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Journal articles on the topic 'Multiple solution'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Casari, Stefano. "Multiple Display Solution." Industrial Vehicle Technology International 27, no. 1 (2019): 157. http://dx.doi.org/10.12968/s1471-115x(23)70456-x.

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INDUSTRIAL VEHICLE OEMs CAN STREAMLINE MACHINE DESIGNS BY INSTALLING A SINGLE COMPUTER THAT IS ABLE TO HANDLE MULTIDISPLAY SYSTEMS, INCLUDING 360° SURROUND VIEW, ON A CHOICE OF TWO OPERATING PLATFORMS

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Karakaya, G., and M. Köksalan. "Evaluating solutions and solution sets under multiple objectives." European Journal of Operational Research 294, no. 1 (2021): 16–28. http://dx.doi.org/10.1016/j.ejor.2021.01.021.

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3

Koutitas, G., and C. Tzaras. "Multiple cylinder UTD solution." Electronics Letters 41, no. 9 (2005): 515. http://dx.doi.org/10.1049/el:20058308.

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Younas, Waqar, Gauhar Ali, Naveed Ahmad, et al. "Improving Convergence Speed of Bat Algorithm Using Multiple Pulse Emissions along Multiple Directions." Sensors 22, no. 23 (2022): 9513. http://dx.doi.org/10.3390/s22239513.

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Metaheuristic algorithms are effectively used in searching some optical solution space. for optical solution. It is basically the type of local search generalization that can provide useful solutions for issues related to optimization. Several benefits are associated with this type of algorithms due to that such algorithms can be better to solve many issues in an effective way. To provide fast and accurate solutions to huge range of complex issues is one main benefit metaheuristic algorithms. Some metaheuristic algorithms are effectively used to classify the problems and BAT Algorithm (BA) is

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ZHU, K., X. H. MO, C. Z. YUAN, and P. WANG. "A MATHEMATICAL REVIEW ON THE MULTIPLE-SOLUTION PROBLEM." International Journal of Modern Physics A 26, no. 25 (2011): 4511–20. http://dx.doi.org/10.1142/s0217751x11054589.

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The recent multiple-solution problem in extracting physics information from a fit to the experimental data in high energy physics is reviewed from a mathematical viewpoint. All these multiple solutions were previously found via a fit process, while in this paper we prove that if the sum of two coherent Breit–Wigner functions is used to fit the measured distribution, there should be two and only two nontrivial solutions, and they are related to each other by analytical formulae. For real experimental measurements in more complicated situations, we also provide a numerical method to derive the o

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Soleimani–Damaneh, Majid, and Moslem Zamani. "On compromise solutions in multiple objective programming." RAIRO - Operations Research 52, no. 2 (2018): 383–90. http://dx.doi.org/10.1051/ro/2017071.

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Compromise solutions, as feasible points as close as possible to the ideal (utopia) point, are important solutions in multiple objective programming. It is known in the literature that each compromise solution is a properly efficient solution if the sum of the image set and conical ordering cone is closed. In this paper, we prove the same result in a general setting without any assumption.

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Lin, Huei-li. "Multiple Solutions of Quasilinear Elliptic Equations in." International Journal of Differential Equations 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/673526.

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Assume that is a positive continuous function in and satisfies some suitable conditions. We prove that the quasilinear elliptic equation in admits at least two solutions in (one is a positive ground-state solution and the other is a sign-changing solution).

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YUAN, C. Z., X. H. MO, and P. WANG. "MULTIPLE SOLUTIONS IN EXTRACTING PHYSICS INFORMATION FROM EXPERIMENTAL DATA." International Journal of Modern Physics A 25, no. 32 (2010): 5963–72. http://dx.doi.org/10.1142/s0217751x10051153.

