on a connection between the pascal vandermonde and stirling matrices ii this article is an extension of the work presented in on a connection between the pascal vandermonde and stirling matrices i applied mathematics and computation 2003 to appear it gives a full matrix t t for which t 1 is exactly the lower triangular stochastic matrix t given in on a connection between the pascal vandermonde and stirling matrices i applied mathematics and computation 2003 to appear a new strategy to generate the elements of the matrix t t 1 is investigated a new conjecture and three combinatorial identities are also given

explicit inverse of a generalized vandermonde matrix in this paper the author gives an explicit closed form expression for the nxn inverse matrix v g k n 1 of the generalized nxn vandermonde matrix v g k n by using the elementary symmetric functions symbolic and numerical results are presented

rank one property for derivatives of functions with bounded variation when u is a function of bounded variation of the open set r into r du is a measure on which takes values in the space rm n of all m n matrices such that du i j ui xj for every i j with 1 i m 1 j n and we denote by dsu the part of the measure du which is singular with respect to lebesgue measure we recall that the rank of a matrix a rm n is dimension of the space spanned by its columns in r or by its rows in r and in particular the rank of a is one if and only if there exist e r and r with e 6 0 6 0 so that a e i e ai j ei j for all i j cf remark 1 7 when is a measure which takes values in the space rm n and d d denotes the radon nikodym derivative of with respect to the total variation we say that has rank one when the rank of the matrix d d x is one for almost every x in this paper we prove we prove the following statement see theorem 4 5 corollary 4 6 and remark 4 9

optimal filtering of complex turbulent systems with memory depth through consistency constraints in this article we develop a linear theory for optimal filtering of complex turbulent signals with model errors through linear autoregressive models we will show that when the autoregressive model parameters are chosen such that they satisfy absolute stability and consistency conditions of at least order 2 of the classical multistep method for solving initial value problems the filtered solutions with autoregressive models of order p 2 are optimal in the sense that they are comparable to the estimates obtained from the true filter with perfect model this result is reminiscent of the lax equivalence fundamental theorem in the analysis of finite difference discretization scheme for the numerical solutions of partial differential equations we will apply this linear theory to filter two nonlinear problems the slowest mode of the truncated burgers hopf and the lorenz 96 model on these nonlinear problems we will show that whenever these linear conditions are satisfied the filtered solutions accuracy is significantly improved finally we will also apply the recently developed offline test criteria to understand the robustness of the multistep filter on various turbulent nature including the stochastically forced linear advection diffusion equation and a toy model for barotropic turbulent rossby waves

inegalites de sobolev produit sur les groupes de lie nilpotents on generalise dans le cadre des groupes de lie nilpotents reels et connexes l inegalite classique due a gagliardo et nirenberg

weighted sobolev poincare inequalities and pointwise estimates for a class of degenerate elliptic equations in this paper we prove a sobolev poincare inequality for a class of function spaces associated with some degenerate elliptic equations these estimates provide us with the basic tool to prove an invariant harnack inequality for weak positive solutions in addition holder regularity of the weak solutions follows in a standard way let y z 7 ai aij9 a be a second order degenerate elliptic operator in divergence form with measurable coefficients in this paper we shall obtain pointwise estimates for the weak solutions of su 0 h61der continuity of the weak solutions and harnack inequality for nonnegative solutions let us recall that the original results for elliptic operators were obtained by de giorgi nash and moser an extensive bibliography about the degenerate case can be found in fli fl2 fs to introduce the results of the present paper let us recall some recent results in fl1 fl2 a suitable metric d is associated with the differential operator y in such a way that we obtain a new geometry which is natural for the degenerate operator as the euclidean geometry is natural for the laplace operator or more precisely as a suitable riemannian geometry is natural for a secondorder elliptic operator in the smooth case this idea is contained in many papers we refer to fp nsw the basic results in fl 1 fl2 are obtained via a precise description of this geometry under suitable technical hypotheses on the coefficients whose aim is to give a nonsmooth formulation of the hormander hypoellipticity condition for sum of squares operators we note that the same idea is used in nsw s j v to obtain pointwise estimates for sum of squares operators on the other hand a different class of degenerate elliptic operators is considered in fks instead of a geometrical degeneracy a measure degeneracy is allowed a typical example of this class is given by yu div wo x vu where cl is a weight function belonging to the a2 class of muckenhoupt unified results for a class containing both the operators in fl 1 and in fks have received by the editors august 1 1989 1980 mathematics subject classification 1985 revision primary 46e35 35j70 partially supported by g n a f a of c n r and m u r s t italy 1991 american mathematical society 0002 9947 91 1 00 25 per page

