Cognitive radar is an intelligent radar system, and adaptive waveform design is one of the core problems in cognitive radar research. In the previous studies, it is assumed that the prior information of the target is known, and the definition of target spectrum variance has not changed. In this paper, we study on robust waveform design problem in multiple targets scene. We hope that the upper and lower

The object of the paper is to study some properties of the generalized Einstein tensor which is recurrent and birecurrent on pseudo-Ricci symmetric manifolds . Considering the generalized Einstein tensor as birecurrent but not recurrent, we state some theorems on the necessary and sufficient conditions for the birecurrency tensor of to be symmetric.

In this paper, we study the following nonlinear Choquard equation , where and is a positive bounded continuous potential on . By applying the reduction method, we proved that for any positive integer , the above equation has a positive solution with spikes near the local maximum point of if is sufficiently small under some suitable conditions on .

In this paper, we discussed the effect of activation energy on mixed convective heat and mass transfer of Williamson nanofluid with heat generation or absorption over a stretching cylinder. Dimensionless ordinary differential equations are obtained from the modeled PDEs by using appropriate transformations. Numerical results of the skin friction coefficient, Nusselt number, and Sherwood number for

The circuit-gate framework of quantum computing relies on the fact that an arbitrary quantum gate in the form of a unitary matrix of unit determinant can be approximated to a desired accuracy by a fairly short sequence of basic gates, of which the exact bounds are provided by the Solovay–Kitaev theorem. In this work, we show that a version of this theorem is applicable to orthogonal matrices with unit

Let be a Hom-Lie-Yamaguti superalgebra. We first introduce the representation and cohomology theory of Hom-Lie-Yamaguti superalgebras. Also, we introduce the notions of generalized derivations and representations of and present some properties. Finally, we investigate the deformations of by choosing some suitable cohomology.

The main goal of the present paper is to obtain several fixed point theorems in the framework of -quasi-metric spaces, which is an extension of -metric spaces. Also, a Hausdorff -distance in these spaces is introduced, and a coincidence point theorem regarding this distance is proved. We also present some examples for the validity of the given results and consider an application to the Volterra-type

In this paper, based on a bilinear differential equation, we study the breather wave solutions by employing the extended homoclinic test method. By constructing the different forms, we also consider the interaction solutions. Furthermore, it is natural to analyse dynamic behaviors of three-dimensional plots.

Annotation. For a second-order parabolic equation, the multipoint in time Cauchy problem is considered. The coefficients of the equation and the boundary condition have power singularities of arbitrary order in time and space variables on a certain set of points. Conditions for the existence and uniqueness of the solution of the problem in Hölder spaces with power weight are found.

Cracks always form at the interface of discrepant materials in composite structures, which influence thermal performances of the structures under transient thermal loadings remarkably. The heat concentration around a cylindrical interface crack in a bilayered composite tube has not been resolved in literature and thus is investigated in this paper based on the singular integral equation method. The

In this paper, we investigate multiple lump wave solutions of the new ()-dimensional Fokas equation by adopting a symbolic computation method. We get its 1-lump solutions, 3-lump solutions, and 6-lump solutions by using its bilinear form. Moreover, some basic characters and structural features of multiple lump waves are explained by depicting the three-dimensional plots.

The multiple Exp-function method is employed for searching the multiple soliton solutions for the new extended ()-dimensional Jimbo-Miwa-like (JM) equation, the extended ()-dimensional Calogero-Bogoyavlenskii-Schiff (eCBS) equation, the generalization of the ()-dimensional Bogoyavlensky-Konopelchenko (BK) equation, and a variable-coefficient extension of the DJKM (vDJKM) equation, which contain one-soliton-

In this paper, we introduce a generalization of rectangular -metric spaces, by changing the rectangular inequality as follows: , for all distinct We prove some fixed point theorems, and we use our results to present a nice application in the last section of this paper.

