completion of multipole theory for the electromagnetic response fields d and h multipole theory of linear constitutive relations for the response fields d and h in dielectrics is incomplete in the sense that it yields unphysical for example origindependent results when taken beyond electric dipole order because of the inherent non uniqueness of d and h in maxwell equations we consider the role of transformations of these fields in multipole theory specifically we construct for a non dissipative magnetic medium to electric quadrupole magnetic dipole order and for e and b fields represented by complex harmonic plane waves the most general transformation which i leaves the inhomogeneous maxwell equations for d and h unchanged ii preserves the linear homogeneous dependence of d and h on the macroscopic polarizability tensors and fields e and b iii is consistent with the requirements of space inversion and time reversal iv maintains the order of the multipole expansion v imposes origin independence on the tensors representing material constants vi preserves necessary symmetries of these tensors the resulting transformed constitutive relations are unique they satisfy the post constraint equality of traces of the magnetoelectric tensors yield a fresnel reflection matrix which satisfies reciprocity and imply multipole moment densities which are origin independent the transformation theory can be applied to higher multipole orders and the results adapted to dissipative media

a milnor condition for nonatomic lipschitz games and its applications one of milnor s reasonable axioms is generalized to nonatomic games several uses of this generalization are discussed in particular the general form of values and semivalues on subspaces of pna is derived

the existence of sylow 2 subloops in finite moufang loops abstract here we prove that if l is a finite moufang loop then every 2 subloop of l is contained in some sylow 2 subloop of l moreover the number of sylow 2 subloops of l is congruent to one modulo two we will also show that if p is any prime congruent to one modulo four then there exist finite moufang loops that do not contain any sylow p subloops

an axiomatic approach to the measurement of the amount of interaction among criteria or players in the framework of multicriteria decision making based on fuzzy measures or cooperative game theory an axiomatization of the concept of amount of interaction index is given it is based on four axioms a natural property called absence of interaction a boundary condition for which the index reduces to the shapley or banzhaf interaction index a pseudo additivity axiom and a recursivity property the resulting index which can be interpreted as a measure of the average degree of independence among criteria or players takes a particularly simple and natural form for supermodular or submodular measures the approach to the notion of interaction adopted in this paper can be seen as complementary to that recently adopted by grabisch and roubens

partially symmetric values we consider spaces of differentiable nonatomic and mixed vector measure games pna andpm with finitely or countably many types of players type symmetric values on these spaces of games are investigated all aumann and shapley conditions except symmetry are assumed the latter being replaced by a weaker assumption of covariance under automorphisms of the space of players that preserve each type we show that if the types are uncountable then type symmetric values are random path values in particular the symmetric values onpm are characterized as mixtures of values defined in hart 1973

nonsymmetric values of nonatomic and mixed games this paper presents a new unifying approach to the study of nonsymmetric or quasi values of nonatomic and mixed games a family ofpath values is defined using an appropriate generalization of mertens diagonal formula a path value possesses the following intuitive description consider a function path attaching to each player a distribution function on 0 1 we think of players as arriving randomly and independently to a meeting when the arrival time of a player is distributed according to each player s payoff is defined as his marginal contribution to the coalition of players that have arrived earlier under certain conditions on a path different subspaces of mixed games pna pm bv fl are shown to be in the domain of the path value the family of path values turns out to be very wide we show that onpna pm and their subspaces the path values are essentially the basic construction blocks extreme points of quasi values

critical behaviour of a surface reaction model with infinitely many absorbing states in a recent letter yaldram et al 1993 studied the critical behaviour of a simple lattice gas model of the co no catalytic reaction the model exhibits a second order non equilibrium phase transition from an active state into one out of infinitely many absorbing states estimates for the critical exponent beta suggested that the model belongs to a new universality class the results reported in this article contradict this notion as estimates for various critical exponents show that the model belongs to the universality class of directed percolation

transformed multipole theory of the response fields d and h to electric octopole magnetic quadrupole order we consider multipole theory of linear constitutive relations for the macroscopic electromagnetic response fields d and h to electric octopolemagnetic quadrupole order we use a recently developed

a stochastic approach to approximate values in cooperative games abstract computing additive values in cooperative games like the shapley value is a hard task because in general it involves the summation of an exponential number of terms we propose a new method based on the stochastic approximation of deterministic games and sampling theory to calculate a statistic estimate of these values and at the same time keeping under control estimation errors we applied this technique to several well known games and we show that in many cases we were able to improve previous results

