Hokkaido Mathematical Journal

No. 2

MORI, Atsuhide;

A concurrence theorem for alpha-connections on the space of t-distributions and its application.

Hokkaido Mathematical Journal, 49 (2020) pp.201-214

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Abstract

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.

MSC(Primary)	57R17
MSC(Secondary)	57R30; 62F15;
Uncontrolled Keywords	information geometry; symplectic and contact topology; Anosov flow; contact flow; Bayesian inference;

KOPALIANI, Tengiz; ZVIADADZE, Shalva;

Note on local properties of the exponents and boundedness of Hardy-Littlewood maximal operator in variable Lebesgue spaces.

Hokkaido Mathematical Journal, 49 (2020) pp.215-226

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Abstract

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.

MSC(Primary)	42B25
MSC(Secondary)	42B35;
Uncontrolled Keywords	variable exponent Lebesgue space; Hardy-Littlewood maximal operator;

LATERVEER, Robert;

On the motive of Kapustka–Rampazzo's Calabi-Yau threefolds.

Hokkaido Mathematical Journal, 49 (2020) pp.227-245

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Abstract

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.

MSC(Primary)	14C15
MSC(Secondary)	14C25; 14C30;
Uncontrolled Keywords	Algebraic cycles; Chow groups; motives; Calabi–Yau varieties; derived equivalence;

ITO, Hiroshi T.;

Eigenvalues and resonances of Dirac operators with dilation analytic potentials diverging at infinity.

Hokkaido Mathematical Journal, 49 (2020) pp.247-296

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Abstract

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.

MSC(Primary)	81Q15
MSC(Secondary)	81Q12;
Uncontrolled Keywords	resonance; Dirac operator; Pauli operator; nonrelativistic limit;

LIMA, Eudes L. de; LIMA, Henrique F. de; LIMA Jr., Eraldo A.; MEDEIROS, Adriano A.;

Constant mean curvature spacelike hypersurfaces in standard static spaces: rigidity and parabolicity.

Hokkaido Mathematical Journal, 49 (2020) pp.297-323

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Abstract

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 $M^n$.

MSC(Primary)	53C42
MSC(Secondary)	53B30; 53C50;
Uncontrolled Keywords	Standard static spaces; complete spacelike hypersurfaces; constant mean curvature; maximal spacelike surfaces; entire Killing graphs;

ADLIFARD, M.; PAYROVI, Sh.;

Some Remarks on the Annihilator Graph of a Commutative Ring.

Hokkaido Mathematical Journal, 49 (2020) pp.325-332

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Abstract

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.

MSC(Primary)	05C25
MSC(Secondary)	13Axx;
Uncontrolled Keywords	Annihilator graph; Zero divisor graph; Commutative ring;

KLIMEK, Slawomir; MCBRIDE, Matt; RATHNAYAKE, Sumedha; SAKAI, Kaoru;

A Value Region Problem for Continued Fractions and Discrete Dirac Equations.

Hokkaido Mathematical Journal, 49 (2020) pp.333-348

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Abstract

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.

MSC(Primary)	11Y65
MSC(Secondary)
Uncontrolled Keywords	continued fractions; discrete Dirac equations;

KARIMOV, Erkinjon; MAMCHUEV, Murat; RUZHANSKY, Michael;

Non-local initial problem for second order time-fractional and space-singular equation.

Hokkaido Mathematical Journal, 49 (2020) pp.349-361

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Abstract

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.

MSC(Primary)	35R11
MSC(Secondary)	33E12;
Uncontrolled Keywords	fractional derivatives; multinomial Mittag-Leffler function; Cauchy problem; Bessel operator;