an explicit stability estimate for an ill posed cauchy problem for the wave equation abstract an explicit stability estimate for the two dimensional wave equation when the cauchy data are prescribed on a part of the lateral boundary is derived our result is obtained using a combination of the friedrichs leray energy integrals and carleman type estimates of hormander linear partial differential operators springer verlag new york berlin 1976 since the calculation of explicit constants produces a number of difficulties this general approach is modified in several ways e g the introduction of a set of special constraints such results are useful in constructing algorithms that generate numerical solutions to these kinds of ill posed problems

combinatorial decompositions of a class of rings in this paper we introduce some combinatorial methods for the study of graded rings and use these methods to analyze a class of rings that are of importance in combinatorics our methods are based on a unique representation theorem which is shown section 2 to hold for any graded algebra and which in a sense is an extension of the direct sum decomposition for cohen macaulay algebras this unique representation is reminiscent of a similar result obtained by rees 20 both results yield a decomposition of the algebra however our result differs from that of rees in that it carries more information about the algebra our main results are concerned with a class of rings see section 3 for the definition associated to simplicial complexes there are several natural operations that can be performed on simplicial complexes to obtain new complexes which in turn have an interpretation for the corresponding rings we show sections 4 5 and 6 that our basic decompositions can be transferred during these operations from the original rings to the newly constructed ones the operations studied here are the chain transform or barycentric subdivision section 4 rank selection both for partially ordered sets and for simplicial complexes section s and localization section 6 as we develop these tools we give some applications in section 5 we give a new topological characterization of the cohen macaulay property for partially ordered sets an immediate consequence of which is the rankselection theorem baclawski 2 this characterization is closely related to those obtained by garsia in 14

simultaneous exact approximate boundary controllability of thermo elastic plates with variable thermal coefficient and moment control abstract we study a controllability problem exact in the mechanical variables w w t and simultaneously approximate in the thermal variable of thermo elastic plates by means of boundary controls in the hinged dirichlet bc case when the thermal expansion term is variable in space

alexander duality and stanley depth of multigraded modules abstract we apply miller s theory on multigraded modules over a polynomial ring to the study of the stanley depth of these modules several tools for stanley s conjecture are developed and a few partial answers are given for example we show that taking the alexander duality twice but with different centers is useful for this subject generalizing a result of apel we prove that stanley s conjecture holds for the quotient by a cogeneric monomial ideal

a generalized gronwall inequality and its application to a fractional differential equation this paper presents a generalized gronwall inequality with singularity using the inequality we study the dependence of the solution on the order and the initial condition of a fractional differential equation

grobner bases of syzygies and stanley depth abstract let f be any free resolution of a finitely generated z n graded module over the polynomial ring k x 1 x n we show that for a suitable term order on f then for 0 p n the initial module of the p 1 th syzygy module z p f p is generated by terms m i e i where the m i are monomials in k x p 1 x n also for a large class of free resolutions f encompassing eliahou kervaire resolutions we show that a grobner basis for z p is given by the boundaries of generators of f p 1 we apply the above to give lower bounds for the stanley depth of the p 1 th syzygy module z p in particular showing it is greater or equal to p 1 we also show that if i is any squarefree ideal in k x 1 x n the stanley depth of i is at least of order 2 n

cohen macaulayness of semi invariants for tori in this paper we give a new method in terms of one parameter subgroups to study semi invariants for algebraic tori in some cases we obtain extensions to results in 7 in other cases we obtain different proofs

general stability result for a viscoelastic plate equation with past history and general kernel abstract in this paper we consider the following plate problem u t t u t t 2 u 0 k s 2 u t s d s 0 and we show that the stability of this problem holds for a much larger class of kernels more precisely we consider the kernel k 0 0 satisfies k t t k t t 0 where and are functions satisfying some specific properties under this very general assumption on the behavior of k at infinity we establish a relation between the decay rate of the solution and the growth of k at infinity this work generalizes and improves earlier results in the literature moreover we drop the boundedness assumption on the history data usually made in the literature

a non partitionable cohen macaulay simplicial complex abstract a long standing conjecture of stanley states that every cohen macaulay simplicial complex is partitionable we disprove the conjecture by constructing an explicit counterexample due to a result of herzog jahan and yassemi our construction also disproves the conjecture that the stanley depth of a monomial ideal is always at least its depth

