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Journal articles on the topic 'Maxima and minima'

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Published: 4 June 2021
Last updated: 29 July 2024

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1

Shukla, Rama. "On maxima-minima." Proceedings of the Indian Academy of Sciences - Section A 106, no. 1 (February 1996): 65–68. http://dx.doi.org/10.1007/bf02837187.

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2

Romanuke, Vadim. "Three-Point Iterated Interval Half-Cutting for Finding All Local Minima of Unknown Single-Variable Function." Electrical, Control and Communication Engineering 18, no. 1 (June 1, 2022): 27–36. http://dx.doi.org/10.2478/ecce-2022-0004.

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Abstract A numerical method is suggested to find all local minima and the global minimum of an unknown single-variable function bounded on a given interval regardless of the interval length. The method has six inputs: three inputs defined straightforwardly and three inputs, which are adjustable. The endpoints of the initial interval and a formula for evaluating the single-variable function at any point of this interval are the straightforward inputs. The three adjustable inputs are a tolerance with the minimal and maximal numbers of subintervals. The tolerance is the secondary adjustable input. Having broken the initial interval into a set of subintervals, the three-point iterated half-cutting “gropes” around every local minimum by successively cutting off a half of the subinterval or dividing the subinterval in two. A range of subinterval sets defined by the minimal and maximal numbers of subintervals is covered by running the threepoint half-cutting on every set of subintervals. As a set of values of currently found local minima points changes less than by the tolerance, the set of local minimum points and the respective set of function values at these points are returned. The presented approach is applicable to whichever task of finding local extrema is. If primarily the purpose is to find all local maxima or the global maximum of the function, the presented approach is applied to the function taken with the negative sign. The presented approach is a significant and important contribution to the field of numerical estimation and approximate analysis. Although the method does not assure obtaining all local minima (or maxima) for any function, setting appropriate minimal and maximal numbers of subintervals makes missing some minima (or maxima) very unlikely.
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3

Romanuke, Vadim. "Nine-Point Iterated Rectangle Dichotomy for Finding All Local Minima of Unknown Bounded Surface." Applied Computer Systems 27, no. 2 (December 1, 2022): 89–100. http://dx.doi.org/10.2478/acss-2022-0010.

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Abstract A method is suggested to find all local minima and the global minimum of an unknown two-variable function bounded on a given rectangle regardless of the rectangle area. The method has eight inputs: five inputs defined straightforwardly and three inputs, which are adjustable. The endpoints of the initial intervals constituting the rectangle and a formula for evaluating the two-variable function at any point of this rectangle are the straightforward inputs. The three adjustable inputs are a tolerance with the minimal and maximal numbers of subintervals along each dimension. The tolerance is the secondary adjustable input. Having broken the initial rectangle into a set of subrectangles, the nine-point iterated rectangle dichotomy “gropes” around every local minimum by successively cutting off 75 % of the subrectangle area or dividing the subrectangle in four. A range of subrectangle sets defined by the minimal and maximal numbers of subintervals along each dimension is covered by running the nine-point rectangle dichotomy on every set of subrectangles. As a set of values of currently found local minima points changes no more than by the tolerance, the set of local minimum points and the respective set of minimum values of the surface are returned. The presented approach is applicable to whichever task of finding local extrema is. If primarily the purpose is to find all local maxima or the global maximum of the two-variable function, the presented approach is applied to the function taken with the negative sign. The presented approach is a significant and important contribution to the field of numerical estimation and approximate analysis. Although the method does not assure obtaining all local minima (or maxima) for any two-variable function, setting appropriate minimal and maximal numbers of subintervals makes missing some minima (or maxima) very unlikely.
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4

Shenitzer, Abe, and V. M. Tikhomirov. "Stories About Maxima and Minima." American Mathematical Monthly 99, no. 2 (February 1992): 182. http://dx.doi.org/10.2307/2324204.

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5

Sun, Zhi-Wei. "Sums of minima and maxima." Discrete Mathematics 257, no. 1 (November 2002): 143–59. http://dx.doi.org/10.1016/s0012-365x(01)00476-9.

