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Journal articles on the topic '"LINEST" function'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Deng, Cheng, and Muhammad Talal Ahmad. "Research on Marketing Management Risk Decision Model Based on LINEST Function." Security and Communication Networks 2022 (April 13, 2022): 1–10. http://dx.doi.org/10.1155/2022/9658148.

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The primary purpose of this research study is to describe the research on the marketing management risk decision model based on the LINEST function. This research is conducted in China and is used for measuring the risk decision model using different questions related to marketing management. The nature of this research is primary, and data were collected from 100 plus responders related to the marketing management fields. The research participants included males, females, employees of marketing, and other people from marketing management organizations. We used smart PLS software to measure th

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2

Communication Networks, Security and. "Retracted: Research on Marketing Management Risk Decision Model Based on LINEST Function." Security and Communication Networks 2022 (December 15, 2022): 1. http://dx.doi.org/10.1155/2022/9872745.

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3

Kontsevoi, A., S. Kontsevoi, and I. Matusevich. "DATA PROCESSING METHOD IN THE RESEARCH OF THREE-COMPONENT SYSTEMS." Znanstvena misel journal, no. 70 (September 20, 2022): 29–32. https://doi.org/10.5281/zenodo.7095682.

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A method of calculations in Excel is proposed for three-component systems with restrictions on the concentration of components ("pseudo component method"). With the use of the "LINEST" function, the coefficients of the regression equation are calculated based on the values of the relative concentrations of the components. This variant of the calculation enables a direct assessment of the influence of real concentrations on the response (property). It is recommended to evaluate the adequacy of the equation by the correlation coefficient.

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4

Darabi-Golestan, Farshad, and Ardeshir Hezarkhani. "Intensification of the polymetallic vein exploration by multivariate analysis and staged LINEST function at Glojeh deposit, NW Iran." Journal of African Earth Sciences 147 (November 2018): 190–98. http://dx.doi.org/10.1016/j.jafrearsci.2018.06.026.

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5

Zhang, Guo-Fu, Xin-Ran Chen, and Zhi-Ren Li. "The Interaction and Coupling Between Enterprise Value Evaluation and Regional Ecological Environment." Ecological Chemistry and Engineering S 30, no. 1 (2023): 125–32. http://dx.doi.org/10.2478/eces-2023-0012.

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Abstract The development of industrial Internet technology enterprises plays an important supporting role in green water and green mountains, as a forestry industry with both economic value and ecological value. at present, it is facing a good opportunity for development. However, industrial Internet technology enterprises are faced with many risks, such as long investment cycle, low comparative income, and their ecological value is easy to be ignored. Based on FCFF model and LINEST function, this paper studies the enterprise value evaluation and ecological development. The main conclusions ar

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6

Гуштан, Т. В. "МОДЕЛЮВАННЯ ВПЛИВУ ЧИННИКІВ НА ЕКСПОРТ ТОРГОВЕЛЬНИХ ПІДПРИЄМСТВ". Наукові записки Львівського університету бізнесу та права. Серія економічна. Серія юридична, № 28 (26 березня 2021): 70–76. https://doi.org/10.5281/zenodo.5106300.

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The article describes the significant participation of trade enterprises in the socio-economic development of the country. The input data for building an econometric model are analyzed. We estimated construction cases of econometric models, where the resulting factor is export to EU countries and considered 4-factor, 3-factor and 2-factor models. We revealed the positive influence of factors on the export of trade enterprises to the EU countries. In early history, people were limited to domestic trade due to a lack of access to international markets. As transportation improved, many countries

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7

Lutkovska, Svitlana, Lyudmula Pronko, Tetiana Tetiana Kolesnyk, and Oksana Pidvalna. "DEVELOPMENT OF LOCAL SELF-GOVERNMENT IN THE CHANGE MANAGEMENT SYSTEM." Actual Problems of Economics 1, no. 278 (2024): 214–34. https://doi.org/10.32752/1993-6788-2024-1-278-214-234.

