3,138 results
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52. The Solipsist's First Paper.
- Author
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Sixta, Sabrina
- Subjects
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MATHEMATICS - Published
- 2022
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53. A relation-theoretic set-valued version of Prešić-Ćirić theorem and applications.
- Author
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Shukla, Satish, Rai, Shweta, and Shukla, Rahul
- Subjects
- *
METRIC spaces , *MATHEMATICS - Abstract
In this paper, we establish a relation-theoretic set-valued version of the fixed point result of Ćirić and Prešić (Acta Math. Univ. Comen. LXXVI(2):143–147, 2007) on metric spaces endowed with an arbitrary binary relation. The results of this paper, generalize and unify the fixed point results of Ćirić and Prešić (Acta Math. Univ. Comen. LXXVI(2):143–147, 2007), Shukla and López (Quaest. Math. 45(3):1–16, 2019), and Shukla and Radenović (An. Ştiinţ. Univ. 'Al.I. Cuza' Iaşi, Mat. 63(2):339–350, 2017) in product spaces. Some examples are provided that justify and establish the importance of our results. As applications of our main result, we have established the existence of solutions to differential inclusion problems and the weak asymptotical stability and a global attractivity of the equilibrium point of a difference inclusion problem. The use of arbitrary binary relations in our results permits us to apply the results to the differential inclusion problems and difference inclusion problems with weaker assumptions than those used in the papers mentioned above. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
54. Mathematical Methods for an Accurate Navigation of the Robotic Telescopes.
- Author
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Savanevych, Vadym, Khlamov, Sergii, Briukhovetskyi, Oleksandr, Trunova, Tetiana, and Tabakova, Iryna
- Subjects
- *
TELESCOPES , *ROBOTICS , *SIGNAL-to-noise ratio , *NAVIGATION , *STANDARD deviations , *IDENTIFICATION - Abstract
Accurate sky identification is one of the most important functions of an automated telescope mount. The more accurately the robotic telescope is navigated to the investigated part of the sky, the better the observations and discoveries made. In this paper, we present mathematical methods for accurate sky identification (celestial coordinates determination). They include the automatic selection of the reference stars, preliminary and full sky identification, as well as an interaction with international databases, which are a part of the astrometric calibration. All described methods help to receive accurately calculated astrometric data and use it for the positional calibration and better navigation of the automated telescope mount. The developed methods were successfully implemented in the Collection Light Technology (CoLiTec) software. Through its use, more than 1600 small solar system objects were discovered. It has been used in more than 700,000 observations and successful sky identifications, during which, five comets were discovered. Additionally, the accuracy indicators of the processing results of the CoLiTec software are provided in the paper, which shows benefits of the CoLiTec software and lower standard deviation of the sky identification in the case of low signal-to-noise ratios. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
55. Benefits of Risk-Taking in Teaching Mathematics.
- Author
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KIRMIZI, Mehmet, QUANSAH, Abigail, and BUBER, Zafer
- Subjects
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MATHEMATICS education , *TEACHING methods , *MATHEMATICS students , *MATHEMATICS , *EDUCATIONAL outcomes , *GRADUATE students - Abstract
In this paper, we, a group of graduate students in mathematics education, discuss some of the metacognitive benefits of the non-traditional teaching methods we observed employed by one of our professors. This professor's methods challenge the common belief that well-managed class time is key for positive learning outcomes. Instead, he orients his teaching to share the exploration and sense-making phases of doing mathematics. The goal of his teaching is to share the idea that learning mathematics is a process of "refining our mathematical thinking". We argue that this approach to teaching helps students see that mathematics is a human endeavor, appreciate the cycles of learning mathematics and the importance of struggle throughout the process, and gain some insight on what it means to be an expert in mathematics. We encourage teachers and professors to move away from obsessing about structured, well-organized class time, and to instead move towards having flexible and risk-oriented class time. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
56. Sharing Four Biscuits Between Three People: An Illustrative Example of How Mathematics is Intertwined with Human Values.
- Author
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Sumpter, Lovisa and Sumpter, David
- Subjects
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VALUES (Ethics) , *BISCUITS , *MACHINE learning , *PHILOSOPHERS , *MATHEMATICIANS , *MATHEMATICS - Abstract
Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread notion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how mathematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demonstrate that different solutions--hiding one biscuit, arbitrarily sharing the extra biscuit, randomizing allocation, dividing the extra biscuit into three parts, and successively dividing it into smaller and smaller parts--involve different mathematical methods and evoke different human values. We discuss the construction of quantum biscuit splitting devices and the use of machine learning to divide biscuits. We argue that the multitude of different mathematically-correct solutions to this problem (each with its own ethical justification) might influence the values held by practicing mathematicians. The example we propose here has been used in teaching to help students understand why mathematics cannot be cleanly separated from human values. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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57. Finding Your Mathematical Roots: Inclusion and Identity Development in Mathematics.
- Author
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McGuire, Linda
- Subjects
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IDENTITY (Psychology) , *SCIENTIFIC knowledge , *GENEALOGY , *UPPER level courses (Education) , *MATHEMATICS , *CONSTRUCTION projects - Abstract
This paper details a semester-long course project that has been successfully adapted for use in mathematics courses ranging from introductory level, generaleducation classes to advanced courses in the mathematics major. Through creating aspirational mathematical family trees and writing mathematical autobiographies, this assignment is designed to help battle belonging uncertainty, to challenge students to self-situate in relation to the history of mathematical and scientific knowledge, and to make visible a student's developing identity in mathematics and, more broadly, in STEM. The construction and scaffolding of the project, assignments, examples of student work, foundational readings, assessment and outcomes, and adaptation strategies for various classroom settings are discussed in detail. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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58. Some existence and uniqueness results for a solution of a system of equations.
