Mathematical Papers Research Articles

EXTENDING TORSORS UNDER QUASI-FINITE FLAT GROUP SCHEMES

Abstract Let R be a discrete valuation ring of field of fractions K and of residue field k of characteristic $p> 0$ . In an earlier work, we studied the question of extending torsors over K-curves into torsors over R-regular models of the curves in the case when the structural K-group scheme of the torsor admits a finite flat model over R. In this paper, we first give a simpler description of the problem in the case where the curve is semistable using recent work in Holmes, Molcho, Orecchia, and Poiret (2023, Journal für die Reine und Angewandte Mathematik [Crelle’s Journal] 230, 115–159) and Molcho and Wise (2022, Compositio Mathematica 158, 1477–1562). Second, if R is assumed to be Henselian and Japanese, we solve the problem of extending torsors by combining our previous work together with results in Antei and Emsalem (2018, Nagoya Mathematical Journal 230, 18–34) and Phung and Dos Santos (2023, Algebraic Geometry 230, 1–40), including the case where the structural group does not admit a finite flat R-model.

Pentagoning the Circle with Straightedge & Compass

This study idea came from the exact solution “Circling the Regular Pentagon with Straightedge & compass in Euclidean Geometry”, published by the Scholars Journal of Physics, Mathematics and Statistics on 22/08/2024 [1]. In this research, the ANALYSIS method is adopted to prove the process of solving this new challenge problem, which has not existed in the Mathematics field till today. The process is an inverse/converse solution solving the inverse problem “Circling the Regular Pentagon with Straightedge & compass in Euclidean Geometry” problem, using a straightedge & a compass. I hereby commit that this is my own personal research project.

Corrigendum to “Singular points of real quartic and quintic curves” by David A. Weinberg and Nicholas J. Willis [Tbilisi Mathematical Journal, Vol. 2, 2009, pp. 95-134

Corrigendum to “Singular points of real quartic and quintic curves” by David A. Weinberg and Nicholas J. Willis [Tbilisi Mathematical Journal, Vol. 2, 2009, pp. 95-134

On Fractional ID-\((g,f)\)-factor-critical Covered Graphs

A graph \(G\) is called a fractional ID-\((g,f)\)-factor-critical covered graph if for any independent set \(I\) of \(G\) and for every edge \(e \in E(G-I)\), \(G-I\) has a fractional \((g,f)\)-factor \(h\) such that \(h(e) = 1\). We give a sufficient condition using degree condition for a graph to be a fractional ID-\((g,f)\)-factor-critical covered graph. Our main result is an extension of Zhou, Bian, and Wu’s previous result [S. Zhou, Q. Bian, J. Wu, A result on fractional ID-\(k\)-factor-critical graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 87(2013) 229–236] and Yashima’s previous result [T. Yashima, A degree condition for graphs to be fractional ID-\([a,b]\)-factor-critical, Australasian Journal of Combinatorics 65(2016) 191–199].

Philosophy and Logic in a Time of War

Abstract This interview was given by Yaroslav Shramko (b. 1963), professor of the Department of Philosophy and rector of the Kryvyi Rih State Pedagogical University (Ukraine). His main research interests lie in the fields of logic and analytical philosophy. He has carried out several projects on modern non-classical logic: 1996–1998, within the Alexander von Humboldt Foundation Fellowship at Humboldt University in Berlin (Germany); 1999–2000, within the Fulbright Program at Indiana University in Bloomington (USA); and 2003–2004, as a Wilhelm Bessel Awardee at Dresden University of Technology (Germany), among others. He has been a frequent invited speaker at international conferences and congresses. He is a member of the editorial boards of several international logic journals, such as Logic and Logical Philosophy (Torun, Poland), Bulletin of the Section of Logic (Łódź, Poland), European Journal of Mathematics (Springer), and Studia Logica (Springer). Prof Shramko is the author of “Truth and falsehood: An inquiry into generalized logical values” (Springer, 2011, joint work with Heinrich Wansing) and a number of articles on logic and analytic philosophy in peer-reviewed international journals.