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Local self-government is an important tool for ensuring sustainable development, as it is closest to the community and is able to respond quickly and flexibly to new conditions. In the conditions of decentralization, the role of local authorities in decision-making is strengthened, which contributes to more efficient use of resources and the involvement of citizens in management. Understanding the mechanisms and processes of change management at the local level makes it possible to increase the resilience of communities to external challenges and contribute to their socio-economic development.

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8

Daujanov, Ainazar Shinnazarovich, Aysanem Kuanishbaevna Turganbaeva, Muxtorbek Raximboyev, and Aynura Xiyasova. "LINEAR CHANGE OF VARIABLES AND ON SIMPLIFICATION OF EXPRESSIONS IN THE SPACE OF GENERALIZED FUNCTIONS." EURASIAN JOURNAL OF ACADEMIC RESEARCH 1, no. 1 (2021): 971–76. https://doi.org/10.5281/zenodo.4742240.

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<em>The rigorous mathematical theory of generalized functions contains the definition of a set of basic functions, the definition of a continuous functional, rules for performing limit transitions, delta-like sequences, etc. Special literature is devoted to these questions, in which one can find formulations and proofs of the corresponding theorems (see, for example, the book by V.S. Vladimirov "Generalized functions in mathematical physics", I.M. Gelfand and G.E.Shilov "Generalized functions and actions on them ", MS Agranovich" Generalized functions and Sobolev space

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9

Tashilova, A. A., L. M. Fedchenko, M. Ch Zalikhanov, and N. V. Kondratyeva. "Analysis of the dynamics of mudflows amid climate changes in the high mountain zone of Kabardino-Balkaria." Nauka Innovatsii Tekhnologii, no. 1 (2024): 71–92. http://dx.doi.org/10.37493/2308-4758.2024.1.4.

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The object of the study is a dangerous slope phenomenon (mudflow) in the mountains of the Kabardino-Balkarian Republic (KBR) against the background of changing climatic conditions of the warm season (May-September). The paper presents the results of statistical, frequency and regression analysis of the dynamics of the number of mudflows, precipitation amounts, and average temperatures in the high-mountain zone of the KBR in the period 1953–2015. Statistical analysis of time series was carried out using the SPSS 20.0 software package. Linear trends were generated using Excel built-in LINEST wor

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10

Labovskiy, S. M. "ON POSITIVITY OF THE GREEN FUNCTION FOR POISSON PROBLEM FOR A LINEAR FUNCTIONAL DIFFERENTIAL EQUATION." Tambov University Reports. Series: Natural and Technical Sciences 22, no. 6-1 (2017): 1229–34. http://dx.doi.org/10.20310/1810-0198-2017-22-6-1229-1234.

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11

Kontsevoy, Andriy. "Development of a kinetic model of magnetite leaching." Technology audit and production reserves 1, no. 3(69) (2023): 6–9. http://dx.doi.org/10.15587/2706-5448.2023.273349.

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The object of the research is the process of magnetite leaching with nitric acid solutions, and the subject of the research is the mathematical justification of the kinetic model and the calculation of kinetic parameters. The article considers the case of leaching in the kinetic region, while magnetite is considered as a polydispersity material of spherical shape. It is proposed to use the distribution function of the number of particles N by their radius r in the form N=a∙rb, where a and b are constants. This distribution was used to derive the equation for the rate of the process W, taking i

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Andriy, Kontsevoy. "Development of a kinetic model of magnetite leaching." Technology audit and production reserves 1, no. 3(69) (2023): 6–9. https://doi.org/10.15587/2706-5448.2023.273349.

