semilinear differential inclusions via weak topologies abstract the paper deals with the multivalued initial value problem x a t x x f t x for a a t a b x a x 0 in a separable reflexive banach space e the nonlinearity f is weakly upper semicontinuous in x and the investigation includes the case when both a and f have a superlinear growth in x we prove the existence of local and global classical solutions in the sobolev space w 1 p a b e with 1 p introducing a suitably defined lyapunov like function we are able to investigate the topological structure of the solution set our main tool is a continuation principle in frechet spaces and we prove the required pushing condition in two different ways some examples complete the discussion

forced vibrations of superquadratic hamiltonian systems on etudie l existence des solutions t periodiques ter t 0 du systeme hamiltonien suivant z gh z f t ou g est la matrice asymetrique standard

periodic solutions of second order equations via rotation numbers abstract we consider the problem of the existence and multiplicity of periodic solutions associated to a class of scalar equations of the form x f t x 0 the class considered is such that the behaviour of its solutions near zero and infinity can be compared two suitable piecewise linear systems we show how a rotation number approach together with the poincare birkhoff theorem and the phase plane analysis of the spiral properties allows to obtain multiplicity results in terms of the gap between the rotation numbers of the referred piecewise linear systems at zero and at infinity these systems may also be resonant in particular our approach can be used to deal with the problems without both global existence of the cauchy problems associated to the equation and the sign assumption on f the typical example is a partially superlinear second order equation our main result generalizes some classical results of jacobowitz and hartman among others

how to make a decision the analytic hierarchy process abstract this paper serves as an introduction to the analytic hierarchy process a multicriteria decision making approach in which factors are arranged in a hierarchic structure the principles and the philosophy of the theory are summarized giving general background information of the type of measurement utilized its properties and applications

multiple solutions of perturbed superquadratic second order hamiltonian systems abstract in this paper the author proves the existence of infinitely many distinct t periodic solutions of the perturbed second order hamiltonian systems q v q f t under the condition that v is c and superquadratic via minimax methods we also obtain similar results for general nonautonomous second order hamiltonian systems and perturbed lagrangian systems keywords invariance asymmetry a priori growth estimates multiple periodic solutions

jie ke versus alphago a ranking approach using decision making method for large scale data with incomplete information abstract ranking historical players in sports is challenging since some players have never played against each other it is even more complex in go because of alphago a project based on artificial intelligence who became the world s number 1 after it defeated the 528th and the 4th human go players alphago is ranked high in the current go ranking system because it is undefeated the objective of this paper is to propose a new ranking method for large scale go players by means of incomplete fuzzy pair wise comparison matrix whose priority vector is derived using a cosine similarity measure using match results provided by go4go net experiments are designed to rank top go players in the past 45 years and examine the change in ranking after alphago faced off against jie ke furthermore the proposed method was applied to rank all 1544 go players available at go4go net to illustrate its efficiency in handling large scale data

on the distributional complexity of disjointness we prove that the distributional communication complexity of the predicate disjointness with respect to a very simple measure on inputs is n

exponential lower bounds for polytopes in combinatorial optimization we solve a 20 year old problem posed by yannakakis and prove that no polynomial size linear program lp exists whose associated polytope projects to the traveling salesman polytope even if the lp is not required to be symmetric moreover we prove that this holds also for the cut polytope and the stable set polytope these results were discovered through a new connection that we make between one way quantum communication protocols and semidefinite programming reformulations of lps

crew prams and decision trees this paper gives a full characterization of the time needed to compute a boolean function on a crew pram with an unlimited number of processors the characterization is given in terms of a new compl

multiple solutions for second order three point boundary value problems with p laplacian operator abstract in this paper we study the second order three point boundary value problem with a p laplacian operator p x t g x t f t x t x t x 0 0 x x 1 where p s s p 2 s p 1 0 1 0 1 1 we obtain sufficient conditions for the existence of multiple solutions by applying generalized polar coordinates and the leray schauder degree theorem

a note on the existence of multiple solutions for a class of systems of second order odes abstract we prove the existence of multiple solutions for some systems of second order odes with dirichlet boundary conditions such systems are obtained by coupling scalar odes with different growth conditions the proof relies on a global continuation technique

