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Journal articles on the topic 'Mathematical formulation of the problem'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Ralston, Anthony, and Stephen S. Willoughby. "Realistic Problem Formulation and Problem Solving." Mathematics Teacher 90, no. 6 (1997): 430–34. http://dx.doi.org/10.5951/mt.90.6.0430.

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Moreover, we seldom introduce students to problems that lend themselves to long-term, in-depth analysis at different levels of intellectual accomplishment. In this article, we discuss such a problem, one that allows significant mathematical endeavor beginning with second graders and extending all the way through college undergraduates.

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2

Lukkassen, Dag, Annette Meidell, and Peter Wall. "Mathematical analysis and homogenization of the torsion problem." Journal of Function Spaces and Applications 6, no. 2 (2008): 155–76. http://dx.doi.org/10.1155/2008/637035.

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In this paper we address the limitations of the classical formulation of the torsion problem and give a self-contained survey of the function spaces and formulations that are more suitable for analysing the torsional behavior of composite materials. We also prove some homogenization results for the torsion problem in both the periodic and stochastic setting. Our theoretical results are illustrated by numerical examples.

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3

Kulian, V. R., and O. O. Yunkova. "Mathetical problem of banking assets diversification." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2021): 85–88. http://dx.doi.org/10.17721/1812-5409.2021/1.11.

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In article we consider a problem of optimal investment strategy by a commercial bank building. This task is actual and the development of a procedure to solve it can help in making investment banking decisions. The general formulation of the problem consists of two criteria. The first one is to maximize the expected return, and the second is to minimize the risk of the investment transaction. Mathematical formulation of the problem is considered as a problem of nonlinear programming under constraints. The procedure for solving such a two-criteria optimization problem allows to obtain many solu

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Stupina, A. A., A. A. Shigina, and A. O. Shigin. "Mathematical formulation of technological processes optimization problem." IOP Conference Series: Materials Science and Engineering 94 (October 12, 2015): 012001. http://dx.doi.org/10.1088/1757-899x/94/1/012001.

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Windras Mara, Setyo Tri, Achmad Pratama Rifai, and Rachmadi Norcahyo. "ON DIFFERENT FORMULATIONS FOR THE MULTI-PERIOD VEHICLE ROUTING PROBLEM WITH SIMULTANEOUS PICKUP AND DELIVERY." ASEAN Engineering Journal 13, no. 1 (2023): 27–39. http://dx.doi.org/10.11113/aej.v13.17888.

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In this paper, we extend the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) with a consideration of multiple planning horizons. We propose three alternative mathematical formulations for Periodic-VRPSPD (P-VRPSPD) based on the available formulations for VRPSPD in the literatures, namely the three-index commodity flow formulation, four-index commodity flow formulation, and three-index vehicle flow formulation. We perform comparison analysis by conducting extensive numerical experiments on a set of instances with various complexities in order to evaluate the performance o

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Ray, Gautam. "Computer Aided Problem Based Learning in Engineering Dynamics." Applied Mechanics and Materials 704 (December 2014): 148–53. http://dx.doi.org/10.4028/www.scientific.net/amm.704.148.

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In this paper we demonstrated the use of Problem Based Learning (PBL) in undergraduate Engineering Dynamics. In PBL, the students enhance their learning by solving problems. In some engineering courses, often the students are not able to explore real life and somewhat complex problems due to inability to handle the mathematical rigor. By using software such as Mathematica® we created modules for some Engineering Dynamics problems. These modules allowed students to concentrate on the formulation and “Physics” and interpretation of the problems of the rather than the rigors of mathematical solut

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Cojocaru, Mariana Chivu, and Andaluzia Matei. "WEAK SOLUTIONS VIA TWO-FIELD LAGRANGE MULTIPLIERS FOR BOUNDARY VALUE PROBLEMS IN MATHEMATICAL PHYSICS." Mathematical Modelling and Analysis 27, no. 4 (2022): 561–72. http://dx.doi.org/10.3846/mma.2022.15827.

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A new variational approach for a boundary value problem in mathematical physics is proposed. By considering two-field Lagrange multipliers, we deliver a variational formulation consisting of a mixed variational problem which is equivalent with a saddle point problem. Thus, the unique solvability of the weak formulation we propose is governed by the saddle point theory. Alternative variational formulations and some of their connections are also discussed.

