benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

on uniform exponential growth for linear groups let be a finitely generated group given a finite set of generators s of the word length ls for an element is defined to be the smallest positive integer for which there exist s1 sn s s 1 such that s1 sn for each n n denote by bs n the set of elements in whose word length with respect to s is at most n it follows from the subadditive property of ls that limn bs n 1 n exists which we denote by s a finitely generated group is said to be of exponential growth if s 1 of polynomial growth if for some c 0 and d n bs n c n d for all n 1 and of intermediate growth otherwise for some finite generating set s of observe that the growth type of does not depend on the choice of generating set s if a finitely generated group is linear it is known that is either of polynomial growth in which case is virtually nilpotent or of exponential growth otherwise tit72 mil68 wol68

fractional calculus for interval valued functions abstract we use a generalization of the hukuhara difference for closed intervals on the real line to develop a theory of the fractional calculus for interval valued functions the properties of riemann liouville fractional integral riemann liouville fractional derivative and caputo fractional derivative for interval valued functions are investigated several examples are presented to illustrate the concepts and results

sandor s inequality for sugeno integrals abstract in this paper we prove a fuzzy integral inequality for convex functions our results improve recent results that appear in literature some examples are given to illustrate our theorems

maximal subgroups of groups of intermediate growth abstract finding the number of maximal subgroups of infinite index of a finitely generated group is a natural problem that has been solved for several classes of geometric groups linear groups hyperbolic groups mapping class groups etc here we provide a solution for a family of groups with a different geometric origin groups of intermediate growth that act on rooted binary trees in particular we show that the non torsion iterated monodromy groups of the tent map a special case of some groups first introduced by sunic in 32 as siblings of the grigorchuk group have exactly countably many maximal subgroups of infinite index and describe them up to conjugacy this is in contrast to the torsion case e g grigorchuk group where there are no maximal subgroups of infinite index it is also in contrast to the above mentioned geometric groups where there are either none or uncountably many such subgroups along the way we show that all the groups defined by sunic have the congruence subgroup property and are just infinite

the tarski numbers of groups abstract the tarski number of a non amenable group g is the minimal number of pieces in a paradoxical decomposition of g in this paper we investigate how tarski numbers may change under various group theoretic operations using these estimates and known properties of golod shafarevich groups we show that the tarski numbers of 2 generated non amenable groups can be arbitrarily large we also use the cost of group actions to show that there exist groups with tarski numbers 5 and 6 these provide the first examples of non amenable groups without free subgroups whose tarski number has been computed precisely

a group of non uniform exponential growth locally isomorphic to img z 2 i we prove that a sequence of marked three generated groups isomorphic to the iterated monodromy group of z 2 i converges to a group of non uniform exponential growth which is an extension of the infinite direct sum of cyclic groups of order 4 by a grigorchuk group

the sugeno integral with respect to α preinvex functions abstract in this paper we establish the left hand side of the hermite hadamard inequality for preinvex functions and illustrate that the hermite hadamard inequality for preinvex functions is not valid for the sugeno integral moreover we give several upper bounds for the sugeno integral related to preinvex functions some examples are also provided to show the validity of our results

hermite hadamard s type inequalities for operator convex functions some hermite hadamard s type inequalities for operator convex functions of selfadjoint operators in hilbert spaces are given applications for particular cases of interest are also provided

validated linear relaxations and preprocessing some experiments based on work originating in the early 1970s a number of recent global optimization algorithms have relied on replacing an original nonconvex nonlinear program by convex or linear relaxations such linear relaxations can be generated automatically through an automatic differentiation process this process decomposes the objective and constraints if any into convex and nonconvex unary and binary operations the convex operations can be approximated arbitrarily well by appending additional constraints while the domain must somehow be subdivided in an overall branch and bound process or in some other local process to handle nonconvex constraints in general a problem can be hard if even a single nonconvex term appears however certain nonconvex terms lead to easier to solve problems than others recently neumaier lebbah michel ourselves and others have paved the way to utilizing such techniques in a validated context in this paper we present a symbolic preprocessing step that provides a measure