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6

Cadeddu, Lucio, and Giampaolo Lai. "Maxima and Minima Without Derivatives?" College Mathematics Journal 46, no. 1 (January 2015): 15–22. http://dx.doi.org/10.4169/college.math.j.46.1.15.

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7

King, Peter, and John Longeway. "William Heytesbury: On Maxima and Minima." Philosophical Review 96, no. 1 (January 1987): 146. http://dx.doi.org/10.2307/2185342.

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8

Braunstein, Myron L., Donald D. Hoffman, and Asad Saidpour. "Parts of Visual Objects: An Experimental Test of the Minima Rule." Perception 18, no. 6 (December 1989): 817–26. http://dx.doi.org/10.1068/p180817.

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Three experiments were conducted to test Hoffman and Richards's (1984) hypothesis that, for purposes of visual recognition, the human visual system divides three-dimensional shapes into parts at negative minima of curvature. In the first two experiments, subjects observed a simulated object (surface of revolution) rotating about a vertical axis, followed by a display of four alternative parts. They were asked to select a part that was from the object. Two of the four parts were divided at negative minima of curvature and two at positive maxima. When both a minima part and a maxima part from the object were presented on each trial (experiment 1), most of the correct responses were minima parts (101 versus 55). When only one part from the object—either a minima part or a maxima part—was shown on each trial (experiment 2), accuracy on trials with correct minima parts and correct maxima parts did not differ significantly. However, some subjects indicated that they reversed figure and ground, thereby changing maxima parts into minima parts. In experiment 3, subjects marked apparent part boundaries. 81% of these marks indicated minima parts, 10% of the marks indicated maxima parts, and 9% of the marks were at other positions. These results provide converging evidence, from two different methods, which supports Hoffman and Richards's minima rule.
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9

Pleacher, David. "Activities: Activities to Introduce Maxima-Minima Problems." Mathematics Teacher 84, no. 5 (May 1991): 379–86. http://dx.doi.org/10.5951/mt.84.5.0379.

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Introduction: Maxima and minima problems have interested mathematicians since the early Greeks. Heron is given credit for one of the most significant discoveries of his time that when light travels from a point to a mirror and then to another point, it takes the shortest possible path. In daily life, practical problems involving maxima and minima arise frequently. Problems about the best shape, shortest distance, or maximum volume are often contemplated.
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10

Shaked, Moshe, and Tityik Wong. "Stochastic comparisons of random minima and maxima." Journal of Applied Probability 34, no. 2 (June 1997): 420–25. http://dx.doi.org/10.2307/3215381.

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Let X1, X2,… be a sequence of independent random variables and let N be a positive integer-valued random variable which is independent of the Xi. In this paper we obtain some stochastic comparison results involving min {X1, X2,…, XN) and max{X1, X2,…, XN}.
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11

Shaked, Moshe, and Tityik Wong. "Stochastic comparisons of random minima and maxima." Journal of Applied Probability 34, no. 02 (June 1997): 420–25. http://dx.doi.org/10.1017/s0021900200101056.

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Let X 1, X 2,… be a sequence of independent random variables and let N be a positive integer-valued random variable which is independent of the Xi. In this paper we obtain some stochastic comparison results involving min {X 1, X 2,…, XN ) and max{X 1, X 2,…, XN }.
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12

Běhounek, Libor. "Maxima and minima in fuzzified linear orderings." Fuzzy Sets and Systems 289 (April 2016): 82–93. http://dx.doi.org/10.1016/j.fss.2015.02.010.

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13

Ragulina, Olena, and Jonas Šiaulys. "Randomly stopped minima and maxima with exponential-type distributions." Nonlinear Analysis: Modelling and Control 24, no. 2 (February 1, 2019): 297–313. http://dx.doi.org/10.15388/na.2019.2.9.

