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 EDTRemovable sets for subcaloric functions and solutions of semilinear heat equations with absorptionhttp://projecteuclid.org/euclid.hokmj/1470139401<strong>Kentaro HIRATA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 2, 195--222.</p><p><strong>Abstract:</strong><br/> We investigate removable sets for subcaloric functions satisfying either a growth condition or an integrability condition by defining suitably upper Minkowski content with respect to the parabolic distance. Results are also applied to obtain removability theorems for nonnegative solutions of a semilinear heat equation with an absorption term. </p>projecteuclid.org/euclid.hokmj/1470139401_20160802080323Tue, 02 Aug 2016 08:03 EDTOn the Separated Bumps Conjecture for Calderón-Zygmund Operatorshttp://projecteuclid.org/euclid.hokmj/1470139402<strong>Michael T. LACEY</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 2, 223--242.</p><p><strong>Abstract:</strong><br/> Let $\sigma (dx) = \sigma (x)dx$ and $w (dx)= w (x)dx$ be two weights with non-negative locally finite densities on $\mathbb R^{d}$, and let $1 \lt p \lt \infty$. A sufficient condition for the norm estimate
\begin{equation*}
\int \lvert T (\sigma f)\rvert^{p} \, w (dx) \le C_{T, \sigma ,w}^{p} \int \lvert f\rvert^{p}\, \sigma (dx) ,
\end{equation*}
valid for all Calder\'on-Zygmund operators $T$ is that the condition below holds.
\begin{equation*}
\sup_{\textup{$Q$ a cube}} \lVert \sigma^{1/{p'}}\rVert_{L^{A} (Q, {dx}/{\lvert Q\rvert})}
\varepsilon \big(\lVert \sigma^{1/{p'}}\rVert_{L^{A} (Q, {dx}/{\lvert Q\rvert})}/ \sigma (Q)^{1/{p'}}\big)
\bigg[\frac{w (Q)}{\lvert Q\rvert} \bigg]^{1/{p}} \lt \infty
\end{equation*}
Here $A$ is Young function, with dual in the P{\'e}rez class $B_{p}$, and the function $\varepsilon (t)$ is increasing on $(1, \infty )$ with $\int^{\infty } \varepsilon (t)^{-p'} ({dt}/ t) \lt \infty$. Moreover, a dual condition holds, with the roles of the weights and $L^{p}$ indices reversed also holds. This is an alternate version of a result of Nazarov, Reznikov and Volberg ($p=2$), one with a simpler formulation, and proof based upon stopping times. </p>projecteuclid.org/euclid.hokmj/1470139402_20160802080323Tue, 02 Aug 2016 08:03 EDTA tower condition characterizing normalityhttp://projecteuclid.org/euclid.hokmj/1470139403<strong>Lars KADISON</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 2, 243--262.</p><p><strong>Abstract:</strong><br/> We define left relative H-separable tower of rings and continue a study of these begun by Sugano. It is proven that a progenerator extension has right depth 2 if and only if the ring extension together with its right endomorphism ring is a left relative H-separable tower. In particular, this applies to twisted or ordinary Frobenius extensions with surjective Frobenius homomorphism. For example, normality for Hopf subalgebras of finite-dimensional Hopf algebras is also characterized in terms of this tower condition. </p>projecteuclid.org/euclid.hokmj/1470139403_20160802080323Tue, 02 Aug 2016 08:03 EDTAbsence of zero resonances of massless Dirac operatorshttp://projecteuclid.org/euclid.hokmj/1470139404<strong>Daisuke AIBA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 2, 263--270.</p><p><strong>Abstract:</strong><br/> We consider the massless Dirac operator $H = \alpha \cdot D + Q(x)$ on the Hilbert space $L^{2}( \mathbb{R}^{3}, \mathbb{C}^{4} )$, where $Q(x)$ is a $4 \times 4$ Hermitian matrix valued function which decays suitably at infinity. We show that the the zero resonance is absent for $H$, extending recent results of Sait\={o}-Umeda [6] and Zhong-Gao [7]. </p>projecteuclid.org/euclid.hokmj/1470139404_20160802080323Tue, 02 Aug 2016 08:03 EDTFiniteness of the Moderate Rational Points of Once-punctured Elliptic Curveshttp://projecteuclid.org/euclid.hokmj/1470139405<strong>Yuichiro HOSHI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 2, 271--291.</p><p><strong>Abstract:</strong><br/> In the present paper, we prove the {\it finiteness} of the set of {\it moderate} rational points of a once-punctured elliptic curve over a number field. This {\it finiteness} may be regarded as an analogue for a once-punctured elliptic curve of the well-known {\it finiteness} of the set of torsion rational points of an abelian variety over a number field. In order to obtain the {\it finiteness}, we discuss the {\it center} of the image of the pro-$l$ outer Galois action associated to a hyperbolic curve. In particular, we give, under the assumption that $l$ is {\it odd}, a {\it necessary and sufficient condition} for a certain hyperbolic curve over a generalized sub-$l$-adic field to have {\it trivial center}. </p>projecteuclid.org/euclid.hokmj/1470139405_20160802080323Tue, 02 Aug 2016 08:03 EDT$S^1$-equivariant Rabinowitz--Floer homologyhttp://projecteuclid.org/euclid.hokmj/1478487612<strong>Urs FRAUENFELDER</strong>, <strong>Felix SCHLENK</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 3, 293--323.</p><p><strong>Abstract:</strong><br/> We define the $S^1$-equivariant Rabinowitz--Floer homology of a bounding
