Massless field equations are fundamental in particle physics. In Clifford analysis, the Euclidean version of these equations has been dealt with but it is not clear, even in dimension 4, what should be the right analogue of massless field equations for fields with values in a general irreducible Spin(4)-module. The main aim of the paper is to explain that a good possibility is to take the so-called generalized Cauchy-Riemann equations proposed a long time ago by E. Stein and G. Weiss. For this choice of the equations, we show that their polynomial solutions form different irreducible Spin(4)-modules. This is an important step in developing the corrresponding function theory.

In this paper, an avian influenza model with saturation and psychological effect on heterogeneous complex networks is proposed. Firstly, the basic reproduction number $\mathscr{R}_{0}$ is given through mathematical analysis, which is a threshold to determine whether or not the disease spreads. Secondly, the locally and globally asymptotical stability of the disease-free equilibrium point and the endemic equilibrium point are investigated by using Lyapunov functions and Kirchhoff’s matrix tree theorem. If $\mathscr{R}_{0}<1$, the disease-free equilibrium is globally asymptotically stable and the disease will die out. If $\mathscr{R}_{0}>1$, the endemic equilibrium is globally asymptotically stable. Thirdly, an optimal control problem is established by taking slaughter rate and cure rate as control variables. Finally, numerical simulations are given to demonstrate the main results.

The inverse problems of determining the energy-temperature relation α(t) and the heat conduction relation k(t) functions in the one-dimensional integro– differential heat equation are investigated. The direct problem is the initial-boundary problem for this equation. The integral terms have the time convolution form of unknown kernels and direct problem solution. As additional information for solving inverse problems, the solution of the direct problem for x = x₀ is given. At the beginning an auxiliary problem, which is equivalent to the original problem is introduced. Then the auxiliary problem is reduced to an equivalent closed system of Volterra-type integral equations with respect to unknown functions. Applying the method of contraction mappings to this system in the continuous class of functions with weighted norms, we prove the main result of the article, which is a global existence and uniqueness theorem of inverse problem solutions.

This paper is devoted to the study of a nonlinear pseudoparabolic equation in an annular with Robin-Dirichlet conditions. At first, by applying the standard Faedo-Galerkin method, we prove existence and uniqueness results. Next, using concavity method, we prove blow-up results for solutions when the initial energy is nonnegative or negative, then we also establish the lifespan for the equation via finding the upper bound and the lower bound for the blow-up times. Finally, we give a sufficient condition for the global existence and decay of weak solutions.

This note presents corrections to our paper

In this article, we introduce the notion of biorthgonoal nonuniform multiresolution analysis on the spectrum $\Lambda=\left\{0, r/N\right\}+2\mathbb Z$, where $N\ge 1$ is an integer and $r$ is an odd integer with $1\le r\le 2N-1$ such that $r$ and $N$ are relatively prime. We first establish the necessary and sufficient conditions for the translates of a single function to form the Riesz bases for their closed linear span. We provide the complete characterization for the biorthogonality of the translates of scaling functions of two nonuniform multiresolution analysis and the associated biorthogonal wavelet families. Furthermore, under the mild assumptions on the scaling functions and the corresponding wavelets associated with nonuniform multiresolution analysis, we show that the wavelets can generate Reisz bases.

This note presents corrections to our paper [1]. We also give remarks and additions related to other papers [2]-[15].

In order to provide a significantly richer representation of non-stationary signals appearing in various disciplines of science and engineering, we introduce here a novel fractional nonuniform multiresolution analysis (FrNUMRA) on the spectrum $\Lambda$ given by $\Lambda = \left\{0,\frac{r}{N}\right\}+2\mathbb{Z}$, where $N \geqq 1$ is an integer and $r$ is an odd integer with $ 1 \leqq r \leqq 2N-1,$ such that $r$ and $N$ are relatively prime. The necessary and sufficient condition for the existence of nonuniform wavelets of fractional order is derived and an algorithm is also presented for the construction of fractional NUMRA starting from a fractional low-pass filter $h_{0}^{\alpha}$ with appropriate conditions. Moreover, we provide a complete characterization for the biorthogonality of the translates of the scaling functions of two fractional nonuniform multiresolution analyses and the associated fractional biorthogonal wavelet families.

