In this paper MV-algebras, the algebras of èukasiewicz in®nite-valued logics, are interpreted in a structure of bets, and a subjective interpretation of ®nitely additive measures on MV-algebras is given. Ó 2000 Elsevier Science Inc. All rights reserved.

A new method is presented for numerically capturing a moving interface of arbitrary dimension and codimension. The method is named the ‘local level set method’, since it localizes the level set method near the interface to significantly reduce the computational expense of the level set method. Following the framework of the level set method, an interface is implicitly represented as the zero le...

3 ABSTRACT. Let c > 0 be a fixed constant. Let 0 ≤ r < s be an arbitrary pair of real numbers. Let a, b be any pair of real numbers such that | b − a | ≤ c(s − r). Define C s r to be the set of continuous real-valued functions on [r, s], and define C r to be the set of continuous real-valued functions on [ r, +∞). Finally, consider the following sets of Lipschitz functions:

In a previous work the authors proved under a complex assumption on the set-valued mapping, the existence of Lipschitz solutions for second order convex sweeping processes in p-uniformly smooth and q-uniformly convex Banach spaces. In the present work we prove the same result, under a condition on the distance function to the images of the set-valued mapping. Our assumption is much simpler than...

We develop the filter theory in triangle algebras. We define several interval valued residuated lattice-filters (IVRL-filters for short) in triangle algebras. We investigate the relationships among these types of IVRL-filters. Also, some special triangle algebras are introduced and studied in details.

Existence of invariant measures for semi-linear stochastic evolution equations in separable real Hilbert spaces is considered, where the noise is generated by Hilbert space valued Lévy processes. It is shown that if the Lévy process has locally bounded second moments, if the semigroup generated by the linear part is hyperbolic, and if the Lipschitz constants of the nonlinearities are sufficient...

We study a variant of the Whitney extension problem [21, 22] for the space C k,ω (R n). We identify C k,ω (R n) with a space of Lipschitz mappings from R n into the space P k × R n of polynomial fields on R n equipped with a certain metric. This identification allows us to reformulate the Whitney problem for C k,ω (R n) as a Lip-schitz selection problem for set-valued mappings into a certain fa...