rss_2.0Mathematics FeedSciendo RSS Feed for Mathematics Feed art design of industrialised manufacturing furniture products based on the simulation of mathematical curves<abstract><title style='display:none'>Abstract</title><p>After a lot of literature reading and practical research, the paper uses the parametric modelling method of curve simulation characteristic line to establish the mathematical model of the furniture product leg shape. This article first uses the surface construction method to analyse the composition of the leg size of the industrialised production and manufacture of furniture products, and makes the solid modelling according to the construction method of non-uniform rational spline mathematical curve and surface simulation. At the same time, the parameter function of furniture leg type is set on SolidWorks, and the research results obtained in the paper are found by simulation, which opens up a new research path for the application of mathematical curve model in furniture design.</p></abstract>ARTICLE2021-09-24T00:00:00.000+00:00Auction theory and a note on game mechanisms<abstract> <title style='display:none'>Abstract</title> <p>This paper will review important topics on the subject of auction theory and mechanism design, these include: efficiency first and foremost, also revenue comparison between different types of auctions and the issue of incentive compatibility, individual rationality with the general idea and proof that bilateral trade is inefficient. Mechanism design theory tells us that if buyers and sellers both have private information full efficiency is impossible, however Vickrey auction (single unit auction) will be efficient i.e. will put the goods in the hands of the buyers that value them most. However, the conclusion from this paper is that because of overvaluation of bidders the main result is inefficient, i.e. bids are too high. When weak and strong bidders are compared the main conclusion is that strong bidders’ expected payoff is higher in second price auction (SPA), while weak bidder prefers first price auction (FPA) bid.</p> </abstract>ARTICLE2021-05-29T00:00:00.000+00:00Business and Economics Students’ Self-Reports on Academic Reading in English as L2: A Factor Analysis<abstract> <title style='display:none'>Abstract</title> <p>Adequate reading behaviour is vital for text comprehension across fields. In today’s professional environment, a well-developed reading skill is also expected in English as a second language (EL2), which happens already in college, although transition to college-level reading may be difficult even in the first language. It is therefore useful to analyse students’ use of reading strategies to facilitate their academic progress. This study investigates the reading behaviour of junior students of business/economics when reading academic texts in EL2. We conducted an exploratory factor analysis (N=134) of a 45-item questionnaire about students’ awareness of reading strategies and their reading confidence (i.e. self-perceived competence in text retelling). The majority of the items were based on self-reports found in the literature (Kolić-Vehovec, Bajšanski, 2001; Mokhtari, Reichard, 2002; Taraban, Kerr, Rynearson, 2004) and several items were added to the questionnaire (e.g. questions related to note taking). Five factors were interpretable: four factors related to Metacognitive Awareness of Reading Strategies (Repeated Reading, Monitoring/Regulation, Note Taking and Elaboration) and the fifth factor covering self-perceived competence in text retelling (Reading Confidence). Internal consistency of the factors indicated by standardized Cronbach’s alphas were 0.83 (Repeated Reading), 0.80 (Monitoring and Regulation), 0.77 (Note Taking), 0.63 (Elaboration) and 0.75 (Reading Confidence). Three strategies positively correlated with each other (Repeated Reading, Monitoring/Regulation and Elaboration), while negative correlation was found between Note Taking and Reading Confidence. The results provide valuable information on the patterns in student reading as a baseline for further analysis of L2 text comprehension in college.</p> </abstract>ARTICLE2021-05-29T00:00:00.000+00:00Remittance in Niger: effects on economic growth and on migrants’ left behind<abstract> <title style='display:none'>Abstract</title> <p>Remittances have long been an important source of revenue for many people in the Republic of Niger. In order to fight poverty, young people choose to migrate. In 2019, a total of 293 million U.S. dollars was sent by migrants to their relatives in Niger; that is 3% of Niger Gross Domestic Product (GDP). The objective of this study is to analyze the effects of remittances on economic growth in Niger and the significance of its contribution in improving the living condition of migrants’ left behind families. The study applies a three-step econometric procedure followed by a survey on the usage of the remittances in the city of Tahoua (Republic of Niger). The study also performed some tests on the residuals for the accuracy of the prediction of the model. The empirical results showed no long run relationship between remittances, economic growth and gross fixed capital formation in Niger. However, in the short-run, the study revealed the existence of causal effect between remittances and economic growth. On the other hand, the results of the conducted survey in the city of Tahoua showed that 45.7% of the received remittance is used in food expenditure, 19.3% in education expenditure, 10.36% in health expenditure and 5.4% is allocated to house rent. The survey also revealed the importance of the remittances for the left behind. It indicates that 14% of the respondent left behind wish to see another family member engage in migration.