an inverse problem for the dynamical lame system with two sets of boundary data we prove uniqueness and a holder type stability of reconstruction of all three time independent elastic parameters in the dynamical isotropic system of elasticity from two special sets of boundary measurements in proofs we use carleman type estimates in sobolev spaces of negative order 2003 wiley periodicals inc

stanley depth of complete intersection monomial ideals and upper discrete partitions abstract let i be an m generated complete intersection monomial ideal in s k x 1 x n we show that the stanley depth of i is n m 2 we also study the upper discrete structure for monomial ideals and prove that if i is a squarefree monomial ideal minimally generated by 3 elements then the stanley depth of i is n 1

how to compute the stanley depth of a monomial ideal abstract let j i be monomial ideals we show that the stanley depth of i j can be computed in a finite number of steps we also introduce the fdepth of a monomial ideal which is defined in terms of prime filtrations and show that it can also be computed in a finite number of steps in both cases it is shown that these invariants can be determined by considering partitions of suitable finite posets into intervals

smooth attractors of finite dimension for von karman evolutions with nonlinear frictional damping localized in a boundary layer abstract in this paper dynamic von karman equations with localized interior damping supported in a boundary collar are considered hadamard well posedness for von karman plates with various types of nonlinear damping are well known and the long time behavior of nonlinear plates has been a topic of recent interest since the von karman plate system is of hyperbolic type with critical nonlinearity noncompact with respect to the phase space this latter topic is particularly challenging in the case of geometrically constrained nonlinear damping in this paper we first show the existence of a compact global attractor for finite energy solutions and we then prove that the attractor is both smooth and finite dimensional thus the hyperbolic like flow is stabilized asymptotically to a smooth and finite dimensional set

a global attractor for the plate equation with displacement dependent damping abstract we study the long time behaviour of solutions of the plate equation with nonlinear damping coefficient we prove under suitable conditions that this equation possesses a global attractor

the number of solutions to linear diophantine equations and multivariate splines etude de la variation du nombre des solutions entieres non negatives de s equations diophantiennes lineaires en fonction des termes non homogenes

dualizing complexes of affine semigroup rings for an affine semigroup ring we construct the dualizing complex in terms of the semigroup and the homology of the face lattice of the polyhedral cone spanned by the semigroup as a consequence there are characterizations of locally cohen macaulay rings buchsbaum rings and cohen macaulay rings as well as serre s condition 9 introduction let s denote a finitely generated submonoid of the additive monoid n n being a positive integer by the affine semigroup ring i s of s over a field x let us denote the subring of x xl xn generated by all monomials xs s e s so one has up to isomorphisms a one to one correspondence between affine semigroup rings and affine varieties given parametrically by monomials now it is of some interest to characterize ring theoretic properties as cohenmacaulay gorenstein etc in terms of the semigroup s a first breakthrough in this direction was done by kempf et al kkms and hochster hol who showed that x s is a cohen macaulay ring provided it is normal moreover the normality of x s is described in terms of s see hol another particular case if s is a simplicial semigroup is treated by goto suzuki and watanabe gsw resp stanley st2 who showed that x s is a cohen macaulay ring if it satisfies the 22 condition of serre note that normality is equivalent to 5y2 and r1 moreover there is a description of the 5 condition in terms of s see theorem 6 3 in general the 52 condition is not sufficient for i s to be a cohen macaulay ring as follows by examples in hol resp th 1 2 on the other side grobner g posed the problem to classify cohen macaulay affine semigroup rings the solution of this problem was done by hoa and trung th related to structural properties of graded rings is a technical tool of the duality theory this is the dualizing complex introduced by grothendieck see ha in recent years it became a helpful tool in commutative algebra in particular its knowledge allows characterizations of cohen macaulay rings locally cohenmacaulay rings buchsbaum rings gorenstein rings and the 5 conditions of received by the editors december 18 1988 1980 mathematics subject classification 1985 revision primary 13h10 secondary 14m05 06a99 1990 american mathematical society 0002 9947 90 1 q0 25 per page

