gevrey regularity of solutions to the non cutoff homogeneous boltzmann equation for soft potential with strong singularity abstract in this study we analyze the cauchy problem for the non cutoff homogeneous boltzmann equation with strong singularity in contrast to our previous work lin 2014 8 the present study considers the soft potential case and derives the gevrey regularity of the c solutions

interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

successive approximations of linear control models we present a technique for approximating sequences of linear programs with varying right hand sides and study the geometric properties of this approximation our approximation has an efficiency advantage over optimal solutions when applied to deterministic control problems the suggested technique outperforms the linear feedback model and provides accurate results error of 5 8 in our numerical example numerical experience with stochastic models indicates that this approach may outperform the limited lookahead policies while maintaining low computational requirements

smoothing estimates for boltzmann equation with full range interactions spatially homogeneous case in this work we are concerned with the regularities of the solutions to the boltzmann equation with physical collision kernels for the full range of intermolecular repulsive potentials r p 1 with p 2 we give new and constructive upper and lower bounds for the collision operator in terms of standard weighted fractional sobolev norms as an application we get the global entropy dissipation estimate which is a little stronger than that described by alexandre et al arch rational mech anal 152 4 327 355 2000 as another application we prove the smoothing effects for the strong solutions constructed by desvillettes and mouhot arch rational mech anal 193 2 227 253 2009 of the spatially homogeneous boltzmann equation with true hard potential and true moderately soft potential

satisfiability in many valued sentential logic is np complete abstract cook s np completeness theorem is extended to all many valued sentential logics including the infinite valued calculus of ukasiewicz

computing bounds for stochastic programming problems by means of a generalized moment problem bounds on the expected value of a convex function are obtained by means of an approximating generalized moment problem numerical implementation is discussed in the context of stochastic programming problems

null controllability of linear systems with constrained controls the paper considers the problem of steering the state of a linear time varying system to the origin when the control is subject to magnitude constraints necessary and sufficient conditions are given for global constrained controllability as well as a necessary and sufficient condition for the existence of a control satisfying the constraints which steers the system to the origin from a specified initial epoch x 0 t 0 the global result does not require zero to be an interior point of the control set omega and the theorem for constrained controllability at x 0 t 0 only requires that omega be compact not that it contain zero the results are compared to those available in the literature furthermore numerical aspects of the problem are discussed as is a technique for determining a steering control

ultra analytic effect of cauchy problem for a class of kinetic equations abstract the smoothing effect of the cauchy problem for a class of kinetic equations is studied we firstly consider the spatially homogeneous nonlinear landau equation with maxwellian molecules and inhomogeneous linear fokker planck equation to show the ultra analytic effects of the cauchy problem those smoothing effect results are optimal and similar to heat equation in the second part we study a model of spatially inhomogeneous linear landau equation with maxwellian molecules and show the analytic effect of the cauchy problem

gevrey regularity of spatially homogeneous boltzmann equation without cutoff abstract in this paper we study the gevrey regularity of spatially homogeneous boltzmann equation without angular cutoff we prove the propagation of gevrey regularity for c solutions with the maxwellian decay to the cauchy problem of spatially homogeneous boltzmann equation the idea we use here is based on the framework of morimoto ukai s recent paper see y morimoto s ukai gevrey smoothing effect of solutions for spatially homogeneous nonlinear boltzmann equation without angular cutoff j pseudo differ oper appl 1 2010 139 159 but we extend the range of the index satisfying 2 s 1 1 s 0 1 2 and in this case we consider the kinetic factor in the form of v v instead of v as morimoto and ukai did before

constrained max min controllability the max min controllability concept of heymann pachter and stern 1 is examined for a more general class of problems both strong and weak max min controllability are characterized it is shown that when magnitude constraints on the control are present the two max min controllability concepts are not the same this differs from the result for problems without control magnitude constraints where it has been shown that the two controllability concepts are identical

simple bratteli diagrams with a godel incomplete c equivalence problem an abstract simplicial complex is a finite family of subsets of a finite set closed under subsets every abstract simplicial complex c naturally determines a bratteli diagram and a stable af algebra a c consider the following problem input a pair of abstract simplicial complexes c and c question is a c isomorphic to a c we show that this problem is godel incomplete i e it is recursively enumerable but not decidable this result is in sharp contrast with the recent decidability result by bratteli jorgensen kim and roush for the isomorphism problem of stable af algebras arising from the iteration of the same positive integer matrix for the proof we use a combinatorial variant of the de concini procesi theorem for toric varieties together with the baker beynon duality theory for lattice ordered abelian groups markov s undecidability result and elliott s classification theory for af algebras

a piecewise linear upper bound on the network recourse function we consider the optimal value of a pure minimum cost network flow problem as a function of supply demand and arc capacities we present a new piecewise linear upper bound on this function which is called the network recourse function the bound is compared to the standard madansky bound and is shown computationally to be a little weaker but much faster to find the amount of work is linear in the number of stochastic variables not exponential as is the case for the madansky bound therefore the reduction in work increases as the number of stochastic variables increases computational results are presented

