Arithmetic Relations Research Articles

Domestic And American Model Of Sanctions For Criminal Violations In The Economic Field: Critical Approach By A Comparativist

The article critically reviews the models of criminal sanctions introduced in Ukraine and the United States for economic criminal offenses. It is emphasized that the meaning of the concept of punishment is inextricably linked to the fundamental category of criminal liability, which means the restrictions provided by criminal law for the exercise of the rights and freedoms of a person for committing a criminal offense.
 It has been noted that most American courts do not practice “linear” philosophy in terms of sentencing, but on the contrary, take the whole set of unique facts and circumstances with legal significance into account in each criminal case. It has been established that this approach partially resembles the content of paragraph 3, part 1 of Art. 65 of the Criminal Code of Ukraine: the court imposes punishment, taking into account severity of the crime, identity of the perpetrator as well as mitigating and aggravating circumstances.
 It has been also established that in comparison with the American domestic practice of sentencing in general and for economic crimes in particular seems unreasonably humane, such that it is not able to fully implement the purpose of punishment, declared in Art. 50 of the Criminal Code, and therefore, such as objectively unable to restrain the manifestations of illegal behavior in the economic sphere. The large- scale humanization of criminal liability for economic encroachments carried out by the Ukrainian legislator at the end of 2011, combined with the decriminalization of certain acts and the replacement of imprisonment with fines in sanctions of other norms, has intensified such negative trend.
 Third, the analysis of the content and application of the federal Penal Code demonstrates not only the advantages of this act of the federal criminal law, but also its individual shortcomings. There is a lot of criticism against this document’s provisions in terms of sentencing for economic crimes. The main reason for criticism is the purely arithmetic relationship between the amount of punishment and the amount of material damage caused by such a crime.
 Based on the results of elaboration of the American experience in terms of normative provision and practice of application of punishments for economic crimes, a position has been expressed on the expediency of introducing a model of limited formalization of punishments in Ukraine.

The number sense does not represent numbers, but cardinality comparisons.

Against Clarke and Beck's proposal that the approximate number system (ANS) represents natural and rational numbers, I suggest that the experimental evidence is better accommodated by the (much weaker) thesis that the ANS represents cardinality comparisons. Cardinality comparisons do not stand in arithmetical relations and being able to apply them does not involve basic arithmetical concepts and operations.

Color incompatibility in Wittgenstein and its relationship with Arithmetic

After Tractatus Logico-Philosophicus, Wittgenstein realized that elementary propositions may logically conflict with each other, due to the fact that the most elementary measurements may contradict each other. This led to the view that logic consists of various calculi. A calculus consists of measurement scales, each scale being a rule for the application of numbers. These scales determine logical relationships between elementary propositions by reason of arithmetical relations. Attempts to reject Wittgenstein's change in viewpoint, which ignore the relevance of measurement and arithmetic, are remiss. In this light, I discuss Sarah Moss’s criticism of intermediate Wittgenstein.

Breaking ties in collective decision-making

Many classic social preference (multiwinner social choice) correspondences are resolute only when two alternatives and an odd number of individuals are considered. Thus, they generally admit several resolute refinements, each of them naturally interpreted as a tie-breaking rule. A tie-breaking rule is compulsory every time a single final decision is needed. Unfortunately, using a tie-breaking rule on some social preference (multiwinner social choice) correspondence can dramatically compromise its properties. In particular, very often, the arithmetic relation between the number of alternatives and the number of voters does not allow to maintain both anonymity and neutrality. In those cases, the only possibility is to look at suitable different forms of symmetry that are coherent with the decision context. We find out conditions which make a social preference (multiwinner social choice) correspondence admit a resolute refinement fulfilling some weak versions of the anonymity and neutrality principles. We also clear when it is possible to obtain, for those resolute refinements, the reversal symmetry (immunity to the reversal bias). The theory we develop turns out to be useful in many common applicative contexts and allows to explicitly construct those refinements.

Relation between the Electronic Properties of Regioregular Donor-Acceptor Terpolymers and Their Binary Copolymers.

By analyzing the optical band gap and energy levels of seven different regioregular terpolymers in which two different electron-rich donor moieties are alternating with a common electron-deficient acceptor unit along the backbone, we establish a direct correlation with the properties of the corresponding binary copolymers in which one donor and one acceptor are combined. For this study, we use diketopyrrolopyrrole as the common acceptor and different π-conjugated aromatic oligomers as donors. We find that the optical band gap and frontier orbital energies of the terpolymers are the arithmetic average of those of the parent copolymers with remarkable accuracy. The same relationship is also found for the open-circuit voltage of the bulk heterojunction solar cells made with the ter- and copolymers in combination with [6,6]-phenyl-C71-butyric acid methyl ester. Comparison of these findings with data in the literature suggests that this is a universal rule that can be used as a tool when designing new π-conjugated polymers. The experimental results are supported by a semiempirical quantum chemical model that accurately describes the energy levels of the terpolymers after parametrization on the energy levels of the copolymers and also provides a theoretical explanation for the observed arithmetic relations.

