Hokkaido Mathematical Journal Articles (Project Euclid)
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The latest articles from Hokkaido Mathematical Journal on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTMon, 14 Mar 2011 09:13 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Projectively flat connections and flat connections on homogeneous spaces
http://projecteuclid.org/euclid.hokmj/1277385658
<strong>Hajime URAKAWA</strong><p><strong>Source: </strong>Hokkaido Math. J., Volume 39, Number 2, 139--155.</p><p><strong>Abstract:</strong><br/> We show a correspondence between the set of all $G$-invariant projectively flat connections on a homogeneous space $M=G/K$, and the one of all $\widetilde{G}$-invariant flat connections on homogeneous spaces $\widetilde{M}=\widetilde{G}/K$, where $\widetilde{G}$ is a central extension of $G$ (Theorem 3.3). </p>projecteuclid.org/euclid.hokmj/1277385658_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTThe extended zero-divisor graph of a commutative ring IIhttps://projecteuclid.org/euclid.hokmj/1510045304<strong>M. BAKHTYIARI</strong>, <strong>M. J. NIKMEHR</strong>, <strong>R. NIKANDISH</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 3, 395--406.</p><p><strong>Abstract:</strong><br/>
Let $R$ be a commutative ring with identity, and let $Z(R)$ be the set of zero-divisors of $R$. The extended zero-divisor graph of $R$ is the undirected (simple) graph $\Gamma'(R)$ with the vertex set $Z(R)^*=Z(R)\setminus\{0\}$, and two distinct vertices $x$ and $y$ are adjacent if and only if either $Rx\cap \mathrm{Ann}(y)\neq (0)$ or $Ry\cap \mathrm{Ann}(x)\neq (0)$. In this paper, we continue our study of the extended zero-divisor graph of a commutative ring that was introduced in [4]. We show that the extended zero-divisor graph associated with an Artinian ring is weakly perfect, i.e., its vertex chromatic number equals its clique number. Furthermore, we classify all rings whose extended zero-divisor graphs are planar.
</p>projecteuclid.org/euclid.hokmj/1510045304_20171107040201Tue, 07 Nov 2017 04:02 ESTOn the class of projective surfaces of general typehttps://projecteuclid.org/euclid.hokmj/1510045305<strong>Yoshiaki FUKUMA</strong>, <strong>Kazuhisa ITO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 3, 407--422.</p><p><strong>Abstract:</strong><br/>
Let $S$ be a smooth complex projective surface of general type, $H$ be a very ample divisor on $S$ and $m(S,H)$ be the class of $(S,H)$. In this paper, we study a lower bound for $m(S,H)-3H^2$ and we improve an inequality obtained by Lanteri. We also study $(S,H)$ with each value of $m(S,H)-3H^2$ and exhibit some examples.
</p>projecteuclid.org/euclid.hokmj/1510045305_20171107040201Tue, 07 Nov 2017 04:02 ESTSpectral analysis of a massless charged scalar field with cutoffshttps://projecteuclid.org/euclid.hokmj/1510045306<strong>Kazuyuki WADA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 3, 423--471.</p><p><strong>Abstract:</strong><br/>
A quantum system of a massless charged scalar field with a self-interaction is investigated. By introducing a spacial cut-off function, a Hamiltonian of the quantum system is realized as a linear operator on a boson Fock space. Under certain conditions, it is proven that the Hamiltonian is bounded below, self-adjoint and has a ground state for an arbitrary coupling constant. Moreover the Hamiltonian strongly commutes with the total charge operator. This fact implies that the state space of the charged scalar field is decomposed into the infinite direct sum of fixed total charge spaces. A total charge of an eigenstate is discussed.
</p>projecteuclid.org/euclid.hokmj/1510045306_20171107040201Tue, 07 Nov 2017 04:02 ESTKinematic expansive suspensions of irrational rotations on the circlehttps://projecteuclid.org/euclid.hokmj/1510045307<strong>Shigenori MATSUMOTO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 3, 473--485.</p><p><strong>Abstract:</strong><br/>
We shall show that the rotation of some irrational rotation number on the circle admits suspensions which are kinematic expansive.
</p>projecteuclid.org/euclid.hokmj/1510045307_20171107040201Tue, 07 Nov 2017 04:02 ESTGrowth of meromorphic solutions of some linear differential equationshttps://projecteuclid.org/euclid.hokmj/1510045308<strong>Hamid BEDDANI</strong>, <strong>Karima HAMANI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 3, 487--512.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the order and the hyper-order of meromorphic solutions of the linear differential equation \begin{equation*} f^{(k)}+\sum^{k-1}_{j=1}(D_{j}+B_{j}e^{P_{j}(z) })f^{(j)}+( D_{0}+A_{1}e^{Q_{1}( z)}+A_{2}e^{Q_{2}( z) }) f=0, \end{equation*} where $k\geq 2$ is an integer, $Q_{1}(z),Q_{2}(z)$, $P_{j}(z) $ $(j=1, \dots ,k-1)$ are nonconstant polynomials and $A_{s}(z)$ $(\not\equiv 0)$ $(s=1,2)$, $B_{j}( z)$ $(\not\equiv 0)$ $(j=1, \dots ,k-1)$, $D_{m}(z)$ $(m=0,1, \dots ,k-1)$ are meromorphic functions. Under some conditions, we prove that every meromorphic solution $f$ $(\not\equiv 0)$ of the above equation is of infinite order and we give an estimate of its hyper-order. Furthermore, we obtain a result about the exponent of convergence and the hyper-exponent of convergence of a sequence of zeros and distinct zeros of $f-\varphi$, where $\varphi$ $(\not\equiv 0)$ is a meromorphic function and $f$ $(\not\equiv 0)$ is a meromorphic solution of the above equation.
</p>projecteuclid.org/euclid.hokmj/1510045308_20171107040201Tue, 07 Nov 2017 04:02 ESTA remark on modified Morrey spaces on metric measure spaceshttps://projecteuclid.org/euclid.hokmj/1520928055<strong>Yoshihiro SAWANO</strong>, <strong>Tetsu SHIMOMURA</strong>, <strong>Hitoshi TANAKA}</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/>
Morrey norms, which are originally endowed with two parameters, are considered on general metric measure spaces. Volberg, Nazarov and Treil showed that the modified Hardy-Littlewood maximal operator is bounded on Legesgue spaces. The modified Hardy-Littlewood maximal operator is known to be bounded on Morrey spaces on Euclidean spaces, if we introduce the third parameter instead of adopting a natural extension of Morrey spaces. When it comes to geometrically doubling, as long as an auxiliary parameter is introduced suitably, the Morrey norm does not depend on the third parameter and this norm extends naturally the original Morrey norm. If the underlying space has a rich geometric structure, there is still no need to introduce auxiliary parameters. However, an example shows that this is not the case in general metric measure spaces. In this paper, we present an example showing that Morrey spaces depend on the auxiliary parameters.
