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2. Appendix to the paper 'On the Billingsley dimension of Birkhoff average in the countable symbolic space'
- Author
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Selmi, Bilel
- Subjects
Mathematics ,QA1-939 - Abstract
This appendix gives a lower bound of the Billingsley-Hausdorff dimension of a level set related to Birkhoff average in the “non-compact” symbolic space $\mathbb{N}^{\mathbb{N}}$, defined by Gibbs measure.
- Published
- 2020
- Full Text
- View/download PDF
3. The unsung de Finetti’s first paper about exchangeability
- Author
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Eugenio Regazzini and Federico Bassetti
- Subjects
characteristic function of a random phenomenon ,de finetti’s contributions to probability ,exchangeable events ,extendibility of exchangeable sequences ,Mathematics ,QA1-939 - Abstract
It is a singular fact that the first and pithy de Finetti’s essay on exchangeability has not earned the same reputation as that of others of his papers about the same subject. In fact, this paper contains, on the one hand, all the main results on sequences of exchangeable events, together with the right subjectivistic interpretation of the role they play in the study of the connections between probability and frequencies. On the other hand, the paper makes use of mathematical methods abandoned, immediately after its publication, by de Finetti himself. The center of this methods is the so–called characteristic function of a random phenomenon. Independently of the destiny of the paper, we think that, apart from its undoubted historical value, it contains ideas susceptible of interesting new developments. Therefore, we have deemed it suitable to give here a detailed and faithful account of its content, for the benefit of the colleagues who are not in a position to understand Italian. Moreover, to emphasize the value of the paper at issue, we develop de Finetti’s brief hint to the extendibility of exchangeable sequences of events, to obtain a new explicit necessary and sufficient condition of an algebraic nature.
- Published
- 2008
4. Exploring the structure and properties of ideal-based zero-divisor graphs in involution near rings
- Author
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Masreshaw Walle Abate and Wang Yao
- Subjects
near ring ,zero-divisor-graph ,ideal based zero-divisor graph ,ideal of *-near-ring ,graph coloring ,chromatic number ,Mathematics ,QA1-939 - Abstract
For an involution near ring 𝒩 and its ideal ℐ, the text introduces an involution ideal-based zero- divisor graph Γℐ*(𝒩) which is an undirected graph with vertex set { x ∈ 𝒩 - ℐ: x𝒩y ⊂ ℐ (or y𝒩x ⊂ ℑ ) for some y ∈ 𝒩-ℐ}, where two distinct vertices x and y are adjacent if and only if y𝒩x* ⊂ ℐ or x𝒩y* ⊂ ℐ. The paper provides characterizations of Γℐ*(𝒩) when it forms a complete graph or a star graph. It also explores the structure of Γℐ*(𝒩), investigates its properties like connectedness with diam(Γℐ*(𝒩)) ≤ 3 and analyzes the connection of Γℐ*(𝒩) with Γℐ*(𝒩/ℐ). Furthermore, the paper discusses the chromatic number and clique number of the graph. It also characterizes all right permutable *-near-rings 𝒩 for which the graph Γℐ*(𝒩) can be with a finite chromatic number.
- Published
- 2024
5. Estimate on logarithmic coefficients of Kamali-type starlike functions associated with four-leaf shaped domain
- Author
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T. Panigrahi, E. Pattnayak, and R. M. El-Ashwah
- Subjects
analytic function ,starlike function ,subordination ,fekete-szegö functional ,four-leaf shaped domain ,Mathematics ,QA1-939 - Abstract
n the present paper, the authors introduce a new subclass namely; RL(φ4L, ν) of Kamali-type starlike functions defined in the open unit disk D connected with four-leaf shaped domain. We investigate the bounds of some initial coefficients, Fekete-Szegö inequality and other results of logarithmic coefficients for the function belonging to above class. Relevant connections of the results derived in this paper with those of earlier works are indicated.
- Published
- 2024
6. Strong convergence theorems by Martinez-Yanes–Xu projection method for mean-demiclosed mappings in Hilbert spaces
- Author
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Atsumasa Kondo
- Subjects
martinez-yanes and xu projection method ,ishikawa iteration ,mean-valued iteration ,mean-demiclosed mapping ,common fixed point ,Mathematics ,QA1-939 - Abstract
Strong convergence theorems that approximate common fixed points of two nonlinear mappings are presented. Our method is based on the Martinez-Yanes–Xu iteration, which extends Nakajo and Takahashi’s CQ method. In this paper, by exploiting the mean-valued iteration procedure, we further develop Nakajo and Takahashi’s CQ method and Takahashi, Takeuchi, and Kubota’s shrinking projection method. The approach of this paper does not require that the two mappings be continuous or commutative. The types of mappings considered in this paper include nonexpansive mappings and other well-known classes of mappings as special cases.
- Published
- 2023
7. On a certain characterisation of the semigroup of positive natural numbers with multiplication
- Author
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Edward Tutaj
- Subjects
beurling numbers ,distribution of prime numbers ,cauchy translation equation ,numerical semigroups ,ap´ery sets ,Mathematics ,QA1-939 - Abstract
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.
