on probabilistic φ contractions on menger spaces abstract recently ciric lj b ciric solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces nonlinear anal 72 2010 2009 2018 obtained a fixed point theorem with the intention to get a probabilistic version of the boyd wong theorem d w boyd j s w wong on nonlinear contractions proc amer math soc 20 1969 458 464 we give a counterexample to the key lemma of ciric and we establish a corrected version of his main theorem we also discuss the relations between our result and fixed point theorems of browder f e browder on the convergence of successive approximations for nonlinear functional equations nederl akad wetensch proc ser a 71 indag math 30 1968 27 35 and matkowski j matkowski integrable solutions of functional equations dissertationes math rozprawy mat 127 1975 68 pp

local uniqueness in the inverse conductivity problem with one measurement we prove local uniqueness of a domain d entering the conductivity equation div 1 x d vu 0 in a bounded planar domain q given the cauchy data for u on a part of oq the main assumption is that vu has zero index on oa which is easy to guarantee by choosing special boundary data for u to achieve our goals we study index of critical points of u on 00 we are interested in finding a simply connected domain d entering the conductivity equation div l x d vu 0 from one exterior boundary measurement the cauchy data for u on a piece of boundary of a given planar domain q2 containing d this problem is fundamental for electrical and seismical prospection but not much is known about it at present the only available uniqueness results are for convex polyhedrons fi or cylinders ip there are more general results when d is assumed to be close to a given domain do in cv a local uniqueness theorem is proved under the technical assumption which involves a condition on the interior values of vu in bfi p under assumptions on the boundary data which guarantee that vu has zero index on d92 and under the restrictive assumption that odo ad are piecewise analytic local uniqueness results have been obtained in this paper we remove this last assumption and we show that solutions d e c a of the inverse problem are isolated notation b a r is the ball of radius r centered at a v is the exterior unit normal to the boundary d dz 1 2 a 9x id dy d d2 1 2 a dx 0 dy a 1 k a q is the norm in the holder space ck a q of functions whose partial derivatives up to order k are holder continuous of exponent a 0 a 1 c denote positive constants which depend only on 2 do and m received by the editors june 29 1993 and in revised form november 9 1994 1991 mathematics subject classification primary 35r30 secondary 31a25 86a22 the first author has been supported in part by fondi murst 40 60 the second author s research is partially supported by the national science foundation grant dms 91 01421 the third author s work was partly funded by the applied mathematical sciences subprogram of the office of energy research of the united states department of energy under the contract w 7405 eng 82 1995 american mathematical society

on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

socle degrees resolutions and frobenius powers we first describe a situation in which every graded betti number in the tail of the resolution of rj may be read from the socle degrees of rj then we apply the above result to the ideals j and j q and thereby describe a situation in which the graded betti numbers in the tail of the resolution of r j q are equal to the graded betti numbers in the tail of a shift of the resolution of r j

an augmented lagrangian method for identifying discontinuous parameters in elliptic systems the identification of discontinuous parameters in elliptic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method the minimization problem is then proved to be equivalent to the saddle point problem of an augmented lagrangian the finite element method is used to discretize the saddle point problem and the convergence of the discretization is also proved finally an uzawa algorithm is suggested for solving the discrete saddle point problem and is shown to be globally convergent

lagrangian subbundles and codimension 3 subcanonical subschemes we show that a gorenstein subcanonical codimension 3 subscheme z x p n 4 can be realized as the locus along which two lagrangian subbundles of a twisted orthogonal bundle meet degenerately and conversely we extend this result to singular z and all quasi projective ambient schemes x under the necessary hypothesis that z is strongly subcanonical in a sense defined below a central point is that a pair of lagrangian subbundles can be transformed locally into an alternating map in the local case our structure theorem reduces to that of d buchsbaum and d eisenbud 6 and says that z is pfaffian we also prove codimension 1 symmetric and skew symmetric analogues of our structure theorems 0 introduction smooth subvarieties of small codimension z x p have been extensively studied in recent years especially in relation to r hartshorne s conjecture that a smooth subvariety of sufficiently small codimension in p is a complete intersection although the conjecture remains open any smooth subvarietyz of small codimension in p is known by a theorem of w barth m larsen and s lefschetz to have the weaker property that it is subcanonical in the sense that its canonical class is a multiple of its hyperplane class more generally a subscheme z of a nonsingular noetherian scheme x is said to be subcanonical if z is gorenstein and its canonical bundle is the restriction of a bundle on x there is a natural generalization to an arbitrary possibly singular scheme x see below in this paper we give a structure theorem for subcanonical subschemes of codimension 3 in p and generalize it to subcanonical subschemes of codimension 3 in an arbitrary quasi projective scheme x satisfying a mild extra cohomological conduke mathematical journal vol 107 no 3 c 2001 received 4 july 1999 revision received 17 july 2000 2000 mathematics subject classification primary 14m07 13d02 secondary 14m12 14f05 authors work partially supported by the national science foundation