Автоморфизмы нильтреугольных подколец алгебр Шевалле типа G2 над полем характеристики 2

Let NΦ(K) be the nil-triangular subalgebra of the Chevalley algebra over an associative commutative ring K with the identity associated with a root system Φ (The basis of NΦ(K) consists of all elements er ∈ Φ+ of the Chevalley basis). This paper studies the well-known problem of describing automorphisms of Lie algebras and rings NΦ(K). Automorphisms of the Lie algebra NΦ(K) under restrictions K = 2K = 3K on ring K are described by Y. Cao, D. Jiang, J. Wang (Intern. J. Algebra and Computation, 2007). When passing from algebras to Lie rings, the group of automorphisms expands. Thus, the subgroup of central automorphisms is extended, i.e. acting modulo the center, ring automorphisms induced by automorphisms of the main ring are added. For the type An, a description of automorphisms of Lie rings NΦ(K) over K was obtained by V.M. Levchuk (Siberian Mathematical Journal, 1983). Automorphisms of the Lie ring NΦ(K) are described by V.M. Levchuk (Algebra and Logic, 1990) for type D4 over K, and for other types by A.V. Litavrin (Thesis for: Cand. Sc. (Physics and Mathematics) – 01.01.06. Siberian Federal University, 2017), excluding types G2 and F4. The author (2022) obtained a description of automorphisms of Lie rings NΦ(K) of type G2 when K is an integrity domain and K = 2K = 3K or 3K = 0. In this paper we describe automorphisms of a niltriangular Lie ring of type G2 over a field K under restriction 2K = 0. To study automorphisms, the upper and lower central series described in this work are essentially used. A new non-standard automorphism was found, called an S-automorphism.

Prime representations in the Hernandez–Leclerc category: classical decompositions

Abstract We use the dual functional realization of loop algebras to study the prime irreducible objects in the Hernandez–Leclerc (HL) category for the quantum affine algebra associated with $\mathfrak {sl}_{n+1}$ . When the HL category is realized as a monoidal categorification of a cluster algebra (Hernandez and Leclerc (2010, Duke Mathematical Journal 154, 265–341); Hernandez and Leclerc (2013, Symmetries, integrable systems and representations, 175–193)), these representations correspond precisely to the cluster variables and the frozen variables are minimal affinizations. For any height function, we determine the classical decomposition of these representations with respect to the Hopf subalgebra $\mathbf {U}_q(\mathfrak {sl}_{n+1})$ and describe the graded multiplicities of their graded limits in terms of lattice points of convex polytopes. Combined with Brito, Chari, and Moura (2018, Journal of the Institute of Mathematics of Jussieu 17, 75–105), we obtain the graded decomposition of stable prime Demazure modules in level two integrable highest weight representations of the corresponding affine Lie algebra.

The second fundamental form of the real Kaehler submanifolds

Abstract Let $f\colon M^{2n}\to \mathbb {R}^{2n+p}$ , $2\leq p\leq n-1$ , be an isometric immersion of a Kaehler manifold into Euclidean space. Yan and Zheng (2013, Michigan Mathematical Journal 62, 421–441) conjectured that if the codimension is $p\leq 11$ , then, along any connected component of an open dense subset of $M^{2n}$ , the submanifold is as follows: it is either foliated by holomorphic submanifolds of dimension at least $2n-2p$ with tangent spaces in the kernel of the second fundamental form whose images are open subsets of affine vector subspaces, or it is embedded holomorphically in a Kaehler submanifold of $\mathbb {R}^{2n+p}$ of larger dimension than $2n$ . This bold conjecture was proved by Dajczer and Gromoll just for codimension 3 and then by Yan and Zheng for codimension 4. In this paper, we prove that the second fundamental form of the submanifold behaves pointwise as expected in case that the conjecture is true. This result is a first fundamental step for a possible classification of the nonholomorphic Kaehler submanifolds lying with low codimension in Euclidean space. A counterexample shows that our proof does not work for higher codimension, indicating that proposing $p=11$ in the conjecture as the largest codimension is appropriate.

