exit problems associated with affine reflection groups we obtain a formula for the distribution of the first exit time of brownian motion from the alcove of an affine weyl group in most cases the formula is expressed compactly in terms of pfaffians expected exit times are derived in the type widetilde a case the results extend to other markov processes we also give formulas for the real eigenfunctions of the dirichlet and neumann laplacians on alcoves observing that the hot spots conjecture of j rauch is true for alcoves

some consequences of cryptographical conjectures for s 1 2 and ef we show that there is a pair of disjoint np sets whose disjointness is provable in s 2 1 and which cannot be separated by a set in p poly if the cryptosystem rsa is secure further we show that factoring and the discrete logarithm are implicitly definable in any extension of s 2 1 admitting an np definition of primes about which it can prove that no number satisfying the definition is composite

a solution to an open problem for wave equations with generalized wentzell boundary conditions in this paper we solve an open problem put forward by a favini g r goldstein j a goldstein and s romanelli concerning the mixed problem for wave equations with generalized wentzell boundary conditions as a consequence we also develop the previous wellposedness result regarding the mixed problem for heat equations with generalized wentzell boundary conditions

symmetric duality for a class of multiobjective fractional programming problems this paper is concerned with symmetric duality for a class of nondifferentiable multiobjective fractional programming problems two weak duality theorems and two strong duality theorems are proved discussion on some special cases shows that results in this paper extend previous work in this area

bounded query classes polynomial time machines having restricted access to an np oracle are investigated restricted access means that the number of queries to the oracle is restricted or the way in which the queries are made is restricted e g queries made during truth table reductions very different kinds of such restrictions result in the same or comparable complexity classes in particular the class p text np o log n can be characterized in very different ways furthermore the boolean hierarchy is generalized in such a way that it is possible to characterize p text np and p text np o log n in terms of the generalization

an application of boolean complexity to separation problems in bounded arithmetic we develop a method for establishing the independence of some i formulas from s i 2 in particular we show that t i 2 is not i conservative over si 2 we characterize the 1 definable functions of t 1 2 as being precisely the functions definable as projections of polynomial local search pls problems although it is still an open problem whether bounded arithmetic s2 is finitely axiomatizable considerable progress on this question has been made s 2 is i 1 conservative over t i 2 3 but it is not i 2 conservative unless pi 2 p i 2 10 and in addition t i 2 is not i 1 conservative over s 2 supported in part by nsf grants dms 8902480 and int 8914569 part of this work performed while visiting the czechoslovakian academy of sciences email address sbuss ucsd edu supported in part by nsf grant int 8914569 part of this work performed while visiting the univ of illinois champaign urbana email address krajicek csearn bitnet

a note on higher order symmetric duality in this paper a pair of wolfe type higher order symmetric dual multiobjective programs is formulated strong and converse duality theorems are established under invexity assumptions duality relations for mond weir type dual models have also been obtained under pseudoinvexity assumptions

classes of representable disjoint np pairs for a propositional proof system p we introduce the complexity class dnpp p of all disjoint np pairs for which the disjointness of the pair is efficiently provable in the proof system p we exhibit structural properties of proof systems which make canonical np pairs associated with these proof systems hard or complete for dnpp p moreover we demonstrate that non equivalent proof systems can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for dnpp p and the reductions between the canonical pairs exist

multiobjective symmetric duality involving cones abstract in this paper a pair of multiobjective symmetric dual programs over arbitrary cones are formulated for cone convex functions weak strong converse and self duality theorems are proved for these programs

symmetric dual multiobjective programming abstract in this paper a pair of symmetric dual multiobjective programming problems is formulated and the duality theorems are established for pseudo convex pseudo concave functions

higher order symmetric duality in vector optimization problem involving generalized cone invex functions in this paper a pair of higher order symmetric dual model in vector optimization problem is formulated the higher order cone pseudoinvex and higher order strongly cone pseudoinvex functions are defined the weak strong and converse duality theorems are established using these defined functions

a nonterminating 8 φ 7 summation for the root system c r using multiple q integrals and a determinant evaluation we establish a nonterminating 8 7 summation for the root system cr we also give some important specializations explicitly