- Author
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KHANTWAL, DEEPAK and PANT, RAJENDRA
- Subjects
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EQUATIONS , *METRIC spaces , *MATHEMATICS - Abstract
This paper presents some existence and uniqueness results for a solution of a system of equations. Our results extend and generalize the well-known and celebrated results of Boyd and Wong [Proc. Amer. Math. Soc. 20 (1969)], Matkowski [Dissertations Math. (Rozprawy Mat.) 127 (1975)], Proinov [Nonlinear Anal. 64 (2006)], Ri [Indag. Math. (N. S.) 27 (2016)] and many others. We also present some illustrative examples to validate our results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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59. Neutrosophic -Structures in Semimodules over Semirings.
- Author
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Muhiuddin, Ghulam, Abughazalah, Nabilah, Elavarasan, Balasubramanian, Porselvi, Kasi, and Al-Kadi, Deena
- Subjects
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TWENTY-first century , *STRUCTURAL frames , *MATHEMATICS , *SYMMETRY - Abstract
The study of symmetry is a fascinating and unifying subject that connects various areas of mathematics in the twenty-first century. Algebraic structures offer a framework for comprehending the symmetries of geometric objects in pure mathematics. This paper introduces new concepts in algebraic structures, concentrating on semimodules over semirings and analysing the neutrosophic structure in this context. We explore the properties of neutrosophic subsemimodules and neutrosophic ideals after defining them. We discuss, utilizing neutrosophic products, the representations of neutrosophic ideals and subsemimodules, as well as the relationship between neutrosophic products and intersections. Finally, we derive equivalent criteria in terms of neutrosophic structures for a semiring to be fully idempotent. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
60. DisCrit noticing: Theorizing at the intersections of race and ability in mathematics education.
- Author
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Yeh, Cathery
- Subjects
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RACE , *MATHEMATICS education , *CRITICAL race theory , *INTERSECTIONALITY , *MATHEMATICS , *ABLEISM - Abstract
While there is increased attention to power, privilege, and access in mathematics education, conversations around race and disability are often left out of the conversation. Disability in mathematics continues to be studied with a lens that focuses on behavior, rather than attending to the situated and sociopolitical context in which teaching and learning takes place. This paper specifically calls on the importance of an intersectional analysis of ability and the need for explicit conversation on the interwoven nature of race and disability to uncover exclusionary practices of hyper‐labeling, hyper‐surveilling, and hyper‐punishing for those outside notions of normalcy. Drawing on sociopolitical perspectives informed by Disability Critical Race Theory (DisCrit) and DisCrit Classroom Ecology, I share a framework of DisCrit noticing to consider the interwoven nature of racism and ableism in mathematics classrooms, provide a context to develop preservice teacher DisCrit noticing during mathematics methods, and a case example to highlight implications and transformative possibilities for (re)organizing classrooms through the DisCrit noticing framework. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
61. Framed mapping class groups and the monodromy of strata of abelian differentials.
- Author
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Calderon, Aaron and Salter, Nick
- Subjects
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ABELIAN groups , *MATHEMATICS , *RIEMANN surfaces , *MONODROMY groups , *GROUP theory - Abstract
This paper investigates the relationship between strata of abelian differentials and various mapping class groups afforded by means of the topological monodromy representation. Building off of prior work of the authors, we show that the fundamental group of a stratum surjects onto the subgroup of the mapping class group which preserves a fixed framing of the underlying Riemann surface, thereby giving a complete characterization of the monodromy group. In the course of our proof we also show that these “framed mapping class groups” are finitely generated (even though they are of infinite index) and give explicit generating sets. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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62. Some combinatorial identities containing central binomial coefficients or Catalan numbers.
- Author
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Feng Qi, Da-Wei Niu, and Dongkyu Lim
- Subjects
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CATALAN numbers , *BINOMIAL coefficients , *MATHEMATICS - Abstract
In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors (1) give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; (2) establish four sum formulas for finite sums containing the ratio or product of two central binomial coefficients or the Catalan numbers. The instant proof simplifies discussions in the journal papers: College Math. J. 43 (2012), no. 2, 141-146; Amer. Math. Monthly 121 (2014), no. 3, 267-267; Amer. Math. Monthly 123 (2016), no. 4, 405-406; Elem. Math. 71 (2016), no. 3, 109-121; and Mathematics 5 (2017), no. 3, Article 40, 31 pages. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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63. Well-Posedness of a Class of Radial Inhomogeneous Hartree Equations.
- Author
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Almuthaybiri, Saleh, Ghanmi, Radhia, and Saanouni, Tarek
- Subjects
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SOBOLEV spaces , *EQUATIONS , *NONLINEAR equations , *MATHEMATICS - Abstract
The present paper investigates the following inhomogeneous generalized Hartree equation i u ˙ + Δ u = ± | u | p − 2 | x | b (I α ∗ | u | p | · | b) u , where the wave function is u : = u (t , x) : R × R N → C , with N ≥ 2 . In addition, the exponent b > 0 gives an unbounded inhomogeneous term | x | b and I α ≈ | · | − (N − α) denotes the Riesz-potential for certain 0 < α < N . In this work, our aim is to establish the local existence of solutions in some radial Sobolev spaces, as well as the global existence for small data and the decay of energy sub-critical defocusing global solutions. Our results complement the recent work (Sharp threshold of global well-posedness versus finite time blow-up for a class of inhomogeneous Choquard equations, J. Math. Phys. 60 (2019), 081514). The main challenge in this work is to overcome the singularity of the unbounded inhomogeneous term | x | b for certain b > 0 . [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
64. Holomorphic H{o}rmander-type functional calculus on sectors and strips.
- Author
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Haase, Markus and Pannasch, Florian
- Subjects
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CALCULUS , *HOLOMORPHIC functions , *MULTIPLIERS (Mathematical analysis) , *MATHEMATICS - Abstract
In this paper, the abstract multiplier theorems for 0-sectorial and 0-strip type operators by Kriegler and Weis [Math. Z. 289 (2018), pp. 405–444] are refined and generalized to arbitrary sectorial and strip-type operators. To this end, holomorphic Hörmander-type functions on sectors and strips are introduced, with even a finer scale of smoothness than the classical polynomial scale. Moreover, we establish alternative descriptions of these spaces involving Schwartz and "holomorphic Schwartz" functions. Finally, the abstract results are combined with a result by Carbonaro and Dragičević [Duke Math. J. 166 (2017), pp. 937–974] to obtain an improvement—with respect to the smoothness condition—of the known Hörmander-type multiplier theorem for general symmetric contraction semigroups. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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65. A remark about asymptotic stability in Duffing equations: lateral stability in Comb-drive finger MEMS.
