Tsukuba Journal of Mathematics Articles (Project Euclid)
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Contents for Tsukuba Journal of Mathematics, Vol 33, No. 2
http://projecteuclid.org/euclid.tkbjm/1267209417
<p><strong>Source: </strong>Tsukuba J. Math., Volume 33, Number 2.</p>projecteuclid.org/euclid.tkbjm/1267209417_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTThe period matrix of the hyperelliptic curve
$w^2=z^{2g+1}-1$http://projecteuclid.org/euclid.tkbjm/1429103717<strong>Yuuki Tadokoro</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 2, 137--158.</p><p><strong>Abstract:</strong><br/>
A geometric algorithm is introduced for finding a symplectic basis of the first integral
homology group of a compact Riemann surface, which is a $p$-cyclic covering of
$\mathbf{C}P_1$ branched over 3 points. The algorithm yields a previously unknown
symplectic basis of the hyperelliptic curve defined by the affine equation
$w^2=z^{2g+1}-1$ for genus $g \ge 2$. We then explicitly obtain the period matrix of this
curve, its entries being elements of the $(2g+1)$-st cyclotomic field. In the proof, the
details of our algorithm play no significant role.
</p>projecteuclid.org/euclid.tkbjm/1429103717_20150415091519Wed, 15 Apr 2015 09:15 EDTDistance between metric measure spaces and distance matrix
distributionshttp://projecteuclid.org/euclid.tkbjm/1429103718<strong>Ryunosuke Ozawa</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 2, 159--170.</p><p><strong>Abstract:</strong><br/>
We study the Prohorov distance between the distance matrix distributions of two metric
measure spaces. We prove that it is not smaller than 1-box distance between two metric
measure spaces and also prove that it is not larger than 0-box distance between two metric
measure spaces.
</p>projecteuclid.org/euclid.tkbjm/1429103718_20150415091519Wed, 15 Apr 2015 09:15 EDTEvaluation of the dimension of the Q -vector space spanned
by the special values of the Lerch functionhttp://projecteuclid.org/euclid.tkbjm/1429103719<strong>Makoto Kawashima</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 2, 171--188.</p><p><strong>Abstract:</strong><br/>
Nikisin [6] proved the linear independence of special values of polylogarithm functions
over the rational number field. (see Theorem 0.1). In this paper, we give a generalization
of the above result of Nikisin to the case of the Lerch function.
</p>projecteuclid.org/euclid.tkbjm/1429103719_20150415091519Wed, 15 Apr 2015 09:15 EDTRefined version of Hasse's Satz 45 on class number parityhttp://projecteuclid.org/euclid.tkbjm/1429103720<strong>Humio Ichimura</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 2, 189--199.</p><p><strong>Abstract:</strong><br/>
For an imaginary abelian field $K$, Hasse [3, Satz 45] obtained a criterion for the
relative class number to be odd in terms of the narrow class number of the maximal real
subfield $K^+$ and the prime numbers which ramify in $K$, by using the analytic class
number formula. In [4], we gave a refined version (= "$\Delta$-decomposed version") of
Satz 45 by an algebraic method. In this paper, we give one more algebraic proof of the
refined version.
</p>projecteuclid.org/euclid.tkbjm/1429103720_20150415091519Wed, 15 Apr 2015 09:15 EDTThe Weierstrass semigroups on double covers of genus two
curveshttp://projecteuclid.org/euclid.tkbjm/1429103721<strong>Takeshi Harui</strong>, <strong>Jiryo Komeda</strong>, <strong>Akira Ohbuchi</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 2, 201--206.</p><p><strong>Abstract:</strong><br/>
We show that three numerical semigroups $\langle 5, 6, 7, 8\rangle, \langle3, 7,
8\rangle$ and $\langle 3, 5\rangle$ are of double covering type, i.e., the Weierstrass
semigroups of ramification points on double covers of curves. Combining the result with
[7] and [4] we can determine the Weierstrass semigroups of the ramification points on
double covers of genus two curves.
</p>projecteuclid.org/euclid.tkbjm/1429103721_20150415091519Wed, 15 Apr 2015 09:15 EDTA characterization of isoparametric hypersurfaces in a sphere
with $g\le 3$http://projecteuclid.org/euclid.tkbjm/1429103722<strong>Setsuo Nagai</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 2, 207--225.</p><p><strong>Abstract:</strong><br/>
Ki and Nakagawa [Tôhoku Math. J., 39 , 27-40 (1987)] characterized the
minimal isoparametric hypersurfaces in a sphere that have three distinct constant
principal curvatures from the stand point of the Ricci tensor. In this paper we generalize
their results and characterize the isoparametric hypersurfaces, again in a sphere and with
three distinct constant principal curvatures, that are either minimal or parallel to a
minimal hypersurface.