notes on particular symmetric polynomials with applications this paper presents some applications using several properties of three important symmetric polynomials elementary symmetric polynomials complete symmetric polynomials and the power sum symmetric polynomials the applications includes a simple proof of el mikkawy conjecture in m e a el mikkawy appl math comput 146 2003 759 769 and a very easy proof of the newton girard formula in addition a generalization of stirling numbers is obtained

fine properties of functions with bounded variation in carnot caratheodory spaces abstract we study properties of functions with bounded variation in carnot caratheodory spaces we prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives under an additional assumption on the space called property r we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative

null controllability of von karman thermoelastic plates under the clamped or free mechanical boundary conditions abstract in this paper we provide results of local and global null controllability for 2 d thermoelastic systems in the absence of rotational inertia and under the influence of the nonlipschitz von karman nonlinearity the plate component may be taken to satisfy either the clamped or higher order and physically relevant free boundary conditions in the accompanying analysis critical use is made of sharp observability estimates which obtain for the linearization of the thermoelastic plate these being derived in g avalos i lasiecka the null controllability of thermoelastic plates and singularity of the associated minimal energy function j math anal appl 294 2004 34 61 and g avalos i lasiecka asymptotic rates of blowup for the minimal energy function for the null controllability of thermoelastic plates the free case in proc of the conference for the control of partial differential equations georgetown university dekker in press moreover another key ingredient in our work to steer the given nonlinear dynamics is the recent result in a favini m a horn i lasiecka d tataru addendum to the paper global existence uniqueness and regularity of solution to a von karman system with nonlinear boundary dissipation differential integral equations 10 1997 197 200 concerning the sharp regularity of the von karman nonlinearity

isoperimetric and sobolev inequalities for carnot caratheodory spaces and the existence of minimal surfaces after hormander s fundamental paper on hypoellipticity 54 the study of partial differential equations arising from families of noncommuting vector fields has developed significantly in this paper we study some basic functional and geometric properties of general families of vector fields that include the hormander type as a special case similar to their classical counterparts such properties play an important role in the analysis of the relevant differential operators both linear and nonlinear to motivate our results we recall some classical inequalities let e c r be a caccioppoli set a measurable set having a locally finite perimeter then one has the isoperimetric inequality

weighted poincare and sobolev inequalities and estimates for weighted peano maximal functions 1 introduction in this paper we derive local poincare and sobolev inequalities involving two weight functions the estimates we obtain include those proved by fabes kenig and serapioni in 8 for the one weight function case we also consider the notion of weighted peano derivatives and show that the peano derivative formed with a given weight function can be estimated in terms of a maximal function involving a second weight function in the special case of ordinary lebesgue measure results of this kind lead to the theorems of a p calderon and a zygmund about local differentiability of functions in sobolev spaces and of functions which are of bounded variation in the sense of tonelli see 3 and 4 all our results are based on variants of the basic estimate in 5 but we do not presuppose any facts from 5 let v x be a weight function on r i e let v x be nonnegative and locally integrable with respect to lebesgue measure we shall use the notation v e se v x dx ordinary lebesgue measure will be denoted ie l if bh x is the open ball with center x and radius h we say v satisfies the doubling condition with respect to lebesgue measure if

weak differentiability of bv functions on stratified groups we prove the almost everywhere approximate differentiability of functions with bounded variation in stratified groups and we study their approximate discontinuity set we introduce functions of bounded higher order variation and obtain a weak version of alexandroff differentiability theorem in this context we present a nontrivial class of functions with second order bounded variation arising from inf convolution formula of a suitable cost function

