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Journal articles on the topic 'Multiplicative binomial'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Shephard, G. C. "Multiplicative Identities for Binomial Coefficients." Fibonacci Quarterly 49, no. 1 (2011): 10–21. http://dx.doi.org/10.1080/00150517.2011.12428069.

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2

Bayo, H. Lawal. "Employing the Double, Multiplicative and The Com-Poisson Binomial Distributions for modeling Over and Under-dispersed Binary Data." Employing the Double, Multiplicative and The Com-Poisson Binomial Distributions for modeling Over and Under-dispersed Binary Data 23, no. 3 (2017): 1–17. https://doi.org/10.9734/JAMCS/2017/33475.

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In this paper, we compare the performances of several models for tting over-dispersed binary data. The distribution models considered in this study include the binomial (BN), the beta- binomial (BB), the multiplicative binomial (MBM), the Com-Poisson binomial (CPB) and the double binomial (DBM) models. Applications of these models to several well known data sets exhibiting under-dispersion and over-dispersion were considered in this paper. We applied these models to two frequency data sets and two data sets with covariates that have been variously analysed in the literature. The rst relates to

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3

Xia, Jianguo, and Hourong Qin. "On the multiplicative independence of binomial coefficients." Acta Arithmetica 116, no. 3 (2005): 289–92. http://dx.doi.org/10.4064/aa116-3-4.

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4

Lovison, G. "An alternative representation of Altham's multiplicative-binomial distribution." Statistics & Probability Letters 36, no. 4 (1998): 415–20. http://dx.doi.org/10.1016/s0167-7152(97)00088-6.

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5

VOJAK, ROBERT, and JACQUES LÉVY VÉHEL. "PREDICTABILITY OF MULTIPLICATIVE PROCESSES: A PRELIMINARY STUDY." Fractals 02, no. 03 (1994): 383–86. http://dx.doi.org/10.1142/s0218348x9400048x.

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We define a multifractal analysis for correlations. We present explicit results in the case of deterministic multinomial measures, and show that the multifractal formalism does not hold for correlations on binomial measures.

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6

Cheng, Q. "Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions." Nonlinear Processes in Geophysics 21, no. 2 (2014): 477–87. http://dx.doi.org/10.5194/npg-21-477-2014.

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Abstract. The concepts and models of multifractals have been employed in various fields in the geosciences to characterize singular fields caused by nonlinear geoprocesses. Several indices involved in multifractal models, i.e., asymmetry, multifractality, and range of singularity, are commonly used to characterize nonlinear properties of multifractal fields. An understanding of how these indices are related to the processes involved in the generation of multifractal fields is essential for multifractal modeling. In this paper, a five-parameter binomial multiplicative cascade model is proposed

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7

de Godoy Stênico, Jeferson Wilian, and Lee Luan Ling. "Modern network traffic modeling based on binomial multiplicative cascades." Journal of Supercomputing 71, no. 5 (2014): 1712–35. http://dx.doi.org/10.1007/s11227-014-1255-1.

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8

Bayo, H. Lawal. "On Modeling the Double and Multiplicative Binomial Models as Log-Linear Models." Advances in Computer Sciences (ISSN:2517-5718) 1, no. 1 (2018): 1–10. https://doi.org/10.31021/acs.20181103.

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<strong>Abstract</strong> In this paper we have fitted the double binomial and multiplicative binomial distributions as log-linear models using sufficient statistics. This approach is not new as several authors have employed this approach, most especially in the analysis of the Human sex ratio in [1]. However, obtaining the estimated parameters of the distributions may be problematic, especially for the double binomial where the parameter estimate of π may not be readily available from the Log-Linear (LL) parameter estimates. Other issues associated with the LL approach is its implementatio

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9

Chen, James J., and Hongshik Ahn. "Marginal Models with Multiplicative Variance Components for Overdispersed Binomial Data." Journal of Agricultural, Biological, and Environmental Statistics 2, no. 4 (1997): 440. http://dx.doi.org/10.2307/1400513.