</p>projecteuclid.org/euclid.hokmj/1520928055_20180313040112Tue, 13 Mar 2018 04:01 EDTLowerable vector fields for a finitely ${\cal L}$-determined multigermhttps://projecteuclid.org/euclid.hokmj/1520928058<strong>Yusuke MIZOTA</strong>, <strong>Takashi NISHIMURA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 17--23.</p><p><strong>Abstract:</strong><br/>
We show that the module of lowerable vector fields for a finitely ${\cal L}$-determined multigerm is finitely generated in a constructive way.
</p>projecteuclid.org/euclid.hokmj/1520928058_20180313040112Tue, 13 Mar 2018 04:01 EDTThe influence of order and conjugacy class length on the structure of finite groupshttps://projecteuclid.org/euclid.hokmj/1520928059<strong>Alireza Khalili ASBOEI</strong>, <strong>Mohammad Reza DARAFSHEH</strong>, <strong>Reza MOHAMMADYARI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 25--32.</p><p><strong>Abstract:</strong><br/>
Let $2^{n}+1 \gt 5$ be a prime number. In this article, we will show $G\cong C_{n}(2)$ if and only if $|G|=|C_{n}(2)|$ and $G$ has a conjugacy class length ${|C_{n}(2)|}/({2^{n}+1})$. Furthermore, we will show Thompson's conjecture is valid under a weak condition for the symplectic groups $C_{n}(2)$.
</p>projecteuclid.org/euclid.hokmj/1520928059_20180313040112Tue, 13 Mar 2018 04:01 EDTLarge-time behavior of solutions to a tumor invasion model of Chaplain–Anderson type with quasi-variational structurehttps://projecteuclid.org/euclid.hokmj/1520928060<strong>Akio ITO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 33--67.</p><p><strong>Abstract:</strong><br/>
We treat 2D and 3D tumor invasion models with quasi-variational structures, which are composed of two PDEs, one ODE and certain constraint conditions. Although the original model was proposed by M. R. A. Chaplain and A. R. A. Anderson in 2003, the difference between their original model and ours is that the constraint conditions for the distributions of tumor cells and the extracellular matrix are imposed in our model, which give a quasi-variational structure. For 2D and 3D tumor invasion models with quasi-variational structures, we show the existence of global-in-time solutions and consider their large-time behaviors. Especially, for the large-time behaviors, we show that there exists at least one global-in-time solution such that it converges to a constant steady state in an appropriate function space as time goes to $\infty$.
</p>projecteuclid.org/euclid.hokmj/1520928060_20180313040112Tue, 13 Mar 2018 04:01 EDTSchwarz maps associated with the triangle groups $(2,4,4)$ and $(2,3,6)$https://projecteuclid.org/euclid.hokmj/1520928061<strong>Yuto KOGUCHI</strong>, <strong>Keiji MATSUMOTO</strong>, <strong>Fuko SETO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 69--108.</p><p><strong>Abstract:</strong><br/>
We consider the Schwarz maps with monodromy groups isomorphic to the triangle groups $(2,4,4)$ and $(2,3,6)$ and their inverses. We apply our formulas to studies of mean iterations.
</p>projecteuclid.org/euclid.hokmj/1520928061_20180313040112Tue, 13 Mar 2018 04:01 EDTThe Fermat septic and the Klein quartic as moduli spaces of hypergeometric Jacobianshttps://projecteuclid.org/euclid.hokmj/1520928062<strong>Kenji KOIKE</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 109--141.</p><p><strong>Abstract:</strong><br/>
We study the Schwarz triangle function with the monodromy group $\Delta(7,7,7)$, and we construct its inverse by theta constants. As consequences, we give uniformizations of the Klein quartic curve and the Fermat septic curve as Shimura curves parametrizing Abelian $6$-folds with endomorphisms $\mathbb{Z}[\zeta_7]$.
</p>projecteuclid.org/euclid.hokmj/1520928062_20180313040112Tue, 13 Mar 2018 04:01 EDTCertain bilinear operators on Morrey spaceshttps://projecteuclid.org/euclid.hokmj/1520928063<strong>Dashan FAN</strong>, <strong>Fayou ZHAO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 143--159.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider that $T(f,g)$ is a bilinear operator satisfying \begin{equation*} |T(f,g)(x)|\preceq \int_{\mathbb{R}^{n}}\frac{|f(x-ty)g(x-y)|}{|y|^{n}}dy \end{equation*} for $x$ such that $0\notin {\rm supp}~(f(x-t\cdot )) \cap {\rm supp}~(g(x+\cdot ))$. We obtain the boundedness of $T(f,g)$ on the Morrey spaces with the assumption of the boundedness of the operator $T(f,g)$ on the Lebesgues spaces. As applications, we yield that many well known bilinear operators, as well as the first Calderón commutator, are bounded from the Morrey spaces $L^{q,\lambda_{1}}\times L^{r,\lambda_{2}}$ to $L^{p,\lambda}$, where $\lambda /p={\lambda_{1}}/{q}+{\lambda_{2}}/{r}$.
</p>projecteuclid.org/euclid.hokmj/1520928063_20180313040112Tue, 13 Mar 2018 04:01 EDTAn almost complex Castelnuovo de Franchis theoremhttps://projecteuclid.org/euclid.hokmj/1520928064<strong>Indranil BISWAS</strong>, <strong>Mahan MJ</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 161--169.</p><p><strong>Abstract:</strong><br/>
Given a compact almost complex manifold, we prove a Castelnuovo–de Franchis type theorem for it.
</p>projecteuclid.org/euclid.hokmj/1520928064_20180313040112Tue, 13 Mar 2018 04:01 EDTOn the symmetric algebras associated to graphs with loopshttps://projecteuclid.org/euclid.hokmj/1520928065<strong>Mariacristina BARBERA</strong>, <strong>Maurizio IMBESI</strong>, <strong>Monica LA BARBIERA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 171--190.</p><p><strong>Abstract:</strong><br/>
We study the symmetric algebra of monomial ideals that arise from graphs with loops. The notion of $s$-sequence is investigated for such ideals in order to compute standard algebraic invariants of their symmetric algebra in terms of the corresponding invariants of special quotients of the polynomial ring related to the graphs.
</p>projecteuclid.org/euclid.hokmj/1520928065_20180313040112Tue, 13 Mar 2018 04:01 EDTCharacteristic function of Cayley projective plane as a harmonic manifoldhttps://projecteuclid.org/euclid.hokmj/1520928066<strong>Yunhee EUH</strong>, <strong>JeongHyeong PARK</strong>, <strong>Kouei SEKIGAWA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 191--203.</p><p><strong>Abstract:</strong><br/>
Any locally rank one Riemannian symmetric space is a harmonic manifold. We give the characteristic function of a Cayley projective plane as a harmonic manifold. The aim of this work is to show the explicit form of the characteristic function of the Cayley projective plane.