La “musica degli angeli”: Josquin Desprez al liceo

Music and singing, which are present in every form of worship in the Christian rite, have acquired from the outset a very particular connotation, in which Jewish tradition and Neoplatonism have merged: every musical manifestation in the liturgy has as its model the perennial praise given to God from the angelic choirs. This conception, combined with the Pythagorean doctrine of the harmony of the spheres, informed throughout the Middle Ages fundamentals aspects of music theory and the aesthetic frame of reference for every sound manifestation, especially in devotional contexts (Gregorian chant, polyphony).The Neo-Platonic Judeo-Christian approach to music, which was associated with a cosmological conception based on music regulated by arithmetical relationships, informed compositional techniques and formal organization of music from the Carolingian era onwards. It is also reflected in great works of art, in architectural solutions in the sacred buildings, and found a scenic manifestation in the first liturgical dramas. Moreover, it was the prototype of the structure of Dante’s Paradise in the Divine Commedy. This essay offers an interpretation of the motet for 24 voices Qui habitat by Josquin Desprez as grounded in these philosophical and aesthetic tenets linking composers from Middle Ages to the Renaissance and presenting still today an extraordinary model of trans-disciplinary education (music, philosophy, art history, literature), when the aim is to preserve exchange and communication among the arts.

Adaptive number knowledge in secondary school students: Profiles and antecedents

The present study aims to examine inter-individual differences in adaptive number knowledge in secondary school students. Adaptive number knowledge is defined as a well-connected network of knowledge of numerical characteristics and arithmetic relations. Substantial and relevant qualitative differences in the strategies and expression of adaptive number knowledge have been found in primary school students still in the process of learning arithmetic. We present a study involving 879 seventh-grade students that examines the structure of individual differences in adaptive number knowledge with students who have completed one year of algebra instruction. Results of a latent profile analysis reveal a model that is similar than was previously found in primary school students. As well, arithmetic fluency and the development of arithmetic fluency are strong predictors of adaptive number knowledge latent profile membership. These results suggest that adaptive number knowledge may be characteristic of high-level performance extending into secondary school, even after formal instruction with arithmetic concludes.

Metode Couple Linear Congruential Generator (CLCG) untuk Ujian Sekolah Berbasis Web

IN SMA N 2 Kota Pariaman school exams still use the answer sheet media at the time of publication. After the exam is complete the answer sheet of the exam will also be corrected by the subject teacher who will discuss the students' problems, each student also receives the same question. SMA N 2 Kota Pariaman was chosen as a research location because this school has not used the Application during school exams, it is easy to achieve and economical. The application to be used can randomize randomly so that exam questions can be varied and dynamic. With the application of the application that is expected to carry out school examinations will be better and obtained optimally by students, teachers, school management and parents / guardians of students. For this reason, the authors will conduct research consisting of the design of Computer Based Test applications using the Coupled Linear Congruential Generator (CLCG) method. The development of the Computer Based Test (CBT) model by using a Coupled Linear Congruent Generator (CLCG) can prevent the questioning of questions for students. CLCG is a random number generator based on the Linear Congruent Generator (LCG). CLCG uses the xj matrix to get random numbers. organized by rows and columns. The matrix prefers a range of numbers and has no arithmetic relationship between its elements. The matrix will have different row and column addresses. The value of the elements of the matrix obtained from the process with the Linear Congruent Generator to get as many random numbers as is done. CBT is one way of overcoming questions in each student. The use of LCG in the matrix value element can have a more complicated random pattern. Reducing the question answer key by entering the answer key time after the exam is finished. Languages supported using the CLCG method can optimize student abilities and reduce the level of cheating. Reducing the question answer key by entering the answer key time after the exam is finished.
 Keywords: CBT Appliaction, Couple Linear Congruential Generator, Linear Congruential Generator, Random Number, School Exam.