nondeterministic functions and the existence of optimal proof systems we provide new characterizations of two previously studied questions on nondeterministic function classes q1 do nondeterministic functions admit efficient deterministic refinements q2 do nondeterministic function classes contain complete functions we show that q1 for the class npmv t is equivalent to the question whether the standard proof system for sat is p optimal and to the assumption that every optimal proof system is p optimal assuming only the existence of a p optimal proof system for sat we show that every set with an optimal proof system has a p optimal proof system under the latter assumption we also obtain a positive answer to q2 for the class npmv t an alternative view on nondeterministic functions is provided by disjoint sets and tuples we pursue this approach for disjoint np pairs and its generalizations to tuples of sets from np and conp with disjointness conditions of varying strength in this way we obtain new characterizations of q2 for the class npsv question q1 for npsv is equivalent to the question of whether every disjoint np pair is easy to separate in addition we characterize this problem by the question of whether every propositional proof system has the effective interpolation property again these interpolation properties are intimately connected to disjoint np pairs and we show how different interpolation properties can be modeled by np pairs associated with the underlying proof system

minimax and symmetric duality for a class of multiobjective variational mixed integer programming problems abstract in this paper we formulate a pair of multiobjective variational mixed integer programs for arbitrary cones under the separability and partial invexity assumptions on the functions involved we establish the weak strong converse and self duality theorems related to efficient solution

infinite horizon backward stochastic differential equations and elliptic equations in hilbert spaces solutions of semilinear elliptic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations the backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition elliptic equations are intended in a mild sense suitable also for applications to optimal control we finally notice that due to the lack of smoothing properties the elliptic partial differential equation considered here could not be treated by analytic methods

prediction of strongly curved turbulent duct flows with reynolds stress model the effects of strong convex and concave curvature on turbulent duct flows are investigated a compressible navier stokes code incorporating reynolds stress models has been developed using a four stage runge kutta scheme numerical computations have been carried out for strongly curved 180 deg turnaround duct flows with a reynolds stress model an algebraic reynolds stress model and a nonlinear e model a detailed assessment of the models capability in predicting the effects of strong streamline curvature has been carried out the effect of curvature parameter r on the development of mean flow and turbulence has been examined by numerical simulations with the reynolds stress model

development of curvature sensitive nonlinear eddy viscosity model current widely used turbulence closures except the full second moment closure cannot properly account for the suppression of turbulence by convex curvature and the enhancing effect by concave curvature particularly the failure of the explicit algebraic stress model easm to capture the curvature strain effects in curved flows can be attributed to the equilibrium assumption embodied in easm thus the algebraic stress model asm approach is reexamined in the framework of a generalized curvilinear coordinate system in the approach the equilibrium assumption applies only to the gradient part of convective transport while the curvature related algebraic terms in the reynolds stress convection process are retained in this way a curvature sensitive asm is derived and is further transformed into an explicit nonlinear eddy viscosity model in an orthogonal coordinate system with this newly developed explicit asm to predict the curved flow in a two dimensional u duct it is observed that the turbulence suppression at the convex wall is successfully captured

pseudorandom functions and factoring the computational hardness of factoring integers is the most established assumption on which cryptographic primitives are based this work presents an efficient construction of pseudorandom functions whose security is based on the intractability of factoring in particular we are able to construct efficient length preserving pseudorandom functions where each evaluation requires only a small constant number of modular multiplications per output bit this is substantially more efficient than any previous construction of pseudorandom functions based on factoring and matches up to a constant factor the efficiency of the best known factoring based pseudorandom bit generators

double centralizing theorems for the alternating groups let v n be the n fold tensor product of a vector space v following i schur we consider the action of the symmetric group sn on v n by permuting coordinates in the super z2 graded case v v0 v1 a sign is added these actions give rise to the corresponding schur algebras s sn v here s sn v is compared with s an v the schur algebra corresponding to the alternating subgroup an sn while in the classical signless case these two schur algebras are the same for n large enough it is proved that in the super case where dim v0 dim v1 s an v is isomorphic to the cross product algebra s an v s sn v z2

minimax mixed integer symmetric duality for multiobjective variational problems abstract a mond weir type multiobjective variational mixed integer symmetric dual program over arbitrary cones is formulated applying the separability and generalized f convexity on the functions involved weak strong and converse duality theorems are established self duality theorem is proved a close relationship between these variational problems and static symmetric dual minimax mixed integer multiobjective programming problems is also presented