- Author
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Núñez, D. and Murcia, L.
- Subjects
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DUFFING equations , *FINGERS , *MATHEMATICS - Abstract
In this short paper we tackle two subjects. First, we provide a lower bound for the first eigenvalue of the antiperiodic problem for a Hill's equation based on L p -conditions, and as a consequence, we introduce an adjusted statement of the main result about the asymptotic stability of periodic solutions for the general Duffing equation in (Torres in Mediterr. J. Math. 1(4):479–486, 2004) (Theorem 4). This appropriate version of the result arises because of one subtlety in the proof provided in (Torres in Mediterr. J. Math. 1(4):479–486, 2004). More precisely, the lower bound of the first antiperiodic eigenvalue associated with Hill's equations of potential a (t) employed there may be negative, thus the conclusion is not completely attained. Hence, the adjustments considered here provide a mathematically correct result. On the other hand, we apply this result to obtain a lateral asymptotic stable periodic oscillation in the Comb-drive finger MEMS model with a cubic nonlinear stiffness term and linear damping. This fact is not typical in Comb-drive finger devices, thus our results could provide a new possibility; a new design principle for stabilization in Comb-drive finger MEMS. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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66. Domination parameters of the splitting graph of a graph.
- Author
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Deepalakshmi, J., Marimuthu, G., Somasundaram, A., and Arumugam, S.
- Subjects
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PARAMETERS (Statistics) , *MATHEMATICS , *RATIONAL numbers , *INTEGERS , *MATHEMATICAL constants - Abstract
Let G = (V;E) be a graph of order n and size m: The graph Sp(G) obtained from G by adding a new vertex v0 for every vertex v 2 V and joining v0 to all neighbors of v in G is called the splitting graph of G: In this paper, we determine the domination number, the total domination number, connected domination number, paired domination number and independent domination number for the splitting graph Sp(G):. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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67. Dynamics of a periodic-parabolic Lotka–Volterra competition-diffusion system in heterogeneous environments.
- Author
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Xueli Bai, Xiaoqing He, and Wei-Ming Ni
- Subjects
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REACTION-diffusion equations , *SPATIAL analysis (Statistics) , *LOTKA-Volterra equations , *MATHEMATICS , *EIGENVALUES - Abstract
The effects of spatial heterogeneity on the dynamics of reaction-diffusion models have been studied extensively. In particular, global dynamics of general spatially heterogeneous (but temporally static) Lotka–Volterra competition-diffusion systems were completely clarified by He and Ni in 2016. However, the evolutionary impacts of temporal periodicity combined with spatial heterogeneity in population ecology remain a challenging issue. In this work, we consider a population model of two competing species in a both spatially varying and temporally periodic environment, where the two species only differ in their random dispersal rates but are otherwise ecologically identical. In a pioneering 2001 work on this model by Hutson et al., by constructing various choices of resource functions and dispersal rates of the two species, the authors demonstrated that all the following three types of dynamics are possible: (i) stable coexistence of the two species; (ii) the slower diffuser invades the faster one but not vice versa; (iii) the faster diffuser invades the slower one but not vice versa. This is in drastic contrast with the spatially heterogeneous but temporally static case, where Dockery et al. showed in 1998 that the slower diffuser always wipes out the faster one. In this paper, we completely and explicitly characterize the asymptotic stability of both semitrivial periodic solutions in terms of the two dispersal rates and the resource function, when either dispersal rate is sufficiently small or large. In particular, the direction of selection on the dispersal rate during the evolution can be elucidated in these instances. Some novel analytical methods are developed to investigate asymptotic behaviors of the underlying time-periodic parabolic eigenvalue problem and its adjoint problem. We hope that these methods are of independent interest in the area of time-periodic parabolic equations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
68. Sharp local well-posedness for quasilinear wave equations with spherical symmetry.
- Author
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Chengbo Wang
- Subjects
- *
QUASILINEARIZATION , *WAVE equation , *CHAIN rule , *SOBOLEV spaces , *MATHEMATICS - Abstract
In this paper, we prove a sharp local well-posedness result for spherically symmetric solutions to quasilinear wave equations with rough initial data, when the spatial dimension is three or higher. Our approach is based on Morawetz type local energy estimates with fractional regularity for linear wave equations with variable C¹ coefficients, which rely on the multiplier method, weighted Littlewood–Paley theory, duality and interpolation. Together with weighted linear and nonlinear estimates (including weighted trace estimates, Hardy’s inequality, a fractional chain rule and a fractional Leibniz rule) which are adapted to the problem, the well-posedness result is proved by iteration. In addition, our argument yields almost global existence for n = 3 and global existence for n ≥ 4 when the initial data are small and spherically symmetric with almost critical Sobolev regularity. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
