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A class of mixture distributions have been derived which we call beta second kind mixtures of distributions. Various integral representations of beta functions can be obtained using these mixture beta distributions. Estimation of unknown parameters along with some characteristics of these distributions...

In this paper, we will construct free-field realizations of the W𝒜n,N algebra associated to an 𝒜n -valued differential operator 𝒧=In∂N+UN−1∂N−1+UN−2∂N−2+⋯U0, where 𝒜n is a Frobenius algebra with the unit In.

We investigate the first cohomology space associated with the embedding of the Lie superalgebra K(2) of contact vector fields on the (1,2)-dimensional supercircle S1|2 in the Lie superalgebra SDO(S1|2 ) of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we show...

It is shown that the deformed Nonlinear Schrödinger (NLS), Hirota and AKNS equations with (1 + 1) dimension admit infinitely many generalized (nonpoint) symmetries and polynomial conserved quantities, master symmetries and recursion operator ensuring their complete integrability. Also shown that each...

Discrete distributions are widely used to model lifetime for count data. In this paper we introduce a new generalization of weighted geometric (GWG) distribution with the weight function w(x) = (1−p^{αx})^β whose special case proposes a discrete generalized weighted exponential distribution. Further,...

In this review we explain interrelations between the Elliptic Calogero-Moser model, the integrable Elliptic Euler-Arnold top, monodromy preserving equations and the Knizhnik-Zamolodchikov-Bernard equation on a torus.

Ranking of triangular intuitionistic fuzzy numbers (TIFNs) is an important problem, which is solved by the value and ambiguity based ranking method developed in this paper. Firstly, the concept of TIFNs is introduced. Arithmetic operations and cut sets over TIFNs are investigated. Then, the values and...

Under investigation in this work is the time-fractional generalized KdV-type equation, which occurs in different contexts in mathematical physics. Lie group analysis method is presented to explicitly study its vector fields and symmetry reductions. Furthermore, two straightforward methods are employed...

This paper is devoted to the subsurface current dynamics in equatorial regions, where the hallmark of a strong stratification is a sharp interface (thermocline), separating two layers of different density, and whose depth is dependent upon the strength of the winds above the ocean's surface. We...

We survey recent results on well-posedness, blow-up phenomena, lifespan and global existence for the Camassa-Holm equation. Results on weak solutions are also consiered.

No-wait flowshop scheduling problem (NW-FSSP) with the objective to minimize the makespan is an important sequencing problem in the production plans and applications of no-wait flowshops can be found in several industries. In a NW-FSSP, jobs are not allowed to wait between two successive machines. The...

Certain nonlinearly-coupled systems of N discrete-time evolution equations are identified, which can be solved by algebraic operations; and some remarkable Diophantine findings are thereby obtained. These results might be useful to test the accuracy of numerical routines yielding the N roots of polynomials...

The aim of the paper is to discuss some new operations on hesitant fuzzy linguistic terms sets based on Archimedean t-norm and t-conorm. The advantage is that the operations on hesitant fuzzy linguistic terms sets are closed, by studying propositions of the operations on hesitant fuzzy linguistic terms...

Firstly, we establish the relation between the loop group method and gauge transformation method for 3×3 spectral problem. Some novel solutions of long wave-short wave model are obtained by Darboux transformation method. Besides, we give the analysis and classification of solution in detail.

In the present paper, we introduce a new axiomatic definition of the inclusion measure for intuitionistic fuzzy sets (IFSs, for short). The close relationships among entropy, similarity measure, and inclusion measure of IFSs are then discussed in detail. Also, we obtain some important theorems by which...

Aiming at the diversity of Nondominated Sorting Genetic Algorithm II (NSGA-II) in screening out nondominated solutions, a crowding distance elimination (CDE) method is proposed. Firstly, the crowding distance is calculated in the same level of nondominated solutions, and the solution of minimum crowding...

In some cases, the relationship between an object set and an attribute set is set up by means of a fuzzy context sequence. A particular case of this situation appears when we want to study the evolution of an L-fuzzy context in time.

In this article we use thve Fokas transform method to analyze boundary value prolems for the sine-Gordon equation posed on a finite interval. The representation of the solution of this problem has already been derived using this transform method. We interchange the role of the independent variables to...

The definition of "classical anomaly" is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamitonian formulation admits symmetries of the action for which the Noether conserved charges, endorsed with the Poisson bracket structure,...

High utility pattern mining is an emerging research topic in the data mining field. Unlike frequent pattern mining, high utility pattern mining deals with non-binary databases, in which the information about purchased quantities of items is maintained. Due to the non-existence of anti-monotone property...

Pseudodifferential operators of several variables are formal Laurent series in the formal inverses of 1, . . . , n with i = d/dxi for 1 i n. As in the single variable case, Lax equations can be constructed using such pseudodifferential operators, whose solutions can be provided by Baker functions. We...

In this paper, we present a new integration approach for managing Information Technology variables within enterprise architecture in an integrated way. Additionially, a novel method based on fuzzy logic for cause-effect variable analysis is proposed as a useful support decision-making tool for companies...

In this paper we want to characterize nonlinear differential equations that describe processes allowing a localization operation in each subdomain of domain in which we consider the process. We formulate this localization condition by means of visual reresentations and give this operation a mathematical...

Representations of the q-deformed Euclidean algebra Uq(iso3), which at q 1 gives the universal enveloping algebra U(iso3) of the Lie algebra iso3 of the Euclidean Lie group ISO(3), are studied. Explicit formulas for operators of irreducible -representations defined by two parameters R and s 1 2 Z are...

