ℋ index for continuous time stochastic systems with markov jump and multiplicative noise this paper investigates the problem of index for stochastic linear continuous time systems involving markov jump and multiplicative noise a set of generalized differential riccati equations gdres are presented and it is shown that the solvability of gdres is necessary and sufficient for the feasibility of an index larger than 0 our results extend the corresponding deterministic cases to stochastic systems furthermore the infinite horizon index problem for square systems is considered finally the effectiveness of the obtained results is tested by two examples

rearrangements of functions let g be measurable non negative functions on r and let tf be their equimeasurable symmetric decreasing rearrangements let f r r r be continuous and suppose that the associated rectangle function defined by f r f a c f b d f a d f b c for r x y r2 a x b c y d is non negative then f g d f tf g d where is lebesgue measure the concept of equimeasurable rearrangement is also defined for functions on a more general class of measure spaces and the inequality holds in the general case if f x y x y where is convex and 0 0 then we obtain tf g d g d in particular if x x p 1 p then we find that the operator s tf is a contraction on lp for 1 p

a variational approach to surface solitary waves abstract two dimensional flow of an incompressible inviscid fluid in a region with a horizontal bottom of infinite extent and a free upper surface is considered the fluid is acted on by gravity and has a non diffusive heterogeneous density which may be discontinuous it is shown that the governing equations allow both periodic and single crested progressing waves of permanent form the analogues respectively of the classical cnoidal and solitary waves these waves are shown to be critical points of flow related functionals and are proved to exist by means of a variational principle

networks with condorcet solutions abstract a condorcet point on a network is a point such that thare is no other point closer to a strict majority of users which are located at the vertices of the network a complete characterization is given of those networks on which no condorcet paradox occurs in the sense that for each distribution of users there exists at least one condorcet point moreover those networks are characterized on which condorcet points and weber points always coincide a polynomial algorithm is obtained which decides whether a given network has condorcet points for all distributions of users on the network

vortex rings in r 3 and rearrangements we study the existence of steady axisymmetric vortex rings in an ideal fluid a functional comprising a linear combination of kinetic energy and impulse is to be maximized subject to the constraint that a quantity related to vorticity belongs to a set of rearrangements of a given function generalized solutions of a quite specific type are shown to exist arising as extreme points of a convex extended constraint set in the case when the given function is the indicator of a set of finite measure the existence of proper maximizers and local maximizers is demonstrated

parametrization of optimal fault detection filters this paper is concerned with the fault detection filter design problem for linear time invariant systems subject to disturbance and possible faults to make a tradeoff between fault sensitivity and disturbance sensitivity frameworks such as 2 and are considered it is shown that for and frameworks all optimal fault detection filters can be characterized by an envelope besieged by the special solutions serving as upper and lower bounds furthermore the explicit parametrization is given in terms of a free contractive system parameter this free parameter provides freedom to emphasize fault and disturbance sensitivities at different frequency ranges which can be used to construct new optimal fault detection filter the results are also extended to the optimization over finite frequency range for which the upper and or lower bound of the optimal solution set may not be rational on the other hand it is shown that the solution set of 2 problem is unique up to square inner system finally examples are given to illustrate the results

rearrangement inequalities for functionals with monotone integrands the inequalities of hardy littlewood and riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement it is known that these inequalities extend to integrands of the form f u1 um where f is supermodular in particular they hold when f has nonnegative mixed second derivatives i jf for all i j this paper concerns the regularity assumptions on f and the equality cases it is shown here that extended hardy littlewood and riesz inequalities are valid for supermodular integrands that are just borel measurable under some nondegeneracy conditions all equality cases are equivalent to radially decreasing functions under transformations that leave the functionals invariant i e measure preserving maps for the hardy littlewood inequality translations for the riesz inequality the proofs rely on monotone changes of variables in the spirit of sklar s theorem