69. Basic color categories and Mandarin Chinese color terms.
- Author
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Sun, Vincent C. and Chen, Chien-Chung
- Subjects
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COLOR vision , *CHINESE color prints , *COLORED paper , *TOUCH screens , *MULTIPLE correspondence analysis (Statistics) - Abstract
Basic color terms used in Mandarin Chinese have been controversial since first discussed by Berlin and Kay in 1969. Previous studies showed much inconsistency on what should be considered as basic color terms in Mandarin Chinese. In the present study, we investigated categories of color rather than merely the color terms used by Taiwanese native Mandarin speakers. Using samples conforming to the Berlin and Kay survey, various colors were chosen from a collection of Natural Color System (NCS) colored papers and mounted on a piece of neutral gray card. The card was then mounted on a touch-screen, under D65 illumination. Thirty-two single-character color related Mandarin terms were selected from a Chinese character database according to frequency of use. Participants were required to select the color sample that matched the term by pressing a virtual button on the touch screen. The results show that certain terms can be directly correlated to basic color terms in English, comparable with the results of Berlin and Kay’s original study and those that followed. However, some terms, such as Mo (墨 ink), Tie (鐵 iron), and Cai (菜vegetable), show a wide spread of term maps and inconsistent use among subjects. Principle component analysis (PCA) procedures were used to analysis the commodity of data among subjects. The findings suggest that the basic color categories among Mandarin Chinese speakers are similar to those found in the World Color Survey (WCS), but are represented by wide-spread and inconsistent color terms among speakers. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
70. That’s a wrap.
- Author
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Steckles, Katie
- Subjects
- *
GIFT wrapping , *MATHEMATICS - Abstract
This article from New Scientist discusses how mathematics can be used to wrap gifts in a precise and efficient manner. The author explains that when wrapping box-shaped gifts, measuring the length and thickness of the box can help determine the amount of paper needed. For cylindrical gifts, the paper should be slightly wider than the diameter of the gift and the length should be the sum of the diameter and the length of the gift. The article also provides instructions for wrapping equilateral triangular prism gifts and large, flat, square-ish gifts using mathematical methods. The author emphasizes the importance of aligning the pattern on the paper for maximum aesthetic appeal. [Extracted from the article]
- Published
- 2023
71. Analysis of Persian Bioinformatics Research with Topic Modeling.
- Author
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Ebrahimi, Fezzeh, Dehghani, Mohammad, and Makkizadeh, Fatemah
- Subjects
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LIFE sciences , *RESEARCH , *BIOMARKERS , *PHONOLOGICAL awareness , *MATHEMATICAL models , *NATURAL language processing , *RESEARCH methodology , *BIBLIOMETRICS , *MOLECULAR models , *BIOINFORMATICS , *MATHEMATICS , *CITATION analysis , *GENE expression , *THEORY , *MEDICAL research , *INFORMATION technology , *ALGORITHMS - Abstract
Purpose. As a scientific field, bioinformatics has drawn remarkable attention from various fields, such as information technology, mathematics, and modern biological sciences, in recent years. The topic models originating from the field of natural language processing have become the focus of attention with the rapid accumulation of biological datasets. Thus, this research is aimed at modeling the topic content of the bioinformatics literature presented by Iranian researchers in the Scopus Citation Database. Methodology. This research was a descriptive-exploratory study, and the studied population included 3899 papers indexed in the Scopus database, which had been indexed in this database until March 9, 2022. The topic modeling was then performed on the abstracts and titles of the papers. A combination of LDA and TF-IDF was utilized for topic modeling. Findings. The data analysis with topic modeling resulted in identifying seven main topics "Molecular Modeling," "Gene Expression," "Biomarker," "Coronavirus," "Immunoinformatics," "Cancer Bioinformatics," and "Systems Biology." Moreover, "Systems Biology" and "Coronavirus" had the largest and smallest clusters, respectively. Conclusion. The present investigation demonstrated an acceptable performance for the LDA algorithm in classifying the topics included in this field. The extracted topic clusters indicated excellent consistency and topic connection with each other. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
72. Exact sequences for dual Toeplitz algebras on hypertori.
- Author
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Benaissa, Lakhdar and Guediri, Hocine
- Subjects
- *
HARDY spaces , *ALGEBRA , *C*-algebras , *TOEPLITZ operators , *CALCULUS , *MATHEMATICS - Abstract
In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk D n in the unitary space C n , that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus T n . [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
73. Some new integral inequalities for higher-order strongly exponentially convex functions.
- Author
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Bisht, Jaya, Sharma, Nidhi, Mishra, Shashi Kant, and Hamdi, Abdelouahed
- Subjects
- *
INTEGRAL inequalities , *CONVEX functions , *FRACTIONAL integrals , *APPLIED mathematics , *GENERALIZED integrals , *MATHEMATICS - Abstract
Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
74. Teaching and Learning of Mathematics through CLIL, CBI, or EMI—A Systematic Literature Review.
- Author
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Ruiz-Cecilia, Raúl, Medina-Sánchez, Leopoldo, and Rodríguez-García, Antonio-Manuel
- Subjects
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SCIENTIFIC literature , *LANGUAGE ability , *LEARNING , *STUDENT records , *LANGUAGE acquisition - Abstract
This study provides a systematic literature review of research in the field of teaching and learning mathematics through Content and Language Integrated Learning (CLIL), Content-Based Instruction (CBI), and English Medium Instruction (EMI). The review aims to examine the most relevant literature with a focus on mathematics and CLIL, CBI, or EMI in Scopus and Web of Science per the Preferred Reporting Items for Systematic Reviews (PRISMA) guidelines. Based on 151 sources, 52 papers were selected according to predefined selection criteria. The papers were analysed and coded according to the following categories: (1) geographical productivity, (2) diachronic productivity growth, (3) main objectives, (4) methodology, and research design, (5) variables and measurement instruments, (6) context and sample details, and (7) main findings. The results reveal that most of the research analysed has been carried out in the Asian continent, followed by Europe. The analysis of diachronic productivity shows that the study of the application of CLIL, CBI, and EMI programs in the teaching-learning process of mathematics has notably increased in recent years, especially in the last triennium (2020–2022). Regarding the objectives of the selected corpus, the majority aimed at teaching practices and learning processes, and outcomes in mathematics and language proficiency in CLIL, CBI, and/or EMI classrooms. The corpus analysed fits within one or more of the following categories: empirical, qualitative, descriptive, correlational, and cross-sectional. The samples utilized in different studies differ significantly, both in terms of quantity –ranging from one person to 700– and in the educational level being studied, which would be primary, secondary, or tertiary education. The main variables studied in the corpus focus on mathematical competence, language proficiency, teaching practices, teacher training, science competence, and teachers' perceptions. The most widely used instruments have been objective tests, such as questionnaires, together with standardized tests to measure some aspects related to mathematical competence and language proficiency. They are followed by an analysis of documents (academic records, teaching materials, official documents...), participant or non-participant observation, interviews, and video and audio recordings. In summary, in the scientific literature analysed, a positive or neutral view predominates on the effects of the CLIL, CBI, and EMI approaches on the learning of mathematics and the L2. This can be due to methodological issues fundamentally related to the methodology, research design, sample, and measurement instruments. Thus, we must highlight that some of the results from the selected papers must be interpreted with caution. Taking this factor into consideration, further comparative studies on a wider scale are required to examine thoroughly the effects of CLIL, CBI, and EMI on the teaching and learning of mathematics in an L2. Besides, it is important to study in greater depth the different levels of language acquisition since the research analysed shows that these have not been sufficiently addressed in the mathematical field of knowledge. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
