analytic smoothing effect for a system of schrodinger equations with three wave interaction we consider the global cauchy problem for a system of schrodinger equations with quadratic interaction two types of analytic smoothing effect for the solutions are formulated in the small data setting under the mass resonance condition one is the usual analytic smoothing effect in space variables in terms of the generator of galilei transforms we prove the existence and uniqueness of global solutions which are analytic with respect to galilei generators for sufficiently small data with exponential decay at infinity in space n with n 3 the other is analytic smoothing effect in space time variables in terms of generator of pseudo conformal and galilei transforms we prove the existence and uniqueness of global solutions which are analytic with respect to pseudo conformal and galilei generators for sufficiently small data with exponential decay in 4 we also discuss the associated lagrange structure

some notes on z matrices abstract an inequality is obtained relating the eigenvalue of minimum modulus of an n0 matrix a to the eigenvalue of minimum modulus of a a11 the schur complement of a11 in a where a11 is an m matrix similar results are obtained for irreducible m matrices and irreducible nonsingular f0 matrices circulant n0 matrices of order three are characterized in terms of their spectrum matrices whose inverses are f0 matrices are shown to have nonpositive almost principal minors

analyticity of solutions to a quadratic system of schrodinger equations without mass resonance condition abstract we consider the cauchy problem for a quadratic system of schrodinger equations in space dimensions n 4 without mass resonance condition analytic smoothing effect for the quadratic system of schrodinger equations under the mass resonance condition for data which satisfy exponentially decaying condition has been studied in 14 in this study we construct global solutions in the analytic hardy space via the phase modulation operator based on the scale critical sobolev space h n 2 2 with data like the test functions of fourier hyperfunctions under the condition m 1 m 2 1 4 n m 1 between two masses m 1 and m 2

analytic smoothing effect for nonlinear schrodinger equation with quintic nonlinearity abstract we prove the global existence of analytic solutions to nonlinear schrodinger equation with quintic nonlinearity in n space dimensions for sufficiently small cauchy data with exponential decay the smallness assumption on the data is imposed in terms of the critical sobolev space h n 2 1 2 moreover a characterization of some class of analytic functions is given

analytic smoothing effect for global solutions to nonlinear schrodinger equations abstract we prove the global existence of analytic solutions to the cauchy problem for the cubic schrodinger equation in space dimension n 3 for sufficiently small data with exponential decay at infinity minimal regularity assumption regarding scaling invariance is imposed on the cauchy data

irreducible characters of groups associated with finite nilpotent algebras with involution abstract an algebra group is a group of the form p 1 j where j is a finite dimensional nilpotent associative algebra a theorem of z halasi asserts that in the case where j is defined over a finite field f every irreducible character of p is induced from a linear character of an algebra subgroup of p if j is a nilpotent algebra with involution then naturally defines a group automorphism of p 1 j and we may consider the fixed point subgroup c p assuming that f has odd characteristic p we show that every irreducible character of c p is induced from a linear character of a subgroup of the form c q where q is a invariant algebra subgroup of p as a particular case the result holds for the sylow p subgroups of the finite classical groups of lie type

bounds on the spectrum of nonnegative matrices and certain z matrices spectral bounds are obtained for a type of z matrix using perron frobenius theory on the inverse these lead to spectral bounds for nonnegative matrices and m matrices these results are then extended using the result of rothblum and tan concerning the coefficient of ergodicity of a nonnegative matrix

a generalization of n matrices abstract ky fan defines an n matrix to be a matrix of the form a ti b b 0 t b where b is the spectral radius of b and is the maximum of the spectral radii of all principal submatrices of b of order n 1 in this paper we define the closure n 0 matrices of n matrices by letting t it is shown that if a z and a 1 a n certain inequalities of n matrices are shown to hold for n 0 matrices and a method for constructing an n matrix from an m matrix is given

analytic finite energy solutions of the nonlinear schrodinger equation the cauchy problem for the schrodinger equation with a monomial nonlinear term is considered under a growth condition on the nonlinear term it is shown that low energy exponentially decaying initial data yield a global solution which is analytic in its space variables and whose domain of analyticity expands in time it is also shown that low energy analytic initial data on a symmetric tube domain lead to a global solution which is analytic on the same tube domain for all time

reduction for characters of finite algebra groups abstract let j be a finite dimensional nilpotent algebra over a finite field f q we formulate a procedure for analysing characters of the group 1 j in particular we study characters of the group u n q of unipotent triangular n n matrices over f q using our procedure we compute the number of irreducible characters of u n q of each degree for n 13 also we explain and generalise a phenomenon concerning the group u 13 2 discovered by isaacs and karagueuzian

analytic solutions to nonelliptic nonlinear schrodinger equations abstract we prove local existence of analytic solutions for nonlinear schrodinger type equations the class we consider includes a number of equations derived from the physical context of water waves

on the spectrum of n0 matrices abstract the author studies the spectrum of n 0 matrices i e matrices of the form a i b where b 0 and 0 b here 0 is the maximum of the spectral radii of all principal submatrices of b of order n 1

iterative character constructions for algebra groups abstract we construct a family of orthogonal characters of an algebra group which decompose the supercharacters defined by diaconis and isaacs 2008 6 like supercharacters these characters are given by nonnegative integer linear combinations of kirillov functions and are induced from linear supercharacters of certain algebra subgroups we derive a formula for these characters and give a condition for their irreducibility generalizing a theorem of otto 2010 20 we also show that each such character has the same number of kirillov functions and irreducible characters as constituents in proving these results we observe as an application how a recent computation by evseev 2010 7 implies that every irreducible character of the unitriangular group ut n q of unipotent n n upper triangular matrices over a finite field with q elements is a kirillov function if and only if n 12 as a further application we discuss some more general conditions showing that kirillov functions are characters and describe some results related to counting the irreducible constituents of supercharacters

on the characters and commutators of finite algebra groups let a be a finite dimensional algebra over a finite field and let j a be the jacobson radical of a we prove a new commutator identity in the group g 1 j a and using this identity we show that every irreducible character of g is induced from a linear character of some subgroup of the form h 1 u where u is a subalgebra of j a this answers a question of i m isaacs

eigenvalue location for nonnegative and z matrices let lk0 denote the class of n n z matrices a tl b with b 0 and k b t k 1 b where k b denotes the maximum spectral radius of k k principal submatrices of b bounds are determined on the number of eigenvalues with positive real parts for a lk0 where k satisfies n2 k n 1 for these classes when k n 1 and n 2 wedges are identified that contain only the unqiue negative eigenvalue of a these results lead to new eigenvalue location regions for nonnegative matrices

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

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

combinatorial methods of character enumeration for the unitriangular group abstract let ut n q denote the group of unipotent n n upper triangular matrices over a field with q elements the degrees of the complex irreducible characters of ut n q are precisely the integers q e with 0 e n 2 n 1 2 and it has been conjectured that the number of irreducible characters of ut n q with degree q e is a polynomial in q 1 with nonnegative integer coefficients depending on n and e we confirm this conjecture when e 8 and n is arbitrary by a computer calculation in particular we describe an algorithm which allows us to derive explicit bivariate polynomials in n and q giving the number of irreducible characters of ut n q with degree q e when n 2 e and e 8 when divided by q n e 2 and written in terms of the variables n 2 e 1 and q 1 these functions are actually bivariate polynomials with nonnegative integer coefficients suggesting an even stronger conjecture concerning such character counts as an application of these calculations we are able to show that all irreducible characters of ut n q with degree q 8 are kirillov functions we also discuss some related results concerning the problem of counting the irreducible constituents of individual supercharacters of ut n q