Ukrainian Mathematical Journal最新文献

We consider a large population of haploid sexually reproducing individuals. It is assumed that one individual initially carries a very strongly advantageous mutation at a single locus. We study the long-term contribution of this initial individual to the genome of the population.

We introduce a new type of submersions, which are called pointwise hemi-slant Riemannian submersions, as a generalization of slant Riemannian submersions, hemi-slant submersions, and pointwise slant submersions from Kaehler manifolds onto Riemannian manifolds. We obtain some geometric interpretations of this kind of submersions with respect to the total manifold, base manifold, and fibers. Moreover, we present nontrivial illustrative examples in order to demonstrate the existence of submersions of this kind. Finally, we obtain some curvature equalities and inequalities with respect to a certain basis.

For a function f from the Sobolev space W^1,p(C), where C ⊂ ℝ^d is an open convex cone, we establish a sharp inequality estimating ∥f∥ _L∞ via the L_p-norm of its gradient and a seminorm of the function. With the help of this inequality, we prove a sharp inequality estimating the L_∞-norm of the Radon–Nikodym derivative of a charge defined on Lebesgue measurable subsets of C via the L_p-norm of the gradient of this derivative and the seminorm of the charge. In the case where C = ℝ₊^m× ℝ^d−m, 0 ≤ m ≤ d, we obtain inequalities estimating the L_∞-norm of a mixed derivative of the function f : C → ℝ via its L_∞-norm and the L_p-norm of the gradient of mixed derivative of this function.

We investigate the sharp bound of certain coefficient functionals associated with a Hankel determinant of the second kind for the inverse function when f belongs to the class of starlike functions with respect to symmetric points.

We study the existence and regularity results for degenerate parabolic problems in the presence of strongly increasing regularizing lower-order terms and L^m-data/Dirac mass.

We study the concepts of projection invariant t-extending modules and projection invariant t-Baer modules, which are generalized to the notions of π-extending and t-Baer modules, respectively. Several structural properties are obtained and some applications are developed. It is shown that the π-t-extending modules and π-t-e. Baer modules are connected with each other. Moreover, we obtain a characterization for π-t-extending modules relative to the annihilator conditions.

We establish a relationship between the subclasses of univalent functions and generalized distribution series. The main aim of our investigation is to obtain necessary and sufficient conditions for the generalized distribution series to belong to the classes 𝒯 ℱ(ρ, ϑ), 𝒯 ℋ(ρ, ϑ), 𝒯 𝒥(ρ, ϑ), and 𝒯 𝒳(ρ, ϑ) . In addition, we obtain some particular cases of our main results.

Let (u, v) be a pair of quasidefinite and symmetric linear functionals with {P_n}_n≥0 and {Q_n}_n≥0 as respective sequences of monic orthogonal polynomial (SMOP). We define a sequence of monic polynomials {R_n}_n≥0 as follows:

(begin{array}{cc}frac{{P}_{n+2}^{mathrm{^{prime}}}left(xright)}{n+2}+{b}_{n}frac{{P}_{n}^{mathrm{^{prime}}}left(xright)}{n}-{Q}_{n+1}left(xright)={d}_{n-1}left(xright),& nge 1.end{array})

We present necessary and sufficient conditions for {R_n}_n≥0 to be orthogonal with respect to a quasidefinite linear functional w. In addition, we consider the case where {P_n}_n≥0 and {Q_n}_n≥0 are monic Chebyshev polynomials of the first and second kinds, respectively, and study the relative outer asymptotics of Sobolev polynomials orthogonal with respect to the Sobolev inner product

(langle p,qrangle s=underset{-1}{overset{1}{int }}pq{left(1-{x}^{2}right)}^{-1/2}dx+{uplambda }_{1}underset{-1}{overset{1}{int }}{p}^{mathrm{^{prime}}}{q}^{mathrm{^{prime}}}{left(1-{x}^{2}right)}^{1/2}dx+{uplambda }_{2}underset{-1}{overset{1}{int }}{p}^{mathrm{^{prime}}mathrm{^{prime}}}{q}^{mathrm{^{prime}}mathrm{^{prime}}}dmu left(xright),)

where μ is a positive Borel measure associated with w and λ₁, λ₂ > 0; λ₂ is a linear polynomial of λ₁.

We study the exponential stability of homogeneous fractional time-varying systems and the existence of Lyapunov homogeneous function for the conformable fractional homogeneous systems. We also prove that the local and global behaviors are similar. A numerical example is given to illustrate the efficiency of the obtained results.

We establish constructive necessary and sufficient conditions of solvability and propose a scheme for the construction of solutions to a nonautonomous nonlinear periodic boundary-value problem for a Rayleightype equation unsolved with respect to the derivative. The urgency of investigation of nonautonomous boundary-value problems unsolved with respect to the derivative is explained by the fact that the analysis of traditional problems solved with respect to the derivative is sometimes significantly complicated, e.g., in the presence of nonlinearities that are not integrable in elementary functions. We consider the critical case in which the equation for generating amplitudes of a weakly nonlinear periodic boundary-value problem for a Rayleigh-type equation does not turn into the identity. The least-squares method is used to establish constructive conditions for the solvability and propose convergent iterative schemes for the construction of approximate solutions to a nonautonomous nonlinear boundary-value problem unsolved with respect to the derivative. As an example of application of the proposed iterative scheme, we find approximations to the solutions of periodic boundary-value problems unsolved with respect to the derivative in the case of periodic problem for the equation that describes the motion of a satellite on the elliptic orbit. We obtain an estimate for the range of values of a small parameter in which the iterative procedure used for the construction of solutions to a weakly nonlinear periodic boundary-value problem for a Rayleigh-type equation unsolved with respect to the derivative is convergent. To check the accuracy of the proposed approximations, we estimate the discrepancies appearing in the equation used to simulate the motion of satellites along the elliptic orbits.