Search

Abstract In the present article, the Hyers–Ulam stability of the following inequality is analyzed: 0.1 { d ( f ( ı + ȷ ) , ( f ( ı ) + f ( ȷ ) ) ) ≤ d ( ρ 1 ( ( f ( ı + ȷ ) + f ( ı − ȷ ) , 2 f ( ı ) ) ) d ( f ( ı + ȷ ) , ( f ( ı ) + f ( ȷ ) ) ) ≤ + d ( ρ 2 ( 2 f ( ı + ȷ 2 ) , ( f ( ı ) + f ( ȷ ) ) ) ) $$ \textstyle\begin{cases} d (f(\imath +\jmath ), \ (f(\imath )+ \ f(\jmath )) )\leq d (\rho _{1}((f(\imath +\jmath )+ f(\imath - \jmath ),\ 2f(\imath )) ) \\ \hphantom{ d (f(\imath +\jmath ), \ (f(\imath )+ \ f(\jmath )) )\leq}{}+ d (\rho _{2} (2f (\frac{\imath +\jmath}{2} ), \ (f(\imath )+ f(\jmath )) ) ) \end{cases} $$ in the setting of digital metric space, where ρ 1 $\rho _{1}$ and ρ 2 $\rho _{2}$ are fixed nonzero complex numbers with 1 > 2 | ρ 1 | + | ρ 2 | $1>\sqrt{2}|\rho _{1}|+|\rho _{2}|$ by using fixed point and direct approach.

In this paper, we study the Onsager-Machlup function and its relationship to the Freidlin-Wentzell function for measures equivalent to arbitrary infinite dimensional Gaussian measures. The Onsager-Machlup function can serve as a density on infinite dimensional spaces, where a uniform measure does not exist, and has been seen as the Lagrangian for the "most likely element". The Freidlin-Wentzell rate function is the large deviations rate function for small-noise limits and has also been identified as a Lagrangian for the "most likely element". This leads to a conundrum - what is the relationship between these two functions? We show both pointwise and G-convergence (which is essentially the convergence of minimizers) of the Onsager-Machlup function under the small-noise limit to the Freidlin-Wentzell function - and give an expression for both. That is, we show that the small-noise limit of the most likely element is the most likely element in the small noise limit for infinite dimensional measures that are equivalent to a Gaussian. Examples of measures include the law of solutions to path-dependent stochastic differential equations and the law of an infinite system of random algebraic equations. [ABSTRACT FROM AUTHOR]

In this article, we consider a nonlinear elliptic unilateral equation whose model is − ∑ i = 1 N ∂ i σ i (x , u , ∇ u) + L (x , u , ∇ u) + N (x , u , ∇ u) = μ − div ϕ (u) in Ω. We prove the existence of entropy solutions for the aforementioned equation in the anisotropic Sobolev space, under the hypotheses, μ = f − div F belongs to L 1 (Ω) + W − 1 , p ′ (Ω) . The nonlinear terms L (x , s , ∇ u) satisfy the sign and growth conditions, and N (x , s , ∇ u) verifies only the growth conditions. [ABSTRACT FROM AUTHOR]

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Mathematics is the most logical and unbiased scientific field there is. What is true in mathematics today will forever stay true, and mathematical arguments will always clearly indicate which side "wins". These are some of the characteristics of mathematics that I have liked very much since I was young. In this article, I will try to demonstrate the beauty of mathematics and show you that it appears in many situations in our daily lives--including places we might not expect. Then, I will give you a taste of two studies I conducted in a mathematical field called combinatorics, and I will explain how they are related to everyday problems. One of these problems is how to perform accurate mathematical analyses of large streams of data that we cannot save in a computer's memory. Finally, I will try to give you an idea of my life as a mathematician--the challenges and difficulties, alongside the immense enjoyment and satisfaction I derive from them. Join me to an extended dive into my work on the wonders of combinatorics. [ABSTRACT FROM AUTHOR]