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10

Del Fava, Emanuele, Ziv Shkedy, Mehreteab Aregay, and Geert Molenberghs. "Modelling multivariate, overdispersed binomial data with additive and multiplicative random effects." Statistical Modelling: An International Journal 14, no. 2 (2014): 99–133. http://dx.doi.org/10.1177/1471082x13503450.

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11

Elamir, Elsayed A. H. "Multiplicative-Binomial Distribution: Some Results on Characterization, Inference and Random Data Generation." Journal of Statistical Theory and Applications 12, no. 1 (2013): 92. http://dx.doi.org/10.2991/jsta.2013.12.1.8.

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12

Han, Yu Du, and Jae Heon Yun. "Performance of the Restarted Homotopy Perturbation Method and Split Bregman Method for Multiplicative Noise Removal." Mathematical Problems in Engineering 2018 (December 6, 2018): 1–21. http://dx.doi.org/10.1155/2018/7696798.

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In this paper, we first propose restarted homotopy perturbation methods (RHPM) for multiplicative noise removal of the RLO and AA2 models. The main difficulty in applying the RHPM to the nonlinear denoising problem is settled by using binomial series techniques. We next propose the split Bregman methods for multiplicative noise removal of the RLO and AA2 models. The difficulty in applying the split Bregman method to the nonlinear denoising problem can be handled by transforming ill-conditioned linear systems into well-conditioned linear systems using splitting techniques of singular matrices.

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13

Laohakosol, Vichian, and Nittiya Pabhapote. "Properties of rational arithmetic functions." International Journal of Mathematics and Mathematical Sciences 2005, no. 24 (2005): 3997–4017. http://dx.doi.org/10.1155/ijmms.2005.3997.

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Rational arithmetic functions are arithmetic functions of the formg1∗⋯∗gr∗h1−1∗⋯∗hs−1, wheregi,hjare completely multiplicative functions and∗denotes the Dirichlet convolution. Four aspects of these functions are studied. First, some characterizations of such functions are established; second, possible Busche-Ramanujan-type identities are investigated; third, binomial-type identities are derived; and finally, properties of the Kesava Menon norm of such functions are proved.

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14

Morgan, I. G., and E. H. Neave. "A Discrete Time Model for Pricing Treasury Bills, Forward, and Futures Contracts." ASTIN Bulletin 23, no. 1 (1993): 3–22. http://dx.doi.org/10.2143/ast.23.1.2005099.

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AbstractThis paper develops a discrete time model for valuing treasury bills and either forward or futures contracts written against them. It provides formulae for bill prices, forward prices, futures prices, and their conditional variances and risk premiums. The interest rate process is described by a multiplicative binomial random walk whose features conform to some principal characteristics of observed processes. Initial forward rates are constrained to match initially observed term structure data.

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15

KIM, SOO YONG, GYUCHANG LIM, KI-HO CHANG, et al. "MULTIFRACTAL BEHAVIORS IN FOREIGN EXCHANGE MARKETS." Fractals 17, no. 01 (2009): 15–21. http://dx.doi.org/10.1142/s0218348x0900420x.

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A two-phase phenomenon in three financial exchange prices is studied. To understand the underlying mechanism for the formation of market prices, we perform the multifractal analysis and the detrended fluctuation analysis in terms of time series of market prices. We also examine higher order temporal correlations for the market price. Although the multifractal properties of market prices are obtained, it cannot be reproduced the binomial multiplicative process through that was used to understand fully developed turbulence.

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16

Wilian de Godoy Stenico, Jeferson, and Lee Luan Ling. "A New Network Traffic Modeling Based in Conservative Multiplicative Cascade with Weights Newton Binomial." IEEE Latin America Transactions 11, no. 5 (2013): 1143–55. http://dx.doi.org/10.1109/tla.2013.6684388.