on the finite element solution of the pure neumann problem this paper considers the finite element approximation and algebraic solution of the pure neumann problem our goal is to present a concise variational framework for the finite element solution of the neumann problem that focuses on the interplay between the algebraic and variational problems while many of the results that stem from our analysis are known by some experts they are seldom derived in a rigorous fashion and remain part of numerical folklore as a result this knowledge is not accessible or appreciated by many practitioners both novices and experts in one source our paper contributes a simple yet insightful link between the continuous and algebraic variational forms that will prove useful

optimal finite element interpolation on curved domains this paper is devoted to a general theory of approximation of functions in finite element spaces in particular the case is considered where the functions to be interpolated are on the one hand not very smooth and on the other are defined on curved domains thus a number of well known optimal interpolation results are generalized

discrete total variation flows without regularization we propose and analyze an algorithm for the solution of the l 2 subgradient flow of the total variation functional the algorithm involves no regularization thus the numerical solution preserves the main features that motivate practitioners to consider this type of energy we propose an iterative scheme for the solution of the arising problems show that the iterations converge and develop a stopping criterion for them we present numerical experiments which illustrate the power of the method explore the solution behavior and compare with regularized flows

deformations of the normalization of hypersurfaces introduction a deformation theory has been introduced by siersma si 11 for the simplest class of non isolated singularities x hypersurfaces with a smooth one dimensional singular locus and transverse to a general point of e an ai singularity he considered deformations loosely speaking such that z stays inside the singular locus of the deformed x this notion has been extended by pellikaan pe 1 and has been studied further by the authors in j s 11 and j s 2 let us be more precise about the deformation functor we are interested in let c be a category of spaces e g those of germs of analytic spaces a diagram of spaces z s xs flat over some base space s is called admissible iffzs xsls where ccxs s is the relative critical space as defined by teissier l te p 5871 now let z x be an admissible diagram over the spectrum of the ground field then the functor of admissible deformations def z x c set is defined by s isomorphism classes of deformations of x over s which are admissible of course in general one expects this deformation functor to be obstructed that this is also the case in general when x is a hypersurface in c 3 with a one dimensional reduced 2 is shown by a beautiful example due to pellikaan he considered the singularity x defined by yz 2 xz 2 xy 2 0 with z defined by the ideal yz xz xy he gave an admissible deformation over the space s defined by the equations ea eb ec 0 in c 4 and showed that there are obstructions this example has been worked out further in j s 1 ij s 2 and j s 3 example 3 3 the first example of an obstructed rational singularity has been given by pinkham pil he showed that the base space of a semi universal deformation of the cone over the rational normal curve of degree 4 is isomorphic to the space s above the nice thing is that the examples of pellikaan and pinkham are closely related the normalization of pellikaan s example is pinkham s example or to put it in another way pellikaan s example is a projection into 3 of pinkham s example

fixed point theorems for multivalued mappings in probabilistic metric spaces abstract in this paper we prove a fixed point theorem for multivalued mappings in probabilistic metric spaces some applications in fuzzy metric and random normed spaces are given

solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces abstract the probabilistic version of the classical banach contraction principle was proved in 1972 by sehgal and bharucha reid v m sehgal a t bharucha reid fixed points of contraction mappings on pm spaces math syst theory 6 97 102 their fixed point theorem is further generalized by many authors in the intervening years many others have proved the probabilistic versions of the other known metric fixed point theorems however the problem to prove the probabilistic versions of the very important generalization of the banach contraction principle obtained in 1969 by boyd and wong d w boyd j s w wong on nonlinear contractions proc am math soc 20 1969 458 464 who proved the fixed point theorem for a self mapping of a metric space satisfying the very general nonlinear contractive condition is unsolved in these days similarly as in the metric space case to prove a fixed point theorem for a mapping satisfying the general probabilistic nonlinear contractive condition it was necessary to find a new approach substantially different from the previous technique for cases where a mapping satisfies the probabilistic linear contraction condition introduced by sehgal and bharucha reid and further used by many authors so the problem to obtain a truthful probabilistic version of the banach fixed point principle for general nonlinear contractions existed unsolved for over 35 years we have solved this problem in this paper