In this short paper, the label printing problem (LPP) is investigated. The LPP can be formulated as a nonlinear integer programming problem and it aims to minimize the total wastage of labels under a fixed number of templates with subject to the minimal required quantities of various labels. Since the...

In this work we consider the Lotka–Volterra system in ℝ3 x˙=−x(x−y−z),      y˙=−y(−x+y−z),       z˙=−z(−x−y+z), introduced recently in [7], and studied also in [8] and [14]. In the first two papers the authors mainly studied the integrability of this differential system, while in the third paper they...

In this paper we identify certain peculiar systems of 2 discrete-time evolution equations, x˜n=F(n)(x1,x2),   n=1,2, which are algebraically solvable. Here ℓ is the “discrete-time” independent variable taking integer values (ℓ = 0, 1, 2,...), xn ≡ xn(ℓ) are 2 dependent variables, and x˜n≡xn(ℓ+1) are...

We provide a Lax pair for the surfaces of Voss and Guichard, and we show that such particular surfaces considered by Gambier are characterized by a third Painlevé function.

In this paper, we present the multi-component Novikov equation and derive it's bi-Hamiltonian structure.

The main purpose of any facility location is to select the optimal places that satisfy project's goals. In location problems, the object is usually to optimize a function - objective function - that defines the problem conditions and efficient decision parameters. Numerous methods are proposed to challenge...

We discuss the non–autonomous nonlinear partial difference equations belonging to Boll classification of quad graph equations consistent around the cube. We show how starting from the compatible equations on a cell we can construct the lattice equations, its Bäcklund transformations and Lax pairs. By...

We treat the particle motion in Stokes’ linear edge wave along a uniformly sloping beach. By a rotation of the coordinate frame, we show that there is no particle motion in the direction orthogonal to the sloping beach, and conclude that particles have a longshore drift in the direction of wave propagation...

Teaching-learning based optimization is a newly developed intelligent optimization algorithm. It imitates the process of teaching and learning simply and has better global searching capability. However, some studies have shown that TLBO is good at exploration but poor at exploitation and often falls...

We have developed Pranav Quasi Gamma Distribution (PQGD) as a mixture of Pranav distribution (θ) and Quasi Gamma distribution (2,θ). We obtained various necessary statistical characteristics of PQGD. The flexibility of proposed model is clear from graph of hazard function. The reliability measures of...

We apply the Darboux theory of integrability to polynomial ODE's of dimension 3. Using this theory and computer algebra, we study the existence of first integrals for the 3­dimensional Lotka­Volterra systems with polynomial invariant algebraic solutions linear and quadratic and determine numerous cases...

We provide the complete classification of all global analytic first integrals of the simplified multistrain/two-stream model for tuberculosis and dengue fever that can be written as x˙=x(β1−b−γ1−β1x−(β1−ν)y),     y˙=y(β2−b−γ2−(β2−ν)x−β2y), with β1, β2, b, γ1, γ2, ν ∈ ℝ.

The fuzzy set theory addresses the development of concepts and techniques for dealing with uncertainty or impression conditions. If the collected data from a process include vagueness due to human subjectively or measurement system, fuzzy control charts are available tools for monitoring and evaluating...

In this paper, we qualitatively study radial solutions of the semilinear elliptic equation Δu+un = 0 with u(0) = 1 and u′(0) = 0 on the positive real line, called the Emden–Fowler or Lane–Emden equation. This equation is of great importance in Newtonian astrophysics and the constant n is called the polytropic...

Recently, a great attention is paid toward developing aggregation operators for Pythagorean fuzzy set (PFS). However, few of them have adopted the rules of Archimedean t-conorm and t-norm (ATT) to aggregate the numbers. Motivated by this, the keep interest of the present work is to define some Pythagorean...

Average biosimilarity is investigated under a three-arm parallel design: one arm corresponds to the test drug T , and the other two arms correspond to two versions of the reference drug, say R1 and R2. The hypothesis of interest is the equivalence of the population average response for T with the mean...

Long-wave equations for an incompressible inviscid free-surface fluid in N + 1 dimesions are derived and shown to be Hamiltonian and liftable into the space of moments.

We show that the smooth traveling waves of the Camassa-Holm equation naturally correspond to traveling waves of the Korteweg-de Vries equation.

It is very important to enhance the accuracy of financial crisis prediction (FCP). Because the traditional probabilistic neural network (PNN) has some deficiencies, such as the difficult estimation of parameters and the high computational complexity, this paper proposes a new combination model, which...

Shape invariance is an important ingredient of many exactly solvable quantum mchanics. Several examples of shape invariant "discrete quantum mechanical systems" are introduced and discussed in some detail. They arise in the problem of descriing the equilibrium positions of Ruijsenaars-Schneider type...

Considering the kinematics of the moving frame associated with a constant mean cuvature surface immersed in S3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S3 . The application of...

We report a new three and four coupled nonlinear partial differential-difference equations each admits Lax representation, possess infinitely many generalized (nonpoint) symmetries, conserved quantities and a recursion operator. Hence they are completely integrable both in the sense of Lax and Liouville.

The key frames extraction technique extracts key postures to describe the original motion sequence, which has been widely used in motion compression, motion retrieval, motion edition and so on. In this paper, we propose a method based on the amplitude of curve to find key frames in a motion captured...

Large-scale spam emails cause a serious waste of time and resources. This paper investigates the text features of email documents and the feature noises among multi-field texts, resulting in an observation of a power law distribution of feature strings within each text field. According to the observation,...

Stationary kinetic equations for a quark plasma (QP) in the Abelian dominance approximation are reduced to the nonlinear system of A2-periodic Toda chains (with elliptic operator). Using solutions of this system, which are found with the help of the first integrals and Hirota's method, such characteristics...