conjugacy growth of commutators abstract for the free group f r on r 1 generators respectively the free product g 1 g 2 of two nontrivial finite groups g 1 and g 2 we obtain the asymptotic for the number of conjugacy classes of commutators in f r respectively g 1 g 2 with a given word length in a fixed set of free generators respectively the set of generators given by the nontrivial elements of g 1 and g 2 our result is proven by using the classification of commutators in free groups and in free products by wicks and builds on the works of rivin and sharp who asymptotically counted the conjugacy classes of commutator subgroup elements in f r with a given word length

amenability and non uniform growth of some directed automorphism groups of a rooted tree a result of amenability of some automorphism groups of a spherically homogeneous rooted tree of bounded valency is given it is used to construct uncountably many amenable groups of non uniform exponential growth their cayley graphs can be made arbitrary close to that of some groups of intermediate growth yet those groups are not in the class sg of subexponentially amenable groups

growth rates _ homology and volumes of hyperbolic 3 manifolds it is shown that if m is a closed orientable irreducible 3 manifold and n is a nonnegative integer and if h 1 m z p has rank n 2 for some prime p then every n generator subgroup of 1 m has infinite index in 1 m and is in fact contained in infinitely many finite index subgroups of 1 m this result is used to estimate the growth rates of the fundamental group of a 3 manifold in terms of the rank of the z p homology

fuzzy fractional differential equations under caputo katugampola fractional derivative approach abstract in this work an initial value problem of caputo katugampola ck fractional differential equations in fuzzy setting is considered and an idea of successive approximations under generalized lipschitz condition is used to prove the existence and uniqueness results of the solution to the given problem in order to obtain the above results some necessary comparison theorems in real valued differential equation under ck fractional derivative are established finally a new technique to find analytical solutions of ck fuzzy fractional differential equations by using the solutions of fuzzy integer order differential equations is proposed some examples illustrating the applications of our results are presented

large hereditarily just infinite groups abstract it is shown that there is a hereditarily just infinite group in which all countably based profinite groups can be embedded and also that there exist hereditarily just infinite prosoluble groups that are not topologically finitely generated

a generalization of hh f divergence abstract the discrimination between two probability distributions is an impotent problem in 1991 lin ieee transactions on information theory 37 1 1991 introduced a novel class of information theoretic divergence measures based on the shannon entropy as a generalization of lin s divergence a new divergence called hermite hadamard hh f divergence based on lin s method of constructing the divergence was introduced by shioya and da te in 1995 in this paper we expand the applicability of hh f divergence by combining the properties of fractional calculus with hh f divergence and then introduce the concept of some fractional hh f divergences which are generalizations of the hh f divergence then some inequalities related to fractional hh f divergence are proposed

on new inequalities of hermite hadamard fejer type for convex functions via fractional integrals in this paper we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex these results are connected with the celebrated hermite hadamard fejer type integral inequality the results presented here would provide extensions of those given in earlier works

hermite hadamard inequality for fuzzy integrals in this paper we prove a hermite hadamard type inequality for fuzzy integrals some examples are given to illustrate the results

convexity according to a pair of quasi arithmetic means and inequalities abstract we consider a class of generalized convex functions which are defined according to a pair of quasi arithmetic means and called m m convex functions and establish various fejer type inequalities for such a function class these inequalities not merely provide a natural and intrinsic characterization of the m m convex functions but actually offer a generalization and refinement of the most part of the concrete hermite hadamard and fejer type inequalities obtained in earlier studies for different kinds of convexity and fractional integrals applications to inequalities involving the gamma function and special means are also included

applications of fractional calculus in solving abel type integral equations surface volume reaction problem abstract in this paper we consider a class of partial integro differential equations of fractional order motivated by an equation which arises as a result of modeling surface volume reactions in optical biosensors we solve these equations by employing techniques from fractional calculus several examples are discussed furthermore for the first time we encounter an order of the fractional derivative other than 1 2 in an applied problem hence in this paper we explore the applicability of fractional calculus in real world applications further strengthening the true nature of fractional calculus

groups of oscillating intermediate growth we construct an uncountable family of nitely generated groups of intermediate growth with growth functions of new type these functions can have large oscillations between lower and upper bounds both of which come from a wide class of functions in particular we can have growth oscillating between e n and any prescribed function growing as rapidly as desired our construction is built on top of any of the grigorchuk groups of intermediate growth and is a variation on the limit of permutational wreath product