</p>projecteuclid.org/euclid.hokmj/1520928066_20180313040112Tue, 13 Mar 2018 04:01 EDTArithmetic identities for class regular partitionshttps://projecteuclid.org/euclid.hokmj/1520928067<strong>Hiroshi MIZUKAWA</strong>, <strong>Hiro-Fumi YAMADA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 205--221.</p><p><strong>Abstract:</strong><br/>
Extending the notion of $r$-(class) regular partitions, we define $(r_{1},\dots,r_{m})$-class regular partitions. Partition identities are presented and described by making use of the Glaisher correspondence.
</p>projecteuclid.org/euclid.hokmj/1520928067_20180313040112Tue, 13 Mar 2018 04:01 EDTElliptic surfaces and contact conics for a 3-nodal quartichttps://projecteuclid.org/euclid.hokmj/1520928068<strong>Khulan TUMENBAYAR</strong>, <strong>Hiro-o TOKUNAGA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 1, 223--244.</p><p><strong>Abstract:</strong><br/>
Let ${\mathcal Q}$ be an irreducible $3$-nodal quartic and let ${\mathcal C}$ be a smooth conic such that ${\mathcal C} \cap {\mathcal Q}$ does not contain any node of ${\mathcal Q}$ and the intersection multiplicity at $z \in {\mathcal C} \cap {\mathcal Q}$ is even for each $z$. In this paper, we study geometry of ${\mathcal C} + {\mathcal Q}$ through that of integral sections of a rational elliptic surface which canonically arises from ${\mathcal Q}$ and $z \in {\mathcal C} \cap {\mathcal Q}$. As an application, we construct Zariski pairs $({\mathcal C}_1 + {\mathcal Q}, {\mathcal C}_2 + {\mathcal Q})$, where ${\mathcal C}_i$ $(i = 1, 2)$ are smooth conics tangent to ${\mathcal Q}$ at four distinct points.
</p>projecteuclid.org/euclid.hokmj/1520928068_20180313040112Tue, 13 Mar 2018 04:01 EDTFold singularities on spacelike CMC surfaces in Lorentz-Minkowski spacehttps://projecteuclid.org/euclid.hokmj/1529308818<strong>Atsufumi HONDA</strong>, <strong>Miyuki KOISO</strong>, <strong>Kentaro SAJI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 2, 245--267.</p><p><strong>Abstract:</strong><br/>
Fold singular points play important roles in the theory of maximal surfaces. For example, if a maximal surface admits fold singular points, it can be extended to a timelike minimal surface analytically. Moreover, there is a duality between conelike singular points and folds. In this paper, we investigate fold singular points on spacelike surfaces with non-zero constant mean curvature (spacelike CMC surfaces). We prove that spacelike CMC surfaces do not admit fold singular points. Moreover, we show that the singular point set of any conjugate CMC surface of a spacelike Delaunay surface with conelike singular points consists of $(2,5)$-cuspidal edges.
</p>projecteuclid.org/euclid.hokmj/1529308818_20180618040033Mon, 18 Jun 2018 04:00 EDTFractal functions with no radial limits in Bergman spaces on treeshttps://projecteuclid.org/euclid.hokmj/1529308819<strong>Joel M. COHEN</strong>, <strong>Flavia COLONNA</strong>, <strong>Massimo A. PICARDELLO</strong>, <strong>David SINGMAN</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 2, 269--289.</p><p><strong>Abstract:</strong><br/>
For each $p \gt 0$ we provide the construction of a harmonic function on a homogeneous isotropic tree $T$ in the Bergman space $A^p(\sigma)$ with no finite radial limits anywhere. Here, $\sigma$ is an analogue of the Lebesgue measure on the tree. With the appropriate modifications, the construction yields a function in $A^1(\sigma)$ when $T$ is a rooted radial tree such that the number of forward neighbors increases so slowly that their reciprocals are not summable.
</p>projecteuclid.org/euclid.hokmj/1529308819_20180618040033Mon, 18 Jun 2018 04:00 EDTCharacterizations of three homogeneous real hypersurfaces in a complex projective spacehttps://projecteuclid.org/euclid.hokmj/1529308820<strong>Makoto KIMURA</strong>, <strong>Sadahiro MAEDA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 2, 291--316.</p><p><strong>Abstract:</strong><br/>
In an $n$-dimensional complex hyperbolic space $\mathbb{C}H^n(c)$ of constant holomorphic sectional curvature $c (\lt 0)$, the horosphere HS, which is defined by ${\rm HS} = \lim_{r\to\infty}G(r)$, is one of nice examples in the class of real hypersurfaces. Here, $G(r)$ is a geodesic sphere of radius $r$ $(0 \lt r \lt \infty)$ in $\mathbb{C}H^n(c)$. The second author ([14]) gave a geometric characterization of HS. In this paper, motivated by this result, we study real hypersurfaces $M^{2n-1}$ isometrically immersed into an $n$-dimensional complex projective space $\mathbb{C}P^n(c)$ of constant holomorphic sectional curvature $c(\gt 0)$.
</p>projecteuclid.org/euclid.hokmj/1529308820_20180618040033Mon, 18 Jun 2018 04:00 EDTReeb components of leafwise complex foliations and their symmetries IIhttps://projecteuclid.org/euclid.hokmj/1529308821<strong>Tomohiro Horiuchi</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 2, 317--337.</p><p><strong>Abstract:</strong><br/>
We study the group of leafwise holomorphic smooth automorphisms of 5-dimensional Reeb components with leafwise complex structure which are obtained by a certain Hopf construction. In particular, in the case where the boundary holonomy is infinitely tangent to the identity, we completely determine the structure of the group of leafwise holomorphic automorphisms of such foliations.
</p>projecteuclid.org/euclid.hokmj/1529308821_20180618040033Mon, 18 Jun 2018 04:00 EDTE-polynomials associated to $\mathbf{Z}_4$-codeshttps://projecteuclid.org/euclid.hokmj/1529308822<strong>Togo MOTOMURA</strong>, <strong>Manabu OURA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 2, 339--350.</p><p><strong>Abstract:</strong><br/>
Coding theory is connected with number theory via the invariant theory of some specified finite groups and theta functions. Under this correspondence we are interested in constructing, from a combinatorial point of view, an analogous theory of Eisenstein series. For this, we previously gave a formulation of E-polynomials based on the theory of binary codes. In the present paper we follow this direction and supply a new class of E-polynomials. To be precise, we introduce the E-polynomials associated to the $\mathbf{Z}_4$-codes and determine both the ring and the field structures generated by them. In addition, we discuss the zeros of the modular forms obtained from E-polynomials under the theta map.
