triangular norms position paper ii general constructions and parameterized families this second part out of three of a series of position papers on triangular norms for part i see triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press deals with general construction methods based on additive and multiplicative generators and on ordinal sums also included are some constructions leading to non continuous t norms and a presentation of some distinguished families of t norms

multiplicity results for some nonlinear schrodinger equations with potentials multiple semiclassical standing waves for a class of nonlinear schrodinger equations with potentials are found by means of a perturbative variational method

symmetry of positive solutions for choquard equations with fractional p laplacian abstract this paper deals with the following choquard equations with fractional p laplacian p s u c n t x 2 t n u q u q 1 in r n u 0 on r n where 0 s t 1 2 p p 1 q and n 2 by constructing a decay at infinity theorem and a narrow region principle we establish the radial symmetry of positive solutions based on the generalized direct method of moving planes

singularly perturbed critical choquard equations abstract in this paper we study the semiclassical limit for the singularly perturbed choquard equation e 2 u v x u e 3 r 3 q y g u y x y d y q x g u in r 3 where 0 3 e is a positive parameter v q are two continuous real function on r 3 and g is the primitive of g which is of critical growth due to the hardy littlewood sobolev inequality under suitable assumptions on g we first establish the existence of ground states for the critical choquard equation with constant coefficients next we establish existence and multiplicity of semi classical solutions and characterize the concentration behavior by variational methods

toward a general theory of information aggregation abstract information aggregation is a pervasive issue in the field of decision making in this paper we begin an attempt to develop a comprehensive theory of this process we investigate the use of a penalty function to help guide in the aggregation process it is suggested that an aggregated value which violates a given piece of data is charged a penalty the problem of aggregation can be seen as finding the aggregated value with the least penalty we show that logical inference systems are characterized by infinite penalty functions this implies that deviation from the data are not easily accepted probability theory is characterized by equal finite penalty costs nonmonotonic logics appear to be characterized by a case in which we have at least two different levels of penalties of differing magnitudes we discuss the relationship between the relevance or bearing a piece of data has on the problem and the penalty cost associated with it we see the central role of the intersection operation

strongly interacting bumps for the schrodinger newton equations we study concentrated bound states of the schrodinger newton equations h2 e x u 0 0 x r3 u 12 2 0 x r3 x 0 u x 0 as x moroz et al an analytical approach to the schrodinger newton equations nonlinearity 12 201 1999 proved the existence and uniqueness of ground states of u 0 0 x r3 u 12 2 0 x r3 x 0 u x 0 as x we first prove that the linearized operator around the unique ground state radial solution 0 u0 with 0 r ae r r 1 o 1 as r x u0 r b r 1 o 1 as r x for some a b 0 has a kernel whose dimension is exactly 3 corresponding to the translational modes using this result we further show that if for some positive integer k the points pi r3 i 1 2 k with pi pj for i j are all local minimum or local maximum or nondegenerate critical points of e p then for h small enough there exist solutions of the schrodinger newton equations with k bumps which concentrate at pi we also prove that given a local maximum point p0 of e p the

aggregation functions based on penalties this article studies a large class of averaging aggregation functions based on minimizing a distance from the vector of inputs or equivalently minimizing a penalty imposed for deviations of individual inputs from the aggregated value we provide a systematization of various types of penalty based aggregation functions and show how many special cases arise as the result we show how new aggregation functions can be constructed either analytically or numerically and provide many examples we establish connection with the maximum likelihood principle and present tools for averaging experimental noisy data with distinct noise distributions

semiclassical states for nonlinear schrodinger equations with sign changing potentials we establish the existence and multiplicity of semiclassical bound states of the following nonlinear schrodinger equation e2 u v x u g x u for x rn u x 0as x where v changes sign and g is superlinear with critical or supercritical growth as u

