Lattice-valued up-sets and down-sets of a poset are investigated under the cutworthy approach. It is proved that the collections of all lattice valued up-sets and down-sets of a given poset are complete lattices under fuzzy inclusion. Properties of these are investigated. For a given collection of crisp up-sets of a poset, necessary and sufficient conditions are given under which the family rep...

Motivated by Ying’ work on automata theory based on quantum logic (Ying, M. S. (2000). International Journal of Therotical Physics, 39(4): 985–996; 39(11): 2545– 2557) and inspired by the close relationship between the automata theory and the theory of formal grammars, we have established a basic framework of grammar theory on quantum logic and shown that the set of l-valued quantum regular lan...

We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory  on  Hilbert $C^*$-modules is studied.

The aim of the paper is to prove that if L is a linear subspace of the space C(K) of all real-valued continuous functions defined on a nonempty compact Hausdorff space K such that min(|f |, 1) ∈ L whenever f ∈ L, then for any nonzero g ∈ L̄ (where L̄ denotes the uniform closure of L in C(K)) and for any sequence (bn)n=1 of positive numbers satisfying the relation P∞ n=1 bn = ‖g‖ there exists a se...

In this paper, we define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation: f (x 1 + · · · + x l) = (l – 1)f x 1 + · · · + x l–1 l – 1 + f (x l) for a fixed integer l with l > 1, and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation.

We demonstrate that parastatistics can be quantized using path integrals by calculating the generating functionals for time-ordered products of both free and interacting parabose and parafermi fields in terms of path integrals. We also give a convenient form of the commutation relations for the Green components of the parabose and parafermi operators in both the canonical and path integral form...

In this paper, we will present a deenability theorem for rst order logic. This theorem is very easy to state, and its proof only uses elementary tools. To explain the theorem, let us rst observe that if M is a model of a theory T in a language L, then, clearly, any deenable subset S M (i.e., a subset S = fa j M j = '(a)g deened by some formula ') is invariant under all automorphisms of M. The s...

X iv :0 70 9. 42 29 v1 [ m at h. FA ] 2 6 Se p 20 07 An Extrapolation of Operator Valued Dyadic Paraproducts Tao MEI 1 Abstract We consider the dyadic paraproducts πφ on T associated with an M-valued function φ. Here T is the unit circle and M is a tracial von Neumann algebra. We prove that their boundedness on L(T, L(M)) for some 1 < p < ∞ implies their boundedness on L(T, L(M)) for all 1 < p ...

Remark 1 In this text, we always work between 0 and 1 with 1/2 playing the rôle of the midpoint. A simple rescaling allows to work between −1 and 1 with 0 playing the rôle of a midpoint. • A valued relation T is said to be reflexive if T (x, x) = 1, for all x ∈ X. A valued relation T on X such that T (x, y) ∈ {0, 1}, for all x, y ∈ X, is said to be crisp. As is usual, we write x T y instead of ...