a steady vortex ring in poiseuille flow and rearrangements of a function this study proves the existence of a steady vortex ring of an ideal fluid in poiseuille flow the method that was used is a variational method proposed by benjamin benjamin 1976 the alliance of practical and analytical insight into the nonlinear problems of fluid mechanics vol 503 pp 8 29 in which a steady vortex ring can be obtained as a maximizer of a functional that is related to kinetic energy and the impulse over the set of rearrangements of a prescribed function

a robust deconvolution scheme for fault detection and isolation of uncertain linear systems an lmi approach optimal h deconvolution filter theory is exploited for the design of robust fault detection and isolation fdi units for uncertain polytopic linear systems such a filter is synthesized under frequency domain conditions which ensure guaranteed levels of disturbance attenuation residual decoupling and deconvolution performance in prescribed frequency ranges by means of the projection lemma a quasi convex formulation of the problem is obtained via lmis a fdi logic based on adaptive thresholds is also proposed for reducing the generation of false alarms the effectiveness of the design technique is illustrated via a numerical example

discrete convexity and polynomial solvability in minimum 0 extension problems a 0 0 extension of graph vargamma is a metric d d on a set v v containing the vertex set v vargamma v of vargamma such that d d extends the shortest path metric of vargamma and for all x in v x v there exists a vertex s s in vargamma with d x s 0 d x s 0 the minimum 0 0 extension problem 0 ext vargamma on vargamma is given a set v supseteq v vargamma v v and a nonnegative cost function c c defined on the set of all pairs of v v find a 0 0 extension d d of vargamma with sum xy c xy d x y xyc xy d x y minimum the 0 0 extension problem generalizes a number of basic combinatorial optimization problems such as minimum s t s t cut problem and multiway cut problem karzanov proved the polynomial solvability of 0 ext vargamma for a certain large class of modular graphs vargamma and raised the question what are the graphs vargamma for which 0 ext vargamma can be solved in polynomial time he also proved that 0 ext vargamma is np hard if vargamma is not modular or not orientable in a certain sense in this paper we prove the converse if vargamma is orientable and modular then 0 ext vargamma can be solved in polynomial time this completes the classification of graphs vargamma for which 0 ext vargamma is tractable to prove our main result we develop a theory of discrete convex functions on orientable modular graphs analogous to discrete convex analysis by murota and utilize a recent result of thapper and ivn on valued csp

polyhedra related to undirected multicommodity flows abstract let g vg eg and h vh eh be two undirected graphs and vh vg we associate with g and h the unbounded polyhedron p g h in q eg which consists of all nonegative rational valued functions vectors l on eg such that for each edge st in h the distance between s and t in the graph g whose edges eg have the lengths l is no less that 1 let h be the least positive integer k such that each vertex of p g h is 1 k integral for any g with vg vh h if such a k does not exist in other terms h is the least positive integer k such that each problem dual to a maximum undirected multicommodity flow problem with the commodity graph h has on optimal solution that is 1 k integral we prove that h can be only 1 2 4 and moreover for each k 1 2 4 we describe the class of h s with h k also results concerning extreme of cones related to feasibility multicommodity flow problems are presented

rearrangements and leibniz type rules of mean oscillations abstract we shall prove a rearrangement inequality in probability measure spaces in order to obtain sharp leibniz type rules of mean oscillations in l p spaces and rearrangement invariant banach function spaces

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

desingularizations of systems of point vortices abstract consider the evolution of an incompressible inviscid fluid in r 2 zabusky conjectured that given a steady system of point vortices there exists a one parameter family of steady system of vortex patches in which each patch shrinks to the corresponding point vortex while keeping the same circulation as the parameter tends to zero such a family is called a desingularization of the given system of point vortices in this article we establish that 1 a zabusky s conjecture holds under a mild condition on the system of point vortices 2 b the desingularizations of the system of point vortices preserve their type of stability 3 c desingularizations of an unfolding of a system of point vortices exist under a typical situation

fault detection over frequency region generalized spectral factorization approach we present results on fault detection in presence of disturbances of descriptor systems over a frequency region instead of the methodology of the generalized kyp lemma used in the literature we use the methodology of generalized spectral factorization illustrative examples are given

desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem steady vortices for the three dimensional euler equation for inviscid incompressible flows and for the shallow water equation are constructed and shown to tend asymptotically to singular vortex filaments the construction is based on a study of solutions to the semilinear elliptic problem left begin aligned rm div left frac nabla u varepsilon b right frac 1 varepsilon 2 b f left u varepsilon log tfrac 1 varepsilon q right text in omega u varepsilon 0 text on partial omega end aligned right for small values of varepsilon 0

a time domain approach to robust fault detection of linear time varying systems this paper gives the optimal solutions to several robust fault detection problems such as 2 and problems for linear time varying systems in a time domain which extends the previous results on linear time invariant systems in a frequency domain it is shown that all three problems have the same optimal detection filter and the filter is a simple observer obtained by solving a standard differential riccati equation finally an example is given to illustrate our results

rearrangements of functions saddle points and uncountable families of steady configurations for a vortex on donne deux resultats sur l existence d une infinite de configurations stationnaires pour un tourbillon bases sur le principe de kelvin de l energie cinetique stationnaire on s interesse a des ecoulements permanents dans lesquels la vorticite est un rearrangement d une fonction donnee et on decrit les circulations de la vitesse autour des composantes convexes de la frontiere

half integrality of node capacitated multiflows and tree shaped facility locations on trees in this paper we establish a novel duality relationship between node capacitated multiflows and tree shaped facility locations we prove that the maximum value of a tree distance weighted maximum node capacitated multiflow problem is equal to the minimum value of the problem of locating subtrees in a tree and the maximum is attained by a half integral multiflow utilizing this duality we show that a half integral optimal multiflow and an optimal location can be found in strongly polynomial time these extend previously known results in the maximum free multiflow problems we also show that the set of tree distance weights is the only class having bounded fractionality in maximum node capacitated multiflow problems

planar vortex patch problem in incompressible steady flow abstract in this paper we consider the planar vortex patch problem in an incompressible steady flow in a bounded domain of r 2 let k be a positive integer and let j be a positive constant j 1 k for any given non degenerate critical point x 0 x 0 1 x 0 k of the kirchhoff routh function defined on k corresponding to 1 k we prove the existence of a planar flow such that the vorticity of this flow equals a large given positive constant in each small neighborhood of x 0 j j 1 k and 0 elsewhere moreover as the vorticity set y y shrinks to j 1 k x 0 j and the local vorticity strength near each x 0 j approaches j j 1 k

a polya szego inequality in a fermi metric abstract let n k n with n 2 and 1 k n given a positive function c r n k we form the riemannian metric g on r n associated to the differential expression d s 2 d x 2 x 2 d y 2 where we write r n x x y with x r n k and y r k let be a log convex measure on r k with smooth density and the product measure l n k on r n where c r n k is a positive function we obtain a polya szego inequality of the form r n f u j g u d r n f u s j g u s d for sobolev functions u where the operation s refers to the k n steiner symmetrisation with respect to the gradient operator g is associated to the metric g and the mapping j may be seen as interpolating between the tangent space at x and r n the nonnegative integrand f is continuous and convex in the gradient variable and satisfies some additional hypotheses as an application we derive a polya szego inequality in the hyperbolic plane that takes the above form

an lmi approach to minimum sensitivity analysis with application to fault detection this paper systematically studies the minimum input sensitivity analysis problem the lowest level of sensitivity of system outputs to system inputs is defined as an h index a full characterization of the h index is given first in terms of matrix equalities and inequalities and then in terms of linear matrix inequalities lmis as a dual of the bounded real lemma a related problem of input observability is also studied with new necessary and sufficient conditions given which are necessary for a fault detection system to have a nonzero worst case fault sensitivity the above results are applied to the problem of fault detection filter analysis with numerical examples given to show the effectiveness of the proposed approaches