</p>projecteuclid.org/euclid.hokmj/1529308822_20180618040033Mon, 18 Jun 2018 04:00 EDTRegular homeomorphisms of $\mathbb{R}^3$ and of $\mathbb{S}^3$https://projecteuclid.org/euclid.hokmj/1529308823<strong>Khadija Ben REJEB</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 2, 351--371.</p><p><strong>Abstract:</strong><br/>
This paper is the paper announced in [Be2, References [2]]. We show that every compact abelian group of homeomorphisms of $\mathbb{R}^3$ is either zero-dimensional or equivalent to a subgroup of the orthogonal group O(3). We prove a similar result if we replace $\mathbb{R}^3$ by $\mathbb{S}^3$, and we study regular homeomorphisms that are conjugate to their inverses.
</p>projecteuclid.org/euclid.hokmj/1529308823_20180618040033Mon, 18 Jun 2018 04:00 EDTWell-chosen weak solutions of the instationary Navier-Stokes system and their uniquenesshttps://projecteuclid.org/euclid.hokmj/1529308824<strong>Reinhard FARWIG</strong>, <strong>Yoshikazu GIGA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 2, 373--385.</p><p><strong>Abstract:</strong><br/>
We clarify the notion of well-chosen weak solutions of the instationary Navier-Stokes system recently introduced by the authors and P.-Y. Hsu in the article {\em Initial values for the Navier-Stokes equations in spaces with weights in time, Funkcialaj Ekvacioj} (2016). Well-chosen weak solutions have initial values in $L^{2}_{\sigma}(\Omega)$ contained also in a quasi-optimal scaling-invariant space of Besov type such that nevertheless Serrin's Uniqueness Theorem cannot be applied. However, we find universal conditions such that a weak solution given by a concrete approximation method coincides with the strong solution in a weighted function class of Serrin type.
</p>projecteuclid.org/euclid.hokmj/1529308824_20180618040033Mon, 18 Jun 2018 04:00 EDTAutomorphisms of order three of the moduli space of Spin-Higgs bundleshttps://projecteuclid.org/euclid.hokmj/1529308825<strong>Álvaro Antón SANCHO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 2, 387--426.</p><p><strong>Abstract:</strong><br/>
In this work we consider a family of ${\rm Spin}$ complex groups constructed in \cite{anton-article} which have outer automorphisms of order three. We define an action of ${\rm Out}({\rm Spin}(n,\mathbb{C}))\times\mathbb{C}^*$ on the moduli space of ${\rm Spin}$-Higgs bundles and we study the subvariety of fixed points of the induced automorphisms of order three. These fixed points can be expressed in terms of some kind of Higgs pairs associated to certain subgroups of ${\rm Spin}(n,\mathbb{C})$ equipped with a representation of the subgroup. We further the study for the simple case, $G={\rm Spin}(8,\mathbb{C})$.
</p>projecteuclid.org/euclid.hokmj/1529308825_20180618040033Mon, 18 Jun 2018 04:00 EDTThe inverse limit of the Burnside ring for a family of subgroups of a finite grouphttps://projecteuclid.org/euclid.hokmj/1529308826<strong>Yasuhiro HARA</strong>, <strong>Masaharu MORIMOTO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 2, 427--444.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a finite nontrivial group and $A(G)$ the Burnside ring of $G$. Let $\mathcal{F}$ be a set of subgroups of $G$ which is closed under taking subgroups and taking conjugations by elements in $G$. Then let $\frak{F}$ denote the category whose objects are elements in $\mathcal{F}$ and whose morphisms are triples $(H, g, K)$ such that $H$, $K \in \mathcal{F}$ and $g \in G$ with $gHg^{-1} \subset K$. Taking the inverse limit of $A(H)$, where $H \in \mathcal{F}$, we obtain the ring $A(\frak{F})$ and the restriction homomorphism ${\rm{res}}^G_{\mathcal{F}} : A(G) \to A(\frak{F})$. We study this restriction homomorphism.
</p>projecteuclid.org/euclid.hokmj/1529308826_20180618040033Mon, 18 Jun 2018 04:00 EDTOn a certain invariant of differential equations associated with nilpotent graded Lie algebrashttps://projecteuclid.org/euclid.hokmj/1537948824<strong>Takahiro NODA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 445--464.</p><p><strong>Abstract:</strong><br/>
In this paper, we provide a new invariant for partial differential equations (PDEs) under contact transformations by using nilpotent graded Lie algebras. By virtue of this invariant, various geometric behavior of PDEs can be understood. As a typical class, we clarify geometric behavior of second-order PDEs in terms of our invariant.
</p>projecteuclid.org/euclid.hokmj/1537948824_20180926040058Wed, 26 Sep 2018 04:00 EDTGeneralized Lucas Numbers of the form $wx^{2}$ and $wV_{m}x^{2}$https://projecteuclid.org/euclid.hokmj/1537948825<strong>Merve GÜNEY DUMAN</strong>, <strong>Ümmügülsüm ÖĞÜT</strong>, <strong>Refik KESKİN</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 465--480.</p><p><strong>Abstract:</strong><br/>
Let $P\geq 3$ be an integer. Let $(V_{n})$ denote generalized Lucas sequence defined by $V_{0}=2$, $V_{1}=P$, and $V_{n+1}=PV_{n}-V_{n-1}$ for $n\geq 1$. In this study, when $P$ is odd, we solve the equation $V_{n}=wx^{2}$ for some values of $w$. Moreover, when $P$ is odd, we solve the equation $V_{n}=wkx^{2}$ with $k \mid P$ and $k \gt 1$ for $w=3,11,13$. Lastly, we solve the equation $V_{n}=wV_{m}x^{2}$ for $w=7,11,13$.
</p>projecteuclid.org/euclid.hokmj/1537948825_20180926040058Wed, 26 Sep 2018 04:00 EDTThe influence of nonnormal noncyclic subgroups on the structure of finite groupshttps://projecteuclid.org/euclid.hokmj/1537948826<strong>Jiangtao SHI</strong>, <strong>Ruchen HOU</strong>, <strong>Cui ZHANG</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 481--486.</p><p><strong>Abstract:</strong><br/>
We obtain a complete classification of finite groups in which all noncyclic proper subgroups are nonnormal, and we apply this classification to investigate some structures of finite groups.