leader following exponential consensus of fractional order nonlinear multi agents system with hybrid time varying delay a heterogeneous impulsive method abstract in this paper we study the leader following exponential consensus of multi agent system each agent in the system is described by nonlinear fractional order differential equation both the internal delay and coupling delay are taken into consideration the heterogeneous impulsive control is used for ensuring the consensus of all agents based on lyapunov function method and matrix analysis some sufficient conditions for exponential consensus are obtained finally some illustrative examples are given to show the effectiveness of the obtained results

computing the stanley depth in the first chapter some definitions and necessary results from commutative algebra are given also some detail are given which leads us towards the stanley decompositions of multigraded s modules where s is a polynomi ring in n varables over a field f in the end of the chapter we give some important results about the stanledecompositions and stanley conjecture in chapter 2 for the given monomial primary ideals and of s we gave an upper bound for the stanley depth of s which is reached if are irreducible also we showed that stanley conjecture holds for i being some irreducible monomial ideals of s these results are published in our paper 23 for integers 1 n consider the ideal i n s in chapter 3 we gave an upper bound for the stanley depth of the ideal we gave similar upper bounds for the stanley depth of the ideal where in 2 is the square free veronese ideal of degree 2 in n variables these results are from our paper 11

stanley depth of multigraded modules abstract the stanley s conjecture on cohen macaulay multigraded modules is studied especially in dimension 2 in codimension 2 similar results were obtained by herzog soleyman jahan and yassemi as a consequence of our results stanley s conjecture holds in 5 variables

dynamical behaviors analysis of memristor based fractional order complex valued neural networks with time delay abstract the robust stability for memristor based fractional order complex valued neural networks fcvnns with time delay is investigated here in complex plane by using the lyapunov method and under the sense of filippov solutions the existence of unique equilibrium and globally asymptotic stability for such neural networks nns have been obtained when the nonlinear complex valued activation functions could be split into two real and imaginary parts moreover locally asymptotic stability for such neural nns have been proposed when the nonlinear complex activation functions are bounded lastly three numerical examples are given to confirm the efficiency of theorems

lmi conditions for global stability of fractional order neural networks fractional order neural networks play a vital role in modeling the information processing of neuronal interactions it is still an open and necessary topic for fractional order neural networks to investigate their global stability this paper proposes some simplified linear matrix inequality lmi stability conditions for fractional order linear and nonlinear systems then the global stability analysis of fractional order neural networks employs the results from the obtained lmi conditions in the lmi form the obtained results include the existence and uniqueness of equilibrium point and its global stability which simplify and extend some previous work on the stability analysis of the fractional order neural networks moreover a generalized projective synchronization method between such neural systems is given along with its corresponding lmi condition finally two numerical examples are provided to illustrate the effectiveness of the established lmi conditions

the mixed two qubit system and the structure of its ring of local invariants the local invariants of a mixed two qubit system are discussed these invariants are polynomials in the elements of the corresponding density matrix they are counted by means of group theoretic branching rules which relate this problem to one arising in spin isospin nuclear shell models the corresponding molien series and a refinement in the form of a four parameter generating function are determined a graphical approach is then used to construct explicitly a fundamental set of 21 invariants relations between them are found in the form of syzygies by using these the structure of the ring of local invariants is determined and complete sets of primary and secondary invariants are identified there are 10 of the former and 15 of the latter

depth and stanley depth of symbolic powers of cover ideals of graphs abstract let g be a graph with n vertices and let s k x 1 x n be the polynomial ring in n variables over a field k assume that j g is the cover ideal of g and j g k is its k th symbolic power we prove that the sequences sdepth s j g k k 1 and sdepth j g k k 1 are non increasing and hence convergent suppose that o g denotes the ordered matching number of g we show that for every integer k 2 o g 1 the modules j g k and s j g k satisfy the stanley s inequality we also provide an alternative proof for 9 theorem 3 4 which states that depth s j g k n o g 1 for every integer k 2 o g 1

stability and bifurcation of a delayed generalized fractional order prey predator model with interspecific competition abstract the present paper considers a delayed generalized fractional order prey predator model with interspecific competition the existence of the nontrivial positive equilibrium is discussed and some sufficient conditions for global asymptotic stability of the equilibrium are developed meanwhile the existence of hopf bifurcation is discussed by choosing time delay as the bifurcation parameter finally some numerical simulations are carried out to support the analytical results