ℋ index for discrete time stochastic systems with markovian jump and multiplicative noise abstract in this paper we discuss the index problem for stochastic linear discrete time systems subject to markovian jump and multiplicative noise for which a necessary and sufficient condition for an index larger than 0 is given in finite time horizon it is shown that the index larger than a given value is equivalent to the solvability of a certain generalized difference riccati equation gdre what we have obtained generalizes the results of deterministic systems to stochastic models moreover the index problem for s q u a r e systems in infinite horizon is also studied finally some examples are presented to illustrate the effectiveness of the proposed theoretical results

existence and multiplicity of solutions for fractional schrodinger kirchhoff equations with trudinger moser nonlinearity abstract we study the existence and multiplicity of solutions for a class of fractional schrodinger kirchhoff type equations with the trudinger moser nonlinearity more precisely we consider m u n s n s s u v x u n s 1 u f x u h x u p 2 u in r n u r 2 n u x u y n s x y 2 n d x d y r n v x u n s d x s n where m 0 0 is a continuous function s 0 1 n 2 0 is a parameter 1 p n s s is the fractional n s laplacian v r n 0 is a continuous function f r n r r is a continuous function and h r n 0 is a measurable function first using the mountain pass theorem a nonnegative solution is obtained when f satisfies exponential growth conditions and is large enough and we prove that the solution converges to zero in w v s n s r n as then using the ekeland variational principle a nonnegative nontrivial solution is obtained when is small enough and we show that the solution converges to zero in w v s n s r n as 0 furthermore using the genus theory infinitely many solutions are obtained when m is a special function and is small enough we note that our paper covers a novel feature of kirchhoff problems that is the kirchhoff function m 0 0

brief paper an lmi approach to h index and mixed h h fault detection observer design using the newly developed worst case fault sensitivity measure the index and the well known worst case robustness measure the norm this paper addresses the problem of index fault detection observer design and multiobjective fault detection observer design problems necessary and sufficient conditions for the existence of such a fault detection observer are given in terms of matrix inequalities both infinite frequency range case 0 and finite frequency range case 0 with overbar are considered iterative linear matrix inequality ilmi algorithms are given to obtain the solutions the effectiveness of the proposed approaches is shown by numerical examples

notes on l m convex functions and the separation theorems the concepts of l convex function and m convex function have recently been introduced by murota as generalizations of submodular function and base polyhedron respectively and discrete separation theorems are established for l convex concave functions and for m convex concave functions as generalizations of frank s discrete separation theorem for submodular supermodular set functions and edmonds matroid intersection theorem this paper shows the equivalence between murota s l convex functions and favati and tardella s submodular integrally convex functions and also gives alternative proofs of the separation theorems that provide a geometric insight by relating them to the ordinary separation theorem in convex analysis

a matrix factorization solution to the h h fault detection problem in this paper we give a matrix factorization solution to the h h fault detection fd problem for linear time invariant dynamic systems an h h fd filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults more specifically it minimizes the largest singular value over the extended imaginary axis of the transfer matrix from the disturbance to the residual signal vectors subject to the constraint that the singular values of the transfer matrix from the fault to the residual vectors are larger than or equal to 1 we show through the use of matrix function factorizations and completions that the problem reduces to a nonstandard model matching problem which is then solved under a mild assumption concerning the rank of a matrix function we also give an illustrative example

an elliptic boundary value problem with a discontinuous nonlinearity ii soit un domaine borne dans r 2 on etudie le probleme aux valeurs limites pour k h k dans r 2 0 sur h est la fonction echelon de heaviside

an approach to symmetrization via polarization we prove that the steiner symmetrization of a function can be approximated in l p r n by a sequence of very simple rearrangements which are called polarizations this result is exploited to develop elementary proofs of many inequalities including the isoperimetric inequality in euclidean space in this way we also obtain new symmetry results for solutions of some varia tional problems furthermore we compare the solutions of two boundary value problems one of them having a polarized geometry and we show some point wise inequalities between the solutions this leads to new proofs of well known functional inequalities which compare the solutions of two elliptic or parabolic problems one of them having a steiner symmetrized geometry the method also allows us to investigate the case of equality in the inequalities roughly speaking we prove that the equality sign is valid only if the original problem has the symmetrized geometry