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Verwer, Sicco, and Yingqian Zhang. "Learning Optimal Classification Trees Using a Binary Linear Program Formulation." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1625–32. http://dx.doi.org/10.1609/aaai.v33i01.33011624.

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We provide a new formulation for the problem of learning the optimal classification tree of a given depth as a binary linear program. A limitation of previously proposed Mathematical Optimization formulations is that they create constraints and variables for every row in the training data. As a result, the running time of the existing Integer Linear programming (ILP) formulations increases dramatically with the size of data. In our new binary formulation, we aim to circumvent this problem by making the formulation size largely independent from the training data size. We show experimentally tha

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Kucherov, B. A. "Formulation of the problem of ground stations scheduling under resource restrictions." Informacionno-technologicheskij vestnik, no. 4 (December 30, 2018): 32–43. http://dx.doi.org/10.21499/2409-1650-2018-4-32-43.

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The tasks solving during ground stations scheduling to ensure satellites control are considered. The hierarchy of scheduling problems is analyzed. Ground stations scheduling problem is compared with general scheduling problem. Various approaches to develop schedule of ground stations are analyzed. Mathematical formulation of ground stations scheduling problem is presented. Research of possible ways to increase efficiency and quality of ground stations scheduling was performed using presented mathematical formulation of mentioned problem.

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Buzaeva, E. A., D. A. Evsevichev, and O. V. Maksimova. "Formulation of the modern indicator devices modelling problem." Journal of Physics: Conference Series 2056, no. 1 (2021): 012053. http://dx.doi.org/10.1088/1742-6596/2056/1/012053.

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Abstract This work is dedicated to study of the structural characteristics and parameters in advanced electroluminescent structures. The important problems in this area are the high complexity and the slowness of the design calculation processes. The problem can be solved by developing a mathematical model of the system based on equivalent circuits. First step in developing a mathematical model is formulation.

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Vinayak Kishan Nirmale. "A Mathematical Problem Formulation Based on Number Theory." Communications on Applied Nonlinear Analysis 32, no. 3 (2024): 592–604. http://dx.doi.org/10.52783/cana.v32.2063.

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A branch of mathematics known as number theory is primarily concerned with the study of whole numbers. In that sense, number theory is used less in design than it is in analytics, computation, and other fields. Its inability to be used directly in any application was the issue. However, when combined with the computing power of modern PCs, number theory provides intriguing solutions to real-world issues. It serves a variety of functions in several industries, including computing, numerical analysis, and cryptography. The study of whole numbers is the primary focus of number theory. The fundame

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Łydżba, Dariusz, Adrian Różański, and Damian Stefaniuk. "Equivalent microstructure problem: Mathematical formulation and numerical solution." International Journal of Engineering Science 123 (February 2018): 20–35. http://dx.doi.org/10.1016/j.ijengsci.2017.11.007.

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13

Zeng, Yong. "ENVIRONMENT-BASED FORMULATION OF DESIGN PROBLEM." Journal of Integrated Design and Process Science: Transactions of the SDPS, Official Journal of the Society for Design and Process Science 8, no. 4 (2004): 45–63. http://dx.doi.org/10.3233/jid-2004-8404.

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This paper proposes a formal definition of design problem using the axiomatic theory of design modeling. Based on the concept of product system and an informal description of design problem, a design problem is formulated into three parts: environment, structural requirements, as well as performance requirements. On the basis of this formulation, both structural requirements and performance requirements are related to product environment, which is divided into natural, built, and human environments. As a result, product environment is identified as the source of product requirements. An enviro

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Nwulu, Nnamdi. "Combined Heat and Power Dynamic Economic Emissions Dispatch with Valve Point Effects and Incentive Based Demand Response Programs." Computation 8, no. 4 (2020): 101. http://dx.doi.org/10.3390/computation8040101.

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In this paper, the Combined Heat and Power Dynamic Economic Emissions Dispatch (CHPDEED) problem formulation is considered. This problem is a complicated nonlinear mathematical formulation with multiple, conflicting objective functions. The aim of this mathematical problem is to obtain the optimal quantities of heat and power output for the committed generating units which includes power and heat only units. Heat and load demand are expected to be satisfied throughout the total dispatch interval. In this paper, Valve Point effects are considered in the fuel cost function of the units which lea

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Ye, Jun Yao, Ke Ning Liu, and Ying Lian Wang. "Research on Ceramic Manufacturing for Creating and Solving Ceramic Formulations Model." Applied Mechanics and Materials 540 (April 2014): 484–87. http://dx.doi.org/10.4028/www.scientific.net/amm.540.484.