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<em>The object of the research is the process of magnetite leaching with nitric acid solutions, and the subject of the research is the mathematical justification of the kinetic model and the calculation of kinetic parameters.</em> <em>The article considers the case of leaching in the kinetic region, while magnetite is considered as a polydispersity material of spherical shape. It is proposed to use the distribution function of the number of particles N by their radius r in the form N=a∙r<sup>b</sup>, where a and b are constants. This distribution was used to derive the equation for the rate of

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13

Ali, Omar. "ON THE UNIFORMLY STARLIKENSS OF THE EXPONENTIAL FUNCTION." International Journal of Novel Research in Interdisciplinary Studies 11, no. 2 (2024): 28–32. https://doi.org/10.5281/zenodo.10997500.

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<strong>Abstract:</strong> We introduce and study a new subclass of uniformly starlike functions by the means of the convolution involving the exponential function in the unit disk. <strong>Keywords:</strong> Uniformly Starlike functions; Hadamard product; Linear operator; Exponential function. <strong>Title:</strong> ON THE UNIFORMLY STARLIKENSS OF THE EXPONENTIAL FUNCTION <strong>Author:</strong> Ali Omar <strong>International Journal of Novel Research in Interdisciplinary Studies</strong> <strong>ISSN 2394-9716</strong> <strong>Vol. 11, Issue 2, March 2024 - April 2024</strong> <strong>Page

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14

S. V., Isayenkov. "PHENOTYPIC ANALYSIS OF OsTPKb LOSS OF FUNCTION MUTANT RICE LINES." Biotechnologia Acta 8, no. 4 (2015): 122–27. http://dx.doi.org/10.15407/biotech8.04.122.

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15

Čerych, Jan. "A remark on linear codimensions of function algebras." Czechoslovak Mathematical Journal 36, no. 4 (1986): 511–15. http://dx.doi.org/10.21136/cmj.1986.102112.

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16

Klen, Kateryna, Vadym Martynyuk, and Mykhailo Yaremenko. "Prediction of the wind speed change function by linear regression method." Computational Problems of Electrical Engineering 9, no. 2 (2019): 28–33. http://dx.doi.org/10.23939/jcpee2019.02.028.

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In the article the approximation of the function of wind speed changes by linear functions based on Walsh functions and the prediction of function values by linear regression method is made. It is shown that under the condition of a linear change of the internal resistance of the wind generator over time, it is advisable to introduce the wind speed change function with linear approximation. The system of orthonormal linear functions based on Walsh functions is given. As an example, the approximation of the linear-increasing function with a system of 4, 8 and 16 linear functions based on the Wa

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17

Karthick, S., and A. Saraswathi. "Solving Fuzzy Non Linear Programming Problems using Ranking Function." International Journal of Science and Research (IJSR) 11, no. 12 (2022): 139–42. http://dx.doi.org/10.21275/sr221201091426.

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18

Jung, Jaewoon, Takaharu Mori, and Yuji Sugita. "2P072 Efficient Lookup Table using a Linear Function of Inverse Distance Squared(01D. Protein: Function,Poster)." Seibutsu Butsuri 53, supplement1-2 (2013): S170. http://dx.doi.org/10.2142/biophys.53.s170_6.

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19

Vijender, Nallapu, and Vasileios Drakopoulos. "On the Bernstein Affine Fractal Interpolation Curved Lines and Surfaces." Axioms 9, no. 4 (2020): 119. http://dx.doi.org/10.3390/axioms9040119.

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In this article, firstly, an overview of affine fractal interpolation functions using a suitable iterated function system is presented and, secondly, the construction of Bernstein affine fractal interpolation functions in two and three dimensions is introduced. Moreover, the convergence of the proposed Bernstein affine fractal interpolation functions towards the data generating function does not require any condition on the scaling factors. Consequently, the proposed Bernstein affine fractal interpolation functions possess irregularity at any stage of convergence towards the data generating fu

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20

Schwabik, Štefan. "Linear operators in the space of regulated functions." Mathematica Bohemica 117, no. 1 (1992): 79–92. http://dx.doi.org/10.21136/mb.1992.126231.