a simple unpredictable pseudo random number generator two closely related pseudo random sequence generators are presented the 1 p generator with input p a prime outputs the quotient digits obtained on dividing 1 by p the x 2 bmod n generato

coding the principal character formula for affine kac moody lie algebras in this paper an algorithm for computing the principal character for affine lie algebras is discussed and presented the principal characters discovered using this program are given and or proven results include level 2 and 3 character formulas in a2n 1 2 and the sole existence of the rogers ramanujan products in a1 1 a2 1 a2 2 c3 1 f4 1 g2 1 a7 2

modular invariant of quantum tori the quantum modular invariant j qt of 2r is defined as a discontin uous pgl2 z invariant multi valued map using the distance to the nearest integer function k k for 2 q it is shown that j qt 1 and for quadratic irrationalities pari gp experiments suggest that j qt is a finite set in the case of the golden mean we produce explicit formulas involving weighted versions of the rogers ramanujan functions for the experimental supremum and infimum we then define a universal modular invariant j a mod c as a continuous and single valued map of ultrasolenoids such that 1 the classical modular invariant is a quotient of the re striction of j to a subsolenoid mod cl a mod fibering over the classical moduli space of elliptic curves and 2 the quantum modular invariant is a quotient of the restric tion of j to a subsolenoid mod qt a mod fibering over the moduli space of elliptic curves equipped with a kronecker foliation

invariant measures and regularity properties of perturbed ornstein uhlenbeck semigroups abstract this paper deals with perturbations of the ornstein uhlenbeck operator on l 2 spaces with respect to a gaussian measure we perturb the generator of the ornstein uhlenbeck semigroup by a certain unbounded non linear drift and show various properties of the perturbed semigroup such as compactness and positivity strong feller property existence and uniqueness of an invariant measure are discussed as well

multiobjective nonlinear second order symmetric duality with k f pseudoconvexity abstract the purpose of this paper is to introduce a new class of generalized cone pseudoconvex functions and strongly cone pseudoconvex functions called second order k f pseudoconvex functions and strongly second order k f pseudoconvex functions a pair of second order symmetric dual multiobjective nonlinear programs is formulated over arbitrary generalized cone pseudoconvex functions for these second order symmetric dual programs the weak strong and converse duality theorems are established using the above generalization of cone pseudoconvex functions a self duality theorem is also given by assuming the functions involved to be skew symmetric

symmetric duality for minimax mixed integer programming problems with pseudo invexity in this paper we consider the pair of symmetric dual multiobjective variational mixed integer programs proposed by chen and yang x chen j yang symmetric duality for minimax multiobjective variational mixed integer programming problems with partial invexity european journal of operational research 181 2007 76 85 and extend some of their results under the assumptions of partial pseudo invexity and separability on the functions involved these results include several results available in literature as special cases

multiobjective second order symmetric duality with f convexity we suggest a pair of second order symmetric dual programs in multiobjective nonlinear programming for these second order symmetric dual programs we prove the weak strong and converse duality theorems under f convexity conditions

on second order symmetric duality in nondifferentiable programming this article is concerned with a pair of second order symmetric dual non differentiable programs and second order f pseudo convexity we establish the weak and the strong duality theorems for the new pair of dual models under the f pseudo convexity assumption several known results including mond and schechter as well as others are obtained as special cases

lattices on simplicial partitions which are not simply connected in this paper d 1 pencil lattices on simplicial partitions in r d which are not simply connected are studied it is shown how the fact that a partition is not simply connected can be used to increase the flexibility of a lattice a local modification algorithm is developed also to deal with slight partition topology changes that may appear afterwards a lattice has already been constructed

multiobjective mixed symmetric duality involving cones a pair of multiobjective mixed symmetric dual programs is formulated over arbitrary cones weak strong converse and self duality theorems are proved for these programs under k preinvexity and k pseudoinvexity assumptions this mixed symmetric dual formulation unifies the symmetric dual formulations of suneja et al 2002 14 and khurana 2005 15

second order symmetric duality for nonlinear multiobjective mixed integer programming we formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones by using the concepts of efficiency and second order invexity we establish weak strong converse and self duality theorems for the dual models several known results are obtained as special cases

