Journal articles: 'Mathematical analysis - functional analysis'

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Olteanu, Octav. "Special Issue of Symmetry: “Symmetry in Mathematical Analysis and Functional Analysis”." Symmetry 14, no. 12 (December 16, 2022): 2665. http://dx.doi.org/10.3390/sym14122665.

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De Haas, W. Bas, José Pedro Magalhães, Frans Wiering, and Remco C. Veltkamp. "Automatic Functional Harmonic Analysis." Computer Music Journal 37, no. 4 (December 2013): 37–53. http://dx.doi.org/10.1162/comj_a_00209.

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Music scholars have been studying tonal harmony intensively for centuries, yielding numerous theories and models. Unfortunately, a large number of these theories are formulated in a rather informal fashion and lack mathematical precision. In this article we present HarmTrace, a functional model of Western tonal harmony that builds on well-known theories of tonal harmony. In contrast to other approaches that remain purely theoretical, we present an implemented system that is evaluated empirically. Given a sequence of symbolic chord labels, HarmTrace automatically derives the harmonic relations between chords. For this, we use advanced functional programming techniques that are uniquely available in the Haskell programming language. We show that our system is fast, easy to modify and maintain, robust against noisy data, and that its harmonic analyses comply with Western tonal harmony theory.

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Xiaoqin Li. "Equilibrium analysis in game theory using nonlinear functional analysis techniques." Journal of Electrical Systems 20, no. 3 (April 25, 2024): 1099–110. http://dx.doi.org/10.52783/jes.3437.

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Game theory provides a mathematical framework for analyzing the tactical choices of rational decision makers. The idea of equilibrium, which states that no player has a motivation to change their existing approach given the strategies of other players, is one of the core ideas of game theory. This study examines a type of undirected graph-based distributed quadratic game. The problem of communication topology constraints is presented and nonlinear dynamics with uncertain time-dependent perturbations are present in the participant's dynamics. Based on a high-gain observer approach, a distributed Nash equilibrium (NE) finding technique is given, and the Lyapunov stability theory is used to study the convergence. It represents that every player approximates the positions of their rival players and that there are differences between the NE and the placements of the minor limitation that finally restricts the players. In addition, chattering problems are eliminated since the offered theory's formulation employs the hyperbolic tangent function to control the perturbation rather than the signum function. In an imitation of the oligopoly match, five enterprises manufacture identical materials in a duopoly market framework; this is done to confirm the effectiveness of the recommended strategy. Our results provide novel perspectives and methods for understanding complicated strategic situations, helping to close the gap between mathematical theory and real-world applications.

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Kreyszig, Erwin. "Book Review: Applied functional analysis (Applications to mathematical physics)." Bulletin of the American Mathematical Society 33, no. 03 (July 1, 1996): 403–8. http://dx.doi.org/10.1090/s0273-0979-96-00672-6.

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Man, Xiaolin, and Colby C. Swan. "A Mathematical Modeling Framework for Analysis of Functional Clothing." Journal of Engineered Fibers and Fabrics 2, no. 3 (September 2007): 155892500700200. http://dx.doi.org/10.1177/155892500700200302.

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In the analysis and design of functional clothing systems, it is helpful to quantify the effects of a system on a wearer's physical performance capabilities. Toward this end, a clothing modeling framework for quantifying the mechanical interactions between a given clothing system design and a specific wearer performing defined physical tasks is proposed. The modeling framework consists of three interacting modules: (1) a macroscale fabric mechanics/dynamics model; (2) a collision detection and contact correction module; and (3) a human motion module. In the proposed framework, the macroscopic fabric model is based on a rigorous large deformation continuum-degenerated shell theory representation. Material models that capture the stress-strain behavior of different clothing fabrics are used in the continuum shell framework. The collision and contact module enforces the impenetrability constraint between the fabric and human body and computes the associated contact forces between the two. The human body is represented in the current framework as an assemblage of overlapping ellipsoids that undergo rigid body motions consistent with human motions while performing actions such as walking, running, or jumping. The transient rigid body motions of each ellipsoidal body segment in time are determined using motion capture technology. The integrated modeling framework is then exercised to quantify the resistance that the clothing exerts on the wearer during the specific activities under consideration. Current results from the framework are presented and its intended applications are discussed along with some of the key challenges remaining in clothing system modeling.

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Alshwaikh, Jehad. "Towards a systemic functional analysis of mathematical visual forms." Research in Mathematics Education 10, no. 1 (March 2008): 87–88. http://dx.doi.org/10.1080/14794800801916770.

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Tamilvanan, K., Nazek Alessa, K. Loganathan, G. Balasubramanian, and Ngawang Namgyel. "General Solution and Stability of Additive-Quadratic Functional Equation in IRN-Space." Journal of Function Spaces 2021 (August 3, 2021): 1–9. http://dx.doi.org/10.1155/2021/8019135.

