a simplified expression of the shapley function for fuzzy game abstract in this paper a simplified expression of the shapley function for games with fuzzy coalition is proposed which can be regarded as the generalization of shapley functions defined in some particular games with fuzzy coalition the simplified expression of the shapley function is compared with two definitions established by butnariu tsurumi et al a conclusion is drawn that the simplified expression of the shapley function is equivalent to butnariu s definition when characteristic function is a game with proportional values and is equivalent to tsurumi s definition when characteristic function is a game with choquet integral forms furthermore from an angle of interaction between two participation levels the properties of the two games defined by butnariu and tsurumi are respectively studied

the consistent value of fuzzy games in the framework of fuzzy games we offer an extension of the reduced game introduced by hart and mas colell which we name the self reduced game according to consistency which related to the self reduced game we provide a definition of the consistent value which is a generalization of the shapley value of fuzzy games we adopt three existing concepts from coalitional game theory and reinterpret them in the framework of fuzzy games the first one is that there exists a unique potential function and the resulting payoff vector coincides with the consistent value second based on the properties of balanced contributions and consistency we offer several axiomatizations of the consistent value finally we propose a dynamic process to illustrate that the consistent value can be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments

an isometry theorem for quadratic differentials on riemann surfaces of finite genus assume both x and y are riemann surfaces which are subsets of compact riemann surfaces xi and yi respectively and that the set xi x has infinitely many points we show that the only surjective complex linear isometries between the spaces of integrable holomorphic quadratic differentials on x and y are the ones induced by conformal homeomorphisms and complex constants of modulus 1 it follows that every biholomorphic map from the teichmiiller space of x onto the teichmiiller space of y is induced by some quasiconformal map of x onto y consequently we can find an uncountable set of riemann surfaces whose teichmiiller spaces are not biholomorphically equivalent

sharp bounds for generalized elliptic integrals of the first kind abstract in this paper we prove that the double inequality 1 r 2 k a r sin a log e r a 2 r 1 r 2 holds for all a 0 1 2 and r 0 1 if and only if r a sin a 1 and a 1 a where r 1 r 2 k a r is the generalized elliptic integral of the first kind and r x is the ramanujan constant function besides as the key tool the series expression for the ramanujan constant function r x is given

inequalities and bounds for generalized complete elliptic integrals computable bounds for the generalized complete elliptic integrals of the first and second kind are obtained also bounds for some combinations and products for integrals under discussion are established it has been proven that both families of integrals are logarithmically convex as functions of the first parameter this property has been employed to obtain several inequalities involving integrals in question

games with fuzzy permission structure a conjunctive approach abstract a cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate regardless of the actions that the other players take a permission structure over the set of players describes a hierarchical organization where there are players who need permission from certain other players before they are allowed to cooperate with others various assumptions can be made about how a permission structure affects the cooperation possibilities in the conjunctive approach it is assumed that each player needs permission from all his superiors this paper deals with fuzzy permission structures in the conjunctive approach in this model players could depend partially on other players that is they may have certain degree of autonomy first we define a value for games with fuzzy permission structure that only takes into account the direct relations among players and provide a characterization for this value finally we study a value for games with fuzzy permission structure which takes account of the indirect relations among players

holomorphic motions and teichmuller spaces we prove an equivariant form of slodkowski s theorem that every holomorphic motion of a subset of the extended complex plane c extends to a holomorphic motion of c as a consequence we prove that every holomorphic map of the unit disc into teichmuller space lifts to a holomorphic map into the space of beltrami forms we use this lifting theorem to study the teichmuller metric

a banzhaf function for a fuzzy game in this paper another important solution for fuzzy games called the banzhaf function is investigated first a sim plified expression for the banzhaf function for games with fuzzy coalition is proposed the relationship between this simplified ex pression and two kinds of particular banzhaf functions are dis cussed in detail furthermore in the framework of games with fuzzy coalitions we give a definition of the potential function of fuzzy games and prove that the marginal values of the potential function are the components of the banzhaf function further more a new axiomatic characterization of the banzhaf function for games with fuzzy coalitions is provided

mills ratio monotonicity patterns and functional inequalities in this paper we study the monotonicity properties of some functions involving the mills ratio of the standard normal law from these we deduce some new functional inequalities involving the mills ratio and we show that the mills ratio is strictly completely monotonic at the end of this paper we present some turan type inequalities for mills ratio

semi discretization method for delayed systems summary the paper presents an ecient numerical method for the stability analysis of linear delayed systems the method is based on a special kind of discretization technique with respect to the past eect only the resulting approximate system is delayed and also time periodic but still it can be transformed analytically into a high dimensional linear discrete system the method is applied to determine the stability charts of the mathieu equation with continuous time delay copyright 2002 john wiley sons ltd