- Published
- 2022
8. On the non-very generic intersections in discriminantal arrangements
- Author
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Settepanella, Simona and Yamagata, So
- Subjects
Mathematics ,QA1-939 - Abstract
In 1985 Crapo introduced in [3] a new mathematical object that he called geometry of circuits. Four years later, in 1989, Manin and Schechtman defined in [13] the same object and called it discriminantal arrangement, the name by which it is known now a days. Those discriminantal arrangements $\mathcal{B}(n,k,\mathcal{A}^0)$ are builded from an arrangement $\mathcal{A}^0$ of $n$ hyperplanes in general position in a $k$-dimensional space and their combinatorics depends on the arrangement $\mathcal{A}^0$. On this basis, in 1997 Bayer and Brandt (see [2]) distinguished two different type of arrangements $\mathcal{A}^0$ calling very generic the ones for which the intersection lattice of $\mathcal{B}(n,k,\mathcal{A}^0)$ has maximum cardinality and non-very generic the others. Results on the combinatorics of $\mathcal{B}(n,k,\mathcal{A}^0)$ in the very generic case already appear in Crapo [3] and in 1997 in Athanasiadis [1] while the first known result on non-very generic case is due to Libgober and the first author in 2018. In their paper [12] they provided a necessary and sufficient condition on $\mathcal{A}^0$ for which the cardinality of rank 2 intersections in $\mathcal{B}(n,k,\mathcal{A}^0)$ is not maximal anymore. In this paper we further develop their result providing a sufficient condition on $\mathcal{A}^0$ for which the cardinality of rank r, $r \ge 2$, intersections in $\mathcal{B}(n,k,\mathcal{A}^0)$ decreases.
- Published
- 2022
- Full Text
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9. A simpler method to get only the true solutions of cubic and quartic equations using Tschirnhaus transformation
- Author
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Raghavendra G. Kulkarni
- Subjects
tschirnhaus transformation ,true solutions ,cubic equations ,quartic equations ,false solutions ,Mathematics ,QA1-939 - Abstract
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.
- Published
- 2022
10. The Sălăgean-type probability distribution
- Author
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Saurabh Porwal and Nanjundan Magesh
- Subjects
probability distribution ,starlike and convex functions ,sălăgean differential operator ,Mathematics ,QA1-939 - Abstract
The purpose of the present paper is to investigate the Sălăgean - type probability distribution of order α. In this paper, we obtain moments, factorial moments and moment generating function for this distribution. Finally, we obtain a entropy of this distribution. Our results improve and generalize the results of Porwal [Starlike and convex type probability distribution, Afr. Mat. 30 (2019)].
- Published
- 2022
11. The necessity of conditions for graph quantum ergodicity and Cartesian products with an infinite graph
- Author
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McKenzie, Theo
- Subjects
Mathematics ,QA1-939 - Abstract
Anantharaman and Le Masson proved that any family of eigenbases of the adjacency operators of a family of graphs is quantum ergodic (a form of delocalization) assuming the graphs satisfy conditions of expansion and high girth. In this paper, we show that neither of these two conditions is sufficient by itself to necessitate quantum ergodicity. We also show that having conditions of expansion and a specific relaxation of the high girth constraint present in later papers on quantum ergodicity is not sufficient. We do so by proving new properties of the Cartesian product of two graphs where one is infinite.
- Published
- 2022
- Full Text
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12. Some Regularity Properties on Bolza problems in the Calculus of Variations
- Author
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Bernis, Julien, Bettiol, Piernicola, and Mariconda, Carlo
- Subjects
Mathematics ,QA1-939 - Abstract
The paper summarizes the main core of the last results that we obtained in [8, 4, 17] on the regularity of the value function for a Bolza problem of a one-dimensional, vectorial problem of the calculus of variations. We are concerned with a nonautonomous Lagrangian that is possibly highly discontinuous in the state and velocity variables, nonconvex in the velocity variable and non coercive. The main results are achieved under the assumption that the Lagrangian is convex on the one-dimensional lines of the velocity variable and satisfies a local Lipschitz continuity condition w.r.t. the time variable, known in the literature as Property (S), and strictly related to the validity of the Erdmann–Du-Bois Reymond equation.Under our assumptions, there exists a minimizing sequence of Lipschitz functions. A first consequence is that we can exclude the presence of the Lavrentiev phenomenon. Moreover, under a further mild growth assumption satisfied by the minimal length functional, fully described in the paper, the above sequence may be taken with the same Lipschitz rank, even when the initial datum and initial value vary on a compact set. The Lipschitz regularity of the value function follows.
- Published
- 2022
- Full Text
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13. Early Childhood Special Science Education: Setting the frame of a newly born and well-promising trend
- Author
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GEORGE KALIAMPOS
- Subjects
science education ,special education ,early childhood education ,Education ,Mathematics ,QA1-939 - Abstract
The last three decades two distinct trends have emerged within Early Childhood Education, namely Early Childhood Science Education and Early Childhood Special Education. The current paper tries to move along these areas and illuminate the common ground that lie between them. In particular, drawing from the formulated empiricist, Piagetian and socio-cognitive trends within Early Childhood Science Education, it tries to explore to what extend they could expand in special needs context. In addition, it proposes diverse, specific strategies that emerge from the above-mentioned trends and could be implemented in teaching science within special needs settings. By so doing, the present paper aspires to set the frame of a newly born and well-promising trend, that of Early Childhood Special Science Education.
