Hasil untuk "Business mathematics. Commercial arithmetic. Including tables, etc."

Maxie Dion Schmidt

Sign changes in sums of arithmetic functions and their inverses are a subtle topic with room to grow new results. Suppose that $S_f(x) := \sum_{n \leq x} f(n)$ is the summatory function of some arithmetic function $f$ such that $f(1) \neq 1$. There are known lower bounds on the limiting growth of $V(S_f, Y)$ -- the number of sign changes of $S_f(y)$ on the interval $y \in (0, Y]$ as $Y \rightarrow \infty$. We observe a partition theoretic sign smoothing by discrete convolution of the local oscillatory properties of the Dirichlet inverse of $f$, $S_{f^{-1}}(x)$. These so-called invertible ``magic partition function`` encodings lead to a sequence of convolution sums which have predictable sign properties provided the sequence of $f(n)$ ($f^{-1}(n)$, respectively) has reasonable asymptotic upper bounds with respect to $n$.

Thi Lan Le, Quang Hieu Le, Duy Hung Pha

The purpose of the study is to identify factors affecting consumers' intention and decision to purchase OCOP products as well as to test the impact of intention to purchase OCOP products on Vietnamese consumers' decision to purchase OCOP products through a case study in Thanh Hoa province. This study uses a combination of qualitative and quantitative research methods. Qualitative research aims to test the reasonableness of each scale and screen observed variables. Quantitative research methods are used through the collection and processing of data from 250 consumers who have purchased OCOP products. Data are collected, processed and analyzed using PLS-SEM software. Based on the use of TAM consumer behavior theory and the development of 4P marketing elements to build a research model. The study added the fifth P, Pride in Local Specialties, as a new factor to match the characteristics of OCOP products. The results of the study showed that the factors: (1) Pride in Local Specialties; (2) Product Awareness; (3) Price Perception; (4) Convenience in Shopping and (5) Product Communication all have a positive impact on consumers' intention to buy OCOP products. The results of the study also showed that the intention to choose OCOP products (INT) has a great impact on consumers' decision to choose OCOP products (DEC).

Nuno Crokidakis

We analyze a mathematical model to understand the dynamics of bullying in schools. The model considers a population divided into four groups: susceptible individuals, bullies, individuals exposed to bullying, and violent individuals. Transitions between these states occur at rates designed to capture the complex interactions among students, influenced by factors such as romantic rejection, conflicts with peers and teachers, and other school-related challenges. These interactions can escalate into bullying and violent behavior. The model also incorporates the role of parents and school administrators in mitigating bullying through intervention strategies. The results suggest that bullying can be effectively controlled if anti-bullying programs implemented by schools are sufficiently robust. Additionally, the conditions under which bullying persists are explored.

Laslo Hunhold

Recent evaluations have highlighted the tapered posit number format as a promising alternative to the uniform precision IEEE 754 floating-point numbers, which suffer from various deficiencies. Although the posit encoding scheme offers superior coding efficiency at values close to unity, its efficiency markedly diminishes with deviation from unity. This reduction in efficiency leads to suboptimal encodings and a consequent diminution in dynamic range, thereby rendering posits suboptimal for general-purpose computer arithmetic. This paper introduces and formally proves 'takum' as a novel general-purpose logarithmic tapered-precision number format, synthesising the advantages of posits in low-bit applications with high encoding efficiency for numbers distant from unity. Takums exhibit an asymptotically constant dynamic range in terms of bit string length, which is delineated in the paper to be suitable for a general-purpose number format. It is demonstrated that takums either match or surpass existing alternatives. Moreover, takums address several issues previously identified in posits while unveiling novel and beneficial arithmetic properties.

