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Автор: Grafiati

Опубліковано: 11 вересня 2023

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1

SHOTAKA, Shigeki, Genji YAMAZAKI, and Masahiro NAKAMURA. "Optimal Number of Automatic Guided Vehicles in FMS. Lower Bound on the Optimal Numbers." Transactions of the Japan Society of Mechanical Engineers Series C 63, no. 605 (1997): 285–90. http://dx.doi.org/10.1299/kikaic.63.285.

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2

Michelin, Sébastien, and Eric Lauga. "Optimal feeding is optimal swimming for all Péclet numbers." Physics of Fluids 23, no. 10 (October 2011): 101901. http://dx.doi.org/10.1063/1.3642645.

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3

Best, D. J. "Optimal determination of most probable numbers." International Journal of Food Microbiology 11, no. 2 (October 1990): 159–65. http://dx.doi.org/10.1016/0168-1605(90)90051-6.

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4

Hemalatha, S., and K. Annadurai. "OPTIMIZATION OF A FUZZY INVENTORY MODEL WITH PENTAGONAL FUZZY NUMBERS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 03 (March 9, 2023): 3277–87. http://dx.doi.org/10.47191/ijmcr/v11i3.01.

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Анотація:

This paper explores an optimal replenishment strategy for a two-echelon inventory model which has been considered and analyzed in a fuzzy environment. In fuzzy environment, carrying cost, ordering cost and the replenishment processing cost are assumed to be pentagonal fuzzy numbers. The purpose of this model is to minimize the total inventory cost in fuzzy scenario. There are two inventory models proposed in this paper. Crisp models are developed with fuzzy total inventory cost but crisp optimal order quantity. Fuzzy model is also formulated with fuzzy total inventory cost and fuzzy optimal order quantity. Graded mean integration formula is employed to defuzzify the total inventory cost and the Kuhn–tucker condition is used to determine the optimal order quantity. Finally, we develop an algorithm to obtain the optimal order quantity. A comparison of fuzzy model with classical inventory model is being made. Numerical results highlighting the sensitivity of various parameters are also elucidated. The result illustrates that this fuzzy model can be quite useful in determining the optimal order quantity and minimum total inventory cost.

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5

Kirkland, Stephen J., Michael Neumann, and Nung-Sing Sze. "On optimal condition numbers for Markov chains." Numerische Mathematik 110, no. 4 (August 26, 2008): 521–37. http://dx.doi.org/10.1007/s00211-008-0172-8.

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6

P. Ghadle, Kirtiwant, and Sanjivani M. Ingle. "Optimal Solution of a Mixed type Fuzzy Transportation Problem." International Journal of Fuzzy Mathematical Archive 15, no. 01 (2018): 83–89. http://dx.doi.org/10.22457/ijfma.v15n1a8.

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Анотація:

In this paper, we solved transportation problem when the data are in mixed type. Transportation problem contains fuzzy numbers, intuitionistic fuzzy numbers and real numbers. The purpose of our paper is to find the least transportation cost in which cost, supply and demand are mixed fuzzy numbers. This procedure is illustrated with numerical example

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7

GUO, XIANPING, QIULI LIU, and TIANSHOU ZHOU. "OPTIMAL CONTROL OF STOCHASTIC FLUCTUATIONS IN BIOCHEMICAL REACTIONS." Journal of Biological Systems 17, no. 02 (June 2009): 283–301. http://dx.doi.org/10.1142/s0218339009002806.

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Different experimental conditions can give rise to changes in rate constants of biochemical reactions, thus resulting in different stochastic fluctuations in the numbers of chemical species molecules. A naturally arising question is how to choose a set of reaction rate constants such that experiment-depending stochastic fluctuations can be optimally controlled. In this paper, we determine the optimal rate constants by optimally controlling stochastic fluctuations in the numbers of chemical species molecules based on the theory of continuous-time Markov decision processes. Specifically, we first propose a stochastic model for a coupled set of biochemical reactions, then solve an optimality problem for rate constants with the mean-maximal numbers of chemical species molecules, and finally find, using a policy iteration algorithm of the continuous-time Markov decision processes, optimal rate constants with the variance-minimal molecule numbers over all possible sets of the rate constants with the maximal-mean molecule numbers obtained.

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8

Shalen, Peter B. "Small optimal Margulis numbers force upper volume bounds." Transactions of the American Mathematical Society 365, no. 2 (July 25, 2012): 973–99. http://dx.doi.org/10.1090/s0002-9947-2012-05657-1.