Transformation is an important means to study problems in analytical mechanics. It is often difficult to solve dynamic equations, and the use of variable transformation can make the equations easier to solve. The theory of canonical transformations plays an important role in solving Hamilton’s canonical equations. Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics. This paper

In this paper, we equip with an indefinite scalar product with a specific Hermitian matrix, and our aim is to develop some block Krylov methods to indefinite mode. In fact, by considering the block Arnoldi, block FOM, and block Lanczos methods, we design the indefinite structures of these block Krylov methods; along with some obtained results, we offer the application of this methods in solving linear

The existing analysis deals with heat transfer occurrence on peristaltic transport of a Carreau fluid in a rectangular duct. Flow is scrutinized in a wave frame of reference moving with velocity away from a fixed frame. A peristaltic wave propagating on the horizontal side walls of a rectangular duct is discussed under lubrication approximation. In order to carry out the analytical solution of velocity

In this paper, we study a class of the Kirchhoff-Schrödinger-Poisson system. By using the quantitative deformation lemma and degree theory, the existence result of the least energy sign-changing solution is obtained. Meanwhile, the energy doubling property is proved, that is, we prove that the energy of any sign-changing solution is strictly larger than twice that of the least energy. Moreover, we

In this paper, the detailed inseparability criteria of entanglement quantification of correlated two-mode light generated by a three-level laser with a coherently driven parametric amplifier and coupled to a two-mode vacuum reservoir is thoroughly analyzed. Using the master equation, we obtain the stochastic differential equation and the correlation properties of the noise forces associated with the

The motive of the present work is to propose an adaptive numerical technique for singularly perturbed convection-diffusion problem in two dimensions. It has been observed that for small singular perturbation parameter, the problem under consideration displays sharp interior or boundary layers in the solution which cannot be captured by standard numerical techniques. In the present work, Hughes stabilization

In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process. The approximation of time fractional derivative is interpreted in the Caputo’s sense by a simple quadrature formula. This RBFs approach was theoretically proved with

In this exploration, a double stratified mixed convective flow of couple stress nanofluid past an inclined stretching cylinder using a Cattaneo-Christov heat and mass flux model is considered. The governing partial differential equation of the boundary layer flow region is reduced to its corresponding ordinary differential equation using a similarity transformation technique. Then, the numerical method

We study the multiparticle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multiparticle lower spectral edges are almost surely constant in absence of ergodicity. We stress that this result is not quite obvious and has to be handled carefully. In addition, we prove

In the present paper, we consider the following Hamiltonian elliptic system with Choquard’s nonlinear term where is a bounded domain with a smooth boundary, , , and is the primitive of , similarly for . By establishing a strongly indefinite variational setting, we prove that the above problem has a ground state solution.

We provide an analysis and statement of the source term in the classical Kaluza field equations, by considering the 5-dimensional (5D) energy-momentum tensor corresponding to the 5D geodesic hypothesis that is typically presumed in the Kaluza theory. By providing the 5D matter Lagrangian, this work completes a Lagrangian analysis of the classical Kaluza theory that began by establishing the proper

We discuss the existence and uniqueness of solutions for the Langevin fractional differential equation and its inclusion counterpart involving the Hilfer fractional derivatives, supplemented with three-point boundary conditions by means of standard tools of the fixed-point theorems for single and multivalued functions. We make use of Banach’s fixed-point theorem to obtain the uniqueness result, while

Different nanostructures of boron nitride have been observed experimentally such as fullerenes, tubes, cones, and graphene. They have received much attention due to their physical, chemical, and electronic properties that lead them to numerous applications in many nanoscale devices. Joining between nanostructures gives rise to new structures with outstanding properties and potential applications for

Let be a simple and undirected graph. The eigenvalues of the adjacency matrix of are called the eigenvalues of . In this paper, we characterize all the -vertex graphs with some eigenvalue of multiplicity and , respectively. Moreover, as an application of the main result, we present a family of nonregular graphs with four distinct eigenvalues.

In this paper, by applying the Jacobian ellipse function method, we obtain a group of periodic traveling wave solution of coupled KdV equations. Furthermore, by the implicit function theorem, the relation between some wave velocity and the solution’s period is researched. Lastly, we show that this type of solution is orbitally stable by periodic perturbations of the same wavelength as the underlying

A multimode process monitoring method based on multiblock projection nonnegative matrix factorization (MPNMF) is proposed for traditional process monitoring methods which often adopt global model of data and ignore local information of data. Firstly, the training data set of each mode is partitioned by the complete link algorithm and the multivariate data space is divided into several subblocks. Then

In this paper, we gave a form of rational solution and their interaction solution to a nonlinear evolution equation. The rational solution contained lump solution, general lump solution, high-order lump solution, lump-type solution, etc. Their interaction solution contained the classical interaction solution, such as the lump-kink solution and the lump-soliton solution. As the example, by using the