determining the first order perturbation of a polyharmonic operator on admissible manifolds abstract we consider the inverse boundary value problem for the first order perturbation of the polyharmonic operator l g x q with x being a w 1 vector field and q being an l function on compact riemannian manifolds with boundary which are conformally embedded in a product of the euclidean line and a simple manifold we show that the knowledge of the dirichlet to neumann map determines x and q uniquely the method is based on the construction of complex geometrical optics solutions using the carleman estimate for the laplace beltrami operator due to dos santos ferreira kenig salo and uhlmann notice that the corresponding uniqueness result does not hold for the first order perturbation of the laplace beltrami operator

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

an iterative method for linear discrete ill posed problems with box constraints many questions in science and engineering give rise to linear discrete ill posed problems often it is desirable that the computed approximate solution satisfies certain constraints e g that some or all elements of the computed solution be nonnegative this paper describes an iterative method of active set type for the solution of large scale problems of this kind the method employs conjugate gradient iteration with a stopping criterion based on the discrepancy principle and allows updates of the active set by more than one index at a time

on a new class of t norms and t conorms on bounded lattices abstract the ordinal sum of triangular norms on unit interval has been used to construct other triangular norms but in general ordinal sum construction of triangular norms and triangular conorms may not work on an arbitrary bounded lattice in this study we focus on ordinal sums of triangular norms and triangular conorms on an arbitrary bounded lattice moreover we show a complete generalization of our ordinal sums of triangular norms and triangular conorms on an arbitrary bounded lattice and some illustrative examples are added for clarity

on ordinal sums of triangular norms on bounded lattices ordinal sums have been introduced in many different contexts e g for posets semigroups t norms copulas aggregation operators or quite recently for hoops in this contribution we focus on ordinal sums of t norms acting on some bounded lattice which is not necessarily a chain or an ordinal sum of posets necessary and sufficient conditions are provided for an ordinal sum operation yielding again a t norm on some bounded lattice whereas the operation is determined by an arbitrary selection of subintervals as carriers for arbitrary summand t norms by such also the structure of the underlying bounded lattice is investigated further it is shown that up to trivial cases there are no ordinal sum t norms on product lattices in general

characterizing when an ordinal sum of t norms is a t norm on bounded lattices one of the most important operators in soft computing are the triangular norms t norms as well as the combination among them the ordinal sum of triangular norms on 0 1 has been used to construct other triangular norms however on a bounded lattice an ordinal sum of t norms may not be a t norm several necessary and sufficient conditions are presented in this paper for ensuring whether an ordinal sum on a bounded lattice of arbitrary t norms is in fact a t norm moreover we show that a large set of ordinal sums verify these conditions hence they are very interesting in order to verify whether an ordinal sum on a bounded lattice is a t norm for a particular family of t norms

a characterization of the classes umin and umax of uninorms on a bounded lattice abstract as generalizations of the classes umin and umax of uninorms on the real unit interval we introduce the classes umin and umax of uninorms on a bounded lattice and lay bare the structure of their members it is shown that uninorms in umin resp umax are characterized by a triangular conorm resp triangular norm and a triangular subnorm resp triangular superconorm the characterization theorems unify all the existing construction methods for these two classes of uninorms known in the literature we also introduce four new related classes of uninorms on a bounded lattice and present dedicated construction methods using triangular subnorms and triangular superconorms finally connections among the introduced classes of uninorms are discussed

construction of nullnorms on bounded lattices and an equivalence relation on nullnorms abstract in this study we present two methods for the construction of nullnorms on bounded lattices based on the existence of t norms as well as t conorms on an arbitrary bounded lattice l we demonstrate that these methods differ from the existing approaches mainly because of their more generalized structures an equivalence relation is also defined based on a class of nullnorms and some properties of this relation are examined

uninorms on bounded lattices we study uninorms on bounded lattices we show the existence of uninorms with the neutral element which is different from the top element and the bottom element using the fact that the t norms and t conorms on arbitrary lattice l always exist as a by product we give a method of constructing uninorms using this method we obtain also the smallest uninorm and the greatest uninorm with a given neutral element e