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The investigation of the stabilities of various types of equations is an interesting and evolving research area in the field of mathematical analysis. Recently, there are many research papers published on this topic, especially additive, quadratic, cubic, and mixed type functional equations. We propose a new functional equation in this study which is quite different from the functional equations already dealt in the literature. The main feature of the equation dealt in this study is that it has three different solutions, namely, additive, quadratic, and mixed type functions. We also prove that the stability results hold good for this equation in intuitionistic random normed space (briefly, IRN-space).

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Yi, Zhong, and Cheng Zhi Yuan. "Mathematical Analysis on Helicoids Architectural Form." Advanced Materials Research 790 (September 2013): 273–77. http://dx.doi.org/10.4028/www.scientific.net/amr.790.273.

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In a sense, architecture may be called as a geometric figure. Although architectural forms are very different, the form from one kind of architecture to another kind of architecture is equivalent to one kind of mathematical transformation in view of mathematics; for example, the transformation between a cube architecture and a spherical architecture belongs to a topological transformation. Currently, many sculptural features appear in the architecture design, which may be called as the nonlinear architecture. Curves and curved surfaces are widely used in the architecture modeling. Moreover, functional spaces are divided inside the architecture shell according to requirements. Architects are inclined to use a mathematical theory especially the geometrical knowledge in an architecture design. However, architects can not imagine many artistic geometric figures in geometry. Besides, such wonderful geometric figures always include some miraculous mathematical and physical properties.

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Folland, Gerald B., Peter D. Lax, John Wiley, Yuli Eidelman, Vitaly Milman, and Antonis Tsolomitis. "Functional Analysis." American Mathematical Monthly 112, no. 10 (December 1, 2005): 937. http://dx.doi.org/10.2307/30037653.

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Dudek, Ewa. "Functional Analysis Of A Selected Airport’s System." Journal of KONBiN 35, no. 1 (November 1, 2015): 35–42. http://dx.doi.org/10.1515/jok-2015-0037.

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Abstract In this paper two selected airport’s systems (Flight Information System and Public Address Voice Annunciation) are defined and described. Then they are used to create an integrated unit, with the presentation of its way of functioning and a schematic picture. The author names main purposes of the integration process, serving to counteract negative consequences arising from implementation of the increasing number of systems on transport objects. In the following part of the article functional analysis of the integrated unit is carried out, defining system’s possible states of work and relations between them. Utilization of mathematical apparatus allows to calculate probabilities of system staying in the respective states, as well as system’s time indexes. Presented results are a fundament for the further analysis of this matter.

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Prishchenko, Olga, Nadezhda Cheremskaya, and Tetyana Chernogor. "CONSTRUCTION OF MATHEMATICAL MODELS USING THE METHODS OF CORRELATION AND REGRESSION ANALYSIS." Bulletin of the National Technical University "KhPI". Series: Innovation researches in students’ scientific work, no. 2 (December 16, 2021): 29–36. http://dx.doi.org/10.20998/2220-4784.2021.02.05.

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The article discusses the construction of a mathematical model using the methods of correlation and regression analysis in determining the functional relationship between the quantities. When conducting an experiment, it is often necessary to establish the interdependence between two or more quantities in order to obtain an empirical formula. In some cases, this is a simple task, because these connections are almost obvious or known in advance. As a rule, to establish the relationship between different indicators, factors and characteristics is not a trivial task. There is a need to use some hypothesis in the form of functional dependence. In other words, it is necessary to replace this functional dependence with a fairly simple mathematical expression. Such a mathematical expression can be a linear equation or a polynomial. In order to use such experimental data to determine such a mathematical or functional relationship between variables, the methods of correlation and regression analysis are used. Correlation analysis provides an answer to the statistical hypothesis of the absence or presence of a relationship between variables with some predetermined confidence probability. Determination of the functional dependence between different values on their experimental values is carried out using regression analysis. It is based on the well-known method of least squares. Proposing one or another regression equation, the researcher determines both the very existence of the relationship between variables and its mathematical form. Regression analysis considers the relationship between the dependent quantity and non-dependent variables. This relationship is represented using a mathematical model, that is, an equation that connects the dependent and independent variables. Processing of experimental data using correlation and regression analysis allows us to build a statistical mathematical model in the form of a regression equation. Thus, the methods of correlation and regression analysis are closely related.

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Yan, Baisheng. "MinimizingL∞-norm functional on divergence-free fields." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 28, no. 3 (May 2011): 325–55. http://dx.doi.org/10.1016/j.anihpc.2011.02.004.

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Ionescu, Cezar, and Patrik Jansson. "Domain-Specific Languages of Mathematics: Presenting Mathematical Analysis Using Functional Programming." Electronic Proceedings in Theoretical Computer Science 230 (November 26, 2016): 1–15. http://dx.doi.org/10.4204/eptcs.230.1.