symmetric duality in multiobjective programming involving generalized cone invex functions abstract in this paper cone pseudoinvex and strongly cone pseudoinvex functions are defined a pair of mond weir type symmetric dual multiobjective programs is formulated over arbitrary cones weak duality strong duality and converse duality theorems are established using the above defined functions a self duality theorem is also given by assuming the functions involved to be skew symmetric

a note on pseudo invexity and symmetric duality a pair of symmetric dual nonlinear programming problems is presented and duality theorems are established under pseudoinvexity type assumptions on the kernel function this formulation removes certain inconsistencies in a recently introduced primal dual pair and gives the correct proof of various duality theorems

understanding cutting planes for qbfs abstract we study the cutting planes system cp red for quantified boolean formulas qbf obtained by augmenting propositional cutting planes with a universal reduction rule and analyse the proof theoretic strength of this new calculus while in the propositional case cutting planes is of intermediate strength between resolution and frege our findings here show that the situation in qbf is slightly more complex while cp red is again weaker than qbf frege and stronger than the cdcl based qbf resolution systems q res and qu res it turns out to be incomparable to even the weakest expansion based qbf resolution system exp res a similar picture holds for a semantic version semcp red technically our results establish the effectiveness of two lower bound techniques for cp red via strategy extraction and via monotone feasible interpolation

pseudo invexity and duality in nonlinear programming abstract the purpose of this paper is to study various duality results in nonlinear programming for pseudo invex functions such results were known in the literature for invex functions

generation of localization in a discrete chain with periodic boundary conditions numerical and analytical results we study the generation of localization in a discrete chain composed of n subsystems and periodic boundary conditions strongly localized motions are studied that is time periodic motions where nearly all of the energy is spatially confined to a single subsystem for varying n numerical results indicate that the strongly localized solutions are generated through a bifurcation from an in phase spatially extended solution however in the limit as n rightarrow infty the bifurcation point tends to infinity and a smooth transition from localization to nonlocalization occurs we then present an analytic technique to complement the numerical results it is based on the matching local asymptotic expansions of a solution branch using pade approximants this leads to global analytic representations of the considered solutions valid over the entire range of the control parameter

minimax and symmetric duality for nonlinear multiobjective mixed integer programming abstract we formulate two pairs of symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones by using the concept of efficiency we establish the weak strong converse and self duality theorems for our symmetric models several known results are obtained as special cases

properties of the x sup 2 mod n pseudorandom number generator in 1986 l blum r i blum and m shub introduced the x sup 2 mod n generator of pseudorandom bit strings and showed given certain plausible but unproved hypotheses that it has the desirable cryptographic property of unpredictability they also studied the period length of the sequences produced by this generator and proposed a way to guarantee that these sequences will have maximum possible period in this correspondence we prove that it is very likely that for many values of n the sequences produced by the x sup 2 mod n generator are usually not balanced that is having equal frequency of 0 s and 1 s we further prove that the proposed method for guaranteeing long periods is also very likely to guarantee relatively large imbalances between the frequencies of 0 s and 1 s however we also prove that the average imbalance for these sequences is no worse than what would be expected in a truly random bit string of the same length thus our results provide further support for the use of the x sup 2 mod n generator in cryptographic applications

converse duality in nonlinear programming with cone constraints abstract the purpose of this paper is to establish various converse duality results for nonlinear programming with cone constraints and its four dual models introduced by chandra and abha s chandra abha a note on pseudo invex and duality in nonlinear programming european journal of operational research 122 2000 161 165

symmetric duality for multiobjective fractional variational problems involving cones in this paper a pair of multiobjective fractional variational symmetric dual problems over cones is formulated weak strong and converse duality theorems are established under generalized f convexity assumptions moreover self duality theorem is also discussed

non differentiable symmetric duality for multiobjective programming with cone constraints abstract two pairs of non differentiable multiobjective symmetric dual problems with cone constraints over arbitrary cones which are wolfe type and mond weir type are considered on the basis of weak efficiency with respect to a convex cone we obtain symmetric duality results for the two pairs of problems under cone invexity and cone pseudoinvexity assumptions on the involved functions our results extend the results in khurana s khurana symmetric duality in multiobjective programming involving generalized cone invex functions european journal of operational research 165 2005 592 597 to the non differentiable multiobjective symmetric dual problem

pseudo invexity and symmetric duality in nonlinear fractional programming abstract the purpose of this paper is to study the symmetric dual fractional programming problem for pseudo invex functions and arbitrary cones several known results are obtained as special cases

new combinatorial interpretations of ramanujan s partition congruences mod 5 7 and 11 soit p n le nombre de partitions non restreintes de n on donne de nouvelles interpretations combinatoires des congruences p 5n 4 p 7n 5 et p 11n 6 0 mod 5 7 et 11 respectivement