state of the art location on networks a survey part ii exploiting tree network structure the discussion of the fundamental p center and p median problems in part i of this paper provides the basis for the work surveyed in part ii part ii deals with the minimax and minisum location problems with mutual communication location problems involving multiple objectives the distance constraints problem and problems involving the location of paths in addition convexity issues in network location problems are discussed virtually all of this work exploits network structure specifically it is based on the assumption that the network is a tree the conclusion section gives a brief discussion of the state of the art and of current trends in network location research

the complexity of conservative valued csps we study the complexity of valued constraint satisfaction problems vcsps parametrized by a constraint language a fixed set of cost functions over a finite domain an instance of the problem is specified by a sum of cost functions from the language and the goal is to minimize the sum under the unique games conjecture the approximability of finite valued vcsps is well understood see raghavendra 2008 however there is no characterization of finite valued vcsps let alone general valued vcsps that can be solved exactly in polynomial time thus giving insights from a combinatorial optimization perspective we consider the case of languages containing all possible unary cost functions in the case of languages consisting of only 0 valued cost functions i e relations such languages have been called conservative and studied by bulatov 2003 2011 and recently by barto 2011 since we study valued languages we call a language conservative if it contains all finite valued unary cost functions the computational complexity of conservative valued languages has been studied by cohen et al 2006 for languages over boolean domains by deineko et al 2008 for 0 1 valued languages a k a max csp and by takhanov 2010a for 0 valued languages containing all finite valued unary cost functions a k a min cost hom we prove a schaefer like dichotomy theorem for conservative valued languages if all cost functions in the language satisfy a certain condition specified by a complementary combination of stp and mjn multimorphisms then any instance can be solved in polynomial time via a new algorithm developed in this article otherwise the language is np hard this is the first complete complexity classification of general valued constraint languages over non boolean domains it is a common phenomenon that complexity classifications of problems over non boolean domains are significantly harder than the boolean cases the polynomial time algorithm we present for the tractable cases is a generalization of the submodular minimization problem and a result of cohen et al 2008 our results generalize previous results by takhanov 2010a and a subset of results by cohen et al 2006 and deineko et al 2008 moreover our results do not rely on any computer assisted search as in deineko et al 2008 and provide a powerful tool for proving hardness of finite valued and general valued languages

optimization problems with fixed volume constraints and stability results related to rearrangement classes abstract the material in this paper has been divided into two main parts in the first part we describe two optimization problems one maximization and one minimization related to a sharp trace inequality that was recently obtained by g auchmuty in both problems the admissible set is the one comprising characteristic functions whose supports have a fixed measure we prove the maximization to be solvable whilst the minimization will turn out not to be solvable in general we will also discuss the case of radial domains in the second part of the paper we study approximation and stability results regarding rearrangement optimization problems first we show that if a sequence of the generators of rearrangement classes converges then the corresponding sequence of the optimal solutions will also converge second a stability result regarding the hausdorff distance between the weak closures of two rearrangement classes is presented

proximity theorems of discrete convex functions a proximity theorem is a statement that given an optimization problem and its relaxation an optimal solution to the original problem exists in a certain neighborhood of a solution to the relaxation proximity theorems have been used successfully for example in designing efficient algorithms for discrete resource allocation problems after reviewing the recent results for l convex and m convex functions this paper establishes proximity theorems for larger classes of discrete convex functions l2 convex functions and m2 convex functions that are relevant to the polymatroid intersection problem and the submodular flow problem