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This paper describes some theories on basic designing optimization problem, and then establishes the multi-objective optimization mathematical model of ceramic blank. It transforms the ceramic formulation problem in real-world into a mathematical algorithm problem. It also provides a good theoretical basis for a computer to process ceramic formulation. Finally, we transforms the ceramic blank problem from mathematical problem into matrix equation, solving the quality percentage of each ingredient in the formulation program, which has achieved some good results to a certain extent, but still re

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Chwatal, Andreas M., and Günther R. Raidl. "Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques." Advances in Operations Research 2011 (2011): 1–38. http://dx.doi.org/10.1155/2011/143732.

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We present exact mixed integer programming approaches including branch-and-cut and branch-and-cut-and-price for the minimum label spanning tree problem as well as a variant of it having multiple labels assigned to each edge. We compare formulations based on network flows and directed connectivity cuts. Further, we show how to use odd-hole inequalities and additional inequalities to strengthen the formulation. Label variables can be added dynamically to the model in the pricing step. Primal heuristics are incorporated into the framework to speed up the overall solution process. After a polyhedr

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Jiang, Yong Jun. "Statistical Tolerance Analysis Based on Constraint Satisfaction Problems and Monte Carlo Simulation." Advanced Materials Research 433-440 (January 2012): 6616–21. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.6616.

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This paper deals with the mathematical formulation of tolerance analysis. The mathematical formulation presented simulates the influences of geometrical deviations on the geometrical behavior of the mechanism, and integrates the quantifier notion. We propose a mathematical formulation of tolerance analysis which simulates the influences of geometrical deviations on the geometrical behavior of the mechanism, and integrates the quantifier notion. To compute this mathematical formulation, two approaches based on Quantified Constraint Satisfaction Problem solvers and Monte Carlo simulation are pro

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18

Heydari, Ahmad, Ali Mahmoodirad, and Sadegh Niroomand. "An Entropy-based Mathematical Formulation for Straight Assembly Line Balancing Problem." International Journal of Strategic Decision Sciences 7, no. 2 (2016): 57–68. http://dx.doi.org/10.4018/ijsds.2016040104.

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This paper focuses on formulating a typical simple assembly line balancing problem. A new objective function based on a nonlinear entropy function is considered for the simple assembly line balancing problem for the first time. This objective function force the stations to have more similar total task processing time, so that the workers of the stations will have similar work load. Using a bounded variable approach, the nonlinear objective function is converted to an approximated linear objective function. Finally, efficiency of the linearized formulation of the entropy-based assembly line bal

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Stodola, Petr. "Unmanned Surveillance Problem: Mathematical Formulation, Solution Algorithms, and Experiments." Military Operations Research 25, no. 2 (2000): 31–47. http://dx.doi.org/10.5711/1082598325231.

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20

Zhao, LiJin, and Liang Huang. "A Mathematical Programming Formulation of Disjoint Dominating Sets Problem." Journal of Computational and Theoretical Nanoscience 13, no. 11 (2016): 8760–64. http://dx.doi.org/10.1166/jctn.2016.6037.

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21

Zehendner, Elisabeth, Marco Caserta, Dominique Feillet, Silvia Schwarze, and Stefan Voß. "An improved mathematical formulation for the blocks relocation problem." European Journal of Operational Research 245, no. 2 (2015): 415–22. http://dx.doi.org/10.1016/j.ejor.2015.03.032.

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22

Wheeler, Lewis T. "Stress Minimum Forms for Elastic Solids." Applied Mechanics Reviews 45, no. 1 (1992): 1–12. http://dx.doi.org/10.1115/1.3119743.

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This article concerns the problem of determining shapes of minimum stress concentration. Special emphasis is placed upon the mathematically precise formulation of these problems and upon the study of cases in which the optimum shape can be found in a highly explicit form. For all the cases discussed, a mathematical proof of the optimality is given.

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23

Ambrosino, Daniela, and Carmine Cerrone. "The Cost-Balanced Path Problem: A Mathematical Formulation and Complexity Analysis." Mathematics 10, no. 5 (2022): 804. http://dx.doi.org/10.3390/math10050804.