On the special issue for the 40th anniversary of the Japan Journal of Industrial and Applied Mathematics

On the special issue for the 40th anniversary of the Japan Journal of Industrial and Applied Mathematics

Solstice: An Electronic Journal of Geography and Mathematics: Vol. 34, No. 1

Solstice: An Electronic Journal of Geography and Mathematics: Vol. 34, No. 1

Machine composition of Korean music via topological data analysis and artificial neural network

Common AI music composition algorithms train a machine by feeding a set of music pieces. This approach is a blackbox optimization, i.e. the underlying composition algorithm is, in general, unknown to users. In this paper, we present a method of machine composition that teaches a machine the compositional principles embedded in the music using the concept of overlap matrix. In (Tran Mai Lan, Changbom Park & Jae-Hun Jung (2023) Topological data analysis of Korean music in Jeongganbo: a cycle structure, Journal of Mathematics and Music, DOI: 10.1080/17459737.2022.2164626), a type of Korean music called Dodeuri music has been analysed using topological data analysis (TDA). To apply TDA, the music data is first reconstructed as a graph. Through TDA on the constructed graph, a unique set of cycles is found. The overlap matrix lets us visualize how those cycles are interconnected in music. We explain how we use the overlap matrix for machine composition. The overlap matrix is suitable for algorithmic composition and also provides seed music to train an artificial neural network.

RETRACTED ARTICLE: A cubic B-spline quasi-interpolation method for solving hyperbolic partial differential equations

We, the Editors and Publisher of International Journal of Computer Mathematics have retracted the following article: Sudhir Kumar, R.C. Mittal & Ram Jiwari (2023) A cubic B-spline quasi-interpolation method for solving hyperbolic partial differential equations, International Journal of Computer Mathematics, DOI: 10.1080/00207160.2023.2205963 Since publication, significant concerns have been raised about the fact that this article has substantial overlap with the following article which was not acknowledged, particularly in Sections 1-4 where there were verbatim sentences and sentence fragments: Mittal, R. C., Kumar, S., & Jiwari, R. (2021). A cubic B-spline quasi-interpolation algorithm to capture the pattern formation of coupled reaction-diffusion models. Engineering with Computers, 1-17 https://doi.org/10.1007/s00366-020-01278-3. Upon query, the authors were not able to address the concerns with their paper or provide a satisfactory explanation for this significant level of overlap. As this is a serious breach of our Editorial Policies, we are retracting the article from the journal. The authors do not agree with the retraction. We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines on retractions. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as ‘Retracted’.

Statistical extension some types of symmetrically continuity

In this paper, the notions symmetric continuity, weak continuity, weak symmetric continuity which wasintroduced in [P.Pongsriiam and T.Thongsiri, Weakly symmetrically continuous function, Chamchuri Journal of Mathematics, vol 8(2016),49-65 ] are generalized by using natural density defined on N. Among the others some basic properties of generalized form of symmetrically continuity is investigate with several useful examples.

New characterizations of the unit vector basis of or

AbstractMotivated by Altshuler’s famous characterization of the unit vector basis of $c_0$ or $\ell _p$ among symmetric bases (Altshuler [1976, Israel Journal of Mathematics, 24, 39–44]), we obtain similar characterizations among democratic bases and among bidemocratic bases. We also prove a separate characterization of the unit vector basis of $\ell _1$ .

