A differential invariant is a function defined on the jet space of functions that remains the same under a group action. It is an important concept to solve the equivalence problem. This paper presents an effective method to derive a special type of affine differential invariants. Given some functions defined on the plane and an affine group acting on the plane, there are induced actions of the...

Let f and g be transcendental entire functions, each with a bounded set of singular values, and suppose that g ◦ φ = ψ ◦ f , where φ, ψ : C → C are affine. We show that the escaping sets of f and g have the same Hausdorff dimension. Using a result of the second author, we deduce that there exists a family of transcendental entire functions for which the escaping set has Hausdorff dimension equa...

For a given vectorial Boolean function F from F2 to itself it was defined an associated Boolean function γF (a, b) in 2n variables by C. Carlet, P. Charpin, V. Zinoviev in 1998 that takes value 1 iff a 6= 0 and equation F (x) +F (x+a) = b has solutions. In this paper we introduce the notion of differentially equivalent functions as vectorial functions that have equal associated Boolean function...

We generalize the notions of user equilibrium and system optimum to nonatomic congestion games with stochastic demands. We establish upper bounds on the price of anarchy for three different settings of link cost functions and demand distributions, namely, (a) affine cost functions and general distributions, (b) polynomial cost functions and general positive-valued distributions, and (c) polynom...

Abstract Let $${\mathcal {C}} \subset {\mathbb {N}}^p$$ C ⊂ N p be a finitely generated integer cone and $$S\subset {\mathcal {C}}$$ S an affine semigroup such that the real cones by S are equal. ...

We introduce a class of induced representations of the degenerate double affine Hecke algebra H of glN (C) and analyze their structure mainly by means of intertwiners of H . We also construct them from ŝlm(C)-modules using Knizhnik-Zamolodchikov connections in the conformal field theory. This construction provides a natural quotient of induced modules, which turns out to be the unique irreducib...

First-order Takagi-Sugeno models are mainly based on the interpolation between several local affine functions usually defined on trapezoidal fuzzy partitions. The standard computational model presents some shapefailures: the approximation does not preserve the positivity, monotony or convexity of the data that belong to the corresponding antecedent term cores. Moreover the standard output does ...

The bent functions are the Boolean functions of an even number of variables which are at the maximum possible distance from the set of all affine functions. In this paper, it is shown that each isometric mapping of the set of Boolean functions of n variables to itself preserving the class of bent functions is a combination of an affine transformation of coordinates and a shift by an affine func...

Cherednik attached to an affineHecke algebramodule a compatible systemof difference equations, called quantum affine Knizhnik–Zamolodchikov (KZ) equations. In the case of a principal series module, we construct a basis of power series solutions of the quantum affine KZ equations. Relating the bases for different asymptotic sectors gives rise to a Weyl group cocycle, which we compute explicitly ...