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This paper introduces a new variant of the Shortest Path Problem (SPP) called the Cost-Balanced Path Problem (CBPP). Various real problems can either be modeled as BCPP or include BCPP as a sub-problem. We prove several properties related to the complexity of the CBPP problem. In particular, we demonstrate that the problem is NP-hard in its general version, but it becomes solvable in polynomial time in a specific family of instances. Moreover, a mathematical formulation of the CBPP, as a mixed-integer programming model, is proposed, and some additional constraints for modeling real requirement

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Jarmolajeva, Ela, and Juozas Atkočiūnas. "SHAKEDOWN LOADING OPTIMIZATION UNDER CONSTRAINED RESIDUAL DISPLACEMENTS—FORMULATION AND SOLUTION FOR CIRCULAR PLATES." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 8, no. 1 (2002): 54–67. http://dx.doi.org/10.3846/13923730.2002.10531250.

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The adapted plate load optimization problem is formulated applying the non-linear mathematical programming methods. The load variation bounds satisfying the optimality criterion in concert with the strength and stiffness requirements are to be identified. The stiffness constraints are realized via residual displacements. The dual mathematical programming problems cannot be applied directly when determining actual stress and strain fields of plate: the strained state depends upon the loading history. Thus the load optimization problem at shakedown is to be stated as a couple of problems solved

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25

Kimball, Robert L. "Activities: Make Your Own Problems- and Then Solve Them." Mathematics Teacher 84, no. 8 (1991): 647–55. http://dx.doi.org/10.5951/mt.84.8.0647.

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The mathematics curriculum should include the refinement and extension of methods of mathematical problem solving so that all students can recognize and formulate problems from situations within and outside mathematics. (NCTM 1989, 137)The mathematics curriculum should include the continued development of language and symbolism to communicate mathematical ideas so that all students can express mathematical ideas ora lly and in writing. (NCTM 1989, 140)The teacher of mathematics should pose tasks that … call for problem formulation, problem solving, and mathematical reasoning [and) promote comm

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26

Kalanta, Stanislovas. "DUAL MATHEMATICAL MODELS OF LIMIT LOAD ANALYSIS PROBLEMS OF STRUCTURES BY MIXED FINITE ELEMENTS." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 3, no. 10 (1997): 43–51. http://dx.doi.org/10.3846/13921525.1997.10531683.

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The general and discrete dual mathematical models of the limit load analysis and optimization problems of rigid-plastic body are created in the article. The discrete models are formulated by mixed finite elements and presented in terms of kinematic and static formulation. In these models the velocity of the energy dissipation is estimated not only within the volume of finite elements, but also at the plastic surfaces between elements, where the discontinuities of displacement velocities functions appear. The theory of plastic flow, the theory of duality and mathematical programming are applied

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27

Bevers, Michael. "A chance constraint estimation approach to optimizing resource management under uncertainty." Canadian Journal of Forest Research 37, no. 11 (2007): 2270–80. http://dx.doi.org/10.1139/x07-076.

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Chance-constrained optimization is an important method for managing risk arising from random variations in natural resource systems, but the probabilistic formulations often pose mathematical programming problems that cannot be solved with exact methods. A heuristic estimation method for these problems is presented that combines a formulation for order statistic observations with the sample average approximation method as a substitute for chance constraints. The estimation method was tested on two problems, a small fire organization budgeting problem for which exact solutions are known and a m

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Kalanta, S. "DUAL MATHEMATICAL MODELS OF ELASTOPLASTIC STRUCTURES ANALYSIS PROBLEM ESTIMATING DISCONTINUITY OF DISPLACEMENTS." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 1, no. 3 (1995): 5–29. http://dx.doi.org/10.3846/13921525.1995.10531517.

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A problem of ideal elastoplastic structures stress-strain field determination is considered in the article. The general dual mathematical models (static and kinematic formulation) of analysis problem is derived on the basis of the extremal energy principles and theory of duality. The different external effects are estimated, namely: load, initial strains, prestressing and support settlements. At first, on the basis of the complementary energy principle the mathematical model of static formulation of the problem is made. The kinematic formulation of the problem is obtained on the basis of Lagra

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Sodré, Gleison De Jesus Marinho, Raquel Soares do Rêgo Ferreira, and Renato Borges Guerra. "Reverse Mathematical Modelling." Acta Scientiae 24, no. 6 (2022): 552–83. http://dx.doi.org/10.17648/acta.scientiae.7372.

