Lie symmetry analysis and new periodic solitary wave solutions of (3+1)-dimensional generalized shallow water wave equation

Many important physical situations such as fluid flows, marine environment, solid-state physics and plasma physics have been represented by shallow water wave equation. In this article, we construct new solitary wave solutions for the (3+1)-dimensional generalized shallow water wave (GSWW) equation by using Lie symmetry method. A variety of analytic (closed-form) solutions such as new periodic solitary wave, cross-kink soliton and doubly periodic breather-type solutions have been obtained by using invariance of the concerned (3+1)-dimensional GSWW equation under one-parameter Lie group of transformations. Lie symmetry transformations have applied to generate the different forms of invariant solutions of the (3+1)-dimensional GSWW equation. For different Lie algebra, Lie symmetry method reduces (3+1)-dimensional GSWW equation into various ordinary differential equations (ODEs) while one of the Lie algebra, it is transformed into the well known (2+1)-dimensional BLMP equation. It is affirmed that the proposed techniques are convenient, genuine and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Under the suitable choices of arbitrary functions and parameters, 2D, 3D and contour graphics to the obtained results of GSWW equation are also analyzed graphically.Comment: 26 pages, 51 figure

1-Multisoliton and other invariant solutions of combined KdV - nKdV equation by using symmetry approach

Lie symmetry method is applied to investigate symmetries of the combined KdV-nKdV equation, that is a new integrable equation by combining the KdV equation and negative order KdV equation. Symmetries which are obtained in this article, are further helpful for reducing the combined KdV-nKdV equation into ordinary differential equation. Moreover, a set of eight invariant solutions for combined KdV-nKdV equation is obtained by using proposed method. Out of the eight solutions so obtained in which two solutions generate progressive wave solutions, five are singular solutions and one multisoliton solutions which is in terms of WeierstrassZeta function.Comment: 11 Pages, 12 figures, Original Research Articl

Optimization and Neural Network-Based Modelling of Surface Passivation Effectiveness by Hydrogenated Amorphous Silicon for Solar Cell Applications

Intrinsic hydrogenated amorphous silicon films can provide outstanding surface passivation of crystalline silicon wafer surfaces. This quality of Intrinsic hydrogenated amorphous silicon makes it valuable in heterojunction with intrinsic thin layer (HIT) solar cell fabrication. This paper describes the material characteristics and electronic properties of Intrinsic hydrogenated amorphous silicon that affects its passivation quality. A study of passivation quality of intrinsic hydrogenated amorphous silicon layer has been done with respect to deposition parameters in Plasma Enhanced Chemical Vapor Deposition (PECVD), the most commonly used method of its deposition. It was found that very good surface passivation with surface recombination velocity < 50 cm/s can be obtained from thickness of 30 nm of Intrinsic hydrogenated amorphous silicon (a-Si:H(i)), which is better than most other passivation techniques. A mathematical model based on Artificial Neural Network (ANN) is designed to predict the carrier lifetime for a given deposition condition and it is shown that the prediction capability of developed ANN model varies with the number of neurons in the hidden layer using Akaike Information Criterion (AIC), which is a widely accepted model selection method for measuring the validity of nonlinear models.Comment: 9 Pages and 9 Figure

Pseudo-symmetric random matrices: semi-Poisson and sub-Wigner statistics

Real non-symmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudo-symmetric as $\eta M \eta^{-1} = M^t$, where the metric $\eta$ could be secular (a constant matrix) or depending upon the matrix elements of $M$. Here, we construct ensembles of a large number $N$ of pseudo-symmetric $n \times n$ ($n$ large) matrices using ${\cal N}$ $(n(n+1)/2 \le {\cal N} \le n^2)$ independent and identically distributed (iid) random numbers as their elements. Based on our numerical calculations, we conjecture that for these ensembles the Nearest Level Spacing Distributions (NLSDs: $p(s)$) are sub-Wigner as $p_{abc}(s)=a s e^{-bs^c} (0<c <2)$ and the distributions of their eigenvalues fit well to D(\epsilon)= A[\mbox{tanh}\{(\epsilon+B)/C \}-\mbox{tanh}\{(\epsilon-B)/C\}] (exceptions also discussed). These sub-Wigner NLSD are encountered in Anderson metal-insulator transition and topological transitions in a Josephson junction. Interestingly, $p(s)$ for $c=1$ is called semi-Poisson and we show that it lies close to the form $p(s)=0.59 s K_0(0.45 s^2)$ derived for the case of $2 \times 2$ pseudo-symmetric matrix where the eigenvalues are most aptly conditionally real: $E_{1,2}=a \pm \sqrt{b^2-c^2}$ which represent characteristic coalescing of eigenvalues in PT(Parity-Time)-symmetric systems.Comment: 7 pages, 5 figures and 1 table, 3 New Refs. added, to appear in Phys. Rev.