the cg position value for games on fuzzy communication structures abstract a cooperative game for a set of agents establishes a fair allocation of the profit obtained for their cooperation the best known of these allocations is the shapley value a communication structure defines the feasible bilateral communication relationships among the agents in a cooperative situation some solutions incorporating this information have been defined from the shapley value the myerson value the position value etc later fuzzy communication structures were introduced in a fuzzy communication structure the membership of the players and the relations among them are leveled several ways of defining the myerson value for games on fuzzy communication structure were proposed one of them is the choquet by graphs cg version now we study in this work the cg position value and its calculation the cg position value is defined as a solution for games with fuzzy communication structure which considers the bilateral communications as players so the shapley value is applied for a new game the link game over the fuzzy sets of links in the fuzzy communication structure and the profit obtained for each link is allocated between both players in the link as we see in our examples and results the cg position value is more concerned with the graphical position of the players and their communications than the other cg values in this paper we also introduce a procedure to compute exactly the position value avoiding to calculate the characteristic function of the link game for all coalitions this procedure is used to determine the cg position value finally we compare the new value with other cg values in an applied example about the power of the groups in the european parliament

some inequalities for the poincare metric of plane domains in this paper the poincare or hyperbolic metric and the associated distance are investigated for a plane domain based on the detailed properties of those for the particular domain open image in new window in particular another proof of a recent result of gardiner and lakic 7 is given with explicit constant this and some other constants in this paper involve particular values of complete elliptic integrals and related special functions a concrete estimate for the hyperbolic distance near a boundary point is also given from which refinements of littlewood s theorem are derived

monotonicity properties and inequalities for the generalized elliptic integral of the first kind abstract the authors obtain some monotonicity and concavity properties and asymptotically sharp bounds for the generalized elliptic integral k a r of the first kind and its special case k r the complete elliptic integral of the first kind by studying the monotonicity and concavity properties of certain combinations defined in terms of the gaussian hypergeometric function f a 1 a 1 x and elementary functions thus improving some well known results

shapley mappings and the cumulative value for n person games with fuzzy coalitions abstract in this paper we prove existence and uniqueness of the so called shapley mapping which is a solution concept for a class of n person games with fuzzy coalitions whose elements are defined by the specific structure of their characteristic functions the shapley mapping when it exists associates to each fuzzy coalition in the game an allocation of the coalitional worth satisfying the efficiency the symmetry and the null player conditions it determines a cumulative value that is the sum of all coalitional allocations for whose computation we provide an explicit formula

on the comparison of semi analytical methods for the stability analysis of delay differential equations abstract this paper provides the first comparison of the semi discretization spectral element and legendre collocation methods each method is a technique for solving delay differential equations ddes as well as determining regions of stability in the dde parameter space we present the necessary concepts assumptions and equations required to implement each method to compare the relative performance between the methods the convergence rate and computational time for each method is compared in three numerical studies consisting of a ship stability example the delayed damped mathieu equation and a helicopter rotor control problem for each study we present one or more stability diagrams in the parameter space and one or more convergence plots the spectral element method is demonstrated to have the quickest convergence rate while the legendre collocation method requires the least computational time the semi discretization method on the other hand has both the slowest convergence rate and requires the most computational time

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

on the higher order semi discretizations for periodic delayed systems semi discretization techniques of periodic delayed systems are presented using zeroth first and higher order approximations of the delayed term it is shown that if the time periodic coefficients in the equation are approximated by piecewise constant functions then there is no need to use higher than first order approximations of the delayed term the results are demonstrated on construction of the stability chart of the delayed mathieu equation

fuzzy approaches to the game of chicken game theory deals with decision making processes involving two or more parties also known as players with partly or completely conflicting interests decision makers in a conflict must often make their decisions under risk and under unclear or fuzzy information in this paper two distinct fuzzy approaches are employed to investigate an extensively studied 2 spl times 2 game model the game of chicken the first approach uses a fuzzy multicriteria decision analysis method to obtain optimal strategies for the players it incorporates subjective factors into the decision makers objectives and aggregates objectives using a weight vector the second approach applies the theory of fuzzy moves tfm to the game of chicken the theory of moves tom is designed to bring a dynamic dimension to the classical theory of games by allowing decision makers to look ahead for one or several steps so that they can make a better decision tom is the crisp counterpart of tfm the approach we implement here to deal with games that include fuzzy and uncertain information the application of fuzzy approaches to the game of chicken demonstrates their effectiveness in manipulating subjective uncertain and fuzzy information and provides valuable insights into the strategic aspects of chicken

new properties for several classes of functions related to the fox wright functions abstract in this paper our aim is to establish several new properties for some class of functions related to the fox wright functions in particular the monotonicity convexity sub additivity and super additivity properties involving the fox wright functions are proved these results are also closely connected with some functional inequalities such as turan type inequalities moreover we investigate certain criteria for the univalence and starlikeness for a certain class of functions associated with the fox wright functions