</p>projecteuclid.org/euclid.tkbjm/1429103722_20150415091519Wed, 15 Apr 2015 09:15 EDTA method for finding a minimal point of the lattice in cubic
number fields (II)http://projecteuclid.org/euclid.tkbjm/1429103723<strong>Kan Kaneko</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 2, 227--237.</p><p><strong>Abstract:</strong><br/>
We give a method for finding a minimal point adjacent to 1 of the reduced lattice in
cubic number fields using an isotropic vector of the quadratic form and two-dimensional
lattice.
</p>projecteuclid.org/euclid.tkbjm/1429103723_20150415091519Wed, 15 Apr 2015 09:15 EDTRealizations of globally exceptional $\mathbf{Z}_2 \times
\mathbf{Z}_2$-symmetric spaceshttp://projecteuclid.org/euclid.tkbjm/1429103724<strong>Toshikazu Miyashita</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 2, 239--311.</p><p><strong>Abstract:</strong><br/>
In [3], a classification is given of the exceptional $\mathbf{Z}_2 \times
\mathbf{Z}_2$-symmetric spaces $G/K$, where $G$ is an exceptional compact Lie group or
$Spin(8)$, and moreover the structure of $K$ is determined as Lie algebra. In the present
article, we give a pair of commuting involutive automorphisms (involutions)
$\tilde{\sigma}$, $\tilde{\tau}$ of $G$ concretely and determine the structure of group
$G^\sigma \cap G^\tau$ corresponding to Lie algebra $\mathfrak{g}^\sigma\cap
\mathfrak{g}^\tau$, where $G$ is an exceptional compact Lie group. Thereby, we realize
exceptional $\mathbf{Z}_2 \times \mathbf{Z}_2$-symmetric spaces, globally.
</p>projecteuclid.org/euclid.tkbjm/1429103724_20150415091519Wed, 15 Apr 2015 09:15 EDTCorrigendum to "Periodicity and eigenvalues of matrices over
quasi-max-plus algebras", Tsukuba J. Math., 37 (2013), pp. 51–71http://projecteuclid.org/euclid.tkbjm/1429103725<strong>H. Brunotte</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 2, 313--313.</p>projecteuclid.org/euclid.tkbjm/1429103725_20150415091519Wed, 15 Apr 2015 09:15 EDTLie algebras associated with a standard quadruplet and prehomogeneous vector spaceshttp://projecteuclid.org/euclid.tkbjm/1438951814<strong>Nagatoshi Sasano</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 1, 1--14.</p><p><strong>Abstract:</strong><br/>
By using the theory of Lie algebras associated with a standard quadruplet, we can embed an arbitrary reductive
prehomogeneous vector space with completely reducible representation into some graded Lie algebra. The purpose
of this paper is to study properties of graded Lie algebras which correspond to the prehomogeneity condition of
triplets. Moreover, we give another proof of castling transformation as an application.
</p>projecteuclid.org/euclid.tkbjm/1438951814_20150807085018Fri, 07 Aug 2015 08:50 EDTGeneralized Fourier-Stieltjes algebrahttp://projecteuclid.org/euclid.tkbjm/1438951815<strong>G. A. Bagheri-Bardi</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 1, 15--28.</p><p><strong>Abstract:</strong><br/>
Let $\{G_{}\}^n_{i=1}$ be locally compact groups and $\mathscr{H}$ be Hilbert space.
We define the n-variable Fourier-Stieltjes algebra $B(\Pi^{n}_{1} G_{i}, \mathrm{ B }(\mathscr{H}))$ consists all functions
\[
\phi : G_{1} \times \cdot \times G_{n} \rightarrow \mathrm{ B }(\mathscr{H})
\]
for which there exists unitary representations $\pi_{i} : \mathbb{G}_{i} \rightarrow \mathrm{ B }(\mathscr{H}_i)$ and a diagram of bounded operators
\[
\mathscr{H} \rightarrow^{V} \mathscr{H}_n \rightarrow^{T_{n-1}} \mathscr{H}_{n-1} \rightarrow^{T_{1}} \mathscr{H_1} \rightarrow^{U} \mathscr{H}
\] with
\[
\phi(s_{1},..., s_{n}) = U\pi_{1}(s_1)T_{1}\pi_{2})s_{2}) \cdot \pi_{n-1}(s_{n-1})T_{n}\pi_{n}(s_{n}V
\]
We extend the pointwise product on $B(\Pi^{n}_{1} G_{i}, \mathrm{ B }(\mathscr{H}))$ under which it forms a completely contractive commutative unital Banach algebra. A diagram of its subalgebras will be introduced.
