prime boolean matrices and factorizations abstract we study the prime boolean matrices in the semigroup of boolean matrices we also study the factorization properties of the n n rank n boolean matrices in terms of elementary matrices and prime matrices finally we consider the minimal and the maximal prime boolean matrices

rigidity of infinite hexagonal triangulation of the plane in the paper we consider the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by luo in 5 our result shows that if a geometric hexagonal triangulation of the plane is pl conformal to the regular hexagonal triangulation and all inner angles are in 2 for any constant 0 then it is the regular hexagonal triangulation this partially solves a conjecture of luo 4 the proof uses the concept of quasi harmonic functions to unfold the properties of the mesh mathematical sciences center tsinghua university beijing 100084 china email mike890505 gmail com department of computer science stony brook university new york 11794 usa email gu cs stonybrook edu mathematical sciences center tsinghua university beijing 100084 china email jsun math tsinghua edu cn 1 ar x iv 1 30 6 36 30 v1 m at h g t 1 6 ju n 20 13

factorizations of matrices over semirings in this paper as a generalization of prime boolean matrices and prime fuzzy matrices we study semiprime matrices over chain semirings using the relationship between semiprime matrices and their row spaces we show that a nonmonomial matrix with full semiring rank can be expressed as a product of elementary matrices and semiprime matrices furthermore we show that a nonmonomial regular matrix with full semiring rank can be expressed as a product of elementary matrices

weighted weak 1 1 and weighted estimates for oscillating kernels weak type 1 1 and strong type p p inequalities are proved for operators defined by oscillating kernels the techniques are sufficiently general to derive versions of these inequalities using weighted norms 0 introduction given a positive real number a o a 7 1 define the oscillating kernel ka by ka x 1 x leilxla and consider the convolution operator ka f in an earlier paper 2 we studied the boundedness properties of such operators on weighted lp spaces 1 1 we define l p f 1l p w a e f x lpw x dx r and say f e lp r if llfllp w 1 the multiplier operator t associated to ka is defixled by t d 0 1 l e 1tl f where 0 is a c function defined by i 0 4 0 if 1 when p 0

primes in several classes of the positive matrices the classification of primes in the semi ring of the positive matrices is of interest to control and system theory a few examples of primes in the positive matrices are known in this paper results on the classification of primes in the positive matrices in the doubly stochastic matrices and in the doubly stochastic circulants are presented

further results on the minimum rank of regular classes of 0 1 matrices abstract let b n k be the set of all 0 1 matrices of order n with constant line sum k and let n k be the minimum rank over b n k it is known that n k n k n k n k k where n k is the rank of a recursively defined matrix a b n k brualdi manber and ross showed that n k n k if and only if k n in this paper we show that n k n k k if and only if n k satisfies one of the following three relations i n 1 mod k k 2 or 3 ii n k 1 k 2 iii n 4 q 3 k 4 and q 1 moreover we obtain the exact values of n 4 for all n 4 and determine all the possible ranks of regular 0 1 matrices in b n 4 we also present some positive integer pairs n k such that n k n k n k k which gives a positive answer to a question posed by pullman and stanford

linear operators that strongly preserve commuting pairs of boolean matrices abstract we characterize those linear operators t on the class m of square boolean matrices respectively on the set l of symmetric boolean matrices for which t x commutes with t y if and only if x commutes with y for all x y in m respectively in l

computation of integrals with oscillatory singular factors of algebraic and logarithmic type in this paper we present the clenshaw curtis filon methods and the higher order methods for computing many classes of oscillatory integrals with algebraic or logarithmic singularities at the two endpoints of the interval of integration the methods first require an interpolant of the nonoscillatory and nonsingular parts of the integrands in n 1 clenshaw curtis points then the required modified moments can be accurately and efficiently computed by constructing some recurrence relations moreover for these quadrature rules their absolute errors in inverse powers of the frequency are given the presented methods share the advantageous property that the accuracy improves greatly for fixed n as increases numerical examples show the accuracy and efficiency of the proposed methods

