direct identification of elastic constants of anisotropic plates by modal analysis theoretical and numerical aspects abstract a direct method of determining the six flexural stiffnesses of thin anisotropic plates is presented in this paper this technique is based on a relevant processing of natural frequencies and mode shapes of free free vibrating plates the unknown plate rigidities are the solution of an overdetermined linear system the equations of which are obtained with a set of relevant weighting functions associated with different natural modes of vibration numerical simulations indicate the accuracy and the sensitivity of this identification method

determining the elastic constants of isotropic materials by modal vibration testing of rectangular thin plates abstract the paper presents a procedure whereby poisson s ratio and the dynamic young s modulus of isotropic and homogeneous materials are determined using two of the first four frequencies of natural vibration in thin rectangular plates the procedure is based on suitable approximate relationships relating the resonance frequencies to the elastic constants of the material these relations were derived from those of warburton by taking into account a correction factor obtained by an extensive series of numerical analyses carried out by a finite element code in order to verify the procedure a comparison with reference solutions has been made

on the coefficients of the coxeter polynomial of an accessible algebra abstract let a be a finite dimensional algebra over an algebraically closed field k assume a is basic connected with n pairwise non isomorphic simple modules we consider the coxeter polynomial a t of a one point extension algebra a b m and the polynomial of the extension p t 1 t 1 t b t a t if m is exceptional then p t 1 p 1 t p n 3 t n 3 t n 2 in that case we call s a b p 1 the linear index of the extension a b m we give conditions for s a b 0 for a tower t k a 1 a 2 a n a of access to a that is a i is a one point co extension of a i 1 by an exceptional module the index s t i 2 n s a i a i 1 n 1 a 2 is an invariant depending on the derived equivalence class of a where a 2 is the quadratic coefficient of a t we show that in the case a is piecewise hereditary then a 2 1 if and only if a is derived equivalent to a quiver algebra of type a n

coxeter energy of graphs abstract we study the concept of the coxeter energy of graphs and digraphs quivers as an analogue of gutman s adjacency energy which has applications in theoretical chemistry and is a recently widely investigated graph invariant coxeter energy ce g of a di graph g is defined to be the sum of the absolute values of all complex eigenvalues of the coxeter matrix associated with g our main inspiration for the study comes from the coxeter formalism appearing in group theory lie theory representation theory of algebras mathematical physics and other contexts we focus on the coxeter energy of trees and we prove that the path resp the maximal star has the smallest resp the greatest coxeter energy among all trees resp two large subclasses of trees with fixed number of vertices we provide several other related results as the characterization of trees with second smallest and second greatest coxeter energy bounds for coxeter energy and general facts on coxeter spectra of graphs extending known results e g for salem trees and for certain special real coxeter eigenvalues of trees additionally we discuss few other energy like quantities for the coxeter spectra of di graphs including coxeter energy normalized by the trace of the coxeter matrix and the quantities derived from variants of coulson integral formula

steady filtration problems with seawater intrusion variational analysis on the basis of brezis kinderlehrer stampacchia variational approach a general steady filtration problem with seawater intrusion is formulated then qualitative properties are analyzed such as existence and uniqueness of solutions and free boundaries behavior

on spectral radii of coxeter transformations let t be a finite tree and dt the maximal branching degree of its vertices let t be the spectral radius of a coxeter transformation defined by t t hen t 4dt 6

a stationary flow of fresh and salt groundwater in a coastal aquifer consider a horizontally situated homogeneous aquifer of constant thickness h in this aquifer fresh and salt water are present and separated by an abrupt interface let the flow be two dimensional in the vertical x z plane

accurate vibration frequencies of circular cylinders from three dimensional analysis a three dimensional 3 d method of analysis developed in a companion paper a w leissa and j so j acoust soc am 98 2122 2135 1995 is used to obtain free vibration frequencies of completely free elastic cylinders extensive accurate data are presented for the first 20 frequencies of each circumferential wave number 0 5 for free free cylinders having length to diameter ratios l d of 1 1 5 2 3 and 5 with a poisson s ratio of 0 3 an additional study for l d 1 over the full range 0 0 5 possible for isotropic materials shows that poisson s ratio effects can be quite important the first known values of frequencies from 3 d analysis of cylinders having one end fixed with all other boundaries free are also presented in considerable detail for free free cylinders comparisons are made with less accurate 3 d results published previously by other researchers

the trace of the coxeter matrix and hochschild cohomology abstract for a basic finite dimensional k algebra of finite global dimension over an algebraically closed field k the coxeter matrix is defined the following formula is shown trm i 1 i dim k h i where tr is the trace and hi is the ith hochschild cohomology space