</p>projecteuclid.org/euclid.tkbjm/1438951815_20150807085018Fri, 07 Aug 2015 08:50 EDTThe Baire property of certain hypo-graph spaceshttp://projecteuclid.org/euclid.tkbjm/1438951816<strong>Katsuhisa Koshino</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 1, 29--38.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a compact metrizable space and $Y$ be a nondegenerate dendrite with an end point
0 . For each continuous function $f : X \rightarrow Y$, we define the hypo-graph
$\downarrow f = \cup_{x \in X \{x} \times [ 0 , f(x]$ of $f$, where $[ 0 , f(x)]$ is
the unique path from 0 to $f(x)$ in $Y$. Then we can regard
$\downarrow \mathrm{C}(X,Y) = \{\downarrow f | f : X \rightarrow Y$
is continuous} as a subspace of the hyperspace consisting of non-empty closed sets in $X \times Y$
equipped with the Vietoris topology. In this paper, we prove that $\downarrow \mathrm{C}(X,Y)$
is a Baire space if and only if the set of isolated points of $X$ is dense.
</p>projecteuclid.org/euclid.tkbjm/1438951816_20150807085018Fri, 07 Aug 2015 08:50 EDTOn certain conformally invariant systems of differential equations II: Further study of type A systemshttp://projecteuclid.org/euclid.tkbjm/1438951817<strong>Anthony C. Kable</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 1, 39--81.</p><p><strong>Abstract:</strong><br/>
Previously, several families of systems of differential equations that generalize the Heisenberg
Laplacian equations were introduced. The study of one of these families is continued here. It is shown that the systems in this family are free of integrability conditions provided that a parameter appearing in the system avoids a certain set of bad values, which is explicitly determined. Properties of polynomial solutions to the systems are investigated and special polynomial solutions involving terminating Lauricella hypergeometric series are given in some cases.
</p>projecteuclid.org/euclid.tkbjm/1438951817_20150807085018Fri, 07 Aug 2015 08:50 EDTStructural properties of ideals over $\mathscr P_{\kappa}\lambda$ Ihttp://projecteuclid.org/euclid.tkbjm/1438951818<strong>Yoshihiro Abe</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 1, 83--95.</p><p><strong>Abstract:</strong><br/>
We try to take a first step to a theory of the structural properties of ideals over
$\mathscr P_{\kappa}\lambda$, that was studied in detail by Baumgartner, Taylor and Wagon [1]
for $\kappa$;. In defining the basic notions, P-points, Q-points, and selective ideals, we put importance on the behavior of the function on
$\mathscr P_{\kappa}\lambda$ to the bounded ideal and Rudin-Keisler ordering.
Several facts hold similarly as on $\kappa$;, for instance, the bounded ideal is a nowhere Q-point. However some
differences exist such as the bounded ideal is isomorphic to another ideal. We state the sufficient condition for
ideals to be Q-points and the weakly normal
ideals selective.
</p>projecteuclid.org/euclid.tkbjm/1438951818_20150807085018Fri, 07 Aug 2015 08:50 EDTA characterization of the tempered distributions supported by a regular closed
set in the Heisenberg grouphttp://projecteuclid.org/euclid.tkbjm/1438951819<strong>Yasuyuki Oka</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 1, 97--119.</p><p><strong>Abstract:</strong><br/>
The aim of this paper is to give a characterization of the tempered distributions supported by a
(Whitney's) regular closed set in the Euclidean space and the Heisenberg group by means of the heat
kernel method. The heat kernel method, introduced by T. Matsuzawa, is the method to characterize the
generalized functions on the Euclidean space by the initial value of the solutions of the heat equation.
</p>projecteuclid.org/euclid.tkbjm/1438951819_20150807085018Fri, 07 Aug 2015 08:50 EDTOn the Cauchy problem for a class of hyperbolic operators whose coefficients
depend only on the time variablehttp://projecteuclid.org/euclid.tkbjm/1438951820<strong>Seiichiro Wakabayashi</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 1, 121--163.</p><p><strong>Abstract:</strong><br/>
In this paper we investigate the Cauchy problem for hyperbolic operators with double characteristics and
hyperbolic operators of third order whose coefficients depend only on the time variable. And we give
sufficient conditions for $C^{\infty}$ well-posedness.
</p>projecteuclid.org/euclid.tkbjm/1438951820_20150807085018Fri, 07 Aug 2015 08:50 EDTErratum to "Asymptotic dimension and boundary dimension of proper CAT(0)
spaces"http://projecteuclid.org/euclid.tkbjm/1438951821<strong>Naotsugu Chinen</strong>, <strong>Tetsuya Hosaka</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 1, 165--166.</p><p><strong>Abstract:</strong><br/>
The review on [1] in Mathematical Reviews points out that the proof of its main result is incorrect.
The aim of this paper is to correct the previous paper's argument and clarify the statement.
</p>projecteuclid.org/euclid.tkbjm/1438951821_20150807085018Fri, 07 Aug 2015 08:50 EDTAn asymptotic extension of Moran construction in metric measure spaceshttp://projecteuclid.org/euclid.tkbjm/1461270054<strong>Daruhan Wu</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 2, 167--179.</p><p><strong>Abstract:</strong><br/>
In this paper, we define asymptotically generalized Cantor sets in metric measure spaces by generalizing the notion of $\lambda$-similarity maps. We define the notion of $(\lambda, c, \nu)$-similarity maps, and extend the Moran theorem about the generalized Cantor set in $\mathbf{R}^d$ to this general setting. As an example, we construct generalized Cantor sets in Riemannian manifolds by using $(\lambda, c, \nu)$-similarity maps.