Frank Quinn

This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what is, or isn't, a foundation; and get clues as to how a foundation can be optimized for effective human use. For this we turn to history and professional practice of the subject. We have no asperations to Philosophy. The first section gives a short abstract discussion, focusing on the significance of consistency. The next briefly describes foundations, explicit and implicit, at a few key periods in mathematical history. We see, for example, that at the primitive level human intuitions are essential, but can be problematic. We also see that traditional axiomatic set theories, Zermillo-Fraenkel-Choice (ZFC) in particular, are not quite consistent with mainstream practice. The final section sketches the proposed new foundation and gives the basic argument that it is uniquely qualified to be considered {the} foundation of mainstream deductive mathematics. The ``coherent limit axiom'' characterizes the new theory among ZFC-like theories. This axiom plays a role in recursion, but is implicitly assumed in mainstream work so does not provide new leverage there. In principle it should settle set-theory questions such as the continuum hypothesis.

Joseph H. Silverman

In this note we give an overview of various quantities that are used to measure the complexity of an algebraic dynamical system f:X-->X, including the dynamical degree d(f), which gives a coarse measure of the geometric complexity of the iterates of f, the arithmetic degree a(f,P), which gives a coarse measure of the arithmetic complexity of the orbit of a an algebraic point P in X, and various versions of the canonical height h_f(P) that provide more refined measures of arithmetic complexity. Emphasis is placed on open problems and directions for further exploration.

Bela Bajnok

We provide an historical overview of how advances in technology influenced high school and university mathematical competitions in the United States and at the International Mathematical Olympiad. While students are not allowed the usage of technological aids during mathematical competitions, the developments in technology (especially graphing technology) throughout the past century and the increasing employment of such aids in the classroom have affected both the nature of the proposed problems and their expected solutions. We examine several interesting examples from competitions going back several decades.

Carlos Carrillo-Tudela, Ludo Visschers

This paper studies the extent to which the cyclicality of occupational mobility shapes that of aggregate unemployment and its duration distribution. We document the relation between workers' occupational mobility and unemployment duration over the long run and business cycle. To interpret this evidence, we develop a multi-sector business cycle model with heterogenous agents. The model is quantitatively consistent with several important features of the US labor market: procyclical gross and countercyclical net occupational mobility, the large volatility of unemployment and the cyclical properties of the unemployment duration distribution, among many others. Our analysis shows that occupational mobility due to workers; changing career prospects, and not occupation-wide differences, interacts with aggregate conditions to drive the fluctuations of the unemployment duration distribution and the aggregate unemployment rate.

Dennis Müller, Maurice Chiodo

We extend Langdon Winner's idea that artifacts have politics into the realm of mathematics. To do so, we first provide a list of examples showing the existence of mathematical artifacts that have politics. In the second step, we provide an argument that shows that all mathematical artifacts have politics. We conclude by showing the implications for embedding ethics into mathematical curricula. We show how acknowledging that mathematical artifacts have politics can help mathematicians design better exercises for their mathematics students.

Ian Benson, Jim Darby, Neil MacDonald et al.

Recent developments in computer programming and in mathematics suggest that there is a strong case for a new way of introducing programming to enhance the learning of school mathematics. The article describes a collaboration of mathematics and computer science teachers to solve the Josephus problem. We demonstrate how a programming approach based on both types and functions can make a vastly improved contribution to learning mathematics than the less successful use of conventional computer programming in Scratch.

Muhammad Fahad, Jérôme Darmont, Cécile Favre

In the current era, many disciplines are seen devoted towards ontology development for their domains with the intention of creating, disseminating and managing resource descriptions of their domain knowledge into machine understandable and processable manner. Ontology construction is a difficult group activity that involves many people with the different expertise. Generally, domain experts are not familiar with the ontology implementation environments and implementation experts do not have all the domain knowledge. We have designed Collaborative Business Intelligence Ontology (CBIOnt) for BI4People project. In this paper, we present CBIOnt that is OWL 2 DL ontology for the description of collaborative session between different collaborators working together on the business intelligent platform. As the collaborative session between various collaborators belongs to some collaborative form, phase and research aspect, therefore CBIOnt captures this knowledge along with the collaborative session content (comments, questions, answers, etc.) so that one can inference various types of information stored on ontologies when required. In addition, it stores the location and temporal-spatial information about the collaboration held between collaborators. We believe CBIOnt serves as a formal framework for dealing with the collaborative session taken place among collaborators on the semantic Web.