boolean rank of upset tournament matrices abstract the boolean rank of an m n 0 1 matrix m is the minimum k for which matrices a and b exist with m ab a is m k b is k n and boolean arithmetic is used the intersection number of a directed graph d is the minimum cardinality of a finite set s for which each vertex v of d can be represented by an ordered pair s v t v of subsets of s such that there is an arc from vertex u to vertex v in d if and only if s u t v o the intersection number of a digraph is equal to the boolean rank of its adjacency matrix using this fact we show that the intersection number of an upset tournament equivalently the boolean rank of its adjacency matrix is equal to the number of maximal subpaths of certain types in its upset path

minimum matrix rank of k regular 0 1 matrices abstract in this paper we present results on minimum boolean and nonnegative integer rank of k regular 0 1 matrices results on these semiring ranks give equivalent results on minimum biclique covering numbers and partition numbers for k regular bipartite graphs and digraphs

structure of the rational monoid algebra for boolean matrices of order 3 abstract we use the computer algebra system maple to study the 512 dimensional associative algebra q b 3 the rational monoid algebra of 3 3 boolean matrices using the lll algorithm for lattice basis reduction we obtain a basis for the radical in bijection with the 42 non regular elements of b 3 the center of the 470 dimensional semisimple quotient has dimension 14 we use a splitting algorithm to find a basis of orthogonal primitive idempotents we show that the semisimple quotient is the direct sum of simple two sided ideals isomorphic to matrix algebras m d q for d 1 1 1 2 3 3 3 3 6 6 7 9 9 12 we construct the irreducible representations of b 3 over q by calculating the representation matrices for a minimal set of generators

hilbert integrals singular integrals and radon transforms i on introduit deux nouvelles classes d operateurs on etudie leur relation et on montre comment on peut les appliquer a l etude des problemes aux valeurs limites

proper holomorphic embeddings of finitely and some infinitely connected subsets of into we show that any finitely connected domain open image in new window can be properly embedded into open image in new window for some sequences open image in new window can also be properly embedded into open image in new window

power convergent boolean matrices abstract an n n binary matrix a is limit dominating if its powers converge to a limit l and a l the inequality holds entrywise and arithmetic on all binary matrices is assumed to be boolean 1 1 1 limit dominating matrices generalize transitive matrices a a 2 if a is limit dominating we show that the power limit l can be found immediately from a and that the residual matrix n a l is nilpotent moreover a k l n k for all positive integers k we prove that v k n n v 1 where k is the index of convergence of a the first integer k such that a k l and v is the index of convergence of n we characterize an extreme class of limit dominating matrices the idempotent matrices a 2 a in particular we show that a binary matrix a is idempotent if and only if it is limit dominating and the number of nonzero diagonal blocks in its frobenius normal form equals its column rank as a boolean matrix finally we give natural generalizations to matrices with entries from an arbitrary finite boolean algebra

singular 0 1 matrices with constant row and column sums abstract we address the problem of explicitly constructing an n n 0 1 matrix with constant line sum k and rank r for each r k 2 mod k for all even k we also solve the problem for all but at most the first 2k 4 possible ranks r 3k

primes in the semigroup of boolean matrices abstract let a b c be n n matrices of zeros and ones using boolean addition and multiplication we say that a is prime if it is not a permutation matrix and if a bc implies that b or c must be a permutation matrix conditions sufficient for a matrix to be prime are provided and a characterization of primes in terms of a nation of rank is given finally an order property of primes is used to obtain a result on prime factors

rigidity of infinite disk patterns let p be a locally flnite disk pattern on the complex plane c whose combinatorics are described by the one skeleton g of a triangulation of the open topological disk and whose dihedral angles are equal to a function e 0 2 on the set of edges let p be a combinatorially equivalent disk pattern on the plane with the same dihedral angle function we show that p and p difier only by a euclidean similarity in particular when the dihedral angle function is identically zero this yields the rigidity theorems of b rodin and d sullivan and of o schramm whose arguments rely essentially on the pairwise disjointness of the interiors of the disks the approach here is analytical and uses the maximum principle the concept of vertex extremal length and the recurrency of a family of electrical networks obtained by placing resistors on the edges in the contact graph of the pattern a similar rigidity property holds for locally flnite disk patterns in the hyperbolic plane where the proof follows by a simple use of the maximum principle also we have a uniformization result for disk patterns in a future paper the techniques of this paper will be extended to the case when 0 in particular we will show a rigidity property for a class of inflnite convex polyhedra in the 3 dimensional hyperbolic space