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Multiple solutions exist in many experimental situations where several interfering amplitudes are summed to fit experimentally measured distributions, such as cross sections, mass spectra, and/or angular distributions. We show a few examples where multiple solutions are found, but only one solution is reported in publications. Since there is no standard rule for choosing one among the solutions as the physics one, we propose a simple rule that agrees with what has been adopted in previous literature: the solution corresponding to the minimal magnitudes of the amplitudes must be the physical so

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Kim, Ki Sung, Kyung Su Kim, and Ki Sup Hong. "Grillage Optimization with Multiple Objectives." Key Engineering Materials 306-308 (March 2006): 517–22. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.517.

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The structural design problems are acknowledged to be commonly multicriteria in nature. The various multicriteria optimization methods are reviewed and the most efficient and easy-to-use Pareto optimal solution methods are applied to structural optimization of grillages under lateral uniform load. The result of the study shows that Pareto optimal solution methods can easily be applied to structural optimization with multiple objectives, and the designer can have a choice from those Pareto optimal solutions to meet an appropriate design environment.

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10

Berezin, Alexander A. "Multiple Submissions: An Abstract Solution." Physics Today 41, no. 1 (1988): 128. http://dx.doi.org/10.1063/1.2811305.

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11

Jackson, Sophie E. "The Solution to Multiple Structures." Structure 16, no. 5 (2008): 659–61. http://dx.doi.org/10.1016/j.str.2008.04.004.

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WANG, PEI. "REFERENCE CLASSES AND MULTIPLE INHERITANCES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 03, no. 01 (1995): 79–91. http://dx.doi.org/10.1142/s0218488595000086.

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The reference class problem in probability theory and the multiple inheritances (extensions) problem in non-monotonic logics are special cases of conflicting beliefs. One popular solution accepted in the two domains is the specificity principle. By analyzing an example, several factors beyond specificity are found to be relevant to the priority of a reference class. A new approach, Non-Axiomatic Reasoning System (NARS), is discussed, where these factors are all taken into account. It is argued that the solution provided by NARS is better than the solutions provided by probability theory and no

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13

Troy, William C. "Multiple solutions of a nonlinear boundary value problem." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 113, no. 3-4 (1989): 191–209. http://dx.doi.org/10.1017/s0308210500024069.

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SynopsisWe consider a system of nonlinear differential equations derived from a model for the self-trapping of light. We prove that there is a parameter range for which there is a fundamental mode solution. Further, given any positive integer N, there also exists a parameter range over which the boundary value problem has N solutions. The first of these is a fundamental mode solution while the next N — 1 solutions represent additional modes.

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14

Renzo, Francesco Di. "Simulating lattice field theories on multiple thimbles." EPJ Web of Conferences 175 (2018): 07015. http://dx.doi.org/10.1051/epjconf/201817507015.

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Simulating thimble regularization of lattice field theory can be tricky when more than one thimble is to be taken into account. A couple of years ago we proposed a solution for this problem. More recently this solution proved to be effective in the case of 0+1 dimensional QCD. A few lessons we can learnt, including the role of symmetries and general hints on algorithmic solutions.

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15

de Araujo, Anderson L. A., and Kennedy Martins Pedroso. "Multiple Periodic solutions and Positive Homoclinic Solution for a differential equation." Bulletin of the Belgian Mathematical Society - Simon Stevin 20, no. 3 (2013): 535–46. http://dx.doi.org/10.36045/bbms/1378314514.

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16

Gething, P. "Optimum solution for multiple emitter location." IEEE Transactions on Antennas and Propagation 35, no. 7 (1987): 876. http://dx.doi.org/10.1109/tap.1987.1144189.

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17

Spyker, Daniel A. "Multiple Chemical Sensitivities–Syndrome and Solution." Journal of Toxicology: Clinical Toxicology 33, no. 2 (1995): 95–99. http://dx.doi.org/10.3109/15563659509000456.

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18

Saville, D. J. "Multiple Comparison Procedures: The Practical Solution." American Statistician 44, no. 2 (1990): 174. http://dx.doi.org/10.2307/2684163.