</p>projecteuclid.org/euclid.hokmj/1537948826_20180926040058Wed, 26 Sep 2018 04:00 EDTThe existence of Leray-Hopf weak solutions with linear strainhttps://projecteuclid.org/euclid.hokmj/1537948827<strong>Ryôhei KAKIZAWA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 487--500.</p><p><strong>Abstract:</strong><br/>
This paper deals with the global existence of weak solutions to the initial value problem for the Navier-Stokes equations in $\mathbb{R}^{n}$ ($n \in \mathbb{Z}$, $n\geq 2$). Concerning initial data of the form $Ax+v(0)$, where $A \in M_{n}(\mathbb{R})$ and $v(0) \in L^{2}_{\sigma}(\mathbb{R}^{n})$, the weak solutions are properly-defined with the aid of the alternativity of the trilinear from $(Ax\cdot\nabla)v\cdot\varphi$. Furthermore, we construct the Leray-Hopf weak solution which satisfies not only the Navier-Stokes equations but also the energy inequality via the Galerkin approximation. From the viewpoint of quadratic forms, the Gronwall-Bellman inequality admits the uniform boundedness of the approximate solution.
</p>projecteuclid.org/euclid.hokmj/1537948827_20180926040058Wed, 26 Sep 2018 04:00 EDTSpatial Asymptotic Profiles of Solutions to the Navier-Stokes System in a Rotating Frame with Fast Decaying Datahttps://projecteuclid.org/euclid.hokmj/1537948828<strong>Reinhard FARWIG</strong>, <strong>Raphael SCHULZ</strong>, <strong>Yasushi TANIUCHI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 501--529.</p><p><strong>Abstract:</strong><br/>
The nonstationary Navier-Stokes system for a viscous, incompressible fluid influenced by a Coriolis force in the whole space ${\mathbb R}^3$ is considered at large distances. The solvability of the corresponding integral equations of these equations in weighted $L^\infty$-spaces is established. Furthermore, the leading terms of the asymptotic profile of the solution at fixed time $t \gt 0$ for $|x| \gt t$ and far from the axis of rotation are investigated.
</p>projecteuclid.org/euclid.hokmj/1537948828_20180926040058Wed, 26 Sep 2018 04:00 EDTA characterization for tropical polynomials being the minimum finishing time of project networkshttps://projecteuclid.org/euclid.hokmj/1537948829<strong>Takaaki ITO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 531--544.</p><p><strong>Abstract:</strong><br/>
A tropical polynomial is called $R$-polynomial if it can be realized as the minimum finishing time of a project network. $R$-polynomials satisfy the term extendability condition, and correspond to simple graphs. We give a characterization of $R$-polynomials in terms of simple graphs.
</p>projecteuclid.org/euclid.hokmj/1537948829_20180926040058Wed, 26 Sep 2018 04:00 EDTTopological bi-$\mathcal{K}$-equivalence of pairs of map germshttps://projecteuclid.org/euclid.hokmj/1537948830<strong>Lev BIRBRAIR</strong>, <strong>João Carlos Ferreira COSTA</strong>, <strong>Edvalter Da Silva Sena FILHO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 545--556.</p><p><strong>Abstract:</strong><br/>
Let $P^{k}(n,p \times q)$ be the set of all pairs of real polynomial map germs $(f, g) : (\mathbb{R}^{n},0) \rightarrow (\mathbb{R}^{p} \times \mathbb{R}^{q} ,0)$ with degree of $ f_1 , \dots, f_p ,$ $g_1 ,\dots, g_q$ less than or equal to $k \in \N$. The main result of this paper shows that the set of equivalence classes of $P^{k}(n,p \times q)$, with respect to bi-$C^{0}$-$\mathcal{K}$-equivalence, is finite.
</p>projecteuclid.org/euclid.hokmj/1537948830_20180926040058Wed, 26 Sep 2018 04:00 EDTMoving frames and conservation laws of a Lagrangian invariant under the Hyperbolic Rotation-Translation grouphttps://projecteuclid.org/euclid.hokmj/1537948831<strong>Yousef MASOUDI</strong>, <strong>Mehdi NADJAFIKHAH</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 557--579.</p><p><strong>Abstract:</strong><br/>
Noether's First Theorem guarantees conservation laws provided that the Lagrangian is invariant under a Lie group action. In this paper, via the concept of Killing vector fields and the Minkowski metric, we first construct an important Lie group, known as Hyperbolic Rotation-Translation group. Then, according to Gonçalves and Mansfield's method, we obtain the invariantized Euler-Lagrange equations and the space of conservation laws in terms of vectors of invariants and the adjoint representation of a moving frame, for Lagrangians, which are invariant under Hyperbolic Rotation-Translation (or HRT) group action, in the case where the independent variables are not invariant.
</p>projecteuclid.org/euclid.hokmj/1537948831_20180926040058Wed, 26 Sep 2018 04:00 EDTRigidity theorems for compact Bach-flat manifolds with positive constant scalar curvaturehttps://projecteuclid.org/euclid.hokmj/1537948832<strong>Haiping FU</strong>, <strong>Jianke PENG</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 581--605.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove some rigidity theorems for compact Bach-flat $n$-manifold with the positive constant scalar curvature. In particular, our conditions in Theorem 2 have the additional properties of being sharp.
</p>projecteuclid.org/euclid.hokmj/1537948832_20180926040058Wed, 26 Sep 2018 04:00 EDTDiscrete Green Potentials with Finite Energyhttps://projecteuclid.org/euclid.hokmj/1537948833<strong>Hisayasu KURATA</strong>, <strong>Maretsugu YAMASAKI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 607--624.</p><p><strong>Abstract:</strong><br/>
For a hyperbolic infinite network, it is well-known that Green potentials with finite energy are Dirichlet potentials. Conversely, if a Dirichlet potential has non-positive Laplacian, then it is a Green potential with finite energy. In this paper, we study whether a Dirichlet potential can be expressed as a difference of two Green potentials with finite energy. Comparisons of the Dirichlet sum of a function and that of its Laplacian play important roles in our study. As a by-product, we obtain a Riesz decomposition of a function whose Laplacian is a Dirichlet function.
</p>projecteuclid.org/euclid.hokmj/1537948833_20180926040058Wed, 26 Sep 2018 04:00 EDTEstimates for the first eigenvalue of the drifting Laplacian on embedded hypersurfaceshttps://projecteuclid.org/euclid.hokmj/1537948834<strong>Jing MAO</strong>, <strong>Ni XIANG</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 625--636.</p><p><strong>Abstract:</strong><br/>
For an $(n-1)$-dimensional compact orientable smooth metric measure space $\big(M,g,e^{-f}dv_{g}\big)$ embedded in an $n$-dimensional compact orientable Riemannian manifold $N$, we successfully give a lower bound for the first nonzero eigenvalue of the drifting Laplacian on $M$, provided the Ricci curvature of $N$ is bounded from below by a positive constant and the weighted function $f$ on $M$ satisfies two constraints.