- Published
- 2021
- Full Text
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14. Positive definiteness: from scalar to operator-valued kernels
- Author
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V. A. Menegatto
- Subjects
positive definiteness ,strict positive definiteness ,scalar kernels ,matrix-valued kernels ,operator-valued kernels ,Mathematics ,QA1-939 - Abstract
In this paper we present a short overview of results that provide relationships among scalar, matrix-valued and certain operator-valued positive definite kernels. We refine and extend some of them in order that they may be applied for strict positive definiteness as well. This is a topic not well explored in the literature but that has potential usefulness in the characterization of several classes of positive definite and strictly positive definite kernels. This is ratified in the paper with the inclusion of a number of applications and examples.
- Published
- 2021
15. A note on the bicategory of Landau-Ginzburg models (ℒ𝒢K)
- Author
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Yves Baudelaire Fomatati
- Subjects
bicategory of landau-ginzburg models ,matrix factorizations ,tensor product ,polynomials ,Mathematics ,QA1-939 - Abstract
The bicategory of Landau-Ginzburg models denoted by ℒ𝒢K possesses adjoints and this helps in explaining a certain duality that exists in the setting of Landau-Ginzburg models in terms of some specified relations. The construction of ℒ𝒢K is reminiscent of, but more complex than, the construction of the bicategory of associative algebras and bimodules. In this paper, we review this complex but very inspiring construction in order to expose it more to pure mathematicians. In particular, we spend some time explaining the intricate construction of unit morphisms in this bicategory from a new vantage point. Besides, we briefly discuss how this bicategory could be constructed in more than one way using the variants of the Yoshino tensor product. Furthermore, without resorting to Atiyah classes, we prove that the left and right unitors in this bicategory have direct right inverses but do not have direct left inverses.
- Published
- 2024
16. Mihailo Petrović Alas’ contribution to development of interest for mathematics
- Author
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Mirko R. Dejić
- Subjects
mihailo petrović alas ,pythagorean theorem ,pedagogical work ,mathematics ,popularization of mathematics. ,Education - Abstract
Apart from his great creative work in mathematical science, Mihailo Petrović Alas, one of the greatest Serbian mathematicians, managed to write several works of methodological character which were intended for teachers at elementary and secondary schools. In these works Mihailo Petrović’s aim was to popularize mathematics and show how teachers can also be creative and inventors within the domain of teaching. We give an overview of these works in our paper and acquaint the readers in detail with his interesting application of the Pythagorean theorem. A short retrospect of the complete scientific and pedagogical opus of Mihailo Petrović Alas will also be given in the paper.
- Published
- 2020
- Full Text
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17. Some stability results for coupled fixed point iterative process in a complete metric space
- Author
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M. O. Olatinwo and K. R. Tijani
- Subjects
coupled fixed point iterations ,continuous dependence of coupled fixed points ,complete metric spaces ,Mathematics ,QA1-939 - Abstract
In the paper [M. O. Olatinwo, Stability of coupled fixed point iterations and the continuous dependence of coupled fixed points, Communications on Applied Nonlinear Analysis 19 (2012), 71-83], the author has extended the notion of stability of fixed point iterative procedures contained in the paper [A. M. Harder and T. L. Hicks, Stability results for fixed point iteration procedures, Math. Japonica 33 (1988), 693-706], as well as the continuous dependence of fixed points to the coupled fixed point settings by employing the contractive conditions and the coupled fixed point iteration in the article [F. Sabetghadam, H. P. Masiha and A. H. Sanatpour, Some coupled fixed point theorems in cone metric spaces, Fixed Point Theory and Applications, Article ID 125426 (2009)]. In the present paper, we obtain some results on stability of coupled fixed point iterative procedures by using rational type contractive conditions.
- Published
- 2019
18. Aspects regarding the existence of fixed points of the iterates of Stancu operators
- Author
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Amelia Bucur
- Subjects
iterate operators ,fixed point ,stancu operators ,Mathematics ,QA1-939 - Abstract
In the papers Iterates of Stancu Operators, via Contraction Principle (2002), respectively Iterates of Bernstein Operators, via Contraction Principle (2004), author I. A. Rus studied the existence of fixed points for Stancu operators Pn,α,β and Bernstein operators Bn. The aim of this paper is to find conditions for which the Stancu operators Pn,α,β are contractions on the graph, in order to demonstrate that the contraction principle can be applied for the study of the existence of fixed points for iterates of Stancu operators. The method used for this paper is the spectral method, which was also used in the paper Over-iterates of Bernstein-Stancu operators (2007), authors Gonska, Piţul and Raşa. The study began with finding constant C∈[0,1[ that would satisfy the inequality ||Pn,α,β2 (f)-Pn,α,β (f)|| ≤ C ||Pn,α,β (f)-f||, for any f∈ C[0,1]. The conclusion is that there are conditions for which the Stancu operators are contractions on the graph, and the methods used for the study of the existence of fixed points of their iterates can also be extended to the study of the existence of fixed points of other linear operators.