contact hypersurface $\Sigma$ in an exact symplectic manifold,
and show by a geometric argument that it vanishes if $\Sigma$ is displaceable. </p>projecteuclid.org/euclid.hokmj/1478487612_20161106220022Sun, 06 Nov 2016 22:00 ESTEstimates of operator convex and operator monotone functions on bounded intervalshttp://projecteuclid.org/euclid.hokmj/1478487613<strong>Hamed NAJAFI</strong>, <strong>Mohammad Sal MOSLEHIAN</strong>, <strong>Masatoshi FUJII</strong>, <strong>Ritsuo NAKAMOTO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 3, 325--336.</p><p><strong>Abstract:</strong><br/> Recently the behavior of operator monotone functions on unbounded intervals with respect to the relation of strictly positivity has been investigated. In this paper we deeply study such behavior not only for operator monotone functions but also for operator convex functions on bounded intervals. More precisely, we prove that if $f$ is a nonlinear operator convex function on a bounded interval $(a,b)$ and $A, B$ are bounded linear operators acting on a Hilbert space with spectra in $(a,b)$ and $A-B$ is invertible, then $sf(A)+(1-s)f(B)>f(sA+(1-s)B)$. A short proof for a similar known result concerning a nonconstant operator monotone function on $[0,\infty)$ is presented. Another purpose is to find a lower bound for $f(A)-f(B)$, where $f$ is a nonconstant operator monotone function, by using a key lemma. We also give an estimation of the Furuta inequality, which is an excellent extension of the L\"owner--Heinz inequality. </p>projecteuclid.org/euclid.hokmj/1478487613_20161106220022Sun, 06 Nov 2016 22:00 ESTA New Characterization of Some Simple Groups by Order and Degree Pattern of Solvable Graphhttp://projecteuclid.org/euclid.hokmj/1478487614<strong>B. AKBARI</strong>, <strong>N. IIYORI</strong>, <strong>A. R. MOGHADDAMFAR</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 3, 337--363.</p><p><strong>Abstract:</strong><br/> The solvable graph of a finite group $G$, denoted by ${\Gamma}_{\rm s}(G)$, is a simple graph whose vertices are the prime divisors of $|G|$ and two distinct primes $p$ and $q$ are joined by an edge if and only if there exists a solvable subgroup of $G$ such that its order is divisible by $pq$. Let $p_1<p_2<\cdots<p_k$ be all prime divisors of $|G|$ and let ${\rm D}_{\rm s}(G)=(d_{\rm s}(p_1), d_{\rm s}(p_2), \ldots, d_{\rm s}(p_k))$, where $d_{\rm s}(p)$ signifies the degree of the vertex $p$ in ${\Gamma}_{\rm s}(G)$. We will simply call ${\rm D}_{\rm s}(G)$ the degree pattern of solvable graph of $G$. In this paper, we determine the structure of any finite group $G$ (up to isomorphism) for which ${\Gamma}_{\rm s}(G)$ is star or bipartite. It is also shown that the sporadic simple groups and some of projective special linear groups $L_2(q)$ are characterized via order and degree pattern of solvable graph. </p>projecteuclid.org/euclid.hokmj/1478487614_20161106220022Sun, 06 Nov 2016 22:00 ESTScreen Semi-Slant Lightlike Submanifolds of Indefinite Sasakian Manifoldshttp://projecteuclid.org/euclid.hokmj/1478487615<strong>S. S. SHUKLA</strong>, <strong>Akhilesh YADAV</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 3, 365--381.</p><p><strong>Abstract:</strong><br/> In this paper, we introduce the notion of screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D 1 , D 2 and RadTM on screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds have been obtained. Further we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic. We also study mixed geodesic screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds and obtain a necessary and sufficient condition for induced connection to be metric connection. </p>projecteuclid.org/euclid.hokmj/1478487615_20161106220022Sun, 06 Nov 2016 22:00 ESTCurve diagrams for Artin groups of type Bhttp://projecteuclid.org/euclid.hokmj/1478487616<strong>Tetsuya ITO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 3, 383--398.