In this work, regularity of $n$-generalized Schützenberger product monoids from the point Group Theory is studied. Here, it determined necessary and sufficient conditions $A_{1}\Diamond A_{2}\Diamond \cdots \Diamond A_{n}$ to be regular while all $A_{i}\text{ }\left( 1\leqslant i\leqslant n\right)$ are monoids. Also, by considering groups, given another result for product.

in this paper, we consider an  i.e., multiple step-stress accelerated life testing (alt) experiment with unequal duration of time . it is assumed that the time to failure of a product follows rayleigh distribution with a log-linear relationship between stress and lifetime and also we assume a generalized khamis-higgins model for the effect of changing stress levels. taking into account that the...

In this article we describe EANT2, Evolutionary Acquisition of Neural Topologies, Version 2, a method that creates neural networks by evolutionary reinforcement learning. The structure of the networks is developed using mutation operators, starting from a minimal structure. Their parameters are optimised using CMA-ES, Covariance Matrix Adaptation Evolution Strategy, a derandomised variant of ev...

1. Fréchet space C∞[a, b] 2. Fréchet space of smooth functions E = C∞(Rn) 3. Fréchet space of Schwartz functions S on R 4. LF-space of test functions D on R 5. Generalized functions (distributions) D∗, S ∗, E∗ as linear functionals 6. Generalized functions D∗, S ∗, E∗ as completions of D 7. Fourier transforms of tempered distributions 8. Distributions supported at a point 9. Appendix: weak dual...

Generalized metric spaces are a common generalization of preorders and ordinary metric spaces. Every generalized metric space can be isometrically embedded in a complete function space by means of a metric version of the categorical Yoneda embedding. This simple fact gives naturally rise to: 1. a topology for generalized metric spaces which for arbitrary preorders corresponds to the Alexandroo ...

Generalized Product (GPC) Codes, an unification of Product Codes and Integrated Interleaved (II) Codes, are presented. Applications for approaches requiring local and global parities are described. The more general problem of extending product codes by adding global parities is studied and an upper bound on the minimum distance of such codes is obtained. Codes with one, two and three global par...

This paper introduces a new class of processor interconnection topology called Eight Row Matrix (ERM). The topology has been named so because of its characteristics that for any number of processors it always has eight rows. The attractive properties of ERM include constant degree, moderate diameter, regularity, symmetry, scalability and simple routing. ERM, when used as one of the components o...

Aggregation functions on [0, 1] with annihilator 0 can be seen as a generalized product on [0, 1]. We study the generalized product on the bipolar scale [−1, 1], stressing the axiomatic point of view ( compare also [9]). Based on newly introduced bipolar properties, such as the bipolar increasingness, bipolar unit element, bipolar idempotent element, several kinds of generalized bipolar product...

This paper introduces a new class of processor interconnection topology called LEA (Linearly Extendable ARM). The attractive properties of LEA topology include constant degree, moderate diameter, regularity, symmetry, scalability and simple routing. LEA, when used as one of the components of an interconnection topology based on product graphs, is capable of maintaining the constant degree over ...

Starting with a carefully formulated Dirichlet process (DP) mixture model, we derive a generalized product partition model (GPPM) in which the partition process is predictor-dependent. The GPPM generalizes DP clustering to relax the exchangeability assumption through the incorporation of predictors, resulting in a generalized Pólya urn scheme. In addition, the GPPM can be used for formulating f...