myerson values for games with fuzzy communication structure in 1977 myerson considered cooperative games with communication structure a communication structure is an undirected graph describing the bilateral relationships among the players he introduced the concept of allocation rule for a game as a function obtaining an outcome for each communication structure among the players of the game the myerson value is a specific allocation rule extending the shapley value of the game more recently the authors studied games with fuzzy communication structures using fuzzy graph theoretic ideas now we propose a general framework in order to define fuzzy myerson values players in a coalition need to measure their profit using their real individual and communication capacities at every moment because these attributes are fuzzy when the game is proposed so they look for forming connected coalitions working at the same level the different ways to obtain these partitions by levels determine different myerson values for the game several interesting examples of these ways are studied in the paper following known models in games with fuzzy coalitions the proportional model and the choquet model

a conformally invariant metric on riemann surfaces associated with integrable holomorphic quadratic differentials in this paper we define a conformally invariant pseudo metric on all riemann surfaces in terms of integrable holomorphic quadratic differentials and analyze it this metric is closely related to an extremal problem on the surface as a result we have a kind of reproducing formula for integrable quadratic differentials furthermore we establish a new characterization of uniform thickness of hyperbolic riemann surfaces in terms of invariant metrics

hyperbolic 2 spheres with conical singularities accessory parameters and kahler metrics on ℳ _ 0 we show that the real valued function s on the moduli space m 0 n of pointed rational curves defined as the critical value of the liouville action functional on a hyperbolic 2 sphere with n 3 conical singularities of arbitrary orders 1 n generates accessory parameters of the associated fuchsian differential equation as their common antiderivative we introduce a family of kahler metrics on m 0 n parameterized by the set of orders a explicitly relate accessory parameters to these metrics and prove that the functions s are their kahler potentials

a spectral element approach for the stability of delay systems we describe a spectral element approach to study the stability and equilibria solutions of delay differential equations ddes in contrast to the prototypical temporal finite element analysis tfea the described spectral element approach admits spectral rates of convergence and allows exploiting hp convergence schemes the described approach also avoids the limitations of analytical integrations in tfea by using highly accurate numerical quadratures enabling the study of more complicated ddes the effectiveness of this new approach is compared with well established methods in the literature using various case studies specifically the stability results are compared with the conventional tfea and legendre collocation methods whereas the equilibria solutions are compared with the numerical simulations and the homotopy perturbation method hpm solutions our results reveal that the presented approach can have higher rates of convergence than both collocation methods and the hpm copyright 2011 john wiley sons ltd

inequalities involving modified bessel functions of the first kind ii the intrinsic properties including logarithmic convexity concavity of the modified bessel functions of the first kind and some other related functions are obtained several inequalities involving functions under discussion are established

games with fuzzy authorization structure a cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate regardless of the actions that the other players take it is often assumed that the players are free to participate in any coalition but in some situations there are dependency relationships among the players that restrict their capacity to cooperate within some coalitions those relationships must be taken into account if we want to distribute the profits fairly in this respect several models have been proposed in literature in all of them dependency relationships are considered to be complete in the sense that either a player is allowed to fully cooperate within a coalition or they cannot cooperate at all nevertheless in some situations it is possible to consider another option that a player has a degree of freedom to cooperate within a coalition a model for those situations is presented

log convexity and log concavity of hypergeometric like functions abstract we find sufficient conditions for log convexity and log concavity for the functions of the forms a f k a k x k a f k a k x k and a f k x k a k the most useful examples of such functions are generalized hypergeometric functions in particular we generalize the turan inequality for the confluent hypergeometric function recently proved by barnard gordy and richards and log convexity results for the same function recently proved by baricz besides we establish a reverse inequality which complements naturally the inequality of barnard gordy and richards similar results are established for the gauss and the generalized hypergeometric functions a conjecture about monotonicity of a quotient of products of confluent hypergeometric functions is made

turan type inequalities for generalized complete elliptic integrals in this paper our aim is to establish some turan type inequalities for gaussian hypergeometric functions and for generalized complete elliptic integrals these results complete the earlier result of p turan proved for legendre polynomials moreover we show that there is a close connection between a turan type inequality and a sharp lower bound for the generalized complete elliptic integral of the first kind at the end of this paper we prove a recent conjecture of t sugawa and m vuorinen related to estimates of the hyperbolic distance of the twice punctured plane

convex fuzzy games and participation monotonic allocation schemes in this paper the cone of convex cooperative fuzzy games is studied as in the classical case of convex crisp games these games have a large core and the fuzzy shapley value is the barycenter of the core surprisingly the core and the weber set coincide as in the classical case but the coincidence of these sets for a fuzzy game does not imply automatically convexity as in the crisp case participation monotonic allocation schemes pamas are introduced and it turns out that each core element of a convex fuzzy game is pamas extendable

twice punctured hyperbolic sphere with a conical singularity and generalized elliptic integral we describe in terms of generalized elliptic integrals the hyperbolic metric of the twice punctured sphere with one conical singularity of prescribed order we also give several monotonicity properties of the metric and a couple of applications

