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In [Y. Kifer, Averaging in difference equations driven by dynamical systems, Asterisque287 (2003) 103–123] a general averaging principle for slow-fast discrete dynamical systems was presented. In this paper we extend this method to weakly coupled slow-fast systems. For this setting we obtain sharper...

Recently a classification of contactly-nonequivalent three-dimensional linearly degenerate equations of the second order was presented by E.V. Ferapontov and J. Moss. The equations are Lax-integrable. In our paper we prove that all these equations are connected with each other by appropriate Bäcklund...

We present a new formula for the Bernoulli numbers as the following integral B2m = (-1)m-1 22m+1 +( dm-1 dxm-1 sech2 x)2 dx. This formula is motivated by the results of Fairlie and Veselov, who discovered the relation of Bernoulli polynomials with soliton theory. Dedicated to Hermann Flaschka on his...

The notion of inclusion is a cornerstone in set theory and therefore, its generalization in fuzzy set theory is of great interest. The degree of f-inclusion is one generalization of such a notion that differs from others existing in the literature because the degree of inclusion is considered as a mapping...

We provide a current expansion for the classical equations of motion of the massles Wess-Zumino model. In the low-energy limit, there appears a massive behavior for bosonic degrees of freedom and, at small coupling, the fermion field shows the same mass and supersymmetry is overall preserved. In the...

We describe all systems of three equations of the form 2uj = Fj(u1, u2, u3), j = 1, 3 invariant under the extended Poincaré group. As a result, we have obtained ten classes of ~P(1, 3)-invariant nonlinear partial differential equations for real vector fields.

We study an interactive linear model that incorporates investigator and/or supervisor interventions in the context of a two-stage sampling design. We obtain an unbiased estimator of the finite population total and derive an unbiased estimator of its variance. Our method builds on Sinha and Maiti (2014),...

A new framework, , for multicriteria decision analysis (MCDA) of a wide range of practical problems on risk management is introduced. framework contains a library of modules that are the basis for two scalable systems: for analysis of multicriteria problems, and for multicriteria analysis of spatial...

We construct a Lax operator for the G2-Calogero-Moser model by means of a double reduction procedure. In the first reduction step we reduce the A6-model to a Bmodel with the help of an embedding of the B3-root system into the A6-root system together with the specification of certain coupling constants....

This paper proposed a framework of segmenting multiple targets basing on multiple shape priors. The key novel idea in the proposed framework is the shape degeneration model. By breaking the balance between the competition regions adaptively, the proposed model can degenerate the region which is with...

One of data mining schemes in statistics is clustering panel data such as longitudinal data and time series data. Classical approaches to cluster such time dependent information do not properly count time dependencies among objects we are interested to analyze. In the present study, we propose an approach...

We consider the anti-de Sitter space 𝔿13 and the hyperbolic Hopf fibration h:𝔿13(1)→𝔿2(1/2). Using their description in terms of paraquaternions, we study the magnetic curves of the hyperbolic Hopf vector field. A complete classification is obtained for light-like magnetic curves, showing in particular...

A theory of bidirectional solitons on water is developed by using the classical Boussnesq equation. Moreover, analytical multi-solitons of Camassa-Holm equation are presented.

Standard (Arnold–Liouville) integrable systems are intimately related to complex rotations. One can define a generalization of these, sharing many of their properties, where complex rotations are replaced by quaternionic ones, and more generally by the action of a Clifford group. Such a generalization...

The research data in this manuscript is drawn from four main sections: First, the union and the intersection of an arbitrary family of soft sets are introduced and further results for various soft set operations are obtained. Second, by using the soft relation introduced by Babitha and Sunil, its some...

The novelty of the study is to propose a hybrid IT2 decision-making approach under the hesitant fuzzy linguistic sets for evaluating the criteria and alternatives. For this purpose, the dimensions and criteria are weighted with interval type-2 fuzzy DEMATEL and the economic development plans are ranked...

