2,177 research outputs found
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
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
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 , where the metric could be secular (a constant matrix)
or depending upon the matrix elements of . Here, we construct ensembles of a
large number of pseudo-symmetric ( large) matrices using
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: ) are sub-Wigner as 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, for is called semi-Poisson and we show that it lies
close to the form derived for the case of pseudo-symmetric matrix where the eigenvalues are most aptly conditionally
real: 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 and distribution of eigenvalues
for ensembles of various real random matrices (of order and ) where the matrix-elements have various Probability
Distribution Function (PDF: ) including Gaussian. We construct ensembles
of , real random matrices , (cyclic) and
(tridiagonal) and real symmetric matrices: , ,
, (cyclic), (tridiagonal),
(pseudo-symmetric Tridiagonal), (Toeplitz) , and
. We find that the spacing distribution of the adjacent levels
of matrices and under any symmetric PDF of matrix
elements is which approximately conforms to the
Wigner surmise as . But under asymmetric PDFs we
observe , where are also sensitive to the choice
of the matrix and the PDF. More interestingly, the real symmetric matrices
, (excepting and )
and (pseudo-symmetric tridiagonal) all conform to the Poisson distribution
, where depends upon the choice of the matrix
and PDF. Let complex eigenvalues of , and be . We show that
all arising due to , and of ,
and are also of Poisson type: . We observe as
half-Gaussian for two real eigenvalues of . For real matrices , we
associate new types of with them. Lastly, we study the distribution
of eigenvalues of symmetric matrices (of large order) discussed
above.Comment: 12 pages, 11 figures and 4 table
Expectation value of 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 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 diverges for even states and converges for odd states. Here,
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 of a Sasakian manifold with structure and proved that if the vector
field is parallel with respect to induced connection on then is
totally geodesic.Comment: 5 page
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