Hokkaido Mathematical Journal Articles (Project Euclid)
http://projecteuclid.org/euclid.hokmj
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
http://projecteuclid.org/
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 EDTRadiation condition at infinity for the high-frequency Helmholtz equation: optimality of a non-refocusing criterionhttp://projecteuclid.org/euclid.hokmj/1416837568<strong>François CASTELLA</strong>, <strong>Aurélien KLAK</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 43, Number 3, 275--325.</p><p><strong>Abstract:</strong><br/> We consider the high frequency Helmholtz equation with a variable refraction index n 2 ( x ) ( x ∈ ℝ d ), supplemented with a given high frequency source term supported near the origin x = 0. A small absorption parameter α ε > 0 is added, which prescribes a radiation condition at infinity for the considered Helmholtz equation. The semi-classical parameter is ε > 0. We let ε and α ε go to zero simultaneously . We study the question whether the prescribed radiation condition at infinity is satisfied uniformly along the asymptotic process ε Ⅺ 0.
This question has been previously studied by the first autor in [4], where it is proved that the radiation condition is indeed satisfied uniformly in ε, provided the refraction index satisfies a specific non-refocusing condition . The non-refocusing condition requires, in essence, that the rays of geometric optics naturally associated with the high-frequency Helmholtz operator, and that are sent from the origin x = 0 at time t = 0, should not refocus at some later time t > 0 near the origin again.
In the present text we show the optimality of the above mentioned non-refocusing condition. We exhibit a refraction index which does refocus the rays of geometric optics sent from the origin near the origin again, and we show that the limiting solution does not satisfy the natural radiation condition at infinity in that case. </p>projecteuclid.org/euclid.hokmj/1416837568_20141124085932Mon, 24 Nov 2014 08:59 ESTFold maps with singular value sets of concentric sphereshttp://projecteuclid.org/euclid.hokmj/1416837569<strong>Naoki KITAZAWA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 43, Number 3, 327--359.</p><p><strong>Abstract:</strong><br/> In this paper, we study fold maps from C ∞ closed manifolds into Euclidean spaces whose singular value sets are disjoint unions of spheres embedded concentrically. We mainly study homology and homotopy groups of manifolds admitting such maps. </p>projecteuclid.org/euclid.hokmj/1416837569_20141124085932Mon, 24 Nov 2014 08:59 ESTUlam's cellular automaton and Rule 150http://projecteuclid.org/euclid.hokmj/1416837570<strong>Akane KAWAHARADA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 43, Number 3, 361--383.</p><p><strong>Abstract:</strong><br/> In this paper we study Ulam's cellular automaton, a nonlinear almost equicontinuous two-dimensional cell-model of crystalline growths. We prove that Ulam's automaton contains a linear chaotic elementary cellular automaton (Rule 150) as a subsystem. We also study the application of the inverse ultradiscretization, a method for deriving partial differential equations from a given cellular automaton, to Ulam's automaton. It is shown that the partial differential equation obtained by the inverse ultradiscretization preserves the self-organizing pattern of Ulam's automaton. </p>projecteuclid.org/euclid.hokmj/1416837570_20141124085932Mon, 24 Nov 2014 08:59 ESTOn the classical limit of self-interacting quantum field Hamiltonians with cutoffshttp://projecteuclid.org/euclid.hokmj/1416837571<strong>Zied AMMARI</strong>, <strong>Maher ZERZERI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 43, Number 3, 385--425.</p><p><strong>Abstract:</strong><br/> We study, using Hepp's method, the propagation of coherent states for a general class of self interacting bosonic quantum field theories with spatial cutoffs. This includes models with non-polynomial interactions in the field variables. We show indeed that the time evolution of coherent states, in the classical limit, is well approximated by time-dependent affine Bogoliubov unitary transformations. Our analysis relies on a non-polynomial Wick quantization and a specific hypercontractive estimate. </p>projecteuclid.org/euclid.hokmj/1416837571_20141124085932Mon, 24 Nov 2014 08:59 ESTA semi-group formula for the Riesz potentialshttp://projecteuclid.org/euclid.hokmj/1470052351<strong>Takahide KUROKAWA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 1, 1--27.