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The article informs about case study of a serious and multiple ethical misconduct after an author submitted a paper to five journals for publication and committed some form of plagiarism. Topics include mathematics and in sciences in general, multiple submissions of the same results or parallel papers are prohibited as serious ethical misconduct; and mathematics simultaneous or concurrent submission of a manuscript describing the same research publication in the electronic online systems.

Copyright of Unterrichtswissenschaft (Springer Science & Business Media B.V.) is the property of Springer Nature 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 article "How many points does your star have?" by Max Hoffmann describes a guide for folding and cutting a star from a square sheet of paper. By folding and cutting, a star with a specific number of points is created. The author suggests using colored paper and using the star as a decoration for the room. The question is also raised whether it is possible to create stars with more or fewer points. The author, Dr. Max Hoffmann, works at the Institute for Mathematics at the University of Paderborn. [Extracted from the article]

Entry-level prerequisites in mathematics are of paramount importance for success in STEM undergraduate programs. Nevertheless, basic mathematical skills from lower secondary school are often neglected in repetition and support measures. Similarly, there is a lack of appropriate diagnostic, quality-controlled instruments for this purpose. This paper presents a reliable and both content as well as differentially and prognostically valid computer-based instrument for diagnosing these skills. A paper and an online version measure the same construct. The online version includes instant feedback that integrates both performance and improvement feedback. In the outlook, outstanding key development and testing steps are addressed. [ABSTRACT FROM AUTHOR]

A lot of feminist and decolonial critiques of knowledge get confronted with the reference to »hard sciences« or »mathematical reasoning« as examples that supposably showcase that there are epistemic spheres of no political dimensions and complete universality. This paper commits to a deconstruction of exactly such a reasoning in directly arguing to view Mathematics not only as also being knowledge production bearing political dimensions but even claiming it to play a particular role in securing hegemonic structures of knowing. In putting forth this argument I have three main claims: a) What is commonly referred to as »mathematics « is actually a specifically Western way of conceptualizing what it means to »think mathematically« (here referred to as Mathematics). b) The Western concept of Mathematics is conceptually entangled with Western concepts of Rationality and Humanism. c) These three concepts and their entanglement can be understood as a re-establishing epistemically violent structures of knowledge. [ABSTRACT FROM AUTHOR]

Copyright of Zeitschrift für interpretative Schul- und Unterrichtsforschung is the property of Verlag Barbara Budrich GmbH 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.)

Copyright of Zeitschrift für Pädagogische Psychologie is the property of Hogrefe AG 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.)

Copyright of Lernen und Lernstörungen is the property of Hogrefe AG 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.)

Copyright of Unterrichtswissenschaft (Springer Science & Business Media B.V.) is the property of Springer Nature 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.)

In this paper we continue our investigation concerning the concept of a liken. This notion has been defined as a sequence of non-negative real numbers, tending to infinity and closed with respect to addition in R. The most important examples of likens are clearly the set of natural numbers N with addition and the set of positive natural numbers N* with multiplication, represented by the sequence (ln(n+1))∞ n=0. The set of all likens can be parameterized by the points of some infinite dimensional, complete metric space. In this space of likens we consider elements up to isomorphism and define properties of likens as such that are isomorphism invariant. The main result of this paper is a theorem characterizing the liken N* of natural numbers with multiplication in the space of all likens.

The classic method of solving the cubic and the quartic equations using Tschirnhaus transformation yields true as well as false solutions. Recently some papers on this topic are published, in which methods are given to get only the true solutions of cubic and quartic equations. However these methods have some limitations. In this paper the author presents a method of solving cubic and quartic equations using Tschirnhaus transformation, which yields only the true solutions. The proposed method is much simpler than the methods published earlier.

Copyright of Annual Review of the Faculty of Philosophy / Godisnjak Filozofskog Fakulteta is the property of Faculty of Philosophy, University of Novi Sad 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.)

Copyright of Mitteilungen der DMV is the property of De Gruyter 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.)

Copyright of Mitteilungen der DMV is the property of De Gruyter 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.)