</p>projecteuclid.org/euclid.hokmj/1537948834_20180926040058Wed, 26 Sep 2018 04:00 EDTRigidity of transversally biharmonic maps between foliated Riemannian manifoldshttps://projecteuclid.org/euclid.hokmj/1537948835<strong>Shinji OHNO</strong>, <strong>Takashi SAKAI</strong>, <strong>Hajime URAKAWA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 637--654.</p><p><strong>Abstract:</strong><br/>
On a smooth foliated map from a complete, possibly non-compact, foliated Riemannian manifold into another foliated Riemannian manifold of which transversal sectional curvature is non-positive, we will show that, if it is transversally biharmonic and has the finite energy and finite bienergy, then it is transversally harmonic.
</p>projecteuclid.org/euclid.hokmj/1537948835_20180926040058Wed, 26 Sep 2018 04:00 EDTIPA-deformations of functions on affine spacehttps://projecteuclid.org/euclid.hokmj/1537948836<strong>David B. MASSEY</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 47, Number 3, 655--676.</p><p><strong>Abstract:</strong><br/>
We investigate deformations of functions on affine space, deformations in which the changes specialize to a distinguished point in the zero-locus of the original function. Such deformations – deformations with isolated polar activity – enable us to obtain nice results on the cohomology of the Milnor fiber of the original function.
</p>projecteuclid.org/euclid.hokmj/1537948836_20180926040058Wed, 26 Sep 2018 04:00 EDTIsometric realization of cross caps as formal power series and its applicationshttps://projecteuclid.org/euclid.hokmj/1550480642<strong>Atsufumi HONDA</strong>, <strong>Kosuke NAOKAWA</strong>, <strong>Masaaki UMEHARA</strong>, <strong>Kotaro YAMADA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 1, 1--44.</p><p><strong>Abstract:</strong><br/>
Two cross caps in Euclidean 3-space are said to be infinitesimally isometric if their Taylor expansions of the first fundamental forms coincide by taking a local coordinate system. For a given $C^\infty$ cross cap $f$, we give a method to find all cross caps which are infinitesimally isomeric to $f$. More generally, we show that for a given $C^{\infty}$ metric with singularity having certain properties like as induced metrics of cross caps (called a Whitney metric ), there exists locally a $C^\infty$ cross cap infinitesimally isometric to the given one. Moreover, the Taylor expansion of such a realization is uniquely determined by a given $C^{\infty}$ function with a certain property (called characteristic function ). As an application, we give a countable family of intrinsic invariants of cross caps which recognizes infinitesimal isometry classes completely.
</p>projecteuclid.org/euclid.hokmj/1550480642_20190218040427Mon, 18 Feb 2019 04:04 ESTA Lê-Greuel type formula for the image Milnor numberhttps://projecteuclid.org/euclid.hokmj/1550480643<strong>J. J. NUÑO-BALLESTEROS</strong>, <strong>I. PALLARÉS-TORRES</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 1, 45--59.</p><p><strong>Abstract:</strong><br/>
Let $f:(\mathbb{C}^n,0)\rightarrow (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p:(\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g:(\mathbb{C}^{n-1},0)\rightarrow (\mathbb{C}^{n},0)$ the transverse slice of $f$ with respect to $p$. We prove that the sum of the image Milnor numbers $\mu_I(f)+\mu_I(g)$ is equal to the number of critical points of $p|_{X_s}:X_s\to\mathbb{C}$ on all the strata of $X_s$, where $X_s$ is the disentanglement of $f$ (i.e., the image of a stabilisation $f_s$ of $f$).
</p>projecteuclid.org/euclid.hokmj/1550480643_20190218040427Mon, 18 Feb 2019 04:04 ESTVector valued inequalities and Littlewood-Paley operators on Hardy spaceshttps://projecteuclid.org/euclid.hokmj/1550480644<strong>Shuichi SATO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 1, 61--84.</p><p><strong>Abstract:</strong><br/>
We prove certain vector valued inequalities on $\Bbb R^n$ related to Littlewood-Paley theory. They can be used in proving characterization of the Hardy spaces in terms of Littlewood-Paley operators by methods of real analysis.
</p>projecteuclid.org/euclid.hokmj/1550480644_20190218040427Mon, 18 Feb 2019 04:04 ESTLipschitz continuity of $\alpha$-harmonic functionshttps://projecteuclid.org/euclid.hokmj/1550480645<strong>Peijin LI</strong>, <strong>Xiantao WANG</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 1, 85--97.</p><p><strong>Abstract:</strong><br/>
The aim of this paper is to discuss the Lipschitz continuity of $\alpha$-harmonic functions.
</p>projecteuclid.org/euclid.hokmj/1550480645_20190218040427Mon, 18 Feb 2019 04:04 ESTApplications of Campanato spaces with variable growth condition to the Navier-Stokes equationhttps://projecteuclid.org/euclid.hokmj/1550480646<strong>Eiichi NAKAI</strong>, <strong>Tsuyoshi YONEDA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 1, 99--140.</p><p><strong>Abstract:</strong><br/>
We give new viewpoints of Campanato spaces with variable growth condition for applications to the Navier-Stokes equation. Namely, we formulate a blowup criteria along maximum points of the 3D-Navier-Stokes flow in terms of stationary Euler flows and show that the properties of Campanato spaces with variable growth condition are very useful for this formulation, since variable growth condition can control the continuity and integrability of functions on the neighborhood at each point. Our criterion is different from the Beale-Kato-Majda type and Constantin-Fefferman type criterion. If geometric behavior of the velocity vector field near the maximum point has a kind of stationary Euler flow configuration up to a possible blowup time, then the solution can be extended to be the strong solution beyond the possible blowup time. As another application we also mention the Cauchy problem for the Navier-Stokes equation.
</p>projecteuclid.org/euclid.hokmj/1550480646_20190218040427Mon, 18 Feb 2019 04:04 ESTBrauer groups of Châtelet surfaces over local fieldshttps://projecteuclid.org/euclid.hokmj/1550480647<strong>Takashi HIROTSU</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 1, 141--154.</p><p><strong>Abstract:</strong><br/>
A Châtelet surface over a field is a typical geometrically rational surface. Its Chow group of zero-cycles has been studied as an important birational invariant by many researchers since the 1970s. Recently, S. Saito and K. Sato obtained a duality between the Chow and Brauer groups from the Brauer-Manin pairing. For a Châtelet surface over a local field, we combine their result with the known calculation of the Chow group to determine the structure and generators of the Brauer group of a regular proper flat model of the surface over the integer ring of the base field.
</p>projecteuclid.org/euclid.hokmj/1550480647_20190218040427Mon, 18 Feb 2019 04:04 ESTEquation system describing the radiation intensity and the air motion with the water phase transitionhttps://projecteuclid.org/euclid.hokmj/1550480648<strong>Meryem BENSSAAD</strong>, <strong>Hanane BELHIRECHE</strong>, <strong>Steave C. SELVADURAY</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 1, 155--193.</p><p><strong>Abstract:</strong><br/>
In this paper we consider the equation system describing the motion of the air and the variation of the radiation intensity and the quantity of water droplets in the air, including also the process of water phase transition. Under a suitable condition we prove the existence and uniqueness of the local solution. By eliminating the approximation by regularization of vapor density and by including the equation of radiation, this result improves previous ones.