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9

Randić, Milan, and Subhash C. Basak. "Optimal Molecular Descriptors Based on Weighted Path Numbers." Journal of Chemical Information and Computer Sciences 39, no. 2 (March 1999): 261–66. http://dx.doi.org/10.1021/ci9800763.

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10

Samuels, Charles L., and Tanner J. Strunk. "Optimal factorizations of rational numbers using factorization trees." International Journal of Number Theory 11, no. 03 (March 31, 2015): 739–69. http://dx.doi.org/10.1142/s1793042115500402.

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Анотація:

Let mt(α) denote the t-metric Mahler measure of the algebraic number α. Recent work of the first author established that the infimum in mt(α) is attained by a single point [Formula: see text] for all sufficiently large t. Nevertheless, no efficient method for locating [Formula: see text] is known. In this paper, we define a new tree data structure, called a factorization tree, which enables us to find [Formula: see text] when α ∈ ℚ. We establish several basic properties of factorization trees, and use these properties to locate [Formula: see text] in previously unknown cases.

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11

Mullen, G. L., and H. Niederreiter. "Optimal characteristic polynomials for digital multistep pseudorandom numbers." Computing 39, no. 2 (June 1987): 155–63. http://dx.doi.org/10.1007/bf02310104.

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12

v. Collani, E. "α-Optimal sampling plans for large acceptance numbers". Metrika 33, № 1 (грудень 1986): 257–73. http://dx.doi.org/10.1007/bf01894755.

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13

Kané, Ladji, Daouda Diawara, Lassina Diabaté, Moussa Konaté, Souleymane Kané, and Hawa Bado. "A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems." Journal of Mathematics 2021 (April 16, 2021): 1–17. http://dx.doi.org/10.1155/2021/5564598.

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Анотація:

We define linear programming problems involving trapezoidal fuzzy numbers (LPTra) as the way of linear programming problems involving interval numbers (LPIn). We will discuss the solution concepts of primal and dual linear programming problems involving trapezoidal fuzzy numbers (LPTra) by converting them into two linear programming problems involving interval numbers (LPIn). By introducing new arithmetic operations between interval numbers and fuzzy numbers, we will check that both primal and dual problems have optimal solutions and the two optimal values are equal. Also, both optimal solutions obey the strong duality theorem and complementary slackness theorem. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable.

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14

Kaynar, Bahar. "OPTIMAL STOPPING IN A STOCHASTIC GAME." Probability in the Engineering and Informational Sciences 23, no. 1 (November 13, 2008): 51–60. http://dx.doi.org/10.1017/s0269964809000059.

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Анотація:

In this article we consider a stochastic game in which each player draws one or two random numbers between 0 and 1. Players can decide to stop after the first draw or to continue for a second draw. The decision is made without knowing the other players’ numbers or whether the other players continue for a second draw. The object of the game is to have the highest total score without going over 1. In the article, we will characterize the optimal stopping rule for each player.

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15

Pathade, Priyanka A., and Kirtiwant P. Ghadle. "Transportation Problem with Triangular Mixed Intutionistic Fuzzy Numbers Solved By BCM." International Journal of Fuzzy Mathematical Archive 15, no. 01 (2018): 55–61. http://dx.doi.org/10.22457/ijfma.v15n1a5.

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Анотація:

In this paper, we formulate a transportation problem in which sources, destinations and costs are different types of fuzzy numbers. We used real, fuzzy and intuitionistic fuzzy numbers are employed to get the optimal solution. Mixed intuitionistic fuzzy BCM is used to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. The method is illustrated by a numerical examples.

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16

RATSCHEK, HELMUT, and JON ROKNE. "EXACT AND OPTIMAL CONVEX HULLS IN 2D." International Journal of Computational Geometry & Applications 10, no. 02 (April 2000): 109–29. http://dx.doi.org/10.1142/s0218195900000085.

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Анотація:

We present an algorithm for computing the convex hull of a finite set of points. The algorithm is based on a version of Graham scan with the following additional features: • If the points are already (single precision) machine numbers, the computation is rounding-error free, that is, the computed hull is the hull that would have been computed if real arithmetic was available. • If the points are arbitrary numbers, the algorithm renders the smallest possible machine representable convex hull that includes the exact convex hull. • The computation time is still O(n log 2n). • Only floating point arithmetic with double mantissa length is required. No mantissa splitting or other mantissa manipulations are needed; one only has to know the exponent parts of the numbers. Also, no fixed point accumulator is needed. • Single precision interval arithmetic is recommended for accelerating the computation, but is not necessary. • All of these aims are achieved with a new method for exact determination of the sign of a sum.