This paper deals with the issue of interdisciplinarity in literature, tracing the mathematical influences — and particularly those of the incompleteness theorems by Kurt Gödel — on the literary works of Hans Magnus Enzensberger. Our attention is focused on Enzensberger’s publications in mathematics, on his poem Hommage à Gödel, and his montage epos The Sinking of the Titanic. This paper submits a new, interdisciplinary interpretation of the poem Hommage à Gödel as a kind of art manifesto, and comes to the conclusion that the reason Enzensberger finds the incompleteness theorems so interesting is that they offer a scientific basis for undecidable problems and paradoxes. He applies Gödel’s theorems to literature, where they enable a creative, playful oscillation between two positions or aspects of an undecidable problem and self-reference in literature.

In this paper the current relationship between physics and its philosophy is examined as well as its possibilities of development. The study is largely based on case studies. Although both disciplines have joint roots in pre-christian philosophy, today their teachings and research occur independently from one another. Both communities consider their systematic dialogue as important for each side. Nevertheless, the huge amount of information and the high degree of specialization of these debates renders the mutual dialogue rare events. As a result, associated inputs are missing in both directions and at all levels and debates lose the content stringency required for a continuous exchange. True interdisciplinarity is therefore no longer given. In the external perception, the two territories appear to belong together, but within the professional communities factual alienation is quite noticeable. Nevertheless, physics and philosophy remain intimately connected, both in their common claim to generate positive knowledge of the world, and at the level of concrete questions. In this essay, the transformation of physical concepts - which always have a philosophical core – is illustrated on the basis of several case studies. Mathematics also plays a key role in the recognition of nature, and should be addressed as well in this context. Today's physics has many facets: Depending on the perspective, it appears as a mathematically extremely sophisticated theory-building exercise, or as THE paradigmatic example of an empirical science with an astounding history of application successes, or as a world science that is at least implicitly normative. In fact, the interaction between theory, experiment and interpretation allows for a deeper understanding and successful predictions. Latest at this point, the intrinsic connection between physics and philosophy is revealed. In the philosophicalhistorical perspective, the time-invariant component of physics or its supporting inner structure becomes visible: conceptual leitmotifs and explanatory strategies are preserved, although in a modified form. As an effective and sustainable corrective of the current state, which is perceived as unsatisfactory by both sides, I propose that logical and epistemological basic contents, as well as specific topics of the philosophy of physics becomes part of the curriculum of the physicist's education. [ABSTRACT FROM AUTHOR]

Copyright of Unterrichtswissenschaft (Julius Beltz GmbH & Co. KG Beltz Juventa) is the property of Julius Beltz GmbH & Co. KG Beltz Juventa 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.)

L. Losonczi [4] determined local solutions of the generalized Cauchy equation f(F(x, y))= f(x) + f(y) on components of the denition of a given associative rational function F. The class of the associative rational function was described by A. Chéritat [1] and his work was followed by paper [3] of the author. The aim of the present paper is to describe local solutions of the equation considered for some singular associative rational functions.

Copyright of Mitteilungen der DMV is the property of De Gruyter 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.)

In this paper, we discuss the no-arbitrage condition in a discrete financial market model which does not hold the same interest rate assumptions. Our research was based on, essentially, one of the most important results in mathematical finance, called the Fundamental Theorem of Asset Pricing. For the standard approach a risk-free bank account process is used as numeraire. In those models it is assumed that the interest rates for borrowing and saving money are the same. In our paper we consider the model of a market (with d risky assets), which does not hold the same interest rate assumptions. We introduce two predictable processes for modelling deposits and loans. We propose a new concept of a martingale pair for the market and prove that if there exists a martingale pair for the considered market, then there is no arbitrage opportunity. We also consider special cases in which the existence of a martingale pair is necessary and the sufficient conditions for these markets to be arbitrage free

This paper is devoted to the study of a multi-step method with divided differences for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the sixth order of the operator under consideration is used to prove the convergence of the method. That restricts the applicability of the method. In this paper we extended the applicability of the sixth-order multi-step method by using only hypotheses on the first derivative of the operator involved. Our convergence conditions are weaker than the conditions used in earlier studies. Numerical examples where earlier results cannot be applied to solve equations but our results can be applied are also given in this study.