</p>projecteuclid.org/euclid.tkbjm/1461270054_20160421162058Thu, 21 Apr 2016 16:20 EDTPartially ordered rings IIhttp://projecteuclid.org/euclid.tkbjm/1461270055<strong>Yoshimi Kitamura</strong>, <strong>Yoshio Tanaka</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 2, 181--198.</p><p><strong>Abstract:</strong><br/>
This paper is a continuation of [6]. We study partially ordered rings in terms of non-negative semi-cones and convex ideals, considering order-preserving homomorphisms, residue class rings, and certain product rings, etc.
</p>projecteuclid.org/euclid.tkbjm/1461270055_20160421162058Thu, 21 Apr 2016 16:20 EDTEmbedding products in symmetric products of continuahttp://projecteuclid.org/euclid.tkbjm/1461270056<strong>Enrique Castañeda-Alvarado</strong>, <strong>Javier Sánchez-Martínez</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 2, 199--206.</p><p><strong>Abstract:</strong><br/>
Let X be a continuum. For each natural number n , F n ( X ) is the n th -symmetric product of X and X n is the product of X with itself n times. In this paper we consider the problem of determining the continua X such that X n can be embedded in F n ( X ). Moreover, we characterize finite graphs X for which X 2 is embeddable in F 2 ( X ).
</p>projecteuclid.org/euclid.tkbjm/1461270056_20160421162058Thu, 21 Apr 2016 16:20 EDTEssential m-sectoriality and essential spectrum of the Schrödinger operators with rapidly oscillating complex-valued potentialshttp://projecteuclid.org/euclid.tkbjm/1461270057<strong>Yorimasa Oshime</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 2, 207--220.</p><p><strong>Abstract:</strong><br/>
Schrödinger operators $T_0 = -∆ + q(x)$ with rapidly oscillating complex-valued potentials q ( x ) are considered. Each of such operators is sectorial and hence has Friedrichs extension. We prove that T 0 is essentially m-sectorial in the sense that the closure of T 0 coincides with its Friedrichs extension T . In particular, T 0 is essentially self-adjoint if the rapidly oscillating potential q ( x ) is realvalued. Further, we prove $\sigma_ess (T) = [0, \infty$) under somewhat stricter condition on the potentials q ( x ).
</p>projecteuclid.org/euclid.tkbjm/1461270057_20160421162058Thu, 21 Apr 2016 16:20 EDTCertain nonlinear differential polynomial sharing a nonzero polynomial IMhttp://projecteuclid.org/euclid.tkbjm/1461270058<strong>Abhijit Banerjee</strong>, <strong>Sujoy Majumder</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 2, 221--250.</p><p><strong>Abstract:</strong><br/>
We study the uniqueness of meromorphic functions when certain nonlinear differential polynomial sharing a nonzero polynomial having common poles and thus radically improve and extend some recent results due to of Wang-Lu-Chen [17], Sahoo [16] and Liu and Yang [14].
</p>projecteuclid.org/euclid.tkbjm/1461270058_20160421162058Thu, 21 Apr 2016 16:20 EDTAutonomous equations of Mahler type and transcendencehttp://projecteuclid.org/euclid.tkbjm/1461270059<strong>Kumiko Nishioka</strong>, <strong>Seiji Nishioka</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 2, 251--257.</p><p><strong>Abstract:</strong><br/>
In this paper, we study transcendence of values of Mahler functions satisfying first-order rational difference equations of Mahler type with constant coefficients.
</p>projecteuclid.org/euclid.tkbjm/1461270059_20160421162058Thu, 21 Apr 2016 16:20 EDTSpacelike constant mean curvature and maximal surfaces in 3-dimensional de Sitter space via Iwasawa splittinghttp://projecteuclid.org/euclid.tkbjm/1461270060<strong>Yuta Ogata</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 2, 259--284.</p><p><strong>Abstract:</strong><br/>
We study the construction of spacelike constant mean curvature (CMC) surfaces with mean curvature $0 \le H \lt 1$ in 3-dimensional de Sitter space S 2, 1 , by using Iwasawa splitting. We also study their singularities and create some criteria for them.
</p>projecteuclid.org/euclid.tkbjm/1461270060_20160421162058Thu, 21 Apr 2016 16:20 EDTQuotients and Hopf images of a smash coproducthttp://projecteuclid.org/euclid.tkbjm/1461270061<strong>Julien Bichon</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 2, 285--310.</p><p><strong>Abstract:</strong><br/>
We describe the Hopf algebra quotients and Hopf images of the smash coproduct of a group algebra by the algebra of functions on a finite group.