A generalization of the infinitary divisibility relation: Algebraic and analytic properties

We consider a generalized type of unique factorization of the positive integers with restrictions on the exponents and view them as a family of arithmetic convolutions and divisibility relations, similar to the convolutions defined by Narkewicz [On a class of arithmetical convolutions, Colloq. Math. 10 (1963) 81–94]. We introduce special types of multiplicativity corresponding to these convolutions, and discuss algebraic properties of the associated arithmetic convolutions and analogs of the Möbius functions. We also prove asymptotics for analogs of the totient function, totient summatory function, and divisor summatory function.

Weaker variants of infinite time Turing machines

Infinite time Turing machines represent a model of computability that extends the operations of Turing machines to transfinite ordinal time by defining the content of each cell at limit steps to be the \(\limsup \) of the sequences of previous contents of that cell. In this paper, we study a computational model obtained by replacing the \(\limsup \) rule with an ‘eventually constant’ rule: at each limit step, the value of each cell is defined if and only if the content of that cell has stabilized before that limit step and is then equal to this constant value. We call these machines weak infinite time Turing machines (wITTMs). We study different variants of wITTMs adding multiple tapes, heads, or bidimensional tapes. We show that some of these models are equivalent to each other concerning their computational strength. We show that wITTMs decide exactly the arithmetic relations on natural numbers.

Fractional Arithmetic in the Tabula Alimentaria of Veleia

AbstractThe Tabula Alimentaria of Veleia records the details of two second-century a.d. imperial alimentary schemes at the northern Italian town of Veleia, providing a rare insight into the workings of these schemes. Imperial loans are made to local landowners in exchange for pledges of specified property. Interest paid by landowners is used to fund cash subsidies for the upbringing of selected local children. In the early twentieth century, the French scholar Félix de Pachtere came close to demonstrating a consistent arithmetical relationship between a landowner's declared property value and the loan received. However, anomalies remained. This article proposes a revised formula which establishes a precise and consistent linkage between loan amounts and property declarations. Based on this arithmetical dataset, the paper proposes some hypotheses about how these fractional computations might have been performed in second-century Rome.

Leadership Styles, Organizational Politics and Employees` Commitment in Selected Public and Private Organizations in Lagos State, Nigeria

The study examined leadership styles, organizational politics and employee’s commitment using selected private and public organizations in Lagos state as case studies . To achieve its objectives, it probed the direct relationship that exists between organizational politics and the leadership styles used in both private and public organization and as well as the extent to which employees’ commitment depends on leadership styles and organizational politics in both private and public organization. A descriptive survey was employed using a sample size of 112 respondents. The main research instrument used was questionnaire. Data collected were analyzed using frequency and percentages; while a one-way ANOVA and regression statistical analyses were used to test the study’s hypotheses. Results from the hypotheses tested revealed a major arithmetical relationship between leadership styles and employees’ commitment; also between organizational politics and employees’ commitment in both public and private organizations in Lagos state, in addition that organizational politics and leadership styles used in both public and private organization have significant difference in their respective abilities to entrust employees’ commitment. The study concluded that there is a positive relationship between leadership styles and the level of employees’ commitment in both private and public organization and that a positive relationship also exists between organizational politics and the level of employees’ commitment in both public and private organization in Lagos State. The study therefore recommended that the management should embrace situational leadership approach to attract employees’ commitment and that they should employ workers who have potential to adjust and adapt to their organizational and political culture. Key words: Organizational politics; Employee commitment; Leadership styles; Affective commitment.

UNIVERSAL MIXED ELLIPTIC MOTIVES

In this paper we construct a $\mathbb{Q}$-linear tannakian category $\mathsf{MEM}_{1}$ of universal mixed elliptic motives over the moduli space ${\mathcal{M}}_{1,1}$ of elliptic curves. It contains $\mathsf{MTM}$, the category of mixed Tate motives unramified over the integers. Each object of $\mathsf{MEM}_{1}$ is an object of $\mathsf{MTM}$ endowed with an action of $\text{SL}_{2}(\mathbb{Z})$ that is compatible with its structure. Universal mixed elliptic motives can be thought of as motivic local systems over ${\mathcal{M}}_{1,1}$ whose fiber over the tangential base point $\unicode[STIX]{x2202}/\unicode[STIX]{x2202}q$ at the cusp is a mixed Tate motive. The basic structure of the tannakian fundamental group of $\mathsf{MEM}$ is determined and the lowest order terms of a set (conjecturally, a minimal generating set) of relations are deduced from computations of Brown. This set of relations includes the arithmetic relations, which describe the ‘infinitesimal Galois action’. We use the presentation to give a new and more conceptual proof of the Ihara–Takao congruences.

