Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
Volume 68 , Issue 2
Showing 1-14 articles out of 14 articles from the selected issue
• Takahiro NAKAGAWA
2014 Volume 68 Issue 2 Pages 223-238
Published: 2014
Released: November 20, 2014
JOURNALS FREE ACCESS
Let p be a prime and q = p s and ζk a fixed primitive kth root of unity in some extension of Q. Let χ be a multiplicative character over Fq of order k and J (χ, χ) the associated Jacobi sum. We give examples of χ which satisfy J (χ, χ) ∈p [s/2]Z[ζk]. Moreover, for s = 3, we prove that there is only a finite number of k such that J(χ, χ) is an element of pZ[ζk] except for the case where k is divisible by nine and p ≡1 ± k/3 (mod k).
• Nguyen DUC MINH, Nguyen THI KHANH HOA, Tran TUAN NAM
2014 Volume 68 Issue 2 Pages 239-248
Published: 2014
Released: November 20, 2014
JOURNALS FREE ACCESS
Let (R, m) be a commutative Noetherian local ring with the maximal ideal m and A an Artinian R-module with N-dimA = d. Let n = (n1,n2,...,nd) be a d-tuple of positive integers. For each system of parameters x = (x1,...,xd) of A, we consider the length R(0 :A (x 1 n1 ,...,x d nd )R) as a function d-variables on n 1 ,...,n d . Then a necessary and sufficient condition for this length to be polynomial (in n1,...,nd) is given. Moreover, we shall introduce a system of parameters for which the length R(0 : A (x 1 n 1,...,x d nd )R) can be computed by a nice formula.
• Yongda WANG , Shuo ZHANG
2014 Volume 68 Issue 2 Pages 249-260
Published: 2014
Released: November 20, 2014
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This article is devoted to dealing with existence of a solution to a quasilinear elliptic problem with the Hardy potential term up−1 / |x|p and critical growth in the gradient |∇u|p as an absorption term. By considering the interaction between the two terms in the equation, we prove that there exists a positive solution to the problem. Moreover, the existence result for a wider class of weight functions can also be obtained.
• Masatoshi OKITA
2014 Volume 68 Issue 2 Pages 261-286
Published: 2014
Released: November 20, 2014
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In this paper we are concerned with the optimal convergence rates of the global strong solution to the stationary solutions for the compressible Navier-Stokes equations with a potential external force ∇Φ in the whole space Rn for n ≥3. It is proved that the perturbation and its first-order derivatives decay in L 2 norm in O(t n/4 ) and O(t n/4−1/2), respectively, which are of the same order as those of the n-dimensional heat kernel, if the initial perturbation is small in H s0(R n ) ∩L 1 (R n) with s0 =[n/2]+ 1 and the potential force Φ is small in some Sobolev space. The results also hold for n ≥ 2 when Φ = 0. When Φ = 0, we also obtain the decay rates of higher-order derivatives of perturbations.
• Hiromasa NAKAYAMA
2014 Volume 68 Issue 2 Pages 287-296
Published: 2014
Released: November 20, 2014
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We derive Gröbner bases for the systems of Lauricella's hypergeometric differential equations. By using these Gröbner bases, we determine characteristic varieties and singular loci of these systems.
2014 Volume 68 Issue 2 Pages 297-305
Published: 2014
Released: November 20, 2014
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We introduce a method which can be used to establish sharp maximal estimates for functions of bounded lower oscillation (BLO). The technique allows us to deduce such estimates from the existence of certain special functions, and can be regarded as a version of Bellman function method, which has gained considerable interest in the recent literature. As an application, we establish a sharp exponential bound, which can be regarded as a version of integral John-Nirenberg inequality for BLO functions.
• Kazuto ASAI
2014 Volume 68 Issue 2 Pages 307-313
Published: 2014
Released: November 20, 2014
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Let G be the multiplicative group generated by the gamma functions Γ(ax + 1) (a = 1, 2,...), and H be the subgroup of all elements of G that converge to non-zero constants as x →∞. The quotient group G/H is the group of equivalence classes of G, where ƒand g are equivalent ⇔ ƒCg (x →∞) for some C ≠ 0. We show that G/H ~ Q+. Similar consideration is possible for the case that the gamma functions Γ(ax + 1) with a ∈R+ are concerned, and we show that G/H ~ Z × R × R. Also, several concrete examples of the elements of H are constructed, e.g. it holds that /  (n →∞), where denotes a multinomial coefficient.
• Ana Irina NISTOR
2014 Volume 68 Issue 2 Pages 315-332
Published: 2014
Released: November 20, 2014
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In this paper we define and completely classify three types of constant angle surfaces in a three-dimensional two-parameter solvable Lie group G(μ1, μ2) corresponding to each of the three left-invariant vector fields.
2014 Volume 68 Issue 2 Pages 333-345
Published: 2014
Released: November 20, 2014
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In this paper we present the notion of de Rham cohomology with compact support for diffeological spaces. Moreover, we shall discuss the existence of three long exact sequences. As a concrete example, we show that long exact sequences exist for the de Rham cohomology of diffeological subcartesian spaces.
• Kei KONDO, Shin-ichi OHTA , Minoru TANAKA
2014 Volume 68 Issue 2 Pages 347-357
Published: 2014
Released: November 20, 2014
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We recently established a Toponogov-type triangle comparison theorem for a certain class of Finsler manifolds whose radial flag curvatures are bounded below by that of a von Mangoldt surface of revolution. In this article, as its applications, we prove the finiteness of topological type and a diffeomorphism theorem to Euclidean spaces.
• Christian MAIRE
2014 Volume 68 Issue 2 Pages 359-376
Published: 2014
Released: November 20, 2014
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Let GS be the Galois group of the maximal pro-p-extension QS of Q unramified outside a finite set S of places of Q not containing the prime p > 2. In this work, we develop a method to produce some examples of mild (and thus FAB) pro-p-groups GS for which some relations are of degree three (according to the Zassenhaus filtration). The key computation are done in some Heisenberg extensions of Q of degree p3. With the help of GP-Pari we produce some examples for p = 3.
• Nagatoshi SASANO
2014 Volume 68 Issue 2 Pages 377-403
Published: 2014
Released: November 20, 2014
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It is known that a finite-dimensional reductive Lie algebra has a non-degenerate symmetric invariant bilinear form. In this paper, for a given reductive Lie algebra and its finite-dimensional completely reducible representation, we will construct a graded Lie algebra by using a non-degenerate symmetric invariant bilinear form on the reductive Lie algebra. This graded Lie algebra also has a non-degenerate symmetric invariant bilinear form and, moreover, the reductive Lie algebra, its representation and the bilinear form which are used to construct the graded Lie algebra can be embedded into it.
• Kazuhito KOZUKA
2014 Volume 68 Issue 2 Pages 405-419
Published: 2014
Released: November 20, 2014
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In this paper, for any multivariable function with a periodicity and a certain distribution relation, we define a multiple Dedekind-type sum. Then by a combinatorialgeometric method, we study generalizations of Knopp's formula for the classical Dedekind sums. The main theorem contains many of the preceding results concerning generalizations of Knopp's formula.