on uniqueness in a lateral cauchy problem with multiple characteristics where f w 1 2 w w indeed we are able to derive from our results on scalar operators in this paper and in the paper 4 that a regular c is enough solution to the system 0 2 is uniquely determined in the domain qo by the cauchy data on 1 provided f c the domain qo q depends on 1 and is explicitly described by some quadratic function we expect that other important systems of mathematical physics can be handled in a similar manner as shown in 6 7 uniqueness in the cauchy article no de963227

uniform stabilizability of a full von karman system with nonlinear boundary feedback full von karman system accounting for in plane accelerations and describing the transient deformations of a thin elastic plate subject to edge loading is considered the energy dissipation is introduced via the nonlinear velocity feedback acting on a part of the edge of the plate it is known j puel and m tucsnak siam j control optim 33 1995 pp 255 273 that in the case of linear dissipation and star shaped domains boundary velocity feedback with the tangential derivatives of horizontal displacements leads to the exponential decay rates for the energy of the resulting closed loop system the main goal of the paper is to derive the uniform energy decay rates valid for the model without the above mentioned restrictions in particular it is shown that simple monotone nonlinear feedback without the tangential derivatives of the horizontal displacements provides the uniform decay rates for the energy in the absence of geometric hypotheses imposed on the controlled part of the boundary this is accomplished by establishing among other things sharp regularity results valid for the boundary traces of solutions corresponding to this nonlinear model and by employing a holmgren type uniqueness result proved recently in v isakov j differential equations 97 1997 pp 134 147 for the dynamical systems of elasticity which are overdetermined on the boundary

global attractors for the plate equation with a localized damping and a critical exponent in an unbounded domain abstract in this paper we study the asymptotic behavior of solutions for the plate equation with a localized damping and a critical exponent we prove the existence regularity and finite dimensionality of a global attractor in w 2 2 r n l 2 r n

projective synchronization of fractional order memristive neural networks with switching jumps mismatch abstract this paper investigates the projective synchronization of fractional order memristor based neural networks fmnns with switching jumps mismatch and time varying delays according to the theory of discontinuous differential system filippov and differential inclusions a fractional order inequality was introduced based on notoriously barbalat s lemma and razumikhin type stability theorem some projective synchronization criteria of fmnns are derived these results extend the previous publications to illustrate the effectiveness of the proposed results two numerical examples are presented

stanley depth of squarefree monomial ideals in this paper we answer a question posed by y h shen we prove that if i is an m generated squarefree monomial ideal in the polynomial ring s k x1 xn with k a field then sdepthi n m 2 the proof is inductive and uses the correspondence between a stanley decomposition of a monomial ideal and a partition of a particular poset into intervals established by herzog vladoiu and zheng

stability analysis of fractional order memristive discontinuous neural networks with partial state control abstract this paper investigates exponential stability of fractional order memristive discontinuous neural networks fmdnns under the framework of the fractional order filippov solution and differential inclusion theory the global existence of the solution for the fmdnns is studied by a given growth conditions based on fractional stability theoryand the properties of the mittag leffler function some new criteria for the stability of fmdnns are obtained by using effective partial state impulsive control which only needs to control a small fraction of the states at every impulsive moment these states of the trajectory far away from the desired trajectory will be firstly controlled the relations between stable region and fractional order control parameters and control rate are discussed finally a numerical simulation is given to verify the effectiveness of the theoretical analysis

extending the binomial coefficients to preserve symmetry and pattern abstract we show how to extend the domain of thee binomial coefficients rn so that n and r may take any integer value we argue from two directions on the one hand we wish to preserve symmetry and pattern within pascal s triangle thus creating pascal s hexagon and on the other hand we wish the binomial coefficients to preserve their algebraic role in terms of the taylor series and laurent series expansions of 1 x n valid when x 1 respectively a geometric configuration within the pascal triangle called the pascal flower has some extraordinary properties these properties persist into the hexagon moreover the binomial coefficients may by the use of the function even be extended to all real or complex values of n and r with the conservation of their principal properties

local cohomology of modules of covariants abstract let g be a connected reductive algebraic group over an algebraically closed field of characteristic zero and let w u be two finite dimensional representations of g in this paper we compute the local cohomology of u sw g provided a certain relatively weak technical condition is true

