In this paper, some best proximity point theorems for generalized weakly contractive mappings which satisfy certain conditions by using three control functions in partially ordered Menger PM-spaces are obtained, and sufficient conditions to guarantee the uniqueness of the best proximity points are also given. Moreover, some corollaries are derived as consequences of the main results.
In this paper, the ill-posed Cauchy problem for two-dimensional Helmholtz equation with mixed boundary is investigated. To obtain stable numerical solution, a mollification regularization method with the de la Vallée Poussin operator is proposed. Error estimate between the exact solution and its approximation is given under the proper choice of a priori parameter. A numerical experiment shows that our procedure is effective and stable with respect to perturbations of noise in the data.
We establish the global well-posedness and analyticity of mild solution to the generalized three-dimensional incompressible Navier–Stokes equations for rotating fluids if the initial data are in Fourier–Herz spaces ?_{q}^{1-2α} (R^{3}) under appropriate conditions for α and q. As corollaries, we also give the corresponding conclusions of the generalized Navier–Stokes equation.
The purpose of this article is to study representations of δ-BiHom-Jordan-Lie superalgebras. In particular, adjoint representations, trivial representations, deformations of δ-Bihom-Jordan-Lie superalgebras are studied in detail. Derivations of δ-BiHom-Jordan-Lie algebras are also discussed as an application.
Let p_{1}, p_{2}, p_{3} be diverse odd primes, and c > 1 be integer. We obtain all nonnegative integer solutions(x, y, z) on the Pell equations x^{2}-(c^{2}-1)y^{2}=y^{2}-2p_{1}p_{2}p_{3}z^{2}=1. It generalizes the previous work of Keskin (2017) and Cipu (2018).
Let f, g be two nonconstant meromorphic functions, let a be a nonzero finite complex number, and let n ≥ 5 be a positive integer. If[f(z)]^{n} and[g(z)]^{n} share a CM, f(z) and g(z) share ∞ CM, and N_{1)}(r, f)=S(r, f), then either f(z) ≡ tg(z), where t^{n}=1, or f(z)g(z) ≡ t, where t^{n}=a^{2}. This improves some unicity results concerning derivatives and differences of meromorphic functions.
In this paper, we discuss the computational problem of a hybrid power mean involving character sums of polynomials and two-term cubic exponential sums, by using analytic methods and the properties of two-term exponential sums and Dirichlet characters. Meanwhile, we obtain a sharp asymptotic formula.
In this paper, we discuss several basic properties of a class of quasiconformal close-to-convex harmonic mappings with starlike analytic part, such results as coefficient inequalities, an integral representation, a growth theorem, an area theorem, and radii of close-to-convexity of partial sums of the class, are derived.
The Pang-Zalcman lemma is an important tool to study normal families of meromorphic functions. In this paper, we extend Pang-Zalcman lemma to the case of holomorphic functions of several complex variables and establish some normality criteria as applications.
The theory of operators on Hilbert spaces is one of fundamental frameworks of quantum mechanics. Hilbert space effect algebra, which is the convex set of positive operators between 0 and the identity, is one of important aspects in quantum mechanics. In the paper, we introduce a kind of sub-sequential effect algebra and explore some algebraic properties of the sequential product on it. We show that these properties on the sub-sequential effect algebra is different from those of existing ones.
We use the quantile residual lifetime models to analyze the length-biased data that are often encountered in observational studies. Ignoring sampling bias may lead to substantial estimation bias and fallacious inference. We consider a conditional log-linear regression model on the residual lifetimes at a fixed time point under right-censored and length-biased data for both covariate-independent censoring and covariate-dependent censoring. Consistency and asymptotically normalities of the regression estimators are established. Simmulation studies are performed to assess finite sample properties of the regression parameter estimator. Finally, we analyze the Oscar real data by the proposed method.
It is well known that a domain R is a Prüfer domain if and only if every divisible module is FP-injective; if and only if every h-divisible module is FP-injective. In this paper, we introduce the concept of Gorenstein FP-injective modules, and show that a domain R is a Gorenstein Prüfer domain if and only if every divisible module is Gorenstein FP-injective; if and only if every h-divisible module is Gorenstein FPinjective.
By means of the way of real analysis and the weight functions, introducing some parameters and intermediate variables, a few equivalent statements of a Hilberttype integral inequality with the general nonhomogeneous kernel in the whole plane are obtained. The constant factor is proved to be the best possible. As applications, a few equivalent statements of a Hilbert-type integral inequality with the general homogeneous kernel in the whole plane are deduced. We also consider some particular cases, the operator expressions and a few examples.
This paper addresses a class of dilation-and-modulation (MD) systems in the space L^{2}(R_{+}) of square integrable functions defined on the right half real line R_{+}. In practice, the time variable cannot be negative. L^{2}(R_{+}) models the causal signal space, but it admits no wavelet and Gabor systems due to R_{+} being not a group under addition. We study the dilation-and-modulation systems in L^{2}(R_{+}) generated by characteristic functions. We introduce the notion of MD-frame sets in R_{+}. Using "dilation-equivalence" and "cardinality function" methods we characterize MD-Bessel and complete sets; obtain two sufficient conditions for MD-Riesz basis sets; and prove that an arbitrary finite and measurable decomposition of an MD-Riesz basis set leads to an MD-frame set.
Let X^{H}={X^{H}t, t ∈ R_{+}} be a subfractional Brownian motion in R^{d}. We establish sharp Hölder conditions and tail probability estimates for the local times of X^{H} in one-parameter case. We also give the existence and the L^{2}-representation for the local time of X^{H} in multi-parameter case.