</p>projecteuclid.org/euclid.tkbjm/1461270061_20160421162058Thu, 21 Apr 2016 16:20 EDTErratumhttp://projecteuclid.org/euclid.tkbjm/1461270062<strong>Toshikazu Miyashita</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 39, Number 2, 311--312.</p>projecteuclid.org/euclid.tkbjm/1461270062_20160421162058Thu, 21 Apr 2016 16:20 EDTA probabilistic approach to the zero-mass limit problem for three magnetic relativistic Schrödinger heat semigroupshttp://projecteuclid.org/euclid.tkbjm/1474747485<strong>Taro Murayama</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 40, Number 1, 1--28.</p><p><strong>Abstract:</strong><br/>
We consider three magnetic relativistic Schrödinger
operators which correspond to the same classical symbol $\sqrt{(\xi - A(x))^2 + m^2} + V(x)$ and whose heat semigroups admit the Feynman-Kac-Itô type path integral representation $E[e^{ - S^m (x,\,t;\,X)} g(x + X(t))]$. Using these representations, we prove the convergence of these heat semigroups when the mass-parameter $m$ goes to zero. Its proof reduces to the convergence of $e^{- S^m (x,\,t;\,X)}$, which yields a limit theorem for exponentials of semimartingales as functionals of Lévy processes $X$.
</p>projecteuclid.org/euclid.tkbjm/1474747485_20160924160445Sat, 24 Sep 2016 16:04 EDTAbstract incomplete degenerate differential equationshttp://projecteuclid.org/euclid.tkbjm/1474747486<strong>Marko Kostić</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 40, Number 1, 28--53.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the abstract incomplete degenerate di.erential equations in locally convex spaces, associated with use of the modified Liuoville right-sided fractional derivatives ([21]). The existence of solutions of abstract incomplete degenerate di.erential equations of second order is proved by considering the corresponding incomplete degenerate differential equations of order $1 / \gamma\;(0 \lt \gamma \lt 1/2$) and using an approximation process when $\gamma \rightarrow 1/2\:-$.
</p>projecteuclid.org/euclid.tkbjm/1474747486_20160924160445Sat, 24 Sep 2016 16:04 EDTTails of the first hitting times of linear diffusionshttp://projecteuclid.org/euclid.tkbjm/1474747487<strong>Yuji Kasahara</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 40, Number 1, 55--79.</p><p><strong>Abstract:</strong><br/>
The tail probability of the first hitting time is discussed for linear diffusions. We obtain the decay rates in terms of the spectral functions and the scale functions. The result is a generalization of recent results of Hamana-Matsumoto for Bessel processes.
</p>projecteuclid.org/euclid.tkbjm/1474747487_20160924160445Sat, 24 Sep 2016 16:04 EDTAnalytic properties of generalized Mordell-Tornheim type of multiple zeta-functions and $L$-functionshttp://projecteuclid.org/euclid.tkbjm/1474747488<strong>Takashi Miyagawa</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 40, Number 1, 81--100.</p><p><strong>Abstract:</strong><br/>
Analytic properties of three types of multiple zeta functions, that is, the Euler-Zagier type, the Mordell-Tornheim type and the Apostol-Vu type have been studied by a lot of authors. In particular, in the study of multiple zeta functions of the Apostol-Vu type, a generalized multiple zeta function, including both the Euler-Zagier type and the Apostol-Vu type, was introduced. In this paper, similarly we consider generalized multiple zeta-functions and $L$-functions, which include both the Euler-Zagier type and the Mordell-Tornheim type as special cases. We prove the meromorphic continuation to the multi-dimensional complex space, and give the results on possible singularities.
</p>projecteuclid.org/euclid.tkbjm/1474747488_20160924160445Sat, 24 Sep 2016 16:04 EDTWeakly UU ringshttp://projecteuclid.org/euclid.tkbjm/1474747489<strong>Peter V. Danchev</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 40, Number 1, 101--118.</p><p><strong>Abstract:</strong><br/>
We introduce and give a comprehensive study of weakly UU rings , calling them WUU rings . This notion is a natural generalization of the so-called UU rings, defined by Calugareanu (Carpath. J. Math., 2015) and investigated in details by Danchev-Lam (Publicat. Math. Debrecen, 2016). It also demarcates the strength of recent results about these kind of rings by giving a strong barrier between some of their crucial properties.
</p>projecteuclid.org/euclid.tkbjm/1474747489_20160924160445Sat, 24 Sep 2016 16:04 EDTA small remark on the filtered $\varphi$-module of Fermat varieties and Stickelberger's theoremhttp://projecteuclid.org/euclid.tkbjm/1474747490<strong>Go Yamashita</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 40, Number 1, 119--124.</p><p><strong>Abstract:</strong><br/>
We show that the weakly admissibility of the filtered $\varphi$-module with coefficients of Fermat varieties in the sense of Fontaine essentially expresses Stickelberger's theorem in Iwasawa theory. In particular, it gives us a simple re-proof of the weakly admissibility of it.