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19

Lipovetsky, Stan. "Multiple Regression in Pair Correlation Solution." Journal of Modern Applied Statistical Methods 8, no. 1 (2009): 122–31. http://dx.doi.org/10.22237/jmasm/1241136600.

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20

Galybin, Konstantin, Leon Dahlhaus, and Sergei Tcherkashnev. "Multiple Analysis – A Borehole Seismic Solution." ASEG Extended Abstracts 2010, no. 1 (2010): 1–3. http://dx.doi.org/10.1081/22020586.2010.12041940.

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Saville, D. J. "Multiple Comparison Procedures: The Practical Solution." American Statistician 44, no. 2 (1990): 174–80. http://dx.doi.org/10.1080/00031305.1990.10475712.

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22

Achiron, A. "The multiple sclerosis labyrinth—Poirot's solution." Autoimmunity Reviews 5, no. 8 (2006): 509–10. http://dx.doi.org/10.1016/j.autrev.2006.02.013.

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23

Nissen, Phillip. "A Geometry Solution from Multiple Perspectives." Mathematics Teacher 93, no. 4 (2000): 324–27. http://dx.doi.org/10.5951/mt.93.4.0324.

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It is perhaps informative for students to see that no one approach to geometry is the best. Students should be encouraged to try a variety of approaches when attempting a solution to any problem, experimenting and discussing which method is helping them find an answer. For some problems, students could develop a hybrid method, which would allow them to experience the creative aspects of mathematics.

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24

Treanţă, Savin, Cristina-Florentina Marghescu, and Laura-Gabriela Matei. "Efficiency conditions in multiple-objective optimal control models under generalized hypotheses." AIMS Mathematics 9, no. 9 (2024): 25184–204. http://dx.doi.org/10.3934/math.20241228.

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<p>Since not every problem in optimization theory involves convex functionals, in this study, we introduced new classes of generalized convex functionals. More precisely, under generalized hypotheses, we stated new efficiency conditions associated with a class of multiple-objective optimal control models. To this end, we first defined the $ G_{\theta} $-Fritz John problem and, by considering it, we established a link between the solutions of $ G_{\theta} $-Fritz John problem and efficient solutions of the considered model $ (P) $. In addition, we formulated the $ G_{\theta} $-necessary e

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Galán-García, José Luis, Pedro Rodríguez-Cielos, Yolanda Padilla-Domínguez, et al. "SMIS: A Stepwise Multiple Integration Solver Using a CAS." Mathematics 9, no. 22 (2021): 2866. http://dx.doi.org/10.3390/math9222866.

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Multiple Integration is a very important topic in different applications in Engineering and other Sciences. Using numerical software to get an approximation to the solution is a normal procedure. Another approach is working in an algebraic form to obtain an exact solution or to get general solutions depending on different parameters. Computer Algebra Systems (CAS) are needed for this last approach. In this paper, we introduce SMIS, a new stepwise solver for multiple integration developed in a CAS. The two main objectives of SMIS are: (1) to increase the capabilities of CAS to help the user to

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26

Yermachenko, I. "MULTIPLE SOLUTIONS OF THE FOURTH‐ORDER EMDEN‐FOWLER EQUATION." Mathematical Modelling and Analysis 11, no. 3 (2006): 347–56. http://dx.doi.org/10.3846/13926292.2006.9637322.

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Two-point boundary value problems for the fourth-order Emden-Fowler equation are considered. If the given equation can be reduced to a quasi‐linear one with a non‐resonant linear part so that both equations are equivalent in some domain D, and if solution of the quasi‐linear problem is located in D, then the original problem has a solution. We show that a quasi‐linear problem has a solution of definite type which corresponds to the type of the linear part. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions.

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27

Nowak, Ethan J., and Matthias G. Imhof. "Amplitude preservation of Radon-based multiple-removal filters." GEOPHYSICS 71, no. 5 (2006): V123—V126. http://dx.doi.org/10.1190/1.2243711.