Rotation number values at a discontinuity

In the space of orientation-preserving circle maps that are not necessarily surjective nor injective, the rotation number does not vary continuously. Each map where one of these discontinuities occurs is itself discontinuous and we can consider the possible values of the rotation number when we modify this map only at its discontinuities. These values are always rational numbers that necessarily obey a certain arithmetic relation. In this paper we show that in several examples this relation totally characterizes the possible values of the rotation number on its discontinuities, but we also prove that in certain circumstances this relation is not sufficient for this characterization.

The arithmetic relations between total expenditure and the resulting current and financial account balances as determinants of the revenue-related need for means of payment in an economy

Introductory note by the translators: In the following paragraphs, Stützel derives some balance mechanic relationships between revenue and expenditure surpluses, on the one hand, and the volume of credit necessary to finance these, on the other. He then moves on to consider the balance sheet of the banking sector and its relationships with the volume of credit. Insights from both exercises are subsequently used to synthesise the ‘orthodox’ and ‘modern’ theories of credit. The few parts of Stützel (1958 [1978]: 208–219) which were excluded from the translation are the ones in which Stützel directly refers to other parts of the book which are not translated here, as well as some footnotes referring to issues or publications which were topical at the time at which Stützel was writing but which are of very limited interest for our purposes. Furthermore, we omit a short passage in which Stützel briefly introduces the ‘straddle effect’, a concept which is important in his discussion of the quantity theory of money (ibid.: 229–255) but which does not feature any further in the section we are translating. For more on the quantity equation from a balance mechanics perspective, see Tarne (2016). The text below is a direct translation from Stützel without any changes or amendments, including Stützel's use of emphases and quotation marks.

Proportiones Perfectus Law and the Physics of the Golden Section

The proportiones perfectus law is introduced. Let . By definition, in the spectrum is a proportione perfectus. With so defined, for an arbitrary positive integer it is shown that there exists an integer sequence satisfying the quasi-geometric relation such that the arithmetic relation holds. The golden mean, designated becomes the most basic and fundamental of proportiones perfectus. New concepts to the study of the golden section are presented: chirality, number genetics and law of polarity, special numerical harmony, and chemical geometry. A geometrical basis for the fine-structure constant in the golden section is established. Our stating of over forty theorems in this reading serves no other purpose than that of expanding the theory of the golden section while equipping the interested reader with instruments for further research and development of this science of number.

M角数恒等式及其应用—从M角数谈起

本文中给出了一些等级相同并满足一定条件的M角数数字关系式。得到了与毕达哥拉斯三角数相关的特殊M角数数字关系式。讨论了一些特殊情况，并得到了一些有趣的结果。 In this paper, we present some arithmetic relationships among same-level M-Gonal numbers in a specific situation. We also illustrate some arithmetic relations on M-Gonal numbers who are related with Pythagorean Triangles Number. A few special cases are discussed to obtain some interesting results.

Mini-Workshop: Friezes

Frieze patterns were introduced in the early 1970s by Coxeter. They are infinite arrays of numbers in which every four neighbouring entries always satisfy the same arithmetic relation. Amazingly, friezes appear in many situations from various areas of mathematics: projective geometry, number theory, algebraic combinatorics, difference equations, integrable systems, representation theory, cluster algebras… The mini-workshop aimed to gather researchers with diverse fields of expertise to present recent developments and to discuss new directions of investigation and open problems around friezes.

Arithmetic identities and congruences for partition triples with 3-cores

Let [Formula: see text] denote the number of partition triples of [Formula: see text] where each partition is 3-core. With the help of generating function manipulations, we find several infinite families of arithmetic identities and congruences for [Formula: see text]. Moreover, let [Formula: see text] denote the number of representations of a non-negative integer [Formula: see text] in the form [Formula: see text] with [Formula: see text] We find three arithmetic relations between [Formula: see text] and [Formula: see text], such as [Formula: see text].

SÍNTESIS DE LA DEMOGRAFÍA Y LA ECONOMÍA: EL PRODUCTO BRUTO INTERNO (PBI) PER CÁPITA - DOI 10.5216/bgg.v36i1.40372

Consideramos que la demografía puede aportar nuevo conocimiento sobre el crecimiento económico. Las diferencias en la dispersión de la distribución de la producción y de la población en las regiones y países del mundo, inciden en el crecimiento económico, expresado en la forma de PBI per cápita. A pesar de noexistir consenso sobre una relación explicativa entre el crecimiento económico y demográfico, no obstante, obligadamente, existe una relación aritmética entre ambos conceptos en la expresión PBI per cápita. El objetivo es analizar en el largo plazo, como han participado ambos efectos en las diferentes regiones y paísesdel mundo considerados.Palabras Claves: Población, PBI, Distribución.