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17

Koukouatikissa Diafouka, M., C. G. Louzayadio, R. O. Malouata, N. R. Ngabassaka, and R. BIdounga. "ON A BIVARIATE KATZ’S DISTRIBUTION." Advances in Mathematics: Scientific Journal 11, no. 10 (2022): 955–68. http://dx.doi.org/10.37418/amsj.11.10.11.

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In this paper, we propose the bivariate distribution of the univariate Katz distribution [7] using the technique of the product of marginal distributions by a multiplicative factor. This method has been examined in [11] and used in [9] to construct a bivariate Poisson distribution. The obtained model is a good way to unify bivariate Poisson, bivariate binomial and bivariate negative binomial distributions and has interesting properties. Among others, the correlation coefficient of the obtained model can be either positive, negative, or null, and the necessary condition of zero correlation is a

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18

Seneta, Eugene, and John Tuhao Chen. "On explicit and Fréchet-optimal lower bounds." Journal of Applied Probability 39, no. 1 (2002): 81–90. http://dx.doi.org/10.1239/jap/1019737989.

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Ease of computation of Fréchet-optimal lower bounds, given numerical values of the binomial moments Sij, i, j = 1, 2, is demonstrated. A sufficient condition is given for an explicit bivariate bound of Dawson-Sankoff structure to be Fréchet optimal. An example demonstrates that in the bivariate case even the multiplicative structure of the Sij does not guarantee a Dawson-Sankoff structure for Fréchet-optimal bounds. A final section is used to illuminate the nature of Fréchet optimality by using generalized explicit bounds. This note is a sequel to both Chen and Seneta (1995) and Chen (1998).

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Seneta, Eugene, and John Tuhao Chen. "On explicit and Fréchet-optimal lower bounds." Journal of Applied Probability 39, no. 01 (2002): 81–90. http://dx.doi.org/10.1017/s0021900200021525.

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Ease of computation of Fréchet-optimal lower bounds, given numerical values of the binomial moments S ij , i, j = 1, 2, is demonstrated. A sufficient condition is given for an explicit bivariate bound of Dawson-Sankoff structure to be Fréchet optimal. An example demonstrates that in the bivariate case even the multiplicative structure of the S ij does not guarantee a Dawson-Sankoff structure for Fréchet-optimal bounds. A final section is used to illuminate the nature of Fréchet optimality by using generalized explicit bounds. This note is a sequel to both Chen and Seneta (1995) and Chen (1998)

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20

Neave, Edwin H. "A Frequency Distribution Method for Valuing Average Options." ASTIN Bulletin 27, no. 2 (1997): 173–205. http://dx.doi.org/10.2143/ast.27.2.542047.

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AbstractThis paper finds payoff frequency distributions for valuing European and American fixed strike average options on a discrete time, recombining multiplicative binomial asset price process. In comparison to other discrete valuation methods the distributions, obtained analytically from a generating function, greatly reduce the computational requirements needed for accurate valuation. Less data are needed to value geometric than arithmetic averages, but the magnitude of calculations is similar for both instruments. Calculations of orderT3are needed to value European instruments, of orderT4

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21

De Santis, Enrico, Parisa Naraei, Alessio Martino, Alireza Sadeghian, and Antonello Rizzi. "Multifractal Characterization and Modeling of Blood Pressure Signals." Algorithms 15, no. 8 (2022): 259. http://dx.doi.org/10.3390/a15080259.

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In this paper, a multi-fractal analysis on a diastolic blood pressure signal is conducted. The signal is measured in a time span of circa one day through the multifractal detrended fluctuation analysis framework. The analysis is performed on asymptotic timescales where complex regulating mechanisms play a fundamental role in the blood pressure stability. Given a suitable frequency range and after removing non-stationarities, the blood pressure signal shows interesting scaling properties and a pronounced multifractality imputed to long-range correlations. Finally, a binomial multiplicative mode

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22

FEENY, B. F. "FAST MULTIFRACTAL ANALYSIS BY RECURSIVE BOX COVERING." International Journal of Bifurcation and Chaos 10, no. 09 (2000): 2277–87. http://dx.doi.org/10.1142/s0218127400001420.