hilbert integrals singular integrals and radon transforms ii etude des transformations de radon singulieres et des integrales de hilbert appliquees aux problemes aux valeurs limites probleme de neumann

nonlocal inversion formulas for the x ray transform etude de la reconstruction d une fonction f x sur r n a partir de ses integrales sur des plans k dimensionnels cas de k 1

singular integrals with rough kernels along real analytic submanifolds in r n l p mapping properties will be established in this paper for singular radon transforms with rough kernels defined by translated of a real analytic submanifold in r n

boolean rank preserving operators and boolean rank 1 spaces abstract we study the extent to which certain theorems on linear operators on field valued matrices carry over to linear operators on boolean matrices we obtain analogues and near analogues of several such theorems one of these leads us to consider linear spaces of m n boolean matrices whose nonzero members all have boolean rank 1 we obtain a structure theorem for such spaces that enables us to determine the maximum boolean dimension of such spaces and their maximum cardinality

integral representations on hermitian manifolds the bar partial neumann solution of the cauchy riemann equations its significance for complex analysis lies in the fact that if n g dom d solves o nf and df 0 then u d nf is the unique solution of du which is orthogonal to kerd j j kohn has established existence and regularity properties of the solution operator iv giving the solution of minimal norm the so called 9 neumann operator in case d is strictly pseudoconvex 5 and in more general cases as well 6 the proofs are based on a priori estimates in l sobolev spaces and therefore they do not give any explicit information about the kernels of n or d n in recent years there has been much interest in finding more explicit and concrete representations of the abstractly defined operators n and d n see 2 3 9 10 12 in 7 we began to study d n by using the calculus of cauchy fantappie kernels in c n in analogy to the work of kerzman and stein 4 and ligocka 8 for the szego respectively bergman kernel in contrast to the scalar case the incompatibility of the euclidean metric with the complex geometry of the boundary of d turned out to be a major obstruction in the general case in the present paper we overcome this obstruction by generalizing the results in 7 to arbitrary hermitian manifolds this enables us to then introduce a special levi metric similar to the one in 2 and to establish the required symmetry properties of the kernels our main result gives a new and completely explicit integral representation of the principal part of d n on

semiring fank versus column rank abstract this paper concerns two notions of rank of matrices over semirings semiring rank and column rank these two rank functions are the same over fields and euclidean rings but differ for matrices over many combinatorially interesting semirings including the nonnegative integer matrices the fuzzy matrices and the binary boolean matrices we investigate the largest value of r for which the column rank and semiring rank of all m n matrices over a given semiring are both r this value is determined for the semirings mentioned above as well as many others

efficient quadrature of highly oscillatory integrals with algebraic singularities in this paper we are concerned with the numerical evaluation of a class of highly oscillatory integrals containing algebraic singularities first we expand such integrals derived by two transformations t x b b 0 t 21 z email protected email protected 1 into asymptotic series in inverse powers of the frequency w then based the asymptotic series two methods are presented one is the filon type method the other is the clenshaw curtis filon type method which is based on a special hermite interpolation polynomial in the clenshaw curtis points and can be evaluated efficiently in o nlogn operations where n 1 is the number of clenshaw curtis points in the interval of integration some error and convergence analysis and robust numerical examples are used to demonstrate the accuracy and effectiveness of the proposed approaches for approximating the class of highly oscillatory singular integrals

the strong maximal function on a nilpotent group an analogue of the strong maximal function of jessen marcinkiewicz and zygmund is shown to be bounded on l p for all p 1 on a nilpotent lie group