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21

Mitsuishi, Takashi. "Some Properties of Membership Functions Composed of Triangle Functions and Piecewise Linear Functions." Formalized Mathematics 29, no. 2 (2021): 103–15. http://dx.doi.org/10.2478/forma-2021-0011.

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Summary. IF-THEN rules in fuzzy inference is composed of multiple fuzzy sets (membership functions). IF-THEN rules can therefore be considered as a pair of membership functions [7]. The evaluation function of fuzzy control is composite function with fuzzy approximate reasoning and is functional on the set of membership functions. We obtained continuity of the evaluation function and compactness of the set of membership functions [12]. Therefore, we proved the existence of pair of membership functions, which maximizes (minimizes) evaluation function and is considered IF-THEN rules, in the set o

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22

Sahin, Ismet. "Minimization over randomly selected lines." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 3, no. 2 (2013): 111–19. http://dx.doi.org/10.11121/ijocta.01.2013.00167.

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This paper presents a population-based evolutionary optimization method for minimizing a given cost function. The mutation operator of this method selects randomly oriented lines in the cost function domain, constructs quadratic functions interpolating the cost function at three different points over each line, and uses extrema of the quadratics as mutated points. The crossover operator modifies each mutated point based on components of two points in population, instead of one point as is usually performed in other evolutionary algorithms. The stopping criterion of this method depends on the n

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23

M Ehteshamul Haque, T. "Surface Plasmon?s in Non Linear Response Function in Metal Optics." International Journal of Scientific Engineering and Research 5, no. 11 (2017): 46–48. https://doi.org/10.70729/ijser172000.

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24

Tvrdý, Milan. "Linear integral equations in the space of regulated functions." Mathematica Bohemica 123, no. 2 (1998): 177–212. http://dx.doi.org/10.21136/mb.1998.126306.

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25

Tan, Wei, Chang Qing Sun, Chun Fang Xue, and Yao Dai. "Method of Lines to Solve 2-D Steady Temperature Field of FGM." Key Engineering Materials 353-358 (September 2007): 2003–6. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.2003.

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Method of Lines (MOLs) is introduced to solve 2-Dimension steady temperature field of functionally graded materials (FGMs). The main idea of the method is to semi–discretized the governing equation of thermal transfer problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs with functions of thermal properties. As numerical examples, six kinds of material thermal conductivity functions, i.e. three kinds of polynomial functions, an exponent function, a loga

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26

Sitek, Grzegorz Antoni, and Janusz Leszek Wywiał. "On Estimation of Bi‑liner Regression Parameters." Acta Universitatis Lodziensis. Folia Oeconomica 6, no. 332 (2018): 87–98. http://dx.doi.org/10.18778/0208-6018.332.06.

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Two non‑parallel lines will be named as bi‑lines. The relationship between the definition of the bi‑lines function and linear regression functions of the distribution mixture is considered. The bi‑lines function parameters are estimated using the least squares method for an implicit interdependence. In general, values of parameter estimators are evaluated by means of an approximation numerical method. In a particular case, the exact expressions for the parameter estimators were derived. In this particular case, the properties of the estimators are examined in details. The bi‑lines are also use

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27

Radenovic, C. N., D. M. Grodzinskij, M. R. Filipovic, N. S. Delic, J. Z. Srdic, and I. M. Pavlov. "Quality traits of maize inbred lines and hybrids with efficient photosynthetic functions." Fiziologia rastenij i genetika 48, no. 5 (2016): 382–92. http://dx.doi.org/10.15407/frg2016.05.382.

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28

A, Karpagam, and Sumathi Dr.P. "New Approach to Solve Fuzzy Linear Programming Problems by the Ranking Function." Bonfring International Journal of Data Mining 4, no. 4 (2014): 22–25. http://dx.doi.org/10.9756/bijdm.6123.

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29

MacDonald, Caroline, Maureen Vass, Brian Willett, Alexander Scott, and Helen Grant. "Expression of Liver Functions in Imrnortalised Rot Hepotocyte Cell Lines." Human & Experimental Toxicology 13, no. 6 (1994): 439–44. http://dx.doi.org/10.1177/096032719401300613.

