Finite-Time Set Reachability of Probabilistic Boolean Multiplex Control Networks

This study focuses on the finite-time set reachability of probabilistic Boolean multiplex control networks (PBMCNs). Firstly, based on the state transfer graph (STG) reconstruction technique, the PBMCNs are extended to random logic dynamical systems. Then, a necessary and sufficient condition for the finite-time set reachability of PBMCNs is obtained. Finally, the obtained results are effectively illustrated by an example.

Weighted Relative Group Entropies and Associated Fisher Metrics

A large family of new α-weighted group entropy functionals is defined and associated Fisher-like metrics are considered. All these notions are well-suited semi-Riemannian tools for the geometrization of entropy-related statistical models, where they may act as sensitive controlling invariants. The main result of the paper establishes a link between such a metric and a canonical one. A sufficient condition is found, in order that the two metrics be conformal (or homothetic). In particular, we recover a recent result, established for α=1 and for non-weighted relative group entropies. Our conformality condition is “universal”, in the sense that it does not depend on the group exponential.

On Existence of Primitive Normal Elements of Cubic Form over Finite Fields

For a prime [Formula: see text]and a positive integer[Formula: see text], let [Formula: see text] and [Formula: see text] be the extension field of [Formula: see text]. We derive a sufficient condition for the existence of a primitive element [Formula: see text] in[Formula: see text] such that [Formula: see text] is also a primitive element of [Formula: see text], a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is a primitive element of [Formula: see text], and a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is also a primitive normal element of [Formula: see text] over [Formula: see text].

Initial state estimation from limited observations of the heat equation in metric graphs

This paper deals with initial state estimation problems of the heat equation in equilateral metric graphs being admitted to have cycles. Particularly, we are concerned with suitable placements of observation points in order to uniquely determine the initial state from observation data. We give a necessary and sufficient condition for suitable placements of observation points, and such suitable placements are determined from transition matrices of metric graphs. From numerical simulations, we confirm effectiveness of a necessary and sufficient condition.

Some Results on Noetherian Warfield Domains

Let [Formula: see text] be a domain. In this paper, we show that if [Formula: see text] is one-dimensional, then [Formula: see text] is a Noetherian Warfield domain if and only if every maximal ideal of [Formula: see text] is 2-generated and for every maximal ideal[Formula: see text] of [Formula: see text], [Formula: see text] is divisorial in the ring [Formula: see text]. We also prove that a Noetherian domain [Formula: see text] is a Noetherian Warfield domain if and only if for every maximal ideal [Formula: see text] of [Formula: see text], [Formula: see text] can be generated by two elements. Finally, we give a sufficient condition under which all ideals of [Formula: see text] are strongly Gorenstein projective.

Success Factors in Management of Development Projects

From the reports of the Inter-American Development Bank (IDB) Office of Evaluation and Oversight (OVE), a limited analysis of the factors affecting the execution of development cooperation projects was identified. Thanks to the review of scientific articles by renowned authors, effectiveness, relevance, competencies and motivation, sustainability, risk management, and additionality were evaluated using the analysis of relationships between variables and causality using IBM SPSS and fsQCA 3.0 software, respectively. As a result, a model was obtained that relates the components, factors, and roles that make up the stakeholder matrix. It was concluded that the effectiveness factor has a significant relationship with the success of a project; however, this could not be possible without a good development of sustainability and risk management, the latter being a necessary and sufficient condition for success in this type of projects. Currently, risk management has not only become a necessity nowadays, but the improvement of risk management will increase sustainability in project management, the main factors for the success of a project.

Sufficient condition for infinite solutions of Diophantine Equation: n! = P(s)

In this article I have used method which tells that number of solutions of Diophantine equation: n! = P(s) is infinite if some condition is satisfied. I have applied Inverse Laplace Transform to n! = P(s) and got function f(t) which is easier to deal with. The condition is given in section below contains zero of f(t) or zero of some modified function of f(t): g(t) = f(t) - h(t).

Building 2D Model of Compound Eye Vision for Machine Learning

This paper presents a two-dimensional mathematical model of compound eye vision. Such a model is useful for solving navigation issues for autonomous mobile robots on the ground plane. The model is inspired by the insect compound eye that consists of ommatidia, which are tiny independent photoreception units, each of which combines a cornea, lens, and rhabdom. The model describes the planar binocular compound eye vision, focusing on measuring distance and azimuth to a circular feature with an arbitrary size. The model provides a necessary and sufficient condition for the visibility of a circular feature by each ommatidium. On this basis, an algorithm is built for generating a training data set to create two deep neural networks (DNN): the first detects the distance, and the second detects the azimuth to a circular feature. The hyperparameter tuning and the configurations of both networks are described. Experimental results showed that the proposed method could effectively and accurately detect the distance and azimuth to objects.