strictly pseudoconvex domains in c n the theory which we have developed so far will be expanded in two ways 1 in this chapter we shall use the cauchy fantappie calculus to transform the bochner martinelli kernel into a kernel adapted to strictly pseudoconvex domains in n and prove a number of finiteness and vanishing theorems for these domains 2 in the next chapter we shall pass from n to arbitrary hermitian manifolds and establish the analogue of the bmk formula in that context obtaining along the way the hodge decomposition theorem on compact manifolds both lines of thought will merge in the subsequent chapters and lead to a solution of the levi problem and finiteness theorems for strictly pseudoconvex manifolds as well as to a solution of the overline partial neumann problem to be formulated later

holder estimates for homotopy operators on strictly pseudoconvex domains with c 2 boundary we derive a new homotopy formula for a strictly pseudoconvex domain of c 2 boundary in mathbf c n by using a method of lieb and range and obtain estimates in lipschitz spaces for the homotopy operators for r 1 and q 0 we obtain a lambda r 1 2 solution u to overline partial u f for a overline partial closed 0 q form f of class lambda r in the domain we apply the estimates to obtain boundary regularities of mathcal d solutions for a domain in mathbf c n times mathbf r m

rank of adjacency matrices of directed strongly regular graphs for a positive integer r we consider the set br of all values of kn for which there exists an n n matrix with entries 0 and 1 such that each row and each column has exactly k 1 s and the matrix has rank r we prove that the set br is finite for every r if there exists a k regular directed graph on n vertices such that its adjacency matrix has rank r then kn br we use this to exclude existence of directed strongly regular graphs for infinitely many feasible parameter sets

the bergman projection and weighted c k estimates for the canonical solution to the bar partial problem on non smooth domains we apply integral representations for functions on non smooth strictly pseudoconvex domains the henkin leiterer domains to derive weighted c k estimates for the component of a given function f which is orthogonal to holomorphic functions in terms of c k norms of f the weights are powers of the gradient of the defining function of the domain

computation of integrals with oscillatory and singular integrands using chebyshev expansions we present a general method for computing oscillatory integrals of the form 1 1f x g x e i w xdx where f is sufficiently smooth on 1 1 w is a positive parameter and g is a product of singular factors of algebraic or logarithmic type based on a chebyshev expansion of f and the properties of chebyshev polynomials the proposed method for such integrals is constructed with the help of the expansion of the oscillatory factor e i w x furthermore due to numerically stable recurrence relations for the modified moments the devised scheme can be employed to compute oscillatory integrals with algebraic or logarithmic singularities at the end or interior points of the interval of integration numerical examples are provided to confirm our analysis

harmonic analysis on nilpotent groups and singular integrals i oscillatory integrals abstract this paper is devoted to the study of the operator given by where k is a standard calderon zygmund kernel and p is a real polynomial on r n r n we show t is bounded on lp to itself when 1

rigidity of infinite circle packings the nerve of a packing is a graph that encodes its combinatorics the vertices of the nerve correspond to the packed sets and an edge occurs between two vertices in the nerve precisely when the corresponding sets of the packing intersect

estimates for singular convolution operators on the heisenberg group soit h n le groupe de heisenberg l operateur a co c h n donne par af f k s etend a un operateur borne de l p dans l p pour 1 p les operateurs ae co c donnes par aef f ke s etendent aux operateurs bornes sur l p pour 1 p avec des normes independantes de e

some one sided estimates for oscillatory singular integrals abstract the purpose of this paper is to establish some one sided estimates for oscillatory singular integrals the boundedness of certain oscillatory singular integrals on weighted hardy spaces h 1 w is proved it is here also shown that the h 1 w theory of oscillatory singular integrals above cannot be extended to the case of h q w when 0 q 1 and w a p a wider weight class than the classical muckenhoupt class furthermore a criterion on the weighted l p boundedness of the oscillatory singular integral is given

singular integrals related to the radon transform and boundary value problems abstract two classes of integral operators are introduced that combine features of calderon zygmund singular integrals the hilbert integral and the radon transform examples and applications arising from integral geometry and several complex variables are discussed