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

on the automatizability of resolution and related propositional proof systems a propositional proof system is automatizable if there is an algorithm that given a tautology produces a proof in time polynomial in the size of its smallest proof this notion can be weakened if we allow the algorithm to produce a proof in a stronger system within the same time bound this new notion is called weak automatizability among other characterizations we prove that a system is weakly automatizable exactly when a weak form of the satisfiability problem is solvable in polynomial time after studying the robustness of the definition we prove the equivalence between i resolution is weakly automatizable ii res k is weakly automatizable and iii res k has feasible interpolation when k 1 in order to prove this result we show that res 2 has polynomial size proofs of the reflection principle of resolution which is a version of consistency we also show that res k for every k 1 proves its consistency in polynomial size while resolution does not in fact we show that resolution proofs of its own consistency require almost exponential size this gives a better lower bound for the monotone interpolation of res 2 and a separation from resolution as a byproduct our techniques also give us a way to obtain a large class of examples that have small resolution refutations but require relatively large width this answers a question of alekhnovich and razborov related to whether resolution is automatizable in quasipolynomial time

non differentiable second order symmetric duality in mathematical programming with f convexity abstract a pair of wolfe type non differentiable second order symmetric primal and dual problems in mathematical programming is formulated the weak and strong duality theorems are then established under second order f convexity assumptions symmetric minimax mixed integer primal and dual problems are also investigated

how to generate cryptographically strong sequences of pseudo random bits we give a set of conditions that allow one to generate 50 50 unpredictable bits based on those conditions we present a general algorithmic scheme for constructing polynomial time deterministic algorithms that stretch a short secret random input into a long sequence of unpredictable pseudo random bits we give an implementation of our scheme and exhibit a pseudo random bit generator for which any efficient strategy for predicting the next output bit with better than 50 50 chance is easily transformable to an equally efficient algorithm for solving the discrete logarithm problem in particular if the discrete logarithm problem cannot be solved in probabilistic polynomial time no probabilistic polynomial time algorithm can guess the next output bit better than by flipping a coin if head guess 0 if tail guess 1

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

mond weir type second order symmetric duality in non differentiable minimax mixed integer programming problems abstract a pair of mond weir type non differentiable second order symmetric minimax mixed integer primal and dual problems in mathematical programming is formulated symmetric and self duality theorems are then established under second order f pseudo convexity assumptions several known results including that of gulati and ahmad eur j oper res 101 1997 122 hou and yang j math anal appl 255 2001 491 and mond and schechter bull aust math soc 53 1996 177 as well as others are obtained as special cases

frege systems for quantified boolean logic we define and investigate frege systems for quantified boolean formulas qbf for these new proof systems we develop a lower bound technique that directly lifts circuit lower bounds for a circuit class c to the qbf frege system operating with lines from c such a direct transfer from circuit to proof complexity lower bounds has often been postulated for propositional systems but had not been formally established in such generality for any proof systems prior to this work this leads to strong lower bounds for restricted versions of qbf frege in particular an exponential lower bound for qbf frege systems operating with ac0 p circuits in contrast any non trivial lower bound for propositional ac0 p frege constitutes a major open problem improving these lower bounds to unrestricted qbf frege tightly corresponds to the major problems in circuit complexity and propositional proof complexity in particular proving a lower bound for qbf frege systems operating with arbitrary p poly circuits is equivalent to either showing a lower bound for p poly or for propositional extended frege which operates with p poly circuits we also compare our new qbf frege systems to standard sequent calculi for qbf and establish a correspondence to intuitionistic bounded arithmetic