ulam hyers stability of fractional langevin equations in this paper we discuss ulam hyers stability of nonlinear fractional langevin equations by using the boundedness monotonicity and nonnegative properties of classical and generalized mittag leffler functions further the same problem for the associated impulsive systems is investigated finally an example is given to illustrate our theoretical results

on amenability of automata groups we show that the group of bounded automatic automorphisms of a rooted tree is amenable which implies amenability of numerous classes of groups generated by finite automata the proof is based on reducing the problem to showing amenability just of a certain explicit family of groups mother groups which is done by analyzing the asymptotic properties of random walks on these groups

safe bounds in linear and mixed integer linear programming current mixed integer linear programming solvers are based on linear programming routines that use floating point arithmetic occasionally this leads to wrong solutions even for problems where all coefficients and all solution components are small integers an example is given where many state of the art milp solvers fail it is then shown how using directed rounding and interval arithmetic cheap pre and postprocessing of the linear programs arising in a branch and cut framework can guarantee that no solution is lost at least for mixed integer programs in which all variables can be bounded rigorously by bounds of reasonable size

mellin transforms of generalized fractional integrals and derivatives we obtain the mellin transforms of the generalized fractional integrals and derivatives that generalize the riemann liouville and the hadamard fractional integrals and derivatives we also obtain interesting results which combine generalized r m operators with generalized stirling numbers and lah numbers for example we show that 1 1 corresponds to the stirling numbers of the 2nd kind and 2 1 corresponds to the unsigned lah numbers further we show that the two operators r m and m r r m n generate the same sequence given by the recurrence relation s n k i 0 r m m r n 2 k i 1 r i r i s n 1 k i 0 k n with s 0 0 1 and s n 0 s n k 0 for n 0 and 1 min r m n 1 k or k 0 finally we define a new class of sequences for r 1 3 1 4 1 5 1 6 and in turn show that 1 2 1 corresponds to the generalized laguerre polynomials

extensions of the hermite hadamard inequality for harmonically convex functions via fractional integrals the main aim of this paper is to give extensions of the hermite hadamard inequality for harmonically convex functions via riemann liouville fractional integrals we show how to relax the harmonically convexity property of the function f obtained results in this work involve a larger class of functions our results are the refinements of the existing results for harmonically convex functions

holder type inequality for sugeno integral two inequalities for the sugeno integral on abstract spaces are studied in rather general forms which generalize most of the results on the same topic obtained by other authors thus closing the series of papers on this topic as an application a holder type inequality is obtained finally some conclusions are drawn and some problems for further investigation are suggested

a comparison of complete global optimization solvers results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables collected from the literature the test problems are available online in ampl and were translated into the input formats of the various solvers using routines from the coconut environment these translators are available online too

hermite hadamard type inequalities via α m convexity in this paper we establish several new inequalities for functions whose second derivative in absolute value aroused to the qth q 1 power are a m convex some applications to special means of positive real numbers are also given

on a version of fuzzy jensen inequality based on the measure of level set abstract in this paper we present a sufficient condition for the continuity of distribution function f based on a condition of the measure of level sets from this result an estimate of jensen type inequality for sugeno integral is stated finally it is applied to establish jensen type estimates for several kinds of fuzzy numbers

regional observability for hadamard caputo time fractional distributed parameter systems abstract in this paper regional gradient exact and approximate observability problems are studied on hadamard caputo time fractional distributed parameter systems without any knowledge of the initial vector and its gradient several equivalent criteria are first provided to achieve the regional observability based on these characterizations for both strategic and gradient strategic zone sensors are developed then by employing the hilbert uniqueness method hum we explicitly reconstruct the initial vector and its gradient respectively a one dimension example is finally included to illustrate our results

global minimization using an augmented lagrangian method with variable lower level constraints a novel global optimization method based on an augmented lagrangian framework is introduced for continuous constrained nonlinear optimization problems at each outer iteration k the method requires the varepsilon k global minimization of the augmented lagrangian with simple constraints where varepsilon k to varepsilon global convergence to an varepsilon global minimizer of the original problem is proved the subproblems are solved using the bb method numerical experiments are presented