fault detection in a mixed h sub 2 h sub spl infin setting in this note we study the problem of fault detection in linear time invariant lti systems which are simultaneously effected by two classes of unknown inputs noises having fixed spectral densities and unknown finite energy disturbances this problem is formulated as a mixed h sub 2 h sub spl infin filtering problem necessary and sufficient conditions for local optimality are presented moreover it is shown that suboptimal solutions can be computed by solving a convex minimization problem with a set of linear matrix inequality lmi constrains a numerical example is given to illustrate the advantage of the mixed h sub 2 h sub spl infin approach as compared to existing techniques which are based on optimization of h sub 2 and h sub spl infin criteria

the maximum multiflow problems with bounded fractionality we consider the weighted maximum multiflow problem with respect to a terminal weight we show that if the dimension of the tight span associated with the weight is at most 2 then this problem has a 1 12 integral optimal multiflow for every eulerian supply graph this result solves a weighted generalization of karzanov s conjecture for classifying commodity graphs with finite fractionality in addition our proof technique proves the existence of an integral or half integrality optimal multiflow for a large class of multiflow maximization problems and it gives a polynomial time algorithm

skew bisubmodularity and valued csps an instance of the finite valued constraint satisfaction problem vcsp is given by a finite set of variables a finite domain of values and a sum of rational valued functions with each function depending on a subset of the variables the goal is to find an assignment of values to the variables that minimizes the sum we study assuming that ptime neq np how the complexity of this very general problem depends on the functions allowed in the instances the case when the variables can take only two values was classified by cohen et al essentially submodular functions give rise to the only tractable case and any non submodular function can be used to express in a certain specific sense the np hard max cut problem we investigate the case when the variables can take three values we identify a new infinite family of conditions that includes bisubmodularity as a special case and which can collectively be called skew bisubmodularity by a recent result of thapper and ivn this condition imp

inequalities for integral means over symmetric sets abstract we prove that the integral of n functions over a symmetric set l in r n with additional properties increases when the functions are replaced by their symmetric decreasing rearrangements the result is known when l is a centrally symmetric convex set and our result extends it to nonconvex sets we deduce as consequences inequalities for the average of a function whose level sets are of the same type as l over measurable sets in r n the average of such a function on e is maximized by the average over the symmetric set e

higher order symmetrization inequalities and applications abstract we prove new extended forms of the polya szego symmetrization principle as a consequence new sharp embedding theorems for generalized sobolev and besov spaces are proved

multivalued fixed point index and nonlocal problems involving relative rearrangement abstract we apply the fixed point index theory for multivalued problems to nonlocal problems involving relative rearrangement mappings these applications need an extension of the almgren lieb theorem and an improvement of the strong continuity of the relative rearrangement mapping on arbitrary open sets bounded or not the proofs of these results are based on some pointwise equations relating the relative rearrangement of the gradient and the weighted de giorgi perimeter

on strong convergence to 3d steady vortex sheets in this paper we first establish a strong convergence criterion of approximate solutions for the 3d steady incompressible euler equations for axisymmetric flows under the assumption that the vorticity is of one sign and uniformly bounded in l 1 space we obtain a sufficient and necessary condition for the strong convergence in l 2 r 3 of approximate solutions furthermore for one sign and l 1 bounded vorticity it is shown that if a sequence of approximate solutions concentrates at an isolated point in r z plane then the concentration point can appear neither in the region near the axis including the symmetry axis itself nor in the region far away from the axis finally we present an example of approximates solutions which converge strongly in l 2 r 3 by using hill s spherical vortex

corotating steady vortex flows with n fold symmetry in this paper we study certain vertical flows of an ideal fluid in two dimensions which are steady relative to a uniformly rotating frame in particular we confine our analysis to those flows for which the vorticity relative to the rotating frame possesses n fold rotational symmetry for some given n 2 3 that is we require that the relative vorticity be invariant under rotation through arbitrary multiples of 2zjn as in our earlier related work 19 20 these relative steady solutions of the euler fluid dynamical equations are obtained as extremals for a certain variational problem the solutions then represent steady vortex flows in the sense defined in 19 namely each such flow has a prescribed distribution of relative vorticity and is separated into regions of zero and of positive relative vorticity in 1883 thomson 18 considered the flow due to a configuration of n unit point vortices spaced equally around the circumference of a circle the relative vorticity of such a configuration on a circle of radius a is given by