new construction of t norms and t conorms on bounded lattices abstract this article studies the construction of ordinal sums of triangular norms t norms and triangular conorms t conorms on bounded lattices first we present a new class of t norms and t conorms on an arbitrary bounded lattice some examples are provided to illustrate that our new construction method is different from some existing methods for the construction of ordinal sums of t norms and t conorms on an arbitrary bounded lattice then we illustrate that our new construction method can be generalized by induction to a modified ordinal sum construction for t norms and t conorms on an arbitrary bounded lattice finally for any bounded sublattice s of a bounded lattice l we provide a sufficient condition that does not need s and l to have the same bottom and top elements such that an ordinal sum function is a t norm on l whereas the function is determined by an arbitrary selection of bounded sublattices as carriers for arbitrary summand t norms in particular we give a necessary and sufficient condition that needs s to have the same bottom element as l such that an ordinal sum function is a t norm on l

generalized ordinal sums of aggregation operators on bounded lattices abstract in this paper four kinds of generalized ordinal sums of aggregation operators on bounded lattices are provided and discussed firstly necessary and sufficient conditions for lower resp upper generalized ordinal sum of many summands to be an aggregation operator are provided in which case that the smallest resp greatest aggregation operator that coincides with each summand is given meanwhile the idempotent lower resp upper generalized ordinal sum of idempotent aggregation operators is also discussed then the relationships between these four kinds of generalized ordinal sums are given finally the lattice structures of some sets of special aggregation operators are investigated

an affine scaling interior point cbb method for box constrained optimization we develop an affine scaling algorithm for box constrained optimization which has the property that each iterate is a scaled cyclic barzilai borwein cbb gradient iterate that lies in the interior of the feasible set global convergence is established for a nonmonotone line search while there is local r linear convergence at a nondegenerate local minimizer where the second order sufficient optimality conditions are satisfied numerical experiments show that the convergence speed is insensitive to problem conditioning the algorithm is particularly well suited for image restoration problems which arise in positron emission tomography where the cost function can be infinite on the boundary of the feasible set

inverse scattering for the magnetic schrodinger operator abstract we show that fixed energy scattering measurements for the magnetic schrodinger operator uniquely determine the magnetic field and electric potential in dimensions n 3 the magnetic potential its first derivatives and the electric potential are assumed to be exponentially decaying this improves an earlier result of eskin and ralston 1995 5 which considered potentials with many derivatives the proof is close to arguments in inverse boundary problems and is based on constructing complex geometrical optics solutions to the schrodinger equation via a pseudodifferential conjugation argument

optical aharonov bohm effect an inverse hyperbolic problems approach we describe the general setting for the optical aharonov bohm effect based on the inverse problem of the identification of the coefficients of the governing hyperbolic equation by the boundary measurements we interpret the inverse problem result as a possibility in principle to detect the optical aharonov bohm effect by the boundary measurements

universal approximation theorem for uninorm based fuzzy systems modeling abstract most existing universal approximation results for fuzzy systems are based on the assumption that we use t norms and t conorms to represent and and or yager has proposed to use within the fuzzy systems modeling paradigm more general operations based on uninorms in this paper we show that the universal approximation property holds for an arbitrary choice of a uninorm

determining anisotropic real analytic conductivities by boundary measurements if an electrical potential is applied to the surface of a solid body the current flux across the surface depends on the conductivity in the interior of the body we want to consider the inverse problem of determining the conductivity by these boundary measurements

constructing uninorms via closure operators on a bounded lattice abstract in this paper via closure resp interior operators on a bounded lattice l we propose a rather effective method to construct uninorms on l with a given triangular norm t resp triangular conorm s on the subinterval 0 e resp e 1 of l our method encompasses as special cases the construction methods introduced by f karacal and r mesiar 2015 16 as well as by g d cayli et al 2016 5 we also exploit a pair of novel closure and interior operators on complete lattices and utilize this pair of operators to construct uninorms several interesting examples are included to illustrate our method