circuit principles and weak pigeonhole variants this paper considers the relational versions of the surjective partial surjective and multifunction weak pigeonhole principles for pv 1 b 1 b and b 1 b formulas as well as relativizations of these formulas to higher levels of the bounded arithmetic hierarchy we show that the partial surjective weak pigeonhole principle for 1 b formulas implies that for each k there is a string of length 2 2 n k which is hard to block recognize by circuits of size n k these principles in turn imply the partial surjective principle for 1 b formulas we show that the surjective weak pigeonhole principle for b 1 b formulas in s 2 1 implies our hard string principle which in turn implies the surjective weak pigeonhole principle for 1 b formulas we introduce a class of predicates corresponding to poly log length iterates of polynomial time computable predicates and show that over s 2 1 the multifunction weak pigeonhole principle for such predicates is equivalent to an iterative circuit block recognition principle a consequence of this is that if s 2 1 proves this principle then rsa is vulnerable to polynomial time attacks

mean payoff games and propositional proofs we associate a cnf formula to every instance of the mean payoff game problem in such a way that if the value of the game is non negative the formula is satisfiable and if the value of the game is negative the formula has a polynomial size refutation in s 2 frege i e dnf resolution this reduces mean payoff games to the weak automatizability of s 2 frege and to the interpolation problem for s 2 2 frege since the interpolation problem for s 1 frege i e resolution is solvable in polynomial time our result is close to optimal up to the computational complexity of solving mean payoff games the proof of the main result requires building low depth formulas that compute the bits of the sum of a constant number of integers in binary notation and low complexity proofs of the required arithmetic properties

turbulence model predictions of strongly curved flow in a u duct the ability of three types of turbulence models to accurately predict the effects of curvature on the flow in a u duct is studied an explicit algebraic stress model performs slightly better than one or two equation linear eddy viscosity models although it is necessary to fully account for the variation of the production to dissipation rate ratio in the algebraic stress model formulation in their original formulations none of these turbulence models fully captures the suppressed turbulence near the convex wall whereas a full reynolds stress model does some of the underlying assumptions used in the development of algebraic stress models are investigated and compared with the computed flowfield from the full reynolds stress model through this analysis the assumption of reynolds stress anisotropy equilibrium used in the algebraic stress model formulation is found to be incorrect in regions of strong curvature by the accounting for the local variation of the principal axes of the strain rate tensor the explicit algebraic stress model correctly predicts the suppressed turbulence in the outer part of the boundary layer near the convex wall

some inequalities for the q beta and the q gamma functions via some q integral inequalities some new inequalities for the q gamma the q beta and the q analogue of the psi functions are established via some q integral inequalities

fragments of bounded arithmetic and bounded query classes we characterize functions and predicates i 1 b definable in s 2 i in particular predicates i 1 b definable in s 2 i are precisely those in bounded query class p ip o log n which equals to log space ip by b h w this implies that s 2 i t 2 i unless p ip o log n i 1 p further we construct oracle a such that for all i 1 p ip o log n i 1 p a it follows that s 2 i t 2 i for all i 1 techniques used come from proof theory and boolean complexity

technical note on symmetric duality in multiobjective programming some remarks on recent results abstract certain shortcomings are pointed out in some recent works of das and nanda european journal of operational research 97 1997 167 171 and kim et al european journal of operational research 107 1998 686 691 which show that these studies are highly restricted

symmetric duality for minimax nonlinear mixed integer programming abstract a pair of symmetric dual minimax integer programming problems is formulated and an appropriate duality theorem is established under the pseudoconvexity pseudoconcavity assumption on the kernel function k x y this model removes certain inconsistencies in an earlier model and helps to study self duality as well

pseudorandom generators hard for k dnf resolution and polynomial calculus resolution a pseudorandom generator gn f0 1g n f0 1g m is hard for a propositional proof system p if roughly speaking p cannot eciently

the security of all rsa and discrete log bits we study the security of individual bits in an rsa encrypted message en x we show that given en x predicting any single bit in x with only a nonnegligible advantage over the trivial guessing strategy is through a polynomial time reduction as hard as breaking rsa moreover we prove that blocks of o log log n bits of x are computationally indistinguishable from random bits the results carry over to the rabin encryption scheme considering the discrete exponentiation function gx modulo p with probability 1 o 1 over random choices of the prime p the analog results are demonstrated the results do not rely on group representation and therefore applies to general cyclic groups as well finally we prove that the bits of ax b modulo p give hard core predicates for any one way function f all our results follow from a general result on the chosen multiplier hidden number problem given an integer n and access to an algorithm px that on input a random a i zn returns a guess of the ith bit of ax mod n recover x we show that for any i if px has at least a nonnegligible advantage in predicting the ith bit we either recover x or obtain a nontrivial factor of n in polynomial time the result also extends to prove the results about simultaneous security of blocks of o log log n bits

