prym varieties curves with automorphisms and the sato grassmannian the aim of the paper is twofold first some results of shiota and plaza martin on prym varieties of curves with an involution are generalized to the general case of an arbitrary automorphism of prime order second the equations defining the moduli space of curves with an automorphism of prime order as a subscheme of the sato grassmannian are given

area and hausdorff dimension of julia sets of entire functions we show the julia set of a sin z has positive area and the action of a sin z on its julia set is not ergodic the julia set of a exp z has hausdorff dimension two but in the presence of an attracting periodic cycle its area is zero

quantum field theory grassmannians and algebraic curves this paper is devoted in part to clarifying some aspects of the relation between quantum field theory and infinite grassmannians and in part to pointing out the existence of a close analogy between conformal field theory on riemann surfaces and the modern theory of automorphic representations along the way we develop a multiplicative analog of the usual additive ward identities of current algebra we also reformulate the additive ward identities in a way which may be useful in terms of the residues of operator valued differential forms a concluding section is devoted to some remarks on string field theory in an appendix we attempt to clarify the recent construction by beilinson manin and schechtman of what might be called global virasoro algebras

triangular norms position paper iii continuous t norms this third and last part of a series of position papers on triangular norms for parts i and ii see e p klement r mesiar e pap triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press e p klement r mesiar e pap triangular norms position paper ii general constructions and parameterized families submitted for publication presents the representation of continuous archimedean t norms by means of additive generators and the representation of continuous t norms by means of ordinal sums with archimedean summands both with full proofs finally some consequences of these representation theorems in the context of comparison and convergence of continuous t norms and of the determination of continuous t norms by their diagonal sections are mentioned

on continuous triangular norms the problem of converging to any given continuous triangular norm by a sequence of continuous archimedean triangular norms is studied such a sequence is built up in a constructive way the class of well founded triangular norms is introduced it is proved that a sequence of triangular norms converges to a given continuous triangular norm if and only if this convergence is uniform finally we prove that every continuous triangular norm is a uniform limit of continuous archimedean triangular norms

characterization of jacobian varieties in terms of soliton equations pour dans le demi espace superieur de siegel h g soit x c g z g z g la variete abelienne principalement polarisee correspondante et soit z z m e z gexp 2 i t mz i t m m la fonction theta de riemann pour x les deux conditions a et b pour x sont equivalentes a 1 il existe des vecteurs a 1 a 2 a 3 c g a 1 0 et une forme quadratique q t i j 1 3 q ij t i t j q ij c tel que pour c g t t exp q t t 1 a 1 t 2 a 2 t 3 a 3 donne une solution a l equation de kadomtsev petviashvili sous la forme d hirota d 1 4 3d 2 2 4d 1 d 3 0 2 le diviseur de x est irreductible b x est isomorphe a la variete jacobienne d une courbe lisse complete de genre g sur c

convergence of residuated operators and connective stability of non classical logics some of the results of jenei 1993 are put in a more general setting in this paper the convergence of the residuated connectives related to a sequence of left continuous triangular norms to the residuated connective of the limit triangular norm is studied two sufficient and necessary conditions are given a derived concept the connective stability of non classical logics is introduced and investigated it is established that godel s logic some girard s logics and further non classical logics are connective stable

characterizations of jacobians of curves with automorphisms we obtain a characterization of theta functions of jacobian varieties of curves with automorphisms among theta functions of principally polarized abelian varieties p p a v we first give a characterization in terms of finite dimensional orbits for a suitable action in the sato grassmannian secondly the introduction of formal baker akhiezer functions and formal t functions attached to a p p a v for the multipuncture case allows us to characterize in terms of bilinear identities those baker akhiezer functions that are baker akhiezer functions of jacobians of curves with automorphisms further in the case of automorphisms with fixed points we rewrite the previous result as a hierarchy of partial differential equations for the function of a p p a v finally since baker akhiezer and t functions are written in terms of theta functions these results give rise to characterizations of p p a v in terms of their theta functions