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The differentiated hepatic function of two rat liver cell lines, P9 and SV40RH1, immortalised by transfection with SV40 DNA has been investigated in terms of the glutathione synthesis, and the activities of γ-glutamyltransferase, glutathione-S-transferase and UDP-glucuronosyltransferase. SV40RH1 is a highly differentiated cell line at early passage, but the expression of some aspects of its differentiated phenotype is unstable and some functions are lost by passage 12-13. P9 is a less-well differentiated cell line, with relatively stable expression of functions between passages 4 and 13. In te

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30

Juan, E. Nápoles Valdes. "A Review of Hermite-Hadamard Inequality." Partners Universal International Research Journal (PUIRJ) ISSN: 2583-5602 01, no. 04 (2022): 98–101. https://doi.org/10.5281/zenodo.7492608.

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<em>In this review we present the most important lines of development, around the well-known Hermite-Hadamard Inequality, as well as some open problems.In this review we present the most important lines of development, around the well-known Hermite-Hadamard Inequality, as well as some open problems.</em>

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31

Pelant, Martin, and Milan Tvrdý. "Linear distributional differential equations in the space of regulated functions." Mathematica Bohemica 118, no. 4 (1993): 379–400. http://dx.doi.org/10.21136/mb.1993.126158.

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32

PAȘA, Tatiana, and Valeriu UNGUREANU. "SOLVING THE TRANSPORTATION PROBLEM WITH PIECEWISE-LINEAR CONCAVE COST FUNCTIONS." Review of the Air Force Academy 15, no. 2 (2017): 49–56. http://dx.doi.org/10.19062/1842-9238.2017.15.2.6.

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33

SERA, K., and S. FUTATSUGAWA. "SPECTRUM ANALYSIS TAKING ACCOUNT OF THE TAIL, ESCAPE FUNCTIONS AND SUB-LINES (SAPIX version 4)." International Journal of PIXE 10, no. 03n04 (2000): 101–14. http://dx.doi.org/10.1142/s0129083500000158.

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A new x-ray-spectrum-analysis program, which is capable of fitting with response functions including a tail function, an escape peak and sub-lines, has been developed. In this code, the tail function is expressed by combination of two or three Gaussian functions. A tail function, an escape and sub- or satellite-lines are regarded as functions belonging to the main peak and are included in it. A small shift of peak position depending on measuring conditions can be easily corrected in the program. As a result of fitting to practical spectra with the response function thus prepared, it becomes po

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34

Trajdos, Pawel, and Robert Burduk. "Probability-driven scoring functions in combining linear classifiers." JUCS - Journal of Universal Computer Science 28, no. (3) (2022): 269–91. https://doi.org/10.3897/jucs.80747.

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Although linear classifiers are one of the oldest methods in machine learning, they are still very popular in the machine learning community. This is due to their low computational complexity and robustness to overfitting. Consequently, linear classifiers are often used as base classifiers of multiple ensemble classification systems. This research is aimed at building a new fusion method dedicated to the ensemble of linear classifiers. The fusion scheme uses both measurement space and geometrical space. Namely, we proposed a probability-driven scoring function which shape depends on the orient

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35

Labovskiy, S. M., and M. F. Getimane. "POISSON PROBLEM FOR A LINEAR FUNCTIONAL DIFFERENTIAL EQUATION." Tambov University Reports. Series: Natural and Technical Sciences 21, no. 1 (2016): 76–81. http://dx.doi.org/10.20310/1810-0198-2016-21-1-76-81.

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36

Erkelens, Casper J. "Geometric Constraints of Visual Space." i-Perception 12, no. 6 (2021): 204166952110552. http://dx.doi.org/10.1177/20416695211055212.