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Let {ξ1, ξ2,...} be a sequence of independent real-valued and possibly nonidentically distributed random variables. Suppose that η is a nonnegative, nondegenerate at 0 and integer-valued random variable, which is independent of {ξ1, ξ2,...}. In this paper, we consider conditions for {ξ1, ξ2,...} and η under which the distributions of the randomly stopped maxima and minima as well as randomly stopped maxima of sums and randomly stopped minima of sums belong to the class of exponential distributions.
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14

A., Liakos. "MINIMA AND MAXIMA TIMINGS OF SEVERAL VARIABLE STARS." Open European Journal on Variable stars, no. 211 (2021): 1–12. http://dx.doi.org/10.5817/oejv2021-0215.

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We present 228 times of minima of 33 eclipsing binaries and nine maxima timings of two pulsating stars. The majority of the objects are newly discovered variables and they were observed as by product. The observations were employed five different telescop
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15

Sebastian, W. "Maxima and minima of moments in hyperstatic spans." Proceedings of the Institution of Civil Engineers - Structures and Buildings 162, no. 6 (December 2009): 381–90. http://dx.doi.org/10.1680/stbu.2009.162.6.381.

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16

Giusti, Enrico. "Les méthodes des maxima et minima de Fermat." Annales de la faculté des sciences de Toulouse Mathématiques 18, S2 (2009): 59–85. http://dx.doi.org/10.5802/afst.1229.

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17

Rivera-Figueroa, Antonio, and Juan Carlos Ponce-Campuzano. "Derivative, maxima and minima in a graphical context." International Journal of Mathematical Education in Science and Technology 44, no. 2 (March 15, 2013): 284–99. http://dx.doi.org/10.1080/0020739x.2012.690896.

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18

Dolati, Ali. "On Dependence Properties of Random Minima and Maxima." Communications in Statistics - Theory and Methods 38, no. 3 (December 19, 2008): 393–99. http://dx.doi.org/10.1080/03610920802213707.

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19

Guillaume, Tristan. "valuation of options on joint minima and maxima." Applied Mathematical Finance 8, no. 4 (December 2001): 209–33. http://dx.doi.org/10.1080/13504860210122384.

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20

Dermendijev, V. N., G. T. Buyukliev, and Y. Y. Shopov. "The Prolonged Minima and Maxima of Solar Activity." International Astronomical Union Colloquium 130 (1991): 268–70. http://dx.doi.org/10.1017/s0252921100079732.

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Abstract We study a new indirect index of solar activity – the Intensity of Luminescence of Cave Flowstone Microzones. This index correlates directly with the solar activity. Using a time series of the index with resolution 4-5 pixels/year we study some of the statistical properties of the solar activity cycle during 28 prolonged minima and 21 prolonged maxima.
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21

Zhou, Mingli, and K. R. Brownstein. "A variational calculation exhibiting both minima and maxima." European Journal of Physics 20, no. 6 (November 1, 1999): 517–22. http://dx.doi.org/10.1088/0143-0807/20/6/318.

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22

Real, António C., José Borges, and Carlos B. Oliveira. "Estimation of daily mean temperatures: an accurate method for the Douro Valley." Ciência e Técnica Vitivinícola 33, no. 2 (2018): 167–76. http://dx.doi.org/10.1051/ctv/20183302167.

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Air temperature data from many locations worldwide are only available as series of daily minima and maxima temperatures. Historically, several different approaches have been used to estimate the actual daily mean temperature, as only in the last two or three decades automatic thermometers are able to compute its actual value. The most common approach is to estimate it by averaging the daily minima and maxima. When only daily minima and maxima are available, an alternative approach, proposed by Dall’Amico and Hornsteiner in 2006, uses the two daily extremes together with next day minima temperature and a coefficient related to the local daily astronomical sunset time. Additionally, the method uses two optimizable coefficients related to the region’s temperature profile. In order to use this approach it is necessary to optimize the region’s unknown parameters. For this optimization, it is necessary a dataset containing the maxima, minima, and the actual daily mean temperatures for at least one year. In this research, for the period 2007-2014, we used three datasets of minima, maxima and actual mean temperatures obtained at three automatic meteorological stations located in the Douro Valley to optimize the two unknown parameters in the Dall’Amico and Hornsteiner approach. Moreover, we compared the actual mean daily temperatures available from the three datasets with the correspondent values estimated by using i) the usual approach of averaging the daily maxima and minima temperatures and ii) the Dall’Amico and Hornsteiner approach. Results show that the former approach overestimates, on average, the daily mean temperatures by 0.5ºC. The Dall’Amico and Hornsteiner approach showed to be a better approximation of mean temperatures for the three meteorological stations used in this research, being unbiased relative to the actual mean values of daily temperatures. In conclusion, this research confirms that the Dall’Amico and Hornsteiner is a better approach to estimate the mean daily temperatures and provides the optimized parameters for three sites located at each of the three sub-regions of the Douro Valley (Baixo Corgo, Cima Corgo and Douro Superior).
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23