cohomological structure in soliton equations and jacobian varieties on etudie la structure des orbites du systeme dynamique definie par la hierarchie kp totale on montre que chaque orbite est localement isomorphe a un certain groupe de cohomologie associe a une algebre commutative le systeme dynamique kp restreint a chaque orbite determine un systeme dynamique de mouvements lineaires sur lui par rapport a la structure lineaire du groupe de cohomologie

wandering domains in the iteration of entire functions fonctions entieres a domaines multiplement connexes de normalite ensembles de fatou julia pour des fonctions qui commuttent exemples de type d herman classes de fonctions entieres sans domaines d errance

on the hausdorff dimension of the escaping set of certain meromorphic functions let f be a transcendental meromorphic function of finite order for which the set of finite singularities of f 1 is bounded suppose that is not an asymptotic value and that there exists m n such that the multiplicity of all poles except possibly finitely many is at most m for r 0 let ir f be the set of all z c for which lim infn fn z r as n here fn denotes the n th iterate of f let i f be the set of all z c such that fn z as n that is i f t r 0 ir f denote the hausdorff dimension of a set a c by hd a it is shown that limr hd ir f 2m 2 m in particular hd i f 2m 2 m these estimates are best possible for given and m we construct a function f such that hd i f 2m 2 m and hd ir f 2m 2 m for all r 0 if f is as above but of infinite order then the area of ir f is zero this result does not hold without a restriction on the multiplicity of the poles

some results on the degree of symmetry of fuzzy relations abstract in this paper we investigate the degree of the symmetry of fuzzy relations on a set x based on the fuzzy e equality derived from uninorms with unit element e the degree of the symmetry of fuzzy relations are defined by two different approaches the type i degree of symmetry and the type ii degree of symmetry the main work of this paper include first we discuss some basic properties of those two degrees especially for the relationship between them in particular for continuous t norms we give a necessary and sufficient condition such that the type i degree of symmetry and the type ii degree of symmetry are equal and then we obtain that the type ii degree of symmetry is more appropriate to character the degree of the symmetry of fuzzy relations than the type i degree of symmetry with respect to whether they preserve the fuzzy e equalities or not in the meantime for a special case with continuous t norms we provide a necessary and sufficient condition such that the type i degree of symmetry preserves the fuzzy equalities finally for conjunctive left continuous idempotent uninorms with neutral element e 0 1 we find out a symmetric fuzzy relation s which is close enough to the given fuzzy relation r with respect to fuzzy e equality such that the degree of fuzzy e equality of s and r is the type ii degree of symmetry of r in particular we obtain analogous results for continuous t norms and one class of left continuous t norms

intersection theory on the moduli space of curves and the matrix airy function we show that two natural approaches to quantum gravity coincide this identity is nontrivial and relies on the equivalence of each approach to kdv equations we also investigate related mathematical problems

idempotent integral as limit of g integrals we show that sup and inf decomposable measures can be obtained as limits of families of pseudo additive measures with respect to generated pseudo additions the corresponding integrals with respect to sup or inf decomposable measures can be obtained as limits of families of g integrals

are there critical points on the boundaries of singular domains generalizing a result of e ghys we prove a general theorem that implies that if a rational functionf of the riemann sphere of degree 2 leaves invariant a singular domainc a disk or a ring on which the rotation number off satisfies a diophantine condition provided that on bar c f is injective then each boundary component ofc contains critical point off the injectivity condition is always satisfied for singular disks associated to linearizable periodic elliptic points off z z n a withne n 2 andae we also show that the singular disks associated to periodic elliptic points off z e az that satisfy a diophantine condition are unbounded in in the end of the paper we give a survey of the theory of iteration of entire functions of

construction of k lipschitz triangular norms and conorms from empirical data this paper examines the practical construction of k lipschitz triangular norms and conorms from empirical data we apply a characterization of such functions based on k convex additive generators and translate k convexity of piecewise linear strictly decreasing functions into a simple set of linear inequalities on their coefficients this is the basis of a simple linear spline fitting algorithm which guarantees k lipschitz property of the resulting triangular norms and conorms