</p><p><strong>Abstract:</strong><br/> We develop a theory of curve diagrams for Artin groups of type $B$. We define the winding number labeling and the wall crossing labeling of curve diagrams, and show that these labelings detect the classical and the dual Garside length, respectively. A remarkable point is that our argument does not require Garside theory machinery like normal forms, and is more geometric in nature. </p>projecteuclid.org/euclid.hokmj/1478487616_20161106220022Sun, 06 Nov 2016 22:00 ESTThe metric growth of the discrete Laplacianhttp://projecteuclid.org/euclid.hokmj/1478487617<strong>Hisayasu KURATA</strong>, <strong>Maretsugu YAMASAKI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 3, 399--417.</p><p><strong>Abstract:</strong><br/> Networks play important roles in the theory of discrete potentials. Especially, the theory of Dirichlet spaces on networks has become one of the most important tools for the study of potentials on networks. In this paper, first we study some relations between the Dirichlet sums of a function and of its Laplacian. We introduce some conditions to investigate properties of several functional spaces related to Dirichlet potentials and to biharmonic functions. Our goal is to study the growth of the Laplacian related to biharmonic functions on an infinite network. As an application, we prove a Riesz Decomposition theorem for Dirichlet functions satisfying various conditions. </p>projecteuclid.org/euclid.hokmj/1478487617_20161106220022Sun, 06 Nov 2016 22:00 ESTA Note on Vertex-transitive K\"ahler graphshttp://projecteuclid.org/euclid.hokmj/1478487618<strong>Yaermaimaiti TUERXUNMAIMAITI</strong>, <strong>Toshiaki ADACHI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 3, 419--433.</p><p><strong>Abstract:</strong><br/> In this paper we construct finite vertex-transitive K\"ahler graphs, which may be considered as discrete models of Hermitian symmetric spaces admitting K\"ahler magnetic fields.
We give a condition on cardinality of the set of vertices and the principal and the auxiliary degrees for a vertex-transitive K\"ahler graphs.
Also we give some examples of K\"ahler graphs corresponding typical vertex-transitive ordinary graphs. </p>projecteuclid.org/euclid.hokmj/1478487618_20161106220022Sun, 06 Nov 2016 22:00 ESTLocal symmetry on almost Kenmotsu three-manifoldshttp://projecteuclid.org/euclid.hokmj/1478487619<strong>Jong Taek CHO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 3, 435--442.</p><p><strong>Abstract:</strong><br/> We prove that a locally symmetric almost Kenmotsu three-manifold is locally isometric to either the hyperbolic space $\mathrm{\Bbb{H}^3(-1)}$ or a product space $\Bbb{H}^2(-4)\times \Bbb{R}$. </p>projecteuclid.org/euclid.hokmj/1478487619_20161106220022Sun, 06 Nov 2016 22:00 EST$CR$ rigidity of pseudo harmonic maps and pseudo biharmonic mapshttp://projecteuclid.org/euclid.hokmj/1498788016<strong>Hajime URAKAWA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 2, 141--187.</p><p><strong>Abstract:</strong><br/>
The $CR$ analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be
shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with
pseudo parallel pseudo mean curvature vector fields, will be characterized.
</p>projecteuclid.org/euclid.hokmj/1498788016_20170629220029Thu, 29 Jun 2017 22:00 EDTA note on skew group categorieshttp://projecteuclid.org/euclid.hokmj/1498788017<strong>Zhenqiang ZHOU</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 2, 189--207.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a finite group, and $\mathscr{C}$ a $G$-abelian category. We prove
that the skew group category $\mathscr{C}(G)$ is an abelian category under the
condition that the order $|G|$ is invertible in $\mathscr{C}$. When the order
$|G|$ is not invertible in $\mathscr{C}$, an example is given to show that
$\mathscr{C}(G)$ is not an abelian category.
</p>projecteuclid.org/euclid.hokmj/1498788017_20170629220029Thu, 29 Jun 2017 22:00 EDTA moment problem on rational numbershttp://projecteuclid.org/euclid.hokmj/1498788018<strong>Koji FURUTA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 2, 209--226.</p><p><strong>Abstract:</strong><br/>
We give integral representations of positive and negative definite functions
defined on an interval in a certain subsemigroup of the semigroup of rational
numbers.