RETRACTED ARTICLE: Mathematical techniques and applications of linear differential equation

“We, the Editors and Publisher of the International Journal of Computer Mathematics, have retracted the following article: R. Balapriya, A. Thiripuram, S. Annadurai & G. Arul Freeda Vinodhini (2023) Mathematical Techniques and Applications of Linear Differential Equation, International Journal of Computer Mathematics, 100:4, 901- 908, DOI: 10.1080/00207160.2022.2164491 Following an investigation by the Taylor & Francis Research Integrity and Ethics team, it was discovered post-publication that this article was not peer reviewed appropriately, in line with the Journal's peer review standards and policy. As the stringency of the peer review process is core to the integrity of the publication process, the Editor and Publisher have taken the decision to retract the article. The journal has not confirmed if the authors were aware of this compromised peer review process. The journal is committed to correcting the scientific record and will fully cooperate with any institutional investigations into this matter. The authors have been informed of this decision. We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines on retractions. The retracted articles will remain online to maintain the scholarly record, but they will be digitally watermarked on each page as ‘Retracted’.”

Maximal theta functions universal optimality of the hexagonal lattice for Madelung-like lattice energies

We present two families of lattice theta functions accompanying the family of lattice theta functions studied by Montgomery in [H. Montgomery, Minimal theta functions. Glasgow Mathematical Journal, 30 (1988), 75–85]. The studied theta functions are generalizations of the Jacobi theta-2 and theta-4 functions. Contrary to Montgomery’s result, we show that, among lattices, the hexagonal lattice is the unique maximizer of both families of theta functions. As an immediate consequence, we obtain a new universal optimality result for the hexagonal lattice among two-dimensional alternating charged lattices and lattices shifted by the center of their unit cell.

A ACCELERATED MODIFIED SHIFT-SPLITTING METHOD FOR NONSYMMETRIC SADDLE POINT PROBLEMS

Recently, Huang and Su [A modified shift-splitting method for nonsymmetric saddle, <i>Journal of Computational and Applied Mathematics</i>, 317 (2017) 535-546] introduced a modified shift-splitting (denoted by MSSP) preconditioner. In this paper, based on modified shift-splitting (denoted by MSSP) iteration technique, we establish a accelerated (named after AMSSP) iterative method for nonsymmetric saddle point problems. Furthermore, we theoretically verify the AMSSP iteration method unconditionally converges to the unique solution of the saddle point problems, compute the spectral radius of the AMSSP iteration matrix. Finally, numerical examples show the spectrum of the new preconditioned matrix for the different parameters.

Single-Subject Research: Mathematical Reasoning Ability of Slow Learners in Straight-Line Equations

A scholarly article by authors Muhammad Irfan, Dewi Mega Mulyani, and Benidiktus Tanujaya, Leonard Leonard, Samsul Maarif, Sri Adi Widodo published in The International Journal of Science, Mathematics and Technology Learning

Soliton resolution for the radial critical wave equation in all odd space dimensions

Consider the energy-critical focusing wave equation in odd space dimension $N\geq 3$. The equation has a nonzero radial stationary solution $W$, which is unique up to scaling and sign change. In this paper we prove that any radial, bounded in the energy norm solution of the equation behaves asymptotically as a sum of modulated $W$s, decoupled by the scaling, and a radiation term. The proof essentially boils down to the fact that the equation does not have purely nonradiative multisoliton solutions. The proof overcomes the fundamental obstruction for the extension of the 3D case (treated in our previous work, Cambridge Journal of Mathematics 2013, arXiv:1204.0031) by reducing the study of a multisoliton solution to a finite dimensional system of ordinary differential equations on the modulation parameters. The key ingredient of the proof is to show that this system of equations creates some radiation, contradicting the existence of pure multisolitons.

A note on "Some properties of second-order weak subdifferentials" [Turkish Journal of Mathematics (2021)45: 955-960

In this note, we provide an example to illustrate that Proposition 2.4 in [Turkish Journal of Mathematics (2021)45: 955-960)] is incorrect, and give a modification of the proposition. Two examples are provided to illustrate the modified result. Meanwhile, we establish a convex function, and correct the proof of Theorem 2.3 in [Turkish Journal of Mathematics (2021)45: 955-960)] by the function.