The space of Student's t-distributions with $\nu$ degrees of freedom is the upper half-plane $\mathbb H$ with the location-scale coordinates. A normal distribution is a t-distribution with $\nu=\infty$. The $\alpha$-connections for t-distributions form a line ${\mathbb L}^\nu$ in the space of affine connections on $\mathbb H$. We show that the family $\{{\mathbb L}^\nu\}_{\nu\in(1,\infty]}$ has the concurrent point which presents the e-connection for normal distributions. As an application, generalizing the previous result of the author, we construct a contact Hamiltonian flow which visualizes certain Bayesian learnings.

It is explored the interaction between the symmetry of the exponent function and log-Hölder continuity in controlling the boundedness of the Hardy-Littlewood maximal operator in variable exponent Lebesgue spaces.

Kapustka and Rampazzo have exhibited pairs of Calabi-Yau threefolds $X$ and $Y$ that are L–equivalent and derived equivalent, without being birational. We complete the picture by showing that $X$ and $Y$ have isomorphic Chow motives.

We study spectra and resonances of Dirac operators with an electric potential diverging at infinity and a bounded magnetic potential with the help of the dilation analytic method and the Foldy-Wouthuysen-Tani transform. After investigating the spectrum, we study on resonance-free regions. We also show that resonances of the Dirac operator exist near eigenvalues of a Pauli operator or resonances of another Pauli operator when the velocity of light $c$ is sufficiently large.

Our purpose in this paper is investigate the geometry of complete constant mean curvature spacelike hypersurfaces immersed in a standard static space, that is, a Lorentzian manifold endowed with a globally defined timelike Killing vector field. In this setting, supposing that the ambient space is a warped product of the type $M^n\times_{\rho}\mathbb{R}_1$ whose Riemannian base $M^n$ has nonnegative sectional curvature and the warping function $\rho$ is convex on $M^n$, we use the generalized maximum principle of Omori-Yau in order to establish rigidity results concerning these spacelike hypersurfaces. We also study the parabolicity of maximal spacelike surfaces in $M^2\times_{\rho}\mathbb{R}_1$ and we obtain uniqueness results for entire Killing graphs constructed over $M^n$.

Let $R$ be a commutative ring with nonzero identity. The annihilator graph of $R$, denoted by $AG(R)$, is the (undirected) graph whose vertex set is the set of all nonzero zero-divisors of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $\ann_R(xy)\neq {\rm ann}_R(x)\cup {\rm ann}_R(y)$. We investigate the interplay between ring-theoretic properties of $R$ and graph-theoretic properties of $AG(R)$. We study the relation between two graphs $\Gamma(R)$ and $AG(R)$, where $R$ is a non-reduced commutative ring. Also, we completely characterize the rings whose annihilator graphs are complete.

Motivated by applications in noncommutative geometry we prove several value range estimates for even convergents and tails, and odd reverse sequences of Stieltjes type continued fractions with bounded ratio of consecutive elements, and show how those estimates control growth of solutions of a system of discrete Dirac equations.

In this work, we consider an initial problem for second order partial differential equations with Caputo fractional derivatives in the time-variable and Bessel operator in the space-variable. For non-local boundary conditions, we present a solution of this problem in an explicit form representing it by the Fourier-Bessel series. The obtained solution is written in terms of multinomial Mittag-Leffler functions and first kind Bessel functions.