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A fractal can be generated by using recursion, and a fractal set of data can be analyzed in the same way. This paper discusses a box-counting algorithm which exploits self-similarity via recursion. The speed of the algorithm is O(n), where n is the number of points in the set. The algorithm is applied to multifractal analysis of the binomial multiplicative process. The algorithm does not involve sorting the floating-point summation; a brief examination of the sorting issue is presented. Scattering for negative q, characteristic of box-counting algorithms, is encountered, and is explained for t

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23

Sagar, B. S. Daya. "Short communication: Quantitative spatial analysis of randomly situated surface water bodies through f-αspectra". Discrete Dynamics in Nature and Society 6, № 3 (2001): 213–17. http://dx.doi.org/10.1155/s1026022601000231.

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A notable similarity is observed between the probability distributions obtained from a data set that contains a large number of randomly situated surface water bodies and the probability distributions estimated by binomial multiplicative process. From these well conformed probability distributions, the generalised information dimensions have been computed through f-αspectra to characterise and quantify the spatial organisation of the surface water bodies. It is noticed from the investigated case study that the results tend to vary by changing the direction of bisecting process. The experimenta

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24

From, Steven G. "A weighted least-squares procedure for estimating the parameters of Altham's multiplicative generalization of the binomial distribution." Statistics & Probability Letters 25, no. 3 (1995): 193–99. http://dx.doi.org/10.1016/0167-7152(94)00222-t.

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25

Shilane, David, and Derek Bean. "Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion." Journal of Probability and Statistics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/602940.

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The negative binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard normal approximation often does not provide adequate inferences about the data's expected value in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expected value. These methods were based upon Gamma and Chi Square approximations or tail probability bounds such as Bernstein's inequality. We now propose growth estimators of the negative binomial mean. Unde

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26

Lawal, Bayo. "Employing the Double, Multiplicative and The Com-Poisson Binomial Distributions for modeling Over and Under-dispersed Binary Data." Journal of Advances in Mathematics and Computer Science 23, no. 3 (2017): 1–17. http://dx.doi.org/10.9734/jamcs/2017/33475.

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27

Dacorogna, Michel, Alessandro Ferriero, and David Krief. "One-Year Change Methodologies for Fixed-Sum Insurance Contracts." Risks 6, no. 3 (2018): 75. http://dx.doi.org/10.3390/risks6030075.

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We study the dynamics of the one-year change in P&C insurance reserves estimation by analyzing the process that leads to the ultimate risk in the case of “fixed-sum” insurance contracts. The random variable ultimately is supposed to follow a binomial distribution. We compute explicitly various quantities of interest, in particular the Solvency Capital Requirement for one year change and the Risk Margin, using the characteristics of the underlying model. We then compare them with the same figures calculated with existing risk estimation methods. In particular, our study shows that standard

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28

Myers, R. A., and J. M. Hoenig. "Direct estimates of gear selectivity from multiple tagging experiments." Canadian Journal of Fisheries and Aquatic Sciences 54, no. 1 (1997): 1–9. http://dx.doi.org/10.1139/f96-262.

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A new method is introduced for estimating selectivity of fishing gear from tagging data in which data from many experiments are combined. Selectivity is modeled as a multiplicative function of length and experiment effects using a generalized linear model with a log link function and a binomial error structure. We apply this method to 137 tagging experiments on Atlantic cod (Gadus morhua) conducted from 1954 to 1991. We show that the selectivity of otter trawls changed from the 1960s to the 1980s; during the earlier period the maximum probability of capture occurred at 55 cm and declined for l

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29

Islam, S. M. S., H. Gunarto, and A. A. K. Majumdar. "On the Sandor-Smarandache Function." Journal of Scientific Research 13, no. 2 (2021): 439–54. http://dx.doi.org/10.3329/jsr.v13i2.49965.