</p>projecteuclid.org/euclid.tkbjm/1474747490_20160924160445Sat, 24 Sep 2016 16:04 EDTOn Doi-Naganuma liftinghttp://projecteuclid.org/euclid.tkbjm/1492104600<strong>Balesh Kumar</strong>, <strong>Murugesan Manickam</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 40, Number 2, 125--137.</p><p><strong>Abstract:</strong><br/>
In this paper, we extend the Doi-Naganuma lifting as suggested by Kudla [4], on the lines of Zagier's work [6]. For each fundamental discriminant D associated with a real quadratic field, we prove that there exists a Hecke-equivarient map ι D which maps the m th Poincare series of weight k , level M and character χ D = (./ D ) into a Hilbert cusp form of weight k , level M/D associated with the real quadratic field of discriminant D of class number one. Through this, we get its adjoint ι * D with respect to the Petersson inner product.
</p>projecteuclid.org/euclid.tkbjm/1492104600_20170413133000Thu, 13 Apr 2017 13:30 EDTA numerical study of Siegel theta series of various degrees for the 48-dimensional even unimodular extremal latticeshttp://projecteuclid.org/euclid.tkbjm/1492104601<strong>Michio Ozeki</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 40, Number 2, 139--186.</p><p><strong>Abstract:</strong><br/>
Salvati Manni showed that the difference of the Siegel theta series of degree 4 associated with the two even unimodular 48-dimensional extremal lattices is a constant multiple of the cube J 3 of the Schottky modular form J , which is a Siegel cusp form of degree 4 and weight 8. His result implies that the Siegel theta series of degree up to 3 is unique. But apparently his method does not supply us the process to compute the Fourier coefficients of these series.
In the present paper we show that the Fourier coefficients of the Siegel theta series associated with the even unimodular 48-dimensional extremal lattices of degrees 2 and 3 can be computed explicitly, and the Fourier coefficients of the Siegel theta series of degree 4 for those lattices are computed almost explicitly.
</p>projecteuclid.org/euclid.tkbjm/1492104601_20170413133000Thu, 13 Apr 2017 13:30 EDTOn the hyperspace ℭ( X ) of continuahttp://projecteuclid.org/euclid.tkbjm/1492104602<strong>R. Escobedo</strong>, <strong>V. Sánchez-Gutierrez</strong>, <strong>J. Sánchez-Martínez</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 40, Number 2, 187--201.</p><p><strong>Abstract:</strong><br/>
Let X be a continuum. Let C ( X ) be the hyperspace of all closed, connected and nonempty subsets of X , with the Hausdorff metric. For a mapping f : X → Y between continua, let C ( f ) : C ( X ) → C ( Y ) be the induced mapping by f , given by C ( f )( A ) = f ( A ). In this paper we study the hyperspace ℭ( X ) = { C ( A ) : A ∈ C ( X )} as a subspace of C ( C ( X )), and define an induced function ℭ( f ) between ℭ( X ) and ℭ( Y ). We prove some relationships between the functions f , C ( f ) and ℭ( f ) for the following classes of mapping: confluent, light, monotone and weakly confluent.
</p>projecteuclid.org/euclid.tkbjm/1492104602_20170413133000Thu, 13 Apr 2017 13:30 EDTSelections and deleted symmetric productshttps://projecteuclid.org/euclid.tkbjm/1506353557<strong>David Buhagiar</strong>, <strong>Valentin Gutev</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 1, 1--20.</p><p><strong>Abstract:</strong><br/>
We give a very simple example of a connected second countable space $X$ whose hyperspace $[X]^{n+1}$ of unordered $(n + 1)$-tuples of points has a continuous selection, but $[X]^n$ has none. This settles an open question posed by Michael Hrušák and Ivan Martánez-Ruiz. The substantial part of the paper sheds some light on this phenomenon by showing that in the presence of connectedness this is essentially the only possible example of such spaces.
</p>projecteuclid.org/euclid.tkbjm/1506353557_20170925113254Mon, 25 Sep 2017 11:32 EDTOn the groups of isometries of simple para-Hermitian symmetric spaceshttps://projecteuclid.org/euclid.tkbjm/1506353558<strong>Takuya Shimokawa</strong>, <strong>Kyoji Sugimoto</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 1, 21--40.</p><p><strong>Abstract:</strong><br/>
The main purpose in this paper is to completely determine the groups of isometries of simple para-Hermitian symmetric spaces. That enables us to also determine the groups of affine transformations of these spaces, with respect to the canonical affine connections.
</p>projecteuclid.org/euclid.tkbjm/1506353558_20170925113254Mon, 25 Sep 2017 11:32 EDTConvex functions and $p$-barycenter on CAT(1)-spaces of small radiihttps://projecteuclid.org/euclid.tkbjm/1506353559<strong>Takumi Yokota</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 1, 43--80.</p><p><strong>Abstract:</strong><br/>
We establish unique existence of $p$-barycenter of any probability measure for $p \ge 2$ on CAT(1)-spaces of small radii. In our proof, we employ Kendall's convex function on a ball of CAT(1)-spaces instead of the convexity of distance function. Various properties of $p$-barycenter on those spaces are also presented. They extend the author's previous work [Yo].