</p> </abstract>ARTICLE2021-05-29T00:00:00.000+00:00Public sector innovation performance in Federation of Bosnia and Herzegovina: An exploratory factor analysis<abstract> <title style='display:none'>Abstract</title> <p>Innovation has nowadays become the main force to cope with challenging times in the fast-changing world. The influence of public sector innovation (PSI) in resolving dynamic economical and societal challenges is undisputable. Regardless of the numerous advantages of innovation in the public sector (PS) which have been recognised worldwide, the concept of public sector innovation is still novel for the Federation of Bosnia and Herzegovina (FBiH). Moreover, there is limited empirical evidence which would facilitate the understanding of public sector innovation performance. The purpose of this paper is to identify main components of PSI performance. The primary research data was obtained through a survey with close-ended questions which was completed by the public sector institution employees in FBiH. The exploratory factor analysis (EFA) was used in order to determine the principal components of measuring public sector innovation performance. The EFA returned the factor-structures for all four suggested constructs, innovation capabilities, wider sector conditions for innovation, sources of information and the share of creative occupation, explaining between 65% and 78% of the variance of the innovation performance measurement construct. The results from the exploratory factor analysis provided a distinct estimation on the factor structure of measuring PSI. The paper has provided and analysed the first instrument in measuring public sector innovation performance in FBiH.</p> </abstract>ARTICLE2021-05-29T00:00:00.000+00:00Economic analysis of rice production by small-holder women farmers in Adamawa State, Nigeria<abstract> <title style='display:none'>Abstract</title> <p>This study is focused on analysing the economics of rice production by the small-holder female rice-farmers in Adamawa State, Nigeria. Specifically, the study described female rice-farmers’ socio-economic characteristics, analysed their technical and allocative efficiencies, and also assessed their economic efficiency in the area. Primary data were collected from 180 randomly selected female rice-farmers in Adamawa State using a semi-structured questionnaire. Descriptive statistics and stochastic frontier function were used analysing the data collected. Findings of the study revealed that the technical in-efficiency of the farmers is influenced by farming experience, education, and access to credit facilities. Also, the allocative in-efficiency of female farmers was influenced by education, household size, and access to credits. The result showed that education and access to credit facilities were common factors affecting the technical and allocative efficiency of female rice farmers in the area. The mean economic efficiency of the female farmers was 0.6. Therefore, the study recommends that the government and other actors in the agricultural sector should facilitate women’s access to credit facilities and other agricultural information relevant to rice production.</p> </abstract>ARTICLE2021-05-29T00:00:00.000+00:00Next Level Odd-One-Out Puzzles<abstract><title style='display:none'>Abstract</title><p>A commonly occurring task in intelligence tests or recreational riddles is to “find the odd one out”, that is, to determine a unique element of a set of objects that is somehow special. It is somewhat arbitrary what exactly the relevant feature is that makes one object different. But once that is settled, the answer becomes obvious. Not so with a puzzle popularized by Tanya Khovanova to express her dislike for this type of puzzle. Here, it is a more complicated relation between the objects and the features that determines the odd object, because there is only one object that does not have a unique feature expression. This puzzle inspired me to look for even more complicated relations between objects, features and feature expressions that appear to be even more symmetric, but actually still single out a “special object”. This paper provides useful definitions, a theoretical basis, solution algorithms, and several examples for this kind of puzzle.</p></abstract>ARTICLE2020-09-18T00:00:00.000+00:00Counting Clues in Crosswords<abstract><title style='display:none'>Abstract</title><p>We consider different ways to count the number of clues in American-style crossword puzzle grids. One yields a basic parity result for symmetric square grids. Another works efficiently even for non-symmetric grids that are already numbered. We further discuss the upper limit on the number of clues in a crossword puzzle with no 2-letter answers, and open questions are given. As a bonus, a mathematically-themed crossword puzzle is included!</p></abstract>ARTICLE2020-09-18T00:00:00.000+00:00Making the Unfair Fair in Command: Optimal Play for Two Person Generala Classification of Magic SET Squares<abstract><title style='display:none'>Abstract</title><p>A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations and reflections of the square. Under these transformations, there are 21 types of magic SET squares. We calculate the number of squares of each type. In addition, we discuss a game of SET tic-tac-toe.