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In the current literature, a new Smarandache-type arithmetic function, involving binomial coefficients, has been proposed by Sandor. The new function, denoted by SS(n), is named the Sandor-Smarandache function. It has been found that, like many Smarandache-type functions, SS(n) is not multiplicative. Sandor found SS(n) when n (≥3) is an odd integer. Since then, the determination of SS(n) for even n remains a challenging problem. It has been shown that the function has a simple form even when n is even and not divisible by 3. This paper finds SS(n) in some particular cases of n, and finds an up

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30

Mathes, Tim, and Oliver Kuss. "Beta-binomial models for meta-analysis with binary outcomes: Variations, extensions, and additional insights from econometrics." Research Methods in Medicine & Health Sciences 2, no. 2 (2021): 82–89. http://dx.doi.org/10.1177/2632084321996225.

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Background Meta-analysis of systematically reviewed studies on interventions is the cornerstone of evidence based medicine. In the following, we will introduce the common-beta beta-binomial (BB) model for meta-analysis with binary outcomes and elucidate its equivalence to panel count data models. Methods We present a variation of the standard “common-rho” BB (BBST model) for meta-analysis, namely a “common-beta” BB model. This model has an interesting connection to fixed-effect negative binomial regression models (FE-NegBin) for panel count data. Using this equivalence, it is possible to estim

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31

Saługa, Piotr W., Paweł Grzesiak, and Jacek Kamiński. "Valuation of Decision Flexibility and Strategic Value in Coal Gasification Projects with the Option-To-Switch between Different Outputs." Energies 13, no. 11 (2020): 2826. http://dx.doi.org/10.3390/en13112826.

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Coal gasification has been promoted as a sophisticated clean energy technology alternative to coal burning these days. Aside from the usual technical difficulties, economic issues of such projects—especially valuation challenges—are important problems that practitioners usually struggle with. This is because of the major extent of managerial flexibility linked with specific characteristics of coal gasification projects, in particular, possibilities to mothball/restart manufacturing lines, or change between different outputs. The value of such flexibilities may be well assessed by real options

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32

Kakchapati, Sampurna, Sulawan Yotthanoo, and Chamnein Choonpradup. "Modeling tuberculosis incidence in Nepal." Asian Biomedicine 4, no. 2 (2010): 355–60. http://dx.doi.org/10.2478/abm-2010-0044.

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Abstract Background: Tuberculosis (TB) constitutes a large burden of infectious disease in Nepal. Objective: Model incidence of TB between 2003 and 2008 in Nepal. Methods: A retrospective study was conducted in Nepal of tuberculosis incidence by gender and location over the six years period. Data were obtained for 198,719 tuberculosis cases from the Nepal Tuberculosis Center (NTC). A negative binomial model with two multiplicative components as predictors was used and provided a good fit. Results: The model extracted a decreasing trend during the first five years followed by a drop in 2008.The

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33

Lindquist, W. Brent, Svetlozar T. Rachev, Jagdish Gnawali, and Frank J. Fabozzi. "Dynamic Asset Pricing in a Unified Bachelier–Black–Scholes–Merton Model." Risks 12, no. 9 (2024): 136. http://dx.doi.org/10.3390/risks12090136.

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We present a unified, market-complete model that integrates both Bachelier and Black–Scholes–Merton frameworks for asset pricing. The model allows for the study, within a unified framework, of asset pricing in a natural world that experiences the possibility of negative security prices or riskless rates. Unlike the classical Black–Scholes–Merton, we show that option pricing in the unified model differs depending on whether the replicating, self-financing portfolio uses riskless bonds or a single riskless bank account. We derive option price formulas and extend our analysis to the term structur

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34

Meneveau, Charles, and K. R. Sreenivasan. "The multifractal nature of turbulent energy dissipation." Journal of Fluid Mechanics 224 (March 1991): 429–84. http://dx.doi.org/10.1017/s0022112091001830.

