Applied Mathematics-A Journal of Chinese Universities Series B最新文献

The main objective of this organized paper is to establish the Poisson distribution conditions for the ϑ-spirallike function classes S_ϑ(γ; ψ) and K_ϑ(γ; ψ). We also investigate an integral operator associated with the Poisson distribution.

Very recently D. Vukičević et al. [8] introduced a new topological index for a molecular graph G named Lanzhou index as (Lzleft( G right) = sumnolimits_{u in Vleft( G right)} {overline {{d_u}} } d_u^2), where d_u and (overline {{d_u}} ) denote the degree of vertex u in G and in its complement respectively. Lanzhou index Lz(G) can be expressed as (n − 1)M₁(G) − F (G), where M₁(G) and F (G) denote the first Zagreb index and the forgotten index of G respectively, and n is the number of vertices in G. It turns out that Lanzhou index outperforms M₁(G) and F(G) in predicting the logarithm of the octanol-water partition coefficient for octane and nonane isomers. It was shown that stars and balanced double stars are the minimal and maximal trees for Lanzhou index respectively. In this paper, we determine the unicyclic graphs and the unicyclic chemical graphs with the minimum and maximum Lanzhou indices separately.

In this paper, we study the underlying properties of optimal Delaunay triangulations (ODT) and propose enhanced ODT methods combined with connectivity regularization. Based on optimizing node positions and Delaunay triangulation iteratively, ODT methods are very effective in mesh improvement. This paper demonstrates that the energy function minimized by ODT is nonconvex and unsmooth, thus, ODT methods suffer the problem of falling into a local minimum inevitably. Unlike general ways that minimize the ODT energy function in terms of mathematics directly, we take an outflanking strategy combining ODT methods with connectivity regularization for this issue. Connectivity regularization reduces the number of irregular nodes by basic topological operations, which can be regarded as a perturbation to help ODT methods jump out of a poor local minimum. Although the enhanced ODT methods cannot guarantee to obtain a global minimum, it starts a new viewpoint of minimizing ODT energy which uses topological operations but mathematical methods. And in terms of practical effect, several experimental results illustrate the enhanced ODT methods are capable of improving the mesh furtherly compared to general ODT methods.

The intention of the current research is to address the conclusion of non-isothermal heterogeneous reaction on the stagnation — point flow of SWCNT — engine oil and MWCNT — engine oil nanofluid over a shrinking/stretching sheet. Further, exemplify the aspect of heat and mass transfer the upshot of magnetohydrodynamics (MHD), thermal radiation, and heat generation/absorption coefficient are exemplified. The bvp4c from Matlab is pledged to acquire the numerical explanation of the problem that contains nonlinear system of ordinary differential equations (ODE). The impacts of miscellaneous important parameters on axial velocity, temperature field, concentration profile, skin friction coefficient, and local Nusselt number, are deliberated through graphical and numerically erected tabulated values. The solid volume fraction diminishes the velocity distribution while enhancing the temperature distribution. Further, the rate of shear stress declines with increasing the magnetic and stretching parameter for both SWCNT and MWCNT.

This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls. First, we prove that the stochastic system has a unique global positive solution. Second, by constructing a series of appropriate stochastic Lyapunov functions, the asymptotic behaviors around the equilibria of deterministic model are obtained, and we demonstrate that the stochastic system exists a stationary Markov process. Third, the conditions for persistence in the mean and extinction of the stochastic system are established. Finally, we carry out some numerical simulations with respect to different stochastic parameters to verify our analytical results. The obtained results indicate that the stochastic perturbations and feedback controls have crucial effects on the survivability of system.

Although the isogeometric collocation (IGA-C) method has been successfully utilized in practical applications due to its simplicity and efficiency, only a little theoretical results have been established on the numerical analysis of the IGA-C method. In this paper, we deduce the convergence rate of the consistency of the IGA-C method. Moreover, based on the formula of the convergence rate, the necessary and sufficient condition for the consistency of the IGA-C method is developed. These results advance the numerical analysis of the IGA-C method.

In this paper, the King’s type modification of (p, q)-Bleimann-Butzer and Hahn operators is defined. Some results based on Korovkin’s approximation theorem for these new operators are studied. With the help of modulus of continuity and the Lipschitz type maximal functions, the rate of convergence for these new operators are obtained. It is shown that the King’s type modification have better rate of convergence, flexibility than classical (p, q)-BBH operators on some subintervals. Further, for comparisons of the operators, we presented some graphical examples and the error estimation in the form of tables through MATLAB (R2015a)

Let Y_t be an autoregressive process with order one, i.e., Y_t = μ + ϕ_nY_t−1 + ε_t, where [ε_t] is a heavy tailed general GARCH noise with tail index α. Let ({{hat phi }_n}) be the least squares estimator (LSE) of ϕ_n For μ = 0 and α < 2, it is shown by Zhang and Ling (2015) that ({{hat phi }_n}) is inconsistent when Y_t is stationary (i.e., ϕ_n ≡ ϕ < 1), however, Chan and Zhang (2010) showed that ({{hat phi }_n}) is still consistent with convergence rate n when Y_t is a unit-root process (i.e., ϕ_n = 1) and [ε_t] is a GARCH(1, 1) noise. There is a gap between the stationary and nonstationary cases. In this paper, two important issues will be considered: (1) what about the nearly unit root case? (2) When can ϕ be estimated consistently by the LSE? We show that when ϕ_n = 1 − c/n, then ({{hat phi }_n}) converges to a functional of stable process with convergence rate n. Further, we show that if lim_n→∞k_n(1 − ϕ_n) = c for a positive constant c, then ({k_n}({hat phi _n} - phi )) converges to a functional of two stable variables with tail index α/2, which means that ϕ_n can be estimated consistently only when k_n → ∞.

In this paper, we investigate a class of abstract neutral fractional delayed evolution equation in the fractional power space. With the aid of the analytic semigroup theories and some fixed point theorems, we establish the existence and uniqueness of the S-asymptotically periodic α-mild solutions. The linear part generates a compact and exponentially stable analytic semigroup and the nonlinear parts satisfy some conditions with respect to the fractional power norm of the linear part, which greatly improve and generalize the relevant results of existing literatures.

Let R[P] be the one point extension of a k-algebra R by a projective R-module P. We prove that the extension of a complete ideal cotorsion pair in R-Mod is still a complete ideal cotorsion pair in R[P]-Mod. As an application, it is obtainable that the operation (−)_m [P] satisfies the so-called distributive law relating the operations of products and extensions of ideals under appropriate conditions.