fuzzy measure of fuzzy events defined by fuzzy integrals abstract we define the concept of fuzzy measure of a fuzzy event by using a general form of fuzzy integral proposed by murofushi called fuzzy t conorm integral encompassing previous definitions zadeh defined the probability measure of a fuzzy event and later the possibility measure of fuzzy event using a duality property of fuzzy t conorm integral we propose a general definition of fuzzy measure of fuzzy events which is compatible with previous definitions of zadeh and possesses all properties of a fuzzy measure in particular the duality property using our definition we examine the case of decomposable measures and belief functions a comparison with previous works is provided

a new shapley value for games with fuzzy coalitions abstract this paper deals with cooperative games over fuzzy coalitions in these situations there is a continuous set of fuzzy coalitions instead of a finite set of them as in the classical case the unit square in an n dimensional space there exist in the literature two different extensions of the known shapley value for crisp games to games with fuzzy coalitions the crisp shapley value and the diagonal value the first value only uses a finite information in the set of fuzzy coalitions the vertices of the square while the second one uses a neighbourhood of the diagonal of the square we propose a new extension of the shapley value improving the crisp shapley value for games with fuzzy coalitions this new version uses the faces of the square namely an infinity quantity of information we analyze several properties of the new value we endow it with an axiomatization and we study the behavior when it is applied to known fuzziness of crisp games

asymptotical bounds for complete elliptic integrals of the second kind abstract in this paper we establish several asymptotical bounds for the complete elliptic integrals of the second kind e r and improve the well known conjecture e r 1 1 r 2 3 4 2 2 3 2 for all r 0 1 proposed by m vuorinen

linear fuzzy game with coalition interaction and its coincident solutions abstract in this study we consider the solution concepts for fuzzy coalition games i e cooperative games with fuzzy coalition under a certain participation level in general cooperative games with fuzzy coalition are based on the assumption that all the fuzzy coalition values for different fuzzy coalitions must be represented by the same formula which may omit the coalition interaction under different participation ratios for players considering these conditions we propose the coincident fuzziness form for games with fuzzy coalition which are represented by a mapping from the characteristic function of the crisp game to that of the fuzzy coalition game the proposed fuzzy coalition games admit the differences in coalition interactions for different fuzzy coalitions where the coalition interactions are represented by the fuzzy coalition values in different ways or formulas for a fixed fuzzy coalition the maximum fuzzy coalition game is proven to be the choquet integral form on the condition that the associate crisp game is convex in order to seek appropriate solutions for the proposed games based on a certain participation level the fuzzy shapley axioms are defined and the explicit shapley value is represented by the shapley value of the associated crisp games moreover the fuzzy core of this proposed fuzzy coalition game is the stable solution set for the given fuzzy coalition which is also denoted by the crisp cores furthermore we study the relationship between the fuzzy shapley value and the fuzzy core by adding restrictions on the fuzzy core we propose a strong fuzzy core which is a more stable solution than the fuzzy core in addition the fuzzy core is equivalent to the strong fuzzy core under some condition

cooperation among agents with a proximity relation abstract a cooperative game consists of a set of players and a characteristic function determining the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate regardless of the actions that the other players take the relationships of closeness among the players should modify the bargaining among them and therefore their payoffs the first models that have studied this closeness used a priori unions or undirected graphs in the a priori union model a partition of the big coalition is supposed each element of the partition represents a group of players with the same interests the groups negotiate among them to form the grand coalition and later inside each one players bargain among them now we propose to use proximity relations to represent leveled closeness of the interests among the players and extending the a priori unions model

an extension of cooperative fuzzy games in this paper a generalized form of fuzzy game is proposed that can be seen as an extension of the cooperative fuzzy game players in the proposed fuzzy game do not need to know precise information about the payoff value or to form a crisp coalition based on the hukuhara difference a game with a fuzzy characteristic function is studied and the explicit form of a shapley function is shown furthermore we introduce and investigate a new class of fuzzy game with fuzzy coalitions and a fuzzy characteristic function based on the hukuhara difference and the choquet integral we give the explicit form of the shapley value for the new class of fuzzy game it has been seen that most of the properties of a crisp game hold well in the proposed fuzzy game a practical application of the proposed model in joint production problem is also provided

a note on the core minimal conversely consistent enlargement abstract the moulin reduction is extended by reducing the number of the players to the framework of fuzzy games based on this extended moulin reduction the axiomatic result of the core in tadenuma s 25 case does not hold in the context of fuzzy games and the core also violates the converse consistency therefore we propose the minimal core which possesses the converse consistency and is also the smallest solution satisfying the core

concavity of the complete elliptic integrals of the second kind with respect to holder means abstract in this paper we establish a necessary and sufficient condition for the concavity of the complete elliptic integrals of the second kind with respect to holder means

turan type inequalities for kratzel functions abstract complete monotonicity laguerre and turan type inequalities are established for the so called kratzel function z defined by z u 0 t 1 e t u t d t where u 0 and r moreover we prove the complete monotonicity of a determinant function of which entries involve the kratzel function