average case polyhedral complexity of the maximum stable set problem we study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs lps in two distinct models in the uniform model the constraints of the lp are not allowed to depend on the input graph which should be encoded solely in the objective function there we prove a 2 omega n log n 2 n logn lower bound with probability at least 1 2 2 n 1 2 2n for every lp that is exact for a randomly selected set of instances each graph on at most n vertices being selected independently with probability p geqslant 2 left begin array c n 4 2 end array right n p 2 n 42 n in the non uniform model the constraints of the lp may depend on the input graph but we allow weights on the vertices the input graph is sampled according to the g n p model there we obtain upper and lower bounds holding with high probability for various ranges of p we obtain a super polynomial lower bound all the way from p omega left frac log 6 varepsilon n n right p log6 nn to p o left frac 1 log n right p o1logn our upper bound is close to this as there is only an essentially quadratic gap in the exponent which currently also exists in the worst case model finally we state a conjecture that would close this gap both in the average case and worst case models

complexity measures and decision tree complexity a survey we discuss several complexity measures for boolean functions certificate complexity sensitivity block sensitivity and the degree of a representing or approximating polynomial we survey the relations and biggest gaps known between these measures and show how they give bounds for the decision tree complexity of boolean functions on deterministic randomized and quantum computers

periodic solutions of semilinear duffing equations with impulsive effects abstract in this paper we are concerned with the existence of periodic solutions for semilinear duffing equations with impulsive effects firstly for its autonomous equation any motion of the solution is same as the motion of the corresponding equation without impulses until it meets the first impulse time under the influence of impulses these two motions are likely to be quite different we introduce some reasonable assumptions on the impulsive functions to control these differences such that the information valid for the equation without impulses can always be used for the impulsive one basing on poincare birkhoff twist theorem we prove the existence of infinitely many periodic solutions secondly as for the nonautonomous equation where the autonomous case is taken as an auxiliary one we find the relation between the solutions of these two equations and then obtain the existence of infinitely many periodic solutions also by poincare birkhoff twist theorem lastly an example with special impulses satisfying the above assumptions is given

a continuation approach to superlinear periodic boundary value problems this paper deals with the problem of the existence of t periodic solutions for the first order differential system x i t x 1 1 where f 0 t x r r is a caratheodory function in what follows we prove some results for the solvability of the periodic bvp in the case when the dimension of the space is even such a limitation is motivated by our interest in applications to the second order equation d g t u u o 1 2 which takes the form of 1 1 when it is written as the equivalent system u v 0 g t u v 1 3

complementing maps continuation and global bifurcation we state and indicate some of the consequences of a theorem whose sole assumption is the nonvanishing of the leray schauder degree of a compact vector field and whose conclusions yield multidimensional existence continuation and bifurcation results

strengths and weaknesses of quantum computing recently a great deal of attention has been focused on quantum computation following a sequence of results bernstein and vazirani in proc 25th annual acm symposium theory comput 1993 pp 11 20 siam j comput 26 1997 pp 1277 1339 simon in proc 35th annual ieee symposium foundations comput sci 1994 pp 116 123 siam j comput 26 1997 pp 1340 1349 shor in proc 35th annual ieee symposium foundations comput sci 1994 pp 124 134 suggesting that quantum computers are more powerful than classical probabilistic computers following shor s result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time it is natural to ask whether all of np can be efficiently solved in quantum polynomial time in this paper we address this question by proving that relative to an oracle chosen uniformly at random with probability 1 the class np cannot be solved on a quantum turing machine qtm in time o 2 n 2 we also show that relative to a permutation oracle chosen uniformly at random with probability 1 the class np cap conp cannot be solved on a qtm in time o 2 n 3 the former bound is tight since recent work of grover in it proc 28 th annual acm symposium theory comput 1996 shows how to accept the class np relative to any oracle on a quantum computer in time o 2 n 2

decision making with the ahp why is the principal eigenvector necessary in this paper it is shown that the principal eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix a aij when a is a small perturbation of a consistent matrix when providing numerical judgments an individual attempts to estimate sequentially an underlying ratio scale and its equivalent consistent matrix of ratios near consistent matrices are essential because when dealing with intangibles human judgment is of necessity inconsistent and if with new information one is able to improve inconsistency to near consistency then that could improve the validity of the priorities of a decision in addition judgment is much more sensitive and responsive to large rather than to small perturbations and hence once near consistency is attained it becomes uncertain which coefficients should be perturbed by small amounts to transform a near consistent matrix to a consistent one if such perturbations were forced they could be arbitrary and thus distort the validity of the derived priority vector in representing the underlying decision