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Perspective space has been introduced as a computational model of visual space. The model is based on geometric features of visual space. The model has proven to describe a range of phenomena related to the visual perception of distance and size. Until now, the model lacks a mathematical description that holds for complete 3D space. Starting from a previously derived equation for perceived distance in the viewing direction, the suitability of various functions is analyzed. Functions must fulfill the requirement that straight lines, oriented in whatever direction in physical space, transfer to

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37

Akniyev, G. G. "Discrete least squares approximation of piecewise-linear functions by trigonometric polynomials." Issues of Analysis 24, no. 2 (2017): 3–24. http://dx.doi.org/10.15393/j3.art.2017.4070.

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38

Klyachin, Alеksеy. "Оценка погрешности вычисления интегральных функционалов с помощью кусочно-линейных функций". Vestnik Volgogradskogo gosudarstvennogo universiteta. Serija 1. Mathematica. Physica, № 1 (23 березня 2015): 6–12. http://dx.doi.org/10.15688/jvolsu1.2015.1.1.

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39

Liu Jihao, 刘济豪, 卢荣胜 Lu Rongsheng, 张紫龙 Zhang Zilong та 张艾琳 Zhang Ailin. "焦距测量中线纹清晰度评价函数的研究". Acta Optica Sinica 43, № 9 (2023): 0912001. http://dx.doi.org/10.3788/aos221813.

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40

Csörnyei, Marianna, David Preiss, and Jaroslav Tišer. "Lipschitz functions with unexpectedly large sets of nondifferentiability points." Abstract and Applied Analysis 2005, no. 4 (2005): 361–73. http://dx.doi.org/10.1155/aaa.2005.361.

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It is known that everyGδsubsetEof the plane containing a dense set of lines, even if it has measure zero, has the property that every real-valued Lipschitz function onℝ2has a point of differentiability inE. Here we show that the set of points of differentiability of Lipschitz functions inside such sets may be surprisingly tiny: we construct aGδsetE⊂ℝ2containing a dense set of lines for which there is a pair of real-valued Lipschitz functions onℝ2having no common point of differentiability inE, and there is a real-valued Lipschitz function onℝ2whose set of points of differentiability inEis unif

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Asma, Fatima Abdul Jabbar, and Vineeta Basotia Dr. "A Survey Of Topological Vector Spaces For Analytic Functions." Young Researcher 12, no. 2 (2023): 240–43. https://doi.org/10.5281/zenodo.10426589.

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In a work that we just published, we created a new space of analytic functions in the unit disc that we termed W(1). This space is the union of a few other spaces called X'(a), and it spans the range 0 to 1. We also demonstrated that if f(z) E *(I), then f(z) can be recovered despite the limitation of its distributional boundary values to an open arc of the unit circle. This was another one of our accomplishments. In this article, we are going to explore some of the attributes of the spaces that we utilised in our prior work. Specifically, we are going to focus on the percentage a. On the othe

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42

Naami, Ghali, Mohamed Ouahi, Teresa Alvarez, and Abdelhamid Rabhi. "Generalized Multiple Delay-dependent H∞, Functional Observer Design for Nonlinear System." Int. J. Control Autom. Syst. 21 (August 30, 2023): 3584–94. https://doi.org/10.1007/s12555-023-0087-2.

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Functional observers are the major alternative to many practical estimation problems where full-order observers cannot be used. This paper introduces a generalized approach to design <em>H</em><sub>∞</sub> functional observers for a class of Lipschitz nonlinear systems with multiple time delays. Moreover, the considered system extends from previously published work in that it presents nonlinearity, multiple delay and external disturbance. Their main findings come from the development of a generalized augmented Lyapunov function that uses both the extended reciprocal convex combinati

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43

H.F. Jwamer, Karwan, Shazad Sh. Ahmed, and Diar Kh. Abdullah. "Numerical Treatment Solution of Volterra Integro-Fractional Differential Equation by Using Linear Spline Function." Journal of Zankoy Sulaimani - Part A 22, no. 2 (2020): 327–38. http://dx.doi.org/10.17656/jzs.10832.