</p></abstract>ARTICLE2020-09-18T00:00:00.000+00:00Existentially closed Leibniz algebras and an embedding theorem<abstract> <title style='display:none'>Abstract</title> <p>In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.</p> </abstract>ARTICLE2021-07-15T00:00:00.000+00:00Rota-type operators on 3-dimensional nilpotent associative algebras<abstract> <title style='display:none'>Abstract</title> <p>We give the description of Rota–Baxter operators, Reynolds operators, Nijenhuis operators and average operators on 3-dimensional nilpotent associative algebras over ℂ.</p> </abstract>ARTICLE2021-07-15T00:00:00.000+00:00A generalisation of Amitsur’s A-polynomials<abstract> <title style='display:none'>Abstract</title> <p>We find examples of polynomials <italic>f</italic> ∈ <italic>D</italic> [<italic>t</italic>; <italic>σ, δ</italic>] whose eigenring <italic>ℰ</italic>(<italic>f</italic>) is a central simple algebra over the field <italic>F</italic> = <italic>C</italic> ∩ Fix(<italic>σ</italic>) ∩ Const(<italic>δ</italic>).</p> </abstract>ARTICLE2021-07-15T00:00:00.000+00:00Conservative algebras of 2-dimensional algebras, III<abstract> <title style='display:none'>Abstract</title> <p>In the present paper we prove that every local and 2-local derivation on conservative algebras of 2-dimensional algebras are derivations. Also, we prove that every local and 2-local automorphism on conservative algebras of 2-dimensional algebras are automorphisms.</p> </abstract>ARTICLE2021-07-15T00:00:00.000+00:00Actions of the additive group on certain noncommutative deformations of the plane<abstract> <title style='display:none'>Abstract</title> <p>We connect the theorems of <xref ref-type="bibr" rid="j_cm-2021-0024_ref_018">Rentschler [18]</xref> and <xref ref-type="bibr" rid="j_cm-2021-0024_ref_010">Dixmier [10]</xref> on locally nilpotent derivations and automorphisms of the polynomial ring <italic>A</italic><sub>0</sub> and of the Weyl algebra <italic>A</italic><sub>1</sub>, both over a field of characteristic zero, by establishing the same type of results for the family of algebras <disp-formula id="j_cm-2021-0024_eq_001"> <alternatives> <graphic xmlns:xlink="" xlink:href="graphic/j_cm-2021-0024_eq_001.png"/> <mml:math xmlns:mml="" display="block"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>〈</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>|</mml:mo><mml:mi>y</mml:mi><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:mi>x</mml:mi><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>〉</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math> <tex-math>{A_h} = \left\langle {x,y|yx - xy = h\left( x \right)} \right\rangle ,</tex-math> </alternatives> </disp-formula> , where <italic>h</italic> is an arbitrary polynomial in <italic>x</italic>. In the second part of the paper we consider a field 𝔽 of prime characteristic and study 𝔽[<italic>t</italic>]-comodule algebra structures on <italic>A<sub>h</sub></italic>. We also compute the Makar-Limanov invariant of absolute constants of <italic>A<sub>h</sub></italic> over a field of arbitrary characteristic and show how this subalgebra determines the automorphism group of <italic>A<sub>h</sub></italic>.</p> </abstract>ARTICLE2021-07-15T00:00:00.000+00:00Weak polynomial identities and their applications<abstract> <title style='display:none'>Abstract</title> <p>Let <italic>R</italic> be an associative algebra over a field <italic>K</italic> generated by a vector subspace <italic>V</italic>. The polynomial <italic>f</italic>(<italic>x</italic><sub>1</sub>, . . . , <italic>x<sub>n</sub></italic>) of the free associative algebra <italic>K</italic>〈<italic>x</italic><sub>1</sub>, <italic>x</italic><sub>2</sub>, . . .〉 is a weak polynomial identity for the pair (<italic>R, V</italic>) if it vanishes in <italic>R</italic> when evaluated on <italic>V</italic>. We survey results on weak polynomial identities and on their applications to polynomial identities and central polynomials of associative and close to them nonassociative algebras and on the finite basis problem. We also present results on weak polynomial identities of degree three.</p> </abstract>ARTICLE2021-07-15T00:00:00.000+00:00Gradedness of the set of rook placements in<abstract> <title style='display:none'>Abstract</title> <p>A rook placement is a subset of a root system consisting of positive roots with pairwise non-positive inner products. To each rook placement in a root system one can assign the coadjoint orbit of the Borel subgroup of a reductive algebraic group with this root system. Degenerations of such orbits induce a natural partial order on the set of rook placements. We study combinatorial structure of the set of rook placements in <italic>A<sub>n−</sub></italic><sub>1</sub> with respect to a slightly different order and prove that this poset is graded.</p> </abstract>ARTICLE2021-07-15T00:00:00.000+00:00Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras<abstract> <title style='display:none'>Abstract</title> <p>In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly nilpotent.</p> </abstract>ARTICLE2021-07-15T00:00:00.000+00:00The image of multilinear polynomials evaluated on 3 × 3 upper triangular matrices<abstract> <title style='display:none'>Abstract</title> <p>We describe the images of multilinear polynomials of arbitrary degree evaluated on the 3×3 upper triangular matrix algebra over an infinite field.</p> </abstract>ARTICLE2021-07-15T00:00:00.000+00:00en-us-1