faces of the cone of euclidean distance matrices characterizations structure and induced geometry in this paper we obtain new characterizations of the faces of the cone of euclidean distance matrices in one case the characterization is based on a special subspace associated with each distance matrix in other case on linear restrictions of coordinate matrices we also relate the faces to the supporting hyperplanes of the cone and we show how the supporting hyperplanes induce certain geometry on the configurations that belong to that face

decomposition of hardy morrey spaces abstract in this paper we establish the decompositions of hardy morrey spaces in terms of atoms concentrated on dyadic cubes which have the same cancellation properties of the classical hardy spaces

semiclassical asymptotics gauge fields and quantum chaos a gauge field is given by a connection on a principal bundle p m we consider the semiclassical behavior of a family of schrodinger operators associated with a gauge field in the limit as h 0 we relate the spectral theory of such operators to behavior of the hamiltonian flow on the natural phase space associated to a gauge field examining in particular situations where this flow exhibits chaotic behavior

morrey boundedness and compactness characterizations of integral commutators with singular kernel on strictly pseudoconvex domains in cn abstract we prove the morrey boundedness and compactness characterization of integral commutators with singular kernel of calderon zygmund type on pseudo convex domains in c n our results extend some of the ones of krantz li in 16 17

block matrices and multispherical structure of distance matrices abstract the block structure of a matrix and its relation to the block structure of the corresponding eigenvectors is investigated a set of points is said to have multispherical structure if they lie on a collection of concentric spheres when the centroid of each of the clusters lies at the common center the associated distance matrix has a block structure with simple relations between the blocks further such block structure may be recognized from the structure of the eigenvectors of the distance matrix a computational procedure is proposed to find the least number of concentric spheres containing the points represented by a distance matrix

connections between the real positive semidefinite and distance matrix completion problems abstract though the real symmetric positive semidefinite psd matrices and the euclidean distance matrices are closely related exact relationships between the corresponding completion problems are not apparent we establish strong partial relationships of two types this permits the transfer of some insights from one problem to the other and allows computational tools for the psd problem to be used for the distance problem

a geometrical characterization of strongly regular graphs abstract we give a necessary and sufficient condition of a euclidean representation of a simple graph to be spherical moreover we show a characterization of strongly regular graphs from the view point of euclidean representations of a graph from this characterization we define a natural generalized concept of a strongly regular graph closely related to euclidean designs and codes

some remarks on the navier stokes equations in r3 we study various existence and uniqueness results for solutions of the navier stokes equations in connection with function spaces related to real harmonic analysis

global well posedness and asymptotic behavior in besov morrey spaces for chemotaxis navier stokes fluids in this work we consider the keller segel system coupled with navier stokes equations in rn for n 2 we prove the global well posedness with small initial data in besov morrey spaces our initial data class extends previous ones found in the literature such as that obtained by kozono miura and sugiyama j funct anal 270 5 1663 1683 2016 it allows us to consider initial cell density and fluid velocity concentrated on smooth curves or at points depending on the spatial dimension self similar solutions are obtained depending on the homogeneity of the initial data and considering the case of a chemical attractant without the degradation rate moreover we analyze the asymptotic stability of solutions at infinity and obtain a class of asymptotically self similar ones in this work we consider the keller segel system coupled with navier stokes equations in rn for n 2 we prove the global well posedness with small initial data in besov morrey spaces our initial data class extends previous ones found in the literature such as that obtained by kozono miura and sugiyama j funct anal 270 5 1663 1683 2016 it allows us to consider initial cell density and fluid velocity concentrated on smooth curves or at points depending on the spatial dimension self similar solutions are obtained depending on the homogeneity of the initial data and considering the case of a chemical attractant without the degradation rate moreover we analyze the asymptotic stability of solutions at infinity and obtain a class of asymptotically self similar ones

three point boundary value problems for second order ordinary differential equations in banach spaces in this paper by using the sadovskii fixed point theorem we study the existence of at least one solution for the second order three point boundary value problem u t f t u t u t email protected 0

global strong solution to the semi linear keller segel system of parabolic parabolic type with small data in scale invariant spaces abstract we shall show existence of global strong solution to the semi linear keller segel system in r n n 3 of parabolic parabolic type with small initial data u 0 h n r 2 r r n and v 0 h n r r r n for max 1 n 4 r n 2 our method is based on the perturbation of linealization together with the l p l q estimates of the heat semigroup and the fractional powers of the laplace operator as a by product of our method we shall prove the decay property of solutions as the time goes to infinity