the complexity of finite valued csps we study the computational complexity of exact minimization of rational valued discrete functions let be a set of rational valued functions on a fixed finite domain such a set is called a finite valued constraint language the valued constraint satisfaction problem vcsp is the problem of minimizing a function given as a sum of functions from we establish a dichotomy theorem with respect to exact solvability for all finite valued constraint languages defined on domains of arbitrary finite size we show that every constraint language either admits a binary symmetric fractional polymorphism in which case the basic linear programming relaxation solves any instance of vcsp exactly or satisfies a simple hardness condition that allows for a polynomial time reduction from max cut to vcsp

a computational method of solving free boundary problems in vortex dynamics abstract a general method for computing two dimensional and axisymmetric three dimensional solutions of the steady euler equations is developed the method is based upon variational principles which are formulated entirely in terms of the natural conserved quantities for the unsteady euler equations the vorticity fields considered have a free boundary and may be defined either in a domain with boundary or in free space moreover the common restriction to the case of constant vorticity regions is not imposed the global convergence of the resulting iterative solver is established the numerical implementation of the method is discussed and several computational examples are given

the uniqueness of hill s spherical vortex the mathematical description of steady vortex rings in an ideal fluid occupying the whole space r3 can be approached in various ways the physical basis of the problem its history up to 1973 and several formulations are outlined in 12 pp 14 21 another quite different formulation and the plan for a corresponding existence theory are presented in 6 further existence theorems variational principles and results are to be found in 3 7 11 13 and 20 here we state only definitions and equations that seem relevant to our immediate purpose

a combinatorial strongly polynomial algorithm for minimizing submodular functions this paper presents a combinatorial polynomial time algorithm for minimizing submodular functions answering an open question posed in 1981 by grotschel lovasz and schrijver the algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter the resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the length of the largest absolute function value the paper also presents a strongly polynomial version in which the number of steps is bounded by a polynomial in the size of the underlying set independent of the function values

semiring based constraint satisfaction and optimization we introduce a general framework for constraint satisfaction and optimization where classical csps fuzzy csps weighted csps partial constraint satisfaction and others can be easily cast the framework is based on a semiring structure where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain and the two semiring operations and x model constraint projection and combination respectively local consistency algorithms as usually used for classical csps can be exploited in this general framework as well provided that certain conditions on the semiring operations are satisfied we then show how this framework can be used to model both old and new constraint solving and optimization schemes thus allowing one to both formally justify many informally taken choices in existing schemes and to prove that local consistency techniques can be used also in newly defined schemes

desingularization of vortices for the euler equation we study the existence of stationary classical solutions of the incompressible euler equation in the planes that approximate singular stationary solutions of this equation the construction is performed by studying the asymptotics of equation varepsilon 2 delta u varepsilon u varepsilon q frac kappa 2 pi log frac 1 varepsilon p with dirichlet boundary conditions and q a given function we also study the desingularization of pairs of vortices by minimal energy nodal solutions and the desingularization of rotating vortices

m convex function on generalized polymatroid the concept of m convex function introduced by murota 1996 is a quantitative generalization of the set of integral points in an integral base polyhedron as well as an extension of valuated matroid of dress and wenzel 1990 in this paper we extend this concept to functions on generalized polymatroids with a view to providing a unified framework for efficiently solvable nonlinear discrete optimization problems

the complexity of multiterminal cuts in the multiterminal cut problem one is given an edge weighted graph and a subset of the vertices called terminals and is asked for a minimum weight set of edges that separates each terminal from all the others when the number k of terminals is two this is simply the mincut max flow problem and can be solved in polynomial time it is shown that the problem becomes np hard as soon as k 3 but can be solved in polynomial time for planar graphs for any fixed k the planar problem is np hard however if k is not fixed a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2 2 k of the optimal cut weight is also described