The paper discusses the problem of infinity with a special reference to mathematical truth. The roots of this problem, in a sense, go back to early efforts to provide a rational account of the phenomena of change, and the phenomenon of motion in particular, and, in connection with this, to the attempt to cast light on the complex relationship between continuity and discreteness. If mathematics is to serve as a tool of a rational description of the world, is it possible to construct a mathematical model of phenomenal continuity? This question was raised already by Zeno when the Pythagorean hypothesis of the essential ‘granularity’ of the world began to crumble as a result of the discovery of incommensurable magnitudes. The discovery of incommensurable magnitudes, and along with it the discovery of irrational numbers, produced well-known paradoxes and gave rise to the question to what extent, if at all, mathematics can deliver a ‘metaphysical’ description of the world. In more recent times, the idea of infinity was built into the infinitesimal calculus which became the foundation of the mathematical description of nature, but the metaphysical questions have not gone away. The issues surrounding actual and potential infinity continue to be the subject of intense debates. Whereas some recognise only potential infinities, others, like Georg Cantor, accept actually existent infinities. This is directly connected with the question of mathematical truth, which, according to the Platonist tradition exists as objectively given. The paper argues that the Cantorian transfinite set theory cannot withstand criticism, and that rather than providing a (metaphysical) description of reality mathematics merely offers possible models in terms of which the world might be better or more conveniently interpreted. The so-called ‘mathematical truth’ reduces to the question of ‘correctness’, viz. whether a given mathematical proposition does or does not follow from given premises.

The article offers briefs related to Deutsche Mathematiker-Vereinigung (DMV). Topics include Science Council published the position paper impetus from the Covid- 19 crisis for further development of the science system in Germany passed to reorientation of science policy; and response capability in policy advice about a lack of sovereignty and Security in the digital space up to strategic challenges in internationalization.

Student knowledge assessment is a key element of the pedagogical process, as it provides students, parents, and educators with important feedback information on students’ knowledge and skills. Assessment of students’ mathematical knowledge is complex, as several factors are normally included in students’ final grade, and simply calculating the average of students’ achievements may not provide a complete picture of their knowledge. Therefore, in this paper, we aimed to investigate the possibility of using fuzzy logic to assess students’ knowledge and competencies by considering (1) students’ overall academic performance, (2) the quality of students’ project work on a topic from the history of mathematics and (3) the regularity of handing in homework. The study was conducted considering 22 Italian high school students. The results show that students’ academic performance is similar to student grades obtained with fuzzy logic.

Copyright of Zeitschrift für Pädagogik is the property of Julius Beltz GmbH & Co. KG Beltz Juventa 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.)

Copyright of Mitteilungen der DMV is the property of De Gruyter 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.)

This article tackles a thorny issue within the reception of Badiou’s philosophy, i.e., the question of the role of the “social” within the ontological framework it outlines. Acknowledging that the question of the social is underdeveloped in Badiou’s system, the paper argues that there are resources in it to develop a social ontology, and attempos to flesh it out through an original and sustained reading of Badiou’s key formula on the distinction between democratic materialism and materialist dialectic: “there are only bodies and languages, except that there are truths”.

This paper explores the recent updating of Badiou's general philosophical proposal in the specific approach of a "speculative strategy" in his recent book The Immanence of Truths. I hypothesize that the idea of a "speculative strategy" is a third stage in Badiou's project called "philosophy of the event", which fulfills and radicalizes the previous stages of "platonism of the multiple" and "communism of Idea", development whose continuity rests on the internal unity of his project flinking his ontological and meta-ontological wager as a necessarily systematic philosophy. First, I will show the general elements of Badiou's philosophy, explaining its stages and the emergence of what I will call "philosophy of the event and multiple being". Secondly, I will delve specifically into the convergence of the ontological thesis and the meta-ontological one, to characterize the author's enterprise as a systematic project detached from ontotheology thanks to the speculative recourse to mathematics to think infinity. Finally, I will argue that the "strategy" of the author's recent work implies a specification of the role of mathematics within his speculative ontology.

The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, pseudo-CI algebras and many other algebras of logic. In this paper, the notion of deductive system in a pseudo-M algebra is introduced and its elementary properties are investigated. Closed deductive systems are defined and studied. The homomorphic properties of (closed) deductive systems are provided. The concepts of translation deductive systems and R-congruences in pseudo-M algebras are introduced and investigated. It is shown that there is a bijection between closed translation deductive systems and R-congruences. Finally, the construction of quotient algebra A/D of a pseudo-M algebra A via a translation deductive system D of A is given.