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This study examines the effect of filtering in the Radon transform domain on reflection amplitudes. Radon filters are often used for removal of multiple reflections from normal moveout-corrected seismic data. The unweighted solution to the Radon transform reduces reflection amplitudes at both near and far offsets due to a truncation effect. However, the weighted solutions to the transform produce localized events in the transform domain, which minimizes this truncation effect. Synthetic examples suggest that filters designed in the Radon domain based on a weighted solution to the linear, parab

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28

KADZIŃSKI, MIŁOSZ, and ROMAN SŁOWIŃSKI. "INTERACTIVE ROBUST CONE CONTRACTION METHOD FOR MULTIPLE OBJECTIVE OPTIMIZATION PROBLEMS." International Journal of Information Technology & Decision Making 11, no. 02 (2012): 327–57. http://dx.doi.org/10.1142/s0219622012400056.

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We introduce a new interactive procedure for multiple objective optimization problems. The identification of the most preferred solution is achieved by means of a systematic dialogue with the decision maker (DM) during which (s)he specifies pairwise comparisons of nondominated solutions from a current sample. We represent this preference information by a compatible form of the achievement scalarizing function, i.e., we are searching for weights of objectives which ensure that the reference solutions are compared by the function in the same way as by the DM. Directions of the isoquants of all c

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29

Zhao, Yongdong, and Suhada Jayasuriya. "A New Formulation of Multiple-Input Multiple-Output Quantitative Feedback Theory." Journal of Dynamic Systems, Measurement, and Control 118, no. 4 (1996): 748–52. http://dx.doi.org/10.1115/1.2802352.

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The QFT robust performance problem in its entirety may be reduced to an H∞ problem by casting each specification as a frequency domain constraint on the nominal sensitivity function and the complementary sensitivity function. It is shown that the existence of a solution to a standard Ha. problem guarantees a solution to the QFT problem whereas the existence of a QFT solution does not necessarily guarantee an H∞ solution. A solution obtained via this formulation for the QFT problem is in general more conservative when compared to what may be obtained from classical QFT loopshaping. However, one

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30

Ding, Wei. "The Problem of Scheduling Multiple Groups of Jobs on Multiple Processors at Different Speeds." Advances in Operations Research 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/748597.

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We mainly study the problem of schedulingngroups of jobs onnspecial-purpose processors andmgeneral-purpose processors at different speeds provided that the setup time of each job is less than times of its processing time. We first propose an improved LS algorithm. Then, by applying this new algorithm, we obtain two bounds for the ratio of the approximate solution to the optimal solutionT* under two different conditions.

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31

Belov, Aleksandr A., and Igor V. Gorbov. "Numerical integration of the Cauchy problem with non-singular special points." Discrete and Continuous Models and Applied Computational Science 31, no. 3 (2023): 218–27. http://dx.doi.org/10.22363/2658-4670-2023-31-3-218-227.

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Solutions of many applied Cauchy problems for ordinary differential equations have one or more multiple zeros on the integration segment. Examples are the equations of special functions of mathematical physics. The presence of multiples of zeros significantly complicates the numerical calculation, since such problems are ill-conditioned. Round-off errors may corrupt all decimal digits of the solution. Therefore, multiple zeros should be treated as special points of the differential equations. In the present paper, a local solution transformation is proposed, which converts the multiple zero in

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Sharma, Abhinav Kumar, and Indrajit Mukherjee. "Enhanced multi-objective solution approach for multiple quality characteristics optimisation problems considering predictive uncertainties." International Journal of Quality & Reliability Management 37, no. 1 (2019): 112–44. http://dx.doi.org/10.1108/ijqrm-01-2019-0011.