nondeterministic quantum query and communication complexities we study nondeterministic quantum algorithms for boolean functions f such algorithms have positive acceptance probability on input x iff f x 1 in the setting of query complexity we show that the nondeterministic quantum complexity of a boolean function is equal to its nondeterministic polynomial degree we also prove a quantum vs classical gap of 1 vs n for nondeterministic query complexity for a total function in the setting of communication complexity we show that the nondeterministic quantum complexity of a two party function is equal to the logarithm of the rank of a nondeterministic version of the communication matrix this implies that the quantum communication complexities of the equality and disjointness functions are n 1 if we do not allow any error probability we also exhibit a total function in which the nondeterministic quantum communication complexity is exponentially smaller than its classical counterpart

estimation of missing judgments in ahp pairwise matrices using a neural network based model selecting relevant features to make a decision and expressing the relationships between these features is not a simple task the decision maker must precisely define the alternatives and criteria which are more important for the decision making process the analytic hierarchy process ahp uses hierarchical structures to facilitate this process the comparison is realized using pairwise matrices which are filled in according to the decision maker judgments subsequently matrix consistency is tested and priorities are obtained by calculating the matrix principal eigenvector given an incomplete pairwise matrix two procedures must be performed first it must be completed with suitable values for the missing entries and second the matrix must be improved until a satisfactory level of consistency is reached several methods are used to fill in missing entries for incomplete pairwise matrices with correct comparison values additionally once pairwise matrices are complete and if comparison judgments between pairs are not consistent some methods must be used to improve the matrix consistency and therefore to obtain coherent results in this paper a model based on the multi layer perceptron mlp neural network is presented given an ahp pairwise matrix this model is capable of completing missing values and improving the matrix consistency at the same time

radially symmetric systems with a singularity and asymptotically linear growth abstract we prove the existence of infinitely many periodic solutions for radially symmetric systems with a singularity of repulsive type the nonlinearity is assumed to have a linear growth at infinity being controlled by two constants which have a precise interpretation in terms of the dancer fucik spectrum our result generalizes an existence theorem by del pino et al 1992 4 obtained in the case of a scalar second order differential equation

a new fixed point theorem and periodic solutions of nonconservative weakly coupled systems abstract in this paper we prove a new fixed point theorem for the coupling of twist conditions and poincare bohl type conditions as its applications we prove the existence of periodic solutions for various nonconservative mixed type weakly coupled systems

determining acceptance possibility for a quantum computation is hard for the polynomial hierarchy abstract it is shown that determining whether a quantum computation has a non zero probability of accepting is at least as hard as the polynomial time hierarchy this hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition or whether a given quantum bit has positive expectation value at the end of a quantum computation this result is achieved by showing that the complexity class nqp of adleman demarrais and huang a quantum analog of np is equal to the counting class co c equals p

backpropagation multi layer perceptron for incomplete pairwise comparison matrices in analytic hierarchy process abstract analytic hierarchy process ahp is a widely used decision making method in many areas such as management sciences the performance ratings of multiple criteria and alternatives can be elicited from pairwise comparisons obtained by expressing the decision maker s perceive however it may be difficult for the decision maker to prudently assign values to comparisons for large number of criteria or alternatives since there exist distinct relationships between any two elements in the real world the relationship between the missing comparison and the assigned comparisons should be taken into account the aim of this paper is to propose a novel method using a well known regression tool namely the backpropagation multi layer perceptron i e mlp to realize the above implicit relationship so as to estimate a missing pairwise judgment from the other assigned entries a computer simulation is employed to demonstrate that the proposed method can effectively find a missing entry of an incomplete pairwise matrix such that its consistency index is minimized

existence of nontrivial solutions for discrete nonlinear two point boundary value problems in this paper by using strongly monotone operator principle and critical point theory the existence of nontrivial solutions for discrete nonlinear two point boundary value problems is established two illustrative examples are given in the last part of the paper

reconstruction methods for ahp pairwise matrices habitually decision makers are exposed to situations that require a lot of knowledge and expertise therefore they need tools to help them choose the best possible alternatives analytic hierarchical process ahp is one of those tools and it is widely used in many fields while the use of ahp is very simple there is a situation that becomes complex the consistency of the pairwise matrices in order to obtain the consistent pairwise matrix from the inconsistent one reconstruction methods can be used but they cannot guarantee getting the right matrix according to the judgments of the decision maker this situation does not allow proper evaluation of methods reliability i e it is not possible to obtain a reliable ranking of alternatives based on an inconsistent matrix in this work a new way to evaluate the reliability of matrix reconstruction methods is proposed this technique uses a novel measure for alternatives ranking comparison based on element positions and distances which is introduced in order to compare several matrix reconstruction methods finally in order to demonstrate the extensibility of this new reliability measure two reconstruction methods based on bio inspired models a genetic algorithm and the firefly algorithm are presented and evaluated by using the aforementioned reliability measure