multiobjective symmetric duality with cone constraints we formulate a pair of multiobjective symmetric dual programs for pseudo invex functions and arbitrary cones our model is unifying the wolfe vector symmetric dual and the mond weir vector symmetric dual models we establish the weak strong converse and self duality theorems for our pair of dual models nanda and das results optimization 28 1994 267 eur j oper res 88 1996 572 are obtained as special cases

a pseudorandom generator from any one way function pseudorandom generators are fundamental to many theoretical and applied aspects of computing we show how to construct a pseudorandom generator from any one way function since it is easy to construct a one way function from a pseudorandom generator this result shows that there is a pseudorandom generator if and only if there is a one way function

the x ray transform and its inversion for the series expansion basis functions in three dimensional tomography a formula for the three dimensional x ray transform and an expression for its inversion have been derived the spherical harmonics and the rotation matrices in terms of euler angles are used in the generalized fourier series expansion some properties of the transformed fourier components are discussed

mixed symmetric duality in non differentiable multiobjective mathematical programming two mixed symmetric dual models for a class of non differentiable multiobjective nonlinear programming problems with multiple arguments are introduced in this paper these two mixed symmetric dual models unify the four existing multiobjective symmetric dual models in the literature weak and strong duality theorems are established for these models under some mild assumptions of generalized convexity several special cases are also obtained

symmetric and self duality in vector optimization problem abstract in this paper we present the first order symmetric and self duality programs in multiobjective nonlinear programming problems for these first order symmetric and dual programs we introduce the weak strong and converse duality theorems under convexity and concavity conditions where the pair of the symmetric dual multiobjective nonlinear programming problems in this paper different which in d s kim y b yun h kuk second order symmetric and self duality in multiobjective programming appl math lett 10 2 1997 17 22 also we prove the self duality theorem for these first order self dual programs and illustrate its example

automating resolution is np hard we show that the problem of finding a resolution refutation that is at most polynomially longer than a shortest one is np hard in the parlance of proof complexity resolution is not automatable unless p np indeed we show that it is np hard to distinguish between formulas that have resolution refutations of polynomial length and those that do not have subexponential length refutations this also implies that resolution is not automatable in subexponential time or quasi polynomial time unless np is included in subexp or qp respectively

an improved sectional anosov closing lemma we prove that all nonwandering points of a sectional anosov flow on a compact 3 manifold can be approximated by periodic points or by points for which the omega limit set is a singularity this improves the closing lemma in morales mich math j 56 1 29 53 2008 we also describe a sectional anosov flow for which the recurrent points are not dense in the nonwandering set

on interpolation and automatization for frege systems the interpolation method has been one of the main tools for proving lower bounds for propositional proof systems loosely speaking if one can prove that a particular proof system has the feasible interpolation property then a generic reduction can usually be applied to prove lower bounds for the proof system sometimes assuming a usually modest complexity theoretic assumption in this paper we show that this method cannot be used to obtain lower bounds for frege systems or even for tc0 frege systems more specifically we show that unless factoring of blum integers is feasible neither frege nor tc0 frege has the feasible interpolation property in order to carry out our argument we show how to carry out proofs of many elementary axioms theorems of arithmetic in polynomial sized tc0 frege as a corollary we obtain that tc0 frege as well as any proof system that polynomially simulates it is not automatizable under the assumption that factoring of blum integers is hard we also show under the same hardness assumption that the k provability problem for frege systems is hard

optimality criteria in nonlinear programming involving nonconvex functions abstract in this paper a new class of functions called convex quasiconvex and pseudoconvex are defined and a number of sufficient optimality criteria are obtained for nonlinear programming problems involving these functions