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Background: Research in mathematics education shows that mathematical modelling is a practice that seeks to “translate” problem situations into possible mathematical models without, however, explaining the complexity involved in the reverse formulation, starting from the mathematical model to delimit the type of situation. Objective: To highlight the problem of reverse mathematical modelling, in the sense of a reverse formulation that goes from the mathematical model to the situation. Design: For this, a course of study and research was carried out guided by the investigative cycle of mathemat

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Yengkhom Satyendra Singh. "Solution of the Forward Problem of ECG using Radial basis Function Network." Tuijin Jishu/Journal of Propulsion Technology 45, no. 04 (2024): 751–57. http://dx.doi.org/10.52783/tjjpt.v45.i04.8170.

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ECG inverse problem is a mathematical formulation of cardiac electrical activity on the heart surface that can be solved to determine the electric potential on the heart surface. In this paper, a forward problem to ECG will be formulated using a mathematical formulation similar to the ECG forward problem. The forward problem will be solved using radial basis collocation techniques by taking different discretization points of N=9 and N=25 points to predict the solution u(x,t) to the forward problem.

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31

Kryvyi, S., and H. Hoherchak. "The Mathematical Safe Problem and Its Solution (Part 1)." Cybernetics and Computer Technologies, no. 4 (December 31, 2020): 15–38. http://dx.doi.org/10.34229/2707-451x.20.4.2.

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Introduction. The problem of the mathematical safe arises in the theory of computer games and cryptographic applications. The article considers the formulation of the mathematical safe problem and the approach to its solution using systems of linear equations in finite rings and fields. The purpose of the article is to formulate a mathematical model of the mathematical safe problem and its reduction to systems of linear equations in different domains; to consider solving the corresponding systems in finite rings and fields; to consider the principles of constructing extensions of residue field

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32

Gayraud, Fabrice, Laurent Deroussi, Nathalie Grangeon, and Sylvie Norre. "A New Mathematical Formulation for the Home Health Care Problem." Procedia Technology 9 (2013): 1041–47. http://dx.doi.org/10.1016/j.protcy.2013.12.116.

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Gan, Li Ping, and Will Recker. "A mathematical programming formulation of the household activity rescheduling problem." Transportation Research Part B: Methodological 42, no. 6 (2008): 571–606. http://dx.doi.org/10.1016/j.trb.2007.11.004.

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Raz, Tzvi, and Nancy A. Botten. "The knowledge base partitioning problem: Mathematical formulation and heuristic clustering." Data & Knowledge Engineering 8, no. 4 (1992): 329–37. http://dx.doi.org/10.1016/0169-023x(92)90045-d.

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Stanimirović, Predrag S., and Artem Stupin. "Dynamic programming in package Mathematica." ITM Web of Conferences 72 (2025): 01001. https://doi.org/10.1051/itmconf/20257201001.

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Dynamic programming (DP) is a powerful algorithmic technique for solving optimization problems by breaking them down into simpler subproblems. This paper presents an implementation of DP algorithms for two classic optimization problems: the Knapsack problem and the Traveling Salesman Problem (TSP). The solutions are developed and demonstrated using the Mathematica® programming language. For the Knapsack problem, we present two variants: with and without item repetition. The paper describes the mathematical formulation of each variant and provides detailed Mathematica code for their implementat

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Vaquero, Álvaro F., and Juan Córcoles. "Convex Formulations for Antenna Array Pattern Optimization Through Linear, Quadratic, and Second-Order Cone Programming." Mathematics 13, no. 11 (2025): 1796. https://doi.org/10.3390/math13111796.

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This work presents a comprehensive study on formulations for the radiation pattern design of antenna arrays through convex optimization techniques, with a focus on linear, quadratic, and second-order cone programming. The proposed approaches heavily rely on the construction of Hermitian forms to systematically build convex optimization problems for synthesizing desired beam patterns while including practical constraints such as sidelobe levels (SLLs), maximum directivity, and null placement. By formulating the radiation pattern synthesis problem through a convex formulation, global optimality

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Waskitoningtyas, Rahayu Sri. "Mathematical Learning with Metacognitive Ability Based on Problems in Solving the Source of Mathematical Stories in SMP Patra Dharma 2 Balikpapan." Variabel 1, no. 1 (2018): 1. http://dx.doi.org/10.26737/var.v1i1.511.