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Suganya, G., and R. Senthamarai. "Mathematical modeling and analysis of Phytoplankton–Zooplankton–Nanoparticle dynamics." Mathematical Modeling and Computing 9, no. 2 (2022): 333–41. http://dx.doi.org/10.23939/mmc2022.02.333.

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In this paper, we investigate the population dynamics of phytoplankton–zooplankton–nanoparticle model with diffusion and density dependent death rate of predator. The functional response of predator in this model is considered as Beddington–DeAngelis type. The stability analysis of the equilibrium points is observed by applying the Routh–Hurwitz criterion. Numerical simulations are given to illustrate the theoretical results.

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Narici, Lawrence, D. H. Luecking, and L. A. Rubel. "Complex Analysis, a Functional Analysis Approach." American Mathematical Monthly 93, no. 3 (March 1986): 230. http://dx.doi.org/10.2307/2323356.

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Kolev, Mikhail. "Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach." Mathematics 7, no. 11 (October 30, 2019): 1024. http://dx.doi.org/10.3390/math7111024.

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A new mathematical model of a general autoimmune disease is presented. Basic information about autoimmune diseases is given and illustrated with examples. The model is developed by using ideas from the kinetic theory describing individuals expressing certain functions. The modeled problem is formulated by ordinary and partial equations involving a variable for a functional state. Numerical results are presented and discussed from a medical view point.

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Epifanio, Irene, and Noelia Ventura-Campos. "Functional data analysis in shape analysis." Computational Statistics & Data Analysis 55, no. 9 (September 2011): 2758–73. http://dx.doi.org/10.1016/j.csda.2011.04.003.

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Toland, J. F. "NONLINEAR FUNCTIONAL ANALYSIS." Bulletin of the London Mathematical Society 18, no. 5 (September 1986): 522–23. http://dx.doi.org/10.1112/blms/18.5.522.

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Ruf, Matthias. "Discrete stochastic approximations of the Mumford–Shah functional." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 36, no. 4 (July 2019): 887–937. http://dx.doi.org/10.1016/j.anihpc.2018.10.004.

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Yang, Jian Xin, Zhen Tao Liu, and Ben Zhao. "A Comparison Study of Mathematical Models for Tolerance Analysis." Advanced Materials Research 765-767 (September 2013): 759–62. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.759.

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This paper reviews two major models (Small Displacement Torsor, Deviation and Clearance Domain) for 3D functional tolerance analysis and compares them. The underlying mathematical representation of geometric tolerances can be classified as inequalities and multi-variate region. The corresponding algebraic or geometric tolerance propagation mechanism of each model is briefly introduced for worst-case and statistical tolerancing. Through a comprehensive comparison of these models, this paper gives some suggestions for choosing the appropriate method for a given tolerancing problem.

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Turner, Leo, Andrew Burbanks, and Marianna Cerasuolo. "Mathematical insights into neuroendocrine transdifferentiation of human prostate cancer cells." Nonlinear Analysis: Modelling and Control 26, no. 5 (September 1, 2021): 884–913. http://dx.doi.org/10.15388/namc.2021.26.24441.

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Prostate cancer represents the second most common cancer diagnosed in men and the fifth most common cause of death from cancer worldwide. In this paper, we consider a nonlinear mathematical model exploring the role of neuroendocrine transdifferentiation in human prostate cancer cell dynamics. Sufficient conditions are given for both the biological relevance of the model’s solutions and for the existence of its equilibria. By means of a suitable Liapunov functional the global asymptotic stability of the tumour-free equilibrium is proven, and through the use of sensitivity and bifurcation analyses we identify the parameters responsible for the occurrence of Hopf and saddle-node bifurcations. Numerical simulations are provided highlighting the behaviour discovered, and the results are discussed together with possible improvements to the model.

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W., L. B., and Colin W. Crye. "Numerical Functional Analysis." Mathematics of Computation 45, no. 171 (July 1985): 270. http://dx.doi.org/10.2307/2008066.

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Fink, James P., and R. E. Moore. "Computational Functional Analysis." Mathematics of Computation 47, no. 175 (July 1986): 372. http://dx.doi.org/10.2307/2008105.

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Areshi, Mounirah, Aly R. Seadawy, Asghar Ali, Amal F. Alharbi, and Abdulrahman F. Aljohani. "Analytical Solutions of the Predator–Prey Model with Fractional Derivative Order via Applications of Three Modified Mathematical Methods." Fractal and Fractional 7, no. 2 (January 30, 2023): 128. http://dx.doi.org/10.3390/fractalfract7020128.