</p><p><strong>Abstract:</strong><br/> The purpose of this article is to establish a semi-group formula for the Riesz potentials of L p -functions. As preparations, we study the Lizorkin space Φ( R n ) and investigate integral estimates of the Riesz potentials of functions in the spaces L p:r,s ( R n ). </p>projecteuclid.org/euclid.hokmj/1470052351_20160801075236Mon, 01 Aug 2016 07:52 EDTOn a second order rational systems of difference equationshttp://projecteuclid.org/euclid.hokmj/1470052352<strong>N. TOUAFEK</strong>, <strong>E. M. ELSAYED</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 1, 29--45.</p><p><strong>Abstract:</strong><br/> In this paper we study the periodicity and the form of the solutions of the following systems of difference equations of order two
x n +1 = \frac{y_{n}x_{n-1}}{\pm x_{n-1}\pm y_{n}}, y n +1 = \frac{x_{n}y_{n-1}}{\pm x_{n}\pm y_{n-1}}, n ∈ ℕ 0 ,
with nonzero real numbers initial conditions. </p>projecteuclid.org/euclid.hokmj/1470052352_20160801075236Mon, 01 Aug 2016 07:52 EDTCohomology of wheels on toric varietieshttp://projecteuclid.org/euclid.hokmj/1470052353<strong>Alastair CRAW</strong>, <strong>Alexander QUINTERO VÉLEZ</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 1, 47--79.</p><p><strong>Abstract:</strong><br/> We describe explicitly the cohomology of the total complex of certain diagrams of invertible sheaves on normal toric varieties. These diagrams, called wheels, arise in the study of toric singularities associated to dimer models. Our main tool describes the generators in a family of syzygy modules associated to the wheel in terms of walks in a family of graphs. </p>projecteuclid.org/euclid.hokmj/1470052353_20160801075236Mon, 01 Aug 2016 07:52 EDTOn topology of some Riemannian manifolds of negative curvature with a compact Lie group of isometrieshttp://projecteuclid.org/euclid.hokmj/1470052354<strong>R. MIRZAIE</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 1, 81--89.</p><p><strong>Abstract:</strong><br/> We topologically characterize negatively curved Riemannian manifolds which are of cohomogeneity two under the action of a compact Lie group of isometries. </p>projecteuclid.org/euclid.hokmj/1470052354_20160801075236Mon, 01 Aug 2016 07:52 EDTOn coretractable moduleshttp://projecteuclid.org/euclid.hokmj/1470052355<strong>Derya KESKİN TÜTÜNCÜ</strong>, <strong>Berke KALEBO~GAZ</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 1, 91--99.</p><p><strong>Abstract:</strong><br/> Let R be any ring. We prove that every right R -module is coretractable if and only if R is right perfect and every right R -module is small coretractable if and only if all torsion theories on R are cohereditary. We also study mono-coretractable modules. We show that coretractable modules are a proper generalization of mono-coretractable modules. </p>projecteuclid.org/euclid.hokmj/1470052355_20160801075236Mon, 01 Aug 2016 07:52 EDTOn the variational problem associated with standard differential systemshttp://projecteuclid.org/euclid.hokmj/1470052356<strong>Noboru TANAKA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 1, 101--164.</p>projecteuclid.org/euclid.hokmj/1470052356_20160801075236Mon, 01 Aug 2016 07:52 EDTA curve of genus 5 having 24 Weierstrass points of weight 5http://projecteuclid.org/euclid.hokmj/1470053288<strong>Takao KATO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 2, 165--173.</p><p><strong>Abstract:</strong><br/> In this paper, we shall prove that if an irreducible curve X of genus 5 over ℂ has 24 Weierstrass points of weight 5, then it has exactly three bielliptic involutions. </p>projecteuclid.org/euclid.hokmj/1470053288_20160801080812Mon, 01 Aug 2016 08:08 EDTMinimal unfolded regions of a convex hull and parallel bodieshttp://projecteuclid.org/euclid.hokmj/1470053289<strong>Jun O'HARA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 2, 175--183.