- Published
- 2019
19. Rethinking the Geometry of the Demand and Supply Functions
- Author
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Saidou Baba Oumar
- Subjects
consumer ,economics ,elasticity ,mathematics ,price ,producer ,quantity ,surplus ,Business ,HF5001-6182 ,Economic theory. Demography ,HB1-3840 - Abstract
This paper attempts to revisit the geometry of the demand and supply functions in economic analysis, taking mathematical exigencies into account. Leaning on the fundamental principles that guide the theory of demand and supply, the paper uses the analytical approach of data analysis to address the objectives of the investigation. Results of the study indicate that whether expressed in the standard mathematical form (Quantity-price relation) or casual mathematical form (Price-quantity relation), the demand and supply functions obey the laws of demand and supply. Also, the results reveal that the first component in the computation of the price-elasticity remains unchanged and takes into account the quantity-price relationship, irrespective of the functional form (Quantity-price function or price-quantity function) used in defining the demand and supply functions. Furthermore, the results show that the consumer and producer surpluses can still be evaluated without violating mathematical requirements with the quantity-price relation model of describing the demand and supply functions to accommodate welfare issues associated with the demand and supply concepts. As a result, it is suggested that mathematical requirements of logic, rigor, consistency, and objectivity be strictly respected when subjecting the analysis of real world economic phenomena to mathematical treatments.
- Published
- 2019
20. Cauchy type functional equations related to some associative rational functions
- Author
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Katarzyna Domańska
- Subjects
functional equation ,rational function ,associativity ,Mathematics ,QA1-939 - Abstract
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.
- Published
- 2019
21. Overview of the Computer Programming Learning Environments for primary education
- Author
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GEORGIOS FESSAKIS, VASSILIS KOMIS, ANGELIQUE DIMITRACOPOULOU, and STAVROULA PRANTSOUDI
- Subjects
educational programming languages ,taxonomy ,learning design ,computational thinking ,coding for learning ,Education ,Mathematics ,QA1-939 - Abstract
Over the past decade, the assessment of the general educational value of computer programming and computational thinking has been constantly increasing and, as a result, they are introduced to increasingly younger ages. In parallel, educational programming environments are significantly progressing, providing a variety of options for different ages. This paper presents an overview of the modern learning programming environments for primary education and proposes a classification system with categories corresponding to the technological and educational dimensions of the area. The paper aims to support teachers in learning design for the interdisciplinary approach of programming and the development of computational thinking.
- Published
- 2019
- Full Text
- View/download PDF
22. New dynamic fixed point results in Menger spaces
- Author
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Besma Laouadi, Taki Eddine Oussaeif, Leila Benaoua, Liliana Guran, and Ioana Camelia Tişe
- Subjects
fixed point ,menger space ,picard sequence ,complete metric space ,Mathematics ,QA1-939 - Abstract
The objective of this paper is to generalize and improve some results in fixed point theorems in both complete metric space and Menger space. These results are generalizations of the analogous ones recently proved by Khojasteh [5], Demma [1], Yildirim [13], where we establish a dynamic information about their other fixed points if there exist i.e the distance between two fixed point in case of metric space and their equivalent in probabilistic metric space. Some illustrative examples are furnished, which demonstrate the validity of the hypotheses. As an application to our main result, we derive a uniqueness fixed point theorem for a self-mapping under strong conditions.
- Published
- 2023
23. Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$
- Author
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Saasi, Faouaz and Daher, Radouan
- Subjects
Fourier–Dunkl series ,Dunkl transform ,generalized translation operator ,$K$-functionals ,modulus of smoothness ,Mathematics ,QA1-939 - Abstract
Our aim in this paper is to show that the modulus of smoothness and the $K$-functionals constructed from the Sobolev-type space corresponding to the Dunkl operator are equivalent on the interval $(-1,1)$.
- Published
- 2023
- Full Text
- View/download PDF
24. Remarks on complexities and entropies for singularity categories
- Author
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Takahashi, Ryo
- Subjects
Mathematics ,QA1-939 - Abstract
Let $R$ be a commutative noetherian local ring which is singular and has an isolated singularity. Let $\mathsf {D_{sg}}(R)$ be the singularity category of $R$ in the sense of Buchweitz and Orlov. In this paper, we find real numbers $t$ such that the complexity $\delta _t(G,X)$ in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich vanishes for any split generator $G$ of $\mathsf {D_{sg}}(R)$ and any object $X$ of $\mathsf {D_{sg}}(R)$. In particular, the entropy $\mathrm{h}_t(F)$ of an exact endofunctor $F$ of $\mathsf {D_{sg}}(R)$ is not defined for such numbers $t$.
- Published
- 2023
- Full Text
- View/download PDF
25. On the coalitional decomposition of parameters of interest
- Author
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Il Idrissi, Marouane, Bousquet, Nicolas, Gamboa, Fabrice, Iooss, Bertrand, and Loubes, Jean-Michel
- Subjects
Mathematics ,QA1-939 - Abstract
Understanding the behavior of a black-box model with probabilistic inputs can be based on the decomposition of a parameter of interest (e.g., its variance) into contributions attributed to each coalition of inputs (i.e., subsets of inputs). In this paper, we produce conditions for obtaining unambiguous and interpretable decompositions of very general parameters of interest. This allows recovering known decompositions, holding under weaker assumptions than the literature states.
