The limit functions of a random iteration system

This paper discusses the limit functions of a random iteration system formed by finitely many rational functions. Applying these results we prove that a hyperbolic iteration system has no wandering domain and that its limit functions are constant. Finally the continuity on its Julia set is considered.     

一致结构的单子及其应用

讨论了乘积一致结构的单子的刻画 .利用一致结构的单子给出了 Cauchy网及含小集集族的非标准特征 .作为应用给出一致空间几个重要定理的离散化证明 .     

Independence concepts in evidence theory

We study three conditions of independence within evidence theory framework. The first condition refers to the selection of pairs of focal sets. The remaining two ones are related to the choice of a pair of elements, once a pair of focal sets has been selected. These three concepts allow us to formalize the ideas of lack of interaction among variables and among their (imprecise) observations. We illustrate the difference between both types of independence with simple examples about drawing balls from urns. We show that there are no implication relationships between both of them. We also study the relationships between the concepts of “independence in the selection” and “random set independence”, showing that they cannot be simultaneously satisfied, except in some very particular cases.     

Basic concepts for a theory of evaluation: Hierarchical aggregation via autodistributive connectives in fuzzy set theory

The ‘aggregative operator’ introduced by Combi (1982) in his analysis of ‘basic concepts for a theory of evaluation’ in this journal is based on the axioms of associativity, continuity, and monotonicity. In this paper, an alternative approach is given where associativity is replaced by another axiom, viz. autodistributivity, implying a kind of hierarchical aggregation instead of the former horizontal one. The new set of properties yields a general class of operators for connecting fuzzy sets which are formally similar to the aggregative operators, but are purely compensative (in a strong sense). Moreover, this modified approach generalizes a recent approach based on generalized means as compensative connectives. It appears to be similar to expected utility approaches in decision making under uncertainty, and seems to be a very promising tool to handle representation problems as they grow from other fields of human decision making, e.g. of multicriteria analysis and of welfare theory.     

On some examples of obstructed irregular surfaces

We determine the base space of the Kuranishi family of some complete intersections in the product of an abelian variety and a projective space.As a consequence,we obtain new examples of obstructed irregular surfaces with ample canonical bundle and maximal Albanese dimension.     

Netlike partial cubes, V: Completion and netlike classes

We define a completion of a netlike partial cube G by replacing each convex 2n-cycle C of G with n≥3 by an n-cube admitting C as an isometric cycle. We prove that a completion of G is a median graph if and only if G has the Median Cycle Property (MCP) (see N. Polat, Netlike partial cubes III. The Median Cycle Property, Discrete Math.). In fact any completion of a netlike partial cube having the MCP is defined by a universal property and turns out to be a minimal median graph containing G as an isometric subgraph. We show that the completions of the netlike partial cubes having the MCP preserves the principal constructions of these graphs, such as: netlike subgraphs, gated amalgams and expansions. Conversely any netlike partial cube having the MCP can be obtained from a median graph by deleting some particular maximal finite hypercubes. We also show that, given a netlike partial cube G having the MCP, the class of all netlike partial cubes having the MCP whose completions are isomorphic to those of G share different properties, such as: depth, lattice dimension, semicube graph and crossing graph.     

Partial cubes: structures, characterizations, and constructions

Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi?’s and Winkler’s relations play an important role in the theory of partial cubes. These structures are employed in the paper to characterize bipartite graphs and partial cubes of arbitrary dimension. New characterizations are established and new proofs of some known results are given.The operations of Cartesian product and pasting, and expansion and contraction processes are utilized in the paper to construct new partial cubes from old ones. In particular, the isometric and lattice dimensions of finite partial cubes obtained by means of these operations are calculated.     

Isometric embeddings of subdivided connected graphs into hypercubes

Isometric subgraphs of hypercubes are known as partial cubes. These graphs have first been investigated by Graham and Pollack [R.L. Graham, H. Pollack, On the addressing problem for loop switching, Bell System Technol. J. 50 (1971) 2495-2519; and D. Djokovi?, Distance preserving subgraphs of hypercubes, J. Combin. Theory Ser. B 14 (1973) 263-267]. Several papers followed with various characterizations of partial cubes. In this paper, we determine all subdivisions of a given configuration which can be embedded isometrically in the hypercube. More specifically, we deal with the case where this configuration is a connected graph of order 4, a complete graph of order 5 and the case of a k-fan F_k(k≥3).     

Conditioned stochastic differential equations: theory, examples and application to finance

We generalize the notion of Brownian bridge. More precisely, we study a standard Brownian motion for which a certain functional is conditioned to follow a given law. Such processes appear as weak solutions of stochastic differential equations that we call conditioned stochastic differential equations. The link with the theory of initial enlargement of filtration is made and after a general presentation several examples are studied: the conditioning of a standard Brownian motion (and more generally of a Markov diffusion) by its value at a given date, the conditioning of a geometric Brownian motion with negative drift by its quadratic variation and finally the conditioning of a standard Brownian motion by its first hitting time of a given level. As an application, we introduce the notion of weak information on a complete market, and we give a “quantitative” value to this weak information.     

Flexible contracting theory and case examples

When companies or governmental agencies arrange for contracts that call for deliveries over extended periods of time, arrangements are often made to adjust the final prices for exogenous changes in the costs of production. This paper shows, under specified conditions, how contracts can be devised which allow for price changes but at the same time still provide incentives for the producing unit to be efficient. For example, only under very specific conditions will a “pass-through” arrangement be acceptable. We show how the techniques of Geometric Programming applied to the economic theory of production can be used to analyze such problems.     

Singularities of minima: a walk on the wild side of the Calculus of Variations

I will report on some recent developments concerning the problem of estimating the Hausdorff dimension of the singular sets of solutions to elliptic and variational problems. Emphasis will be given on some open issues. Connections with measure data problems will be outlined.     

Proper partial geometries with Singer groups and pseudogeometric partial difference sets

A partial geometry admitting a Singer group G is equivalent to a partial difference set in G admitting a certain decomposition into cosets of line stabilizers. We develop methods for the classification of these objects, in particular, for the case of abelian Singer groups. As an application, we show that a proper partial geometry Π=pg(s+1,t+1,2) with an abelian Singer group G can only exist if t=2(s+2) and G is an elementary abelian 3-group of order ³(s+1) or Π is the Van Lint-Schrijver partial geometry. As part of the proof, we show that the Diophantine equation (m³−1)/2=(²rw−1)/(r²−1) has no solutions in integers m,r?1, w?2, settling a case of Goormaghtigh's equation.     

Partial regularity and singular set of solutions to second order parabolic systems

In this paper we deal with the study of regularity properties of weak solutions to nonlinear, second-order parabolic systems of the type

     

Second order parabolic systems, optimal regularity, and singular sets of solutions

We present a new, complete approach to the partial regularity of solutions to non-linear, second order parabolic systems of the form

u_t−divA(x,t,u,Du)=0.