hopf algebras with triality in this joint work with g benkart and j m perez izquierdo we revisit and extend the constructions of glauberman and doro on groups with triality and moufang loops to hopf algebras we prove that the universal enveloping algebra of any lie algebra with triality is a hopf algebra with triality this allows a new construction of the universal enveloping algebras of malcev algebras our work relays on the approach of grishkov and zavarnitsine to groups with triality

electromagnetic theorems for complex anisotropic media complex anisotropic media can generally be described by a 6 times 6 macroscopic constitutive tensor hat c using hat c properties a reaction integral formula is derived from which an anisotropic reaction theorem modified reciprocity theorem is developed reduction of the hat c medium into a reciprocal medium is discussed including tensor symmetry attributes and limiting cases the anisotropic reaction theorem is utilized to derive a zero reaction theorem and then treated in relation to the moment method mutual and self impedance elements of a network are also derived in terms of reaction integrals symmetry covered using the anisotropic reaction theorem and impedance elements related to moment calculations use of spectral domain analysis is also covered

on the existence of linear non reciprocal bi isotropic nrbi media a recent letter in this journal and a number of related publications have purported to prove that maxwell s equations forbid the existence of linear non reciprocal bi isotropic nrbi media the basis of such proofs is shown to be unfounded with the constraint on matter being due not to electromagnetism but to symmetry it is also shown that linear nrbi media may exist in some situations in the form of certain magnetic cubic crystals in addition in their response to an electromagnetic wave there are also magnetic cubics in which propagation although not perfectly isotropic deviates in practice to an extent which is probably undetectable finally the existence of a tellegen medium as an example of a nrbi substance is shown to be possible in principle in contrast to the findings of recent papers

equivalent n person games and the null space of the shapley value two n person games may be said to be equivalent if they have the same shapley value in this paper we attempt to simplify the determination of the equivalence of two games we do this by recognizing that a pair of games are equivalent if and only if their difference lies in the null space of the shapley value using the representation theory of the symmetric groups we construct a direct sum decomposition of this null space into invariant subspaces we then use this same theory to derive a characterization of a very general type of value of which the shapley value is one particular example

on the non existence of linear non reciprocal bi isotropic nrbi media we show that raab and sihvola s theses on the recognizable existence of linear nonreciprocal bi isotropic media are either incorrect or inconsequential to modern electromagnetic theory which has purely microscopic foundations

maximal subloops of finite simple moufang loops abstract we classify the maximal subloops of finite simple non associative moufang loops up to conjugacy with respect to automorphisms

hall s theorem for moufang loops abstract a loop k is solvable if there exists a normal series 1 k 0 k 1 k 2 k n k of subloops k i such that each factor k i k i 1 is an abelian group back in 1966 g glauberman proved g glauberman on loops of odd order ii j algebra 8 1968 393 414 that every moufang loop of odd order is solvable he also showed that if is any set of primes then every moufang loop of odd order contains a hall subloop since then it has been an open question whether or not p hall s theorem holds for all finite moufang loops here we affirmatively answer this question by showing that a finite moufang loop is solvable if and only if it contains a hall subloop for any set of primes

some new convergence acceleration methods abstract the algorithm is a general extrapolation method which includes most of thesequence transformations actually known some new convergence acceleration methods arederived from the f algorithm by applying the so called procedure the algorithms thusobtained are studied some theoretical results are proved and numerical examples are given 1 introduction the general idea for accelerating the convergence of a slowlyconvergent sequence is to transform it into another sequence which will undercertain assumptions converge faster to the same limit among the most famoussequence transformations are linear summation processes richardson polynomialextrapolation aitken s a2 process 1 and shanks transformation 15 wynn s algorithm 17 an extensive study of these methods can be found in 3 whilenumerical examples applications and fortran subroutines are given in 4 each of these methods usually works in some particular cases since a universalmethod accelerating the convergence of wide classes of sequences cannot exist 10 however numerical examples 11 16 and also some theoretical results 6 8 revealthat the best sequence transformations that is those working in most of theexamples seem to be levin s u and v transforms 14 and the algorithm 2 the algorithm is a method derived from the rule of the e algorithm by a procedurewhich will be recalled in the next section recently a general sequence transformation as well as the corresponding recursivealgorithm was obtained by havie 13 and brezinski 5 this transformation calledthe transformation includes most of the convergence acceleration methods actu ally known thus it seemed interesting to apply to the algorithm the sameprocedure which was used to derive the algorithm from the e algorithm and tostudy the new convergence acceleration methods obtained in that way it is the aimof this paper 2 the procedure 8 let us first begin by some reminiscences about shanks transformation and the e algorithm let sn be a sequence of real or complex numbers shanks transformationconsists in transforming sn into a set of sequences ek sn given by