Aims: To let students know that packaging design teaching is both a science and an art like any other course, only when students understand this, can they teach and educate people once they are engaged in this profession. Methods: Observation, experiment, investigation, and other methods were used to carry out a relatively long time of teaching practice in the course of Packaging Design, and the teaching art was explored. Results: Practice shows that if students want to truly realize that teaching is both a science and an art, they must adhere to the purpose of instilling in teaching for a long time, and fully understand the history of teaching artistry, its characteristics, and its functions. Conclusion: Through the mathematical statistical analysis and research of teaching art practice and effect, we believe that any course is not a simple knowledge teaching, it is a process of educating people. We must cultivate the next generation to be well-rounded individuals, ensuring they are intellectually enriched and nurtured in moral values, physical health, aesthetic appreciation, and work skills. This holistic approach ensures that while they acquire knowledge, they are also exposed to and trained in the arts and practical skills. Only when people are well-trained can society be harmonious and beautiful. Therefore, the research on teaching art in packaging design has analyzed the three most important artistic effects of teaching blackboard art, language art, and teaching preparation art. Those with good teaching art effects account for 16-18%, those with medium teaching art effects account for 70-80%, and those with poor teaching art effects account for 10-16%.

This article introduces the development history of fractional calculus and expounds on the positive significance of fractional calculus in integrating higher mathematics teaching. The author introduces an ordinary differential equation model case appropriately. In this way, ordinary differential equations play an important role in improving college students’ mathematical thinking ability and mathematical application ability.

We give some remarks on the recent paper [J. Math. Inequal. 13 (4) (2019), 1235– 1244]. Some misleading conclusions of their stability results are carefully discussed and corrected. Moreover, we reestablish their results with a more general assumption and a stronger conclusion. [ABSTRACT FROM AUTHOR]

Our study commemorates this event by presenting a retrospective of the publications related to the use of mathematical tools for the analysis of economic, ecological, and environmental phenomena. We analyzed 1257 scientific publications using bibliometric techniques to examine the most productive and influential authors and their contributions in the economic, ecological, and environmental fields. Co-authorship among the top authors and countries, co-occurrence of the keywords, bibliographic coupling of the documents and authors, and author co-citation were analyzed by applying network analysis techniques using VOSviewer software, identifying the intellectual structure of the research and the collaborative networks in the fields. The results show that mathematics has grown impressively in terms of publication and citation. The contributions come from all over the world, but the majority are from the People's Republic of China and Spain. The results also show themes and trends in the economic, environmental, and ecological fields and a predominant use of mathematical tools in optimization processes in order to rigorously substantiate the decisions of investors and policymakers. Thus, our study offers support for any researcher to understand the current state of the art and develop a comprehensive understanding of journal publications. [ABSTRACT FROM AUTHOR]

Copyright of Veritas is the property of EDIPUCRS - Editora Universitaria da PUCRS and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The mathematics used in physical chemistry has changed greatly in the past forty years and it will certainly continue to change more quickly. Theoretical chemists and physicists must have an acquaintance with abstract mathematics if they are to keep up with their field, as the mathematical language in which it is expressed changes. Thinking about it, in this article, we want to show some of the most important concepts of Mathematical Analysis involved in obtaining analytical functions to represent the potential energy interaction for diatomic systems. A basic guide for the construction of a potential based on Dunham's coefficients and an example of a new potential obtained from this methodology is also presented.

Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field.

In addition to reducing R&D investment and changing senior managers or corporate name, the significant uncertainty and reputation shock brought by civil litigation may also have a vital impact on corporate governance of the sued company. We use A-share listed companies in Shanghai and Shenzhen stock exchanges from 2011 to 2018 to empirically examine the impact of civil litigation on corporate governance and its mechanism. It is found that, civil litigation is negatively correlated with corporate governance, and financing liabilities (FL) play an intermediary role in the negative correlation. Furthermore, judicial local protectionism weakens the negative correlation between civil litigation and corporate governance. Finally we close with directions for future research.

Creative thinking is the ability to generate new ideas. The affective aspect related to creativity is self-confidence. This study aims to describe the characteristics of students' mathematical creative thinking skills based on self-confidence. Involved as many as 60 students who took the Differential Calculus course. The method used is descriptive qualitative. Data collection was obtained through questionnaires, tests, and interviews. Data analysis techniques include data reduction, data presentation, and concluding. Subjects were grouped into three self-confidence categories: low, moderate, and high, based on the questionnaire results. Using the purposive sampling technique, two people were taken as subjects in each category. The study results explain that students with low, moderate, and high self-confidence can write down several different answers and review them in detail. Students in the high self-confidence category can find relationships between concepts and answer questions in various or unique solving algorithms. Selfconfidence is directly proportional to the achievement of creative thinking skills. [ABSTRACT FROM AUTHOR]