</p>projecteuclid.org/euclid.tkbjm/1506353559_20170925113254Mon, 25 Sep 2017 11:32 EDTOn the asymptotic behavior of Bessel-like diffusionshttps://projecteuclid.org/euclid.tkbjm/1506353560<strong>Yuuki Shimizu</strong>, <strong>Fumihiko Nakano</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 1, 81--90.</p><p><strong>Abstract:</strong><br/>
We derive the asymptotic behavior of the transition probability density of the Bessel-like diffusions for “dimension” $\rho = 0$.
</p>projecteuclid.org/euclid.tkbjm/1506353560_20170925113254Mon, 25 Sep 2017 11:32 EDTRealizations of inner automorphisms of order 4 and fixed points subgroups by them on the connected compact exceptional lie group $E_8$, Part Ihttps://projecteuclid.org/euclid.tkbjm/1506353561<strong>Toshikazu Miyashita</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 1, 91--166.</p><p><strong>Abstract:</strong><br/>
The compact simply connected Riemannian 4-symmetric spaces were classified by J. A. Jiménez as the type of Lie algebra. Needless to say, these spaces as homogeneous manifolds are of the form $G/H$, where $G$ is a connected compact simple Lie group with an automorphism $\tilde{\gamma}$ of order 4 on $G$ and $H$ is a fixed points subgroup $G^\gamma$ of $G$. In the present article, as Part I, for the connected compact exceptional Lie group $E_8$, we give the explicit form of automorphism $\tilde{\sigma}'_4$ of order 4 on $E_8$ induced by the $C$-linear transformation $\sigma'_4$ of 248-dimensional vector space $𝔢^{C}_{8}$ and determine the structure of the group $(E_8)^{\sigma'_4}$. This amounts to the global realization of one of seven cases with an automorphism of order 4 corresponding to the Lie algebra $𝔥 = 𝔰𝔬(6) \oplus 𝔰𝔬(10)$.
</p>projecteuclid.org/euclid.tkbjm/1506353561_20170925113254Mon, 25 Sep 2017 11:32 EDTCorrigendum to “On the Cartier duality of certain finite group schemes of order $p^n$, II” [Tsukuba J. Math. 37 (2) (2013) 259-269]https://projecteuclid.org/euclid.tkbjm/1506353562<strong>Michio Amano</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 1, 167--168.</p><p><strong>Abstract:</strong><br/>
We correct an error of the proof of Lemma 1 in the author's paper [1]. Also a typographical error is corrected.
</p>projecteuclid.org/euclid.tkbjm/1506353562_20170925113254Mon, 25 Sep 2017 11:32 EDTThe mean values of the double zeta-functionhttps://projecteuclid.org/euclid.tkbjm/1521597621<strong>Soichi Ikeda</strong>, <strong>Isao Kiuchi</strong>, <strong>Kaneaki Matsuoka</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 2, 169--187.</p><p><strong>Abstract:</strong><br/>
We investigate the mean square formulas of the Euler–Zagier type double zeta-function $\zeta_2(s_1,s_2)$ and provide the $\Omega$ results of the double zeta-function. We also calculate the double integral under certain conditions.
</p>projecteuclid.org/euclid.tkbjm/1521597621_20180320220026Tue, 20 Mar 2018 22:00 EDTKöhler theory for countable quadruple systemshttps://projecteuclid.org/euclid.tkbjm/1521597622<strong>Hirotaka Kikyo</strong>, <strong>Masanori Sawa</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 2, 189--213.</p><p><strong>Abstract:</strong><br/>
From the late 1970s to the early 1980s, Köhler developed a theory for constructing finite quadruple systems with point-transitive Dihedral automorphism groups by introducing a certain algebraic graph, now widely known as the (first) Köhler graph in finite combinatorics. In this paper, we define the countable Köhler graph and discuss countable extensions of a series of Köhler's works, with emphasis on various gaps between the finite and countable cases. We show that there is a simple 2-fold quadruple system over Z with a point-transitive Dihedral automorphism group if the countable Köhler graph has a so-called [1, 2]-factor originally introduced by Kano (1986) in the study of finite graphs. We prove that a simple Dihedral $\ell$-fold quadruple system over Z exists if and only if $\ell = 2$. The paper also covers some related remarks about Hrushovski's constructions of countable projective planes.
</p>projecteuclid.org/euclid.tkbjm/1521597622_20180320220026Tue, 20 Mar 2018 22:00 EDTOn $T$-coercive interior transmission eigenvalue problems on compact manifolds with smooth boundaryhttps://projecteuclid.org/euclid.tkbjm/1521597623<strong>Naotaka Shoji</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 2, 215--233.</p><p><strong>Abstract:</strong><br/>
We consider an interior transmission eigenvalue problem on two compact Riemannian manifolds with common smooth boundary. We assume that this problem is locally anisotropic type . Then we prove that the set of interior transmission eigenvalues forms a discrete subset of complex plane. Moreover, we also mention the interior transmission eigenvalue free region. In order to prove our results, we employ the so-called $T$-coercivity method.