nonlinear variational formulation for a cavitation problem in lubrication abstract the fluid behaviour in a journal bearing where cavitation takes place is studied this leads to solving a nonlinear variational inequality with normal discontinuity of derivative on a part of the free boundary under some hypotheses using penalization the proof of the existence of a solution is given which is compared with one of a simpler model governed by a classical variational inequality

steady filtration problems with seawater intrusion penalized finite element approximations abstract penalized finite element approximations of steady filtration problems are studied for a general section of an open aquifer with seawater intrusion the corresponding variational model is the one proposed and analyzed in g alduncin j esquivel avila l reyes avila comput methods appl mech engrg 151 1998 13 25 which characterizes a two free boundary problem in terms of a nonsubdifferential inequality convergence of conforming finite element approximations is established and for numerical stabilization the tabata upwind technique is applied for resolution purposes the resulting discrete nonlinear penalized model is characterized by a fixed point problem and an iterative algorithm is considered finally some numerical applications exemplify the theory

comparisons of vibration frequencies for rods and beams from one dimensional and three dimensional analyses a method of three dimensional 3 d analysis is developed for the free vibration frequencies and mode shapes of solid circular cylinders of elastic material the method assumes for the three displacement components a fourier series in the circumferential direction and algebraic polynomials in the radial r and axial z directions all types of boundary conditions and arbitrary length to diameter ratios l d may be accommodated extensive convergence studies show that frequencies which are exact to five or six significant figures may be obtained for cylinders with free free ends and that three or four figure accuracy is achievable for fixed free ends these accurate frequencies are compared with ones determined from known elementary and improved 1 d theories for longitudinal torsional and bending modes for various l d ratios thereby establishing the ranges of accuracy of the 1 d analyses for circular cross sections

characteristics method for the formulation and computation of a free boundary cavitation problem in this paper a semidiscretized scheme based on characteristics method is analyzed when it is applied to a free boundary problem the free boundary problem issued from a cavitation model in lubrication involves specific boundary conditions the idea is to associate to the departure problem a sequence of variational inequalities depending on a discretization parameter the theoretical convergence result from the solution of the semidiscretized problem to the solution of the continuous one is stated for a flux imposed boundary condition for this purpose due to the specific boundary conditions technical modifications of the classical version of characteristics are needed then obstacle problem tools are applied to a set of variational inequalities with neumann boundary conditions in order to obtain l estimates which provide the convergence result in this way a result of existence of solution for the continuous problem and a theoretical justification for the usage of the proposed numerical methods are concluded finally some numerical test examples are presented to illustrate the good performance of the method

bounds related to coxeter spectral measures of graphs abstract let m be a real square matrix we give upper bounds for the sum of the absolute values of the real part of the eigenvalues of m quantity in some particular cases known as real energy of m from these results we obtain a combinatorial bound for the real energy of the coxeter matrix q of a tree digraph q with n vertices e r e q min n 2 a b c d 2 where a is the number of edges b and c are respectively the number of bifurcation and congregation paths of q as defined below d i 1 n i 1 i 2 with i the degree of a vertex i and where the minimum is taken over all possible orientations of edges in q as particular case we consider dynkin euclidean and star graphs obtaining practical bounds for the real coxeter energy of these classes of digraphs

on the dam problem this paper is concerned with the qualitative behavior of solutions of the dam problem for flow of an incompressible fluid through a two dimensional porous medium the cross section of the flow region is allowed to have a complicated boundary the flow domain is assumed to have a lipschitz boundary and minimal assumptions are made on the parts where various boundary conditions are to be satisfied the main contribution of the paper is to determine the corresponding properties of the solution after giving a concise proof of the known result that a solution exists the authors introduce the so called s 3 connected solutions s 3 is the impervious part of the boundary and prove several interesting results about them solutions which do not have these properties are such that there are pools of fluid not in contact with the outside reservoir and they prove that any solution can be written as a sum of an s 3 connected solution and pools also it is shown that s 3 connected solutions are unique for some boundaries it can be shown that only s 3 connected solutions exist so that uniqueness holds without qualification