Kane, R. P. "Evolutions of various solar indices around sunspot maximum and sunspot minimum years." Annales Geophysicae 20, no. 6 (June 30, 2002): 741–55. http://dx.doi.org/10.5194/angeo-20-741-2002.

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Abstract. The smoothed monthly sunspot numbers showed that in many solar cycles, (a) during years around sunspot maxima, there was only one prominent maximum, but in some cycles there was a broad plateau. If the beginning and end of these are termed as first and second maxima (separated by several months), the first maximum was generally the higher one, and the valley in between was very shallow. Solar indices at or near the photosphere generally showed similar structures with maxima matching with sunspot maxima within a month or two. Indices originating in the chromosphere and above showed two peaks in roughly the same months as sunspots (with some exceptions, notably the Coronal green line, and the Total Solar Irradiance). Yet often, the second maximum was larger than the first maximum, and the valley between the two maxima was deeper, as compared to sunspot maxima, and (b) during years around sunspot minima, the smoothed sunspot minimum could be sharp and distinct, lasting for a month or two, or could spread over several months. Among the indices originating at or near the photosphere, the Ca K line intensity showed good matching with sunspots, but the Ca Plage area, the Sunspot Group Area, and the solar magnetic fields seemed to show minima earlier than the sunspots, indicating that these activities died out first. These also showed recoveries from the minima later than sunspots. Most of the other indices originating in the chromosphere and corona attained minima coincident with sunspot minima, but in some cases, minima earlier than sunspots were seen, while in some other cases minima occurred after the sunspot minima. Thus, the energy dissipation in the upper part of the solar atmosphere sometimes lagged or led the evolution of sunspots near sunspot minimum. In a few cases, after the minimum, the indices recovered faster than the sunspots. In general, the chromospheric indices seemed to evolve similar to sunspots, but the evolution of coronal indices was not always similar to sunspots, and may differ considerably between themselves.Key words. Solar physics, astrophysics and astronomy (Corona and transition region; Magnetic fields; Photosphere and chromosphere)
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24

P, Parameswaran. "New Approach to Find the Maxima and Minima of a Function." International Journal of Trend in Scientific Research and Development Volume-3, Issue-2 (February 28, 2019): 789–90. http://dx.doi.org/10.31142/ijtsrd21483.

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25

Mohin, S., A. V. Raveendran, and M. V. Mekkaden. "Photometry of the RS CVn binary II Peg." Symposium - International Astronomical Union 118 (1986): 309–11. http://dx.doi.org/10.1017/s0074180900151642.

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B and V photometry of II Peg obtained at Kavalur on 39 nights during 1980–81, 1981–82 and 1984–85 observing seasons is presented in Fig. 1. From an analysis of the available data on this object we find that no two light curves agree in any of the following: shape, amplitude, phases of the light maxima and minima, mean light level, or brightness at the light maxima and minima.
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26

Kennedy, James B., and Jonathan Rohleder. "On the hot spots of quantum graphs." Communications on Pure & Applied Analysis 20, no. 9 (2021): 3029. http://dx.doi.org/10.3934/cpaa.2021095.