on the refutational completeness of signed binary resolution and hyperresolution signed binary resolution and hyperresolution belong to the basic resolution proof methods both the resolution methods are refutation sound and under some finitary restrictions refutation complete our aim is to investigate their refutational completeness in a more general case we shall assume that clausal theories may be countable sets and the set of truth values an arbitrary one there are unsatisfiable countable clausal theories for which there do not exist refutations by signed binary resolution and hyperresolution we propose a criterion on the existence of a refutation of an unsatisfiable countable clausal theory by the investigated resolution methods two important applications of the achieved results to automated deduction in signed logic herbrand s theorem and a signed davis putnam logemann loveland dpll procedure will be discussed

gevrey hypoellipticity for linear and non linear fokker planck equations abstract this paper studies the gevrey regularity of weak solutions of a class of linear and semi linear fokker planck equations

lazy evaluations in łukasiewicz type fuzzy logic abstract lazy evaluations are playing important roles in various fields of computer science including hardware design programming decision making in this paper one of the most known and used fuzzy logic system the ukasiewicz logic is considered pruning algorithms are presented to quicken the evaluations of logical formulae in ukasiewicz logic by cutting out those branches of the formula tree that have no influence on the final result for some reasons correctness of the algorithm is also proven

mapping abelian l groups with strong unit one one into mv algebras abstract we exhibit a functor from lattice ordered abelian groups with strong unit l fuchs partially ordered algebraic systems pergamon new york 1963 to c c chang s mv algebras trans amer math soc 88 1958 467 490 in such a way that every mv algebra is the image of at most one such group

mniblos a smt based solver for continuous t norm based logics and some of their modal expansions in the literature little attention has been paid to the development of solvers for systems of mathematical fuzzy logic and in particular there are few works concerned with infinitely valued logics in this paper it is presented mniblos a modal nice bl logics solver a modular smt based solver complete with respect to a wide family of continuous t norm based fuzzy modal logics both with finite and infinite universes restricting the modal structures to the finite ones at the propositional level the solver works with some of the best known infinitely valued fuzzy logics including bl ukasiewicz godel and product logics and with all the continuous t norm based logics that can be finitely expressed in terms of the previous ones concerning the modal expansion mniblos imposes no boundary on the cardinality of the modal structures considered the solver allows to test 1 satisfiability of equations tautologicity and logical consequence problems the logical language supported extends the usual one of fuzzy modal logics with rational constants and the monteiro baaz operator the code of mniblos is of free distribution and can be found in the web page of the author

resolution and model building in the infinite valued calculus of lukasiewicz abstract we discuss resolution and its complexity in the infinite valued sentential calculus of l ukasiewicz with special emphasis on model building algorithms for satisfiable sets of clauses we prove that resolution and model building are polynomially tractable in the fragments given by horn clauses and by krom clauses i e clauses with at most two literals generalizing the pre existing literature on resolution in infinite valued logic by a positive literal we mean a negationless formula in one variable built only from the connectives we prove that the expressive power of our literals encompasses all monotone mcnaughton functions of one variable

the boltzmann equation without angular cutoff in the whole space qualitative properties of solutions this is a continuation of our series of works for the inhomogeneous boltzmann equation we study qualitative properties of classical solutions the full regularization in all variables uniqueness non negativity and convergence rate to the equilibrium to be precise together with the results of parts i and ii about the well posedness of the cauchy problem around the maxwellian we conclude this series with a satisfactory mathematical theory for the boltzmann equation without angular cutoff

on the mathematical foundations of nondifferentiable optimization in engineering design it is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions such problems are commonly referred to as semi infinite optimization problems the bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms related to phase i phase ii methods of feasible directions which solve these semi infinite optimization problems the applicability of the theory is illustrated with examples that are relevant to engineering design

boole bonferroni inequalities and linear programming we present a method to obtain sharp lower and upper bounds for the probability that at least one out of a number of events in an arbitrary probability space will occur the input data are some of the binomial moments of the occurrences such as the sum of the probabilities of the individual events or the sum of the joint probabilities of all pairs of events we develop a special very simple linear programming algorithm to obtain these bounds the method allows us to compute good bounds in an optimal way utilizing only the first few terms in the inclusion exclusion formula possible applications include obtaining bounds for the reliability of a stochastic system solving algorithmically some stochastic programming problems and approximating multivariate probabilities in statistics in a numerical example we approximate the probability that a gaussian process runs below a given level in a number of consecutive epochs

the consequence relation in the logic of commutative gbl algebras is pspace complete commutative integral and bounded gbl algebras form a subvariety of residuated lattices which provides the algebraic semantics of an interesting common fragment of intuitionistic logic and of several fuzzy logics it is known that both the equational theory and the quasiequational theory of commutative gbl algebras are decidable in contrast to the noncommutative case but their complexity has not been studied yet in this paper we prove that both theories are in pspace and that the quasiequational theory is pspace hard

