Abstract: Abstract Many real-life problems using mathematical modeling can be reduced to scalar and system of nonlinear equations. In this paper, we develop a family of three-step sixth-order method for solving nonlinear equations by employing weight functions in the second and third step of the scheme. Furthermore, we extend this family to the multidimensional case preserving the same order of convergence. Moreover, we have made numerical comparisons with the efficient methods of this domain to verify the suitability of our method. PubDate: 2022-12-01
Abstract: Abstract In this article, with an essential assumption, we provide an evolution formula for the Yamabe constant along of the Ricci–Bourguignon flow of an n-dimensional closed Riemannian manifold for \(n\ge 3\) . In particular, we show that Yamabe constant is increasing on \([0, \delta ]\) for some \(\delta >0\) . PubDate: 2022-12-01
Abstract: Abstract Approximating the closest positive semi-definite bisymmetric matrix using the Frobenius norm to a data matrix is important in many engineering applications, communication theory and quantum physics. In this paper, we will use the interior point method to solve this problem. The problem will be reformulated into various forms, in the beginning as a semi-definite programming problem and later, into the form of a mixed semidefintie and second-order cone optimization problem. Numerical results comparing the efficiency of these methods with the alternating projection algorithm will be reported. PubDate: 2022-12-01
Abstract: Abstract The major goal of this research is to develop and test a numerical technique for solving a linear one-dimensional telegraph problem. The generalized polynomials, namely, the generalized Lucas polynomials are selected as basis functions. To solve the linear one-dimensional telegraph type equation, we solve instead its corresponding integral equation via the application of the spectral Galerkin method that serves to convert the equation with its underlying conditions into a system of linear algebraic equations that may be solved by a suitable numerical solver. The convergence and error analysis of the generalized Lucas expansion are discussed in depth. The current analysis is based on the assumption that the problem’s solution is separable. Finally, some explanatory numerical examples are displayed together with comparisons to some other articles, to demonstrate the suggested method’s validity, applicability, and accuracy. PubDate: 2022-12-01
Abstract: Abstract In this paper, we establish an identity involving Sarikaya fractional integrals for twice differentiable functions. We obtain some new generalized fractional inequalities for the functions whose second derivatives in absolute value are convex by utilizing obtained equality. Utilizing the new inequalities obtained, some new inequalities for Riemann–Liouville fractional integrals and k-Riemann–Liouville fractional integrals are obtained. In addition, some of these results generalize ones obtained in earlier works. PubDate: 2022-12-01
Abstract: Abstract The convergence balls as well as the dynamical characteristics of two sixth order Jarratt-like methods (JLM1 and JLM2) are compared. First, the ball analysis theorems for these algorithms are proved by applying generalized Lipschitz conditions on derivative of the first order. As a result, significant information on the radii of convergence and the regions of uniqueness for the solution are found along with calculable error distances. Also, the scope of utilization of these algorithms is extended. Then, we compare the dynamical properties, using the attraction basin approach, of these iterative schemes. At the end, standard application problems are considered to demonstrate the efficacy of our theoretical findings on ball convergence. For these problems, the convergence balls are computed and compared. From these comparisons, it is confirmed that JLM1 has the bigger convergence balls than JLM2. Also, the attraction basins for JLM1 are larger in comparison to JLM2. Thus, for numerical applications, JLM1 is better than JLM2. PubDate: 2022-12-01
Abstract: Abstract A theorem on the number of distinct eigenvalues of diagonalizable matrices is obtained. Some applications related to the problem of separation of close eigenvalues, triangular defective matrices as well as adjacency and walk matrices of graphs are discussed. Other ideas and examples are provided. PubDate: 2022-12-01