image regularization by nonnegatively constrained conjugate gradient abstract in the image reconstruction context the nonnegativity of the computed solution is often required conjugate gradient cg used as a reliable regularization tool may give solutions with negative entries particularly when large nearly zero plateaus are present the active constraints set detected by projection onto the nonnegative orthant turns out to be largely incomplete leading to poor effects on the accuracy of the reconstructed image in this paper an inner outer method based on cg is proposed to compute nonnegative reconstructed images with a strategy which enlarges subsequently the active constraints set this method appears to be especially suitable for the reconstruction of images having large nearly zero backgrounds the numerical experimentation validates the effectiveness of the proposed method when compared to other strategies for nonnegative reconstruction

modulus based iterative methods for constrained tikhonov regularization tikhonov regularization is one of the most popular methods for the solution of linear discrete ill posed problems in many applications the desired solution is known to lie in the nonnegative cone it is then natural to require that the approximate solution determined by tikhonov regularization also lies in this cone the present paper describes two iterative methods that employ modulus based iterative methods to compute approximate solutions in the nonnegative cone of large scale tikhonov regularization problems the first method considered consists of two steps first the given linear discrete ill posed problem is reduced to a small problem by a krylov subspace method and then the reduced tikhonov regularization problems so obtained is solved the second method described explores the structure of certain image restoration problems computed examples illustrate the performances of these methods

on the structure of uninorms on bounded lattices abstract uninorms are a generalization of triangular norms and triangular conorms with a neutral element in the interior of a bounded lattice in this study we present two methods to construct uninorms from a given triangular norm and triangular conorm on bounded lattices under some constraints as a by product of these methods we obtain new types of idempotent uninorms with a neutral element on bounded lattices in addition some illustrative examples for the constructions of uninorms on bounded lattices are provided

uninorms on bounded lattices constructed by t norms and t subconorms abstract the construction of uninorms on bounded lattices has been a attractive research area in this paper we introduce some new classes of uninorms on bounded lattices via t subnorms and t subconorms with a neutral element e under some constraints we also give some illustrative examples to help understand the structure of these new uninorms moreover we provide an answer to the open problem raised by cayli in 2019 finally the differences between our methods and existing approaches are assessed

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

van melle s combining function in mycin is a representable uninorm an alternative proof abstract recently tsadiras and margaritis have shown that the function implemented in the expert system mycin for combining certainty factors is a uninorm in this paper we present a compact alternative to the given direct and lengthy proof based on the construction of representable uninorms by means of an additive generator consequently we show that van melle s combining function is a representable uninorm in fact it is a rescaled version of the representable uninorm on the unit interval constructed from the algebraic product and the probabilistic sum

a new structure for uninorms on bounded lattices abstract this article investigates the construction of uninorms on bounded lattices first by using the fact that triangular norms t norms and triangular conorms t conorms on an arbitrary bounded lattice always exist we introduce a new construction of uninorms on arbitrary bounded lattices with the neutral element then we illustrate how our new construction method is different from some existing methods for the construction of uninorms on bounded lattices some illustrative examples for the construction of uninorms on bounded lattices are provided

quasi newton approach to nonnegative image restorations abstract image restoration or deblurring is the process of attempting to correct for degradation in a recorded image typically the blurring system is assumed to be linear and spatially invariant and fast fourier transform fft based schemes result in efficient computational image restoration methods however real images have properties that cannot always be handled by linear methods in particular an image consists of positive light intensities and thus a nonnegativity constraint should be enforced this constraint and other ways of incorporating a priori information have been suggested in various applications and can lead to substantial improvements in the reconstructions nevertheless such constraints are rarely implemented because they lead to nonlinear problems which require demanding computations we suggest efficient implementations for three nonnegatively constrained restorations schemes constrained least squares maximum likelihood and maximum entropy we show that with a certain parameterization and using a quasi newton scheme these methods are very similar in addition our formulation reveals a connection between our approach for maximum likelihood and the expectation maximization em method used extensively by astronomers numerical experiments illustrate that our approach is superior to em both in terms of accuracy and efficiency

a reduced newton method for constrained linear least squares problems we propose an iterative method that solves constrained linear least squares problems by formulating them as nonlinear systems of equations and applying the newton scheme the method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables hence the linear system can be solved more efficiently we prove that the method is locally quadratic convergent applications to image deblurring problems show that our method gives better restored images than those obtained by projecting or scaling the solution into the dynamic range