pseudospectral differencing methods for characteristic roots of delay differential equations in d breda s maset and r vermiglio ima j numer anal 24 2004 pp 1 19 and d breda the infinitesimal generator approach for the computation of characteristic roots for delay differential equations using bdf methods research report udmi rr17 2002 dipartimento di matematica e informatica universita degli studi di udine udine italy 2002 the authors proposed to compute the characteristic roots of delay differential equations ddes with multiple discrete and distributed delays by approximating the derivative in the infinitesimal generator of the solution operator semigroup by runge kutta rk and linear multistep lms methods respectively in this work the same approach is proposed in a new version based on pseudospectral differencing techniques we prove the spectral accuracy convergence behavior typical of pseudospectral schemes as also illustrated by some numerical experiments

high order vector numerical integration schemes applied in state space milling stability analysis third and fourth order vector numerical integration schemes were proposed in this work and applied in more accurate handling of difficult integration problem in milling stability analysis error vector analysis was carried out on a generalized discrete interval for each of the first and second order vector numerical integration methods known in literature 9 and also for the proposed third and fourth order vector numerical integration methods the results from error vector analysis suggested that accuracy increases in the order first second third and fourth order vector numerical integration methods the suggestion was verified with both numerical rate of convergence and stability analysis of both 1 degree of freedom 1dof and 2 degree of freedom 2dof milling processes the advantage of the proposed high order vector numerical integration methods in terms of accuracy and their disadvantage in terms of computational time relative to recent methods are highlighted avenue for future work was identified as discussed in the conclusion

stability of elastic columns with periodic retarded follower forces the objective of this work is to present a stability analysis for elastic columns under the influence of periodically varying follower forces whose orientation is retarded i e depends on the position of the system at a previous time one and two degree of freedom dof discretized systems under the simultaneous influence of both parametric excitation and time delay whose effects on such systems have previously been only considered separately are studied by employing an orthogonal polynomial approximation the infinite dimensional floquet transition matrix associated with the time periodic differential delay system is approximated the stability criteria that all the eigenvalues floquet multipliers of this matrix must lie within the unit circle is then applied the stability charts for different combinations of the remaining system parameters are shown and the previously reported results for the special cases where either the parametric excitation or the time delay vanishes are verified two cases when the parametric forcing period is equal to or twice the delay period are taken into consideration in this work for special cases of the single dof system the numerical stability plots are verified by considering the analytical expressions for the corresponding stability boundaries for an analogous delayed mathieu equation

a banzhaf value for games with fuzzy communication structure computing the power of the political groups in the european parliament abstract in 2013 jimenez losada et al introduced several extensions of the myerson value for games with fuzzy communication structure in a fuzzy communication structure the membership of the players and the relations among them are leveled now we study a banzhaf value for these situations the myerson model is followed to define the fuzzy graph banzhaf value taking as base point the choquet integral we propose an axiomatization for this value introducing leveled amalgamation of players an algorithm to calculate this value is provided and its complexity is studied finally we show an applied example computing by this fuzzy value the power of the groups in the european parliament

a shapley function on a class of cooperative fuzzy games abstract in this paper we make a study of the shapley values for cooperative fuzzy games games with fuzzy coalitions which admit the representation of rates of players participation to each coalition a shapley function has been introduced by another author as a function which derives the shapley value from a given pair of a fuzzy game and a fuzzy coalition however the previously proposed axioms of the shapley function can be considered unnatural furthermore the explicit form of the function has been given only on an unnatural class of fuzzy games we introduce and investigate a more natural class of fuzzy games axioms of the shapley function are renewed and an explicit form of the shapley function on the natural class is given we make sure that the obtained shapley value for a fuzzy game in the natural class has several rational properties finally an illustrative example is given

updated semi discretization method for periodic delay differential equations with discrete delay an updated version of the semi discretization method is presented for periodic systems with a single discrete time delay the delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined stability charts are constructed for the damped and delayed mathieu equation for different time period time delay ratios the convergence of the method is investigated by examples stability charts are constructed for 1 and 2 degree of freedom milling models the codes of the algorithm are also attached in the appendix copyright 2004 john wiley sons ltd

generalized hersch pfluger distortion function and complete elliptic integrals abstract in this paper we study the relationship between the generalized hersch pfluger distortion function k a r and complete elliptic integrals of the second kind e r and establish several inequalities for k a r and e r

max consistency complement consistency and the core of fuzzy games recently hwang introduced two extensions of the max reduced game to fuzzy games by reducing the number of the players based on these reduced games he offered analogous axiomatizations of the core related to serrano and volij in the context of fuzzy games here we continue and develop hwang s work on similar topics however we turn to a different definition of the reduced game by simultaneously reducing both the number of the players and the participation levels we propose such extensions of the complement reduced game and of the max reduced game to fuzzy games and define the related properties of consistency and converse consistency based on these properties we offer several analogous characterizations of the core related to peleg serrano and volij and tadenuma respectively