on critical point theory for indefinite functionals in the presence of symmetries we consider functionals which are not bounded from above or from below even modulo compact perturbations and which exhibit certain symmetries with respect to the action of a compact lie group we develop a method which permits us to prove the existence of multiple critical points for such functionals the proofs are carried out directly in an infinite dimensional hilbert space and they are based on minimax arguments the applications given here are to hamiltonian systems of ordinary differential equations where the existence of multiple time periodic solutions is established for several classes of hamiltonians symmetry properties of these hamiltonians such as time translation invariancy or evenness are exploited introduction many variational problems which arise from physics or mathematical physics are indefinite in the sense that the functionals involved are not bounded from below or from above however some of these functionals defined in an appropriate function space are semidefinite in the sense that they are bounded from below or from above if perturbed with a weakly continuous functional this paper deals with functionals which are not semidefinite usually problems involving indefinite functionals are more difficult to handle and only very recently a method has been developed which permits us to treat such problems directly in an infinite dimensional function space 7 in 7 some theorems have been proved which establish the existence of at least one nontrivial critical point for such functionals in many physical situations there are problems which have symmetries with respect to the action of some lie group in this case we expect the existence of many critical points this has been established for semidefinite functionals cf e g 8 and 3 for even functionals 9 for a zp action with p prime numbers 15 16 10 and 6 for an s action in this paper we develop a method which allows us to estimate the number of critical points of indefinite functionals in the presence of symmetries more precisely received by the editors july 16 1980 and in revised form june 26 1981 1980 mathematics subject classification primary 58e05 70h05 secondary 34c25

enhancing multiclass classification in farc hd fuzzy classifier on the synergy between n dimensional overlap functions and decomposition strategies there are many real world classification problems involving multiple classes e g in bioinformatics computer vision or medicine these problems are generally more difficult than their binary counterparts in this scenario decomposition strategies usually improve the performance of classifiers hence in this paper we aim to improve the behavior of fuzzy association rule based classification model for high dimensional problems farc hd fuzzy classifier in multiclass classification problems using decomposition strategies and more specifically one versus one ovo and one versus all ova strategies however when these strategies are applied on farc hd a problem emerges due to the low confidence values provided by the fuzzy reasoning method this undesirable condition comes from the application of the product t norm when computing the matching and association degrees obtaining low values which are also dependent on the number of antecedents of the fuzzy rules as a result robust aggregation strategies in ovo such as the weighted voting obtain poor results with this fuzzy classifier in order to solve these problems we propose to adapt the inference system of farc hd replacing the product t norm with overlap functions to do so we define n dimensional overlap functions the usage of these new functions allows one to obtain more adequate outputs from the base classifiers for the subsequent aggregation in ovo and ova schemes furthermore we propose a new aggregation strategy for ovo to deal with the problem of the weighted voting derived from the inappropriate confidences provided by farc hd for this aggregation method the quality of our new approach is analyzed using 20 datasets and the conclusions are supported by a proper statistical analysis in order to check the usefulness of our proposal we carry out a comparison against some of the state of the art fuzzy classifiers experimental results show the competitiveness of our method

classification of positive solitary solutions of the nonlinear choquard equation in this paper we settle the longstanding open problem concerning the classification of all positive solutions to the nonlinear stationary choquard equation delta u u 2u left frac 1 x u 2 right 0 quad u in h 1 mathbb r 3 which can be considered as a certain approximation of the hartree fock theory for a one component plasma as explained in lieb and lieb simon s papers starting from 1970s we first prove that all the positive solutions of this equation must be radially symmetric and monotone decreasing about some fixed point interestingly to use the new method of moving planes introduced by chen li ou we deduce the problem into an elliptic system as a key step we transform this differential system into a system of integral equations with the help of riesz and bessel potentials and then use the method of a moving plane in an integral form next using radial symmetry we deduce the uniqueness result from lieb s work our argument can be adapted well to study the radial symmetry of positive solutions of the equation in the generalized form u k 1 f left u k 2 u right

existence and concentration of ground state solutions for a critical nonlocal schrodinger equation in r2 we study the following singularly perturbed nonlocal schrodinger equation e2 u v x u e 2 1 x f u f u inr2 where v x is a continuous real function on r2 f s is the primitive of f s 0 2 and e is a positive parameter assuming that the nonlinearity f s has critical exponential growth in the sense of trudinger moser we establish the existence and concentration of solutions by variational methods