global attractors for von karman evolutions with a nonlinear boundary dissipation abstract dynamic von karman equations with a nonlinear boundary dissipation are considered questions related to long time behaviour existence and structure of global attractors are studied it is shown that a nonlinear boundary dissipation with a large damping parameter leads to an existence of global compact attractor for all weak finite energy solutions this result has been known in the case of full interior dissipation but it is new in the case when the boundary damping is the main dissipative mechanism in the system in addition we prove that fractal dimension of the attractor is finite the proofs depend critically on the infinite speed of propagation associated with the von karman model considered

rectifiability and perimeter in the heisenberg group in this paper we fully extend to the heisenberg group endowed with its intrinsic carnot caratheodory metric and perimeter the classical de giorgi s rectifiability divergence theorems

global attractors for von karman equations with nonlinear interior dissipation abstract in this paper we study the asymptotic behavior of weak solutions for von karman equations with nonlinear interior dissipation we prove the existence of a global attractor in the space w 2 2 l 2

analysis on lie groups theorie locale diffusion de la chaleur sur des groupes de lie connexes la theorie globale les inegalites de sobolev bases graduees sur des corps lisses construction des bases graduees estimation locale du noyau diffusion de la chaleur demonstration de l inegalite de sobolev locale formes de dirichlet sur des groupes le semi groupe de convolution les conditions de sobolev modifiees

remarks on two symmetric polynomials and some matrices by means of complete symmetric polynomials this paper gives a new proof for the vandermonde determinant formula another alternative proof for this formula is obtained via the collocation matrices it also gives a generalized relationship between the vandermonde the pascal and the stirling matrices a new approach to obtain the explicit inverse of the vandermonde matrix is investigated closed form expressions for some vandermonde related determinants are obtained

rank one theorem and subgraphs of bv functions in carnot groups abstract we prove a rank one theorem a la g alberti for the derivatives of vector valued maps with bounded variation in a class of carnot groups that includes heisenberg groups h n for n 2 the main tools are properties relating the horizontal derivatives of a real valued function with bounded variation and its subgraph

global existence and stability for a von karman equations with memory in noncylindrical domains in this paper we study the initial boundary value problem for the von karman equations inside domains with moving ends global existence uniqueness of solutions and the exponential decay to the energy are established provided the initial data are bounded

on solving linear systems of the pascal type in the current paper we study the pascal matrix of order n an algorithm is developed to find its inverse in an explicit form another algorithm for solving any linear system with coefficient matrix of this type is also developed an illustrative example for solving a linear system of the pascal type is given for the case n 6 the implementation of the two algorithms in maple maple v programming reference manual is presented

the weighted isoperimetric type and sobolev type inequalities for hypersurfaces in carnot groups abstract this paper mainly studies hypersurfaces immersed in a sub riemannian step k carnot group g with a density e f where f is a smooth function on g we give the first variation formula about the weighted horizontal area of hypersurfaces furthermore on the base of some work we derive the weighted isoperimetric type and sobolev type inequalities for hypersurfaces

recursive numerical recipes for the high efficient inversion of the confluent vandermonde matrices in the article we propose a recursive algorithm for calculating the inversion of the confluent vandermonde matrix besides contrary to other works in this field the article derives an explicit analytic formula for the calculation of the inverse of the confluent vandermonde matrix the results of this article do not require any symbolic calculations and therefore can be performed by a numerical algorithm implemented in any general purpose programming language moreover a ready to use c full implementation of the recursive algorithm is attached

an algorithm for the finite difference approximation of derivatives with arbitrary degree and order of accuracy in this paper we introduce an algorithm and a computer code for numerical differentiation of discrete functions the algorithm presented is suitable for calculating derivatives of any degree with any arbitrary order of accuracy over all the known function sampling points the algorithm introduced avoids the labour of preliminary differencing and is in fact more convenient than using the tabulated finite difference formulas in particular when the derivatives are required with high approximation accuracy moreover the given matlab computer code can be implemented to solve boundary value ordinary and partial differential equations with high numerical accuracy the numerical technique is based on the undetermined coefficient method in conjunction with taylor s expansion to avoid the difficulty of solving a system of linear equations an explicit closed form equation for the weighting coefficients is derived in terms of the elementary symmetric functions this is done by using an explicit closed formula for the vandermonde matrix inverse moreover the code is designed to give a unified approximation order throughout the given domain a numerical differentiation example is used to investigate the validity and feasibility of the algorithm and the code it is found that the method and the code work properly for any degree of derivative and any order of accuracy