on the stanley depth of powers of edge ideals abstract let k be a field and s k x 1 x n be the polynomial ring in n variables over k let g be a graph with n vertices assume that i i g is the edge ideal of g and p is the number of its bipartite connected components we prove that for every positive integer k the inequalities sdepth i k i k 1 p and sdepth s i k p hold as a consequence we conclude that s i k satisfies stanley s inequality for every integer k n 1 also it follows that i k i k 1 satisfies stanley s inequality for every integer k 0 furthermore we prove that if i g is a non bipartite graph or ii at least one of the connected components of g is a tree with at least one edge then i k satisfies stanley s inequality for every integer k n 1 moreover we verify a conjecture of the author in special cases

stanley depths of certain stanley reisner rings abstract let be a simplicial complex on n s k x 1 x n the polynomial ring in n variables over a field k and k s i the stanley reisner ring of with respect to k it is proved that the stanley conjecture holds for k i e sdepth s k depth s k when i has four associated prime ideals it is also obtained that sdepth s k size s i

prime filtrations of monomial ideals and polarizations abstract we show that an arbitrary monomial ideal i is pretty clean if and only if its polarization i p is clean this yields a new characterization of pretty clean monomial ideals in terms of the arithmetic degree and it also implies that a multicomplex is shellable if and only the simplicial complex corresponding to its polarization is non pure shellable we also discuss stanley decompositions in relation to prime filtrations

non commutative resolutions of toric varieties abstract let r be the coordinate ring of an affine toric variety we prove using direct elementary methods that the endomorphism ring end r a where a is the finite direct sum of all isomorphism classes of conic r modules has finite global dimension equal to the dimension of r this gives a precise version and an elementary proof of a theorem of spenko and van den bergh implying that end r a has finite global dimension furthermore we show that end r a is a non commutative crepant resolution if and only if the toric variety is simplicial for toric varieties over a perfect field k of prime characteristic we show that the ring of differential operators d k r has finite global dimension

the ubiquity of smooth hilbert schemes we investigate the geography of hilbert schemes parametrizing closed subschemes of projective space with specified hilbert polynomials we classify hilbert schemes with unique borel fixed points via combinatorial expressions for their hilbert polynomials these expressions naturally lead to an arrangement of nonempty hilbert schemes as the vertices of an infinite full binary tree here we discover regularities in the geometry of hilbert schemes specifically under natural probability distributions on the tree we prove that hilbert schemes are irreducible and nonsingular with probability greater than 0 5

the action of the special orthogonal group on planar vectors integrity bases via a generalization of the symbolic interpretation of molien functions the present article completes the mathematical description initiated in the paper by dhont and zhilinskii 2013 the action of the orthogonal group on planar vectors invariants covariants and syzygies j phys a math theor 46 455202 of the algebraic structures that emerge from the symmetry adapted polynomials in the coordinates of n planar vectors under the action of the so 2 group the set of covariant polynomials contains all the polynomials that transform according to the weight of so 2 and is a free module for but a non free module for the sum of the rational functions of the molien function for covariants describes the decomposition of the ring of invariants or the module of covariants as a direct sum of submodules a method for extracting the generating function for covariants from the comprehensive generating function for all polynomials is introduced the approach allows the direct construction of the integrity basis for the module of covariants decomposed as a direct sum of submodules and gives insight into the expressions for the molien functions found in our earlier paper in particular a generalized symbolic interpretation in terms of the integrity basis of a rational function is discussed where the requirement of associating the different terms in the numerator of one rational function with the same subring of invariants is relaxed

a nonhyperbolic cauchy problem for b c and its applications to elasticity theory on etudie l unicite et la stabilite d une fonction u satisfaisant les conditions suivantes b c u a 3 u f sur t t g n j u g j sur t t j 3 ou b u bu tt u a k est un operateur differentiel d ordre k g r n une partie de sa frontiere et n la normale a

lipschitz stability in determining density and two lame coefficients we consider an inverse problem of determining spatially varying density and two lame coefficients in a non stationary isotropic elastic equation by a single measurement of data on the whole lateral boundary we prove the lipschitz stability provided that initial data are suitably chosen the proof is based on a carleman estimate which can be obtained by the decomposition of the lame system into the rotation and the divergence components