Abstract: Abstract It is the purpose of this work to study the Choquard equation $$\begin{aligned} i\dot{u}-(-\Delta )^s u=\pm x ^{\gamma }(I_\alpha * \cdot ^\gamma u ^p) u ^{p-2}u \end{aligned}$$ in the space \(\dot{H}^s\cap \dot{H}^{s_c}\) , where \(0<s_c<s\) corresponds to the scale invariant homogeneous Sobolev norm. Here, one considers to two separate cases. The first one is the classical case \(s=1\) and the second one is the fractional regime \(0<s<1\) with radial data. One tries to develop a local theory using a new adapted sharp Gagliardo–Nirenberg estimate. Moreover, one investigates the concentration of non-global solutions in \(L^\infty _{T^*}(\dot{H}^{s_c})\) . One needs to deal with the lack of a mass conservation, since the data are not supposed to be in \(L^2\) . This note gives a complementary to the previous works about the same problem in the energy space \(H^1\) . PubDate: 2022-12-01
Abstract: Abstract In this paper, we will focus on following nonlocal quasilinear elliptic system with singular nonlinearities: $$\begin{aligned} (S) \left\{ \begin{array}{ll} (-\Delta )_{p}^{s_1} u =\dfrac{1}{v^{\alpha _1}}+v^{\beta _1}&{} \text { in }\Omega , \\ (-\Delta )_{q}^{s_2} u =\dfrac{1}{u^{\alpha _2}}+u^{\beta _2}&{} \text { in }\Omega , \\ u,v=0 &{} \text { in } ({I\!\!R}^N\setminus \Omega ) , \\ u,v>0 &{} \text { in } \Omega , \end{array} \right. \end{aligned}$$ where \(\Omega \subset {I\!\!R}^N\) be a smooth bounded domain, \(s_1,\,s_2\in (0,1)\) , \(\alpha _1\) , \(\alpha _2\) , \(\beta _1\) , \(\beta _2\) are suitable positive constants, \((-\Delta )_{p}^{s_1}\) and \((-\Delta )_{q}^{s_2}\) are the fractional \(p-\text {Laplacian}\) and \(q-\text {Laplacian}\) operators. Using approximating arguments, Rabinowitz bifurcation Theorem, and fractional Hardy inequality, we are able to show the existence of positive solution to the above system. PubDate: 2022-12-01
Abstract: Abstract In this work, we study the vibration control of a flexible mechanical system. The dynamic of the problem is modeled as a viscoelastic nonlinear Euler–Bernoulli beam. To suppress the undesirable transversal vibrations of the beam, we adopt a control at the right boundary of the beam. This control law is simple to implement. We prove uniform stability of the system using a viscoelastic material, the multiplier method and some ideas introduced in [20]. It is shown that a large range of rates of decay of the energy can be achieved through a determined class of kernels. Unlike most of the existing classes in the market, ours are not necessarily strictly decreasing. PubDate: 2022-12-01
Abstract: Abstract Seasonal variability strongly affects the animal population in wildlife. It becomes essential to model seasonality in eco-epidemic dynamics to know the effect of system parameters in a periodic environment. This article presents a set of non-autonomous differential equations with time-varying disease transmission rates among prey and predators, the mortality rate of a diseased predator, the predation rate of healthy prey, and an additional food supply. The positiveness, boundedness, and presence of solution are derived. We have proved that the infection-free state is stable if periodic basic reproduction number \(R_C(t)<1\) . The stability of the coexistence state is shown at \(R_C(t)>1\) using the Poincare map and comparison theory. The significance of the parameters related to disease transmission and prevalence is described using sensitivity analysis. Numerical simulation verified our analytical findings and proved that the predator control strategies in the periodic environment via controlling predation rate, disease transmission rate among predators, and death rate of diseased prey lead the system towards an infection-free environment. PubDate: 2022-12-01
Abstract: Abstract In this paper, we introduce and study a modified Halpern-type proximal point algorithm which comprises a finite family of resolvents of mixed equilibrium problems and a finite family of k-demimetric mappings. We prove that the algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems, which is also a common fixed point of a finite family of k-demimetric mappings in a Hadamard space. Furthermore, we give a numerical example of our algorithm to show the applicability of our algorithm. PubDate: 2022-12-01
Abstract: Abstract Let \(k\ge 2\) . A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence, the first k terms are \(0,\ldots ,0,1\) and each term afterwards is given by the linear recurrence $$\begin{aligned} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}. \end{aligned}$$ In this paper, we extend the previous work (Rihane and Togbé in Ann Math Inform 54:57–71, 2021) and investigate the Padovan and Perrin numbers in the k-Pell sequence. PubDate: 2022-11-28
Abstract: Abstract In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk \({\mathbb {D}}^n\) in the unitary space \({\mathbb {C}}^n\) , that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus \({\mathbb {T}}^n\) . PubDate: 2022-11-28