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The intermittency of the rate of turbulent energy dissipation ε is investigated experimentally, with special emphasis on its scale-similar facets. This is done using a general formulation in terms of multifractals, and by interpreting measurements in that light. The concept of multiplicative processes in turbulence is (heuristically) shown to lead to multifractal distributions, whose formalism is described in some detail. To prepare proper ground for the interpretation of experimental results, a variety of cascade models is reviewed and their physical contents are analysed qualitatively. Point

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35

Ellegård Larsen, Hanne Marie, Eric Steen Hansen, Thomas Nord-Larsen, and Hanne Nina Rasmussen. "Deciduous trees as lichen phorophytes: biodiversity and colonization patterns under common garden conditions." Lichenologist 52, no. 3 (2020): 221–32. http://dx.doi.org/10.1017/s0024282920000018.

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AbstractCommon gardens are experimental plantations for comparing the performance of tree species while eliminating many of the variables that prevail in natural tree stands. The aim of this study was to evaluate the biodiversity of corticolous lichens on Danish tree species (Acer pseudoplatanus, Alnus glutinosa, Betula pendula, Fagus sylvatica, Fraxinus excelsior, Quercus robur and Tilia cordata) under common garden conditions and to examine the height distribution of particular lichen species. Observations were recorded through regular sampling of at least 36 lichen species on the main stems

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36

Orlov, A. I. "Mathematical methods for studying risks (resumptive article)." Industrial laboratory. Diagnostics of materials 87, no. 11 (2021): 70–80. http://dx.doi.org/10.26896/1028-6861-2021-87-11-70-80.

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We define risk as an unwanted opportunity and divide risk theory into three stages — risk analysis, risk estimation, risk management. Safety and risk are directly related to each other, being like a «mirror image» of each other which necessitates developing both the general theory of risk and particular theories of risk in specific areas. General risk theory allows for a uniform approach to the analysis, estimation and management of risks in specific situations. Currently, three main approaches to accounting for the uncertainty and describing risks are used — probabilistic and statistical appr

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37

Pratt, Sarah Smitherman. "Area models to image integer and binomial multiplication." Investigations in Mathematics Learning 10, no. 2 (2017): 85–105. http://dx.doi.org/10.1080/19477503.2017.1375352.

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Annamalai, Chinnaraji, and Antonio Marcos de Oliveira Siqueira. "Vector Space on the Binomial Coefficients in Combinatorial Geometric Series." Journal of Engineering and Exact Sciences 9, no. 6 (2023): 15413–01. http://dx.doi.org/10.18540/jcecvl9iss6pp15413-01e.

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A vector space is a group of objects that is closed under finite vector addition and scalar multiplication. This paper discusses a vector space under addition and multiplication of binomial coefficients defined in combinatorial geometric series. The combinatorial geometric series is a geometric series with binomial coefficients that is derived from the multiple summations of geometric series. This idea can enable the scientific researchers to solve the real world problems.

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39

Araves, Jinky Lhers L., Marialie Niña F. Cabaral, Marian Cabilugan, Mary Rose Nolasco, Richelle G. Delmo, and Levi E. Elipane. "Finding numerical coefficients of the product of two binomials with the same degrees using japanese multiplication method." South Florida Journal of Development 6, no. 7 (2025): e5537. https://doi.org/10.46932/sfjdv6n7-007.