a class of nonlinear nonseparable continuous knapsack and multiple choice knapsack problems this paper considers a general class of continuous nonlinear and nonseparable knapsack problems special cases of which arise in numerous operations and financial contexts we develop important properties of optimal solutions for this problem class based on the properties of a closely related class of linear programs using these properties we provide a solution method that runs in polynomial time in the number of decision variables while also depending on the time required to solve a particular one dimensional optimization problem thus for the many applications in which this one dimensional function is reasonably well behaved e g unimodal the resulting algorithm runs in polynomial time we next develop a related solution approach to a class of continuous nonlinear and nonseparable multiple choice knapsack problems this algorithm runs in polynomial time in both the number of variables and the number of variants per item while again dependent on the complexity of the same one dimensional optimization problem as for the knapsack problem computational testing demonstrates the power of the proposed algorithms over a commercial global optimization software package

transposition theorems and qualification free optimality conditions new theorems of the alternative for polynomial constraints based on the positivstellensatz from real algebraic geometry and for linear constraints generalizing the transposition theorems of motzkin and tucker are proved based on these two karush john optimality conditions holding without any constraint qualification are proved for single or multiobjective constrained optimization problems the first condition applies to polynomial optimization problems only and gives for the first time necessary and sufficient global optimality conditions for polynomial problems the second condition applies to smooth local optimization problems and strengthens known local conditions if some linear or concave constraints are present the new version reduces the number of constraints for which a constraint qualification is needed to get the kuhn tucker conditions

hermite hadamard type inequalities for harmonically convex functions via fractional integrals abstract in this paper the authors established hermite hadamard s inequalities for harmonically convex functions via fractional integrals and obtained some hermite hadamard type inequalities of these classes of functions

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

a finitely generated branch group of exponential growth without free subgroups abstract we will give an example of a branch group g that has exponential growth but does not contain any non abelian free subgroups this answers question 16 from bartholdi et al 2003 1 positively the proof demonstrates how to construct a non trivial word w a b x y for any a b g such that w a b a b 1 the group g is not just infinite we prove that every normal subgroup of g is finitely generated as an abstract group and every proper quotient soluble further g has infinite virtual first betti number but is not large

thurston equivalence of topological polynomials we answer hubbard s question on determining the thurston equivalence class of twisted rabbits i e composita of the rabbit polynomial with nth powers of the dehn twists about its ears the answer is expressed in terms of the 4 adic expansion of n we also answer the equivalent question for the other two families of degree 2 topological polynomials with three post critical points in the process we rephrase the questions in group theoretical language in terms of wreath recursions

lattice fractional diffusion equation in terms of a riesz caputo difference abstract a fractional difference is defined by the use of the right and the left caputo fractional differences the definition is a two sided operator of riesz type and introduces back and forward memory effects in space difference then a fractional difference equation method is suggested for anomalous diffusion in discrete finite domains a lattice fractional diffusion equation is proposed and the numerical simulation of the diffusion process is discussed for various difference orders the result shows that the riesz difference model is particularly suitable for modeling complicated dynamical behaviors on discrete media

hermite hadamard and hermite hadamard fejer type inequalities for generalized fractional integrals abstract in this paper we obtain the hermite hadamard and hermite hadamard fejer type inequalities for fractional integrals which generalize the two familiar fractional integrals namely the riemann liouville and the hadamard fractional integrals into a single form we prove that in most cases we obtain the riemann liouville and the hadamard equivalence just by taking limits when a parameter 1 and 0 respectively

extensions of amenable groups by recurrent groupoids we show that the amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital schreier graphs this applies to a wide class of groups the amenability of which was an open problem as well as unifies many known examples to one general proof in particular this includes grigorchuk s group basilica group group associated to fibonacci tiling the topological full groups of cantor minimal systems groups acting on rooted trees by bounded automorphisms groups generated by finite automata of linear activity growth and groups naturally appearing in holomorphic dynamics

anomalous diffusion modeling by fractal and fractional derivatives this paper makes an attempt to develop a fractal derivative model of anomalous diffusion we also derive the fundamental solution of the fractal derivative equation for anomalous diffusion which characterizes a clear power law this new model is compared with the corresponding fractional derivative model in terms of computational efficiency diffusion velocity and heavy tail property the merits and distinctions of these two models of anomalous diffusion are then summarized

