ax 0 the situation is less straightforward the necessity of the existence of a copositive matrix c such that q a ca is positive semidefinite is proved only under various additional hypotheses regarding the size or rank of a and counterexamples are given to show that in general no such matrix may exist even when slater s constraint qualification holds our approach to these existence questions also furnishes certain tests for positivity or mere nonnegativity of x qx subject to ax 0 in which specific symmetric matrices constructed by rational operations from a and q and depending upon a single real parameter v must be tested for positive definiteness or strict copositivity for large values of v this technique is illustrated by several examples

a polynomial time test for m matrices abstract a real square matrix with nonpositive off diagonal elements is a z matrix and a z matrix with nonnegative principal minors is an m matrix using principal pivoting we derive a polynomial time algorithm for testing whether a z matrix is an m matrix our algorithm is much simpler than a recent one proposed by ramamurthy we also study the zero nonzero structure of the inverse of a nonsingular m matrix and compare a 1 and b 1 in the case that a and b are nonsingular m matrices and b a

some results on structured m matrices with an application to wireless communications in this paper we study conditions under which a specially structured z matrix is an m matrix we apply the result to a capacity problem in wireless communications

theorems on schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems abstract we firstly consider the block dominant degree for i ii block strictly diagonally dominant matrix and their schur complements showing that the block dominant degree for the schur complement of an i ii block strictly diagonally dominant matrix is greater than that of the original grand block matrix then as application we present some disc theorems and some bounds for the eigenvalues of the schur complement by the elements of the original matrix further by means of matrix partition and the schur complement of block matrix based on the derived disc theorems we give a kind of iteration called the schur based iteration which can solve large scale linear systems though reducing the order by the schur complement and the numerical example illustrates that the iteration can compute out the results faster

notes on f0 matrices abstract the author studies f 0 matrices and shows that n n matrix a f 0 if and only if a ti b with b 0 and n 2 b t n 1 b where k b denotes the maximum of the spectral radii of all k principal submatrices of b also an inverse f 0 matrix problem is considered

second order boltzmann schemes for compressible euler equations in one and two space dimensions a class of second order numerical schemes for the compressible euler equations is described and their l 1 stability i e rho geqq 0 t geqq 0 is proved following van leer s approach the solution rho u sqrt t here is represented as piecewise linear functions the necessity of a slope limitation appears naturally in the derivation of the schemes but it can be less strict than the slope reconstructions usually used these schemes are written in terms of explicit flux splitting formula and are naturally multidimensional in space the upwinding is obtained through a very generalized notion of characteristics the kinetic one

on classes of inverse z matrices abstract recently a classification of matrices of class z was introduced by fiedler and markham this classification contains the classes of m matrices and the classes of n 0 and f 0 matrices studied by fan g johnson and smith the problem of determining which nonsingular matrices have inverses which are z matrices is called the inverse z matrix problem for special classes of z matrices such as the m and n 0 matrices there exist at least partial results i e special classes of matrices have been introduced for which the inverse of such a matrix is an m matrix or an n 0 matrix here we define a system of classes of matrices for which the inverse of each matrix of each class belongs to one class of the classification of z matrices defined by fiedler and markham moreover certain properties of the matrices of each class are established e g inequalities for the sum of the entries of the inverse and the structure of certain schur complements we also give a necessary and sufficient condition for regularity the class of inverse n 0 matrices given here generalizes the class of inverse n 0 matrices discussed by johnson all results established here can be applied to a class of distance matrices which corresponds to a nonarchimedean metric this metric arises in p adic number theory and in taxonomy

the schur complement and the inverse m matrix problem abstract it is well known that if m is a nonnegative nonsingular inverse m matrix and if a is a nonsingular block in the upper left hand corner then the schur complement of a in m m a is an inverse m matrix the converse of this is generally false in this paper we give added restrictions on m or a to insure the converse and give some necessary and sufficient conditions for hmh 1 where h i i to be an m matrix

the linear order complementarity problem the classical complementarity problem in euclidean space can be viewed alternatively as a variational inequality or as a lattice orthogonality problem generalizations of the former have been extensively studied but infinite dimensional analogues of the latter have been largely ignored moreover as we show many well known results about the classical complementarity problem are more appropriately viewed order theoretically this is particularly true of least element solutions which are central to the present study of order complementarity in vector lattices we emphasize that the lattice theoretic descriptions we employ are very useful even in the standard finite dimensional setting

tridiagonal and upper triangular inverse m matrices abstract in this paper we characterize the nonnegative nonsingular tridiagonal matrices belonging to the class of inverse m matrices we give a geometric equivalence for a nonnegative nonsingular upper triangular matrix to be in this class this equivalence is extended to include some reducible matrices