Von Mises-Fisher Loss for Training Sequence to Sequence Models with Continuous Outputs

The Softmax function is used in the final layer of nearly all existing sequence-to-sequence models for language generation. However, it is usually the slowest layer to compute which limits the vocabulary size to a subset of most frequent types; and it has a large memory footprint. We propose a general technique for replacing the softmax layer with a continuous embedding layer. Our primary innovations are a novel probabilistic loss, and a training and inference procedure in which we generate a probability distribution over pre-trained word embeddings, instead of a multinomial distribution over the vocabulary obtained via softmax. We evaluate this new class of sequence-to-sequence models with continuous outputs on the task of neural machine translation. We show that our models obtain upto 2.5x speed-up in training time while performing on par with the state-of-the-art models in terms of translation quality. These models are capable of handling very large vocabularies without compromising on translation quality. They also produce more meaningful errors than in the softmax-based models, as these errors typically lie in a subspace of the vector space of the reference translations.Comment: Seventh International Conference on Learning Representations (ICLR 2019

Spectral statistics for ensembles of various real random matrices

We investigate spacing statistics $p(s)$ and distribution of eigenvalues $D(\epsilon)$ for ensembles of various real random matrices (of order $n \times n, n=2$ and $n>>2$) where the matrix-elements have various Probability Distribution Function (PDF: $f(x)$) including Gaussian. We construct ensembles of $1000$, $100 \times 100$ real random matrices $R$, $C$ (cyclic) and $T$ (tridiagonal) and real symmetric matrices: ${\cal R}'$, ${\cal R}=R+R^t$, ${\cal Q}=RR^t$, ${\cal C}$ (cyclic), ${\cal T}$ (tridiagonal), $T'$ (pseudo-symmetric Tridiagonal), $\Theta$ (Toeplitz) , ${\cal D}=CC^t$ and ${\cal S}=TT^t$. We find that the spacing distribution of the adjacent levels of matrices ${\cal R}$ and ${\cal R}'$ under any symmetric PDF of matrix elements is $p_{AB}(s)=A s e^{-Bs^2}$ which approximately conforms to the Wigner surmise as $A/2 \approx B \approx \pi/4$. But under asymmetric PDFs we observe $A/2 \approx B >>\pi/4$, where $A,B$ are also sensitive to the choice of the matrix and the PDF. More interestingly, the real symmetric matrices ${\cal C}, {\cal T}, {\cal Q}$, $\Theta$ (excepting ${\cal D}$ and ${\cal S}$) and $T'$ (pseudo-symmetric tridiagonal) all conform to the Poisson distribution $p_{\mu}(s) =\mu e^{-\mu s}$, where $\mu$ depends upon the choice of the matrix and PDF. Let complex eigenvalues of $R$, $C$ and $T$ be $E^c_n$. We show that all $p(s)$ arising due to $\Re(E^c_n)$, $\Im(E^c_n)$ and $|E^c_n|$ of $R$, $C$ and $T$ are also of Poisson type: $\mu e^{-\mu s}$. We observe $p(s)$ as half-Gaussian for two real eigenvalues of $C$. For real matrices $R, C, T$, we associate new types of $p(s)$ with them. Lastly, we study the distribution $D(\epsilon)$ of eigenvalues of symmetric matrices (of large order) discussed above.Comment: 12 pages, 11 figures and 4 table

Expectation value of p6p^6 in continuous two-piece symmetric potential wells

Earlier, potentials like square well and several other half-potential wells with discontinuous jump have been found to have the expectation value $<\! p^6 \!>$ to be divergent for all bound states. Here, we consider two-piece symmetric potential wells to prove and demonstrate that in them the expectation value of $p^6$ diverges for even states and converges for odd states. Here, $p$ denotes momentum. We also present three exactly solvable models.Comment: 9 pages 4 figures and no tables. arXiv admin note: text overlap with arXiv:1803.0159

DolNet: A Division Of Labour Based Distributed Object Oriented Software Process Model

Distributed Software Development today is in its childhood and not too widespread as a method of developing software in the global IT Industry. In this context, Petrinets are a mathematical model for describing distributed systems theoretically, whereas AttNets are one of their offshoots. But development of true distributed software is limited to network operating systems majorly. Software that runs on many machines with separate programs for each machine, are very few. This paper introduces and defines Distributed Object Oriented Software Engineering DOOSE as a new field in software engineering. The paper further gives a Distributed Object Oriented Software Process Model DOOSPM, called the DolNet, which describes how work may be done by a software development organization while working on Distributed Object Oriented DOO Projects.Comment: 9 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1209.445

System and Methods for Converting Speech to SQL

This paper concerns with the conversion of a Spoken English Language Query into SQL for retrieving data from RDBMS. A User submits a query as speech signal through the user interface and gets the result of the query in the text format. We have developed the acoustic and language models using which a speech utterance can be converted into English text query and thus natural language processing techniques can be applied on this English text query to generate an equivalent SQL query. For conversion of speech into English text HTK and Julius tools have been used and for conversion of English text query into SQL query we have implemented a System which uses rule based translation to translate English Language Query into SQL Query. The translation uses lexical analyzer, parser and syntax directed translation techniques like in compilers. JFLex and BYACC tools have been used to build lexical analyzer and parser respectively. System is domain independent i.e. system can run on different database as it generates lex files from the underlying database.Comment: Appeared In proceedings of International Conference ERCICA 2013 pp: 291-298, Published by Elsevier Ltd, ISBN:978935107102

Parallel vector fields on the noninvariant hypersurface of a Sasakian manifold

In 1970, Samuel I. Goldberg and Kentaro Yano defined the notion of noninvariant hypersurface of a Sasakian manifold [1]. In this paper we have studied the properties of parallel vector fields with respect to induced connection on the noninvariant hypersurface $M$ of a Sasakian manifold $\tilde M$ with $(\phi, g, u, v, \lambda)-$ structure and proved that if the vector field $V$ is parallel with respect to induced connection on $M$ then $M$ is totally geodesic.Comment: 5 page