isoperimetry of group actions the isoperimetric profile of a discrete group was introduced by vershik however it is well defined only for a restrictive class amenable groups we generalize the notion of isoperimetric profile beyond the world of amenable groups by defining isoperimetric profiles of amenable actions of finitely generated groups on compact topological spaces this allows to extend the definition of the isoperimetric profile to all groups which are exact in such a way that for amenable groups it is equal to vershik s isoperimetric profile the main feature of our construction is that it preserves many of the properties known from the classical case we use these results to compute exact asymptotics of the isoperimetric profiles for several classes of non amenable groups

fuzzy algebra in triangular norm system abstract triangular norm is a powerful tool in the theory research and application development of fuzzy sets in this paper using the triangular norm we introduce some concepts such as fuzzy algebra fuzzy algebra fuzzy monotone class fuzzy class and fuzzy class and discuss the relations among them obtaining a series of conclusions main ones of which are fuzzy monotone class theorems cf theorems 1 3

uniform non amenability abstract for any finitely generated group g an invariant fol g 0 is introduced which measures the amount of non amenability of g if g is amenable then fol g 0 if fol g 0 we call g uniformly non amenable we study the basic properties of this invariant for example its behaviour when passing to subgroups and quotients of g we prove that the following classes of groups are uniformly non amenable non abelian free groups non elementary word hyperbolic groups large groups free burnside groups of large enough odd exponent and groups acting acylindrically on a tree uniform non amenability implies uniform exponential growth we also exhibit a family of non amenable groups in particular including all non solvable baumslag solitar groups which are not uniformly non amenable that is they satisfy fol g 0 finally we derive a relation between our uniform folner constant and the uniform kazhdan constant with respect to the left regular representation of g

fractional differential equations of caputo katugampola type and numerical solutions abstract this paper is concerned with a numerical method for solving generalized fractional differential equation of caputo katugampola derivative a corresponding discretization technique is proposed numerical solutions are obtained and convergence of numerical formulae is discussed the convergence speed arrives at o t 1 numerical examples are given to test the accuracy

what is a fractional derivative this paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals two criteria for required by a fractional operator are formulated the grunwald letnikov riemann liouville and caputo fractional derivatives and the riesz potential are accessed in the light of the proposed criteria a leibniz rule is also obtained for the riesz potential

a note on katugampola fractional calculus and fractal dimensions abstract the goal of this paper is to study the katugampola fractional integral of a continuous function of bounded variation defined on a closed bounded interval we note that the katugampola fractional integral of a function shares some analytical properties such as boundedness continuity and bounded variation of the function defining it consequently we deduce that fractal dimensions minkowski dimension and hausdorff dimension of the graph of the katugampola fractional integral of a continuous function of bounded variation are one a natural question then arises is whether there exists a continuous function which is not of bounded variation with its graph having fractal dimensions one in the last part of the article we construct a continuous function which is not of bounded variation and for which the graph has fractal dimensions one the construction enunciated herein includes previous constructions found in the recent literature as special cases the article also hints at an upper bound for the upper box dimension of the graph of the katugampola fractional derivative of a continuously differentiable function

hermite hadamard hermite hadamard fejer dragomir agarwal and pachpatte type inequalities for convex functions via new fractional integrals abstract the aim of this paper is to establish hermite hadamard hermite hadamard fejer dragomir agarwal and pachpatte type inequalities for new fractional integral operators with exponential kernel these results allow us to obtain a new class of functional inequalities which generalizes known inequalities involving convex functions furthermore the obtained results may act as a useful source of inspiration for future research in convex analysis and related optimization fields

berwald type inequality for sugeno integral abstract nonadditive measure is a generalization of additive probability measure sugeno integral is a useful tool in several theoretical and applied statistics which has been built on non additive measure integral inequalities play important roles in classical probability and measure theory the classical berwald integral inequality is one of the famous inequalities this inequality turns out to have interesting applications in information theory in this paper berwald type inequality for the sugeno integral based on a concave function is studied several examples are given to illustrate the validity of this inequality finally a conclusion is drawn and a problem for further investigations is given