75. Formalising Autonomous Construction Sites with the Help of Abstract Mathematics.
- Author
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Legatiuk, Dmitrii and Luckey, Daniel
- Subjects
- *
BUILDING sites , *CIVIL engineering , *CATEGORIES (Mathematics) , *MATHEMATICS , *CONCEPTUAL models , *CIVIL engineers - Abstract
With the rapid development of modern technologies, autonomous or robotic construction sites are becoming a new reality in civil engineering. Despite various potential benefits of the automation of construction sites, there is still a lack of understanding of their complex nature combining physical and cyber components in one system. A typical approach to describing complex system structures is to use tools of abstract mathematics, which provide a high level of abstraction, allowing a formal description of the entire system while omitting non-essential details. Therefore, in this paper, autonomous construction is formalised using categorical ontology logs enhanced by abstract definitions of individual components of an autonomous construction system. In this context, followed by a brief introduction to category theory and ologs, exemplary algebraic definitions are given as a basis for the olog-based conceptual modelling of autonomous construction systems. As a result, any automated construction system can be described without providing exhausting detailed definitions of the system components. Existing ologs can be extended, contracted or revised to fit the given system or situation. To illustrate the descriptive capacity of ologs, a lattice of representations is presented. The main advantage of using the conceptual modelling approach presented in this paper is that any given real-world or engineering problem could be modelled with a mathematically sound background. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
76. Waiting for a Mathematical Theory of Living Systems from a Critical Review to Research Perspectives.
- Author
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Burini, Diletta, Chouhad, Nadia, and Bellomo, Nicola
- Subjects
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SYSTEMS theory , *SYSTEM dynamics , *CRITICAL analysis , *MATHEMATICS - Abstract
This paper presents a survey of advanced concepts and research perspectives, of a philosophical-mathematical approach to describe the dynamics of systems of many interacting living entities. The first part introduces the general conceptual framework. Then, a critical analysis of the existing literature is developed and referred to a multiscale view of a mathematics of living organisms. This paper attempts to understand how far the present state-of-the-art is far from the achievement of such challenging objective. The overall study leads to identify research perspectives and possible hints to deal with them. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
77. HOW TO DESIGN Fun Math Games for Kids, Teens, Seniors, and In-Betweeners.
- Author
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Shapiro, Phil
- Subjects
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ART , *COMPUTER peripherals , *GAMES , *MATHEMATICS , *SOFTWARE architecture , *EDUCATIONAL technology , *ELECTRONIC spreadsheets , *PUBLIC libraries , *WORLD Wide Web , *VIDEO recording - Abstract
The article reports on the author's initiative to design and share fun, paper-based math games for diverse age groups, utilizing tools like LibreOffice Calc, and details the evolution of the Pairs Math Game, its varied versions, and potential uses in educational and community settings. The author also emphasizes promoting playful conversations about numbers and fostering a sense of agency in students to invent their math questions.
- Published
- 2024
78. Inequalities for Rational Functions with Prescribed Poles.
- Author
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Rather, N. A., Iqbal, A., and Dar, Ishfaq
- Subjects
- *
POLISH people , *POLYNOMIALS , *GENERALIZATION , *MATHEMATICS - Abstract
For rational functions , where is a polynomial of degree at the most and , with we use simple but elegant techniques to strengthen generalizations of certain results which extend some widely known polynomial inequalities of Erdős-Lax and Turán to rational functions . In return these reinforced results, in the limiting case, lead to the corresponding refinements of the said polynomial inequalities. As an illustration and as an application of our results, we obtain some new improvements of the Erdős-Lax and Turán type inequalities for polynomials. These improved results take into account the size of the constant term and the leading coefficient of the given polynomial. As a further factor of consideration, during the course of this paper we will demonstrate how some recently obtained results could have been proved without invoking the results of Dubinin [Distortion theorems for polynomials on the circle, Sb. Math. 191(12) (2000) 1797–1807]. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
79. A Way of Human Capital Accumulation: Heterogeneous Impact of Shadow Education on Students' Academic Performance in China.