Faical Ndairou, Ivan Area, Delfim F. M. Torres

We propose a mathematical model for the spread of Japanese encephalitis, with emphasis on environmental effects on the aquatic phase of mosquitoes. The model is shown to be biologically well-posed and to have a biologically and ecologically meaningful disease free equilibrium point. Local stability is analyzed in terms of the basic reproduction number and numerical simulations presented and discussed.

Mikhail Belolipetsky, Matilde Lalín, Plinio G. P. Murillo et al.

It is known that the lengths of closed geodesics of an arithmetic hyperbolic orbifold are related to Salem numbers. We initiate a quantitative study of this phenomenon. We show that any non-compact arithmetic $3$-dimensional orbifold defines $c Q^{1/2} + O(Q^{1/4})$ square-rootable Salem numbers of degree $4$ which are less than or equal to $Q$. This quantity can be compared to the total number of such Salem numbers, which is shown to be asymptotic to $\frac{4}{3}Q^{3/2}+O(Q)$. Assuming the gap conjecture of Marklof, we can extend these results to compact arithmetic $3$-orbifolds. As an application, we obtain lower bounds for the strong exponential growth of mean multiplicities in the geodesic spectrum of non-compact even dimensional arithmetic orbifolds. Previously, such lower bounds had only been obtained in dimensions $2$ and $3$.

Luc Quadackers

In June 2019, the fourth conference of the Foundation for Auditing Research (FAR) has been held. The theme of the conference was ‘Evidence informed policy making for the future of the auditing profession’. Professor Willem Buijink (Open Universiteit and FAR Academic Board member) chaired nine plenary sessions, spread over two days. In this article, the focus will be on the keynote speeches by Robert Knechel and Miguel Minutti-Mezo and on the panel discussion regarding the theme of the conference.

Ana P. Lemos-Paiao, Cristiana J. Silva, Delfim F. M. Torres

We propose and analyse a mathematical model for cholera considering vaccination. We show that the model is epidemiologically and mathematically well posed and prove the existence and uniqueness of disease-free and endemic equilibrium points. The basic reproduction number is determined and the local asymptotic stability of equilibria is studied. The biggest cholera outbreak of world's history began on 27th April 2017, in Yemen. Between 27th April 2017 and 15th April 2018 there were 2275 deaths due to this epidemic. A vaccination campaign began on 6th May 2018 and ended on 15th May 2018. We show that our model is able to describe well this outbreak. Moreover, we prove that the number of infected individuals would have been much lower provided the vaccination campaign had begun earlier.

Avraham Aizenbud, Nir Avni

We relate the singularities of a scheme $X$ to the asymptotics of the number of points of $X$ over finite rings. This gives a partial answer to a question of Mustata. We use this result to count representations of arithmetic lattices. More precisely, if $Γ$ is an arithmetic lattice whose $\mathbb{Q}$-rank is greater than one, let $r_n(Γ)$ be the number of irreducible $n$-dimensional representations of $Γ$ up to isomorphism. We prove that there is a constant $C$ (for example, $C=746$ suffices) such that $r_n(Γ)=O(n^C)$ for every such $Γ$. This answers a question of Larsen and Lubotzky.

Tawat Noipom

M. Silva

Meng-Jong Kuan, Yee Ming Chen

The efficient evaluation of technological innovation capabilities of enterprises is an important factor to enhance competitiveness. This paper aims to assess and to rank technological innovation evaluation criteria in order to provide a practical insight of systematic analysis by gathering the qualified experts’ opinions combined with three methods of multi-criteria decision making approach. A framework is proposed and uses a novel hybrid multiple criteria decision-making (MCDM) model to address the dependence relationships of criteria with the aid of the Decision-Making Trial and Evaluation Laboratory (DEMATEL), analytical network process (ANP) and VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje). The study reports that the interaction between criteria is essential and influences technological innovation capabilities; furthermore, this ranking development of technological innovation capabilities assessment is also one of key management tools for managements of other related high- tech enterprises. Managers can then judge the need to improve and determine which criteria provide the most effective direction towards improvement.

N. Glazer