the use of finite difference element approaches for solving the time fractional subdiffusion equation in this paper two finite difference element approaches for the time fractional subdiffusion equation with dirichlet boundary conditions are developed in which the time direction is approximated by the fractional linear multistep method and the space direction is approximated by the finite element method the two methods are unconditionally stable and convergent of order o tau q h r 1 in the l 2 norm where q 2 beta or 2 when the analytical solution to the subdiffusion equation is sufficiently smooth beta 0 beta 1 is the order of the fractional derivative tau and h are the step sizes in time and space respectively and r is the degree of the polynomial space the corresponding schemes for the subdiffusion equation with neumann boundary conditions are presented as well where the stability and convergence are shown numerical examples are provided to verify the theoretical analysis comparisons between the algorithms derived in this paper and the existing algorithms are given

new approach to a generalized fractional integral abstract the paper presents a new fractional integration which generalizes the riemann liouville and hadamard fractional integrals into a single form conditions are given for such a fractional integration operator to be bounded in an extended lebesgue measurable space semigroup property for the above operator is also proved we give a general definition of the fractional derivatives and give some examples

global optimization of mixed integer nonlinear programs a theoretical and computational study this work addresses the development of an efficient solution strategy for obtaining global optima of continuous integer and mixed integer nonlinear programs towards this end we develop novel relaxation schemes range reduction tests and branching strategies which we incorporate into the prototypical branch and bound algorithm in the theoretical algorithmic part of the paper we begin by developing novel strategies for constructing linear relaxations of mixed integer nonlinear programs and prove that these relaxations enjoy quadratic convergence properties we then use lagrangian linear programming duality to develop a unifying theory of domain reduction strategies as a consequence of which we derive many range reduction strategies currently used in nonlinear programming and integer linear programming this theory leads to new range reduction schemes including a learning heuristic that improves initial branching decisions by relaying data across siblings in a branch and bound tree finally we incorporate these relaxation and reduction strategies in a branch and bound algorithm that incorporates branching strategies that guarantee finiteness for certain classes of continuous global optimization problems in the computational part of the paper we describe our implementation discussing wherever appropriate the use of suitable data structures and associated algorithms we present computational experience with benchmark separable concave quadratic programs fractional 0 1 programs and mixed integer nonlinear programs from applications in synthesis of chemical processes engineering design just in time manufacturing and molecular design

hermite hadamard type inequality for sugeno integrals abstract in this paper hermite hadamard type inequality for sugeno integrals based on m convex function is studied some examples are given to illustrate the results

uniform independence in linear groups we show that for any non virtually solvable finitely generated group of matrices over any field there is an integer m such that given an arbitrary finite generating set for the group one may find two elements a and b that are both products of at most m generators such that a and b are free generators of a free subgroup this uniformity result improves the original statement of the tits alternative

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

uniform pointwise bounds for matrix coefficients of unitary representations and applications to kazhdan constants let k be a local field and g the group of k rational points of a connected reductive linear algebraic group over k with k semisimple rank g 2 let k be a good maximal compact subgroup of g for a unitary representation of g a vector v in is called kfinite if the subspace spanned bykv is finite dimensional we will use the termk matrix coefficients resp k finite matrix coefficients of to refer to its matrix coefficients with respect to k invariant resp k finite unit vectors following bt we denote by g the subgroup generated by the unipotent k split subgroups of g the main goal of the present paper is to construct a class of uniform pointwise bounds for the k finite matrix coefficients of all infinite dimensional irreducible unitary representations of g or more generally of all unitary representations of g without a non zero g invariant vector let a be a maximal k split torus and a the closed positive weyl chamber of a such that the cartan decomposition g ka k holds where is a finite subset of the

kazhdan quotients of golod shafarevich groups the main goal of this paper is to prove that every golod shafarevich group has an infinite quotient with kazhdan s property t in particular this gives an affirmative answer to the well known question about non amenability of golod shafarevich groups

chebyshev inequality for sugeno integrals in this paper we study chebyshev inequality for sugeno integrals on an arbitrary fuzzy measure space particularly we obtain other chebyshev type inequalities which relate the measure of a level set of the maximum and the sum of two non negative integrable functions and their integrals finally we apply our results to the case of comonotone functions