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Purpose The purpose of this paper is to address three key objectives. The first is the proposal of an enhanced multiobjective optimisation (MOO) solution approach for the mean and mean-variance optimisation of multiple “quality characteristics” (or “responses”), considering predictive uncertainties. The second objective is comparing the solution qualities of the proposed approach with those of existing approaches. The third objective is the proposal of a modified non-dominated sorting genetic algorithm-II (NSGA-II), which improves the solution quality for multiple response optimisation (MRO) p

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Hsu, Tsing-San. "Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains." Abstract and Applied Analysis 2007 (2007): 1–19. http://dx.doi.org/10.1155/2007/43018.

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We will show that under suitable conditions onfandh, there exists a positive numberλ∗such that the nonhomogeneous elliptic equation−Δu+u=λ(f(x,u)+h(x))inΩ,u∈H01(Ω),N≥2, has at least two positive solutions ifλ∈(0,λ∗), a unique positive solution ifλ=λ∗, and no positive solution ifλ>λ∗, whereΩis the entire space or an exterior domain or an unbounded cylinder domain or the complement in a strip domain of a bounded domain. We also obtain some properties of the set of solutions.

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Yin, Kai-Hua, Xue-Ping Cheng, and Ji Lin. "Soliton Molecule and Breather-Soliton Molecule Structures for a General Sixth-Order Nonlinear Equation." Chinese Physics Letters 38, no. 8 (2021): 080201. http://dx.doi.org/10.1088/0256-307x/38/8/080201.

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Starting from a general sixth-order nonlinear wave equation, we present its multiple kink solutions, which are related to the famous Hirota form. We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures. By introducing the velocity resonance mechanism to the multiple kink solutions, we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients. The three-dimensional image and the density map of these soliton molecule solutions with certain c

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35

Tsushima, Honami, Takafumi Matsuura, and Tohru Ikeguchi. "Searching Strategies with Low Computational Costs for Multiple-Vehicle Bike Sharing System Routing Problem." Applied Sciences 12, no. 5 (2022): 2675. http://dx.doi.org/10.3390/app12052675.

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We have already proposed a multiple-vehicle bike sharing system routing problem (mBSSRP) to adjust the number of bicycles at each port using multiple vehicles in short time. However, there are many strict constraints in the mBSSRP, thus it is difficult to obtain feasible solutions of the mBSSRP for some instances. To obtain feasible solutions of the mBSSRP, we have proposed a mBSSRP with soft constraints (mBSSRP-S) that removes some constraints from mBSSRP and appends violations to an objective function as penalties, and a searching strategy that explores both the feasible and infeasible solut

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36

Tang, Hao, and Mingwei Hu. "Dynamic Vehicle Routing Problem with Multiple Objectives." Transportation Research Record: Journal of the Transportation Research Board 1923, no. 1 (2005): 199–207. http://dx.doi.org/10.1177/0361198105192300121.

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This paper addresses a dynamic vehicle routing problem related to courier mail services with explicit consideration of multiple objectives. This problem is modeled as a dynamic traveling repairman problem with time windows, and with three objectives considered: maximization of the number of serviced customers, minimization of customer waiting, and minimization of total travel time. A solution (simulation) framework, extending techniques developed for single-objective dynamic routing problems in the literature, is proposed to tackle this multiobjective problem. An efficient chained local search

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BAKRI, TAOUFIK, YURI A. KUZNETSOV, FERDINAND VERHULST, and EUSEBIUS DOEDEL. "MULTIPLE SOLUTIONS OF A GENERALIZED SINGULAR PERTURBED BRATU PROBLEM." International Journal of Bifurcation and Chaos 22, no. 04 (2012): 1250095. http://dx.doi.org/10.1142/s0218127412500952.

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Nonlinear two-point boundary value problems (BVPs) may have none or more than one solution. For the singularly perturbed two-point BVP εu″ + 2u′ + f(u) = 0, 0 < x < 1, u(0) = 0, u(1) = 0, a condition is given to have one and only one solution; also cases of more solutions have been analyzed. After attention to the form and validity of the corresponding asymptotic expansions, partially based on slow manifold theory, we reconsider the BVP within the framework of small and large values of the parameter. In the case of a special nonlinearity, numerical bifurcation patterns are studied that i

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38

Ma, Hongcai, Xiaoyu Chen, and Aiping Deng. "Novel Exact Solution for the Bidirectional Sixth-Order Sawada–Kotera Equation." Universe 9, no. 1 (2023): 55. http://dx.doi.org/10.3390/universe9010055.