quantum communication and complexity in the setting of communication complexity two distributed parties want to compute a function depending on both their inputs using as little communication as possible the required communication can sometimes be significantly lowered if we allow the parties the use of quantum communication we survey the main results of the young area of quantum communication complexity its relation to teleportation and dense coding the main examples of fast quantum communication protocols lower bounds and some applications

the existence of periodic solutions for a class of nonautonomous lattices with bounded coupling abstract in this paper by using a definition of topological degree and limiting arguments we study the existence of periodic solutions of a class of one dimensional nonautonomous chains with bounded coupling an approach is developed to deal with the case of lack of the a priori bounds for an infinite lattices

quantum weakly nondeterministic communication complexity in this paper we study a weak version of quantum nondeterministic communication complexity in which a classical proof has to be checked with probability one by a quantum protocol we prove that in the framework of communication complexity even this weak version of quantum nondeterminism is strictly stronger than classical nondeterminism more precisely we show a separation for a total function of quantum weakly nondeterministic and classical nondeterministic communication complexity this separation is quadratic and shows that classical proofs can be checked more efficiently by quantum protocols than by classical ones

existence of forced oscillations for some nonlinear differential equations abstract this article studies the existence of t periodic solutions for systems of nonlinear second order ordinary differential equations assuming function v to be superquadratic it is shown that this system possesses infinitely many t periodic solutions the proof of this result rests on showing that certain homotopy groups of level sets of the functional associated with the system are not trivial some more general results concerning systems of another type are also presented

on the extension complexity of combinatorial polytopes in this paper we extend recent results of fiorini et al on the extension complexity of the cut polytope and related polyhedra we first describe a lifting argument to show exponential extension complexity for a number of np complete problems including subset sum and three dimensional matching we then obtain a relationship between the extension complexity of the cut polytope of a graph and that of its graph minors using this we are able to show exponential extension complexity for the cut polytope of a large number of graphs including those used in quantum information and suspensions of cubic planar graphs

periodic solutions of superlinear impulsive differential equations a geometric approach abstract a geometric method is introduced to study superlinear second order differential equations with impulsive effects basing on a reference continuous polar lifting of a planar orientation preserving homeomorphism we prove via the poincare birkhoff twist theorem the existence of infinitely many periodic solutions of conservative superlinear second order equations with the finite twist impulsive terms we also prove by developing a new twist fixed point theorem the existence of periodic solutions for non conservative superlinear second order equations with degenerate impulsive terms

rapid solution of problems by quantum computation a class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method the quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation

global bifurcation for 2mth order boundary value problems and infinitely many solutions of superlinear problems we consider the boundary value problem lu x p x u x g x u 0 x u 2m 1 x u x x 0 where i l is a 2mth order self adjoint disconjugate ordinary differential operator on 0 together with separated boundary conditions at 0 and ii p is continuous and p 0 on 0 while p 0 on any interval in 0 iii g 0 r2m r is continuous and there exist increasing functions u l 0 0 such that u 1 g x l 1 0 lim 0g x 0 with limt l t the non linear term in is superlinear as u x we obtain a global bifurcation result for a related bifurcation problem we then use this to obtain infinitely many solutions of having specified nodal properties

existence of periodic solutions of duffing equations on considere le probleme aux valeurs limites periodiques de type duffing u t ku t g t u t f t t 0 2 u 0 u 2 u 0 u 2 on demontre un resultat d existence general qui montre que si la croissance de g t u a l infini appartient a un ensemble avec la propriete p alors pour tout f l 1 0 2 le probleme a au moins une solution

on a pseudo fuccik spectrum for strongly nonlinear second order odes and an existence result abstract we study here the existence of solutions to the nonlinear dirichlet problem p u f t u q t a e for t a b u a u b 0 where is an increasing odd homeomorphism of r f a b r r satisfies the caratheodory assumptions and q l 1 a b r with a view towards defining a pseudo fucik spectrum pfs we study using a time mapping approach the eigenvalue like problem u a u b u 0 u a 0 u b where a 0 b 0 we show here that this pfs which we denote by l consists of a set of curves in r 2 resembling the classical fucik spectrum i e when s s our main existence result which deals with nonresonance with respect to the pfs can be roughly stated as follows if for s 0 sufficiently large and for almost every t a b the pair f t s s f t s s lies in a compact rectangle contained in an open component of r 2 l which intersects the diagonal then problem p has at least a solution