a note on schrodinger newton systems with decaying electric potential abstract we prove the existence of solutions for the singularly perturbed schrodinger newton system 2 v x u 0 2 u 4 2 0 in r 3 with an electric potential v that decays polynomially fast at infinity the solution concentrates as 0 around structurally stable critical points of the electric potential as a particular case isolated strict extrema of v are allowed

shift invariant binary aggregation operators when applying an information fusion method usually the output results are required to be a scalar value in multiple situations the application of the fusion method to input values shifted by a constant should result in an output that is shifted likewise in this paper we present a study of the shift invariance property of aggregation operators the relationship between shift invariant binary aggregation operators and 1 lipschitz aggregation operators is shown and a full description of shift invariant aggregation operators is given

on the definition of penalty functions in data aggregation abstract in this paper we point out several problems in the different definitions and related results of penalty functions found in the literature then we propose a new standard definition of penalty functions that overcomes such problems some results related to averaging aggregation functions in terms of penalty functions are presented as the characterization of averaging aggregation functions based on penalty functions some examples are shown as the penalty functions based on spread measures which happen to be continuous we also discuss the definition of quasi penalty functions in order to deal with non monotonic or weakly directionally monotonic averaging functions

standing waves with a critical frequency for nonlinear choquard equations abstract we study the nonlocal choquard equation e 2 u e v u e i u e p u e p 2 u e in r n where n 1 i is the riesz potential of order 0 n and e 0 is a parameter when the nonnegative potential v c r n achieves 0 with a homogeneous behavior or on the closure of an open set but remains bounded away from 0 at infinity we show the existence of groundstate solutions for small e 0 and exhibit the concentration behavior as e 0

groundstates of nonlinear choquard equations existence qualitative properties and decay asymptotics we consider a semilinear elliptic problem delta u u i alpha ast abs u p abs u p 2 u quad text in r n where i alpha is a riesz potential and p 1 this family of equations includes the choquard or nonlinear schr odinger newton equation for an optimal range of parameters we prove the existence of a positive groundstate solution of the equation we also establish regularity and positivity of the groundstates and prove that all positive groundstates are radially symmetric and monotone decaying about some point finally we derive the decay asymptotics at infinity of the groundstates

on a periodic schrodinger equation with nonlocal superlinear part we consider the choquard pekar equation open image in new window and focus on the case of periodic potential v for a large class of even functions w we show existence and multiplicity of solutions essentially the conditions are that 0 is not in the spectrum of the linear part v and that w does not change sign our results carry over to more general nonlinear terms in arbitrary space dimension n 2

existence of semiclassical ground state solutions for a generalized choquard equation abstract in this paper we study a generalized quasilinear choquard equation e p p u v x u p 2 u e n r n q y f u y x y q x f u in r n where p is the p laplacian operator 1 p n v and q are two continuous real functions on r n 0 n f s is the primate function of f s and e is a positive parameter under suitable assumptions on p and f we establish a new concentration behavior of solutions for the quasilinear choquard equation by variational methods the results are also new for the semilinear case p 2

existence of groundstates for a class of nonlinear choquard equations we prove the existence of a nontrivial solution h n to the nonlinear choquard equation i in n where i is a riesz potential under almost necessary conditions on the nonlinearity in the spirit of berestycki and lions this solution is a groundstate if moreover is even and monotone on 0 then is of constant sign and radially symmetric

algebraic riccati equation arising in boundary control problems an algebraic riccati equation is studied with application to the optimal control of deterministic and stochastic parabolic systems with boundary control the control function can act on the boundary through dirichlet or neumann conditions

existence of multiple semiclassical solutions for a critical choquard equation with indefinite potential abstract we study the existence and multiplicity of semiclassical states for the choquard equation with critical growth e 2 u v x u r n g y u y x y d y g x u in r n where n 3 0 min 4 n v x is sign changing and g is the primitive of g which is of critical growth due to the well known hardy littlewood sobolev inequality under suitable assumptions on v and g we prove the existence and multiplicity of semiclassical states by critical point theory