an interior point method for large constrained discrete ill posed problems ill posed problems are numerically underdetermined it is therefore often beneficial to impose known properties of the desired solution such as nonnegativity during the solution process this paper proposes the use of an interior point method in conjunction with truncated iteration for the solution of large scale linear discrete ill posed problems with box constraints an estimate of the error in the data is assumed to be available numerical examples demonstrate the competitiveness of this approach

alternating direction method with gaussian back substitution for separable convex programming we consider the linearly constrained separable convex minimization problem whose objective function is separable into m individual convex functions with nonoverlapping variables a douglas rachford alternating direction method of multipliers adm has been well studied in the literature for the special case of m 2 but the convergence of extending adm to the general case of m ge 3 is still open in this paper we show that the straightforward extension of adm is valid for the general case of m ge 3 if it is combined with a gaussian back substitution procedure the resulting adm with gaussian back substitution is a novel approach towards the extension of adm from m 2 to m ge 3 and its algorithmic framework is new in the literature for the adm with gaussian back substitution we prove its convergence via the analytic framework of contractive type methods and we show its numerical efficiency by some application problems

semi t operators on bounded lattices abstract we study semi t operators on bounded lattices and show the existence of semi t operators using the fact that there exist some pseudo t norms and pseudo t conorms on the arbitrary fixed bounded lattice l as a by product some constructive approaches to semi t operators are discussed using these approaches we obtain the least semi t operators and the greatest semi t operators on bounded lattices a partial order relation is also defined based on the semi t operator and some properties of this relation are examined

carleman estimate for the schrodinger equation and application to magnetic inverse problems abstract in this paper we prove lipschitz stable determination of the complex valued electric potential and the direction of the magnetic field appearing in the dynamic schrodinger equation with static coefficients by finitely many partial boundary measurements of the solution this is by means of the bukhgeim klibanov method based on an appropriate carleman estimate since the time symmetrization of the static magnetic schrodinger equation around t 0 is not possible we preliminarily establish a carleman inequality specifically designed for this problem

a customized douglas rachford splitting algorithm for separable convex minimization with linear constraints we consider applying the douglas rachford splitting method drsm to the convex minimization problem with linear constraints and a separable objective function the dual application of drsm has been well studied in the literature resulting in the well known alternating direction method of multipliers admm in this paper we show that the primal application of drsm in combination with an appropriate decomposition can yield an efficient structure exploiting algorithm for the model under consideration whose subproblems could be easier than those of admm both the exact and inexact versions of this customized drsm are studied and their numerical efficiency is demonstrated by some preliminary numerical results

convex hull of a fuzzy set and triangular norms abstract the t norm fuzzy sets is a class of fuzzy sets equipped with a pair of algebraic operation a notion of t convexity and a metric where all these notions are based on a strict triangular norm t in this paper we introduce in this class a notion of t convex hull of a fuzzy set we prove theorem that binds the t convex hull of an upper semicontinuous fuzzy set with the convex hull of a crisp set we further show two applications of this result first we prove that the operation of forming t convex hull behaves well with respect to algebraic operations second we show an analogue of shapley folkman theorem shapley folkman theorem is a well known result that provides an upper bound on the distance between minkowski sum of sets and the convex hull of this sum in this paper we show that the distance between the sum of upper semicontinuous fuzzy subsets of a finite dimensional euclidean space and the t convex hull of this sum has an upper bound as a consequence of this result we present an iterative procedure for forming t convex hull of an upper semicontinuous fuzzy set as an application of the results regarding t norm fuzzy sets we show an example from a game theoretic setting where t norm fuzzy sets were used to handle uncertainty in a repeated two player game

conditional gradient tikhonov method for a convex optimization problem in image restoration in this paper we consider the problem of image restoration with tikhonov regularization as a convex constrained minimization problem using a kronecker decomposition of the blurring matrix and the tikhonov regularization matrix we reduce the size of the image restoration problem therefore we apply the conditional gradient method combined with the tikhonov regularization technique and derive a new method we demonstrate the convergence of this method and perform some numerical examples to illustrate the effectiveness of the proposed method as compared to other existing methods