- Published
- 2023
- Full Text
- View/download PDF
26. Homological dimension based on a class of Gorenstein flat modules
- Author
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Dalezios, Georgios and Emmanouil, Ioannis
- Subjects
Mathematics ,QA1-939 - Abstract
In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek in [26]. The resulting PGF-dimension of modules has several properties in common with the Gorenstein projective dimension, the relative homological theory based on the class of Gorenstein projective modules. In particular, there is a hereditary Hovey triple in the category of modules of finite PGF-dimension, whose associated homotopy category is triangulated equivalent to the stable category of PGF-modules. Studying the finiteness of the PGF global dimension reveals a connection between classical homological invariants of left and right modules over the ring, that leads to generalizations of certain results by Jensen [24], Gedrich and Gruenberg [17] that were originally proved in the realm of commutative Noetherian rings.
- Published
- 2023
- Full Text
- View/download PDF
27. An entropic generalization of Caffarelli’s contraction theorem via covariance inequalities
- Author
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Chewi, Sinho and Pooladian, Aram-Alexandre
- Subjects
Mathematics ,QA1-939 - Abstract
The optimal transport map between the standard Gaussian measure and an $\alpha $-strongly log-concave probability measure is $\alpha ^{-1/2}$-Lipschitz, as first observed in a celebrated theorem of Caffarelli. In this paper, we apply two classical covariance inequalities (the Brascamp–Lieb and Cramér–Rao inequalities) to prove a sharp bound on the Lipschitz constant of the map that arises from entropically regularized optimal transport. In the limit as the regularization tends to zero, we obtain an elegant and short proof of Caffarelli’s original result. We also extend Caffarelli’s theorem to the setting in which the Hessians of the log-densities of the measures are bounded by arbitrary positive definite commuting matrices.
- Published
- 2023
- Full Text
- View/download PDF
28. A stability estimate for data assimilation subject to the heat equation with initial datum
- Author
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Burman, Erik, Delay, Guillaume, Ern, Alexandre, and Oksanen, Lauri
- Subjects
Mathematics ,QA1-939 - Abstract
This paper studies the unique continuation problem for the heat equation. We prove a so-called conditional stability estimate for the solution. We are interested in local estimates that are Hölder stable with the weakest possible norms of data on the right-hand side. Such an estimate is useful for the convergence analysis of computational methods dealing with data assimilation. We focus on the case of a known solution at initial time and in some subdomain but that is unknown on the boundary. To the best of our knowledge, this situation has not yet been studied in the literature.
- Published
- 2023
- Full Text
- View/download PDF
29. Congruences modulo $4$ for the number of $3$-regular partitions
- Author
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Ballantine, Cristina and Merca, Mircea
- Subjects
partitions ,regular partitions ,congruences ,Mathematics ,QA1-939 - Abstract
The last decade has seen an abundance of congruences for $b_\ell (n)$, the number of $\ell $-regular partitions of $n$. Notably absent are congruences modulo $4$ for $b_3(n)$. In this paper, we introduce Ramanujan type congruences modulo $4$ for $b_3(2n)$ involving some primes $p$ congruent to $ 11, 13, 17, 19, 23$ modulo $24$.
- Published
- 2023
- Full Text
- View/download PDF
30. Geometric distribution series connected with certain subclasses of univalent functions
- Author
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M. Taliyan, Sh. Najafzadeh, and M. R. Azimi
- Subjects
analytic functions ,convolution product ,subordinate ,geometric distribution series ,Mathematics ,QA1-939 - Abstract
In this paper, we consider the class of normalized analytic functions of the form f(z)=z+∑n=2∞ anzn. Following this functions, we define the functions whose coefficients are probabilities of the geometric distribution series and other special modes of this series. Also, we consider different special classes of f(z). In the following we consider some lemmas that make connection between defined special classes with the function f(z). Follower of this topic we will consider the theorems that make connection between defined classes with the functions whose coefficients are probabilities of geometric distribution series. Also we define Alexander-type integral operator and find the necessary and sufficient conditions for being this operator to defined general classes.
- Published
- 2023
31. Five lectures on cluster theory
- Author
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Ray Maresca
- Subjects
clusters ,tilting modules ,2-term silting complex ,quiver grassmannian ,Mathematics ,QA1-939 - Abstract
In this paper, we will present the author's interpretation and embellishment of five lectures on cluster theory given by Kiyoshi Igusa during the Spring semester of 2022 at Brandeis University. They are meant to be used as an introduction to cluster theory from a representation-theoretic point of view.