inverse h matrices abstract the notion of inverse m matrices has been quite well studied and many of their properties have been documented in the literature in this article a proposal to consider the larger class of inverse h matrices is made first certain special types of real matrices are identified as inverse h matrices while these matrices are not inverse m matrices in general their definitions are inspired by matrices that are known to be inverse m matrices in the rest of the article motivated by results that hold for inverse m matrices the endeavor will be to attempt at proving corresponding results for inverse h matrices it is shown that for the full class of inverse h matrices many of these extensions are false nevertheless two subclasses of real inverse h matrices are identified where these generalizations are shown to hold

on diagonal schur complements of block diagonally dominant matrices it is known that the diagonal schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices j z liu y q huang some properties on schur complements of h matrices and diagonally dominant matrices linear algebra appl 389 2004 365 380 and the same is true for nonsingular h matrices j z liu j c li z t huang x kong some properties of schur complements and diagonal schur complements of diagonally dominant matrices linear algebra appl 428 2008 1009 1030 in this paper we research the properties on diagonal schur complements of block diagonally dominant matrices and prove that the diagonal schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices and the same holds for generalized block strictly diagonally dominant matrices

monotonicity and positivity of coefficients of power series expansions associated with newton and halley methods for the matrix pth root abstract if a is a matrix with all eigenvalues in the disk z 1 1 the principal pth root of a can be computed by newton s method or halley s method the study of newton s method and halley s method for the matrix pth root can be done through a study of power series expansions of some sequences of scalar functions in this paper we prove monotonicity results for the coefficients in the power series expansions for both newton s method and halley s method and for all integer p 2 the sign patterns of these coefficients can be seen directly from the monotonicity results we then use these monotonicity results and their consequences to obtain some new error estimates in the matrix case to obtain a monotonic convergence result when a is a nonsingular m matrix and to obtain a structure preserving result when a is a nonsingular m matrix or a real nonsingular h matrix with positive diagonal entries

mniblos a smt based solver for continuous t norm based logics and some of their modal expansions in the literature little attention has been paid to the development of solvers for systems of mathematical fuzzy logic and in particular there are few works concerned with infinitely valued logics in this paper it is presented mniblos a modal nice bl logics solver a modular smt based solver complete with respect to a wide family of continuous t norm based fuzzy modal logics both with finite and infinite universes restricting the modal structures to the finite ones at the propositional level the solver works with some of the best known infinitely valued fuzzy logics including bl ukasiewicz godel and product logics and with all the continuous t norm based logics that can be finitely expressed in terms of the previous ones concerning the modal expansion mniblos imposes no boundary on the cardinality of the modal structures considered the solver allows to test 1 satisfiability of equations tautologicity and logical consequence problems the logical language supported extends the usual one of fuzzy modal logics with rational constants and the monteiro baaz operator the code of mniblos is of free distribution and can be found in the web page of the author

efficient numerical methods for radiation in gas turbines numerical methods for radiative heat transfer equations coupled to a temperature equation are considered efficient solution methods and approximate equations for this system are investigated and a comparative numerical study of the different approximations is given the approximate equations considered in this paper include moment methods and diffusive approximations fast iterative solvers for the problem like multilevel methods with suitable preconditioning are considered in detail numerical experiments and comparisons in different space dimensions and for various physical situations are presented

partial moment minimum entropy models for kinetic chemotaxis equations in one and two dimensions the aim of this work is to investigate the application of partial moment approximations to kinetic chemotaxis equations in one and two spatial dimensions starting with a kinetic equation for the cell densities we apply a half quarter moments method with different closure relations to derive macroscopic equations appropriate numerical schemes are presented as well as numerical results for several test cases the resulting solutions are compared to kinetic reference solutions and solutions computed using a full moment method with a linear superposition strategy

matrices and the linear complementarity problem the paper is a collection of results on the linear complementarity problem q m the results are stated in terms of the matrix m

on the hadamard product of inverse m matrices abstract we investigate the hadamard product of inverse m matrices and present two classes of inverse m matrices that are closed under the hadamard multiplication in the end we give some inequalities on the fan product of m matrices and schur complements

the schur complements of γ diagonally and product γ diagonally dominant matrix and their disc separation in this paper we obtain some estimates for the diagonally and product diagonally dominant degree of the schur complement of matrices as application we present some bounds for the eigenvalues of schur complement by the entries of the original matrix based on these results we give a kind of iteration called the schur based iteration which can solve large scale linear systems though reducing the order by the schur complement and can compute out the results faster