The accuracy and repeatability of the color reproduction in print is determined by the fine tuning of the tone reproduction curves of the basic printing colorants (most often this is CMYK). However, the diversity of manufacturers of printing equipment and dyes introduces an element of significant uncertainty about color uniformity. In addition, the traditional approach does not take into account the effect of hue change when applying the original dyes, as well as, the non-linearity of the hue rise in high and low density areas. Determining the color of base colorants that produces the most uniform tone change is an important engineering challenge. Previously, there was no scientific basis for such calculations. We recently proposed an alternative color correction model based on gradation trajectories as an analogue of gradation curves in the CIE Lab space. We have also described the extension of the approach to double color overlay (gradation surfaces) and its analytical and discrete implications. The trajectories are the geodetic lines on gradation surfaces. In this paper, we propose using the gradation trajectories to determine “ideal” or “true” initial printing dyes for electrophotography. To simplify calculations, natural color discretization in digital printing is used.

In this work we the study of the asymptotic behavior in the whole line of a thermoelastic structure with interfacial slip and second sound. We prove several polynomial decay estimates depending on the smoothness of initial data. The proof is based on the semigroup approach, the energy method by introducing a Lyapunov functional and Fourier transform.

In this paper, we consider a region occupied by viscous or inviscid compressible magnetohydrodynamic fluids, and surrounded by vacuum. It is shown that the fluid region will expand at least linearly in time as soon as there are no singularities. The expanding rate is proportional to initial total energy and is inversely proportional to initial mass. The result indicates an interesting fact that the expansion of the viscous monatomic fluids seems similar to the inviscid fluids.

In present study, we investigate steady MHD Casson fluid flow effect with stretching porous walls together with thermal radiation amid two equidistant sheets. The heat and mass transport experience on dimensionless parameters Soret and Dufour effect on squeezing flow are interpreted along with the impression of thermal radiation also with heat source/sink. We change the partial differential equations (PDEs) into ordinary differential equations (ODEs) dealing convenient proportionality transformations & after then solve ODEs by Runge-Kutta 4th-order scheme and shooting technology. The sequel of different parameters demonstrated by graph and table of temperature, velocity, and concentration impact. We studied the efficacy of Grashof numbers, Reynolds number, dimensionless Casson fluid parameter, and Hartman/magnetic quantity on velocity, temperature, and on concentration. The skin friction coefficient (Cf), Nusselt number (Nu), and Sherwood number (Sh) are reported and calculated at the end.

In this paper, we consider switched coupled system of nonlinear implicit impulsive Langevin equations with mixed derivatives. Some sufficient conditions are constructed to observe the existence, uniqueness and generalized Ulam--Hyers--Rassias stability of our proposed model, with the help of Generalized Diaz--Margolis's fixed point approach, over generalized complete metric space. We give an example which supports our main result.

A Kalman reduced form is obtained for linear systems over Hermite rings. This reduced form gives information of the set of assignable polynomials to a given linear system.

This paper considers minimizers of the following inhomogeneous $L^2$-subcritical energy functional \[E(u):=\int_{\R^N}|\nabla u|^{2}dx-\frac{2}{p+1}\int_{\R^N}m(x)|u|^{p+1}dx,%\ u\in H^{1}(\R^N), \] under the mass constraint $\|u\|^{2}_{2}=M$. Here $N\geq1$, $p\in(1,1+\frac{4}{N})$, $M>0$ and the inhomogeneous term $m(x)$ satisfies $0

The dynamic of fractional covid-19 epidemic model with a convex incidence rate is studied in this article. Under Caputo operator, existence and uniqueness for the solutions of the fractional covid-19 epidemic model have been ana- lyzed using xed point theorems. We study all the basic properties and results including local and global stability. We show the global stability of disease free equilibrium using the method of Lyapunov function theory while for disease endemic, we use the method of geometrical approach. Moreover, sensitivity analysis complemented by simulations are performed to determine how changes in parameters affect the dynamical behavior of the system.

In this paper, we study a mixed problem for the nonlinear hyperbolic equation with a strong dissipation and a dynamical transmission condition. The existence and uniqueness theorems of local and global solutions are proved

We consider nonlocal problems in which the leading operator contains a sign-changing weight which can be unbounded. We begin studying the existence and the properties of the first eigenvalue. Then we study a nonlinear problem in which the nonlinearity does not satisfy the usual Ambrosetti-Rabinowitz condition. Finally, we study a problem with general concave-convex nonlinearities.