iosr-Jm   Volume-17 ~ Issue-5 ~ Sep. – Oct. 2021

Abstract: In this work, we are interested to the study of the one-dimensional stochastic nonlinear Schrödinger (NLS) equation with both a subcritical and a supercritical power nonlinearities in the presence of an additive noise. The deterministic equation occurs as a basic model in many areas of physics, hydrodynamics, plasma physics, nonlinear optics, molecular biology. It describes the propagation of waves in media with both nonlinear and dispersive responses. It is an idealized model and does not take into account many aspects such as in-homogeneities, high order terms, thermal fluctuations......

[1]. A. Debussche and L . Di Menza, Numerical simulation of focusing stochastic nonliner Schrödinger equations, Physica D, 162 (2002), 131-154.
[2]. S. A. Derevyanko, S. K. Turitsyn and D. A. Yakushev, Non-Gaussian statistics of an optical soliton in the presence of amplified spontaneous emission, Opt. Lett., 28 (2003), 2097-2099.
[3]. P. D. Drummond and J. F. Corney, Quantum noise in optical fibers. II. Raman jitter in soliton communications, J. Opt. Soc. Am. B, 18 (2001), 153-161.
[4]. G. E. Falkovich, I. Kolokolov, V. Lebedev and S. K. Turitsyn, Statistics of soliton-bearing systems with additive noise, Phys. Rev. E, 63 (2001), 025601(R).
[5]. G. E. Falkovich, I. Kolokolov, V. Lebedev, V. Mezentsev and S. K. Turitsyn, Non-Gaussian error probability in optical soliton transmission, Physica D, 195 (2004), 1-28

Abstract: in this present study, we discuss and generalize the proof that, if the sequence of Banach spaces......

Keywords: Isomorphic classification of.....

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[3]. J.A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (3) (1936) 396–414.
[4]. E.M. Galego, On subspaces and quotients of Banach spaces Monatsh. Math. 136 (2) (2002) 87–97.
[5]. H.E. Lacey, The Isometric Theory of Classical Banach Spaces, Grundlehren Math. Wiss., vol. 208, Springer-Verlag, New York–Heidelberg, 1974.

Abstract: In this paper we have discussed the differential geometry of rheonomic Lagrange space with Matsumoto metric.We find the coefficients of semispray, integral curve of semispray, Canonical nonlinear connection, differential equations of auto parallel curves and canonical metrical N-linear connection of rheonomic Lagrange space with Matsumoto metric.

Keywords: Rheonomic Lagrange space, Matsumoto metric, semispray, and autoparallel curves.

[1]. Antonelli, P. L., Ed.,:Handbook of Finsler Geometry, Kluwer Academic, Dordrecht, The Netherlands, 2003.
[2]. Anastasiei, M., Kawaguchi, H.,: A geometrical theory of time dependent Lagrangians: I, Nonlinear connections, Tensor (N. S.),48 (1989), 273-282, II, M connections, Tensor (N. S.), 48 (1989), 283-292, III, Applications, Tensor (N. S.),49 (1990),296-304.
[3]. Frigioiu, C.:Lagrangian geometrization in mechanics, Tensor (N. S.),65, No. 3 (2004), 225-233
[4]. Ingarden, R. S. and Lawrynowicz, J.,:" Randers antisymmetric metric in the space-time of general relativity 1. Outline of the method," Bullentin de la Société des Sciences et des Lettres de Łódź Série: Recherches sur les Déformations, vol. 59, no. 1, pp. 117-130, 2009
[5]. Kitayama, M., Azuma, M. and Matsumoto, M., : " On Finsler space with - metricregularity, geodesics and main scalars," Journals of Hokkaido University of Education, vol. 46, no. 1, pp. 1- 10, 1995.