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<p style='text-indent:20px;'>We undertake a systematic investigation of the maxima and minima of the eigenfunctions associated with the first nontrivial eigenvalue of the Laplacian on a metric graph equipped with standard (continuity–Kirchhoff) vertex conditions. This is inspired by the famous hot spots conjecture for the Laplacian on a Euclidean domain, and the points on the graph where maxima and minima are achieved represent the generically "hottest" and "coldest" spots of the graph. We prove results on both the number and location of the hot spots of a metric graph, and also present a large number of examples, many of which run contrary to what one might naïvely expect. Amongst other results we prove the following: (i) generically, up to arbitrarily small perturbations of the graph, the points where minimum and maximum, respectively, are attained are unique; (ii) the minima and maxima can only be located at the vertices of degree one or inside the doubly connected part of the metric graph; and (iii) for any fixed graph topology, for some choices of edge lengths all minima and maxima will occur only at degree-one vertices, while for others they will only occur in the doubly connected part of the graph.</p>
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27

Bishop, Michael. "La poésie de Gérard Titus-Carmel: minima et maxima." Irish Journal of French Studies 3, no. 1 (December 1, 2003): 1–19. http://dx.doi.org/10.7173/164913303818644450.

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28

Hashorva, Enkelejd. "Minima and maxima of elliptical arrays and spherical processes." Bernoulli 19, no. 3 (August 2013): 886–904. http://dx.doi.org/10.3150/12-bej463.

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29

Richter, Klaus O. "A Simple Gauge for Water-Level Maxima and Minima." Ecological Restoration 15, no. 1 (1997): 60–63. http://dx.doi.org/10.3368/er.15.1.60.

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30

Sebastian, Wendel, and William M. Jenkins. "Discussion: Maxima and minima of moments in hyperstatic spans." Proceedings of the Institution of Civil Engineers - Structures and Buildings 164, no. 4 (August 2011): 287–88. http://dx.doi.org/10.1680/stbu.2011.164.4.287.

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31

Giuliano, Rita, and Claudio Macci. "Large Deviation Principles for Sequences of Maxima and Minima." Communications in Statistics - Theory and Methods 43, no. 6 (February 14, 2014): 1077–98. http://dx.doi.org/10.1080/03610926.2012.668606.

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32

Hashorva, Enkelejd, and Zhichao Weng. "Maxima and minima of complete and incomplete stationary sequences." Stochastics 86, no. 5 (March 24, 2014): 707–20. http://dx.doi.org/10.1080/17442508.2013.876423.

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33

Shenitzer, Abe, and L. Euler. "Stories About Maxima and Minima. By V. M. Tikhomirov." American Mathematical Monthly 99, no. 2 (February 1992): 182–83. http://dx.doi.org/10.1080/00029890.1992.11995830.

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34

Pudlák, Pavel, and Neil Thapen. "Alternating minima and maxima, Nash equilibria and Bounded Arithmetic." Annals of Pure and Applied Logic 163, no. 5 (May 2012): 604–14. http://dx.doi.org/10.1016/j.apal.2011.06.014.

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35

Jayalekshmi, G. L., and P. R. Prince. "Prediction of upcoming grand episodes of solar activity." Proceedings of the International Astronomical Union 13, S340 (February 2018): 325–26. http://dx.doi.org/10.1017/s1743921318001734.

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AbstractSunspots are active regions on the surface of the Sun having strong magnetic fields. Activity level of the Sun shows long-time scale phenomena known as grand episodes-Grand maxima and Grand minima. Present study examines grand episodes shown by sunspot numbers (1090-2017), using methods of wavelet transform and sinusoidal regression. Time interval analysed includes two grand maxima and four grand minima. Interval in between grand episodes are regular oscillations. Phase changes found from periodicity analysis clearly show the presence of upcoming grand episodes. The forthcoming grand episodes are suggested to be two grand minima which are likely to occur between the years 2100-2160 and 2220-2300.
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36

Earle, David C. "Surface Contours, Glass Patterns, and a Slant Illusion." Perception 15, no. 5 (October 1986): 537–40. http://dx.doi.org/10.1068/p150537.