</p><p><strong>Abstract:</strong><br/> The minimal unfolded region (or the heart ) of a bounded subset Ω in the Euclidean space is a subset of the convex hull of Ω the definition of which is based on reflections in hyperplanes. It was introduced to restrict the location of the points that give extreme values of certain functions, such as potentials whose kernels are monotone functions of the distance, and solutions of differential equations to which Aleksandrov's reflection principle can be applied. We show that the minimal unfolded regions of the convex hull and parallel bodies of Ω are both included in that of Ω. </p>projecteuclid.org/euclid.hokmj/1470053289_20160801080812Mon, 01 Aug 2016 08:08 EDTBoundedness of maximal operators and Sobolev's theorem for non-homogeneous central Morrey spaces of variable exponenthttp://projecteuclid.org/euclid.hokmj/1470053290<strong>Yoshihiro MIZUTA</strong>, <strong>Takao OHNO</strong>, <strong>Tetsu SHIMOMURA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 2, 185--201.</p><p><strong>Abstract:</strong><br/> Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator in non-homogeneous central Morrey spaces of variable exponent. Further, we give Sobolev's inequality and Trudinger's exponential integrability for generalized Riesz potentials. </p>projecteuclid.org/euclid.hokmj/1470053290_20160801080812Mon, 01 Aug 2016 08:08 EDTBi-flows on a networkhttp://projecteuclid.org/euclid.hokmj/1470053291<strong>Hisayasu KURATA</strong>, <strong>Maretsugu YAMASAKI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 2, 203--220.</p><p><strong>Abstract:</strong><br/> Flows on a network play an important role in the theory of discrete harmonic functions. In the study of discrete bi-harmonic functions, we encounter a concept of bi-flows. In this paper, we are concerned with minimization problems for bi-flows which are analogous to those for flows. </p>projecteuclid.org/euclid.hokmj/1470053291_20160801080812Mon, 01 Aug 2016 08:08 EDTProjection of generic 1 and 2-parameter families of space curveshttp://projecteuclid.org/euclid.hokmj/1470053292<strong>Fabio Scalco DIAS</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 2, 221--250.</p><p><strong>Abstract:</strong><br/> The present paper deals with the study of the geometrical properties of generic 1 and 2-parameter families of space curves by using projections into planes. It presents directions of projection and conditions on the coefficients of these families such that the projection exhibits Morsifications of the A 4 , A 6 and E 6 singularities and transitions between the Morsifications of the E 8 singularity. </p>projecteuclid.org/euclid.hokmj/1470053292_20160801080812Mon, 01 Aug 2016 08:08 EDTOn the indices of minimal orbits of Hermann actionshttp://projecteuclid.org/euclid.hokmj/1470053293<strong>Naoyuki KOIKE</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 2, 251--275.</p><p><strong>Abstract:</strong><br/> We give a formula to determine the indices of special (non-totally geodesic) minimal orbits of Hermann actions. Also, we give examples of such minimal orbits of Hermann actions and calculate their indices by using the formula. </p>projecteuclid.org/euclid.hokmj/1470053293_20160801080812Mon, 01 Aug 2016 08:08 EDTFinding numerically Newhouse sinks near a homoclinic tangency and investigation of their chaotic transientshttp://projecteuclid.org/euclid.hokmj/1470053294<strong>Takayuki YAMAGUCHI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 2, 277--312.</p><p><strong>Abstract:</strong><br/> For Hénon map of nearly classical parameter values, we search numerically for Newhouse sinks. We show how to find successively the Newhouse sinks of higher period, which is the estimation of coordinates of the sinks from power laws of properties of the sinks, and investigate numerically a sequence of sinks of period from 8 to 60 that we obtained. We also show how to verify the existences of obtained sinks by interval arithmetic. The sinks of period from 8 to 14 from among our obtained sinks was verified mathematically.
