on probability possibility transformations abstract a probability possibility transformation is a purely mechanical transformation of probabilistic support to possibilistic support and vice versa that is a conversion of the measure of support of one theory into that of the other that is independent of the problem domain in this paper it is shown that any bijective mapping between probability distributions and normalized possibility distributions that is symmetric and expansible cannot preserve the properties of projection noninteraction or conditionalization

existence and uniqueness of weak solutions for a non uniformly parabolic equation in this paper we develop a unifying method to prove the existence and uniqueness of weak solutions for the initial boundary value problem of a non uniformly parabolic equation some well known parabolic equations are the special cases of this equation

diverse confidence levels in a probabilistic semantics for conditional logics abstract it has long been known that several popular default and conditional logics exactly describe infinitesimal probability constructs which betoken virtual certainty regarding the truth of one sentence if some other sentence is true that the rules for default inference also describe a scheme of approximate inference for all positive valued conditional probabilities has also long been known more recently a class of standard probability measures has been found whose expression of more likely than not is exactly described by default rules this class can be extended by straightforward algebra so that the range of confidence levels expressed by standard probability distributions which are exactly described by the rules is as complete as for the approximate methods

nonlinear elliptic systems with general growth we prove local lipschitz continuity and as a consequence c k and c regularity of weak solutions u for a class of nonlinear elliptic differential systems of the formn 1 xi a i du 0 1 2 m the growth conditions on the dependence of functions a i on the gradient du are so mild to allow us to embrace growths between the linear and the exponential cases and they are more general than those known in the literature

an existence result for dissipative nonhomogeneous hyperbolic equations via a minimization approach abstract we discuss a purely variational approach to the study of a wide class of second order nonhomogeneous dissipative hyperbolic pdes precisely we focus on the wave like equations that present also a nonzero source term and a first order in time linear term the paper carries on the research program initiated in 14 and developed in 15 21 on the de giorgi approach to hyperbolic equations

nonlinear wave equations as limits of convex minimization problems proof of a conjecture by de giorgi we prove a conjecture by de giorgi which states that global weak solutions of nonlinear wave equations such as w jwj p 2 w 0 can be obtained as limits of functions that minimize suitable functionals of the calculus of variations these functionals which are integrals in space time of a convex lagrangian contain an exponential weight with a parameter and the initial data of the wave equation serve as boundary conditions as tends to zero the minimizers v converge up to subsequences to a solution of the nonlinear wave equation there is no restriction on the nonlinearity exponent and the method is easily extended to more general equations

on the specificity of a possibility distribution abstract the specificity of a possibility distribution measures the degree to which the distribution allows one and only one element as its manifestation as such it is a measure of amount of uncertainty or information we investigate a number of issues related to specificity measures we discuss the connection between the specificity of a possibility distribution and the entropy of a probability distribution we describe unifying view for constructing specificity measures we look at the relationship of the specificity of a distribution and its negation we consider the case where the base set is continuous

existence of parabolic minimizers on metric measure spaces abstract the objects of our studies are vector valued parabolic minimizers u associated to a convex caratheodory integrand f obeying a p growth assumption from below and a certain monotonicity condition in the gradient variable here the functions being considered are defined on a metric measure space x d for such parabolic minimizers that coincide with a time independent cauchy dirichlet datum u 0 on the parabolic boundary of a space time cylinder 0 t with an open subset x and t 0 we prove existence in the parabolic newtonian space l p 0 t n 1 p r n in this paper we generalize results from bogelein et al 2014 2015 to the metric setting and argue completely on a variational level

numerical multipole analysis of ultrawideband antennas a recently introduced systematic approach to efficiently obtain the time domain electromagnetic field of an arbitrary antenna radiating into the free space is applied to numerically analyze the frequency domain features of an ultrawideband antenna in a first stage the finite difference time domain method is employed to obtain the time domain spherical multipole amplitudes for the antenna which is driven by a wide band signal this time domain representation is valid in the far field only but a single numerically performed fourier transform leads to the frequency domain spherical multipole amplitudes valid for the entire spectrum of the input impulse and at any point outside a minimum sphere containing all radiating elements the approach is applied to an antipodal vivaldi antenna to obtain three dimensional radiation patterns which are compared to experimental results as well as to the outcomes of other numerical schemes moreover a total scattering error is defined and numerically evaluated to estimate the overall accuracy of the proposed method