The precision and accuracy of any estimation can inform one whether to use or not to use the estimated values. It is the crux of the matter to many if not all statisticians. For this to be realized biases of the estimates are normally checked and eliminated or at least minimized. Even with this in mind...

The connection between the complex Sine and Sinh-Gordon equations associated with a Weierstrass type system and the possibility of construction of several classes of multivortex solutions is discussed in detail. We perform the Painlevé Test and analyse the possibility of deriving the Bäcklund transformation...

Using results from sheaf theory combined with the phenomenological theory of the two-dimensional superfluid, the precipitation of quantum vortices is shown to be the genesis of a macroscopic order parameter for a phase transition in two dimensions.

Asymptotic formulae for resolution of L-diagonal systems of ordinary differential equations with symmetrical matrices are derived.

A nonlinear model describing DNA dynamics, called helicoidal Peyrard–Bishop model, is described. It is shown that the model can explain a local opening of a DNA helix during transcription. An impact of friction forces is also studied. It is pointed out that a role of viscosity is crucial for DNA-RNA...

N-coupled nonlinear Schrödinger (NLS) equations have been proposed to describe N-pulse simultaneous propagation in optical fibers. When the fiber is nonuniform, N-coupled variable-coefficient NLS equations can arise. In this paper, a family of N-coupled integrable variable-coefficient NLS equations are...

We investigate the integrability of a class of 1+1 dimensional models describing nolinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations.

The fundamental problem of Farley-Buneman turbulence in the auroral E-region has been discussed and debated extensively in the past two decades. In the present paper we intend to clarify the different steps that the auroral E-region plasma has to undergo before reaching a steady state. The mode-coupling...

We consider the anharmonic oscillator with an arbitrary-degree anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u ′′ + g1 (x)u ′ + g2 (x)u + g3 (x)u n + g4 (x) = 0, n real. Its physical applications range from the atomic Thomas-Fermi model to Emden gas dynamics...

It is shown that in water of finite depth, there are no periodic traveling waves with the property that the pressure in the underlying fluid flow is constant along streamlines. In the case of infinite depth, there is only one such solution, which is due to Gerstner.

Renewable energy is the energy generated from natural resources such as sunlight, wind, rain, tides and geothermal heat. Turkey has a great renewable energy potential with its natural resources such as biomass, geothermal, hydropower, solar, and wind. Selection among energy alternatives is a multicriteria...

Intuitionistic fuzzy preference relation (IFPR), which express experts’ preferences from the preferred, the non-preferred and the indeterminate aspects, has turned out to be an efficient tool in describing the rough and subjective opinions of experts. This paper focuses on the consensus measures for...

Being a new generation of green solvents and high-tech reaction media of the future, ionic liquids have increasingly attracted much attention. Of particular interest in this context are room temperature ionic liquids (in short as ILs in this paper). Due to the relatively high viscosity, ILs is expected...

In this paper, we consider linearizability and orbital linearizability properties of the Lotka–Volterra system in the neighborhood of a singular point with eigenvalues 1 and -q. In this paper we give the explicit smooth near-identity change of variables that linearizes or orbital linearizes such Lotka–Volterra...

We apply the recently developed theory of symmetry of stochastic differential equations to a stochastic version of the logistic equation, obtaining an explicit integration, i.e. an explicit formula for the process in terms of any single realization of the driving Wiener process.

In this paper, nonlocal symmetry of the (2+1) dimensional modified generalized long dispersive wave system and its applications are investigated. The nonlocal symmetry related to the eigenfunctions in Lax pairs is derived, and infinitely many nonlocal symmetries are obtained. By introducing three potentials,...

An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equtions disintegrates into independent equations for non-resonance systems. We consider the resonance conditions for some classes of solutions....