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This study aims to investigate the use of Japanese Multiplication Method in finding the numerical coefficients of the product of two binomials with integral coefficients. It provides educators and learners a visual and an easier technique in multiplying integers and multiplying two binomials with integral coefficients, especially those that involve negative integers. To measure the effectiveness of the technique and to determine possible difficulties that educators and learners may encounter, the researchers conducted a lesson study to a group of 14 randomly chosen grade eight students, whose

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40

Annamalai, Chinnaraji, and Antonio Marcos de Oliveira Siqueira. "Skew Field on the Binomial Coefficients in Combinatorial Geometric Series." Journal of Engineering and Exact Sciences 8, no. 11 (2022): 14859–01. http://dx.doi.org/10.18540/jcecvl8iss11pp14859-01i.

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This paper discusses a commutative group, ring, and field under addition and multiplication of the binomial coefficients in combinatorial geometric series. The combinatorial geometric series is derived from the multiple summations of geometric series. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient. This idea can enable the scientific researchers to solve the real life problems.

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41

Borysenko, Oleksiy. "ON THE BINOMIAL METHOD FOR CALCULATION OF ENTROPY." Grail of Science, no. 21 (November 5, 2022): 113–18. http://dx.doi.org/10.36074/grail-of-science.28.10.2022.020.

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The article solves the problem of calculating the entropy value of binary messages of increased length generated by Bernoulli information sources. Such a problem arises during compression, error-correcting coding, combinatorial optimization, etc. In its usual solution, first, by means of statistical tests, the probabilities of messages are found, and then operations of logarithm, multiplication, and addition are performed on them, the number of which grows exponentially with increasing message length. In this work, it is proposed to reduce the number of calculations by replacing a number of ad

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42

Taşdemir, Funda. "Triple sums including Fibonacci numbers with three binomial coefficients." Notes on Number Theory and Discrete Mathematics 27, no. 1 (2021): 188–97. http://dx.doi.org/10.7546/nntdm.2021.27.1.188-197.

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In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial coefficients. We chose the indices of Fibonacci numbers as linear combination of the summation indices. Moreover, various types of alternating analogues of them whose powers depend on the index or indices are computed. These sums are evaluated in nice multiplication forms in terms of Fibonacci and Lucas numbers.

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43

Chii-Huei, Yu. "Arbitrary Order Fractional Derivative of Inverse Fractional Trigonometric Function." International Journal of Novel Research in Computer Science and Software Engineering 9, no. 2 (2022): 37–43. https://doi.org/10.5281/zenodo.6900497.

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<strong>Abstract:</strong> In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional derivative, any order fractional derivative of inverse fractional trigonometric function is obtained. The fractional binomial series and a new multiplication of fractional analytic functions play important roles in this article. In fact, these results we obtained are generalizations of those in traditional calculus. Moreover, the new multiplication is a natural operation of fractional analytic functions. <strong>Keywords:</strong> Jumarie’s modified R-L fractional derivative, In

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44

Bovdi, V., A. Diene, and R. Popovych. "Elements of high order in finite fields specified by binomials." Carpathian Mathematical Publications 14, no. 1 (2022): 238–46. http://dx.doi.org/10.15330/cmp.14.1.238-246.

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Let $F_q$ be a field with $q$ elements, where $q$ is a power of a prime number $p\geq 5$. For any integer $m\geq 2$ and $a\in F_q^*$ such that the polynomial $x^m-a$ is irreducible in $F_q[x]$, we combine two different methods to explicitly construct elements of high order in the field $F_q[x]/\langle x^m-a\rangle$. Namely, we find elements with multiplicative order of at least $5^{\sqrt[3]{m/2}}$, which is better than previously obtained bound for such family of extension fields.

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Lewis, Jacob M. "Teacher to Teacher: Indian Lightning Multiplication." Mathematics Teaching in the Middle School 11, no. 2 (2005): 101–3. http://dx.doi.org/10.5951/mtms.11.2.0101.