The rhythmic and stable operation of trolleybuses and autonomous trolleybuses or urban electric buses, depends to a large extent on the reliability of the equipment installed on the trolleybus. The actual operational reliability of trolleybus electrical equipment (EE) depends on its technical condition. Under the influence of external factors and specific operating modes, the technical condition of the equipment is continuously deteriorating, reliability indicators are decreasing, and the number of failures is increasing. Using the mathematical theory of reliability, probability theory and mathematical statistics, numerical methods of solving nonlinear and transcendental equations, this article defines the conditions of diagnostics depending on the intensity of failures and the given probability of failure-free operation of the equipment. Additionally, the inverse problem of determining the current reliability of electrical engineering systems depends on the terms of diagnostics and the intensity of failures being solved. As a result of the processing of statistical information on failures it is established that for the electrical equipment of a trolleybus, after a number of repair measures, the maximum density of failures occurs at a lower mileage, and the probability of failure-free operation can vary depending on the degree of wear of the equipment, i.e., on the number of previous failures. It is theoretically substantiated and experimentally confirmed that the reliability of trolleybus electrical equipment changes according to the exponential law of distribution of a random variable. It has been established that the real averaged diagnostic terms regulated by instructions are not optimal in most cases and differ several times from those defined in this paper. The dependence of switching equipment run-in on time has been clarified, which served as a prerequisite for specifying the inter-repair period for various types of trolleybus electrical equipment. A method of adjustment of the inter-repair time for the electrical equipment of trolleybuses is proposed.

To understand the reasons for the decline in the birth rate of our country, the effects of the decline in the birth rate and the countermeasures needed to reduce the birth rate, as well as the urgency of the reform of education, especially art education.

The purpose of this paper is twofold. The first goal is to provide a simple and constructive proof of Korn inequalities in half-space with weighted norms. The proof leads to explicit values of the constants. The second objective is to use these inequalities to show that the linear elasticity system in half-space admits a coercive variational formulation. This formulation corresponds to the physical case in which the solution is evanescent at infinity. [ABSTRACT FROM AUTHOR]

We consider the non-resonance with one-sided superlinear growth conditions for the indefinite planar system z' = f (t, z) from a rotation number viewpoint, and obtain the existence of 2π- periodic solutions by applying a rotation number approach together with the Poincar´e-Bohl theorem. We allow that the angular velocity of solutions of z' = f (t, z) is controlled by the angular velocity of solutions of two positively homogeneous and oddly symmetric systems z' = Li(t, z), i = 1, 2 on the left half-plane, which have rotation numbers that satisfy ρ(L1) > n/2 and ρ(L2) < (n + 1)/2, and allow f (t, z) to grow superlinearly on the right half-plane. In order to estimate the rotation angle difference of solutions, we develop a system methodology of "tracking" the angle difference of solutions of the system z' = f (t, z) on each small interval on the given side under sign-varying conditions. [ABSTRACT FROM AUTHOR]

In this paper, a new class of Hermite-Hadamard type integral inequalities using a strong type of convexity, known as n-polynomial exponential type s-convex function, is studied. This class is established by utilizing the Hölder's inequality, which has several applications in optimization theory. Some existing results of the literature are obtained from newly explored consequences. Finally, some novel limits for specific means of positive real numbers are shown as applications. [ABSTRACT FROM AUTHOR]

A regular left-order on a finitely generated group GG is a total, left-multiplication invariant order on GG whose corresponding positive cone is the image of a regular language over the generating set of the group under the evaluation map. We show that admitting regular left-orders is stable under extensions and wreath products and we give a classification of the groups whose left-orders are all regular left-orders. In addition, we prove that a solvable Baumslag–Solitar group B(1,n) admits a regular left-order if and only if n ≥ −1. Finally, Hermiller and Šunić showed that no free product admits a regular left-order. We show that if A and B are groups with regular left-orders, then (A ∗ B) × Z admits a regular left-order. [ABSTRACT FROM AUTHOR]

Developing an idea of M. Gromov (1993), we study the intersection formula for random subsets with density. The density of a subset A in a finite set E is defined by dens A := log|E|(|A|)dens A := log ∣E∣ ​ (∣A∣). The aim of this article is to give a precise meaning of Gromov’s intersection formula: “Random subsets” A and B of a finite set EE satisfy dens A ∩ B = dens A + dens B -1dens (A ∩ B) = dens A + dens B−1. As an application, we exhibit a phase transition phenomenon for random presentations of groups at density λ/2 for any 0 < λ <10 < λ <1, characterizing the C'(λ)C ′ (λ)-small cancellation condition. We also improve an important result of random groups by G. Arzhantseva and A. Ol’shanskii (1996) from density 0 to density 0 ≤ d < 1 / (120m²ln(2m)). [ABSTRACT FROM AUTHOR]