- Published
- 2023
32. Моtivation for Learning Science and Mathematics: Timss Research in Serbia
- Author
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Nataša Z. Lalić-Vučetić and Snežana I. Mirkov
- Subjects
timss research ,learning motivation ,self-concept ,mathematics ,sciences ,Education - Abstract
Student motivation is one of the affective components that plays a key role in learning science. Research shows that in developed countries there is a trend of declining students’ interest in science and technology. In this paper, the relationships between intrinsic motivation, self-concept, and the achievement of the fourth-grade elementary school students in mathematics and sciences were investigated. The authors also present the results of the secondary data analyses obtained in Serbia by means of student questionnaires and knowledge tests in the last two cycles of the TIMSS research in 2015 and 2019. The questionnaire contains two scales in which motivational variables are operationalized: students’ attitudes towards mathematics/sciences and mathematical/ scientific self-confidence. Students’ attitude is an indicator of an intrinsic motivation, and self-confidence is an indicator of self-concept. The results show that students express a high motivation for learning mathematics and sciences and a high level of self-concept. A higher level of self-concept is accompanied by a higher level of motivation for learning mathematics and sciences. Individual characteristics of students have a greater influence on achievement than the influence of schools and teachers. Students who express a more positive attitude towards mathematics and science and a higher level of self-concept in these areas also have a higher level of achievement. The influence of mathematical self-concept on achievement is particularly significant. The obtained results are in accordance with the findings of the earlier research that indicate complex and controversial relationships between intrinsic motivation, self-concept, and mathematical achievement, as well as that other constructs, including self-concept, can mediate the links between motivation and achievement. The authors point out the possibilities of encouraging students’ motivation for learning. If students are trained in the teaching process to organize their own activities, this will contribute to their experience of autonomy and the development of confidence in their own competence, which positively impacts their motivation for learning.
- Published
- 2023
- Full Text
- View/download PDF
33. Compactly supported cohomology of a tower of graphs and generic representations of $\protect \mathrm{PGL}_{n}$ over a local field
- Author
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Rajhi, Anis
- Subjects
Mathematics ,QA1-939 - Abstract
Let $\mathrm{F}$ be a non-archimedean locally compact field and let $\mathrm{G}_{n}$ be the group $\mathrm{PGL}_{n}(\mathrm{F})$. In this paper we construct a tower $(\tilde{\mathrm{X}}_{k})_{k\geqslant 0}$ of graphs fibred over the one-skeleton of the Bruhat–Tits building of $\mathrm{G}_{n}$. We prove that a non-spherical and irreducible generic complex representation of $\mathrm{G}_{n}$ can be realized as a quotient of the compactly supported cohomology of the graph $\tilde{\mathrm{X}}_{k}$ for $k$ large enough. Moreover, when the representation is cuspidal then it has a unique realization in a such model.
- Published
- 2023
- Full Text
- View/download PDF
34. Dirichlet type extensions of Euler sums
- Author
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Xu, Ce and Wang, Weiping
- Subjects
Mathematics ,QA1-939 - Abstract
In this paper, we study the alternating Euler $T$-sums and $\tilde{S}$-sums, which are infinite series involving (alternating) odd harmonic numbers, and have similar forms and close relations to the Dirichlet beta functions. By using the method of residue computations, we establish the explicit formulas for the (alternating) linear and quadratic Euler $T$-sums and $\tilde{S}$-sums, from which, the parity theorems of Hoffman’s double and triple $t$-values and Kaneko–Tsumura’s double and triple $T$-values are further obtained. As supplements, we also show that the linear $T$-sums and $\tilde{S}$-sums are expressible in terms of colored multiple zeta values. Some interesting consequences and illustrative examples are presented.
- Published
- 2023
- Full Text
- View/download PDF
35. On the Eneström–Kakeya theorem for quaternionic polynomials
- Author
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Mir, Abdullah and Ahmad, Abrar
- Subjects
Mathematics ,QA1-939 - Abstract
In this paper, we present certain results concerning the distribution of zeros of polynomials of a quaternionic variable and with quaternionic coefficients. We obtain ring shaped regions of Eneström–Kakeya type for the zeros of these polynomials and also extend some classical results from the complex to quaternionic setting.
- Published
- 2023
- Full Text
- View/download PDF
36. Aquathermolysis of heavy oil catalyzed by transition metal salts and clay
- Author
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Du, Yingna, Zhang, Liyuan, Jing, Rui, Li, Yongfei, Yang, Bo, and Chen, Gang
- Subjects
Aquathermolysis ,Viscosity reduction ,Heavy oil ,Transition metal ,Clay ,Catalysis ,Biochemistry ,QD415-436 ,Physical and theoretical chemistry ,QD450-801 ,Mathematics ,QA1-939 - Abstract
Currently, researchers have indicated that inorganic minerals in reservoirs, such as clay minerals, carbonates and quartz, can catalyze the evolution of organic matter into oil and gas. Therefore it is reasonable to believe that the minerals in reservoirs may act as a catalyst support with the metal-containing catalyst added from outside during the thermal recovery of heavy oil. This paper studied the aquathermolysis of heavy oil catalyzed by minerals and transition metal. The reaction conditions of two heavy oil samples were investigated. The results show that the optimal reaction conditions of heavy oil from Xinjiang Baikouquan Oilfield (XBO) are the reaction temperature of 250 °C and the reaction time of 6 h; for the crude oil from Xinjiang Tahe Oilfield (XTO), the optimal reaction conditions are determined to be the reaction temperature of 250 °C and the reaction time of 12 h, the water–oil ratio of the two oils is 0.3. Under optimal conditions, viscosity and pour point of heavy oil are significantly reduced. Differential scanning calorimetry (DSC), GC-MS analysis, thermogravimetric analysis (TGA), and elemental analysis were used to study the properties of the two heavy oil samples before and after reaction to explore the mechanism of the catalyzed aquathermolysis of heavy oil. This work will benefit the related heavy oil recovery work in this field.