accessibility in oriented networks the aim of this work consists of allocating a value that allows us to emphasize the importance of each player in a cooperative game when the cooperation possibilities are limited according to the links of an oriented network the proposed concept of accessibility tries to conjugate the marginal contributions of each node as a game player with the cooperation geometry imposed by the digraph that models the network we study general properties of this concept and particularly with respect to oriented paths concrete applications are proposed

value theory without efficiency a semivalue is a symmetric positive linear operator on a space of games which leaves the additive games fixed such an operator satisfies all of the axioms defining the shapley value with the possible exception of the efficiency axiom the class of semivalues is completely characterized for the space of finite player games and for the space pna of nonatomic games

further results on light propagation in helicoidal bianisotropic mediums oblique propagation the recent fabrication of thin film helicoidal bianisotropic mediums hbms has created an impetus for understanding their electromagnetic response using the oseen transformation we have derived a 4 4 matrix ordinary differential equation for oblique i e non axial propagation in general linear hbms a perturbational technique is presented for almost axial propagation and two other techniques one semi analytic and the other analytic are presented for general oblique propagation all three techniques yield exact closed form results for axial propagation our use of the oseen transformation amounts to viewing oblique propagation not by itself but as a graft on axial propagation and is thus responsible for the stability of all three techniques

constraint on linear homogeneous constitutive relations a constraint on linear homogeneous constitutive relations is presented it does not affect the sources and the primitive fields its effect being solely on the induction fields as the maxwell postulates are satisfied without question its use amounts to a simplification of the description of linear homogeneous magnetoelectric media the constraint is in complete harmony with the covariant character of modern electromagnetic theory

potentials and weighted values of nonatomic games the potential approach to value theory for finite games was introduced by hart and mas colell hart s a mas colell 1989 potential value and consistency econometrica57 589 614 here this approach is extended to non atomic games on appropriate spaces of differentiable games there is a unique potential operator that generates the aumann and shapley aumann r j l s shapley 1974 values of nonatomic games princeton university press princeton new jersey value as a corollary we obtain the uniqueness of the aumann shapley value on certain subspaces of games next the potential approach is applied to the weighted case leading to weighted non atomic values it is further shown that the asymptotic weighted value is well defined and that it coincides with the weighted value generated by the potential

refinement derivatives and values of games a definition of setwise differentiability for set functions is given through refining the partitions of sets such a construction is closely related to the one proposed by rosenmuller rosenmuller j 1977 extreme games and their solutions springer verlag berlin epstein epstein l 1999 a definition of uncertainty aversion rev econom stud 66 579 608 and epstein and marinacci epstein l m marinacci 2001 the core of large differentiable tu games j econom theory100 235 273 we present several classes of transferable utility tu games that are differentiable and study differentiation rules the last part of this paper applies refinement derivatives to the computation of value of games following hart and mas colell hart s a mas colell 1989 potential value and consistency econometrica57 589 614 we define an operator through the refinement derivative of the potential of the game we show that this operator is a value when restricted to the spaces pm and pot2 the latter space is closely related to myerson s balanced contributions axiom

semivalues of simple games it is shown that each semivalue bounded semivalue on the class sg of monotonic simple games with a finite support can be uniquely extended to a semivalue continuous semivalue on the class g of all games with a finite support we use this to show that the formula that is given for semivalues continuous semivalues on g by dubey neyman and weber also holds for semivalues bounded semivalues on sg we also derive another formula for semivalues on sg in terms of the minimal winning coalitions of the game

power and potential maps induced by any semivalue some algebraic properties and computation by multilinear extensions the notions of total power and potential both defined for any semivalue give rise to two endomorphisms of the vector space of cooperative games on any given player set where the semivalue is defined several properties of these linear mappings are stated and the role of unanimity games as eigenvectors is described we also relate in both cases the multilinear extension of the image game to the multilinear extension of the original game as a consequence we derive a method to compute for any semivalue by means of multilinear extensions in the original game and also in all its subgames a the total power b the potential and c the allocation to each player given by the semivalue