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<em>This study aims to describe the learning of mathematics with metacognitive ability based on problem solving in solving mathematics story problem in SMP Patra Dharma 2 Balikpapan. The type of this research is qualitative research, while the sampling technique is purposive sample. The results showed that through solving problems in solving mathematical problems, (1) learners will be trained to always involve metacognitive skills from the beginning of solving the problem of mathematics to the end of the form of formulation of answers and evaluate the results of work, (2) learners who ha

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Khmelnik, Solomon. "A new formulation of the three-body problem." Papers of Independent Authors, 2025, 64 64, no. 1 (2025): 13–22. https://doi.org/10.5281/zenodo.14761190.

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It is noted that the existing solution to the three-body problem establishes the chaotic nature of this motion. It is proposed that the mathematical formulation of this problem be changed, which will allow for the finding of unambiguous solutions. The results of solving a simple three-body problem found by a new method are given. The author is looking for proposals for cooperation

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Kalanta, S. "MIXED AND COMPATIBLE FINITE ELEMENTS IN THE ANALYSIS PROBLEM OF ELASTOPLASTIC STRUCTURES." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 2, no. 5 (1996): 29–43. http://dx.doi.org/10.3846/13921525.1996.10531546.

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A problem of ideal elastoplastic structures stress-strain field determination is considered The dual general and discrete mathematical models of analysis problem are made on the basis of the extremal energy principles and finite element method. In these models the possible discontinuity of displacements and the dissipation of energy in the place of those discontinuities, also the different external effects (load, initial strains and support settlements) are estimated. At first, on the basis of the mixed functional and mixed finite elements the discrete expressions of fundamental relationships

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40

Carrión, Miguel, Rafael Zárate-Miñano, and Ruth Domínguez. "A Practical Formulation for Ex-Ante Scheduling of Energy and Reserve in Renewable-Dominated Power Systems: Case Study of the Iberian Peninsula." Energies 11, no. 8 (2018): 1939. http://dx.doi.org/10.3390/en11081939.

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Scheduling energy and reserve in power systems with a large number of intermittent units is a challenging problem. Traditionally, the reserve requirements are assigned after clearing the day-ahead energy market using ad hoc rules or solving computationally intense mathematical programming problems to co-optimize energy and reserve. While the former approach often leads to costly oversized reserve provisions, the computational time required by the latter makes it generally incompatible with the daily power system operational practices. This paper proposes an alternative deterministic formulatio

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41

Hamidat, A., and A. Aissaoui. "A QUASISTATIC FRICTIONAL CONTACT PROBLEM WITH NORMAL DAMPED RESPONSE FOR THERMO-ELECTRO-ELASTIC-VISCOPLASTIC BODIES." Advances in Mathematics: Scientific Journal 10, no. 12 (2021): 3549–68. http://dx.doi.org/10.37418/amsj.10.12.3.

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We consider a mathematical problem for quasistatic contact between a thermo-electro--elastic-viscoplastic body and an obstacle. The contact is modeled by a general normal damped response condition with friction law and heat exchange. We present a variational formulation of the problem and prove the existence and uniqueness of the weak solution. The proof is based on the formulation of four intermediate problems for the displacement field, the electric potential field and the temperature field, respectively. We prove the unique solvability of the intermediate problems, then we construct a contr

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Dewynne, J. N., S. D. Howison, I. Rupf, and P. Wilmott. "Some mathematical results in the pricing of American options." European Journal of Applied Mathematics 4, no. 4 (1993): 381–98. http://dx.doi.org/10.1017/s0956792500001194.

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We examine the Black–Scholes partial differential equation for the pricing of a traded option (an American call option on an asset paying a continuous dividend) and make comparisons with other well known free boundary diffusion problems, such as the oxygen consumption problem. The pricing of American options can be viewed as a free boundary problem and is, therefore, inherently nonlinear. We consider the short and long time behaviour of the free boundary, present analytic results for the option value in such limits, and consider the formulation of the problem as a variational inequality, and i

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Kadirov, M.Y. "ENGINEERING FORMULATION AND MATHEMATICAL FORMULATION OF THE PROBLEM OF ENERGY EQUIVALENCE OF WATER SUPPLY SYSTEMS." Educational Research in Universal Sciences 1, no. 7 (2023): 673–80. https://doi.org/10.5281/zenodo.7523658.