In the case that we observed, when the sink exists, most orbits converge to it, and the orbit that seems to be Hénon attractor is not an attractor but just a long chaotic transient. The narrowness of the main bands of basins of the sinks causes the long chaotic transients. We also investigate numerically the chaotic transients and their rambling time. </p>projecteuclid.org/euclid.hokmj/1470053294_20160801080812Mon, 01 Aug 2016 08:08 EDTOn the sizes of the Jordan blocks of monodromies at infinityhttp://projecteuclid.org/euclid.hokmj/1470053366<strong>Yutaka MATSUI</strong>, <strong>Kiyoshi TAKEUCHI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 3, 313--326.</p><p><strong>Abstract:</strong><br/> We obtain general upper bounds of the sizes and the numbers of Jordan blocks for the eigenvalues λ ≠ 1 in the monodromies at infinity of polynomial maps. </p>projecteuclid.org/euclid.hokmj/1470053366_20160801080932Mon, 01 Aug 2016 08:09 EDTA new class of reconstructible graphs from some neighbourhood conditionshttp://projecteuclid.org/euclid.hokmj/1470053367<strong>Tetsuya HOSAKA</strong>, <strong>Yonghuo XIAO</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 3, 327--340.</p><p><strong>Abstract:</strong><br/> In this paper, we provide a new class of reconstructible finite graphs. We show the following theorem: Let k be a positive integer number. Let Γ be a finite graph with at least 3 vertices. Suppose that Γ satisfies the following two conditions: (i) for any two distinct vertices w,w ′ ∈ V (Γ), [ w,w ′] ∈ E (Γ) ⬄ N ( w )-{ w ′} ≇ N ( s ) for any vertex s ∈ V (Γ); (ii) there exists a vertex v ∈ V (Γ) of degree k such that for any k -vertices v 1 , v 2 , …, v k ∈ V (Γ)-{ v }, there exists a vertex u ∈ V (Γ) such that St 2 ( u ,Γ) ⋂ { v , v 1 , v 2 , …, v k } = ∅, where N ( w ) is the full subgraph of Γ whose vertex set is { v ∈ V (Γ)|[ w,v ] ∈ E (Γ)} and St 2 ( u ,Γ) = ⋂ { St ( w ,Γ)| w ∈ V ( St ( u ,Γ))}. Then the graph Γ is reconstructible. We also provide some applications and examples. </p>projecteuclid.org/euclid.hokmj/1470053367_20160801080932Mon, 01 Aug 2016 08:09 EDTBounds for the Betti numbers of successive stellar subdivisions of a simplexhttp://projecteuclid.org/euclid.hokmj/1470053368<strong>Janko BÖHM</strong>, <strong>Stavros Argyrios PAPADAKIS</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 3, 341--364.</p><p><strong>Abstract:</strong><br/> We give a bound for the Betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex by applying unprojection theory. From this we derive a bound for the Betti numbers of iterated stellar subdivisions of the boundary complex of a simplex. The bound depends only on the number of subdivisions, and we construct examples which prove that it is sharp. </p>projecteuclid.org/euclid.hokmj/1470053368_20160801080932Mon, 01 Aug 2016 08:09 EDTLog Néron models over surfaces, IIhttp://projecteuclid.org/euclid.hokmj/1470053369<strong>Chikara NAKAYAMA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 3, 365--385.</p><p><strong>Abstract:</strong><br/> We prove that an admissible normal function over a surface and the zero section simultaneously extend to sections of a log Néron model. This gives a new proof of the surface base case of the algebraicity of zero loci of admissible normal functions. </p>projecteuclid.org/euclid.hokmj/1470053369_20160801080932Mon, 01 Aug 2016 08:09 EDTFinite groups with some nonnormal subgroups of non-prime-power orderhttp://projecteuclid.org/euclid.hokmj/1470053370<strong>Jiangtao SHI</strong>, <strong>Cui ZHANG</strong>, <strong>Dengfeng LIANG</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 3, 387--396.