</p>projecteuclid.org/euclid.hokmj/1550480648_20190218040427Mon, 18 Feb 2019 04:04 ESTOn the annihilators of formal local cohomology moduleshttps://projecteuclid.org/euclid.hokmj/1550480649<strong>Shahram REZAEI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 1, 195--206.</p><p><strong>Abstract:</strong><br/>
Let $\frak{a}$ denote an ideal in a commutative Noetherian local ring $(R,\frak{m})$ and $M$ a non-zero finitely generated $R$-module of dimension $d$. Let $d:=\dim(M/\frak{a} M)$. In this paper we calculate the annihilator of the top formal local cohomology module $\mathfrak{F}_{\frak{a}}^d (M)$. In fact, we prove that ${\rm Ann}_R(\mathfrak{F}_{\frak{a}}^d (M))={\rm Ann}_R(M/U_R(\frak{a}, M))$, where $$ U_R(\frak{a}, M):=\cup\lbrace N: N\leqslant M \text{ and } \dim(N/\frak{a}N) \lt \dim(M/\frak{a}M) \rbrace. $$ We give a description of $U_R(\frak{a}, M)$ and we will show that $$ {\rm Ann}_R (\mathfrak{F}_{\frak{a}}^d(M)) = {\rm Ann}_R (M/\cap_{\frak{p}_j \in {\rm Assh}_R M \cap {\rm V}(\frak{a})} N_j), $$ where $0=\bigcap_{j=1}^{n} N_{j}$ denotes a reduced primary decomposition of the zero submodule $0$ in $M$ and $N_j$ is a $\frak{p}_j$-primary submodule of $M$, for all $j=1,\dots, n$. Also, we determine the radical of the annihilator of $\mathfrak{F}_{\frak{a}}^d (M)$. We will prove that $$ \sqrt{{\rm Ann}_R(\mathfrak{F}_{\frak{a}}^d (M))} = {\rm Ann}_R(M/G_R(\frak{a}, M)), $$ where $G_R(\frak{a}, M)$ denotes the largest submodule of $M$ such that ${\rm Assh}_R(M)\cap {\rm V}(\frak{a}) \subseteq {\rm Ass}_R(M/G_R(\frak{a}, M))$ and ${\rm Assh}_R(M)$ denotes the set $\{\frak{p} \in {\rm Ass} M:\dim R/\frak{p} = \dim M\}.$
</p>projecteuclid.org/euclid.hokmj/1550480649_20190218040427Mon, 18 Feb 2019 04:04 ESTLocal well-posedness for the derivative nonlinear Schrödinger Equation in Besov Spaceshttps://projecteuclid.org/euclid.hokmj/1550480650<strong>Cai Constantin CLOOS</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 1, 207--244.</p><p><strong>Abstract:</strong><br/>
It is shown that the cubic derivative nonlinear Schrödinger equation is locally well-posed in Besov spaces $B^{s}_{2,\infty}(\mathbb X)$, $s\ge 1/2$, where we treat the non-periodic setting $\mathbb X=\mathbb R$ and the periodic setting $\mathbb X=\mathbb T$ simultaneously. The proof is based on the strategy of Herr for initial data in $H^{s}(\mathbb T)$, $s\ge 1/2$.
</p>projecteuclid.org/euclid.hokmj/1550480650_20190218040427Mon, 18 Feb 2019 04:04 ESTThe critical values of $L$-functions of base change for Hilbert modular formshttps://projecteuclid.org/euclid.hokmj/1562810506<strong>Cristian VIRDOL</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 245--252.</p><p><strong>Abstract:</strong><br/>
In this paper we generalize some results, obtained by Shimura, Yoshida and the author, on critical values of $L$-functions of $l$-adic representations attached to Hilbert modular forms twisted by finite order characters, to the critical values of $L$-functions of arbitrary base change to totally real number fields of $l$-adic representations attached to Hilbert modular forms twisted by some general finite-dimensional representations.
</p>projecteuclid.org/euclid.hokmj/1562810506_20190710220242Wed, 10 Jul 2019 22:02 EDTGraded weak comultiplication moduleshttps://projecteuclid.org/euclid.hokmj/1562810507<strong>Rashid ABU-DAWWAS</strong>, <strong>Malik BATAINEH</strong>, <strong>Adeela DA'KEEK</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 253--261.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a group with identity $e$, $R$ be a $G$-graded ring and $M$ be a $G$-graded $R$-module. In this article, we introduce the concept of graded weak comultiplication modules. A graded $R$-module $M$ is said to be graded weak comultiplication if for every graded prime $R$-submodule $N$ of $M$, $N=(0:_{M}I)$ for some graded ideal $I$ of $R$. We study graded weak comultiplication modules and give several results.
</p>projecteuclid.org/euclid.hokmj/1562810507_20190710220242Wed, 10 Jul 2019 22:02 EDTUniform convergence of orthogonal polynomial expansions for exponential weightshttps://projecteuclid.org/euclid.hokmj/1562810508<strong>Kentaro ITOH</strong>, <strong>Ryozi SAKAI</strong>, <strong>Noriaki SUZUKI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 263--280.</p><p><strong>Abstract:</strong><br/>
We consider an exponential weight $w(x) = \exp(-Q(x))$ on ${\mathbb R} = (-\infty,\infty)$, where $Q$ is an even and nonnegative function on ${\mathbb R}$. We always assume that $w$ belongs to a relevant class $\mathcal{F}(C^2+)$. Let $\{p_n\}$ be orthogonal polynomials for a weight $w$. For a function $f$ on ${\mathbb R}$, $s_n(f)$ denote the $(n-1)$-th partial sum of Fourier series. In this paper, we discuss uniformly convergence of $s_n(f)$ under the conditions that $f$ is continuous and has a bounded variation on any compact interval of ${\mathbb R}$. In the proof of main theorem, Nikolskii-type inequality and boundedness of the de la Vall{\'{e}}e Poussin mean of $f$ play important roles.
</p>projecteuclid.org/euclid.hokmj/1562810508_20190710220242Wed, 10 Jul 2019 22:02 EDTCharacterizing singularities of a surface in Lie sphere geometryhttps://projecteuclid.org/euclid.hokmj/1562810509<strong>Mason PEMBER</strong>, <strong>Wayne ROSSMAN</strong>, <strong>Kentaro SAJI</strong>, <strong>Keisuke TERAMOTO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 281--308.</p><p><strong>Abstract:</strong><br/>
The conditions for a cuspidal edge, swallowtail and other fundamental singularities are given in the context of Lie sphere geometry. We then use these conditions to study the Lie sphere transformations of a surface.