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We have investigated wave solutions of the Predator–Prey (PP) model with fractional derivative order by novel three modified mathematical methods with the help of the Mathematica platform. The derived solutions are in the form of distinct functions such as trigonometric, hyperbolic, exponential and rational functional. For the physical phenomena of fractional model, some solutions are plotted in 2-dimensional and 3-dimensional by inserting specific values to attached parameters under sufficient condition on each solution. Hence, proposed schemes are enormously superbly mathematical tools to review wave solutions of several fractional models in nonlinear science.

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Turab, Ali, Awad A. Bakery, O. M. Kalthum S. K. Mohamed, and Wajahat Ali. "On a Unique Solution of the Stochastic Functional Equation Arising in Gambling Theory and Human Learning Process." Journal of Function Spaces 2022 (January 20, 2022): 1–8. http://dx.doi.org/10.1155/2022/1064803.

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The term “learning” is often used to refer to a generally stable behavioral change resulting from practice. However, it is a fundamental biological capacity far more developed in humans than in other living beings. In an animal or human being, the learning phase may often be viewed as a series of choices between multiple possible reactions. Here, we analyze a specific type of human learning process related to gambling in which a subject inserts a poker chip to operate a two-armed bandit device and then presses one of the two keys. Through the use of an electromagnet, one or more poker chips are given to the individual in a container located in the apparatus’s center. If a chip is provided, it is declared a winner; otherwise, it is considered a loser. The goal of this paper is to look at the subject’s actions in such situations and provide a mathematical model that is appropriate for it. The existence of a unique solution to the suggested human learning model is examined using relevant fixed point results.

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Gómez, Miller Cerón, Eduardo Ibarguen Mondragon, and Paulo Cesar Carmona Tabares. "Mathematical model of evasion of immune system by virus." Journal of Interdisciplinary Mathematics 26, no. 4 (2023): 733–45. http://dx.doi.org/10.47974/jim-1508.

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Virus needs to infect cells to spread the disease in the host and to achieve this, they have developed specific tactics to evade the immune system, which is in charge of trying to prevent any infection. In this way, we develop a mathematical model to represent the evasion of immune system by virus using a non-monotonic functional response describing an antipredator behavior, where the virus is the prey and the immune cells are the predator. We found four equilibrium points, the disease free equilibrium, immune evasion equilibrium and two immune activation equilibrium points. The disease free equilibrium is globally asymptotically stable if R0 ≤ 1, the immune evasion equilibrium and two immune activation equilibria are locally asymptotically stable if R0 >1. We conclude that in our model the evasion of immune system is always possible when there is a inoculation of virus in the host, but there is also a chance to control the infection or to activate the immune system when there are a cross-reactive antibodies.

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Rezapour, S., S. Etemad, M. Sinan, J. Alzabut, and A. Vinodkumar. "A Mathematical Analysis on the New Fractal-Fractional Model of Second-Hand Smokers via the Power Law Type Kernel: Numerical Solutions, Equilibrium Points, and Sensitivity Analysis." Journal of Function Spaces 2022 (May 10, 2022): 1–26. http://dx.doi.org/10.1155/2022/3553021.

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The second-hand smoke is a phenomenon that needs to be investigated, and its effects on the health of the people are to be examined. To analyze such an issue, the mathematical models are the best tools that help us to study the dynamical behaviors of this phenomenon. For this purpose, in the present paper, we consider a three-compartmental fractal-fractional mathematical model of a specific population of smokers or people that are exposed to second-hand smoke. By assuming some conditions on ϕ - ψ -contractions and compact operators, we prove some theorems in relation to the existence of solutions. The Banach principle for the usual contractions is used for proving the uniqueness of solutions. Next, by some notions of functional analysis, two types of Ulam-Hyers stability for the fractal-fractional second-hand smoker model are established. Moreover, we have a steady-state analysis and obtain equilibrium points and basic reproduction number R 0 . Then, we investigate the sensitivity of the fractal-fractional system with respect to each parameter. For numerical simulation, the Adams-Bashforth (AB) method is used to derive numerical schemes for plotting and simulating the approximate solutions. Finally, the obtained solutions are tested with real data and different values of fractal dimensions and fractional orders.

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Fechner, Włodzimierz. "On a functional inequality connected with quadratic functionals." Journal of Mathematical Analysis and Applications 332, no. 1 (August 2007): 381–89. http://dx.doi.org/10.1016/j.jmaa.2006.10.033.

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Preiss, David. "GEOMETRIC NONLINEAR FUNCTIONAL ANALYSIS, Volume 1 (American Mathematical Society Colloquium Publications 48)." Bulletin of the London Mathematical Society 33, no. 1 (January 2001): 122–25. http://dx.doi.org/10.1112/blms/33.1.122.

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Perevoshchikova, E. N., and A. V. Bychkov. "Освоение будущими учителями математики приемов формирования функциональной математической грамотности учащихся основной школы." Вестник Вятского государственного университета, no. 4(146) (June 2, 2023): 133–40. http://dx.doi.org/10.25730/vsu.7606.22.062.