Abstract: Abstract Here the assessment of entropy generation with Soret and Dufour impact in flow of MHD Prandtl fluid along an unsteady stretching surface has been measured. Nonlinear mixed convection and convective conditions for heat/mass transfer are imposed at the surface. The outcome of viscous dissipation and radiation is considered in heat transfer features. The obtained system of nonlinear PDEs is converted to ODEs by consuming dimensionless variables. Resulting systems are solved for the convergent solutions. Impacts of Prandtl fluid parameters, unsteadiness parameter, Soret and Dufour numbers, magnetic parameter, nonlinear thermal and concentration parameter, Prandtl number, radiation parameter, thermal and concentration Biot numbers, ratio of concentration to thermal buoyancy, Eckert number and Schmidt number are addressed. Skin friction coefficient, local Nusselt and Sherwood numbers are analyzed graphically. Unsteady parameter \({ \epsilon }\) has reverse behavior on the velocity and temperature profiles, velocity declines while temperature raises. Prandtl fluid parameter \({ \alpha }\) and \({ \beta }\) boost the velocity field. Mixed convection parameter le and N* (ratio of concentration and buoyancy force) enhance the velocity field and resultant boundary layer thickness. Magnetic parameter change its behavior on \(f(\eta )\) \(\theta (\eta )\) and . Soret/Dufour number enhances the energy flux due to mass transfer rate and mass flux which radically increases the temperature. Far away from the wall entropy generation grows rapidly for greater values of a and b. Magnetic and radiation parameter increase the entropy generation while radiation parameter decreases. PubDate: 2022-11-18
Abstract: Abstract In this paper, we study the current \(T \wedge \text {{dd}}^{c}\psi \) for positive currents T and semi-exhaustive, not necessarily plurisubharmonic, functions \(\psi \) . The study leads to new definitions of capacity and Lelong–Demailly numbers with respect to the weight \(\psi \) . PubDate: 2022-11-11
Abstract: Abstract Under the assumption that the second fundamental form is locally timelike, we establish new nonexistence and umbilicity results concerning n-dimensional spacelike submanifolds immersed with parallel mean curvature vector in the \((n+p)\) -dimensional de Sitter space \(\mathbb {S}^{n+p}_q\) of index q, such that \(1\le q\le p\) . Our approach is based on a Simon’s type inequality involving the norm of the total umbilicity tensor, obtained by Mariano in [17], jointly with suitable maximum principles due to Alías, Caminha and do Nascimento [6, 7] for complete noncompact Riemannian manifolds and a weak version of Omori–Yau’s maximum principle for stochastically complete Riemanian manifolds proved by Pigola, Rigoli and Setti [20, 21]. PubDate: 2022-10-28
Abstract: Abstract We consider the problem of maximal regularity for the semilinear non-autonomous evolution equations $$\begin{aligned} u'(t)+A(t)u(t)=F(t,u),\, t \text {-a.e.}, \, u(0)=u_0. \end{aligned}$$ Here, the time-dependent operators A(t) are associated with (time dependent) sesquilinear forms on a Hilbert space \(\mathcal {H}.\) We prove the maximal regularity result in temporally weighted \(L^2\) -spaces and other regularity properties for the solution of the previous problem under minimal regularity assumptions on the forms, the initial value \(u_0\) and the inhomogeneous term F. Our results are motivated by boundary value problems. PubDate: 2022-09-07
Abstract: Abstract In this work, we apply the hypercircle method to Discontinuous Galerkin (DG) approximations of second order diffusion problems featuring inhomogeneous Dirichlet and Neumann boundary conditions. We focus on the interior penalty discontinuous Galerkin (IPDG) approximations of diffusion problems in primal variational formulation and produce a Prager–Synge theorem for such DG methods. Using the hypercircle method, we derive an a posteriori error estimator in terms of an equilibrated flux. The estimator is proven to be reliable and efficient. Numerical results are presented which illustrate the estimator’s performance. PubDate: 2022-09-05
Abstract: Abstract Let \( (P_n)_{n\ge 0}\) be the sequence of Perrin numbers defined by ternary relation \( P_0=3 \) , \( P_1=0 \) , \( P_2=2 \) , and \( P_{n+3}=P_{n+1}+P_n \) for all \( n\ge 0 \) . In this paper, we use Baker’s theory for nonzero linear forms in logarithms of algebraic numbers and the reduction procedure involving the theory of continued fractions, to explicitly determine all Perrin numbers that are concatenations of two repeated digit numbers. PubDate: 2022-08-25
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