existence and uniqueness theorem on mild solutions to the keller segel system coupled with the navier stokes fluid abstract we consider the keller segel system coupled with the navier stokes fluid in the whole space and prove the existence of global mild solutions with the small initial data in the scaling invariant space our method is based on the implicit function theorem which yields necessarily continuous dependence of solutions for the initial data as a byproduct we show the asymptotic stability of solutions as the time goes to infinity since we may deal with the initial data in the weak l p spaces the existence of self similar solutions provided the initial data are small homogeneous functions

scaling in nonlinear parabolic equations the cauchy problem for parabolic equations with quadratic nonlinearity is studied we investigate the existence of global in time solutions and their large time behavior assuming some scaling property of the equation as well as of the norm of the banach space in which the solutions are constructed some applications of these abstract results are indicated

multispherical euclidean distance matrices abstract in this paper we introduce new necessary and sufficient conditions for an euclidean distance matrix to be multispherical the class of multispherical distance matrices studied in this paper contains not only most of the matrices studied by hayden et al 1996 2 but also many other multispherical structures that do not satisfy the conditions in hayden et al 1996 2 we also study the information provided by the origin of coordinates when it is placed at the center of the spheres and the origin representation property is satisfied these vectors associated with the origin of coordinates generate a number of supporting hyperplanes for a family of multispherical matrices and also describe part of the null space of the corresponding distance matrices

circum euclidean distance matrices and faces abstract we study the structure of circum euclidean distance matrices those euclidean distance matrices generated by points lying on a hypersphere we show for example that such euclidean distance matrices are characterized as having constant row sums and they constitute the interior of the cone of all euclidean distance matrices also we provide a formula for computing the radius of a representing configuration in the smallest embedding dimension r and show that rk d r 1 finally we obtain a geometric characterization of the faces of this cone given a configuration of points and its euclidean distance matrix d any matrix in the minimal face containing d comes from a configuration that is a linear perturbation of the points that generate d

a discrete transform and decompositions of distribution spaces abstract we study a representation formula of the form q q q for a distribution on r n this formula is obtained by discretizing and localizing a standard littlewood paley decomposition the map taking to the sequence q q with q running over the dyadic cubes in r n is called the transform the functions q and q have a particularly simple form moreover most of the familiar distribution spaces lp spaces 1 r n we also consider pointwise multipliers for the characteristic function of a domain we obtain boundedness results for a general class of domains which properly includes lipschitz domains several interpolation methods are easily analyzed via the sequence spaces for real interpolation we obtain among other things an extension to the case p 0 this in turn gives a new approach to the traditional atomic decomposition of hardy spaces

well posedness for the navier stokes equations where u is the velocity and p is the pressure it is well known that the navierstokes equations are locally well posed for smooth enough initial data as long as one imposes appropriate boundary conditions on the pressure at for instance it is easy to see see 9 for much more general results that if s n 2 then for any h initial data there exists a unique c 0 t h r local solution with a pressure p c 0 t h r in the sequel we consider solutions for less regular initial data this has to be understood in the sense that the map from the initial data to the solution extends continuously to rougher function spaces the question we are interested in is the global well posedness for small data and local well posedness for large data with respect to a certain space of

existence of positive solutions for multi point boundary value problems on infinite intervals in banach spaces in this paper the cone theory and monch fixed point theorem combined with a monotone iterative technique are used to investigate the positive solutions of a class of boundary problems for second order nonlinear singular differential equations with multi point boundary value conditions on an infinite interval in banach spaces the conditions for the existence of a positive solution are established in addition an explicit iterative approximation of the solution for the boundary value problem is also derived

boundary value problems for impulsive integro differential equations on unbounded domains in a banach space in this paper the fixed point theory is used to investigate the existence and uniqueness of solutions of two point boundary value problems bvps for second order non linear impulsive integro differential equations on infinite intervals in a banach space

global well posedness for nonlocal fractional keller segel systems in critical besov spaces abstract in this paper we study keller segel systems with fractional diffusion and a nonlocal term we establish the global existence uniqueness and stability of solutions for systems with small initial data in critical besov spaces our main tools are the l p l q estimates for e t 2 in besov spaces and the perturbation of linearization

heteroclinic connections for fully non linear non autonomous second order differential equations we investigate the solvability of the following strongly non linear non autonomous boundary value problem p a x t x t f t x t x t a e t r x x with given constants where a x is a generic continuous positive function and f is a caratheodory non linear function we show that the solvability of p is strictly connected to a sharp relation between the behaviors of f t x as x 0 and f x x as t such a relation is optimal for a wide class of problems for which we prove that p is not solvable when it does not hold

the cell matrix closest to a given euclidean distance matrix abstract cell matrix introduced by jaklic and modic 6 is a special euclidean distance matrix edm that has a quite attractive and simple structure it is of interest to approximate an edm by a cell matrix in this paper we consider the problem of finding the cell matrix that is closest to a given edm with respect to the frobenius norm the majorization ordering of the eigenvalues of a cell matrix is also discussed