directed submodularity ditroids and directed submodular flows set relations and operations such as inclusion union and intersection are generalized to directed subsets whose elements are distinguished between forward and backward elements the concepts of submodular functions matroids and polymatroidal network flows are extended to the concepts of directed submodular functions ditroids and directed submodular flows on directed subsets two unrelated matroids submodular functions can be embedded in one ditroid directed submodular function total dual integrality is preserved in these generalizations and proved for very general set function class directed odd submodular functions

characterization of ℋ index for linear time varying systems the increasing interest in index in fault detection has led to some recent development in time domain investigation this paper at first presents a necessary and sufficient condition of the index in finite time horizon for linear time varying systems it is shown that the feasibility of the index which is given when the index is greater than a predefined value is equivalent to the existence of a certain backward differential riccati equation under a constraint the square system as a special case is discussed the corresponding results are extended to systems with unknown initial condition with a modified definition of the index the condition for weighted index to emphasize the signal effect at different time instant is also derived by transformation the result is also compared with the famous bounded real lemma the connection with the linear time invariant lti case is also discussed finally examples are given to illustrate the main results

approximation algorithms for classification problems with pairwise relationships metric labeling and markov random fields in a traditional classification problem we wish to assign one of k labels or classes to each of n objects in a way that is consistent with some observed data that we have about the problem an active line of research in this area is concerned with classification when one has information about pairwise relationships among the objects to be classified this issue is one of the principal motivations for the framework of markov random fields and it arises in areas such as image processing biometry and document analysis in its most basic form this style of analysis seeks to find a classification that optimizes a combinatorial function consisting of assignment costs based on the individual choice of label we make for each object and separation costs based on the pair of choices we make for two related objects we formulate a general classification problem of this type the metric labeling problem we show that it contains as special cases a number of standard classification frameworks including several arising from the theory of markov random fields from the perspective of combinatorial optimization our problem can be viewed as a substantial generalization of the multiway cut problem and equivalent to a type of uncapacitated quadratic assignment problem we provide the first nontrivial polynomial time approximation algorithms for a general family of classification problems of this type our main result is an o log k log log k approximation algorithm for the metric labeling problem with respect to an arbitrary metric on a set of k labels and an arbitrary weighted graph of relationships on a set of objects for the special case in which the labels are endowed with the uniform metric all distances are the same our methods provide a 2 approximation algorithm

variational problem for vortices attached to seamounts abstract the existence of an energy maximizer relative to a class of rearrangements of a given function is proved the maximizers are stationary and stable solutions of the two dimensional barotropic vorticity equation governing the evolution of geophysical flow over a surface of variable height the theorem proved implies the existence of a family of stable vortices with anticyclonic potential vorticity over a seamount and a similar family of vortices with cyclonic potential vorticity over a localized depression

smooth approximations and exact solutions of the 3d steady axisymmetric euler equations in this paper we prove that a class of c1 smooth approximate solutions ue pe to the 3d steady axisymmetric euler equations will converge strongly to 0 in l 2 loc r 3 the main assumptions are that the approximate solutions have uniformly finite energy and approach a constant state at far fields we also show a liouville type theorem that there are no non trivial c1 smooth exact solutions with finite energy and uniform constant state at far fields

polynomial combinatorial algorithms for skew bisubmodular function minimization huber et al siam j comput 43 1064 1084 2014 introduced a concept of skew bisubmodularity as a generalization of bisubmodularity in their complexity dichotomy theorem for valued constraint satisfaction problems over the three value domain and huber and krokhin siam j discrete math 28 1828 1837 2014 showed the oracle tractability of minimization of skew bisubmodular functions fujishige et al discrete optim 12 1 9 2014 also showed a min max theorem that characterizes the skew bisubmodular function minimization but devising a combinatorial polynomial algorithm for skew bisubmodular function minimization was left open in the present paper we give first combinatorial weakly and strongly polynomial algorithms for skew bisubmodular function minimization