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In addition to teaching content area information, we as teachers also want to help our students develop a conceptual framework for mathematics. Without this conceptual framework, students often have trouble internalizing new information and mastering topics. For example, a student who does not really understand whole-number multiplication will more than likely have difficulty multiplying binomials. For this reason, in an introductory algebra course, a teacher needs a way to reinforce multiplication skills in an age-appropriate way while laying the groundwork for algebra topics involving multip

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Osanyinpeju, Kifilideen. "Implementation of Kifilideen Trinomial Theorem based on Matrix Approach in Computation of the Power of Base of Tri-Digits Number." Caliphate Journal of Science and Technology 4, no. 2 (2022): 119–32. http://dx.doi.org/10.4314/cajost.v4i2.1.

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The use of binomial theorem to expand trinomial expression of particular power n requires a bit by bit breaking down of the expansion until the final answer is obtained. This method had been seen not to be direct enough and involves repeated application up to the final result is achieved which makes the method to be unattractive. There is need to develop a direct and straight way in expanding trinomial expression of any power. This study implemented Kifilideen trinomial theorem based on matrix approach in computation of the power of base of tri – digits number. This method adopts Kif matrix ap

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Chii-Huei, Yu. "Fractional Derivatives of Some Fractional Functions." International Journal of Mechanical and Industrial Technology 12, no. 2 (2024): 1–5. https://doi.org/10.5281/zenodo.13969072.

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<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional derivative and a new multiplication of fractional analytic functions, we find arbitrary order fractional derivative of two fractional functions. Fractional binomial theorem plays an important role in this study. In fact, our results are generalizations of the results in classical calculus. <strong>Keywords:</strong> Jumarie type of R-L fractional derivative, new multiplication, fractional analytic functions, fractional binomial theorem. <strong>Title:</strong> Fractional Derivatives of Some Fr

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Pinchback, C. L., and Damber S. Tomer. "A Multiplication Algorithm for Two Integers." Mathematics Teacher 95, no. 1 (2002): 37–39. http://dx.doi.org/10.5951/mt.95.1.0037.

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The term Vedic mathematics usually refers to a set of sixteen word formulas, or sutras, along with their corollaries, that have origin in the Vedas. The Vedas are ancient holy texts from India that can be characterized as the allencompassing repository of Hindu knowledge from eons past. The Urdhva-tiryagbhyam sutra, or algorithm, has similarities to the FOIL (first, outer, inner, last) method that is used in algebra to multiply two binomials. We first illustrate this sutra with examples. Then we focus on similarities between Urdhva-tiryagbhyam and the standard multiplication algorithm, justifi

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Chii-Huei, Yu. "Fractional Partial Differential Problem of Some Matrix Two-Variables Fractional Functions." International Journal of Mechanical and Industrial Technology 12, no. 2 (2024): 6–13. https://doi.org/10.5281/zenodo.14039419.

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<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional derivative and a new multiplication of fractional analytic functions, we find arbitrary order fractional partial derivative of two types of matrix two-variables fractional functions. Fractional binomial theorem plays an important role in this article. In fact, our results are generalizations of ordinary calculus results. <strong>Keywords:</strong> Jumarie type of R-L fractional derivative, new multiplication, fractional analytic functions, fractional partial derivative, fractional binomial the

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Chii-Huei, Yu. "Evaluating Fractional Derivatives of Two Matrix Fractional Functions Based on Jumarie Type of Riemann-Liouville Fractional Derivative." International Journal of Engineering Research and Reviews 12, no. 4 (2024): 39–43. https://doi.org/10.5281/zenodo.14006057.

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<strong>Abstract:</strong> In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional derivative and a new multiplication of fractional analytic functions, we obtain arbitrary order fractional derivative of two matrix fractional functions. Fractional binomial theorem plays an important role in this article. In fact, our results are generalizations of ordinary calculus results. <strong>Keywords:</strong> Jumarie’s modified R-L fractional derivative, new multiplication, fractional analytic functions, matrix fractional functions, fractional binomial theorem. <strong

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