- Author
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Tan, Minda and Liu, Shuiyun
- Subjects
- *
HUMAN capital , *ACADEMIC achievement , *MULTILEVEL models , *TUTORS & tutoring , *MATHEMATICS - Abstract
Shadow education helps students become academically competitive. Currently, little is known about whether shadow education can effectively fulfill either remedial or enrichment purposes in China. Using the nationally representative data from the China Education Panel Survey (CEPS) collected in 2013 and 2014, this paper explored the opportunity gap in shadow education and its impact on Chinese eighth-grade students' mathematics and English reading performance. This study further examined how this effect differs by students' prior performance and school ranks by hierarchical linear modeling (HLM). The results show that affluent socioeconomic resources and parental pressure predicted larger chances of students using shadow education. On average, supplementary tutoring had a positive effect on academic achievement. After re-estimating the effect by groups, this study found that students disadvantaged by prior knowledge and quality of schooling benefited more from supplementary tutoring. The findings suggest that the expansion of shadow education may contribute to social reproduction within the current education system. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
80. On the Structure of Singular Points of a Solution to Newton's Least Resistance Problem.
- Author
-
Plakhov, Alexander
- Subjects
- *
CONVEX domains , *CONVEX geometry , *CONVEX bodies , *CONCAVE functions , *MATHEMATICS - Abstract
We consider the following problem stated in 1993 by Buttazzo and Kawohl (Math Intell 15:7–12, 1993): minimize the functional ∫ ∫ Ω (1 + | ∇ u (x , y) | 2 ) - 1 d x d y in the class of concave functions u : Ω → [0,M], where Ω ⊂ R 2 is a convex domain and M > 0. It generalizes the classical minimization problem, which was initially stated by I. Newton in 1687 in the more restricted class of radial functions. The problem is not solved until now; there is even nothing known about the structure of singular points of a solution. In this paper we, first, solve a family of auxiliary 2D least resistance problems and, second, apply the obtained results to study singular points of a solution to our original problem. More precisely, we derive a necessary condition for a point being a ridge singular point of a solution and prove, in particular, that all ridge singular points with horizontal edge lie on the top level and zero level sets. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
81. Implementation of Efficient Vedic Multiplier and Its Performance Evaluation.
- Author
-
Mugatkar, Ashutosh and Gajre, Suhas S.
- Subjects
- *
INTEGRATED circuits , *COMPUTER architecture , *MULTIPLIERS (Mathematical analysis) , *MULTIPLICATION , *MATHEMATICS - Abstract
The ancient Vedic mathematics is well known for quicker handy multiplications but its recognition as an integrated circuit core against existing hardware multipliers is not established. As optimized hardware implementation of binary multiplier is one of the prominent unsolved problems in computer architecture, this paper proposes efficient Urdhava Tiryakbhyam Vedic multiplier architecture and compares it with the set of hierarchical multiplication algorithms which generate multiplication result in a single clock cycle. Two innovative algorithms are proposed here, one with a compact structure and another for faster execution. Also, its optimized transistor level layout is designed and implemented. To maintain homogeneity for comparison, all the algorithms are programmed on a common HDL language platform and analyzed with the same tool and technology. Final results indicate that the proposed architecture delivers 15.5% less power delay product (PDP) compared to closest competitor algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
82. An Inconvenient Truth about Forecast Combinations.
- Author
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Pincheira-Brown, Pablo, Bentancor, Andrea, and Hardy, Nicolás
- Subjects
- *
INFLATION forecasting , *FORECASTING , *DATA envelopment analysis - Abstract
It is well-known that the weighted averages of two competing forecasts may reduce mean squared prediction errors (MSPE) and may also introduce certain inefficiencies. In this paper, we take an in-depth view of one particular type of inefficiency stemming from simple combination schemes: Mincer and Zarnowitz inefficiency or auto-inefficiency for short. Under mild assumptions, we show that linear convex forecast combinations are almost always auto-inefficient, and, therefore, greater reductions in MSPE are almost always possible. In particular, we show that the process of taking averages of forecasts may induce inefficiencies in the combination, even when individual forecasts are efficient. Furthermore, we show that the so-called "optimal weighted average" traditionally presented in the literature may indeed be inefficient as well. Finally, we illustrate our findings with simulations and an empirical application in the context of the combination of headline inflation forecasts for eight European economies. Overall, our results indicate that in situations in which a number of different forecasts are available, the combination of all of them should not be the last step taken in the search of forecast accuracy. Attempts to take advantage of potential inefficiencies stemming from the combination process should also be considered. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
83. Adjunction greatest element to ordered hypersemigroups.
- Author
-
KEHAYOPULU, Niovi
- Subjects
- *
TURKS , *MATHEMATICS - Abstract
As a continuation of the paper "Adjunction Identity to Hypersemigroup" in Turk J Math 2022; 46 (7): 2834-2853, it has been proved here that the adjunction of a greatest element to an ordered hypersemigroup is actually an embedding problem. The concept of pseudoideal has been introduced and has been proved that for each ordered hypersemigroup S an ordered hypersemigroup V having a greatest element (poe-hypersemigroup) can be constructed in such a way that there exists a pseudoideal T of S such that S is isomorphic to T. If S does not have a greatest element, then this can be regarded as the embedding of an ordered hypersemigroup in an ordered semigroup with greatest element. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
84. ENERGY OF STRONG RECIPROCAL GRAPHS.
- Author
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GHAHREMANI, MARYAM, TEHRANIAN, ABOLFAZL, RASOULI, HAMID, and HOSSEINZADEH, MOHAMMAD ALI
- Subjects
- *
CHARTS, diagrams, etc. , *ABSOLUTE value , *COMPLETE graphs , *EIGENVALUES , *MATHEMATICS - Abstract
The energy of a graph G, denoted by E(G), is defined as the sum of absolute values of all eigenvalues of G. A graph G is called reciprocal if 1/≥ is an eigenvalue of G whenever λ is an eigenvalue of G. Further, if λ and 1 λ have the same multiplicities, for each eigenvalue λ, then it is called strong reciprocal. In (MATCH Commun. Math. Comput. Chem. 83 (2020) 631{633), it was conjectured that for every graph G with maximum degree Δ(G) and minimum degree ∞(G) whose adjacency matrix is non-singular, E(G) λ Δ(G) + ∞(G) and the equality holds if and only if G is a complete graph. Here, we prove the validity of this conjecture for some strong reciprocal graphs. Moreover, we show that if G is a strong reciprocal graph, then E(G) λ Δ(G) + ∞(G) - 1 2. Recently, it has been proved that if G is a reciprocal graph of order n and its spectral radius, ?, is at least 4λmin, where λmin is the smallest absolute value of eigenvalues of G, then E(G) λ n + 1 2. In this paper, we extend this result to almost all strong reciprocal graphs without the mentioned assumption. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