synchronization phenomena for coupled delay line oscillators two coupled delay line oscillators are modeled by a system of delay differential equations and their oscillations are analyzed by reducing the delay equations to a system of ordinary differential equations on a finite dimensional center manifold in the corresponding infinite dimensional state space after averaging the finite dimensional system a bifurcation analysis reveals a complex structure of oscillatory behavior a complete bifurcation analysis is postponed in favor of a bifurcation analysis that is focused on applications to sensor design in particular the case of two adjacently mounted identically built surface acoustic wave saw delay line oscillators is examined a bifurcation analysis reveals the operation envelope for a dual saw sensor based on measurements of frequency differences the effective operating envelope of this design is limited due to synchronization caused by cross coupling on the other hand the operation envelope of a dual saw sensor can be enlarged by constructing a sensor based on phase differences in the synchronization regime

inequalities for the generalized marcum q function abstract in this paper we consider the generalized marcum q function of order 0 real defined by q a b 1 a 1 b t e t 2 a 2 2 i 1 at d t where a b 0 i stands for the modified bessel function of the first kind and the right hand side of the above equation is replaced by its limiting value when a 0 our aim is to prove that the function q a b is strictly increasing on 0 for each a 0 b 0 and to deduce some interesting inequalities for the function q moreover we present a somewhat new viewpoint of the generalized marcum q function by showing that satisfies the new is better than used nbu property which arises in economic theory

combination of sign inverting and delay scheduling control concepts for multiple delay dynamics abstract in this paper we treat a novel combination of two controversial control concepts sign inverting control sic and delay scheduling ds for systems with multiple independent and large delays sic suggests the inversion of the control polarity and ds prolongs the existing delays the combined scheme functions with a single requirement that the union of the control schemes provides a larger stable operating region than each of its components does in the domain of the delays the critical knowledge that is needed to execute such a unified control strategy is the crisp description of these stable regions for each time delayed control scheme this need can be fulfilled using the recent cluster treatment of characteristic roots ctcr paradigm which establishes the stable regions exhaustively and non conservatively the resulting options in selecting operating modes render more robust control performance against much larger delay variations than each of the schemes we also investigate the disturbance rejection speeds within these enlarged stable regions in order to improve the control performance even further such multi faceted paradoxical combinations provide previously unexplored tools to control designers experimental validations of these novel concepts are presented on a simple setup with a single axis manipulator

analysis of milling dynamics for simultaneously engaged cutting teeth this paper investigates the stability of a milling process with simultaneously engaged teeth and contrasts it to prior work for a single tooth in the cut the stability analyses are performed with the chebyshev collocation method and the state space tfea technique these analyses show that a substantially different stability behavior is observed in addition the stability lobes are shown to undergo rapid transitions for relatively small changes in the radial immersion ratio these transitions are explained in terms of the specific cutting force profiles the stable periodic motion of the tool was also investigated using a harmonic balance approach and a dynamic map created with the tfea technique the findings suggest that a large number of harmonics are required for the harmonic balance approach to obtain the correct solution

a note on turan type and mean inequalities for the kummer function abstract turan type inequalities for combinations of kummer functions involving a c x and a c x have been recently investigated in a baricz functional inequalities involving bessel and modified bessel functions of the first kind expo math 26 3 2008 279 293 m e h ismail a laforgia monotonicity properties of determinants of special functions constr approx 26 2007 1 9 in the current paper we resolve the corresponding turan type and closely related mean inequalities for the additional case involving a c x the application to modeling credit risk is also summarized

the fuzzy core in games with fuzzy coalitions in this paper the fuzzy core of games with fuzzy coalition is proposed which can be regarded as the generalization of crisp core the fuzzy core is based on the assumption that the total worth of a fuzzy coalition will be allocated to the players whose participation rate is larger than zero the nonempty condition of the fuzzy core is given based on the fuzzy convexity three kinds of special fuzzy cores in games with fuzzy coalition are studied and the explicit fuzzy core represented by the crisp core is also given because the fuzzy shapley value had been proposed as a kind of solution for the fuzzy games the relationship between fuzzy core and the fuzzy shapley function is also shown surprisingly the relationship between fuzzy core and the fuzzy shapley value does coincide as in the classical case

generalized convexity and inequalities abstract let r 0 and let m be the family of all mean values of two numbers in r some examples are the arithmetic geometric and harmonic means given m 1 m 2 m we say that a function f r r is m 1 m 2 convex if f m 1 x y m 2 f x f y for all x y r the usual convexity is the special case when both mean values are arithmetic means we study the dependence of m 1 m 2 convexity on m 1 and m 2 and give sufficient conditions for m 1 m 2 convexity of functions defined by maclaurin series the criteria involve the maclaurin coefficients our results yield a class of new inequalities for several special functions such as the gaussian hypergeometric function and a generalized bessel function

variation of cone metrics on riemann surfaces we discuss the variational properties of the unique conical metric of constant curvature 1 associated to a compact riemann surface together with a weighted divisor 2005 elsevier inc all rights reserved