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According to the Concept of teacher training for the education system for the period up to 2030, the development of a unified approach to the implementation of subject and methodological training of future mathematics teachers aimed at the formation of functional mathematical literacy of students becomes an urgent task. At the same time, the analysis of publications and the practice of preparing students for professional activity showed that procedural issues related to the methodology of forming functional literacy remain insufficiently studied. The search for a solution to the highlighted problem determines the purpose of our research, which consists in describing the procedural component of the methodological preparation of a future mathematics teacher for the formation of functional mathematical literacy of students. In the course of the study, theoretical and empirical research methods were used: analysis, synthesis, generalization, comparison and comparison. The research was based on systematic, activity-based and competence-based approaches. As a result of the study, it was found that the process of methodical preparation of students of mathematics for professional activity should be co-directed with the process of formation of functional mathematical literacy of schoolchildren and built taking into account the motivational and value stages, the stage of formation of knowledge about the totality of actions used in the process of formalization of the real situation and interpretation of the results obtained, the stage of formation of skills to operate with these actions in the process teaching mathematics, the stage of applying methodological knowledge. The conclusion formulated in the article is that in order to achieve this goal, it is necessary to organize the activities of future mathematics teachers to master various methods of forming actions underlying mathematical modeling, to identify the types of tasks and methods of activity necessary for the formation of functional mathematical literacy. The results of the research can be used in the design of work programs in the disciplines of mathematical and methodological cycles, including practical training of students during the practice period. Согласно Концепции подготовки педагогических кадров для системы образования на период до 2030 г. актуальной задачей становится разработка единого подхода к осуществлению предметной и методической подготовки будущих учителей математики, направленной на формирование функциональной математической грамотности учащихся. Вместе с тем анализ публикаций и практики подготовки студентов к профессиональной деятельности показал, что процессуальные вопросы, связанные с методикой формирования функциональной грамотности, остаются недостаточно изученными. Поиск решения выделенной проблемы определяет цель нашего исследования, которая состоит в описании процессуального компонента методической подготовки будущего учителя математики к формированию функциональной математической грамотности учащихся. В ходе исследования использовались теоретические и эмпирические методы исследования: анализ, синтез, обобщение, сравнение и сопоставление. В основу исследования были положены системный, деятельностный и компетентностный подходы. В результате исследования установлено, что процесс методической подготовки студентов-математиков к профессиональной деятельности должен быть сонаправлен с процессом формирования функциональной математической грамотности школьников и построен с учетом мотивационного и ценностного этапов, этапа формирования знаний о совокупности действий, используемых в процессе формализации реальной ситуации и интерпретации полученных результатов, этапа формирования умений оперировать названными действиями в процессе обучения математике, этапа применения методических знаний. Вывод, сформулированный в статье, состоит в том, что для достижения поставленной цели необходимо организовать деятельность будущих учителей математики по освоению различных приемов формирования действий, лежащих в основе математического моделирования, по выделению типов заданий и способов деятельности, необходимых для формирования функциональной математической грамотности. Результаты исследования могут быть использованы при проектировании рабочих программ по дисциплинам математического и методического циклов, включая практическую подготовку студентов в период практики.

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SHIRKOV, DMITRIJ V. "RENORMALIZATION GROUP SYMMETRY AND SOPHUS LIE GROUP ANALYSIS." International Journal of Modern Physics C 06, no. 04 (August 1995): 503–12. http://dx.doi.org/10.1142/s0129183195000356.

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We start with a short discussion of the content of a term Renormalisation Group in modern use. By treating the underlying solution property as a reparametrisation symmetry, we relate it with the self-similarity symmetry well-known in mathematical physics and explain the notion of Functional Self-similarity. Then we formulate a program of constructing a regular approach for discovering RG-type symmetries in different problems of mathematical physics. This approach based upon S. Lie group analysis allows one to analyse a wide class of boundary problems for different type of equations. Several examples are mentioned.

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Shinde, Priya S. "Modeling and Analysis of the Grinding Parameters." Applied Mechanics and Materials 110-116 (October 2011): 2548–53. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.2548.

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Efficient grinding of structural ceramics requires judicious selection of operating parameters to maximize removal rate while controlling surface integrity. Grinding of ceramics is difficult because of its low fracture toughness, making it very sensitive to cracking. In the present work, experiments were carried out to study the effect of wheel parameters such as grain size and grinding parameters like depth of cut and feed rate on the surface roughness and surface damage. The significance of the grinding parameters on the selected responses is evaluated using analysis of variance. Mathematical statistics like “Minitab” is used to analyzed the grinding conditions for maximum material removal, using a multi-objective function model, by imposing surface roughness, surface force and surface damage constraints. The choice of including manufacturer & apposes constraints on the basis of functional requirements of the component for maximizing the production rate is also embedded in the Mathematical statistics. For the verification of present work, the Mathematical statistics results are compared with experimental work.