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17

OWUSU-ANSAH, F., R. N. CURNOW, and Y. ADU-AMPOMAH. "OPTIMAL PLANNING OF COCOA CLONAL SELECTION PROGRAMMES–CORRIGENDUM." Experimental Agriculture 54, no. 3 (April 24, 2017): 467–69. http://dx.doi.org/10.1017/s0014479717000175.

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Анотація:

We regret that the computer program used to generate the simulations of the examples presented in Owusu-Ansah, Curnow and Adu-Ampomah, 2013 contained an error. The corrected simulations for trial M2 now show that a single replication of many clones gives slightly higher selection gains than greater replication of fewer clones. The very small advantages of large numbers of years of harvest remain correct. The selection gains from the trials were considerably underestimated and, with the corrected simulations, the expected performance in terms of yield of the selected clones with the right combination of numbers of clones and replicates often exceeded the performance of the best standard clone. The selected clones still underperformed compared with the best standard clone when selection was based on percentage of diseased pods or numbers of healthy pods.

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18

Gong, Yuxin, Jianxin Xiang, and Jiawei Yao. "Analysis Concerning the Problem of the Optimal Delivery in Three Towns." Journal of Physics: Conference Series 2386, no. 1 (December 1, 2022): 012013. http://dx.doi.org/10.1088/1742-6596/2386/1/012013.

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Abstract The aim intimately pertinent to this research program is to use constructive mathematical notions to analyze how constructive real numbers and rational numbers are likely to have an influence on the outcomes involving economic problems. Researchers endeavor to find a computer program to determine the optimal location of a production plant and to find out that provided that the distances from the production plant to the sales location are rational numbers, then the problem is algorithmically solvable, though, if the distances are constructive real numbers, then the existence of the computer program that solves all such problems will not be possible.

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19

Lyall, Neil, and Ákos Magyar. "Optimal Polynomial Recurrence." Canadian Journal of Mathematics 65, no. 1 (February 1, 2013): 171–94. http://dx.doi.org/10.4153/cjm-2012-003-8.

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AbstractLet P ∊ ℤ[n] with P(0) = 0 and “ > 0. We show, using Fourier analytic techniques, that if then there must exist n ∊ ℕ such thatIn addition to this we show, using the same Fourier analytic methods, that if A ⊆ ℕ, then the set of ε-optimal return timesis syndetic for every ε > 0. Moreover, we show that R(A, P, ε) is dense in every sufficiently long interval, in particular we show that there exists an L = L(ε, P, A) such thatfor all intervals I of natural numbers with

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20

Fegade, Madhav, and Aniket Muley. "Optimal Solution to Transportation Problem with Heptagonal Fuzzy Numbers." European Journal of Mathematics and Statistics 3, no. 4 (July 21, 2022): 1–5. http://dx.doi.org/10.24018/ejmath.2022.3.4.121.

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In this paper, we have proposed another calculation to track down optimalanswers for the fuzzy transportation problem. Here, positioning strategy is utilized to defuzzify the Heptagonal fuzzy numbers. This article gives procedure that cuts down the optimal arrangement. The mathematical model represents the legitimacy of our proposed technique.

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21

Sobel, Mare J. "Optimal transitive procedures for comparing large numbers of parameters." Communications in Statistics - Theory and Methods 25, no. 6 (January 1996): 1155–72. http://dx.doi.org/10.1080/03610929608831755.

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22

van Rees, Wim M., Mattia Gazzola, and Petros Koumoutsakos. "Optimal morphokinematics for undulatory swimmers at intermediate Reynolds numbers." Journal of Fluid Mechanics 775 (June 19, 2015): 178–88. http://dx.doi.org/10.1017/jfm.2015.283.

