We continue the study of arrays of coupled identical cells that possess both global and internal symmetries, begun in part I. Here we concentrate on the ‘direct product’ case, for which the symmetry group of the system decomposes as the direct product L×G of the internal group L and the global group G. Again, the main aim is to find general existence conditions for symmetry-breaking steady-stat...

The theory of fuzzy logic provides a good mathematical and methodological basis for capturing the uncertainties associated with human cognitive processes, such as i d e n t i f y i n g c a u s a l relationships, thinking and reasoning. The conventional approaches to knowledge representation lack the means for representing the meaning of vague and incompletely understood concepts. As a consequen...

For given p ∈ [1, ∞] and g ∈ L p(R), we establish the existence and uniqueness of solutions f ∈ L p(R), to the equation f (x) − a f (bx) = g(x), where a ∈ R, b ∈ R\{0}, and |a| ≠ |b|1/p . Solutions include well-known nowhere differentiable functions such as those of Bolzano, Weierstrass, Hardy, and many others. Connections and consequences in the theory of fractal interpolation, approximation t...

The t r i g g e r i n g o f the Liquid-gas phase t r a n s i t i o n i n hot nuclear matter by quantum and s t a t i s t i c a l f l u c t u a t i o n s i s s tud ied i n a microscopic approach t o nucleation, which i s a f luid-dynamical vers ion o f the imaginary t ime dependent mean f i e l d theory a t f i n i t e temperature.

Over the last 10 years, the field of mathematical epidemiology has piqued the interest of complex-systems researchers, resulting in a tremendous volume of work exploring the effects of population structure on disease propagation. Much of this research focuses on computing epidemic threshold tests, and in practice several different tests are often used interchangeably.We summarize recent literat...

Let F be a finite extension of Qp and K a quadratic extension of F . If (Π, V ) is a representation of GL2(K), H a subgroup of GL2(K) and μ a character of the image subgroup det(H) of K∗, then Π is said to be μ-distinguished with respect to H if there exists a nonzero linear form l on V such that l(Π(g)v) = μ(det g)l(v) for g ∈ H and v ∈ V . We provide new proofs, using entirely local methods, ...

Introduction. For'several years one of the outstanding problems of lattice theory has been the following: Is every lattice with unique complements a Boolean algebra? Any number of weak additional restrictions are sufficient for an affirmative answer. For example, if a lattice is modular (G. Bergman [l](1)) or ortho-complemented (G. Birkhoff [l]) or atomic (G. Birkhoff and M. Ward [l]), then uni...

These are some notes on the basic properties of algebraic K-theory and G-theory derived spaces stacks, theory fundamental classes in this setting.