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Ajmone Marsan, Giulia, Nicola Bellomo, and Massimo Egidi. "Towards a mathematical theory of complex socio-economical systems by functional subsystems representation." Kinetic & Related Models 1, no. 2 (2008): 249–78. http://dx.doi.org/10.3934/krm.2008.1.249.

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Rahimpour, Elaheh, and Taha Samad-Soltani. "Immunoinformatics: A Basic Bibliometric Analysis." ImmunoAnalysis 1, no. 1 (April 17, 2021): 2. http://dx.doi.org/10.34172/ia.2021.02.

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Background: Traditionally, immunologists have been using experimental methods for a long time, which have generated functional, clinical and epidemiological data. So, it is inevitable to develop and apply novel computational approaches to collect, store, analyze, and report the latent knowledge behind these data. Immunoinformatics as a new-emerging field uses computational tools that cover multi dimensions of bioinformatics such as databases management and development definition of both structural and functional signatures and the modeling of predictive algorithms. Recently, with the dramatic growth in research documents publishing, the need for new methodologies to structure and visualize knowledge emerged. Methods: Capability to analyze huge amounts of published items with a detailed level of granularity and report statistical, mathematical and visual knowledge within it, introduced an approach called bibliometrics analysis. According to the best of our knowledge, there isn’t any bibliometrics analysis based on immunoinformatics keyword. So, the aim of current study was to perform a brief and basic bibliometrics analysis on the immunoinformatics publications to report the most influencers on this field by statistical and mathematical methods to identify key authors, titles, keywords and other parameters that extracted from publication’s metadata. Results: Results were summarized in statistical tables and diagrams. It was revealed that the immunoinformatics is a relatively novel field and the time trends showed that the strategic research plans can be directed to expand this field. Conclusion: We can conclude that the future is the age of immunoinformatics for immunologists and related specialties.

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Zhu, Meijun. "Book Review: Functional analysis." Bulletin of the American Mathematical Society 43, no. 01 (July 6, 2005): 123–27. http://dx.doi.org/10.1090/s0273-0979-05-01073-6.

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Wang, Dehua, Xiao-Li Ding, and Juan J. Nieto. "Stability analysis of fractional-order systems with randomly time-varying parameters." Nonlinear Analysis: Modelling and Control 26, no. 3 (May 1, 2021): 440–60. http://dx.doi.org/10.15388/namc.2021.26.23053.

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This paper is concerned with the stability of fractional-order systems with randomly timevarying parameters. Two approaches are provided to check the stability of such systems in mean sense. The first approach is based on suitable Lyapunov functionals to assess the stability, which is of vital importance in the theory of stability. By an example one finds that the stability conditions obtained by the first approach can be tabulated for some special cases. For some complicated linear and nonlinear systems, the stability conditions present computational difficulties. The second alternative approach is based on integral inequalities and ingenious mathematical method. Finally, we also give two examples to demonstrate the feasibility and advantage of the second approach. Compared with the stability conditions obtained by the first approach, the stability conditions obtained by the second one are easily verified by simple computation rather than complicated functional construction. The derived criteria improve the existing related results.

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BENOIT, DAVID, LINGBING HE, CLAUDE LE BRIS, and TONY LELIÈVRE. "MATHEMATICAL ANALYSIS OF A ONE-DIMENSIONAL MODEL FOR AN AGING FLUID." Mathematical Models and Methods in Applied Sciences 23, no. 09 (May 13, 2013): 1561–602. http://dx.doi.org/10.1142/s0218202513500164.

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We study mathematically a system of partial differential equations arising in the modeling of an aging fluid, a particular class of non-Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and investigate the longtime behavior of the solutions.

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Churkin, Alexander, Franziska Totzeck, Rami Zakh, Marina Parr, Tamir Tuller, Dmitrij Frishman, and Danny Barash. "A Mathematical Analysis of RNA Structural Motifs in Viruses." Mathematics 9, no. 6 (March 10, 2021): 585. http://dx.doi.org/10.3390/math9060585.

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RNA stem-loop structures play an important role in almost every step of the viral replication cycle. In this contribution, a mathematical analysis is performed on a large dataset of RNA secondary structure elements in the coding regions of viruses by using topological indices that capture the Laplacian eigenvalues of the associated RNA graph representations and thereby enable structural classification, supplemented by folding energy and mutational robustness. The application of such an analysis for viral RNA structural motifs is described, being able to extract structural categories such as stem-loop structures of different sizes according to the tree-graph representation of the RNA structure, in our attempt to find novel functional motifs. While the analysis is carried on a large dataset of viral RNA structures, it can be applied more generally to other data that involve RNA secondary structures in biological agents.