z matrices and inverse z matrices abstract we consider z matrices and inverse z matrices i e those nonsingular matrices whose inverses are z matrices recently fiedler and markham introduced a classification of z matrices this classification directly leads to a classification of inverse z matrices among all classes of z matrices and inverse z matrices the classes of m matrices n 0 matrices f 0 matrices and inverse m matrices inverse n 0 matrices and inverse f 0 matrices respectively have been studied in detail here we discuss each single class of z matrices and inverse z matrices as well as considering the whole classes of z matrices and inverse z matrices we establish some common properties of the classes such as eigenvalue bounds and determinant inequalities and we give a new characterization of some classes of z matrices and inverse z matrices moreover we prove that other classes besides those of m matrices n 0 matrices and f 0 matrices consist of matrices whose determinants have the same sign some of the results generalize known results for m matrices n 0 matrices and f 0 matrices and for inverse m matrices inverse n 0 matrices and inverse f 0 matrices however we also show that some properties of the specific classes mentioned above do not hold for all classes of z matrices and inverse z matrices

matrix completion problems for pairs of related classes of matrices abstract for a class x of real matrices a list of positions in an n n matrix a pattern is said to have x completion if every partial x matrix that specifies exactly these positions can be completed to an x matrix if x and x0 are classes that satisfy the conditions any partial x matrix is a partial x0 matrix for any x0 matrix a and e 0 a ei is a x matrix and for any partial x matrix a there exists 0 such that a i is a partial x matrix where is the partial identity matrix specifying the same pattern as a then any pattern that has x0 completion must also have x completion however there are usually patterns that have x completion that fail to have x0 completion this result applies to many pairs of subclasses of p and p0 matrices defined by the same restriction on entries including the classes p p0 matrices weakly sign symmetric p p0 matrices and non negative p p0 matrices it also applies to other related pairs of subclasses of p0 matrices such as the pairs classes of p p0 1 matrices weakly sign symmetric p p0 1 matrices and non negative p p0 1 matrices furthermore any pattern that has weakly sign symmetric sign symmetric non negative p0 completion must also have weakly sign symmetric sign symmetric non negative p0 1 completion although these pairs of classes do not satisfy condition 3 similarly the class of inverse m matrices and its topological closure do not satisfy condition 3 but the conclusion remains true and the matrix completion problem for the topological closure of the class of inverse m matrices is solved for patterns containing the diagonal

rectangular submatrices of inverse m matrices and the decomposition of a positive matrix as a sum abstract we characterize those square partial matrices whose specified entries constitute a rectangular submatrix that may be completed to an inverse m matrix together with the notion of an interior inverse m matrix this is used to show that any positive matrix is a sum of inverse m matrices and to estimate the number of summands needed to represent a given matrix nonnegative matrices are also considered there are substantial differences from the analogous problem of decomposing a positive matrix as a sum of totally positive matrices in particular the upper bound on the number of inverse m matrix summands is much less than that in the totally positive case although an example is given to show that the number of totally positive summands may be less than the required number of inverse m matrix summands

almost principal minors of inverse m matrices abstract it is well known that if an inverse m matrix has a 0 entry then it must be reducible and thus have many more 0 entries this property is actually a special case of a deeper phenomenon that might be loosely described as relations among vanishing almost principal minors in an inverse m matrix this phenomenon encompasses both minors of nested dimension a certain loose monotonicity and minors of the same size in loosely related positions this phenomenon is limited to almost principal minors and where possible converses and examples are given to show the limit of the extent of this phenomenon it is also shown that if one almost principle minor is contained in another then the magnitude of the former is larger than that of the latter

reasoning in fuzzy description logics using automata automata based methods have been successfully employed to prove tight complexity bounds for reasoning in many classical logics and in particular in description logics dls very recently the ideas behind these automata based approaches were adapted for reasoning also in fuzzy extensions of dls with semantics based either on finitely many truth degrees or the godel t norm over the interval 0 1 clearly due to the different semantics in these logics the construction of the automata for fuzzy dls is more involved than for the classical case in this paper we provide an overview of the existing automata based methods for reasoning in fuzzy dls with a special emphasis on explaining the ideas and the requirements behind them the methods vary from deciding emptiness of automata on infinite trees to inclusions between automata on finite words overall we provide a comprehensive perspective on the automata based methods currently in use and the many complexity results obtained through them

on the spectra of matrices having nonnegative sums of principal minors abstract the localization of the eigenvalues of matrices with nonnegative sums of principal minors is studied the discussion is carried out in particular for p matrices such matrices for which almost all the eigenvalues lie on the left half plane are constructed