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We consider a symmetric, steady, and periodic water wave. It is shown that a locally vanishing vertical velocity component implies a flat or oscillating surface profile.

The goals of feature selection are to remove redundant and irrelevant features from high-dimensional data, extract the “optimal feature subset” of the original feature space to improve the classification accuracy, and reduce the time complexity. Traditional feature selection algorithms are based on static...

Universal gravitation is a natural phenomenon. Inspired by Newton's universal gravitation model and based on binary differences strategy, we propose an algorithm for global optimization problems, which is called the binary difference gravitational evolution (BDGE) algorithm. BDGE is a population-based...

In a previous paper the real evolution of the system of ODEs ¨zn + zn = N m=1, m=n gnm(zn - zm) -3 , zn zn(t), zn dzn(t) dt , n = 1, . . . , N is discussed in CN , namely the N dependent variables zn, as well as the N(N - 1) (arbitrary!) "coupling constants" gnm, are considered to be complex numbers,...

Abstract telegrapher's equations and some random walks of Poisson type are shown to fit into the framework of the Hamiltonian formalism after an appropriate timedependent rescaling of the basic variables has been made.

An alternative approach of Poisson and Geometric distributions having a more general form of sampling method are suggested in this paper and defined them as generalized Poisson and generalized Geometric distributions respectively. It is evident that the traditional forms of both the distributions are...

We study solutions of the KdV equation governed by a stationary equation for symmetries from the non-commutative subalgebra, namely, for a linear combination of the master-symmetry and the scaling symmetry. The constraint under study is equivalent to a sixth order nonautonomous ODE possessing two first...

We perform a Inönü­Wigner contraction on Gaudin models, showing how the integrbility property is preserved by this algebraic procedure. Starting from Gaudin models we obtain new integrable chains, that we call Lagrange chains, associated to the same linear r-matrix structure. We give a general construction...

Solutions invariant under subalgebras of the affine algebra AIGL(3, R) are found.

In this paper we study the integrability of the Muthuswamy–Chua system x'=y,y'=-x3+y2-yz22,z'=y-αz-yz. For α = 0 we characterize all its generalized rational first integrals, which contains the Darboux type first integrals. For α ≠ 0 we show that the system has no Darboux type first...

This paper aims to study the lightpaths provisioning problem in optical WDM networks with scarce available wavelengths under the static (off-line) traffic demands such that network operator’s (NO’s) revenue is maximized. To achieve this goal, a NO has to be addressed with the issue how to solve the call...

Feature extraction and selection are the most important techniques for ultrasonic flaw signal classification. In this study, empirical mode decomposition (EMD) is used to obtain the intrinsic mode functions (IMFs) of original signal, and their corresponding traditional time and frequency domain based...

Recent improvements in deep learning techniques applied to images allow the detection of people with a high success rate. However, other types of sensors, such as laser rangefinders, are still useful due to their wide field of vision and their ability to operate in different environments and lighting...

The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and in a third section we apply these methods for the diffeomorphism...

We describe constructing solutions of the field equations of Chern-Simons and toplogical BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations) are considered. A method of calculating (nonlocal) dressing symmetries...

We show that the free Schrödinger equation admits Lorentz space-time transformations when corresponding transformations of the -function are nonlocal. Some consequences of this symmetry are discussed.

A central hyperplane arrangement in ℂ2 with multiplicity is called a “locus configuration” if it satisfies a series of “locus equations” on each hyperplane. Following [4], we demonstrate that the first locus equation for each hyperplane corresponds to a force-balancing equation on a related interacting...

We describe a problem that can be tackled more-or-less routinely using the ideas of classical fluid mechanics, but it is a complex flow and even the linearised problem involves considerable algebraic complexity. The presentation here emphasises the approach that we adopt in order to formulate an accessible...

We consider generalized Liénard polynomial differential systems of the form ẋ = y, ẏ = -g(x) - f (x) y, with f (x) and g(x) two polynomials satisfying deg(g) ≤ deg(f). In their work, Llibre and Valls have shown that, except in some particular cases, such systems have no Liouvillian first integral. In...

In this paper, we get an asymptotic expansion of the q-gamma function q(x). Also, we deduced q-analogues of Gauss' multiplication formula and Legendre's relation which give the known results when q tends to 1.

Let pN (z; t) be a (monic) time-dependent polynomial of arbitrary degree N in z, and let zn ≡ zn (t) be its N zeros: pN (z;t)=∏n=1N[z-zn(t)] . In this paper we report a convenient expression of the k-th time-derivative zn(k)(t) of the zero zn (t). This formula plays a key role in the...

We describe a class of generalized gas dynamics equations invariant under the extended Galilei algebra A ~G(1, n).

In 2011 Pehlivan proposed a three–dimensional forced–damped autonomous differential system which can display simultaneously unbounded and chaotic solutions. This untypical phenomenon has been studied recently by several authors. In this paper we study the opposite to its chaotic motion, i.e. its integrability,...

This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Hunter-Saxton (HS2) hierarchy through an algebro-geometric initial value problem. Our main tools include the polynomial recursive formalism, the hyperelliptic...

This paper investigates the issue on adaptive synchronization of delayed inertial Cohen–Grossberg neural networks (ICGNNs). By adopting the method of variable transformation, the addressed model, which includes the so-called inertial term, is transformed into first-order differential equations. On the...