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Undulatory locomotion is an archetypal mode of propulsion for natural swimmers across scales. Undulatory swimmers convert transverse body oscillations into forward velocity by a complex interplay between their flexural movements, morphological features and the fluid environment. Natural evolution has produced a wide range of morphokinematic examples of undulatory swimmers that often serve as inspiration for engineering devices. It is, however, unknown to what extent natural swimmers are optimized for hydrodynamic performance. In this work, we reverse-engineer the morphology and gait for fast and efficient swimmers by coupling an evolution strategy to three-dimensional direct numerical simulations of flows at intermediate Reynolds numbers. The fastest swimmer is slender with a narrow tail fin and performs a sequence of C-starts to maximize its average velocity. The most efficient swimmer combines moderate transverse movements with a voluminous head, tapering into a streamlined profile via a pronounced inflection point. These optimal solutions outperform anguilliform swimming zebrafish in both efficiency and speed. We investigate the transition between morphokinematic solutions in the speed–energy space, laying the foundations for the design of high-performance artificial swimming devices.

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23

Smolenskii, E. A., V. M. Bavykin, A. N. Ryzhov, O. L. Slovokhotova, I. V. Chuvaeva, and A. L. Lapidus. "Cetane numbers of hydrocarbons: calculations using optimal topological indices." Russian Chemical Bulletin 57, no. 3 (March 2008): 461–67. http://dx.doi.org/10.1007/s11172-008-0073-0.

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24

Brutyan, M. A., P. L. Krapivskii, and V. V. Sychev. "Optimal control of viscous flow at high reynolds numbers." Fluid Dynamics 21, no. 3 (May 1986): 485–88. http://dx.doi.org/10.1007/bf01409738.

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25

Sugiyama, Shingo, and Masao Tsuzuki. "Optimal estimates for an average of Hurwitz class numbers." Ramanujan Journal 52, no. 1 (July 3, 2019): 91–104. http://dx.doi.org/10.1007/s11139-019-00146-z.

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26

Ostilla, Rodolfo, Richard J. A. M. Stevens, Siegfried Grossmann, Roberto Verzicco, and Detlef Lohse. "Optimal Taylor–Couette flow: direct numerical simulations." Journal of Fluid Mechanics 719 (February 19, 2013): 14–46. http://dx.doi.org/10.1017/jfm.2012.596.

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Анотація:

AbstractWe numerically simulate turbulent Taylor–Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh–Bénard flow. Reynolds numbers of $R{e}_{i} = 8\times 1{0}^{3} $ and $R{e}_{o} = \pm 4\times 1{0}^{3} $ of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers $Ta$ up to $1{0}^{8} $. Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente Turbulent Taylor–Couette (${T}^{3} C$) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed an optimum transport at a certain non-zero rotation rate ratio $a= - {\omega }_{o} / {\omega }_{i} $ of about ${a}_{\mathit{opt}} = 0. 33$. For large enough $Ta$ in the numerically accessible range we also find such an optimum transport at non-zero counter-rotation. The position of this maximum is found to shift with the driving, reaching a maximum of ${a}_{\mathit{opt}} = 0. 15$ for $Ta= 2. 5\times 1{0}^{7} $. An explanation for this shift is elucidated, consistent with the experimental result that ${a}_{\mathit{opt}} $ becomes approximately independent of the driving strength for large enough Reynolds numbers. We furthermore numerically calculate the angular velocity profiles and visualize the different flow structures for the various regimes. By writing the equations in a frame co-rotating with the outer cylinder a link is found between the local angular velocity profiles and the global transport quantities.

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27

Davoodi, S. M., and N. A. Abdul Rahman. "Predicting the optimal solution in fuzzy linear programming problem." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 101, no. 1 (March 30, 2021): 25–36. http://dx.doi.org/10.31489/2021m1/25-36.

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Анотація:

In this paper we try to define a percentage form of LR fuzzy numbers which is a useful form of fuzzy numbers and its’ arithmetics. So, we show how the maximum variation range of optimal value of fuzzy objective function can be predicted by using this form of fuzzy numbers. Since fuzzy problems are generally solved through a complicated manner, the purpose of this study is releasing a kind of prediction for the final solution in the way that the manager can access to an outlook to optimal solution (Z∗) without solving the problem. Finally, optimal value of fuzzy objective function on fuzzy linear programming is predicted when maximum variation range of fuzzy variable have been predetermined.

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28

Zlatopolski, D. M. "Non-standard methods for converting numbers from one number system to another." Informatics in school 1, no. 9 (December 1, 2020): 28–30. http://dx.doi.org/10.32517/2221-1993-2020-19-9-28-30.

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Анотація:

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

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29

Vybíral, Jan. "On dilation operators and sampling numbers." Journal of Function Spaces and Applications 6, no. 1 (2008): 17–46. http://dx.doi.org/10.1155/2008/610196.