numerical methods for the variable order fractional advection diffusion equation with a nonlinear source term in this paper we consider a variable order fractional advection diffusion equation with a nonlinear source term on a finite domain explicit and implicit euler approximations for the equation are proposed stability and convergence of the methods are discussed moveover we also present a fractional method of lines a matrix transfer technique and an extrapolation method for the equation some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis

correction to what is a fractional derivative by ortigueira and machado journal of computational physics volume 293 15 july 2015 pages 4 13 special issue on fractional pdes there is a debate among contemporary mathematicians about what it really means by a fractional derivative the question arose as a consequence of introducing a new definition of a fractional derivative in 1 in a reply ortigueira and machado 2 came up with several very important criteria to determine whether a given derivative is a fractional derivative according to their criterion the new fractional derivative called conformable fractional derivative introduced by khalil et al 1 turns out not to be a fractional derivative but rather a controlled or conformable derivative in proving the claim the authors in 2 use an example 2 p 6 it turns out that the explanation given there needs some corrections and it is the sole purpose of this note

moving horizon state estimation for nonlinear discrete time systems new stability results and approximation schemes a moving horizon state estimation problem is addressed for a class of nonlinear discrete time systems with bounded noises acting on the system and measurement equations as the statistics of such disturbances and of the initial state are assumed to be unknown we use a generalized least squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding window strategy for the resulting estimator the existence of bounding sequences on the estimation error is proved in the absence of noises exponential convergence to zero is obtained moreover suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value the approximate solution can be determined either on line by directly minimizing the cost function or off line by using a nonlinear parameterized function simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended kalman filter

acylindrically hyperbolic groups with exotic properties abstract we prove that every countable family of countable acylindrically hyperbolic groups has a common finitely generated acylindrically hyperbolic quotient as an application we obtain an acylindrically hyperbolic group q with strong fixed point properties q has property f l p for all p 1 and every action of q on a finite dimensional contractible topological space has a fixed point in addition q has other properties which are rather unusual for groups exhibiting hyperbolic like behavior e g q is not uniformly non amenable and has finite generating sets with arbitrary large balls consisting of torsion elements

on the isolated points in the space of groups we investigate the isolated points in the space of finitely generated groups we give a workable characterization of isolated groups and study their hereditary properties various examples of groups are shown to yield isolated groups we also discuss a connection between isolated groups and solvability of the word problem

a fourth order compact adi scheme for two dimensional nonlinear space fractional schrodinger equation in this paper a novel compact operator is derived for the approximation of the riesz derivative with order alpha in 1 2 the compact operator is proved with fourth order accuracy combining the compact operator in space discretization a linearized difference scheme is proposed for a two dimensional nonlinear space fractional schrodinger equation it is proved that the difference scheme is uniquely solvable stable and convergent with order o tau 2 h 4 where tau is the time step size h max h 1 h 2 and h 1 h 2 are space grid sizes in the x direction and the y direction respectively based on the linearized difference scheme a compact alternating direction implicit scheme is presented and analyzed numerical results demonstrate that the compact operator does not bring in extra computational cost but improves the accuracy of the scheme greatly

general minkowski type inequalities for sugeno integrals minkowski type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the pseudo additive operation

the growth of free products abstract we improve estimates for the exponential growth rates of free products with or without amalgamation hnn extensions one relator groups and groups of positive deficiency some examples of groups for which the growth rates are realized are given

computation of parameter stability margins using polynomial programming techniques in this paper we consider linear time invariant lti systems with parameter uncertainty for such systems we present global optimization techniques to determine permissible perturbations of the parameters of the system that maintain stability the so called parameter stability margins for cases in which the coefficients of the characteristic equation of the system are polynomial functions of the uncertain parameters the parameter uncertainty domains for maintaining stability are characterized as hypersolids defined with respect to lp norms for various values of p 1 algorithms are devised based on the reformulation linearization convexification technique rlt in concert with branch and bound methods to solve the underlying parametric non convex subproblems for computing the stability margins several illustrative examples are solved to demonstrate the efficacy of the proposed approach towards producing global optimal solutions we also present comparative computational experience with the

the hermite hadamard inequality for log convex functions abstract we discuss the existence of a strengthening of hermite hadamard inequality in the case of log convex functions unlike the classical case which belongs to the field of linear functional analysis this analogue involves nonlinear means such as the geometric mean and the logarithmic mean