This paper introduces a new four-parameter extension of the generalized Gompertz distributions. This distribution involves some well-known distributions such as extension of generalized exponential, generalized exponential, and generalized Gompertz distributions. In addition, it can have a decreasing,...

This paper advocates the problem of estimating the population mean on the current occasion in two occasion successive (rotation) sampling under the transformed auxiliary variable using exponential method of estimation. Four different type estimators are suggested for estimating the current population...

This paper proposes a comparative model for the day-ahead electricity price forecasting that could be realized using multi-layer neural network (MLNN) with levenberg-marquardt (LM) algorithm, generalized regression neural network (GRNN) and cascade-forward neural network (CFNN). In this work applications...

Chinese named entity recognition (NER) has important effect on natural language processing (NLP) applications. This recognition task is complicated in its strong dependent-relation, missing delimiters in the text and insufficient feature representation in a single model. This paper thus proposes a dual...

A soliton cellular automaton on a one dimensional semi-infinite lattice with a reflecting end is presented. It extends a box-ball system on an infinite lattice associated with the crystal base of Uq(sln). A commuting family of time evolutions are obtained by adapting the K matrices and the double row...

In this work, we study the Lie-point symmetries of Kepler­Ermakov systems presented by C Athorne in J. Phys. A24 (1991), L1385­L1389. We determine the forms of arbitrary function H(x, y) in order to find the members of this class possessing the sl(2, R) symmetry and a Lagrangian. We show that these systems...

We show that the concept of complete symmetry group introduced by Krause (J. Math. Phys. 35 (1994), 5734­5748) in the context of the Newtonian Kepler problem has wider applicability, extending to the relativistic context of the Einstein equations dscribing spherically symmetric bodies with certain conformal...

Indeed, interesting properties of artificial neural networks approach made this non-parametric model a powerful tool in solving various complicated mathematical problems. The current research attempts to produce an approximate polynomial solution for special type of fractional order Volterra integro-differential...

By means of splitting subgroups of the generalized Poincaré group P(1, 4), ansatzes which reduce the eikonal equation to differential equations with fewer independent variables have been constructed. The corresponding symmetry reduction has been done. By means of the solutions of the reduced equations...

We show that by deforming the Riemann-Hilbert (RH) formalism associated with certain linear PDEs and using the so-called dressing method, it is possible to derive in an algorithmic way nonlinear integrable versions of these equations. In the usual Dressing Method, one first postulates a matrix RH problem...

The evaluation of solutions is an important phase in power distribution system planning (PDSP) which allows issues such as quality of supply, cost, social service and environmental implications to be considered and usually involves the judgments of a group of experts. The planning problem is thus suitable...

It is necessary for automated vehicles (AVs) and advanced driver assistance systems (ADASs) to have a better understanding of the traffic environment including driving behaviors. This study aims to build a driving behavior awareness (DBA) model that can infer driving behaviors such as lane change. In...

A novel, remarkably neat, differential algorithm is introduced, which is suitable to evaluate all the zeros of a generic polynomial of arbitrary degree N.

A system of algebraic equations satisfied by the zeros of the sum of three polynomials are reported.

This paper identifies a new paradigm of prediction, of ongoing temporal sequences, which achieves an acceptable accuracy just by the historical subsequences as short as possible and as close to the predicted time point as possible. To address agile prediction, a new concept, (DRS for short), is first...

Multi-groups decision making (MGDM) problems, which contain multiple groups of experts acting collectively to evaluate a set of alternatives with respect to several criteria, are focused on in this study. The existing solutions for MGDM are to aggregate the evaluations three times at different levels,...

We present quasi-periodic solutions in terms of Riemann theta functions of the Heisenberg ferromagnet hierarchy by using algebrogeometric method. Our main tools include algebraic curve and Riemann surface, polynomial recursive formulation and a special meromorphic function.

Growth phenomena are ubiquitous and pervasive not only in biology and the medical sciences, but also in economics, marketing and the computer and social sciences. We introduce a three-parameter version of the classic pure-birth process growth model when suitably instantiated, can be used to model growth...

Least Squares Support Vector Machine (LS-SVM) is powerful to solve problems such as multi-class nonlinear classification. In this study, a LS-SVM with kernel-based was applied to multi-class IC packaging type dataset classification problem. In the first stage, the greedy search algorithm in feature selection...

We consider two-dimensional water-waves of permanent shape with a constant proagation speed. Two theorems concerning the uniqueness of certain solutions are rported. Uniqueness of Crapper's pure capillary waves is proved under a positivity assumption. The proof is based on the theory of positive operators....

For an integrable shallow water equation we describe a geometrical approach shoing that any two nearby fluid configurations are successive states of a unique flow minimizing the kinetic energy.

We examine the growth properties of second-order mappings which are integrable by linearisation and which generically exhibit a linear growth of the homogeneous degree of initial conditions. We show that for Gambier-type mappings for which the growth proceeds generically with a step of 1 there exist...

We study symmetry properties of the heat equation with convection term (the equation of convection diffusion) and the Schrödinger equation with convection term. We also investigate the symmetry of systems of these equations with additional conditions for potentials. The obtained results are applied to...