85. APPROXIMATION BY A SPECIAL DE LA VALLÉE POUSSIN TYPE MATRIX TRANSFORM MEAN OF WALSH-FOURIER SERIES.
- Author
-
BLAHOTA, ISTVÁN
- Subjects
- *
FOURIER analysis , *MATHEMATICS , *POUSSINISTS , *MODULUS of rigidity , *ARITHMETIC - Abstract
In this paper, we consider norm convergence for a special matrix-based de la Vallée Poussin-like mean of Fourier series for the Walsh system. We estimate the difference between the named mean above and the corresponding function in norm, and the upper estimation is given by the modulus of continuity of the function. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
86. CONVERGENCE, OPTIMAL POINTS AND APPLICATIONS.
- Author
-
SHARMA, SHAGUN and CHANDOK, SUMIT
- Subjects
- *
STOCHASTIC convergence , *LINEAR operators , *MATHEMATICS , *FIXED point theory , *NONLINEAR operators - Abstract
In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
87. ON A SOLVABLE SYSTEM OF DIFFERENCE EQUATIONS OF SIXTH-ORDER.
- Author
-
KARAKAYA, DILEK, YAZLIK, YASIN, and KARA, MERVE
- Subjects
- *
VARIATIONAL inequalities (Mathematics) , *MATHEMATICS , *DIFFERENTIAL equations , *REAL numbers , *ARITHMETIC - Abstract
In this paper, we study the following two-dimesional system of difference equations ... where the parameters a;b; c;d and the initial values x i; y i, i 2 f1;2;3;4;5;6g, are real numbers. We show that some subclasses of nonlinear two-dimensional system of difference equations are solvable in closed form. We also describe the forbidden set of solutions of the system of differ- ence equations. Some numerical examples are given to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
88. MITTAG-LEFFLER FUNCTION FOR REAL INDEX AND ITS APPLICATION IN SOLVING DIFFERENCE AND DIFFERENTIAL EQUATIONS.
- Author
-
SIMON, JARALDPUSHPARAJ, XAVIER, GNANAPRAKASAM BRITTO ANTONY, ETEMAD, SINA, and REZAPOUR, SHAHRAM
- Subjects
- *
FRACTIONAL differential equations , *BINOMIAL theorem , *POLYNOMIALS , *ALGEBRA , *MATHEMATICS - Abstract
In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into l-difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
89. NEW APPROACHES FOR m-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRAL OPERATORS WITH STRONG KERNELS.
- Author
-
ARDIÇ, MERVE AVCI, ÖNALAN, HAVVA KAVURMACI, AKDEMIR, AHMET OCAK, and NGUYEN, ANH TUAN
- Subjects
- *
CONVEX functions , *REAL variables , *MATHEMATICS , *INTEGRAL operators , *OPERATOR theory - Abstract
We have established this paper on m convex functions, which can be expressed as a general form of the convex function concept. First of all, some inequalities of Hadamard type are proved with fairly simple conditions. Next, an integral identity containing Atangana-Baleanu fractional integral operators is obtained to prove new inequalities for differentiable m-convex functions. Using this identity, various properties of m convex functions and classical inequalities, some new integral inequalities have been proved. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
90. A FIXED POINT THEOREM FOR GENERALIZED NONEXPANSIVE MAPPINGS.
- Author
-
AMINI-HARANDI, ALIREZA, GOLI, MAHDI, and HAJISHARIFI, HAMID REZA
- Subjects
- *
FIXED point theory , *METRIC spaces , *MATHEMATICS - Abstract
In this paper, we obtain a generalization of a fixed point theorem given by Popescu [O. Popescu, Comput. Math. Appl., vol. 62, no. 10, pp. 3912-3919, 2011]. An example is also given to support our main result. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
91. NEW OSCILLATION CRITERIA FOR SECOND-ORDER DELAY DYNAMIC EQUATIONS WITH A SUB-LINEAR NEGATIVE NEUTRAL TERM ON TIME SCALES.
- Author
-
HASSAN, AHMED MOHAMED and AFFAN, SAMY
- Subjects
- *
INTEGERS , *MATHEMATICS , *CONTRACTION operators , *CONVEX functions , *REAL variables - Abstract
In this paper, some sufficient conditions for the oscillation of all solutions of second order dynamic equations with a negative sub-linear neutral term are established. The obtained results provide a unified platform that adequately covers both discrete and continuous equations. Furthermore, it covers a wide range of equations by utilizing different time scales. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
92. NEW GENERALIZATIONS OF SOME IMPORTANT INEQUALITIES FOR SARıKAYA FRACTIONAL INTEGRALS.
- Author
-
HEZENCI, FATIH and BUDAK, HUSEYIN
- Subjects
- *
INTEGERS , *MATHEMATICS , *CONTRACTION operators , *CONVEX functions , *REAL variables - Abstract
In this research paper, we investigate some new identifies for Sarıkaya fractional integrals which introduced by Sarıkaya and Ertugral in [20]. The fractional integral operators also have been applied to Hermite-Hadamard type integral inequalities to provide their generalized properties. Furthermore, as special cases of our main results, we present several known inequalities such as Simpson, Bullen, trapezoid for convex functions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
93. CONSTRUCTION OF A NEW CLASS OF FUNCTIONS WITH THEIR SOME PROPERTIES AND CERTAIN INEQUALITIES: n-FRACTIONAL POLYNOMIAL CONVEX FUNCTIONS.