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We consider the dilation operatorsTk:f→f(2k.)in the frame of Besov spacesBpqs(ℝd)with 1≤p,q≤∞. Ifs> 0,Tkis a bounded linear operator fromBpqs(ℝd)into itself and there are optimal bounds for its norm, see [4, 2.3.1]. We study the situation in the cases= 0, an open problem mentioned also in [4]. It turns out, that new effects based on Littlewood-Paley theory appear. In the second part of the paper, we apply these results to the study of the so-called sampling numbers of the embeddingid:Bpq1s1(Ω)→Bpq20(Ω), whereΩ=(0,1)d. It was observed already in [13] that the estimates from above for the norm of the dilation operator have their immediate counterpart in the estimates from above for the sampling numbers. In this paper we show that even in the limiting cases2=0(left open so far), this general method supplies optimal results.

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30

LEVY, AMNON, FRANK NERI, and DIETER GRASS. "MACROECONOMIC ASPECTS OF SUBSTANCE ABUSE: DIFFUSION, PRODUCTIVITY AND OPTIMAL CONTROL." Macroeconomic Dynamics 10, no. 2 (March 24, 2006): 145–64. http://dx.doi.org/10.1017/s1365100506050140.

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Анотація:

This paper deals with macroeconomic aspects of widespread substance abuse with a reference to illicit drugs as an example. Substance abuse impedes the productivity of the labor force and reduces economic growth. Workers are either nonusers and therefore fully productive, a number of whom are employed by the government in drug-control activities, or users who are only partially productive. Efficient management of the nation's portfolio of workers involves eradicating drug use when initial user numbers are lower than a critical level, but allows user numbers to rise to, and be accommodated at, a stationary level when initial user numbers exceed a critical level.

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31

Srinivasan, A., and G. Geetharamani. "Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints." Journal of Applied Mathematics 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/8496812.

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Анотація:

Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example.

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32

Farano, Mirko, Stefania Cherubini, Jean-Christophe Robinet, and Pietro De Palma. "Optimal bursts in turbulent channel flow." Journal of Fluid Mechanics 817 (March 15, 2017): 35–60. http://dx.doi.org/10.1017/jfm.2017.107.

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Анотація:

Bursts are recurrent, transient, highly energetic events characterized by localized variations of velocity and vorticity in turbulent wall-bounded flows. In this work, a nonlinear energy optimization strategy is employed to investigate whether the origin of such bursting events in a turbulent channel flow can be related to the presence of high-amplitude coherent structures. The results show that bursting events correspond to optimal energy flow structures embedded in the fully turbulent flow. In particular, optimal structures inducing energy peaks at short time are initially composed of highly oscillating vortices and streaks near the wall. At moderate friction Reynolds numbers, through the bursts, energy is exchanged between the streaks and packets of hairpin vortices of different sizes reaching the outer scale. Such an optimal flow configuration reproduces well the spatial spectra as well as the probability density function typical of turbulent flows, recovering the mechanism of direct-inverse energy cascade. These results represent an important step towards understanding the dynamics of turbulence at moderate Reynolds numbers and pave the way to new nonlinear techniques to manipulate and control the self-sustained turbulence dynamics.

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33

YANG, BOTING, RUNTAO ZHANG, YI CAO, and FARONG ZHONG. "Search Numbers in Networks with Special Topologies." Journal of Interconnection Networks 19, no. 01 (March 2019): 1940004. http://dx.doi.org/10.1142/s0219265919400048.

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Анотація:

In this paper, we consider the problem of finding the minimum number of searchers to sweep networks/graphs with special topological structures. Such a number is called the search number. We first study graphs, which contain only one cycle, and present a linear time algorithm to compute the vertex separation and the optimal layout of such graphs; by a linear-time transformation, we can find the search number of this kind of graphs in linear time. We also investigate graphs, in which every vertex lies on at most one cycle and each cycle contains at most three vertices of degree more than two, and we propose a linear time algorithm to compute their search number and optimal search strategy. We prove explicit formulas for the search number of the graphs obtained from complete k-ary trees by replacing vertices by cycles. We also present some results on approximation algorithms.

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34

Gurukumaresan, D., C. Duraisamy, and R. Srinivasan. "Optimal Solution of Fuzzy Transportation Problem Using Octagonal Fuzzy Numbers." Computer Systems Science and Engineering 37, no. 3 (2021): 415–21. http://dx.doi.org/10.32604/csse.2021.014130.