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

on finite element approximations of problems having inhomogeneous essential boundary conditions abstract the analysis and implementation of finite element methods for problems with inhomogeneous essential boundary conditions are considered the results are given for linear second order elliptic partial differential equations and for the nonlinear stationary navier stokes equations for certain easily implemented boundary treatments optimal error estimates and numerical examples are provided for problems posed on polyhedral domains

a note on probabilistic φ contractions in menger spaces abstract in this note we prove that each probabilistic e contraction in a complete menger space x f with of h type is a picard mapping where 0 0 be a function with the properties i 0 1 0 1 ii for each t 0 there exists r t such that lim n n r 0 as a consequence we answer an open question raised by mihet and zaharia affirmatively

on contractions in probabilistic and fuzzy metric spaces in this paper by means of weakening conditions of the gauge function a new fixed point theorem for probabilistic contraction in menger probabilistic metric spaces with a t norm of h type is established this theorem improves and generalizes the recent results of iric 2010 4 jachymski 2010 12 and xiao et al 2013 25 by using the theorem we also obtain some important corollaries and the fixed point theorems for contraction in fuzzy metric spaces

koszul modules and gorenstein algebras abstract i first define koszul modules which are a generalization to arbitrary rank of complete intersections after a study of some of their properties it is proved that gorenstein algebras of codimension one or two over a local or graded cm ring are koszul modules thus generalizing a well known statement for rank one modules the general techniques used to describe koszul modules are then used to obtain a structure theorem for gorenstein algebras in codimension one and two over a local or graded cm ring

on linearly topological structure and property of fuzzy normed linear space in this paper the simplified definition of fuzzy normed linear space is introduced the different structure of fuzzy normed linear space with variable right norm r is discussed in terms of topological vector space and its properties such as compactness completeness and density are studied under more general left norm l and right norm r as application the linearly topological structure of menger pn space is obtained

identifying conductivity in electrical impedance tomography with total variation regularization in this paper we investigate the problem of identifying the conductivity in electrical impedance tomography from one boundary measurement a variational method with total variation regularization is here proposed to tackle this problem we discretize the pde as well as the conductivity with piecewise linear continuous finite elements we prove the stability and convergence of this technique for the numerical solution we propose a projected armijo algorithm finally a numerical experiment is presented to illustrate our theoretical results

variational method for multiple parameter identification in elliptic pdes abstract in the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix source term and boundary condition in the neumann boundary value problem for an elliptic partial differential equation pde from a measurement data which is weaker than required of the exact state a variational method based on energy functions with tikhonov regularization is here proposed to treat the identification problem we discretize the pde with the finite element method and prove the convergence as well as analyze error bounds of this approach

core and residual intersections of ideals d rees and j sally defined the core of an r ideal i as the in tersection of all minimal reductions of i however it is not easy to give an explicit characterization of it in terms of data attached to the ideal until recently the only case in which a closed formula was known is the one of inte grally closed ideals in a two dimensional regular local ring due to c huneke and i swanson the main result of this paper explicitly describes the core of a broad class of ideals with good residual properties in an arbitrary local cohen macaulay ring we also find sharp bounds on the number of minimal reductions that one needs to intersect to get the core

global uniqueness for a two dimensional inverse boundary value problem we show that the coefficient y x of the elliptic equation vie qyvu 0 in a two dimensional domain is uniquely determined by the corresponding dirichlet to neumann map on the boundary and give a reconstruction pro

a local regularization operator for triangular and quadrilateral finite elements this paper develops a local regularization operator on triangular or quadrilateral finite elements built on structured or unstructured meshes this operator is a variant of the regularization operator of clement however ours is constructed via a local projection in a reference domain we prove in this paper that it has the same optimal approximation properties as the standard interpolation operator and we present some applications

on probabilistic ψ contractions in menger probabilistic metric spaces abstract in this paper we prove some equivalence for probabilistic contractions in menger probabilistic metric spaces by which we answer open question 3 in mihet and zaharia 2016 11 affirmatively

on probabilistic φ contractions in menger spaces abstract in this note we show that the fixed point theorems given for menger spaces by j jachymski 2010 5 theorem 1 and j x fang 2015 2 theorem 3 1 are equivalent

existence and uniqueness for electrode models for electric current computed tomography the following experiment is considered to a body of given conductivity a number of electrodes are attached through which current is sent on the same electrodes the resulting voltages are measured this experiment can be described by a number of mathematical models k s cheng et al ieee transactions on biomedical engineering 36 1989 pp 918 924 these models are discussed and their predictions compared with experiment in particular a model is exhibited that is capable of predicting the experimentally measured voltages to within 0 1 percent for this model existence and uniqueness of the associated electrical potential is proved

on some classes of nonlinear contractions in probabilistic metric spaces motivated by a question in j x fang 2015 6 we investigate the existence of fixed points for several classes of probabilistic contractions under fang type conditions