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In this paper, we take the bidirectional sixth-order Sawada–Kotera equation as an instance and use a new limit approach to generate a multiple-pole solution and the degenerate of the breather wave from the N-order soliton solution. We show not only the substitution method, but also the specific mathematical expression of the double-pole, triple-pole, and the degenerate breather solution after the substitution. Meanwhile, we give the dynamic images and trajectories of the different multiple-pole solution. Moreover, we also acquire the interaction between two double-pole solutions and different

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39

Dasgupta, Sajib, Richard Golden, and Vincent Ng. "Clustering Documents Along Multiple Dimensions." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (2021): 879–85. http://dx.doi.org/10.1609/aaai.v26i1.8325.

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Traditional clustering algorithms are designed to search for a single clustering solution despite the fact that multiple alternative solutions might exist for a particular dataset. For example, a set of news articles might be clustered by topic or by the author's gender or age. Similarly, book reviews might be clustered by sentiment or comprehensiveness. In this paper, we address the problem of identifying alternative clustering solutions by developing a Probabilistic Multi-Clustering (PMC) model that discovers multiple, maximally different clusterings of a data sample. Empirical results on si

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Lin, Longfei, Yansheng Liu, and Daliang Zhao. "Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems." Symmetry 12, no. 12 (2020): 1989. http://dx.doi.org/10.3390/sym12121989.

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This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are obtained under some suitable assumptions. The main feature of obtained solutions (u(t),v(t)) is that the solution u(t) is positive, and the other solution v(t) may change sign. Finally, two examples with continuous function f1 being positive and f2 being semipositone are worked out to illustrate the main results.

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Rossen, William Richard, and Johannes Bruining. "Foam Displacements with Multiple Steady States." SPE Journal 12, no. 01 (2007): 5–18. http://dx.doi.org/10.2118/89397-pa.

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Summary A number of experimental and theoretical studies suggest that the fractional-flow function for foam can be either multivalued in water saturation or else can comprise distinct fractional-flow curves for two or more foam regimes, with jumps between them where each regime reaches its limiting condition. We construct fractional-flow solutions for these cases. When such a foam is employed in a surfactant-alternating-gas (SAG) process, the usual "tangency" condition is modified and the foam can be considerably weaker than the foam formed at what appears to be the point of tangency of the mu

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Chen, Chiu-Hung. "Application of Multiple Deep Neural Networks to Multi-Solution Synthesis of Linkage Mechanisms." Machines 11, no. 11 (2023): 1018. http://dx.doi.org/10.3390/machines11111018.

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This paper studies the problem of linkage-bar synthesis by means of multiple deep neural networks (DNNs), which requires the inverse solution of linkage parameters based on a desired trajectory curve. This problem is highly complex due to the fact that the solution space is nonlinear and may contain multiple solutions, while a good quality of learning cannot be obtained by a single neural network approach. Therefore, this paper proposes employing Fourier descriptors to represent trajectory curves in a systematic and normalized form, developing a multi-solution distribution evaluation by random

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43

Pavolo, Domingo, and Delson Chikobvu. "Estimating Rubber Covered Conveyor Belting Cure Times Using Multiple Simultaneous Optimizations Ensemble." Operational Research in Engineering Sciences: Theory and Applications 5, no. 1 (2022): 90–106. http://dx.doi.org/10.31181/oresta180222016p.