The aim of this paper is to present background information in relation with some fractional-order type operators in the complex plane, which is designed by the fractional-order derivative operator(s). Next we state various implications of that operator and then we show some interesting-special results of those applications.

It is widely believed that math classes in primary school belong into the category of least favorite classes. Entire teams of psychologists, educators and mathematicians have studied the student aversion (and, to a certain extent, parent antipathy) to math classes, but they have also studied methods and ways to overcome this problem. They have tried to find a way to improve students’ activities, to make them more engaged in classes, and to increase their motivation. One of the opinions is that the student success requires their strong will, persistence, diligence and perseverance. Certainly, the competence, motivation and consistency of teachers, wholead them to the world of knowledge, have a great influence. One of the methods of achieving a positive influence of teachers, in the domain of increasing interest in mathematics and reducing aversion to it, is the use of interesting mathematical problems, in which the numerical value of the current calendar year or even the current date appears. The aim of this paper is to point out how the motivation of primary school students to adopt mathematical content can be increased. With concrete examples of interesting algebra problems, which tickle students’ fancy and make them think, we show how some lessons can be learned.

In Plato’s later ethics, the key challenge to one’s personal progress is unorderly thoughts and motions of soul. This disorder should be corrected by recognising and repeating the orderly thoughts and motions of cosmic gods. This paper examines the theoretical assumptions of Plato’s later ethics. A closer analysis of the Timaeus reveals a peculiar conception of mathematics, according to which numbers and their relations not only reveal facts about the reality, but also express values and ideals. By learning mathematics human beings come to know the everyday ethical life of cosmic gods and become like them.

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder's and Banach's fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

The paper describes the situation of teaching mathematics and its position at Prague University in the second half of the 18th century. In order to be able to adequately present the specific changes during this period, I first explain the development of the role of mathematics as a modern science among the Prague Jesuits in the two centuries before. It is pointed out that the Jesuits initially assigned only a very minor importance to mathematics. From the middle of the 17th century, however, there was significant development. In the middle of the 18th century, under the influence of the Enlightenment, state reforms set in, which also significantly influenced the structure and content of education at Prague University. I describe the consequences of these reforms – that also led to the dissolution of the Jesuit Order – for mathematics. Finally, I deal with the life and work of mathematicians and astronomers at Prague University in the second half of the 18th century.

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder's and Banach's fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

In this paper, we use a characterization of the mutual multifractal Hausdorff dimension in terms of auxiliary measures to investigate the projections of measures with small supports.

The aim of this paper is to prove the existence and stability of solutions of a system of quadratic integral equations in the Banach algebra of continuous and bounded functions on unbounded rectangle. The main tool used in our considerations is the multiple fixed point theorem which is a consequence of Darbo's fixed point theorem and the technique associated with measures of noncompactness. We also present an illustrative example.

The main purpose of the present paper is to demonstrate that as early as 1904 pre-eminent American mathematician Maxime Bôcher was an adherent to the presently relevant argument of reasonableness, or even necessity of parallel development of two philosophical methods of reflection on mathematics, so that its essence could be more fully comprehended. The goal of the research gives rise to the question: what two types of philosophical deliberation on mathematics were proposed by Bôcher?

In this paper, we introduce multi-Jensen-cubic mappings and unify the system of functional equations defining the multi-Jensen-cubic mapping to a single equation. Applying a fixed point theorem, we establish the generalized Hyers-Ulam stability of multi-Jensen-cubic mappings. As a known outcome, we show that every approximate multi-Jensen-cubic mapping can be multi-Jensen-cubic.

In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius ε centered at 0 on the upper half space Rd-1× ]0,+∞[. Second, we prove weak-type L1-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain the Lp-boundedness of this operator for 1 < p ≤+∞. As application, we define a large class of operators such that each operator of this class satisfies these Lp-inequalities. In particular, the maximal operator associated respectively with the Weinstein heat semigroup and the Weinstein-Poisson semigroup belong to this class.