</p>projecteuclid.org/euclid.hokmj/1562810509_20190710220242Wed, 10 Jul 2019 22:02 EDTA finite group in which all non-nilpotent maximal subgroups are normal has a Sylow towerhttps://projecteuclid.org/euclid.hokmj/1562810510<strong>Jiangtao SHI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 309--312.</p><p><strong>Abstract:</strong><br/>
In this paper we prove that a finite group in which all non-nilpotent maximal subgroups are normal must have a Sylow tower, which improves Theorem 1.3 of [Finite groups with non-nilpotent maximal subgroups, Monatsh Math. 171 (2013) 425–431.].
</p>projecteuclid.org/euclid.hokmj/1562810510_20190710220242Wed, 10 Jul 2019 22:02 EDTHypergeometric functions interpolating Appell-Lauricella's $F_D$ and $F_A$https://projecteuclid.org/euclid.hokmj/1562810511<strong>Masaaki YOSHIDA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 313--325.</p><p><strong>Abstract:</strong><br/>
For Appell-Lauricella's $F_D$, solutions represented by integrals of Euler type over various chambers are studied to re-discover the multiple hypergeometric functions introduced in [Ex]. A family of hypergeometric functions interpolating $F_D$ and $F_A$ is presented.
</p>projecteuclid.org/euclid.hokmj/1562810511_20190710220242Wed, 10 Jul 2019 22:02 EDTNote on the integral operators in weighted Morrey spaceshttps://projecteuclid.org/euclid.hokmj/1562810512<strong>Takeshi IIDA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 327--343.</p><p><strong>Abstract:</strong><br/>
We investigate the boundedness of the maximal operator, the fractional maximal operator, and the fractional integral operator within the framework of weighted Morrey spaces. In particular, we consider the endpoint cases. This result can be recognized as the endpoint case of two weight multilinear norm inequality [4, Theorem 3.3] and, as a special case, recovers the Olsen inequality with small parameters [9, Examples 4.7].
</p>projecteuclid.org/euclid.hokmj/1562810512_20190710220242Wed, 10 Jul 2019 22:02 EDTThe unit group of a partial Burnside ring of a reducible Coxeter group of type Ahttps://projecteuclid.org/euclid.hokmj/1562810514<strong>Fumihito ODA</strong>, <strong>Masahiro WAKATAKE</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 345--356.</p><p><strong>Abstract:</strong><br/>
We determine the structure of the unit group of the partial Burnside ring relative to the set of parabolic subgroups of a finite reducible Coxeter group of type $\mathrm{A}$.
</p>projecteuclid.org/euclid.hokmj/1562810514_20190710220242Wed, 10 Jul 2019 22:02 EDTNote on asymptotic profile of solutions to the linearized compressible Navier-Stokes flowhttps://projecteuclid.org/euclid.hokmj/1562810515<strong>Ruy COIMBRA CHARÃO</strong>, <strong>Ryo IKEHATA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 357--383.</p><p><strong>Abstract:</strong><br/>
We consider the asymptotic behavior as $t \to +\infty$ of the $L^{2}$-norm of the velocity of the linearized compressible Navier-Stokes equations in ${\bf R}^{n}$ ($n \geq 2$). As an application we shall study the optimality of the decay rate for the $L^{2}$-norm of the velocity by deriving a decay estimate from below as $t \to +\infty$. To get the estimates in the zone of high frequency we use a version of the energy method in the Fourier space combined with the Haraux-Komornik inequality and this seems much different from known techniques to study compressible Navier-Stokes system.
</p>projecteuclid.org/euclid.hokmj/1562810515_20190710220242Wed, 10 Jul 2019 22:02 EDTGrassmann geometry on the 3-dimensional non-unimodular Lie groupshttps://projecteuclid.org/euclid.hokmj/1562810516<strong>Jun-ichi INOGUCHI</strong>, <strong>Hiroo NAITOH</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 385--406.</p><p><strong>Abstract:</strong><br/>
We study the Grassmann geometry of surfaces when the ambient space is a 3-dimensional non-unimodular Lie group with left invariant metric. This work together with our previous papers yield a complete classification of Grassmann geometry of orbit type in all 3-dimensional homogeneous spaces.
</p>projecteuclid.org/euclid.hokmj/1562810516_20190710220242Wed, 10 Jul 2019 22:02 EDTCoefficient inequalities for $q$-starlike functions associated with the Janowski functionshttps://projecteuclid.org/euclid.hokmj/1562810517<strong>H. M. SRIVASTAVA</strong>, <strong>Bilal KHAN</strong>, <strong>Nazar KHAN</strong>, <strong>Qazi Zahoor AHMAD</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 407--425.</p><p><strong>Abstract:</strong><br/>
The main purpose of this investigation is to find several coefficient inequalities and a sufficient condition for $q$-starlike functions which are associated with the Janowski functions. Relevant connections of the results presented in this paper with those in a number of other related works on this subject are also pointed out.
</p>projecteuclid.org/euclid.hokmj/1562810517_20190710220242Wed, 10 Jul 2019 22:02 EDTComparison theorems on trajectory-harps for Kähler magnetic fields which are holomorphic at their archeshttps://projecteuclid.org/euclid.hokmj/1562810518<strong>Qingsong SHI</strong>, <strong>Toshiaki ADACHI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 427--441.</p><p><strong>Abstract:</strong><br/>
A trajectory-harp is a variation of geodesics associated with a trajectory. We estimate how trajectories for Kähler magnetic fields go away from their initial points and show how they are bended by comparing trajectory-harps on a Kähler manifolds with those on complex space forms. Under a condition on sectional curvatures, we show that when the length of a geodesic segment of a trajectory-harp coincides with that on a complex space form it forms a part of a totally geodesic complex line.
</p>projecteuclid.org/euclid.hokmj/1562810518_20190710220242Wed, 10 Jul 2019 22:02 EDTHyponormality of singular Cauchy integral operators with matrix-valued symbolshttps://projecteuclid.org/euclid.hokmj/1562810519<strong>Yoenha KIM</strong>, <strong>Eungil KO</strong>, <strong>Jongrak LEE</strong>, <strong>Takahiko NAKAZI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 48, Number 2, 443--459.</p><p><strong>Abstract:</strong><br/>
In this paper, we study a class of hyponormal singular integral operators with matrix-valued symbols. First, we characterize hyponormal singular integral operators $S_{\Phi,\Psi}$ with trigonometric polynomial symbols $\Phi$ and $\Psi$. Next, we concentrate on the hyponormality of $S_{\Phi,\Psi}$ with some assumptions for the symbols $\Phi$ and $\Psi$.
</p>projecteuclid.org/euclid.hokmj/1562810519_20190710220242Wed, 10 Jul 2019 22:02 EDT