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Khan, Nadeem, Amjad Ali, Aman Ullah, and Zareen A. Khan. "Mathematical analysis of neurological disorder under fractional order derivative." AIMS Mathematics 8, no. 8 (2023): 18846–65. http://dx.doi.org/10.3934/math.2023959.

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<abstract><p>Multiple sclerosis (MS) is a common neurological disorder that affects the central nervous system (CNS) and can cause lesions that spread over space and time. Our study proposes a mathematical model that illustrates the progression of the disease and its likelihood of recurrence. We use Caputo fractional-order (FO) derivative operators to represent non-negative solutions and to establish a steady-state point and basic reproductive number. We also employ functional analysis to prove the existence of unique solutions and use the Ulam-Hyres (UH) notion to demonstrate the stability of the solution for the proposed model. Furthermore, we conduct numerical simulations using an Euler-type numerical technique to validate our theoretical results. Our findings are presented through graphs that depict various behaviors of the model for different parameter values.</p></abstract>

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Babadjian, Jean-François, and Vincent Millot. "Unilateral gradient flow of the Ambrosio–Tortorelli functional by minimizing movements." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 31, no. 4 (July 2014): 779–822. http://dx.doi.org/10.1016/j.anihpc.2013.07.005.

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Abimannan, Satheesh, and Kumaravelu R. "A Mathematical Model of HMST Model on Malware Static Analysis." International Journal of Information Security and Privacy 13, no. 2 (April 2019): 86–103. http://dx.doi.org/10.4018/ijisp.2019040106.

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Malware is a malicious software that can contaminate communication devices, where information can be lost, encrypting or deleting the sensitive data, altering or hijacking core computing activities and monitoring a user's computer activity without proper authorization. Analyzing the behavior of any new type of malware, that threatens the security of information is the challenging task. Previous studies and research has used static and dynamic based analysis. Althrough there are various methods to analysis the behaviour of the malware, the innovation of new technology lead to undesirable growth of malware. A procedure to analyze the characteristics and its nature is the need of the day. To mitigate this issue, malware specific procedures need to be evolved by analysing its behaviour. In this article, the authors present a heuristic-based malware static analysis testing (HMST) through a six step process including hash verification, PE structure analysis, packer signature analysis, entropy analysis, antivirus check and string analysis. Heuristic-based malware static analysis (MSA) depends on the six characterstics. The six characteristics sequence is quantified mathematially. Hash verification is presented as a dynamic function, PE structure analysis (PESA) as the functional string, Packer Signature (PS) by functional boundedness, Entropy Analysis (EA) with probability, antivirus check (AC) of the discrete lagorthm-bit representation and string analysis (SA) lies with the comutational complexity. Hence, an optimized string is proposed for transmitting securely. CFF Explorer, BinText, PeID, DIE and VirusTotal are used for analyzing the behavior of the samples in this study.

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Майструк, A. Maystruk, Боркин, and V. Borkin. "System Analysis and Modeling of Potentially Hazardous Operating Procedures." Safety in Technosphere 3, no. 3 (July 8, 2014): 3–8. http://dx.doi.org/10.12737/4934.

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The article addresses system analysis and modeling of potentially hazardous operating procedures as ergatic systems. It presents a mathematical model of a potentially hazardous process; thus allows to comprehensively evaluate functional state of human operator and reliability of technical systems.

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Wang, Aiyin, Ls Yong, Weili Zeng, and Yang Wang. "The Optimal Analysis of Default Probability for a Credit Risk Model." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/878306.

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A credit risk mathematical model is investigated. Under regular conditions, a different recovery scheme is proposed, which is an extension of the recovery of treasury value scheme(RTV)with time-continuous liquidation. Assuming that a function depends on the optimal time for the liquidation and the recovery rate, we obtain the functional expression of the risky bond price. When the firm value follows a jump-diffusion process with a Log-exponentially distributed jump, we develop a method to obtain the optimal default probability with time-continuous liquidation.

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Zhu, Linhe, Gui Guan, and Zhengdi Zhang. "Mathematical analysis of information propagation model in complex networks." International Journal of Modern Physics B 34, no. 26 (October 6, 2020): 2050240. http://dx.doi.org/10.1142/s0217979220502409.

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In virtue of identifying the influence of nodes, the spatial distance of rumor propagation is defined with the partition and clustering in the network. Considering the temporal and spatial propagation characteristics of rumors in online social networks, we establish a delayed rumor propagation model based on the graph theory and partial functional differential equations. Firstly, the unique existence and uniform boundedness of the nonnegative solution are explored. Secondly, we discuss the existence of positive equilibrium points sufficiently. Thirdly, stabilities of the rumor-free and rumor-spreading equilibrium points are investigated according to the linearization approach and Lyapunov function. Finally, we perform several numerical simulations to validate theoretical results and show the influence of time delay on rumor propagation. Experimental results further illustrate that taking forceful actions such as increasing the time delay in the rumor-spreading process can control rumor propagation due to the timely effectiveness of the information.