on the structure of spectra of periodic elliptic operators the paper discusses the problem of absolute continuity of spectra of periodic elliptic operators a new result on absolute continuity for a matrix operator of schrodinger type is obtained it is shown that all types of operators for which the absolute continuity has previously been established can be reduced to this one it is also discovered that some natural generalizations stumble upon an obstacle in the form of non triviality of a certain analytic bundle on the two dimensional torus

on the structure of semi t operators on bounded lattices abstract in this study we show some construction methods to obtain a semi t operator from a given pseudo t conorm and pseudo t norm on bounded lattices using these methods we prove that the known methods of constructing semi t operators on bounded lattices proposed by fang and hu are incorrect and present the correct forms at the same time furthermore some other construction methods for semi t operators on bounded lattices are also added

a multiplicative iterative algorithm for box constrained penalized likelihood image restoration image restoration is a computationally intensive problem as a large number of pixel values have to be determined since the pixel values of digital images can attain only a finite number of values e g 8 bit images can have only 256 gray levels one would like to recover an image within some dynamic range this leads to the imposition of box constraints on the pixel values the traditional gradient projection methods for constrained optimization can be used to impose box constraints but they may suffer from either slow convergence or repeated searching for active sets in each iteration in this paper we develop a new box constrained multiplicative iterative bcmi algorithm for box constrained image restoration the bcmi algorithm just requires pixelwise updates in each iteration and there is no need to invert any matrices we give the convergence proof of this algorithm and apply it to total variation image restoration problems where the observed blurry images contain poisson gaussian or salt and pepper noises

limiting carleman weights and anisotropic inverse problems in this article we consider the anisotropic calderon problem and related inverse problems the approach is based on limiting carleman weights introduced in kenig et al ann math 165 567 591 2007 in the euclidean case we characterize those riemannian manifolds which admit limiting carleman weights and give a complex geometrical optics construction for a class of such manifolds this is used to prove uniqueness results for anisotropic inverse problems via the attenuated geodesic ray transform earlier results in dimension n 3 were restricted to real analytic metrics

inverse problems for the schrodinger equations with time dependent electromagnetic potentials and the aharonov bohm effect we consider the inverse boundary value problem for the schrodinger operator with time dependent electromagnetic potentials in domains with obstacles we extend the resuls of the author s works inverse probl 19 49 2003 19 985 2003 20 1497 2004 to the case of time dependent potentials we relate our results to the aharonov bohm effect caused by magnetic and electric fluxes

global uniqueness for an inverse boundary value problem arising in elasticity we prove that we can determine the lame parameters of an elastic isotropic inhomogeneous medium in dimensionsn 3 by making measurements of the displacements and corresponding stresses at the boundary of the medium

lattice based sum of t norms on bounded lattices abstract the concept of ordinal sums in the sense of clifford have long been blamed for their limitations in constructing new t norms including inability to cope with general bounded lattices motivated by this observation and based on the lattice based sum of lattices that has been recently introduced by el zekey et al we propose a new sum type construction of t norms called a lattice based sum of t norms for building new t norms on bounded lattices from given ones the proposed sum is generalizing the well known ordinal and horizontal sum constructions of t norms by allowing for lattice ordered index sets we demonstrate that like the ordinal sum of t norms the lattice based sum of t norms can be generalized using as summands so called t subnorms still leading to a t norm subsequently we apply the results for constructing several new families of t norms and t subnorms on bounded lattices in the same spirit by the duality we will also introduce lattice based sums of t conorms and t subconorms

on the convergence of nonconvex minimization methods for image recovery nonconvex nonsmooth regularization method has been shown to be effective for restoring images with neat edges fast alternating minimization schemes have also been proposed and developed to solve the nonconvex nonsmooth minimization problem the main contribution of this paper is to show the convergence of these alternating minimization schemes based on the kurdyka ojasiewicz property in particular we show that the iterates generated by the alternating minimization scheme converges to a critical point of this nonconvex nonsmooth objective function we also extend the analysis to nonconvex nonsmooth regularization model with box constraints and obtain similar convergence results of the related minimization algorithm numerical examples are given to illustrate our convergence analysis

