In this paper, we characterize multiresolution analysis(MRA) Parseval frame multiwavelets in L^2(R^d) with matrix dilations of the form (D f )(x) = sqrt{2}f (Ax), where A is an arbitrary expanding dtimes d matrix with integer coefficients, such that |detA| =2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwa...

Topos-theoretic semantics for modal logic usually considers structures induced by a surjective geometric morphism f : F → E . f restricts to an injective (complete) distributive lattice homomorphism ∆A : SubE(A) −→ SubF (f∗A), for each A in E and natural in A w.r.t. to pullback. Each ∆A has a right adjoint ΓA that composes with ∆A to an endofunctor ∆AΓA on the Heyting algebra SubF (f ∗A) that s...

This paper presents a method for the segmentation and recognition of facial features and face tracking in digital video sequences based on inexact graph matching. It extends a previous approach proposed for static images to video sequences by incorporating the temporal aspect that is inherent to such sequences. Facial features are represented by attributed relational graphs, in which vertices c...

Characterizing the universal coverings of smooth projective varieties is an old and hard question. Central to the subject is a conjecture of Shafarevich according to which the universal cover X̃ of a smooth projective variety is holomorphically convex, meaning that for every infinite sequence of points without limit points in X̃ there exists a holomorphic function unbounded on this sequence. In t...

(ii) (Lazard’s Theorem) L is the polynomial algebra Z[x1, x2, ...]. We proved Lazard’s theorem last semester. We also proved that MU∗ is isomorphic to Z[x1, x2, ...], so MU∗ and L are both polynomial algebras with generators in even degrees (positive even degrees in MU∗, and negative even degrees in L). The usual complex orientation on MU gives rise to a formal group law, and thus we have a hom...

Starting with the underlying motivation of developing a general theory of L-fuzzy sets where L is a multilattice (a particular case of non-deterministic algebra), we study the relationship between the crisp notions of congruence, homomorphism and substructure on some non-deterministic algebras which have been used in the literature, i.e. hypergroups, and join spaces. Moreover, we provide suitab...

In this paper we will study the properties of the least extension n(Λ) of a given intermediate logic Λ by a strong negation. It is shown that the mapping from Λ to n(Λ) is a homomorphism of complete lattices, preserving and reflecting finite model property, frame–completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form ...

Abstract. A Weyl-Heisenberg frame for L(R) is a frame consisting of translates and modulates of a fixed function in L(R), i.e. (EmbTnag)m,n∈Z , with a, b > 0, and g ∈ L(R). In this paper we will give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g so that (EmbTnag) is an orthonormal basis for L (R). These resu...

The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between  $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is  bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.

Let H be a finitely-generated free abelian group and L(H) the graded free Lie algebra on H . There is a natural homomorphism H ⊗ L(H)→ L(H) defined by bracketing, whose kernel is denoted D(H). If H supports a non-singular symplectic form, eg H = H1(Σ), where Σ is a closed orientable surface, with symplectic basis {xi, yi}, then D(H) is, in fact, a Lie algebra. It can be identified with the Lie ...