an efficient procedure for solving a fuzzy relational equation with max archimedean t norm composition in the literature a necessary condition for minimal solutions of a fuzzy relational equation with max product composition shows that each of its components is either zero or the corresponding component s value of the greatest solution in this paper we first extend this necessary condition to the situation with max archimedean triangular norm t norm composition based on this necessary condition we then propose rules to reduce the problem size so that the complete set of minimal solutions can be computed efficiently furthermore rather than work with the actual equations we employ a simple matrix whose elements capture all of the properties of the equations in finding the minimal solutions numerical examples with specific cases of the max archimedean t norm composition are provided to illustrate the procedure

smoothly generated archimedean approximation of continuous triangular norms a constructive method is given for approximating a given continuous triangular norm by a sequence of smoothly generated archimedean triangular norms in the uniform metric

geometric realization of conformal field theory on riemann surfaces conformal field theory on a family of riemann surfaces is formulated we derive equations of motion of vacua which are parametrized by moduli of riemann surfaces and show that these vacua are characterized uniquely by these equations our theory has a deep connection with sato s theory of kp equations

on archimedean triangular norms abstract the behaviour of the additive generator functions related to a sequence of convergent continuous archimedean triangular norm where the limit triangular norm is continuous archimedean is examined in this paper it is proved that the related generator functions converge to the generator function of the limit triangular norm in some sense under the assumption that the limit triangular norm is strict a bit weaker convergence is proved if the limit triangular norm has 0 divisor an example is given for the fact that the stronger type of convergence cannot be obtained in the 0 divisor limit case

a direct proof of the steinberg property of the contou carrere symbol abstract the aim of this work is to show that when a is an artinian local ring the contou carrere symbol satisfies the property of steinberg symbols f 1 f a t 1 for all elements f 1 f a t moreover we offer a cohomological characterization of the contou carrere symbol from the commutator of a central extension of groups

selective solutions to transcendental equations abstract this paper presents a combination of global iterative methods based on the fatou julia theory and local methods to find selected roots of elementary transcendental equations z f z c z and c complex that occur in complex sturm liouville eigenvalue problems in dielectric spectroscopy and in orbit determination suitable starting values for the iteration function z n 1 f z n c and appropriate regions for each determination of the inverse iteration function z n f 1 z n c are presented convergence criteria are derived from the facts that f has very few attractive fixed points and that the attractive fixed points of f 1 have relatively large basins of attraction in the above mentioned regions certain fixed points of f can be reached quickly by means of a local method like newton s method it is shown by means of digital figures that in general newton s method may lead to attractive cycles or to unpredictable roots when the starting values are near the fatou julia set convergence to parasitic roots or even to strange attractors may occur with iterative methods of higher order

moduli of curves grobner bases and the krichever map abstract we study moduli spaces of possibly non nodal curves c p 1 p n of arithmetic genus g with n smooth marked points equipped with nonzero tangent vectors such that o c p 1 p n is ample and h 1 o c a 1 p 1 a n p n 0 for given integer weights a a 1 a n such that a i 0 and a i g we show that each such moduli space u g n n s a is an affine scheme of finite type and the krichever map identifies it with the quotient of an explicit locally closed subscheme of the sato grassmannian by the free action of the group of changes of formal parameters we study the git quotients of u g n n s a by the natural torus action and show that some of the corresponding stack quotients give modular compactifications of m g n with projective coarse moduli spaces more generally using similar techniques we construct moduli spaces of curves with chains of divisors supported at marked points with prescribed number of sections which in the case n 1 corresponds to specifying the weierstrass gap sequence at the marked point

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

hausdorff measure of escaping sets on certain meromorphic functions abstract we consider transcendental meromorphic function for which the set of finite singularities of its inverse is bounded bergweiler and kotus gave bounds for the hausdorff dimension of the escaping sets if the function has no logarithmic singularities over the multiplicities of poles are bounded and the order is finite we study the case of infinite order and find gauge functions for which the hausdorff measure of escaping sets is zero or

equations of the moduli of pointed curves in the infinite grassmannian the main result of this paper is the explicit computa tion of the equations defining the moduli space of triples c p where c is an integral and complete algebraic curve p a smooth rational point anda certain isomorphism this is achieved by introducing algebraically infinite grassmannians tau and baker ahkiezer functions and by proving an addition formula for tau functions