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35

Eisenberg, Bennett. "Triangular Numbers and the N-Sided Die Optimal Stopping Problem." Mathematics Magazine 94, no. 4 (August 8, 2021): 281–87. http://dx.doi.org/10.1080/0025570x.2021.1951574.

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36

Wu, Xianfang, Meng Di, Minggao Tan, and Houlin Liu. "Optimal Design of Photovoltaic Irrigation System with Different Nozzle Numbers." Applied Engineering in Agriculture 37, no. 6 (2021): 1089–95. http://dx.doi.org/10.13031/aea.14750.

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HighlightsWhen the photovoltaic irrigation system is loaded with different numbers of nozzles, the working pressure of the nozzle will change. This is because the pipeline characteristics have changed with the variation of nozzle number. So the pump operating point changes and its head will also change, which leads to the change of working pressure of nozzle. To solve this problem, by theory analysis based on the test results, it is feasible to make the pump flow rate/head curve flatter. In this case, when the system pipeline characteristics change, the pump head changes little.This article presents a new optimization method to improve the performance of photovoltaic irrigation systems under variable load. The method just needs to optimize the four pump impeller structure parameters, which can make the pump flow rate/head curve flatter. So the pump head changes a little when the system is loaded with different numbers of nozzles, which can make the working pressure of the nozzle stable and improve the system performance.Taking the slope of flow-head curve as the optimization objective, and the impeller blade outlet angle ß2, blade outlet width b2, blade number Z, and rear cover diameter D2min as the optimization variables, the performance of the photovoltaic irrigation system is optimized by orthogonal test design optimization scheme. After optimization, when the system is loaded with a different number of nozzles, it can provide relatively similar pressure under different ranges of light intensity.Abstract. The performance of the photovoltaic irrigation system under variable load were obtained and analyzed through test measurement. The adaptability of the system under variable load could be improved by optimizing the pump impeller structure, and then the irrigation uniformity of the photovoltaic irrigation system under different loads could be improved. Taking the slope of flow-head curve as the optimization objective, and the impeller blade outlet angle ß2, blade outlet width b2, blade number Z, and rear cover diameter D2min as the optimization variables, the performance of the photovoltaic irrigation system is optimized by orthogonal test design optimization scheme and the test verification was carried out. The range method was applied to analyze the simulation results. It can be found that when the geometric parameters of the impeller are D2 = 86 mm, ß2 = 41°, b2 = 4.0 mm, and Z = 9, the slope of the pump flow-head curve is the highest. The system performance after optimization was measured and compared with the original scheme. By comparison, it was drawn that when the system is loaded with different numbers of nozzles, the nozzle pressure can be maintained near the optimal pressure of the nozzle within a wider light intensity. After optimization, when the system is loaded with a different number of nozzles, it can provide relatively similar pressure under different ranges of light intensity. Keywords: Nozzle, Orthogonal test, Optimal design, Photovoltaic irrigation, Pump.

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37

Xu, Guiqiao, Zehong Liu, and Hui Wang. "Sample Numbers and Optimal Lagrange Interpolation of Sobolev Spaces Wr1." Chinese Annals of Mathematics, Series B 42, no. 4 (July 2021): 519–28. http://dx.doi.org/10.1007/s11401-021-0275-4.

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38

Xu, Guiqiao, Yongping Liu, and Dandan Guo. "Optimal Birkhoff Interpolation and Birkhoff Numbers in Some Function Spaces." Acta Mathematica Scientia 43, no. 1 (October 18, 2022): 125–42. http://dx.doi.org/10.1007/s10473-023-0108-5.

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39

Goodson, Troy, Jason C. H. Chuang, and John Hanson. "Optimal Finite Thrust Orbit Transfers with Large Numbers of Burns." Journal of Guidance, Control, and Dynamics 22, no. 1 (January 1999): 139–48. http://dx.doi.org/10.2514/2.4360.

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40

Katona, Gyula Y., and Nándor Sieben. "Bounds on the Rubbling and Optimal Rubbling Numbers of Graphs." Graphs and Combinatorics 29, no. 3 (March 11, 2012): 535–51. http://dx.doi.org/10.1007/s00373-012-1146-2.