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44

Lang, Weeranuch, Yuya Kumagai, Juri Sadahiro, et al. "Bp-6 Amphiphilic function of linear-isomaltomegalosaccharides (L-IMS) on ethyl red (ER) solubility." Bulletin of Applied Glycoscience 4, no. 3 (2014): B42. http://dx.doi.org/10.5458/bag.4.3_b42-3.

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45

Zhai Fangchao, 翟方超, 曾庆化 Zeng Qinghua, 张越杰 Zhang Yuejie, 王合龙 Wang Helong та 李杰 Li Jie. "考虑传函零点的光电稳定平台抗扰控制设计". Infrared and Laser Engineering 53, № 5 (2024): 20240030. http://dx.doi.org/10.3788/irla20240030.

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46

Ruzimbay, M. Madrakhimov. "'Analogue of Hartogs' Lemma for Pluriharmonic Functions." Sarcouncil Journal of Applied Sciences 4, no. 10 (2024): 10–14. https://doi.org/10.5281/zenodo.13998712.

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In this paper, an analogue of the Hartogs’ lemma for pluriharmonic functions is proved. The conditions of the theorem are, of course, necessary for the pluriharmonicity of functions of many variables. Conditions 1, characterizing the harmonicity of a function in direction   is standard in theorems of continuation along lines. It defines the principle of continuation of a function in a direction

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47

Wang, Xing, and Ling Xu. "Design and Realization of the Intelligent Scheduling and Management System of Transmission Lines." Advanced Materials Research 381 (November 2011): 109–13. http://dx.doi.org/10.4028/www.scientific.net/amr.381.109.

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Transmission line intelligent distribution and management system is the latest systematic product for optical network intelligent distribution, with the function of detecting, warning and information processing, whose purpose is to realize the delicacy management of transmission line resources and solve the problems appearing in the process of using resource management system., such as input complexity, function singleness and so on. The thesis introduces different functions of each module in this system, puts forward the solutions to this systematic function and provides some realization code

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48

Dhanuk, B. B., K. Pudasainee, H. P. Lamichhane, and R. P. Adhikari. "Dirac Delta Function from Closure Relation of Orthonormal Basis and its Use in Expanding Analytic Functions." Journal of Nepal Physical Society 6, no. 2 (2020): 158–63. http://dx.doi.org/10.3126/jnphyssoc.v6i2.34872.

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One of revealing and widely used concepts in Physics and mathematics is the Dirac delta function. The Dirac delta function is a distribution on real lines which is zero everywhere except at a single point, where it is infinite. Dirac delta function has vital role in solving inhomogeneous differential equations. In addition, the Dirac delta functions can be used to explore harmonic information’s imbedded in the physical signals, various forms of Dirac delta function and can be constructed from the closure relation of orthonormal basis functions of functional space. Among many special functions,

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Pershyna, I. I. "RESTORATION OF DISCONTINUOUS FUNCTIONS BY DISCONTINUOUS INTERLINATION SPLINES." Radio Electronics, Computer Science, Control, no. 4 (December 4, 2022): 29. http://dx.doi.org/10.15588/1607-3274-2022-4-3.

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Context. The problem of development and research of methods for approximation of discontinuous functions by discontinuous interlination splines and its further application to problems of computed tomography. The object of the study was the modeling of objects with a discontinuous internal structure. Objective. The aim of this study is to develop a general method for constructing discontinuous interlining polynomial splines, which, as a special case, include discontinuous and continuously differentiated splines. Method. Modern methods of restoring functions are characterized by new

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Kanda, Shunsuke, Kazuhiro Morita, Masao Fuketa, and Jun Ichi Aoe. "Experimental Observations of Construction Methods for Double Array Structures Using Linear Functions." Journal of Software 10, no. 6 (2015): 739–47. http://dx.doi.org/10.17706//jsw.10.6.739-747.

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