bounds for quasiconformal distortion functions abstract several new inequalities are proved for the distortion function k r appearing in the quasiconformal schwarz lemma other related special functions are studied and applications are given to quasiconformal maps in the plane some open problems are solved too

on approximating the arithmetic geometric mean and complete elliptic integral of the first kind abstract in the article we prove that the double inequalities 1 6 p 7 r p 5 p 6 r tanh 1 r 2 r k r 1 6 q 7 r q 5 q 6 r tanh 1 r 2 r q a 1 r 5 q 6 g 1 r a 1 r 6 q 7 g 1 r l 1 r a g m 1 r p a 1 r 5 p 6 g 1 r a 1 r 6 p 7 g 1 r l 1 r hold for all r 0 1 if and only if p 2 1 570796 and q 89 69 1 289855 where k r 0 2 1 r 2 sin 2 t 1 2 d t is the complete elliptic integral of the first kind tanh 1 r log 1 r 1 r 2 is the inverse hyperbolic tangent function r 1 r 2 and a 1 r 1 r 2 g 1 r r l 1 r r 1 log r and a g m 1 r are the arithmetic geometric logarithmic and gaussian arithmetic geometric means of 1 and r respectively

cores of fuzzy games and their convexity in this paper the proper core and dominance core of a fuzzy game are introduced to guarantee equality between the proper core and the dominance core some mild conditions are provided another important issue for the convexity of the dominance core is also addressed

games on fuzzy communication structures with choquet players myerson 1977 used graph theoretic ideas to analyze cooperation structures in games in his model he considered the players in a cooperative game as vertices of a graph which undirected edges defined their communication possibilities he modified the initial games taking into account the graph and he established a fair allocation rule based on applying the shapley value to the modified game now we consider a fuzzy graph to introduce leveled communications in this paper players play in a particular cooperative way they are always interested first in the biggest feasible coalition and second in the greatest level choquet players we propose a modified game for this situation and a rule of the myerson kind

a turan type inequality for the gamma function abstract we prove that the following turan type inequality holds for euler s gamma function for all odd integers n 1 and real numbers x 0 we have n 1 x n 1 x n x 2 with the best possible constant min 1 5 x 2 x 2 x 0 6359

nontransferable utility games with fuzzy coalition restrictions abstract a value for nontransferable utility ntu games with fuzzy coalition restrictions is introduced and characterized in a similar way as the shapley value for transferable utility tu games has been extended in the literature to study games with restricted cooperation we extend the shapley ntu value to deal with ntu games in situations in which there are fuzzy dependency relationships among the players

existence of fuzzy prekernels and mas colell bargaining sets in tu games abstract in this paper we first prove the existence of fuzzy prekernels and fuzzy nucleolus in tu fuzzy games which generalize the corresponding results for classical tu games as an application we apply the existence of fuzzy prekernels to derive an existence theorem for mas colell fuzzy bargaining sets and a stronger existence theorem for mas colell bargaining sets than the one by vohra 1991 18 we also provide an axiomatization theorem for fuzzy prekernels

comparing poincare densities however there is no formula for the poincare density pn of a general plane domain q and so one must resort to estimates many research articles have been devoted to finding and working with such estimates see for example 4 5 15 19 24 and 25 the first tool to establish such estimates is schwarz s lemma which says that every holomorphic map is a contraction with respect to the poincare metric that is ps f ldf i pd z idzl for any holomorphic map f from a riemann surface d to another riemann surface q applying this lemma

order monotonic solutions for generalized characteristic functions abstract generalized characteristic functions extend characteristic functions of classical tu games by assigning a real number to every ordered coalition being a permutation of any subset of the player set such generalized characteristic functions can be applied when the earnings or costs of cooperation among a set of players depend on the order in which the players enter a coalition in the literature the two main solutions for generalized characteristic functions are the one of nowak and radzik 1994 shortly called nr value and the one introduced by sanchez and bergantinos 1997 shortly called sb value in this paper we introduce the axiom of order monotonicity with respect to the order of the players in a unanimity coalition requiring that players who enter earlier should get not more in the corresponding ordered unanimity game than players who enter later we propose several classes of order monotonic solutions for generalized characteristic functions that contain the nr value and sb value as special extreme cases we also provide axiomatizations of these classes

the equal allocation of nonseparable costs an extension under fuzzy behavior by considering the players and the activity levels simultaneously we propose a consistent solution which is a generalization of the equal allocation of nonseparable costs eansc on fuzzy games we also adopt two pre existing concepts from traditional game theory and reinterpret them in the framework of fuzzy games first based on the consistency which related to an extended reduced game we offer two axiomatizations of the extended eansc second by applying the excess function we propose a dynamic process to illustrate that the extended eansc can be reached by players who start from an arbitrary efficient solution and make consecutive amendments