</p><p><strong>Abstract:</strong><br/> We prove that a group G with exactly three classes of nonnormal proper subgroups of the same non-prime-power order is nonsolvable if and only if G ≃ A 5 , and a group G with exactly four classes of nonnormal proper subgroups of the same non-prime-power order is nonsolvable if and only if G ≃ PSL (2,7) or PSL (2,8). Moreover, we prove that any group G with at most nine classes of nonnormal nontrivial subgroups of the same order is always solvable except for G ≃ A 5 , PSL 2 (7) or SL 2 (5). </p>projecteuclid.org/euclid.hokmj/1470053370_20160801080932Mon, 01 Aug 2016 08:09 EDTSemi-local units at p of a cyclotomic ${\mathbb Z}_p$-extension congruent to 1 modulo $\zeta_p - 1$http://projecteuclid.org/euclid.hokmj/1470053371<strong>Humio ICHIMURA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 3, 397--407.</p><p><strong>Abstract:</strong><br/> Let p be a prime number. Let K be an abelian number field with p ∤ [ K : ℚ] and ζ p ∈ K , K ∞ / K the cyclotomic ℤ p -extension, and K n the n th layer with K 0 = K . Let $\mathcal U$ n be the group of semi-local principal units of K n at the prime p , and $\mathcal U$ n (1) the elements u of $\mathcal U$ n satisfying the congruence u ≣ 1 modulo ζ p - 1. The Galois module structure of $\mathcal U$ n is well understood. The purpose of this paper is to determine the Galois module structure of $\mathcal U$ n (1) . </p>projecteuclid.org/euclid.hokmj/1470053371_20160801080932Mon, 01 Aug 2016 08:09 EDTSelf-adjointness of the generalized spin-boson Hamiltonian with a quadratic boson interactionhttp://projecteuclid.org/euclid.hokmj/1470053372<strong>Noriaki TERANISHI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 3, 409--423.</p><p><strong>Abstract:</strong><br/> We consider an abstract model which describes an interaction of non-relativistic particles with a Bose field. We show that the essential self-adjointness of the generalized spin-boson Hamiltonian with a quadratic boson interaction for all coupling constant and the Hamiltonian is self-adjoint if it is bounded from below under some conditions. </p>projecteuclid.org/euclid.hokmj/1470053372_20160801080932Mon, 01 Aug 2016 08:09 EDTThe Schwartz kernel theorem for the tempered distributions on the Heisenberg grouphttp://projecteuclid.org/euclid.hokmj/1470053373<strong>Yasuyuki OKA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 3, 425--439.</p><p><strong>Abstract:</strong><br/> The aim of this paper is to give the Schwartz kernel theorem for the space of the tempered distributions on the Heisenberg group. </p>projecteuclid.org/euclid.hokmj/1470053373_20160801080932Mon, 01 Aug 2016 08:09 EDTTransformations between Singer-Thorpe bases in 4-dimensional Einstein manifoldshttp://projecteuclid.org/euclid.hokmj/1470053374<strong>Zdeněk DUŠEK</strong>, <strong>Oldřich KOWALSKI</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 44, Number 3, 441--458.</p><p><strong>Abstract:</strong><br/> It is well known that, at each point of a 4-dimensional Einstein Riemannian manifold ( M,g ), the tangent space admits at least one so-called Singer-Thorpe basis with respect to the curvature tensor R at p . K. Sekigawa put the question "how many" Singer-Thorpe bases exist for a fixed curvature tensor R . Here we work only with algebraic structures ($\mathbb{V}$, ⟨,⟩, R ), where ⟨,⟩ is a positive scalar product and R is an algebraic curvature tensor (in the sense of P. Gilkey) which satisfies the Einstein property. We give a partial answer to the Sekigawa problem and we state a reasonable conjecture for the general case. Moreover, we solve completely a modified problem: how many there are orthonormal bases which are Singer-Thorpe bases simultaneously for a natural 5-dimensional family of Einstein curvature tensors R . The answer is given by what we call "the universal Singer-Thorpe group" and we show that it is a finite group with 2304 elements. </p>projecteuclid.org/euclid.hokmj/1470053374_20160801080932Mon, 01 Aug 2016 08:09 EDTDimer models and crepant resolutionshttp://projecteuclid.org/euclid.hokmj/1470080746<strong>Akira ISHII</strong>, <strong>Kazushi UEDA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 1, 1--42.