Abstract:A mixture of two or more ingredients forms several products. In mixture experiments of m ingredients, the measured response is assumed to depend on the relative proportions. This study aims at developing a generalized E-optimal criterion formula for ingredients which can be used to obtain the smallest eigen value for m number of ingredient. Using the Kronecker model by Draper and Pukelsheim, coefficient matrices for non-maximal parameter subsystem is developed. After obtaining coefficient matrix, information matrices for the respective parameter subsystem for two and m ingredient is then obtained. We then derived E-optimal weighted centroid designs for non-maximal.....

Keywords: Mixture experiments, Kronecker product, Moment matrices, Weighted Centroid Designs, Information matrices

[1]. Cornell, J. A. (1990).Designing experiments with mixtures. New York; wiley inference
[2]. Draper, N.R. and Pukelsheim, F., (1998).Kiefer ordering of simplex designs for first-and second degree mixture models. In: Journal
of statistical planning and inference, vol. 79:325-348.
[3]. Draper, N.R., Heilingers, B., Pukelsheim, F. (2000).Kiefer ordering of simplex designs for mixture models with four or more
ingredients. In: Annals of statistics, vol. 28: 578-590.
[4]. Kinyanjui, J. K., (2007). Some optimal designs for second-degree Kronecker model mixture experiments. PhD. Thesis. Moi
University, Eldoret.
[5]. Klein, T. (2004), Invariant Symmetric Block matrices for the design mixture experiments. In: Linear Algebra and its application.
Vol. 388: 261-278

Abstract: Background: The limitations of parametric regression make nonparametric regression an alternative method that prioritizes flexibility. One of the nonparametric regression methods is the Multivariate Adaptive Regression Spline (MARS). Many researchers have used MARS to analyze the data with numerical or categorical responses. However, there is one type of numerical data that requires special attention in modeling, which is count data. The count data is often encountered, especially in the health sector, such as the number of diseases. The purpose of modeling the number of diseases is predicting, so that prevention and treatment can be carried out appropriately. However, the conventional MARS methods cannot consider count data type. The specific objective of this study was to develop the parameter estimation and the hypothesis test of the Multivariate Adaptive Poisson Regression Spline (......

Key Word: Count Data; Multivariate Adaptive Regression Spline (MARS); Multivariate Adaptive Poisson Regression Spline (MAPRS); Poisson Regression.

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[2] Otok, B.W.; Musa, M.; Purhadi; Yasmirullah, S.D.P. Propensity score stratification using bootstrap aggregating classification trees
analysis. Heliyon 2020, 6, e04288.
[3] Friedman, J. H. Multivariate Adaptive Regression Splines. The Annals of Statistics 1991, 19, 1-67.
[4] Otok, B.W.; Putra, R.Y.; Sutikno; Yasmirullah, S.D.P. Bootstrap Aggregating Multivariate Adaptive Regression Spline for
Observational Studies in Diabetes Cases. SRP 2020, 11, 406-413.
[5] Liu, L.; Zhang, S.; Cheng, Y. M.; Liang, L. Advanced reliability analysis of slopes in spatially variable soils using multivariate
adaptive regression splines. Geoscience Frontiers 2019, 10, 671–682..

Abstract: Neural network is an important area of research due to its usage in various fields of engineering and sciences. Orthogonal neural network is a special kind of neural network where basis functions are orthogonal to each other. In this paper, orthogonal neural network is discussed and its important properties are detailed. It is found that its properties very much resemble with Fourier series properties.

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[3]. Specht, D.F., 1991. A general regression neural network. IEEE transactions on neural networks, 2(6), pp.568-576.
[4]. Hertz, J., Krogh, A. and Palmer, R.G., 1991. Introduction to the theory of neural computation. Addison-Wesley/Addison Wesley Longman.
[5]. Goldman, M.S., 2009. Memory without feedback in a neural network. Neuron, 61(4), pp.621-634
[6]. Yang, S.S. and Tseng, C.S., 1996. An orthogonal neural network for function approximation. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 26(5), pp.779-785.