The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...

This paper describes a new variant of the least-mean-squares (LMS) algorithm, with low computational complexity, for updating an adaptive lter. The reduction in complexity is obtained by using values of the input data and the output error, quantized to the nearest power of two, to compute the gradient. This eliminates the need for multipliers or shifters in the algorithm's update section. The q...

In this article we will present some problems that have weak symmetries. In contrast to a proper symmetry, a weak symmetry acts only on a subset of the variables and preserves the feasibility state only with respect to a subset of the constraints. Therefore, breaking weak symmetries with standard techniques would lead to a loss of solutions. This article presents also a modelling technique whic...

In this paper, we classify all generalized quadrangles weakly embedded of degree 2 in projective space. More exactly, given a (possibly infinite) generalized quadrangle Γ = (P,L, I ) and a map π from P (respectively L) to the set of points (respectively lines) of a projective space PG(V ), V a vector space over some skew field (not necessarily finite-dimensional), such that: (i) π is injective ...

We introduce the notion of \partial Occam algorithm". A partial Occam algorithm produces a succinct hypothesis that is partially consistent with given examples, where the proportion of consistent examples is a bit more than half. By using this new notion, we propose one approach for obtaining a PAC learning algorithm. First, as shown in this paper, a partial Occam algorithm is equivalent to a w...

We introduce BPDL, a combination of propositional dynamic logic PDL with the basic four-valued modal logic BK studied by Odintsov and Wansing (‘Modal logics with Belnapian truth values’, J. Appl. Non-Class. Log. 20, 279–301 (2010)). We modify the standard arguments based on canonical models and filtration to suit the four-valued context and prove weak completeness and decidability of BPDL.

We find more self-tuning solutions by introducing a general form for Lagrangian of a 3-index antisymmetric tensor field AMNP in the RS II model. In particular, for the logarithmic Lagrangian, ∝ log(−H2), we obtained a closed form weak self-tuning solution.

We study multicast capacity for a large-scale spatial inhomogeneous mobile network consisting of n ad hoc nodes. Under our mobility model, the stationary spatial distribution of a node is non-uniform; each node spends most of the time in a certain region, and rarely (or never) visits out of such region. To characterize the inhomogeneity of the mobility model, we define an activity exponent c an...

We discuss the axioms for vertex algebras and their modules, using formal calculus. Following certain standard treatments, we take the Jacobi identity as our main axiom and we recall weak commutativity and weak associativity. We derive a third, companion property that we call “weak skew-associativity.” This third property in some sense completes an S3-symmetry of the axioms, which is related to...