Journal of Mathematics

In this paper, we explore the concept of topologically dense injectivity of monoid acts. It is shown that topologically dense injective acts constitute a class strictly larger than the class of ordinary injective ones. We determine a number of acts satisfying topologically dense injectivity. Specifically, any strongly divisible as well as strongly torsion free -act over a monoid is topologically dense injective if and only if is a left reversible monoid. Furthermore, we establish a counterpart of the Skornjakov criterion and also identify a class of acts satisfying the Baer criterion for topologically dense injectivity. Lastly, some homological classifications for monoids by means of this type of injectivity of monoid acts are also provided.

Since ancient times, infectious diseases have been a major source of harm to human health. Therefore, scientists have established many mathematical models in the history of fighting infectious diseases to study the law of infection and then analyzed the practicability and effectiveness of various prevention and control measures, providing a scientific basis for human prevention and research of infectious diseases. However, due to the great differences in the transmission mechanisms and modes of many diseases, there are many kinds of infectious disease dynamic models, which make the research more and more difficult. With the continuous progress of infectious disease research technology, people have adopted more ways to prevent and interfere with the derivation and spread of infectious disease, which will make the state of infectious disease system change in an instant. The mutation of this state can be described more scientifically and reasonably by the mathematical impulse dynamic system, which makes the research more practical. Based on this, a time-delay differential system model of infectious disease under impulse effect was established by means of impulse differential equation theory. A class of periodic boundary value problems for impulsive integrodifferential equations of mixed type with integral boundary conditions was studied. The existence of periodic solutions of these equations was obtained by using the comparison theorem, upper and lower solution methods, and the monotone iteration technique. Finally, combined with the practical application, the established time-delay differential system model was applied to the prediction of the stability and persistence of the infectious disease dynamic system, and the correctness of the conclusion was further verified. This study provides some reference for the prevention and treatment of infectious diseases.

This paper is dedicated to the study of the geometric composition of a perfect fluid space-time with a conformal Ricci-Bourguignon soliton, which is the extended version of the soliton to the Ricci-Bourguignon flow. Here, we have delineated the conditions for conformal Ricci-Bourguignon soliton to be expanding, steady, or shrinking. We have studied certain curvature conditions on the spacetime that admit conformal Ricci-Bourguignon soliton. We have also discussed conformal Ricci-Bourguignon soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid, and radiation era.

In this paper, we introduce the concept of weakly semiprime ideals and weakly -systems in noncommutative rings. We establish the equivalence between an ideal being a weakly semiprime ideal and being a weakly -system. We provide alternative definitions and explore the properties of weakly semiprime ideals. Additionally, we investigate scenarios where all ideals in a given ring are weakly semiprime and demonstrate that in Noetherian rings, where every ideal is weakly semiprime, the prime radical and the Jacobson radical coincide.

A topological index (TI) is a numeric digit that signalizes the whole chemical structure of a molecular network. TIs are helpful in predicting the bioactivity of molecular substances in investigations of quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). TIs correlate various chemical and physical attributes of chemical substances such as melting and freezing point, strain energy, stability, temperature, volume, density, and pressure. There are several distance-based descriptors available in the literature, but connection-based TIs are considered more effective than degree-based TIs in measuring the chemical characteristics of molecular compounds. The present study focuses on computing the connection-based TIs for the most significant type of chemical structures, namely, rhombus silicate and rhombus oxide networks. At the end, we compare these structures on the basis of their computed result.

The purpose of this paper is to examine the condition for a Finsler space with a generalized -metric to be projectively flat. In addition, we establish that the Finsler space with generalized -metric is a flat-parallel Minkowski space and derive the condition under which the -change for the aforementioned metric is projective. We also explored the projective nature of -change for various significant Finsler metrics derived from the generalized -metric.