existence of evolutionary variational solutions via the calculus of variations abstract in this paper we introduce a purely variational approach to time dependent problems yielding the existence of global parabolic minimizers that is 0 t u t f x d u d x d t 0 t f x d u d d x d t whenever t 0 and c 0 0 t r n for the integrand f r n n 0 we merely assume convexity with respect to the gradient variable and coercivity these evolutionary variational solutions are obtained as limits of maps depending on space and time minimizing certain convex variational functionals in the simplest situation with some growth conditions on f the method provides the existence of global weak solutions to cauchy dirichlet problems of parabolic systems of the type t u div d f x d u 0 in 0

a new approach to specificity in possibility theory decision making point of view abstract the paper investigates the problem of defining a specificity relation in pyt ev possibility theory that branch of possibility theory developed by prof yu p pyt ev in the late 1990s defines possibility as a monotone measure which numerical values except 0 and 1 are meaningless the following information and its consequent implications are meaningful a 0 a is impossible or a b a is more possible than b or a b a and b are equally possible all results obtained with pyt ev possibility theory are invariant to any strictly increasing lower semi continuous transformation of all possibility values with the fixed points 0 and 1 this fact allows anyone to assign numerical values to possibilities using an individual subjective scale of possibility values unlike zadeh possibility theory based on fuzzy sets where specificity of possibility distributions is evaluated by means of fuzzy set inclusion and distribution 1 is more specific than 2 iff 1 2 pointwise in pyt ev possibility theory such an approach can not be applied if numerical values of 1 and 2 are assigned through different subjective scales a thesis we put forward in this paper states that the specificity relation definition has to be consistent with the possibilistic decision making approaches the following is intended to be true the more specific an underlying possibility and a corresponding possibility distribution are the narrower more specific a set of the optimal decisions is a decision is optimal if it minimizes the possibility of error a specificity relation satisfying such a requirement is defined and studied

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

finite dimensional attractors for the quasi linear strongly damped wave equation abstract we present a new method of investigating the so called quasi linear strongly damped wave equations t 2 u t x u x u f u x x u g in bounded 3d domains this method allows us to establish the existence and uniqueness of energy solutions in the case where the growth exponent of the non linearity is less than 6 and f may have arbitrary polynomial growth rate moreover the existence of a finite dimensional global and exponential attractors for the solution semigroup associated with that equation and their additional regularity are also established in a particular case 0 which corresponds to the so called semi linear strongly damped wave equation our result allows to remove the long standing growth restriction f u c 1 u 5

local holder continuity of weak solutions to a diffusive shallow medium equation abstract we show the local holder continuity of bounded weak solutions to a doubly nonlinear parabolic equation used in models for diffusion of shallow media

a variational approach to parabolic equations under general and p q growth conditions abstract we consider variational solutions to the cauchy dirichlet problem t u div d f x u d u d u f x u d u in t u u 0 on par t where the function f f x u f r n r n r n n 0 is convex with respect to u and coercive in r n n but it not necessarily satisfies a growth condition from above a motivation to consider a class of such energy functions f can be also easily found in the stationary case where a large literature in the calculus of variations is devoted to the minimization of p q growth problems 45 and to double phase problems 23 24 4 5 6 in the parabolic context the notion of variational solution see the references from 8 to 15 is compatible with the lack of the same polynomial growth from below and from above

weighted energy dissipation functionals for doubly nonlinear evolution abstract this paper is concerned with the weighted energy dissipation wed functional approach to doubly nonlinear evolutionary problems this approach consists in minimizing wed functionals defined over entire trajectories we present the features of the wed variational formalism and analyze the related euler lagrange problems moreover we check that minimizers of the wed functionals converge to the corresponding limiting doubly nonlinear evolution finally we present a discussion on the functional convergence of sequences of wed functionals and present some application of the abstract theory to nonlinear pdes