- Published
- 2023
- Full Text
- View/download PDF
37. S-Noetherian rings, modules and their generalizations
- Author
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Tushar Singh, Ajim Uddin Ansari, and Shiv Datt Kumar
- Subjects
s-noetherian ring ,s-noetherian module ,s-noetherian property ,Mathematics ,QA1-939 - Abstract
Let R be a commutative ring with identity, M an R-module and S ⊆ R a multiplicative set. Then M is called S-finite if there exist an s ∈ S and a finitely generated submodule N of M such that sM ⊆ N. Also, M is called S-Noetherian if each submodule of M is S-finite. A ring R is called S-Noetherian if it is S-Noetherian as an R-module. This paper surveys the most recent developments in describing the structural properties of S-Noetherian rings, S-Noetherian modules and their generalizations. Some interesting constructed examples of S-Noetherian rings and modules are also presented.
- Published
- 2023
38. Theoretical and numerical results for the nonlinear shallow water problem
- Author
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Mohammed Lachache and Fatma Zohra Nouri
- Subjects
shallow water model ,traveling wave solutions ,well posedness ,finite differences ,Mathematics ,QA1-939 - Abstract
In this paper, the nonlinear shallow water problem is studied analytically and numerically. This problem has been studied by different authors in the linear case; here we consider a nonlinear one with non constant coefficients. We first start by a mathematical analysis, where the well posedness is proved via the use of traveling wave solutions. The existence and uniqueness of the solution is demonstrated by the means of Schaulder's and Banach's fixed point theorems. Then, we explore the proposed model and investigate the stability conditions and the efficiency numerically.
- Published
- 2023
39. Opers of higher types, Quot-schemes and Frobenius instability loci
- Author
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Kirti Joshi and Christian Pauly
- Subjects
mathematics - algebraic geometry ,Mathematics ,QA1-939 - Abstract
In this paper we continue our study of the Frobenius instability locus in the coarse moduli space of semi-stable vector bundles of rank $r$ and degree $0$ over a smooth projective curve defined over an algebraically closed field of characteristic $p>0$. In a previous paper we identified the "maximal" Frobenius instability strata with opers (more precisely as opers of type $1$ in the terminology of the present paper) and related them to certain Quot-schemes of Frobenius direct images of line bundles. The main aim of this paper is to describe for any integer $q \geq 1$ a conjectural generalization of this correspondence between opers of type $q$ (which we introduce here) and Quot-schemes of Frobenius direct images of vector bundles of rank $q$. We also give a conjectural formula for the dimension of the Frobenius instability locus.
- Published
- 2020
- Full Text
- View/download PDF
40. A note on the weighted log canonical threshold
- Author
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Nguyen Van Phu
- Subjects
Mathematics ,QA1-939 - Abstract
In this paper, we introduce and study a set relative to singularities of plurisubharmonic functions. We prove that this set is countable under the condition $h>0$ on $\mathbb{B}\setminus \lbrace 0\rbrace .$
- Published
- 2023
- Full Text
- View/download PDF
41. Positive Cohen p-nuclear m-homogeneous polynomials
- Author
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Asma Hammou, Amar Belacel, Amar Bougoutaia, and Abdelmoumen Tiaiba
- Subjects
banach lattice ,positive cohen p-nuclear polynomials ,positive cohen strongly p-summing polynomials ,Mathematics ,QA1-939 - Abstract
In this paper we introduce the concept of positive Cohen p-nuclear polynomials between Banach lattice spaces. We give an analogue to Pietsch domination theorem and we study some properties concerning this notion.
- Published
- 2023
42. Some new integral inequalities for negative summation parameters
- Author
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Abdelkader Senouci, Bouharket Benaissa, and Mohammed Sofrani
- Subjects
hardy-type integral inequality ,negative summation parameters ,Mathematics ,QA1-939 - Abstract
In this paper, we prove some Hardy type and Hardy-Steklov type integral inequalities for two negative summation parameters and we deduce some well-known results with sharp constants.
- Published
- 2023
43. Generalized logistic equation on Networks
- Author
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Elbetch, Bilel
- Subjects
Mathematics ,QA1-939 - Abstract
In this paper, we consider a general single species model in a heterogeneous environment of $n$ patches ($n\ge 2$), where each patch follows a generalized logistic law. First, we prove the global stability of the model. Second, in the case of perfect mixing, i.e. when the migration rate tends to infinity, the total population follows a generalized logistic law with a carrying capacity which in general is different from the sum of the $n$ carrying capacities. Next, we give some properties of the total equilibrium population and we compute its derivative at no dispersal. In some particular cases, we determine the conditions under which fragmentation and migration can lead to a total equilibrium population which might be greater or smaller than the sum of the $n $ carrying capacities. Finally, we study an example of two-patch model where the first patch follows a logistic law and the second a Richard’s law, we give a complete classification of the model parameter space as to whether dispersal is beneficial or detrimental to the sum of two carrying capacities.