Copyright of Journal of Theoretical Educational Science / Kuramsal Eğitimbilim Dergisi is the property of Afyon Kocatepe University, Faculty of Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

New oscillatory properties for the oscillation of unbounded solutions to a class of thirdorder neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems. [ABSTRACT FROM AUTHOR]

The article informs on Pan-American Women's Mathematics Olympiad 2021. It mentions that problems with different levels of difficulty and varied in terms of content, which have been carefully analyzed, and all the participants were able to enjoy various activities that made it possible to partially correct the deficiencies of an online event and enjoy interaction with other girls with similar concerns.

The article informs on the 62nd International Mathematical Olympiad (IMO) that took place between July 14 and 24, organized by the Ministerio de Educación de la Federación Russia in the city of Saint Petersburg, and the University of Herzen. It mentions that problems with different levels of difficulty and varied in terms of content, which have been carefully analyzed.

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The infection dynamics of COVID-19 is difficult to contain due to the mutation nature of the SARS-CoV-2 virus. This has been a public health concern globally with the impact of the pandemic on the world’s economy and mode of living. In the present work, we formulate and examine a fractional model of COVID-19 considering the two variants of concern on the disease transmission pathways, namely SARS-CoV-2 and D614G on our model formulation. The existence and uniqueness of our model solutions were analyzed using the fixed point theory. Mathematical analyses were presented, and the model’s basic reproduction numbers R01 and R02 were determined. The model has three equilibria: the disease-free equilibrium, that endemic for strain 1, and that endemic for strain 2. The locally asymptotic stability of the equilibria was established based on the R01 and R02 values. Caputo fractional operator was used to simulate the model to study the dynamics of the model solution. Results from numerical simulations envisaged that an increase in the transmission parameters of strain 1 leads to an increase in the number of infected individuals. On the other hand, an increase in the strain 2 transmission rate gives rise to more infection. Furthermore, it was established that there is an increased number of infections with a negative impact of strain 1 on strain 2 dynamics and vice versa.

Nisin, an antibacterial compound produced by Lactococcus lactis strains, has been approved by the US Food and Drug Administration to be used as a safe food additive to control the growth of undesirable pathogenic bacteria. Nisin is commonly described as a pH-dependent primary metabolite since its production depends on growth and culture pH evolution. However, the relationships between bacteriocin synthesis (BT), biomass production (X), culture pH, and the consumption of the limiting nutrient (total nitrogen: TN) have not been described until now. Therefore, this study aims to develop a competitive four-dimensional Lotka–Volterra-like Equation (predator-prey system) to describe these complex relationships in three series of batch fermentations with L. lactis CECT 539 in diluted whey (DW)-based media. The developed four-dimensional predator-prey system accurately described each individual culture, providing a good description of the relationships between pH, TN, X, and BT, higher values for R2 and F-ratios, lower values (

This paper explores the time dependent squeezing flow of a viscous fluid between parallel plates with internal heat generation and homogeneous/heterogeneous reactions. The motive of the present effort is to upgrade the heat transformation rate for engineering and industrial purpose with the rate of chemical reaction. For this purpose the equations for the conservation of mass, momentum, energy and homogeneous/heterogeneous reactions are transformed to a system of coupled equations using the similarity transformation. According to HAM, with the proper starting assumptions and other factors, a similarity solution may be found. On the way to verifying the validity and correctness of HAM findings, we compare the HAM solution with numerical solver programme BVP4c to see whether it matches up. The results of a parametric inquiry are summarized and presented with the use of graphs.

This work describes how the combination of the mistakes committed by a group of pre-service teachers when solving a Fermi problem, with the representation of the temporal analysis of their resolutions, can offer more in-depth information about their conceptual misconceptions regarding mathematical and modelling concepts. The combined representation allows knowing when mistakes occur and provides a powerful tool for instructors to adapt the teaching–learning processes of mathematics at all levels of education. Our study is based on a recent categorisation of students' mistakes, together with the creation of a new representation tool, called MAD+, that can combine all this information. The macroscopic view provided by the MAD+ diagrams gives insight into the context in which the mistakes take place and makes the analysis of the resolution of a Fermi problem more efficient. [ABSTRACT FROM AUTHOR]