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Tanaka, Yasuhito. "AD-AS Analysis from the Perspective of Functional Finance Theory and MMT." Folia Oeconomica Stetinensia 23, no. 1 (June 1, 2023): 263–83. http://dx.doi.org/10.2478/foli-2023-0014.

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Abstract Research background In the past few years, MMT (Modern Money Theory or Modern Monetary Theory) has been increasingly discussed in Japan as well as in the U.S. However, both in the U.S. and Japan, analysis using mathematics is lacking and analysis using IS-LM and AD-AS analysis methods in macroeconomics is almost non-existent. Purpose We present an AD-AS analysis from the perspective of Functional Finance Theory and MMT (Modern Monetary Theory). Research methodology Graphical analyses with some mathematical analyses. Mathematical analyses include graphic analysis using AD and AS curves and calculations to derive equations representing them based on models of consumer and firm behavior. Results Using an overlapping generations model under monopolistic competition we show the following results by calculations and graphical analyses. 1. The budget deficit (including interest payments on government bonds) equals an increase in the savings of consumers from period to period. This result means that the debt-GDP ratio would not diverge to infinity, but would remain at a finite value whether the interest rate of government bonds is larger or smaller than the growth rate. 2. We need a budget deficit (including interest payments) to maintain full employment without inflation under economic growth. However, if the interest rate of government bonds is larger than the growth rate, we need a budget surplus (excluding interest payments) to maintain full employment without inflation. 3. A return to full employment from a recession can be achieved by implementing the appropriate fiscal policies through increased government spending or tax cuts. 4. Excessive government expenditure or an insufficient tax under full employment induces inflation. Novelty This is probably the first AD-AS analysis done from the standpoint of Functional Finance Theory and MMT.

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Jakubowski, Jacek, and Maciej Wiśniewolski. "Another Look at the Hartman-Watson Distributions." Potential Analysis 53, no. 4 (November 5, 2019): 1269–97. http://dx.doi.org/10.1007/s11118-019-09806-7.

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Abstract The article deals with the Hartman-Watson distributions and presents a new approach to them by investigating a special function u. The function u is strictly related to the distribution of the exponential functional of Brownian motion appearing in the mathematical finance framework. The study of the latter leads to new explicit representations for the function u. One of them is through a new parabolic PDE. Integral relations of convolution type between Hartman-Watson distributions and modified Bessel functions are presented. It turns out that u can be represented as an integral convolution of itself and the modified Bessel function K0. Finally, excursion theory and a subordinator connected to the hyperbolic cosine of Brownian motion are involved in order to obtain yet another representation for u. Possible applications of the resulting explicit formulas are discussed, among others Monte Carlo evaluations of u.

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Martynyuk, A. A. "Matrix-valued functionals approach for stability analysis of functional differential equations." Nonlinear Analysis: Theory, Methods & Applications 56, no. 6 (March 2004): 793–802. http://dx.doi.org/10.1016/j.na.2003.10.016.

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Shen, Jianhua, Zhiguo Luo, and Xinzhi Liu. "Impulsive Stabilization of Functional Differential Equations via Liapunov Functionals." Journal of Mathematical Analysis and Applications 240, no. 1 (December 1999): 1–15. http://dx.doi.org/10.1006/jmaa.1999.6551.

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Cuenya, Héctor H. "A Functional Equation of Bohnemblust and Positive Homogeneous Functionals." Journal of Mathematical Analysis and Applications 246, no. 1 (June 2000): 164–73. http://dx.doi.org/10.1006/jmaa.2000.6775.

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Sansom, Clare. "CCP11 Group Meeting—Towards the Functional Analysis of Microarrays." Comparative and Functional Genomics 3, no. 5 (2002): 451–54. http://dx.doi.org/10.1002/cfg.201.

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The CCP11 project [2] aims to foster bioinformatics in the UK through conferences, workshops and the provision of Web resources. In March 2002, CCP11 held a meeting in Manchester, UK, on the functional analysis of microarrays. This was part of Manchester BioinformaticsWeek—three consecutive short bioinformatics meetings held in the attractive setting of the Chancellor's Conference Centre at the University of Manchester. The other meetings in the series were a workshop on ontologies and the 12th Annual MASAMB (Mathematical and Statistical Aspects of Molecular Biology) Conference. Many delegates were able to attend more than one meeting, which led to a useful cross-fertilization of ideas across the bioinformatics community. The CCP11 meeting shared with MASAMB a strong emphasis on the statistical analysis and interpretation of data—most often image intensity data.

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Journal articles on the topic 'Mathematical analysis - functional analysis'

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