stanley conjecture in small embedding dimension we show that stanley s conjecture holds for a polynomial ring over a field in four variables in the case of polynomial ring in five variables we prove that the monomial ideals with all associated primes of height two are stanley ideals

simplicity of rings of differential operators in prime characteristic let w be a finite dimensional representation of a linearly reductive group g over a field k motivated by their work on classical rings of invariants levasseur and stafford asked whether the ring of invariants under g of the symmetric algebra of w has a simple ring of differential operators in this paper we show that this is true in prime characteristic indeed if r is a graded subring of a polynomial ring over a perfect field of characteristic p 0 and if the inclusion r hookrightarrow s splits then d k r is a simple ring in the last section of the paper we discuss how one might try to deduce the characteristic zero case from this result as yet however this is a subtle problem and the answer to the question of levasseur and stafford remains open in characteristic zero http www luc ac be research algebra 1991 mathematics subject classification 16s32 16g60 13a35

implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity abstract uniform exponential decay of solution is established for the elastodynamic system of elasticity using boundary feedback control energy dissipation is introduced via linear velocity feedbacks acting through a portion of the boundary as traction forces two primary goals are achieved first these results are proven without the imposition of strong geometric assumptions on the controlled portion of the boundary thus extending earlier work which required that the domain be star shaped second the feedback is only a function of velocity as opposed to also containing the tangential derivative of the displacement resulting in a physically viable feedback proof is based on the multiplier method and relies critically on sharp trace estimates for the tangential derivative of the displacement on the boundary as well as on unique continuation results for the corresponding static system

the action of the orthogonal group on planar vectors invariants covariants and syzygies the construction of invariant and covariant polynomials from the x y components of n planar vectors under the so 2 and o 2 orthogonal groups is addressed molien functions determined under the so 2 symmetry group are used as a guide to propose integrity bases for the algebra of invariants and the modules of covariants the molien functions that describe the structure of the algebra of invariants and the free modules of m covariants m n 1 are written as a ratio of a numerator in with positive coefficients over a 1 2 2n 1 denominator this form of single rational function is standard in invariant theory and has a clear symbolic interpretation however its usefulness is lost for the non free modules of m covariants m n due to negative coefficients in the numerator we propose for these non free modules a new representation of the molien function as a sum of n rational functions with positive coefficients in the numerators and different numbers of terms in the denominators this non standard form is symbolically interpreted in terms of a generalized integrity basis integrity bases are explicitly given for n 2 3 4 planar vectors and m ranging from 0 to 5 the integrity bases obtained under the so 2 symmetry group are subsequently extended to the o 2 group

fractional diffusion equations by the kansa method this study makes the first attempt to apply the kansa method in the solution of the time fractional diffusion equations in which the multiquadrics and thin plate spline serve as the radial basis function in the discretization formulation the finite difference scheme and the kansa method are respectively used to discretize time fractional derivative and spatial derivative terms the numerical solutions of one and two dimensional cases are presented and discussed which agree well with the corresponding analytical solution

local cohomology with support in ideals of maximal minors and sub maximal pfaffians abstract we compute the gl equivariant description of the local cohomology modules with support in the ideal of maximal minors of a generic matrix as well as of those with support in the ideal of 2 n 2 n pfaffians of a 2 n 1 2 n 1 generic skew symmetric matrix as an application we characterize the cohen macaulay modules of covariants for the action of the special linear group sl g on g m the main tool we develop is a method for computing certain ext modules based on the geometric technique for computing syzygies and on matlis duality

global well posedness and stability of semilinear mindlin timoshenko system abstract we study long term behavior of reissner mindlin timoshenko rmt plate systems focusing on the interplay between nonlinear viscous damping and source terms the sources may represent restoring forces but may also be focusing thus potentially amplifying the total energy which is the primary scenario of interest this work complements 28 which established local well posedness of this problem global well posedness when damping dominates the sources in an appropriate sense and a blow up in the complementary scenario assuming negative total initial energy the current paper develops the potential well theory for the rmt system it proves global existence for potential well solutions without restricting the source exponents derives explicit energy decay rates dependent on the order of the damping exponents and verifies a blow up result for positive total initial energy