</p><p><strong>Abstract:</strong><br/> We study variations of tautological bundles on moduli spaces of representations of quivers with relations associated with dimer models under a change of stability parameters. We prove that if the tautological bundle induces a derived equivalence for some stability parameter, then the same holds for any generic stability parameter, and any projective crepant resolution can be obtained as the moduli space for some stability parameter. This result is used in [IU] to prove the abelian McKay correspondence without using the result of Bridgeland, King and Reid [BKR01]. </p>projecteuclid.org/euclid.hokmj/1470080746_20160801154548Mon, 01 Aug 2016 15:45 EDTOn a symmetry of complex and real multiplicationhttp://projecteuclid.org/euclid.hokmj/1470080747<strong>Igor V. NIKOLAEV</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 1, 43--51.</p><p><strong>Abstract:</strong><br/> It is proved that each lattice with complex multiplication by $f\sqrt{-D}$ corresponds to a pseudo-lattice with real multiplication by $f'\sqrt{D}$, where $f'$ is an integer defined by $f$. </p>projecteuclid.org/euclid.hokmj/1470080747_20160801154548Mon, 01 Aug 2016 15:45 EDTA projective characterization of a class of abelian groupshttp://projecteuclid.org/euclid.hokmj/1470080748<strong>Patrick W. KEEF</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 1, 53--74.</p><p><strong>Abstract:</strong><br/> This paper considers the class of abelian groups that are extensions of subgroups that are direct sums of cyclic groups by factor groups that are also of this form. This class is shown to be the projectives with respect to a natural collection of short exact sequences, and that the corresponding class of injectives consists of those groups whose first Ulm subgroup is pure-injective. This class of projectives is quite extensive, but satisfactory descriptions are given for the countable groups in the class that are either torsion-free, or else mixed groups of torsion-free rank one. Particular attention is paid to the behavior of the groups in these classes under localization at some prime. </p>projecteuclid.org/euclid.hokmj/1470080748_20160801154548Mon, 01 Aug 2016 15:45 EDTZeta functions of adjacency algebras of association schemes of prime order or rank twohttp://projecteuclid.org/euclid.hokmj/1470080749<strong>Akihide HANAKI</strong>, <strong>Mitsugu HIRASAKA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 1, 75--91.</p><p><strong>Abstract:</strong><br/> For a module $L$ which has only finitely many submodules with a given finite index we define the zeta function of $L$ to be a formal Dirichlet series $\zeta_L(s)=\sum_{n\geq 1}a_nn^{-s}$ where $a_n$ is the number of submodules of $L$ with index $n$. For a commutative ring $R$ and an association scheme $(X,S)$ we denote the adjacency algebra of $(X,S)$ over $R$ by $RS$. In this article we aim to compute $\zeta_{\mathbb{Z}S}(s)$, where $\mathbb{Z}S$ is viewed as a regular $\mathbb{Z}S$-module, under the assumption that $|X|$ is a prime or $|S|=2$. </p>projecteuclid.org/euclid.hokmj/1470080749_20160801154548Mon, 01 Aug 2016 15:45 EDTDegenerate and dihedral Heun functions with parametershttp://projecteuclid.org/euclid.hokmj/1470080750<strong>Raimundas VIDŪNAS</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 1, 93--108.