- Published
- 2023
- Full Text
- View/download PDF
44. A COMPOSED MATHEMATICS GRADE OF ACADEMIC KNOWLEDGE, PROJECT WORK AND HOMEWORK: A FUZZY LOGIC APPROACH
- Author
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Daniel Doz, Darjo Felda, and Mara Cotič
- Subjects
mathematics ,project work ,homework ,fuzzy logic ,Education (General) ,L7-991 ,History of education ,LA5-2396 ,Special aspects of education ,LC8-6691 ,Theory and practice of education ,LB5-3640 - Abstract
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.
- Published
- 2023
- Full Text
- View/download PDF
45. Characterisation of the professional identity of teachers of vocational and technical training in Senegal: an exploratory study
- Author
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BABA DIÈYE DIAGNE and HÉLÈNE CHENEVAL-ARMAND
- Subjects
professional identity ,beliefs ,representations ,knowledge ,Education ,Mathematics ,QA1-939 - Abstract
This paper presents an approach to characterising the professional identity of technical vocational teachers based on psychosociological indicators. The indicators are based on the scientific literature and refer to the representation of colleagues and the profession to oneself and the representation of oneself as a person. A questionnaire survey was submitted to two groups of teachers with several years of service. The first group was made up of teachers with a professional degree. The second group consisted of contract teachers who teach without a professional diploma. This study shows the existence of several identity profiles of technical vocational training (TVET) teachers in Senegal.
- Published
- 2023
- Full Text
- View/download PDF
46. On bounded complex Jacobi matrices and related moment problems in the complex plane
- Author
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Sergey M. Zagorodnyuk
- Subjects
complex jacobi matrix ,moment problem ,orthogonal polynomials ,linear functional ,Mathematics ,QA1-939 - Abstract
In this paper we consider the following moment problem: find a positive Borel measure μ on ℂ subject to conditions ∫ zn dμ = sn, n∈ℤ+, where sn are prescribed complex numbers (moments). This moment problem may be viewed (informally) as an extension of the Stieltjes and Hamburger moment problems to the complex plane. A criterion for the moment problem for the existence of a compactly supported solution is given. In particular, such moment problems appear naturally in the domain of complex Jacobi matrices. For every bounded complex Jacobi matrix its associated functional S has the following integral representation: S(p) = ∫ℂ p(z) dμ, with a positive Borel measure μ in the complex plane. An interrelation of the associated to the complex Jacobi matrix operator A0, acting in l2 on finitely supported vectors, and the multiplication by z operator in L2μ is discussed.
- Published
- 2023
47. Conformable functional evolution equations with nonlocal conditions in Banach spaces
- Author
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Abderrahmane Boukenkoul and Mohamed Ziane
- Subjects
conformable fractional derivative ,mild solutions ,measure of noncompactness ,Mathematics ,QA1-939 - Abstract
In this paper, we study semilinear conformable fractional evolution equations with finite delay subjected to nonlocal initial conditions in an arbitrary Banach space. We prove the existence of mild solutions under compactness type conditions on the nonlinear forcing term. Our result improves and complements several earlier related works. We apply our result to study a functional conformable partial differential equation of transport type.
- Published
- 2023
48. An application of the Pascal distribution series for a certain subclass of analytic functions
- Author
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B.A. Frasin
- Subjects
analytic functions ,hadamard product ,pascal distribution series ,Mathematics ,QA1-939 - Abstract
In the present paper, we determine necessary and sufficient conditions for the subclass T(α, b) of analytic functions associated with Pascal distribution. Further, we consider properties of a special function related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.
- Published
- 2023
49. From formal smoothings to geometric smoothings
- Author
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Alessandro Nobile
- Subjects
formal deformation theory ,formal smoothing ,geometric smoothing ,Mathematics ,QA1-939 - Abstract
Let X be a projective, equidimensional, singular scheme over an algebraically closed field. Then the existence of a geometric smoothing (i.e. a family of deformations of X over a smooth base curve whose generic fibre is smooth) implies the existence of a formal smoothing as defined by Tziolas. In this paper we address the reverse question giving sufficient conditions on X that guarantee the converse, i.e. formal smoothability implies geometric smoothability. This is useful in light of Tziolas’ results giving sufficient criteria for the existence of formal smoothings.
- Published
- 2023
50. Local fractional metric dimension of rotationally symmetric planar graphs arisen from planar chorded cycles
- Author
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Shahbaz Ali, Raúl M. Falcón, and Muhammad Khalid Mahmood
- Subjects
local fractional metric dimension ,rotationally symmetric planar graph ,planar chorded cycle ,local resolving neighbourhood ,Mathematics ,QA1-939 - Abstract
In this paper, a new family of rotationally symmetric planar graphs is described based on an edge coalescence of planar chorded cycles. Their local fractional metric dimension is established for those ones arisen from chorded cycles of order up to six. Their asymptotic behaviour enables us to ensure the existence of new families of rotationally symmetric planar graphs with either constant or bounded local fractional dimension.
- Published
- 2023
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