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A surface contour pattern constructed from continuous sine waves is subject to several visual interpretations, whereby the separate regions containing the maxima and the minima of the sine waves may be seen as representing either convex or concave areas of a three-dimensional surface. In a pattern of segments of contours comprising only the regions containing the maxima and minima of the sine waves, a set of surfaces is perceived, each of which tends to be seen as convex, and which possesses an illusory slant which is different for columns of contour segments containing maxima as compared with columns containing minima. It is conjectured that the slant illusion is a manifestation of the processes by which depth is derived from surface contour information. It is demonstrated that corresponding figures constructed from sinusoidal Glass patterns produce similar effects. From this it is concluded that the structure of Glass patterns provides a sufficient input representation for the processes by which surface shape is recovered from surface contours.
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37

Cuccu, Fabrizio, and Giovanni Porru. "Symmetry of solutions to optimization problems related to partial differential equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 5 (October 2006): 921–34. http://dx.doi.org/10.1017/s0308210500004807.

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We investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. We prove existence results and, under suitable restrictions on the data, we show that any maximal configuration satisfies a special system of two equations. Next, we use the moving-plane method to find symmetry results for solutions of a system. We apply these results in our discussion of symmetry for the maximal configurations of the previous problem.
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38

Gruber, Jason, Denise C. George, Andrew P. Kuprat, Gregory S. Rohrer, and Anthony D. Rollett. "Effect of Anisotropic Interfacial Energy on Grain Boundary Distributions during Grain Growth." Materials Science Forum 467-470 (October 2004): 733–38. http://dx.doi.org/10.4028/www.scientific.net/msf.467-470.733.

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Through simulations with the moving finite element program GRAIN3D, we have studied the effect of anisotropic grain boundary energy on the distribution of boundary types in a polycrystal during normal grain growth. An energy function similar to that hypothesized for magnesia was used, and the simulated grain boundary distributions were found to agree well with measured distributions. The simulated results suggest that initially random microstructures develop nearly steady state grain boundary distributions that have local maxima and minima corresponding to local minima and maxima, respectively, of the energy function.
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39

Kumar, Kante Raj, and V. Thrimurthulu. "Efficient Sorting Mechanism For Finding First W Maxima/Minima Values." i-manager's Journal on Embedded Systems 3, no. 3 (October 15, 2014): 39–44. http://dx.doi.org/10.26634/jes.3.3.3299.

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40

Wang, Qian-Jin, Cheng-Ping Huang, Jia-Qi Li, and Yong-Yuan Zhu. "Suppression of transmission minima and maxima with structured metal surface." Applied Physics Letters 89, no. 22 (November 27, 2006): 221121. http://dx.doi.org/10.1063/1.2400098.

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41

Buss, Emily, Joseph Hall, and John Grose. "MLDs for signals placed in masker envelope minima and maxima." Journal of the Acoustical Society of America 109, no. 5 (May 2001): 2375–76. http://dx.doi.org/10.1121/1.4744366.

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42

Dı́az Herrera, Fernando, Elizabeth Sierra Uribe, L. Fernando Bückle Ramirez, and Arturo Garrido Mora. "Critical thermal maxima and minima of Macrobrachium rosenbergii (Decapoda: Palaemonidae)." Journal of Thermal Biology 23, no. 6 (December 1998): 381–85. http://dx.doi.org/10.1016/s0306-4565(98)00029-1.

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43

Bartoszewicz, Jarosław. "Stochastic comparisons of random minima and maxima from life distributions." Statistics & Probability Letters 55, no. 1 (November 2001): 107–12. http://dx.doi.org/10.1016/s0167-7152(01)00139-0.

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44

Alsmeyer, Gerold, and Uwe Rösler. "A stochastic fixed point equation for weighted minima and maxima." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 44, no. 1 (February 2008): 89–103. http://dx.doi.org/10.1214/07-aihp104.

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45

Usoskin, I. G., S. K. Solanki, and G. A. Kovaltsov. "Grand minima and maxima of solar activity: new observational constraints." Astronomy & Astrophysics 471, no. 1 (June 6, 2007): 301–9. http://dx.doi.org/10.1051/0004-6361:20077704.

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46

Hall, Joseph W., Emily Buss, John H. Grose, and Madhu B. Dev. "Developmental Effects in the Masking-Level Difference." Journal of Speech, Language, and Hearing Research 47, no. 1 (February 2004): 13–20. http://dx.doi.org/10.1044/1092-4388(2004/002).