optimal sign inverting control for time delayed systems a concept study with experiments an intriguing control logic sign inverting control sic is considered for control systems with delayed feedback it starts with a nominal control law formulated for non delayed case and simply inverts the sign of the control gains for some surprising benefits when used with the delays this operation sounds paradoxical as the sign inversion potentially harms the stability of the non delayed dynamics however sic with large delays may yield some complementary benefits to the nominal control logic from delay robustness perspective the main question we address in this paper is how to select the nominal control law so that such a contribution can be a feasible b optimal in some sense a structured methodology is proposed to achieve this starting with a linear quadratic regulator based controller a single scaling factor on the corresponding control gains is used for one dimensional optimisation experimental validation of the concept of this optimal sic procedure is also reported on a single axis

the general prenucleolus of n person cooperative fuzzy games abstract in this paper we define the concept of the general prenucleolus minimizing the player complaint vector in the lexicographic order over the preimputation set for the cooperative games with fuzzy coalitions for the general prenucleolus we get a sufficient condition that the complaints of all players are in equal amount under the case of linear complaint functions concluding the proposed player excess sakawa and nishizaki 1994 15 as a result we can obtain the proposed fuzzy solutions with the corresponding linear complaint functions such as the equalizer solution molina and tejada 2002 5 and shapley function etc we prove that the least square general prenucleolus minimizing the variance of the resulting player complaints is the general prenucleolus thus an optimal solution considered from two aspects of the lexicographic order and the least square criterion is obtained in addition several general prenucleoli are proposed in terms of specific situations

fuzzy harsanyi solution for a kind of fuzzy coalition games abstract the fuzzy linear game in ref 32 is a class of fuzzy cooperative games with fuzzy coalition fuzzy coalition game for short which admits the difference of interactions for different fuzzy coalitions the fuzzy shapley value for fuzzy linear game has been studied as shapley value is just one point in the harsanyi solution it is interesting to study the explicit form of harsanyi solution in the fuzzy coalition game this paper defines the fuzzy harsanyi solution which distributes the harsanyi dividends such that the dividend shares of players in each fuzzy coalition are proportional to the corresponding players participation index when the fuzzy coalition payoff is average distributed between players in the fuzzy coalition the fuzzy harsanyi solution also coincides with the fuzzy shapley value just as their relationship in a crisp cooperative game we provide two axiomatic characterizations for the fuzzy harsanyi solution one uses axioms and the other uses distribution matrices the fuzzy harsanyi solution is a unique value on the fuzzy linear game that satisfies fuzzy efficiency fuzzy null player and fuzzy additivity property meanwhile based on probability distribution fuzzy harsanyi solution is seen as an expected marginal contribution of each player in the fuzzy coalition which provides more choices for players in the fuzzy coalition

inequalities for the generalized elliptic integrals with respect to holder means abstract in this paper the authors prove some inequalities for the generalized elliptic integrals with respect to holder means

monotonicity theorems and inequalities for the complete elliptic integrals we prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind k and e these results lead to sharp symmetrical bounds for k and e which improve recently discovered inequalities

cooperative games with fuzzy coalitions and fuzzy characteristic functions in this paper an extension of a cooperative fuzzy game is proposed which admits the representation of the rate of participation of every player in a coalition and also associates fuzziness with the value of the game games subject to fuzzy coalitions as well as those pertaining to fuzzy characteristic functions or vague expectations are separately studied in the literature we propose an extension of a fuzzy game with fuzzy coalitions and vague expectations together and obtain some interesting properties it has been observed that most of the properties satisfied by a crisp game hold good in the fuzzy sense in this extension a practical application of the proposed model in investment theory is being provided further a shapley function in the fuzzy sense has been proposed as a solution concept to this class of games the notion of a fuzzy population monotonic allocation function fpmaf is defined and established that the proposed shapley function is an fpmaf also

estimation of the hyperbolic metric by using the punctured plane let rho omega denote the density of the hyperbolic metric for a domain in the extended complex plane overline mathbb c we prove the inequality rho omega z leq c rm sup rho mathbb c setminus a b z a b in partial omega quad z in omega omega subset mathbb c with c 8 27 the inequality was proved by sugawa and vuorinen with c 10 33 the proof uses monotonicity properties of the hyperbolic metric for the thrice punctured extended plane gardiner and lakic proved the inequality rho omega z leq c 1 rm sup rho overline mathbb c setminus a b c z a b c in partial omega quad z in omega with an unspecified constant c1 we show that the best constant 1 in this inequality is between 3 25 and 8 27 we also prove a related conjecture formulated by sugawa and vuorinen

stability chart for the delayed mathieu equation in the space of system parameters the closedform stability chart is determined for the delayed mathieu equation defined as t cost x t bx t2 this stability chart makes the connection between t

fuzzy games a characterization of the core in this paper we extend to the cooperative fuzzy games case the reduced game introduced by davis and maschler the kernel of a cooperative game naval res logist quart 12 1965 223 259 we shall introduce two types of such a reduced game to cooperative fuzzy games and define the related properties of consistency and converse consistency we further offer two axiomatizations of the core on the domain of all cooperative fuzzy games by means of consistency and its converse