(1.1) det(uzj z̄k) = ψ(z, u,∇u) in Ω, u = φ on ∂Ω and related questions. When Ω is a strongly pseudoconvex domain, this problem has received extensive study. In [4]-[6], E. Bedford and B. A. Taylor established the existence, uniqueness and global Lipschitz regularity of generalized pluri-subharmonic solutions. S.-Y. Cheng and S.-T. Yau [8], in their work on complete Kähler-Einstein metrics on no...

If an agent desires that φ and desires that ψ, this agent often also desires that φ and ψ hold at the same time (φ∧ψ). However, there are cases where φ ∧ ψ may be found less satisfactory for the agent than each of φ or ψ alone. This paper is a first attempt at modeling such nonmonotonic desires. The approach is developed in the setting of possibility theory, since it has been recently pointed o...

In this paper we present a theory of qualitative probability. Work in the area goes back at least to de Finetti. The usual approach is to specify a binary operator with φ ψ having the intended interpretation that φ is not more probable than ψ. We generalise these approaches by extending the domain of the operator from the set of events to the set of finite sequences of events. If Φ and Ψ are fi...

Abstract Let S be a semigroup, and let φ, ψ : → two endomorphisms (which are not necessarily involutive). Our main goal in this paper is to solve the following generalized variant of d’Alembert’s functional equation f ( x ϕ y ) <m...

We consider topological dynamical systems ( X , T ) where is a compact metrizable space and denotes an action of countable amenable group G on by homeomorphisms. For two such Y S factor map π : → intermediate system Z R for which can be written as composition maps ψ φ . In this paper, we show that any -subshifts the set entropies subshift factors dense in interval [ h ] As corollary, also prove...

LetA be a finite-dimensional commutative algebra over the complex numbers with nonzero multiplicative identity element e. Let M denote the set of homomorphisms from A onto the complex numbers. Thus we get a homomorphism from A into the algebra of complex-valued functions on M, with respect to pointwise addition and multiplication of functions, by sending an element x of A to the function on M w...

For a binary quartic form φ without multiple factors, we classify the quartic K3 surfaces φ(x, y) = φ(z, t) whose Néron-Severi group is (rationally) generated by lines. For generic binary forms φ, ψ of prime degree without multiple factors, we prove that the Néron-Severi group of the surface φ(x, y) = ψ(z, t) is rationally generated by lines.

Article history: Received 16 March 2011 Accepted 19 April 2011 Available online 5 May 2011 Presented by Gilles Pisier An example is constructed of two Riemann maps φ and ψ of the unit disk onto the same domain such that φ′/ψ ′ is bounded but not bounded away from zero. This is shown by producing explicit analytic expressions of φ and ψ . © 2011 Académie des sciences. Published by Elsevier Masso...

0 −−−−→ {O, (0, 0)} −−−−→ E(Q) φ −−−−→ E(Q) α −−−−→ Q×/Q× 2 0 −−−−→ {O, (0, 0)} −−−−→ E(Q) ψ −−−−→ E(Q) β −−−−→ Q×/Q× . Finally, we have ψ ◦ φ = [2]E (multiplication by 2 on E) and φ ◦ ψ = [2]E. Thus although the situation is more involved than for the 2-descent on curves with three rational points of order 2, we have managed to break up the multiplicationby-2 map into two homomorphisms φ and ψ...

Let A, B be unital C*-algebras and assume that A is separable and quasidiagonal relative to B. Let φ,ψ : A → B be unital ∗-homomorphisms. If A is nuclear and satisfies the UCT, we prove that φ is approximately stably unitarily equivalent to ψ if and only if φ∗ = ψ∗ : K∗(A,Z/n) → K∗(B,Z/n) for all n ≥ 0. We give a new proof of a result of [DE2] which states that if A is separable and quasidiagon...