inverse boundary value problems for the perturbed polyharmonic operator author s krupchyk k lassas m uhlmann g abstract we show that a first order perturbation a x d q x of the polyharmonic operator m m 2 can be determined uniquely from the set of the cauchy data for the perturbed polyharmonic operator on a bounded domain in n n 3 notice that the corresponding result does not hold in general when m 1 2013 american mathematical society

on the direct decomposability of strong negations and s implication operators on product lattices in this paper we discuss the direct product of strong negations we characterize strong negations on product lattices that are direct products of strong negations furthermore we present a method for constructing t norms on product lattices which are not direct products this method is quite general and useful to generate a wide class of such t norms and solves an open problem posed in 2003 by jenei and de baets finally we study direct decompositions of s implication operators on product lattices

uniqueness in an inverse boundary problem for a magnetic schrodinger operator with a bounded magnetic potential we show that the knowledge of the set of the cauchy data on the boundary of a bounded open set in mathbb r n n geq 3 for the magnetic schrodinger operator with l magnetic and electric potentials determines the magnetic field and electric potential inside the set uniquely the proof is based on a carleman estimate for the magnetic schrodinger operator with a gain of two derivatives

determining a first order perturbation of the biharmonic operator by partial boundary measurements abstract we consider an operator 2 a x d q x with the navier boundary conditions on a bounded domain in r n n 3 we show that a first order perturbation a x d q can be determined uniquely by measuring the dirichlet to neumann map on possibly very small subsets of the boundary of the domain notice that the corresponding result does not hold in general for a first order perturbation of the laplacian

defending against strategic manipulation in uninorm based multi agent decision making abstract we consider the problem of multi agent group decision making we describe the possible use of the uninorm aggregation operator as a way of combining individual agents preference functions to obtain a group preference function we then discuss the possibility of an agent using a type of strategic manipulation of the preference information it provides in order to get the group to select its most preferred alternative a mechanism is then suggested for modifying the construction of the group decision function to defend against this type of strategic manipulation in addition to considering the case where the preference information is provided numerically we consider the case of ordinal preference information

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

triangular norm based iterative compensatory operators abstract aggregation operators based on a fixed t norm and on suitable transformations of processed data are introduced a special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic geometric and harmonic means several properties of introduced operators are studied e g the symmetry the associativity the idempotency the anihilation etc several examples are given including continuous idempotent bisymmetric iterative compensatory operators with zero anihilator

the reflection principle and calderon problems with partial data we propose a geometric approach towards for solving the partial data calderon problem for the magnetic schrodinger operator in dimension two this allowed us to clarify some of the ideas in the previous works while simultaneously consider the problem on general riemann surfaces with boundary

uni nullnorms on bounded lattices abstract in this paper we study uni nullnorms with both neutral elements and zero elements on bounded lattices in order to illustrate the existence of uni nullnorms on bounded lattices we present two construction methods for obtaining such a uni nullnorm also we show two additional methods for the construction of idempotent nullnorms on bounded lattices which are generalizations of the one proposed by cayli and karacal furthermore we discuss the presence of idempotent uni nullnorms on bounded lattices and propose two construction methods to obtain an idempotent uni nullnorm on any bounded lattice

a predictor corrector iterated tikhonov regularization for linear ill posed inverse problems many questions in science and engineering often give rise to linear ill posed inverse problems to enable meaningful approximate solutions of the inverse problems various regularization methods have subsequently been proposed to make these problems less sensitive to perturbations one of the most popular regularization techniques is iterated tikhonov regularization which has attracted considerable attention due to its interesting applications in practical however this regularization often suffers from inaccurate results and low computational efficiency in some situations in this paper we proposed an accelerated predictor corrector iterated tikhonov regularization this method combined the classical iterated tikhonov regularization with modified euler method which could improve computational efficiency without sacrificing numerical accuracy the convergence rate of the accelerated regularization was investigated theoretically when the right hand side was corrupted by noise in particular we derived an error estimate of optimal order for the convergence of the accelerated regularization both one and two dimensional numerical experiments were implemented to illustrate the accuracy and efficiency of the accelerated version of iterated tikhonov regularization