a constructive proof of the fefferman stein decomposition of bmo rn let s vec r left left f r 1 f cdots r n f right f in h 1 left text r n text r right right subset h 1 left text r n text r n 1 right 22 1 begin gathered s vec r left vec g left g j right j 0 cdots n right in text bmo left text r n text r n 1 right sum limits j 0 n vec r j g j 0 text in bmo left text r n text r n 1 right left text r right end gathered 22 2 j 0

characterization of multispherical and block structures of euclidean distance matrices abstract this paper presents some new characterizations of euclidean distance matrices edms of special structures more specifically we discuss multispherical and block structured edms each of which can be viewed as a generalization of spherical edm we focus on a well known inequality that characterizes spherical edms and extend it to the sets of multispherical and block structured edms some related results are also presented

properties of euclidean and non euclidean distance matrices abstract a distance matrix d of order n is symmetric with elements 1 2 d ij 2 where dii 0 d is euclidean when the 1 2 n n 1 quantities dij can be generated as the distances between a set of n points x n p in a euclidean space of dimension p the dimensionality of d is defined as the least value of p rank x of any generating x in general p 1 and p 2 are also acceptable but may include imaginary coordinates even when d is euclidean basic properties of euclidean distance matrices are established in particular when rank d it is shown that depending on whether etd e is not or is zero the generating points lie in either p 1 dimensions in which case they lie on a hypersphere or in p 2 dimensions in which case they do not the notation e is used for a vector all of whose values are one when d is non euclidean its dimensionality p r s will comprise r real and s imaginary columns of x and r s are invariant for all generating x of minimal rank higher ranking representations can arise only from p 1 r 1 s or p 1 r s 1 or p 2 r 1 s 1 so that not only are r s invariant but they are both minimal for all admissible representations x

besov morrey spaces function space theory and applications to non linear pde this paper is devoted to the analysis of function spaces modeled on besov spaces and their applications to non linear partial differential equations with emphasis on the incompressible isotropic navier stokes system and semilinear heat equations specifically we consider the class introduced by hideo kozono and masao yamazaki of besov spaces based on morrey spaces which we call besov morrey or bm spaces we obtain equivalent representations in terms of the weierstrass semigroup and wavelets and various embeddings in classical spaces we then establish pseudo differential and para differential estimates our results cover non regular and exotic symbols although the heat semigroup is not strongly continuous on morrey spaces we show that its action defines an equivalent norm in particular homogeneous bm spaces belong to a larger class constructed by grzegorz karch to analyze scaling in parabolic equations we compare karch s results with those of kozono and yamazaki and generalize them by obtaining short time existence and uniqueness of solutions for arbitrary data with subcritical regularity we exploit pseudo differential calculus to extend the analysis to compact smooth boundaryless riemannian manifolds bm spaces are defined by means of partitions of unity and coordinate patches and intrinsically in terms of functions of the laplace operator

infinite boundary value problems for nth order nonlinear impulsive integro differential equations in banach spaces abstract in this paper the existence of unbounded nonnegative solutions of a boundary value problem for n th order impulsive integro differential equations on an infinite interval in banach spaces is obtained by means of the monch fixed point theory in a banach space

coordinate shadows of semidefinite and euclidean distance matrices we consider the projected semidefinite and euclidean distance cones onto a subset of the matrix entries these two sets are precisely the input data defining feasible semidefinite and euclidean distance completion problems we classify when these sets are closed and use the boundary structure of these two sets to elucidate the krislock wolkowicz facial reduction algorithm in particular we show that under a chordality assumption the minimal cones of these problems admit combinatorial characterizations as a by product we record a striking relationship between the complexity of the general facial reduction algorithm singularity degree and facial exposedness of conic images under a linear mapping

boundary value problems for second order differential equations on unbounded domains in a banach space in this paper the sadovskii fixed point theorem is used to investigate the existence of solutions of two point boundary value problems bvp for second order nonlinear differential equations on infinite intervals in a banach space

positive solutions for singular semipositone boundary value problems on infinite intervals by using the fixed point theory on a cone with a special norm and space we discuss the existence of positive solutions for a class of semipositone boundary value problems on infinite intervals the work improves many known results including singular and non singular cases

global existence result for chemotaxis navier stokes equations in the critical besov spaces abstract we consider the chemotaxis navier stokes equations which are the keller segel model coupled to the incompressible navier stokes equations in dimension three we prove the global existence of the solution in the critical besov spaces with small initial data only which is a new result and improves the previous result