23 papers · ranked by Valyu relevance
Luis Sordo Vieira, Reinhard C. Laubenbacher, David Murrugarra
Many problems in biology and medicine have a control component. Often, the goal might be to modify intracellular networks, such as gene regulatory networks or signaling networks, in order for cells to achieve a certain phenotype, such as happens in cancer. If the network is represented by a mathematical model for which…
Authors not listed
The SCF part of the HF-SCF method is responsible for finding the ground state as the global minimum of the one-determinant approximation of the electronic energy, which is a 4th order multivariable polynomial of the LCAO coefficients and Lagrange multipliers. In this work we replace this SCF part with algebraic…
Arkady Plotnitsky
The article reconsiders quantum theory in terms of the following principle, which can be symbolically represented as QUANTUMNESS → PROBABILITY → ALGEBRA and will be referred to as the QPA principle. The principle states that the quantumness of physical phenomena, that is, the specific character of physical phenomena…
Jan Pełczyński
The equivalence of the finite element method and the algebraic formulation of the equations of moderately thick and thin elastic frames, beams, trusses, and grillages within the Timoshenko and Euler-Bernoullie theory derived earlier by Pełczyński, Gilewski (2019) is presented. The proposed algebraic formulas lead to…
Arturo Tozzi
A wide range of biological and evolutionary processes is determined not merely by the occurrence of specific events, but by the exact order in which those events unfold. Gene regulation, developmental pathways, metabolic cascades and genetic evolution often display non-commutative behaviour, in which reversing the…
Kangbien Park
Humans have long employed directed evolution (DE) to engineer desired biological traits. In this paper, I introduce an algebraic framework that provides a quantitative representation of the general phenotypic traits of asexual populations, enabling the systematic modeling of DE processes. Within this framework, key…
Damian Moosbrugger
In this article, I propose a new approach to analyze the interrelations between mathematics and technology. It has the potential to contribute methodologically to both the fields of history of mathematics as well as the study of computational technologies in the current context. Based on the conception of mathematics…
S. Blake Allan
What is the role of algebra in classical mathematics education? How does it relate to the four quadrivial arts? These questions have troubled the mathematical community since the introduction of algebra into the Renaissance academy by men like Fran¸cois Vi`ete, Guillame Gosselin, and Ren´e Descartes. Their challenge is…
Po‐Shen Loh
The quadratic formula was a remarkable triumph of early mathematicians, marking the completion of a long quest to solve quadratic equations, with a storied history stretching as far back as the Old Babylonian Period around 2000–1600 B.C. [18, 21]. Over four millennia, many recognized names in mathematics left their…
Authors not listed
Atomic electrons exist under the central Coulomb potential of the nucleus, a constraint that mandates their wave functions be described by spherical harmonics. While standard quantum mechanics treats these functions as static geometric solutions, the empirical structure of the periodic table (2, 8, 8, 18, 18, ...)…
Rodrigo E. Menchón, Santiago H. Luna, A.L. Fourty, H. D. Navone
En este trabajo se presenta una estrategia de enseñanza implementada en Introducción a la Física, correspondiente al primer año del Profesorado en Física de la Universidad Nacional de Rosario, cuyo propósito principal es brindar a los estudiantes herramientas para comprender enunciados de problemas y ejercicios y para…
Li Zuo, Fengtai Mei
Since the nonlinear parabolic equation has many variables, its calculation process is mostly an algebraic operation, which makes it difficult to express the discrete process concisely, which makes it difficult to effectively solve the two grid algorithm problems and the convergence problem of reaction diffusion. The…
Authors not listed
While the method of manual inspection reliably produces correct results at the introductory level, it can often appear untidy and unintuitive and lacks teachable depth. This paper presents a novel alternative approach designed to achieve the same outcomes as manual inspection but with enhanced clarity. It serves as…
Ibragim E. Suleimenov, Yelizaveta S. Vitulyova, Sherniyaz B. Kabdushev, Akhat S. Bakirov
'Sherniyaz B. Kabdushev' 'Akhat S. Bakirov'] It is shown that in order to increase the efficiency of using methods of abstract algebra in modern information technologies, it is important to establish an explicit connection between operations corresponding to various varieties of multivalued logics and algebraic…
Carl Winsløw
Undergraduate students of mathematics continue to solve equations in virtually any course they attend, just as they did in secondary school – yet what do they learn about equations and their solutions at university? Are they capable to combine elements of abstract algebra and real analysis to assess what it means to…
Padavinangady Nakul Bhat, Debnath Pal
This study introduces a formal framework for modeling inheritance patterns based on an algebraic representation of genotype distributions. The approach defines genotypes as probability measures rather than discrete states, enabling the computation of genetic expectations, a probabilistic analogue that captures the…
Yang Yu
The symmetry and group in degeneracy of the standard genetic code (SGC) have been studied. However, the core role of equations of degree n with one unknown between symmetry and group theory has been ignored. In this study, algebraic concept was employed to abstract all genetic codons in the SGC table into a series of…
Peyman Nasehpour
The word "algebra" is derived from the Arabic word Al-Jabr, and this comes from the treatise written in 820 by the medieval Persian mathematician [44], Muhammad ibn Musa al-Khwarizmi, entitled, in Arabic "Kitab al-mukhtas ¯ .ar f¯i h. isab al-gabr wa-'l- ˇ muqabala ¯ ", which can be translated as "The Compendious Book…
John Ramsden, Руслан Шарипов
A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. Its existence is equivalent to the existence of a perfect cuboid with all integer edges and diagonals. Finding such a cuboid or proving its non-existence is…
Dazhi Cheng, Mengyi Li, Jiaxin Cui, Li Wang + 5 more
'Liangyuan Ouyang' 'Xiaozhuang Wang' 'Xuejun Bai' 'Xinlin Zhou'] Background Mathematical expressions mainly include arithmetic (such as 8 − (1 + 3)) and algebra (such as a − (b + c)). Previous studies have shown that both algebraic processing and arithmetic involved the bilateral parietal brain regions. Although…
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Building on prior mathematical formulations of the periodic law, this paper demonstrates that the algebraic formula S(k) = 2 * (floor(k/2) + 1)^2 accurately predicts the period lengths (2, 8, 8, 18, 18, 32, ...) of the periodic table. This pattern is not a numerical coincidence but a direct consequence of the…
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This paper introduces Post-Inspection Analysis (PIA), a concept for understanding and reverse engineering balanced equations of similar reactions. Here we explore the idea that balanced equations contain useable information observed by grouping and analysing similar equations, allowing us to uncover observations that…
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A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…