consistency for the additive efficient normalization of semivalues abstract this paper contributes to consistency for the additive efficient normalization of semivalues motivated from the additive efficient normalization of a semivalue being a b revision of the shapley value we introduce the b reduced game which is an extension of sobolev s reduced game then the additive efficient normalization of a semivalue is axiomatized as the unique value satisfying covariance symmetry and b consistency furthermore by means of the path independently linear consistency together with the standardness for two person games the additive efficient normalization of semivalues is also characterized accessorily the additive efficient normalization of semivalues is directly verified as the linear consistent least square values see ruiz et al 1998

measure based values of non atomic games a complete characterization of symmetric linear continuous operators from pna to fa is given this is used to prove the existence of a unique value on pna and to deduce the general form of a semivalue and the general form of a degenerate value

further remarks on the non existence of linear non reciprocal bi isotropic media this communication follows four manuscripts published in this journal in particular it is motivated by the most recent comments made by raab and sihvola here we show that these comments of raab and sihvola affirming the recognizable existence of linear non reciprocal bi isotropic nrbi media are based on i a factually incorrect statement and ii a confusion between static fields and fields with slow temporal variations

weighted majority games have asymptotic value the asymptotic value of a game v with a continuum set of players i is defined whenever all the sequences of the shapley values of finite games that approximate v have the same limit a weighted majority game is a game of the form f where is a positive measure and fx 1 if x q and fx 0 otherwise and q is a real number 0 q i in this paper we prove that all weighted majority games have asymptotic values this result is then used further to show that if v is of the form v f where is a probability measure and f is a function of bounded variation on 0 1 that is continuous at 0 and at 1 then v has an asymptotic value this bad previously been known only when f is absolutely continuous or when has at most finitely many atoms or when is purely atomic thus the essential novelty is that even when has countably many atoms and a nonatomic part f has an asymptotic value we also show that f does not necessarily have an asymptotic value when is a signed measure

additivizations of nonadditive measures the concept of an additivization of a nonadditive probability measure is introduced and studied the relation to cooperative game theory is explored and it is shown that in many cases of interest additivizations may be considered as a special type of semivalues

circumstantial power optimal persuadable voters abstract let us suppose that certain committee is going to decide using some fixed voting rules either to accept or to reject a proposal that affects your interests from your perception about each voter s position you can make an a priori estimation of the probability of the proposal being accepted wishing to increase this probability of acceptance before the votes are cast assume further that you are able to convince at least one voter to improve his her perception in favor of the proposal the question is which voters should be persuaded in order to get the highest possible increase in the probability of acceptance in other words which are the optimal persuadable voters to answer this question a measure of circumstantial power is considered in this paper which is useful to identify optimal persuadable voters three preorderings in the set of voters based on the voting rules are defined and they are used for finding optimal persuadable voters even in the case that only a qualitative ranking of each voter s inclination for the proposal has been made

on a medium constraint arising directly from maxwell s equations the mathematical structure of maxwell s equations provides a constraint on the constitutive parameters of linear homogeneous media this is exemplified by showing that the nonreciprocity parameter of bi isotropic media is superfluous confirming independent results based on covariance and uniqueness arguments that nonreciprocal bi isotropic media do not exist

the development of sylow p subloops in finite moufang loops we show that if l is a finite moufang loop and p is a sylow prime for l then there exists a sylow p subloop of l moreover if l1 is a p subloop of l then l1 is contained in a sylow p subloop of l finally for finite moufang loops that don t contain sylow p subloops any p subloop can be embedded in some quasi sylow p subloop

sylow s theorem for moufang loops abstract for finite moufang loops we prove an analog of the first sylow theorem giving a criterion for the existence of a p sylow subloop we also find the maximal order of p subloops in the moufang loops that do not possess p sylow subloops

semivalues as power indices abstract a restricted notion of semivalue as a power index i e as a value on the lattice of simple games is axiomatically introduced by using the symmetry positivity and dummy player standard properties together with the transfer property the main theorem that parallels the existing statement for semivalues on general cooperative games provides a combinatorial definition of each semivalue on simple games in terms of weighting coefficients and shows the crucial role of the transfer property in this class of games a similar characterization is also given that refers to unanimity coefficients which describe the action of the semivalue on unanimity games we then combine the notion of induced semivalue on lower cardinalities with regularity and obtain a series of characteristic properties of regular semivalues on simple games that concern null and nonnull players subgames quotients and weighted majority games