synthesis of wire antennas using the multipole expansion method a rigorous mathematical solution to the problem of synthesizing wire antennas using the multipole expansion method mem is presented the input current and required size of the antenna are estimated using the knowledge of the required field pattern this solution is based on three steps first obtaining the expansion s weighting coefficients that carry both the signature of the current and size of the antenna in essence the analysis of the direct modeling needs to be addressed first in order to define these coefficients second extracting the coefficients from the required field pattern using the natural orthogonality property of the spherical harmonic functions finally performing a numerical search for the argument of the spherical bessel functions to satisfy the ratio between two successive moments once the size of the antenna is found a recursive expression is used to obtain the input current for the current distributions assumed herein the odd order coefficients of the mem are shown to be the only necessary coefficients to construct the radiation far field also it is found that the estimated model parameters are in excellent agreement with the analytical ones

the obstacle problem for a fourth order semilinear parabolic equation abstract this paper is concerned with the obstacle problem for the l 2 gradient flow for a functional which is higher order non convex and unbounded from below we prove i the existence and uniqueness of local in time solutions to the obstacle problem and ii a gradient structure of the functional of the solutions via minimizing movements moreover we show the existence of solutions which blow up in a finite time

local calderon zygmund estimates for parabolic minimizers abstract we establish local calderon zygmund estimates for parabolic minimizers u to certain variational inequalities the formal corresponding parabolic partial differential equation would be t u div f z u d u u f z u d u div f p 2 f h with p 2 n n 2 however since we do not impose any condition on the existence of the derivative u f the pde above may not have any meaning at all for proving the calderon zygmund estimates we thus remain solely on the level of parabolic minimizers precisely for q p we prove that d u l loc q if u is locally holder continuous and f l loc q and h l loc q for a q depending on q

a variational principle for nonpotential perturbations of gradient flows of nonconvex energies abstract we investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in hilbert spaces we prove existence of solutions to elliptic in time regularizations of gradient flows by combining the minimization of a parameter dependent functional over entire trajectories and a fixed point argument these regularized solutions converge up to subsequences to solutions of the gradient flow as the regularization parameter goes to zero applications of the abstract theory to nonlinear reaction diffusion systems are presented

nonlocal diffusion equations abstract in this paper we present a variational approach to establish the existence and uniqueness of variational solutions to nonlocal evolutionary problems the model we have in mind is the following nonlocal version of the parabolic p laplacian u t div a d u t l p p d u p 2 d u h which has recently attracted many authors we emphasize that our approach also applies in situations where the considered functionals do not allow the derivation of the associated euler lagrange equation

parabolic systems with p q growth a variational approach we consider the evolution problem associated with a convex integrand f mathbb r nn to 0 infty satisfying a non standard p q growth assumption to establish the existence of solutions we introduce the concept of variational solutions in contrast to weak solutions that is mappings u colon omega t to mathbb r n which solve partial tu rm div df du 0 weakly in omega t variational solutions exist under a much weaker assumption on the gap q p here we prove the existence of variational solutions provided the integrand f is strictly convex and frac 2n n 2 p le q p 1 these variational solutions turn out to be unique under certain mild additional assumptions on the data moreover if the gap satisfies the natural stronger assumption 2 le p le q p rm min big 1 frac 4 n big we show that variational solutions are actually weak solutions this means that solutions u admit the necessary higher integrability of the spatial derivative du to satisfy the parabolic system in the weak sense that is we prove that u in l q rm loc big 0 t w 1 q rm loc omega mathbb r n big

near to far field transformation by a time domain spherical multipole analysis the contribution deals with a new time domain near to far field nff transformation which is particularly suited for the finite difference time domain fdtd method the far field is derived from the tangential field components on a surface enclosing the scatterer by employing a time domain spherical multipole representation the necessary time domain convolution is performed as on the fly in parallel with the fdtd time stepping algorithm the efficiency of the method is improved by incorporating a temporal linear interpolation of the near field data with the once obtained multipole amplitudes an analytic series representation of the time domain far field is achieved which allows a physical interpretability of the result moreover this expansion serves as an ideal basis for a systematic and efficient post processing the proposed technique may also be useful for other numerical and for asymptotic methods

global gradient estimates for non quadratic vector valued parabolic quasi minimizers abstract we establish local and global higher integrability estimates for the gradient of vector valued parabolic quasi minimizers of integral functionals with polynomial p growth p 2 n n 2 on a parabolic domain t in r n 1 n 2 and under a weak regularity assumption on the parabolic boundary of t