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One of the main circulations of today’s water supply system is the emergence of various circulations in the long-term maintenance of the network, the system allows for shortcomings in the calculation of the volume and the rapid growth of the population, and as a result of this, the pipes lead to rapid failure. Given the fact that the master’s thesis comes from these circulations and the rapid wear of the pipes, it is aimed at calculating the system and solving the problems in the design of this system with the most optimal one. Due to these circulations in the water supply, the way

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Cataldo-Díaz, Cristian, Rodrigo Linfati, and John Willmer Escobar. "Mathematical Model for the Electric Vehicle Routing Problem Considering the State of Charge of the Batteries." Sustainability 14, no. 3 (2022): 1645. http://dx.doi.org/10.3390/su14031645.

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In recent decades, scientific interest has grown in tackling the vehicle routing problem with a sustainable approach (Green VRP). There are numerous studies in the literature addressing environmental problems from the point of view of efficient planning that allows visualizing the benefits associated with the use of the new technologies in electric vehicles. This paper focuses on the electric vehicle routing problem and considers the batteries’ state of charge (SoC). The problem considers a set of customers, where each one has a specific demand and a time window. Deliveries are performed throu

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Silver, Edward A., and Kwame Yankson. "Book Review: Roots and Sprouts: Cultivating Research on Mathematical Problem Posing." Journal for Research in Mathematics Education 48, no. 1 (2017): 111–16. http://dx.doi.org/10.5951/jresematheduc.48.1.0111.

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The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science. (Einstein & Infeld, 1938, p. 95)

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CSÖNDES, TIBOR, and BALÁZS KOTNYEK. "GREEDY ALGORITHMS FOR THE TEST SELECTION PROBLEM IN PROTOCOL CONFORMANCE TESTING." Journal of Circuits, Systems and Computers 11, no. 03 (2002): 273–81. http://dx.doi.org/10.1142/s0218126602000446.

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This paper presents a mathematical model for the test selection problem in protocol conformance testing, the goal of which is to select a suitable test set from a given test suite. The problem is described together with its mathematical formulation including two optimization problems and four different models for the coverage. The test selection problem is shown to be NP-hard. The Integer Programming transformation of the problems is also discussed. We propose greedy algorithms for the selection, which perform much better than the existing methods and can provide very good solutions as experim

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Stark, Sebastian. "A Systematic Approach to Standard Dissipative Continua." Axioms 12, no. 3 (2023): 267. http://dx.doi.org/10.3390/axioms12030267.

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Many isothermal dissipative continuum problems can be formulated in a variational setting using the concept of “standard dissipative continua”. A major advantage of this approach is that complex problems can be cast into a compact, thermodynamically consistent formulation based on a single space–time continuous functional together with a corresponding variational principle. Formulating the problem in terms of a functional provides an immediate avenue for performing spatial and temporal discretization, which are the prerequisites for a numerical solution. Within the present contribution, a nove

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DUMONT, S., and N. IGBIDA. "On a dual formulation for the growing sandpile problem." European Journal of Applied Mathematics 20, no. 2 (2009): 169–85. http://dx.doi.org/10.1017/s0956792508007754.

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In this paper, we are interested in the mathematical and numerical study of the Prigozhin model for a growing sandpile. Based on implicit Euler discretization in time, we give a simple improvement of theoretical and numerical analyses of the dual formulation for the problem. By using this model, we also give some application to the Monge–Kantorovich problem for optimal mass transportation.

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Abdou, Idriss, and Mohamed Tkiouat. "Unit Commitment Problem in Electrical Power System: A Literature Review." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 3 (2018): 1357. http://dx.doi.org/10.11591/ijece.v8i3.pp1357-1372.

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Unit commitment (UC) is a popular problem in electric power system that aims at minimizing the total cost of power generation in a specific period, by defining an adequate scheduling of the generating units. The UC solution must respect many operational constraints. In the past half century, there was several researches treated the UC problem. Many works have proposed new formulations to the UC problem, others have offered several methodologies and techniques to solve the problem. This paper gives a literature review of UC problem, its mathematical formulation, methods for solving it and Diffe

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Idriss, Abdou, and Tkiouat Mohamed. "Unit Commitment Problem in Electrical Power System: A Literature Review." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 3 (2018): 1357–72. https://doi.org/10.11591/ijece.v8i3.pp1357-1372.

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Unit commitment (UC) is a popular problem in electric power system that aims at minimizing the total cost of power generation in a specific period, by defining an adequate scheduling of the generating units. The UC solution must respect many operational constraints. In the past half century, there was several researches treated the UC problem. Many works have proposed new formulations to the UC problem, others have offered several methodologies and techniques to solve the problem. This paper gives a literature review of UC problem, its mathematical formulation, methods for solving it and Diffe

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