Fundamental solutions (FS) with a given boundary condition on the characteristics of relativistic problems with axial symmetry are considered. This is so-called the Goursat problem (GP) or zero plane formalism in Dirac's terminology, or modification of the proper time method in the Fock-Nambu-Schwinger...

Nap is an effective way to reduce daily-level fatigue after several hours of work. However, no alarm clock, which intelligently manages the nap duration with good autonomic nervous recovery (ANR) from fatigue, has been reported in literature. In this work, an intelligent biological alarm clock algorithm...

In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries [1], mixed heavenly equation and Husain equation appear as closely related canonical equations admitting partner symmetries. Here...

In this paper, a new method is proposed to identify the parameters of fractional order chaotic system. The parameter identification is achieved by minimizing the mean square error between the states of original fractional chaotic system and those of the estimated one, in which the parameters to be identified...

In this paper, we construct a new hierarchy based on the third q-discrete Painlevé equation (qPIII) and also study the hierarchy of the second q-discrete Painlevé equation (qPII). Both hierarchies are derived by using reductions of the general lattice modified Korteweg-de Vries equation. Our results...

The Seiberg-Witten equations are of great importance in the study of topology of smooth four-dimensional manifolds. In this work, we propose similar equations for 7-dimensional compact manifolds with G2-structure.

This paper presents an integrated Artificial Neural Network - Hybrid Meta Heuristic(ANN-HMH) method to solve the nonlinear time-cost tradeoff(TCT) problem of real life engineering projects. ANN models help to capture the existing nonlinear time-cost relationship in project activities. ANN models are...

This paper deals with the NP-hard single-machine total weighted tardiness problem with sequence dependent setup times. Incorporating fuzzy sets and genetic operators, a novel ant colony optimization algorithm is developed for the problem. In the proposed algorithm, artificial ants construct solutions...

Personalized individual semantics (PIS) is not unusual in our daily life, and it has an important influence on the final decision results in linguistic decision making. The analytic hierarchy process (AHP) has now become a popular decision tool because of its sound mathematical design and ease of applicability...

A procedure which obviates the constraint imposed by the conflict between consistent quantization and the invariance of the Hamiltonian description under nonlinear canonical transformation is proposed. This new quantization scheme preserves the Noether point symmetries of the underlying Lagrangian in...

Hybrid sorting immune simulated annealing technique (HSISAT), a Meta - heuristic is proposed for solving the multi objective flexible job-shop scheduling problem (FJSP). The major objectives are distributing the time of machines among the set of operations and scheduling them to minimize the criterion...

Let M be a manifold and T M be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of M with values in the space of linear differential operators acting on C (T M). When M is the n-dimensional sphere, Sn , we use this

The Moser type reductions of modified Boussinessq and super-Korteweg-de Vries equations upon the finite-dimensional invariant subspaces of solutions are considered. For the Hamiltonian and Liouville integrable finite-dimensional dynamical systems concerned with the invariant subspaces, the Lax representations...

Opinion surveys are widely admitted as a valuable source of information which becomes complementary to the information extracted from data by machine learning techniques. This paper focuses on a challenging and still open problem which is related to how to handle properly the inherent uncertainty of...

Transmuted geometric distribution (TGD) was recently introduced and investigated by Chakraborty and Bhati [Stat. Oper. Res. Trans. 40 (2016), 153–176]. This is a flexible extension of geometric distribution having an additional parameter that determines its zero inflation as well as the tail length....

Differential forms are used for construction of nonlocal symmetries of partial differential equations with conservation laws. Every conservation law allows to introduce a nonlocal variable corresponding to a conserved quantity. A prolongation technique is suggested for action of symmetry operators on...

We consider the initial boundary value (IBV) problem for the focusing nonlinear Schrödinger equation in the quarter plane x>0, t >0 in the case of periodic initial data, u(x,0) = α exp(−2iβx) (or asymptotically periodic, u(x, 0) =α exp(−2iβx)→0 as x→∞), and a Robin boundary condition at x = 0:...