rsa and rabin functions certain parts are as hard as the whole the rsa and rabin encryption functions e n cdot are respectively defined by raising x in z n to the power e where e is relatively prime to varphi n and squaring modulo n i e e n x x e bmod n e n x x 2 bmod n respectively we prove that for both functions the following problems are computationally equivalent each is probabilistic polynomial time reducible to the other 1 given e n x find x 2 given e n x guess the least significant bit of x with success probability tfrac 1 2 1 operatorname poly n where n is the length of the modulus n this equivalence implies that an adversary given the rsa rabin ciphertext cannot have a non negligible advantage over a random coin flip in guessing the least significant bit of the plaintext unless he can invert rsa factor n the proof techniques also yield the simultaneous security of the log n least significant bits our results improve the efficiency of pseudorandom number generation and

n point pade approximants to real valued stieltjes series with nonzero radii of convergence abstract by employing special continued fractions to two stieltjes series with nonzero radii of convergence we extend the inequalities for one point pade approximants reported by baker 1975 corollory 17 1 to the case of two point pade approximants we prove that some convergents of the continued fractions form a monotone sequences of upper and lower bounds converging uniformly to stieltjes function x1 x on compact subsets of r where r is a radius of convergence of an expansion of x f1 x at x 0 for an illustration of theoretical results we provide nontrivial numerical examples as an application to real physical problems second order pade approximants bounds on the effective conductivity of a square array of cylinders are evaluated

on the complexity of resolution with bounded conjunctions we analyze size and space complexity of res k a family of propositional proof systems introduced by krajicek in fund math 170 1 3 2001 123 which extend resolution by allowing disjunctions of conjunctions of up to k 1 literals we show that the treelike res k proof systems form a strict hierarchy with respect to proof size and also with respect to space moreover resolution while simulating treelike res k is almost exponentially separated from treelike res k to study space complexity for general res k we introduce the concept of dynamical satisfiability which allows us to prove in a unified way all known space lower bounds for resolution and to extend them to res k

a note on pseudo invexity and duality in nonlinear programming abstract certain shortcomings are pointed out in the recent work of s nanda l n das european journal of operational research 88 1996 572 577 and appropriate modifications are suggested for studying duality under pseudo invexity assumptions

analysis of streamline curvature effects on wall bounded turbulent flows we deal with numerical analysis for the effects of surface curvature particularly the concave curvature on turbulent duct flows and boundary layers a compressible navier stokes code incorporating reynolds stress models has been developed using a four stage runge kutta scheme numerical computations have been carried out for curved flows in 180 deg and 90 deg turning ducts and a turbulent boundary layer using reynolds stress models with without modifications to the dissipation rate e equation various modifications to the e equation are discussed a quantitative relationship has been established between two seemingly different modifications to the e equation it is observed that the modeling of concave curvature effect is qualitatively different from the modeling of convex curvature effect detailed comparisons between computations and data indicate that to capture the strong amplification of turbulence near a concave wall the standard e equation needs to be modified

on modular homology in the boolean algebra iii abstract let be a set ra ring of characteristicp 0 and denote bymkther module withk element subsets of as basis theset inclusion map mk mk 1is the homomorphism which associates to ak element subset the sum 1 2 kof all its k 1 element subsets i in this paper we study the chain formula arising from we introduce the notion ofp exactness for a sequence if is infinite we show that isp exact for all prime characteristicsp 0 this result can be extended to various submodules and quotient modules and we give general constructions arising from permutation groups with a finitary section two particular applications are the following the orbit module sequence of such a permutation group on isp exact for every primep and we give a formula for thep rank of the orbit inclusion matrix if the group has finitely many orbits onk element subsets

exponents of nonnegative matrix pairs the notions of primitivity and exponent of a square nonnegative matrix a are classical a is primitive provided there is a nonnegative integer k such that a k is entrywise positive and in the case a is primitive the exponent of a is the smallest such k fornasini and valcher have extended the notion of primitivity to pairs a b of square nonnegative matrices of the same order the pair a b is primitive provided there exist nonnegative integers h and k such that the sum of all products formed by words consisting of ha s and kb s is entrywise positive this paper defines the exponent of a nonnegative matrix pair to be the smallest value of h k over all such h and k it is then shown that the largest exponent of a primitive pair of n by n nonnegative matrices lies in the interval n 3 5n 2 2 3n 3 2n 2 2n 2 in addition the exponent of a pair of nonnegative matrices is related to properties of an associated twodimensional dynamical system 2001 elsevier science inc all rights reserved