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Multiple response surface methodology (MRSM) has been the favorite method for optimizing multiple response processes though it has two weaknesses which challenge the credibility of its solutions. The first weakness is the use of experimentally generated small sample size datasets, and the second is the selection, using classical model selection criteria, of single best models for each response for use in simultaneous optimization to obtain the optimum or desired solution. Classical model selection criteria do not always agree on the best model resulting in model uncertainty. The selection of s

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Panfilov, T. E., A. A. Shchepkin, D. V. Grosman, and D. V. Karlovets. "The contribution of multiple reflections to transition radiation." Journal of Instrumentation 20, no. 05 (2025): P05031. https://doi.org/10.1088/1748-0221/20/05/p05031.

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Abstract An electron passing through a slab induces transition radiation, and the multiple reflections inside the slab boundaries can influence the observed intensity. We employ the polarization current method to derive a reflectionless solution and compare it with that of Pafomov, which accounts for the multiple reflections exactly. Our findings demonstrate that depending on the slab thickness, permittivity, the angle and frequency of the radiation, the electron velocity, Pafomov and reflectionless solutions can differ or be in a rather good agreement. We search for the parameters that allow

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45

LUO, X. Y., and T. J. PEDLEY. "Multiple solutions and flow limitation in collapsible channel flows." Journal of Fluid Mechanics 420 (October 10, 2000): 301–24. http://dx.doi.org/10.1017/s002211200000152x.

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Steady and unsteady numerical simulations of two-dimensional flow in a collapsible channel were carried out to study the flow limitation which typically occurs when the upstream transmural pressure is held constant while flow rate and pressure gradient along the collapsible channel can vary independently. Multiple steady solutions are found for a range of upstream transmural pressures and Reynolds number using an arclength control method. The stability of these steady solutions is tested in order to check the correlation between flow limitation and self-excited oscillations (the latter being a

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46

Hwang, Tzy-Wei, and Ching-An Wang. "On multiple solutions for Berman's problem." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 121, no. 3-4 (1992): 219–30. http://dx.doi.org/10.1017/s0308210500027876.

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SynopsisWe study Berman's problemsubjects to the conditions f(0) =f″(0) = f′(1) = f(1)− 1 = 0, which arises from the study of laminar flows in channels with porous walls. Positive (negative) Re denotes the case of suction (injection) flows. Preliminary numerical studies indicated the existence of three different types of solutions and a small portion of mathematical evidence was provided. In this paper, we are able to show that there exist connected sets in the Re-K plane on which different types of solutions occur. In particular, our result verifies that the problem possesses all three types

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Cezikturk, Ozlem. "Multiple solution problems and mathematical thinking: Wasan geometry example." Academic Perspective Procedia 2, no. 1 (2019): 37–46. http://dx.doi.org/10.33793/acperpro.02.01.10.

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Abstract:

Wasan geometry flourished in Edo period of Japan as arty, multiple solutioned and systematic. Teachers are not open and papers are not evaluated. Multiple solutions are seen in parallel with advanced mathematics thinking. 80 middle school and 37 high school pre service math teachers were given a Wasan problem and grouped according to correct answers, different answers, and originality. 24 different answers (equality of diagonals of a square, symmetry, equality of tangent lines, auxiliary lines and auxiliary shapes, cosines’ theorem, tan (67.5), similarities, types of triangles etc.) were detec

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KANG, Kun-peng. "Core-based multidimensional multiple-choice knapsack solution." Journal of Computer Applications 32, no. 8 (2013): 2168–71. http://dx.doi.org/10.3724/sp.j.1087.2012.02168.

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Lim, Woong, Hongjoong Kim, Lynn Stallings, and Ji-Won Son. "Celebrating Diversity by Sharing Multiple Solution Methods." Mathematics Teacher 109, no. 4 (2015): 290–97. http://dx.doi.org/10.5951/mathteacher.109.4.0290.

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Chung, Y. N., D. L. Gustafson, and E. Emre. "Extended solution to multiple maneuvering target tracking." IEEE Transactions on Aerospace and Electronic Systems 26, no. 5 (1990): 876–87. http://dx.doi.org/10.1109/7.102720.

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