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Adults and children (aged 5 years 1 month to 10 years 8 months) were tested in a masking-level difference (MLD) paradigm in which detection of brief signals was contrasted for signal placement in masker envelope maxima versus masker envelope minima. Maskers were 50-Hz-wide noise bands centered on 500 Hz, and the signals were So or Sπ 30-ms, 500-Hz tones. In agreement with previous studies, it was found that MLDs were greater for masker envelope minima placement than for masker envelope maxima placement. Across the age range of the children tested here, the binaural advantage associated with the masker envelope minima increased with the age of the child. One interpretation of the present results is that there is a developmental improvement in binaural temporal resolution over the age range tested here.
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47

Rehman, Muhammad Zubair, Abdullah Khan, Rozaida Ghazali, Muhammad Aamir, and Nazri Mohd Nawi. "A new Multi Sine-Cosine algorithm for unconstrained optimization problems." PLOS ONE 16, no. 8 (August 6, 2021): e0255269. http://dx.doi.org/10.1371/journal.pone.0255269.

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The Sine-Cosine algorithm (SCA) is a population-based metaheuristic algorithm utilizing sine and cosine functions to perform search. To enable the search process, SCA incorporates several search parameters. But sometimes, these parameters make the search in SCA vulnerable to local minima/maxima. To overcome this problem, a new Multi Sine-Cosine algorithm (MSCA) is proposed in this paper. MSCA utilizes multiple swarm clusters to diversify & intensify the search in-order to avoid the local minima/maxima problem. Secondly, during update MSCA also checks for better search clusters that offer convergence to global minima effectively. To assess its performance, we tested the MSCA on unimodal, multimodal and composite benchmark functions taken from the literature. Experimental results reveal that the MSCA is statistically superior with regards to convergence as compared to recent state-of-the-art metaheuristic algorithms, including the original SCA.
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48

Jokimaitis, Arvydas, and Algimantas Aksomaitis. "Ekstremaliųjų reikšmių tankių perkėlimo teoremos." Lietuvos matematikos rinkinys 45 (December 18, 2005): 542–46. http://dx.doi.org/10.15388/lmr.2005.29321.

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49

Kozlíková, Katarína, and Juraj Martinka. "Age and Sex Variability of Initial Parts of the QRS Complex Displayed in Isointegral Maps of Young People." Acta Medica (Hradec Kralove, Czech Republic) 47, no. 4 (2004): 317–21. http://dx.doi.org/10.14712/18059694.2018.115.

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Although body surface electrocardiographic mapping is used also in clinical practice, there are only a few papers concerning the isointegral maps (IIMs) in children. We constructed IIMs of 169 healthy young people during the initial parts of the QRS complex: the first 20 ms (QRS20), 30 ms (QRS30), 40 ms (QRS40), and from 20 ms to 40 ms (QRS20–40). Subjects were divided into 6 groups: 9–10 y (F1, M1), 13–14 y (F2, M2), 18–19 y (F3; M3). We analysed the extreme values of each time integral. We found maxima and peak-to-peak values decreasing with age, while minima tended to increase (became less negative). Most age differences were found in IIM QRS20–40 and between peak-to-peak values. Least differences were between minima. Maxima and peak-to-peak values were higher in males than in females. No significant differences were found in any extreme value between groups F1 and M1 except for IIM QRS20 maxima. Significant sex differences increased with age. The only significant difference found in minima was between F2 and M2. Most sex differences were found in IIM QRS20. We assume that our findings can be explained (at least in part) by the influence of heart – chest geometry.
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50

Priest, Eric. "The nature and significance of solar minima." Proceedings of the International Astronomical Union 7, S286 (October 2011): 3–14. http://dx.doi.org/10.1017/s1743921312004577.

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AbstractAs an introduction to the theme of this symposium, I give a simple review of the photospheric magnetic field, the properties of the solar cycle, the way in which the magnetic field is thought to be generated by dynamo action, and finally the unusual properties of the recent solar minimum. This has awakened an interest in improving predictions of the solar cycle and in the nature of solar minima not just as gaps between maxima but as phenomena of intrinsic interest in their own right.
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