- Author
-
İŞCAN, İMDAT
- Subjects
- *
POLYNOMIALS , *HADAMARD matrices , *INTEGERS , *MATHEMATICS , *VARIATIONAL inequalities (Mathematics) - Abstract
In this paper, we introduce a new function class called n-fractional polynomial convex function and their some algebric properties. We obtain some refinements of the right-hand side of Hermite-Hadamard inequality for the class of functions whose derivatives in absolutely value at certain powers are n-fractional polynomial convex. Also, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with Hölder-İşcan and improved power-mean inequalities give better approach than the others. Some applications to special means of real numbers are also given. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
94. NEW CURVATURE TENSORS ALONG RIEMANNIAN SUBMERSIONS.
- Author
-
AYAR, GÜLHAN and AKYOL, MEHMET AKIF
- Subjects
- *
RIEMANNIAN geometry , *GENERALIZED spaces , *TENSOR algebra , *ALGEBRA , *MATHEMATICS - Abstract
In 1966, B. O'Neill [The fundamental equations of a submersion, Michigan Math. J., Volume 13, Issue 4 (1966), 459-469.] defined some fundamental equations and curvature rela- tions between the total space, the base space and the fibres on a submersion. In the present paper, we define new curvature tensors on Riemannian submersions such as Weyl projective curvature tensor, concircular curvature tensor, conharmonic curvature tensor, conformal curvature tensor and M projective curvature tensor, respectively. Finally, we obtain some results in case of the total space of Riemannian submersions has umbilical fibres for any curvature tensors mentioned by the above. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
95. ADDITIVE MAPPINGS SATISFYING CERTAIN ALGEBRAIC EQUATIONS IN PRIME RINGS.
- Author
-
MIR, HAJAR EL, MAMOUNI, ABDELLAH, and OUKHTITE, LAHCEN
- Subjects
- *
LAPLACIAN operator , *FRACTIONAL differential equations , *DIFFERENTIAL equations , *MATHEMATICS , *FIXED point theory - Abstract
In this paper we give a classification of endomorphisms and additive mappings of a prime ring satisfying certain algebraic identities. Moreover, we provide an example proving that the primeness hypothesis imposed in our theorems is not superfluous. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
96. AN EXISTENCE ETUDY FOR A TRIPLED SYSTEM WITH p-LAPLACIAN INVOLVING γ-CAPUTO DERIVATIVES.
- Author
-
BEDDANI, HAMID, BEDDANI, MOUSTAFA, and DAHMANI, ZOUBIR
- Subjects
- *
LAPLACIAN operator , *FRACTIONAL differential equations , *DIFFERENTIAL equations , *MATHEMATICS , *FIXED point theory - Abstract
In this paper, we study the existence and uniqueness of solutions for a tripled system of fractional differential equations with nonlocal integro multi point boundary conditions by using the p-Laplacian operator and the γ-Caputo derivatives. The presented results are obtained by the two fixed point theorems of Banach and Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
97. PSEUDO CORE INVERTIBILITY AND DMP INVERTIBILITY IN TWO SEMIGROUPS OF A RING WITH INVOLUTION.
- Author
-
WENDE LI, JIANLONG CHEN, YUKUN ZHOU, and YUANYUAN KE
- Subjects
- *
PSEUDOCODE (Computer program language) , *MATHEMATICS , *FINITE element method , *SEMIGROUPS (Algebra) , *GROUP theory - Abstract
In 2004, Patrício and Puystjens characterized the relation between Drazin invertible elements (resp., Moore-Penrose invertible elements) of two semigroups pRp and pRp+1 p of a ring R for some idempotent (resp., projection) p ∈ R. In this paper, we consider the relevant result for pseudo core invertible elements of such two semigroups of a ring for some projection, which is then applied to characterize the relation between pseudo core invertible elements of the matrix semigroup AA†RmxmAA†+Im AA† and the matrix semigroup A†ARnxnA†A+In A†A, where A ∈ Rmxn with A† existing. Also, similar equivalence involving DMP invertible elements is investigated. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
98. TAUBERIAN THEOREMS FOR NÖRLUND-CESÁRO MEAN VIA STATISTICALLY CONVERGENCE IN m-NORMED SPACES.
- Author
-
BRAHA, NAIM, LOKU, VALDETE, and MOHAPATRA, RAM
- Subjects
- *
TAUBERIAN theorems , *INFINITE series (Mathematics) , *MATHEMATICS , *GROUP theory , *SEMIGROUPS (Algebra) - Abstract
In this paper, we have proved certain kinds of Tauberian theorems for Nörlund-Cesáro summability methods in m-normed space X in statistically sense. We give necessary and sufficient Tauberian condition for this method of summability, in statistically sense. Also, we prove that Tauberian theorems under these summability methods are valid under oscillating slow condition of Schmidt-type and Hardy-type conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
99. Alternative proofs of some classical metric fixed point theorems by using approximate fixed point sequences.
- Author
-
Berinde, Vasile and P̆acurar, M̆ad̆alina
- Subjects
- *
NONEXPANSIVE mappings , *BANACH spaces , *MATHEMATICS - Abstract
The notion of approximate fixed point sequence, emphasized in Chidume (Geometric properties of Banach spaces and nonlinear iterations. Lecture Notes in Mathematics, 1965. Springer-Verlag London, Ltd., London, 2009), is a very useful tool in proving convergence theorems for fixed point iterative schemes in the class of nonexpansive-type mappings. In the present paper, our aim is to present simple and unified alternative proofs of some classical fixed point theorems emerging from Banach contraction principle, by using a technique based on the concepts of approximate fixed point sequence and graphic contraction. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
100. Symmetric Difference Operators Derived from Overlap and Grouping Functions.
- Author
-
Hu, Bo, He, Di, and Dai, Songsong
- Subjects
- *
SYMMETRIC operators , *POSITIVE operators , *DIFFERENCE operators , *TRIANGULAR norms , *MATHEMATICS - Abstract
This paper introduces the concept of symmetric difference operators in terms of overlap and grouping functions, for which the associativity property is not strongly required. These symmetric difference operators are weaker than symmetric difference operators in terms of positive and continuous t-norms and t-conorms. Therefore, in the sense of the characters of mathematics, these operators do not necessarily satisfy certain properties, such as associativity and the neutrality principle. We analyze several related important properties based on two models of symmetric differences. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
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