</p>projecteuclid.org/euclid.hokmj/1498788018_20170629220029Thu, 29 Jun 2017 22:00 EDTHomology of a certain associative algebrahttp://projecteuclid.org/euclid.hokmj/1498788019<strong>Nobuo IIYORI</strong>, <strong>Masato SAWABE</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 2, 227--256.</p><p><strong>Abstract:</strong><br/>
Let $R$ be a commutative ring, and let $A$ be an associative $R$-algebra
possessing an $R$-free basis $B$. In this paper, we introduce a homology
$H_{n}(A,B)$ associated to a pair $(A,B)$ under suitable hypotheses. It depends
on not only $A$ itself but also a choice of $B$. In order to define
$H_{n}(A,B)$, we make use of a certain submodule of the $(n+1)$-fold tensor
product of $A$. We develop a general theory of $H_{n}(A,B)$. Various examples of
a pair $(A,B)$ and $H_{n}(A,B)$ are also provided.
</p>projecteuclid.org/euclid.hokmj/1498788019_20170629220029Thu, 29 Jun 2017 22:00 EDTThe lifespan of solutions to wave equations with weighted nonlinear terms in one
space dimensionhttp://projecteuclid.org/euclid.hokmj/1498788020<strong>Kyouhei WAKASA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 2, 257--276.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider the initial value problem for nonlinear wave equation
with weighted nonlinear terms in one space dimension. Kubo & Osaka &
Yazici [4] studied global solvability of the problem under different conditions
on the nonlinearity and initial data, together with an upper bound of the
lifespan for the problem. The aim of this paper is to improve the upper bound of
the lifespan and to derive its lower bound which shows the optimality of our new
upper bound.
</p>projecteuclid.org/euclid.hokmj/1498788020_20170629220029Thu, 29 Jun 2017 22:00 EDTSufficient conditions for decay estimates of the local energy and a behavior of the total energy of dissipative wave equations in exterior domainshttps://projecteuclid.org/euclid.hokmj/1510045300<strong>Mishio KAWASHITA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 3, 277--313.</p><p><strong>Abstract:</strong><br/>
Decaying properties of the local energy for the dissipative wave equations with the Dirichlet boundary conditions in exterior domains are discussed. For the dissipation coefficient, natural conditions ensuring that waves trapped by obstacles may lose their energy are considered. Under this setting, two sufficient conditions for getting the decay estimates for the energy in bounded regions (i.e. the local energy) are given. These conditions bring some relaxation on classes of the dissipation coefficient which uniformly decaying estimates for the local energy hold. Further, decaying properties of the total energy are also discussed.
</p>projecteuclid.org/euclid.hokmj/1510045300_20171107040201Tue, 07 Nov 2017 04:02 ESTThe DPW method for constant mean curvature surfaces in 3-dimensional Lorentzian spaceforms, with applications to Smyth type surfaceshttps://projecteuclid.org/euclid.hokmj/1510045301<strong>Yuta OGATA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 3, 315--350.</p><p><strong>Abstract:</strong><br/>
We give criteria for singularities of spacelike constant mean curvature surfaces in 3-dimensional de Sitter and anti-de Sitter spaces constructed by the DPW method, which is a generalized Weierstrass representation. We also construct some examples of spacelike CMC surfaces, including analogs of Smyth surfaces with singularities, using appropriate models to visualize them.
</p>projecteuclid.org/euclid.hokmj/1510045301_20171107040201Tue, 07 Nov 2017 04:02 ESTA vector-valued estimate of multilinear Calderón-Zygmund operators in Herz-Morrey spaces with variable exponentshttps://projecteuclid.org/euclid.hokmj/1510045302<strong>Conghui SHEN</strong>, <strong>Jingshi XU</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 3, 351--380.</p><p><strong>Abstract:</strong><br/>
In this paper, we obtain a vector valued inequality of multilinear Calderón-Zygmund operators on products of Herz-Morrey spaces with variable exponents.
</p>projecteuclid.org/euclid.hokmj/1510045302_20171107040201Tue, 07 Nov 2017 04:02 ESTThe extended zero-divisor graph of a commutative ring Ihttps://projecteuclid.org/euclid.hokmj/1510045303<strong>M. BAKHTYIARI</strong>, <strong>M. J. NIKMEHR</strong>, <strong>R. NIKANDISH</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 46, Number 3, 381--393.</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 $Ry\cap \mathrm{Ann}(x)\neq (0)$. It follows that the zero-divisor graph $\Gamma(R)$ is a subgraph of $\Gamma'(R)$. It is proved that $\Gamma'(R)$ is connected with diameter at most two and with girth at most four, if $\Gamma'(R)$ contains a cycle. Moreover, we characterize all rings whose extended zero-divisor graphs are complete or star. Furthermore, we study the affinity between extended zero-divisor graph and zero-divisor graph associated with a commutative ring. For instance, for a non-reduced ring $R$, it is proved that the extended zero-divisor graph and the zero-divisor graph of $R$ are identical to the join of a complete graph and a null graph if and only if $ann_R(Z(R))$ is a prime ideal.
</p>projecteuclid.org/euclid.hokmj/1510045303_20171107040201Tue, 07 Nov 2017 04:02 ESTThe 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 EDT