measurement of the dynamic elastic constants of short isotropic cylinders abstract a method based on a single test is proposed to characterize the elasticity of an isotropic homogeneous material in the shape of a cylinder of any slenderness length diameter ratio firstly the rayleigh ritz method is used to determine the natural frequencies of the cylinders vibrating axisymmetrically the study is focused on cylindrical samples with diameter and length of similar magnitude so that the shear modulus and the poisson ratio can be calculated simultaneously subsequently the theoretical results for cylinders of slenderness ratio between 0 1 and 3 are analyzed in order to obtain the data required to determine the elastic constants from one of the two lowest measured natural frequencies and their quotient the analysis of the results demonstrates that any slenderness ratio is useful in the calculation of the elastic constants although in some cases the third natural frequency should be used furthermore the influence of the length diameter quotient on the sensitivity of the method is analyzed by evaluating the systematic uncertainties for both dynamic elastic constants finally the method is experimentally tested by characterizing two steel cylinders with slenderness ratios 0 1 and 1 respectively the results demonstrate that uncertainties for both poisson ratio and the shear modulus are smaller when the slenderness ratio is 1

the energy of graphs and matrices abstract given a complex m n matrix a we index its singular values as 1 a 2 a and call the value e a 1 a 2 a the energy of a thereby extending the concept of graph energy introduced by gutman let 2 m n a be an m n nonnegative matrix with maximum entry and a 1 n extending previous results of koolen and moulton for graphs we prove that e a a 1 m n m 1 a 2 2 a 1 2 m n n m m 2 furthermore if a is any nonconstant matrix then e a 1 a a 2 2 1 2 a 2 a finally we note that wigner s semicircle law implies that e g 4 3 o 1 n 3 2 for almost all graphs g

on the uniqueness of the solution of the evolution dam problem the purpose here is to investigate some aspects of the evolution dam problem partial chi alpha u partial t delta u rm div chi e in q chi in h u in q u geq 0 in q u phi in sigma 2 partial u partial v chi ev leq 0 on sigma 2 cap phi 0 e in bf r n e 0 cdots 0 1 partial u partial v chi ev 0 on sigma 1 here h is the heaviside maximal graph h s 1 if s 0 h s 0 1 if s 0 alpha is the storativity constant alpha 0 if the fluid is incompressible and alpha 0 if the fluid is compressible also q omega times 0 t where omega is a bounded domain in bf r n omega represents a porous medium separating a finite number of reservoirs with lipschitz boundary g where g is divided into two parts g 1 which is the impervious part and g 2 which is the pervious part with the following assumptions g 2 is an open subset of g g 2 not emptyset g 2 cap g 1 emptyset g 2 cup g 1 g and e nu leq 0 a e on g 1 sigma i denotes g i times 0 t i 1 2 the pressure at sigma 2 is known and is represented by a nonnegative function phi in c 0 1 overline q the above problem can be completed by prescribing an initial value to chi alpha u the existence of a weak solution of the evolution dam problem is well known however many properties of the solutions of the initial value dam problem in particular comparison and uniqueness theorems continue to be open for a general domain omega the results of this paper give precise information about the comparison theorem 4 7 and the uniqueness corollary 4 9 statements the key point to prove comparison and uniqueness results is that the function h mapsto chi x x n h t h x in bf r n 1 is a e nonincreasing

the mcclelland inequality for the energy of digraphs abstract the energy of a digraph d is defined as e d i 1 n re z i where z 1 z n are the possibly complex eigenvalues of d in this article we extend to general digraphs mcclelland s inequality for the energy of a graph we also determine sharp upper bounds for the energy of a digraph in terms of the number of arcs

the coxeter polynomial for a one point extension algebra let be a finite dimensional algebra over an algebraically closed field k of finite global dimension let m be a finitely generated module and let m be the one point extension algebra we show how to compute the coxeter polynomial for from the coxeter polynomial of and homological invariants of m

on the mahler measure of the coxeter polynomial of an algebra abstract let a be a finite dimensional algebra over an algebraically closed field k assume a is a basic connected and triangular algebra with n pairwise non isomorphic simple modules we consider the coxeter transformation a t as the automorphism of the grothendieck group k 0 a induced by the auslander reiten translation in the derived category der b mod a of the module category mod a of finite dimensional left a modules we say that a is of cyclotomic type if the characteristic polynomial a of a is a product of cyclotomic polynomials equivalently if the mahler measure m a 1 in 6 we have considered many examples of algebras of cyclotomic type in the representation theory literature in this paper we study the mahler measure of the coxeter polynomial of accessible algebras in 1933 d h lehmer found that the polynomial t 10 t 9 t 7 t 6 t 5 t 4 t 3 t 1 has mahler measure 0 1 176280 and he asked whether there exist any smaller values exceeding 1 in this paper we prove that for any accessible algebra a either m a 1 or m b 0 for some convex subcategory b of a we introduce interlaced tower of algebras a m a n with m n 2 satisfying a s 1 t 1 a s t a s 1 for m 1 s n 1 we prove that if spec a n s 1 r and a n is not of cyclotomic type then m a m m a n we construct several examples