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41

Perillo, Gerardo M. E., and Eduardo Marone. "Determination of optimal numbers of class intervals using maximum entropy." Mathematical Geology 18, no. 4 (May 1986): 401–7. http://dx.doi.org/10.1007/bf00906063.

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42

Lohéac, Jérôme, Jean-François Scheid, and Marius Tucsnak. "Controllability and Time Optimal Control for Low Reynolds Numbers Swimmers." Acta Applicandae Mathematicae 123, no. 1 (June 2, 2012): 175–200. http://dx.doi.org/10.1007/s10440-012-9760-9.

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43

Kolehmainen, J. "Optimal Dovetail Permanent Magnet Rotor Solutions for Various Pole Numbers." IEEE Transactions on Industrial Electronics 57, no. 1 (January 2010): 70–77. http://dx.doi.org/10.1109/tie.2009.2029590.

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44

Katona, Gyula Y., and Nándor Sieben. "Bounds on the Rubbling and Optimal Rubbling Numbers of Graphs." Electronic Notes in Discrete Mathematics 38 (December 2011): 487–92. http://dx.doi.org/10.1016/j.endm.2011.09.079.

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45

Schindl, David. "Optimal student sectioning on mandatory courses with various sections numbers." Annals of Operations Research 275, no. 1 (September 2, 2017): 209–21. http://dx.doi.org/10.1007/s10479-017-2621-1.

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46

Marcel Ioan, BOLOS, SABAU-POPA Claudia Diana, and RUS Luminita. "Optimal Management of Production Stocks with the Neutrosophic Fuzzy Numbers." ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH 57, no. 2/2023 (June 21, 2023): 21–40. http://dx.doi.org/10.24818/18423264/57.2.23.02.

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47

Joshi, Nidhi, and Surjeet Singh Chauhan. "A new Approach for Obtaining Optimal Solution of Unbalanced Fuzzy Transportation Problem." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 15, no. 6 (April 20, 2016): 6824–32. http://dx.doi.org/10.24297/ijct.v15i6.3977.

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The present paper attempts to study the unbalanced fuzzy transportation problem so as to minimize the transportationcost of products when supply, demand and cost of the products are represented by fuzzy numbers. In this paper, authorsuse Roubast ranking technique to transform trapezoidal fuzzy numbers to crisp numbers and propose a new algorithm tofind the fuzzy optimal solution of unbalanced fuzzy transportation problem. The proposed algorithm is more efficient thanother existing algorithms like simple VAM and is illustrated via numerical example. Also, a comparison between the resultsof the new algorithm and the result of algorithm using simple VAM is provided.

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48

Chen, Yin. "Some New Optimal Bounds for Wallis Ratio." Asian Research Journal of Mathematics 19, no. 10 (August 31, 2023): 169–78. http://dx.doi.org/10.9734/arjom/2023/v19i10739.

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Wallis ratio can be expressed as an asymptotic expansion using Stirling series and Bernoulli numbers. We prove the general inequalities for Wallis ratio for arbitrary number of terms in the asymptotic expansion. We show that the coefficients in the asymptotic expansion are the best possible.

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49

Nair, R. "On the metric theory of the optimal continued fraction expansion." Bulletin of the Australian Mathematical Society 56, no. 1 (August 1997): 69–79. http://dx.doi.org/10.1017/s0004972700030744.

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Suppose kn denotes either φ(n) or φ(rn) (n = 1, 2, …) where the polynomial φ maps the natural numbers to themselves and rk denotes the kth rational prime. Let denote the sequence of convergents to a real numbers x for the optimal continued fraction expansion. Define the sequence of approximation constants byIn this paper we study the behaviour of the sequence for all most all x with respect to Lebesgue measure. In the special case where kn = n (n = 1, 2, …) these results are due to Bosma and Kraaikamp.

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50

Zhang, Rui, Rui Xin, Margo Seltzer, and Cynthia Rudin. "Optimal Sparse Regression Trees." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 9 (June 26, 2023): 11270–79. http://dx.doi.org/10.1609/aaai.v37i9.26334.

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Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees, there has been little effort towards full provable optimization, mainly due to the computational hardness of the problem. This work proposes a dynamic programming-with-bounds approach to the construction of provably-optimal sparse regression trees. We leverage a novel lower bound based on an optimal solution to the k-Means clustering algorithm on one dimensional data. We are often able to find optimal sparse trees in seconds, even for challenging datasets that involve large numbers of samples and highly-correlated features.

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