determining a magnetic schrodinger operator from partial cauchy data in this paper we show in dimension n 3 that knowledge of the cauchy data for the schrodinger equation in the presence of a magnetic potential measured on possibly very small subsets of the boundary determines uniquely the magnetic field and the electric potential we follow the general strategy of 7 using a richer set of solutions to the dirichlet problem that has been used in previous works on this problem

characterization of uninorms on bounded lattices in this paper we propose a characterization of uninorms on a general bounded lattice l by means of a sextuple of a triangular norm a triangular conorm and four aggregation functions on l observe that in the case when l is a chain it is enough to consider a triple consisting of a t norm a t conorm and an averaging aggregation function an example of a proper uninorm which has an absorbing element differing from both 0 and 1 is also shown note that this cannot happen if we consider uninorms acting on a chain two general constructions of uninorms on l are added letting a t norm a t conorm linked to a fixed neutral element e of the constructed uninorm to be free and fixing the remaining functions

on preconditioned and relaxed avmm methods for quadratic programming problems with equality constraints abstract to iteratively compute a solution of the equality constraint quadratic programming problem by successively introducing relaxation parameters and skillfully adopting a preconditioning matrix we establish a preconditioned and relaxed alternating variable minimization with multiplier pravmm method which is a further generalization of the preconditioned alternating variable minimization with multiplier pavmm method proposed by bai and tao 2016 bit numer math 56 2016 399 422 based on rigorous matrix analysis we demonstrate the asymptotic convergence property of the pravmm method numerical results show that the pravmm method is feasible and effective for solving the equality constraint quadratic programming problems

distributive and infinitely distributive t norms on complete lattices abstract a relation between the direct decomposability of an infinitely distributive t norm on a complete lattice l and direct decompositions of the neutral element 1 of l is obtained some useful applications of this relation are given in particularly the description of all t 1 lattices without infinitely distributive t norms on complete lattices and the description of all distributive t norms on lattices of length 2 are given the paper also contains the solutions of two open problems

some properties of idempotent uninorms on a special class of bounded lattices abstract binary operations have many applications in fuzzy set theory one of them is uninorms in this paper we study some properties of idempotent uninorms on bounded lattices it is shown that idempotent uninorms on an arbitrary bounded lattice need not always be internal with the extended definition of the term internal we give a sufficient condition for the bounded lattice to any idempotent uninorm be internal in addition that it is given many properties of idempotent uninorms in this case

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

least squares problems with inequality constraints as quadratic constraints abstract linear least squares problems with box constraints are commonly solved to find model parameters within bounds based on physical considerations common algorithms include bounded variable least squares bvls and the matlab function lsqlin here the goal is to find solutions to ill posed inverse problems that lie within box constraints to do this we formulate the box constraints as quadratic constraints and solve the corresponding unconstrained regularized least squares problem using box constraints as quadratic constraints is an efficient approach because the optimization problem has a closed form solution the effectiveness of the proposed algorithm is investigated through solving three benchmark problems and one from a hydrological application results are compared with solutions found by lsqlin and the quadratically constrained formulation is solved using the l curve maximum a posteriori estimation map and the 2 regularization method the 2 regularization method with quadratic constraints is the most effective method for solving least squares problems with box constraints

superlinear and quadratic convergence of affine scaling interior point newton methods for problems with simple bounds without strict complementarity assumption a class of affine scaling interior point methods for bound constrained optimization problems is introduced which are locally q superlinear or q quadratic convergent it is assumed that the strong second order sufficient optimality conditions at the solution are satisfied but strict complementarity is not required the methods are modifications of the affine scaling interior point newton methods introduced by t f coleman and y li math programming 67 189 224 1994 there are two modifications one is a modification of the scaling matrix the other one is the use of a projection of the step to maintain strict feasibility rather than a simple scaling of the step a comprehensive local convergence analysis is given a simple example is presented to illustrate the pitfalls of the original approach by coleman and li in the degenerate case and to demonstrate the performance of the fast converging modifications developed in this paper