controllability results for systems with a nonconvex target this paper considers the problem of steering the state x t of the system dot x t a t x t f t u t to a prescribed target x the input u t is restricted to lie in a prespecified set which is assumed compact unlike the results of previous authors we allow x to be any set and do not require x to be convex or closed necessary conditions and sufficient conditions for the existence of a control which steers the system to the target from a specified initial condition are given conditions for global controllability to the target are also derived an additional concept of controllability that we investigate is that of complete controllability complete controllability is concerned with the ability to steer the system from any initial point to any final point one of the most important results of this paper is that we develop a technique for constructing a steering control previous work on the constrained controllability problem has dealt with methods for determining a steering control in only a limited way finally numerical techniques for checking controllability and for constructing a steering control are described and the results obtained from the application of our algorithm to several examples are presented

on the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent s rational beliefs on gradable propositions it has recently been shown that in the same way as autoepistemic logic generalizes answer set programming fuzzy autoepistemic logic generalizes fuzzy answer set programming as well besides being related to answer set programming autoepistemic logic is also closely related to several modal logics to investigate whether a similar relationship holds in a fuzzy logical setting we firstly generalize the main modal logics for belief to the setting of finitely valued ukasiewicz logic with truth constants k c and secondly we relate them with fuzzy autoepistemic logics moreover we show that the problem of satisfiability checking in these logics is np complete finally we generalize levesque s results on stable expansions belief sets and only knowing operators to our setting and provide a complete axiomatization for a logic of only knowing in the k c framework

the complexity of propositional linear temporal logics the complexity of satisfiability and determination of truth in a particular finite structure are considered for different propositional linear temporal logics it is shown that these problems are np complete for the logic with f and are pspace complete for the logics with f x with u with u s x operators and for the extended logic with regular operators given by wolper

constrained controllability of discrete time systems the constrained controllability of the discrete time system xk 1 a k xk b k u k is considered where the control uk is termed admissible if it satisfies specified magnitude constraints constrained controllability is concerned with the existence of an admissible control which steers the state x to a given target set from a specified initial state conditions for checking constrained controllability to a given target set from a specified initial state are presented these conditions involve solving finite dimensional optimization problems and can be checked via numerical computation in addition conditions for checking global constrained controllability to a given target set are presented a system is globally constrained controllable if for every initial state there exists an admissible control that steers the system to the target if a given discrete time system is constrained controllable it may be desirable to obtain an admissible control that steers the system to the target from a specified initial s

making fuzzy description logic more general a version of fuzzy description logic based on the basic continuous t norm based fuzzy predicate logic bl is presented problems of satisfiability validity and subsumption of concepts are discussed and reduced to problems of fuzzy propositional logic known to be decidable for any continuous t norm for lukasiewicz t norm some stronger results are obtained

restricted recourse bounds for stochastic linear programming we consider the problem of bounding the expected value of a linear program lp containing random coefficients with applications to solving two stage stochastic programs an upper bound for minimizations is derived from a restriction of an equivalent penalty based formulation of the primal stochastic lp and a lower bound is obtained from a restriction of a reformulation of the dual our restricted recourse bounds are more general and more easily computed than most other bounds because random coefficients may appear anywhere in the lp neither independence nor boundedness of the coefficients is needed and the bound is computed by solving a single lp or nonlinear program analytical examples demonstrate that the new bounds can be stronger than complementary jensen bounds an upper bound is complementary to a lower bound and vice versa in computational work we apply the bounds to a two stage stochastic program for semiconductor manufacturing with uncertain demand and production rates

term satisfiability in flew algebras fl ew algebras form the algebraic semantics of the full lambek calculus with exchange and weakening we investigate two relations called satisfiability and positive satisfiability between fl ew terms and fl ew algebras for each fl ew algebra the sets of its satisfiable and positively satisfiable terms can be viewed as fragments of its existential theory we identify and investigate the complements as fragments of its universal theory we offer characterizations of those algebras that positively satisfy just those terms that are satisfiable in the two element boolean algebra providing its semantics to classical propositional logic in case of positive satisfiability these algebras are just the nontrivial weakly contractive fl ew algebras in case of satisfiability we give a characterization by means of another property of the algebra the existence of a two element congruence further we argue that positive satisfiability problems in fl ew algebras are computationally hard some previous results in the area of term satisfiability in mv algebras or bl algebras are thus brought to a common footing with known facts on satisfiability in heyting algebras

sublinear upper bounds for stochastic programs with recourse separable sublinear functions are used to provide upper bounds on the recourse function of a stochastic program the resulting problem s objective involves the inf convolution of convex functions a dual of this problem is formulated to obtain an implementable procedure to calculate the bound function evaluations for the resulting convex program only require a small number of single integrations in contrast with previous upper bounds that require a number of function evaluations that grows exponentially in the number of random variables the sublinear bound can often be used when other suggested upper bounds are intractable computational results indicate that the sublinear approximation provides good efficient bounds on the stochastic program objective value