</p><p><strong>Abstract:</strong><br/> Just as with the Gauss hypergeometric function, particular cases of the local Heun function can be Liouvillian (that is, ``elementary'') functions. One way to obtain these functions is by pull-back transformations of Gauss hypergeometric equations with Liouvillian solutions. This paper presents the Liouvillian solutions of Heun's equations that are pull-backs of the parametric hypergeometric equations with cyclic or dihedral monodromy groups. </p>projecteuclid.org/euclid.hokmj/1470080750_20160801154548Mon, 01 Aug 2016 15:45 EDTPeriodic solutions for a class of nonlinear difference equationshttp://projecteuclid.org/euclid.hokmj/1470080751<strong>Haiping SHI</strong>, <strong>Xia LIU</strong>, <strong>Yuanbiao ZHANG</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 1, 109--126.</p><p><strong>Abstract:</strong><br/> By using the critical point theory, some new criteria are obtained for the existence and multiplicity of periodic solutions to a class of nonlinear difference equations. The proof is based on the Linking Theorem in combination with variational technique. Our results successfully generalize and improve some existing results in the literature. </p>projecteuclid.org/euclid.hokmj/1470080751_20160801154548Mon, 01 Aug 2016 15:45 EDTPeriod-additivity and multistability in piecewise smooth systemshttp://projecteuclid.org/euclid.hokmj/1470080752<strong>Hunseok KANG</strong>, <strong>Ah Reum LEE</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 1, 127--139.</p><p><strong>Abstract:</strong><br/> Piecewise smooth systems have been consistently considered and investigated in nonlinear dynamics due to their practical applications. In this paper, we study a generic type of piecewise smooth dynamical system to deal with period-additivity and multistability in the system; an arithmetic sequence of periodic attractors appearing in the period-adding bifurcation and the coexistence of multiple attractors in the system. We state a physical observation of the phenomena and then provide rigorous mathematical arguments and numerical simulations. </p>projecteuclid.org/euclid.hokmj/1470080752_20160801154548Mon, 01 Aug 2016 15:45 EDTLow energy spectral and scattering theory for relativistic Schroedinger operatorshttp://projecteuclid.org/euclid.hokmj/1470139399<strong>Serge RICHARD</strong>, <strong>Tomio UMEDA</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 2, 141--179.</p><p><strong>Abstract:</strong><br/> Spectral and scattering theory at low energy for the relativistic Schr\"odinger operator are investigated. Some striking properties at thresholds of this operator are exhibited, as for example the absence of 0-energy resonance. Low energy behavior of the wave operators and of the scattering operator are studied, and stationary expressions in terms of generalized eigenfunctions are proved for the former operators. Under slightly stronger conditions on the perturbation the absolute continuity of the spectrum on the positive semi axis is demonstrated. Finally, an explicit formula for the action of the free evolution group is derived. Such a formula, which is well known in the usual Schr\"odinger case, was apparently not available in the relativistic setting. </p>projecteuclid.org/euclid.hokmj/1470139399_20160802080323Tue, 02 Aug 2016 08:03 EDTIntegral Homology of the Moduli Space of Tropical Curves of Genus 1 with Marked Pointshttp://projecteuclid.org/euclid.hokmj/1470139400<strong>Ye LIU</strong>. <p><strong>Source: </strong>Hokkaido Mathematical Journal, Volume 45, Number 2, 181--194.</p><p><strong>Abstract:</strong><br/> Kozlov has studied the topological properties of the moduli space of tropical curves of genus 1 with marked points, such as its mod 2 homology, while the integral homology remained a conjecture. In this paper, we present a complete proof of Kozlov's conjecture concerning the integral homology of this moduli space. </p>projecteuclid.org/euclid.hokmj/1470139400_20160802080323Tue, 02 Aug 2016 08:03 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 EDT