</p>projecteuclid.org/euclid.tkbjm/1521597623_20180320220026Tue, 20 Mar 2018 22:00 EDTFinitely generated semi-cones in product ringshttps://projecteuclid.org/euclid.tkbjm/1521597624<strong>Yoshimi Kitamura</strong>, <strong>Yoshio Tanaka</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 2, 235--249.</p><p><strong>Abstract:</strong><br/>
Semi-cones of rings determine the partial orders in the rings. We consider semi-cones in the direct product rings and the product extension rings, inducing finitely generated semi-cones. In particular, we give characterizations for semi-cones of the direct product rings and the basic product extension rings of the ring of integers.
</p>projecteuclid.org/euclid.tkbjm/1521597624_20180320220026Tue, 20 Mar 2018 22:00 EDTOn multivalent functions in the unit dischttps://projecteuclid.org/euclid.tkbjm/1521597625<strong>Mamoru Nunokawa</strong>, <strong>Janusz Sokół</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 2, 251--263.</p><p><strong>Abstract:</strong><br/>
Let $\mathcal{A}(p)$ be the class of functions $f(z)$, analytic in $|z| \lt 1$ in the complex plane, of the form $f(z) = z^p + \cdots$. We study the question, that naturally rises, about the relation between the expressions $\frac{zf^{(p)}(z)}{f^{(p-1)}(z)}$ and $\frac{zf^{(p-1)}(z)}{f^{(p-2)}(z)}$, when $f(z) \in \mathcal{A}(p)$. Some relations of this type imply that $f(z)$ is $p$-valent or $p$-valent starlike in $|z| \lt 1$.
</p>projecteuclid.org/euclid.tkbjm/1521597625_20180320220026Tue, 20 Mar 2018 22:00 EDTExtending functors from the category of strict morphisms of inverse systems to the associated pro-category with applications to the first derived limithttps://projecteuclid.org/euclid.tkbjm/1521597626<strong>Peter Mrozik</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 2, 265--296.</p><p><strong>Abstract:</strong><br/>
We show that functors on the category of strict morphisms of inverse systems which are indexed by arbitrary cofiltered small categories have at most one extension to the associated procategory and give conditions characterizing the existence of extensions. This is applied to provide a concrete extension of the first derived limit to the category of pro-groups.
</p>projecteuclid.org/euclid.tkbjm/1521597626_20180320220026Tue, 20 Mar 2018 22:00 EDTAn inverse spectral uniqueness in exterior transmission problemhttps://projecteuclid.org/euclid.tkbjm/1521597627<strong>Lung-Hui Chen</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 41, Number 2, 297--312.</p><p><strong>Abstract:</strong><br/>
We consider an inverse spectral theory in a domain with the cavity in a penetrable inhomogeneous medium. An ODE system is constructed piecewise through the ODE eigenfunctions inside and outside the cavity. Then the ODE system is connected to the PDE system via the analytic continuation property of the Helmholtz equation. For each scattered angle, we describe its eigenvalue density in the complex plane, and prove an inverse uniqueness on the inhomogeneity by the measurements in the far-fields. We take advantage of the symmetry near infinity.
</p>projecteuclid.org/euclid.tkbjm/1521597627_20180320220026Tue, 20 Mar 2018 22:00 EDTContragredient Lie algebras and Lie algebras associated with a standard pentadhttps://projecteuclid.org/euclid.tkbjm/1541559647<strong>Nagatoshi Sasano</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 1, 1--51.</p><p><strong>Abstract:</strong><br/>
From a given standard pentad, we can construct a finite or infinite-dimensional graded Lie algebra. In this paper, we will define standard pentads which are analogues of Cartan subalgebras, and moreover, we will study graded Lie algebras corresponding to these standard pentads. We call such pentads pentads of Cartan type and describe them by two positive integers and three matrices. Using pentads of Cartan type, we can obtain arbitrary contragredient Lie algebras with an invertible symmetrizable Cartan matrix. Moreover, we can use pentads of Cartan type in order to find the structure of a Lie algebra. When a given standard pentad consists of a finite-dimensional reductive Lie algebra, its finite-dimensional completely reducible representation and a symmetric bilinear form, we can find the structure of its corresponding Lie algebra under some assumptions.
</p>projecteuclid.org/euclid.tkbjm/1541559647_20181106220130Tue, 06 Nov 2018 22:01 ESTRing of the weight enumerators of $d_n^+$https://projecteuclid.org/euclid.tkbjm/1541559648<strong>Makoto Fujii</strong>, <strong>Manabu Oura</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 1, 53--63.</p><p><strong>Abstract:</strong><br/>
We show that the ring of the weight enumerators of a self-dual doubly even code $d_n^+$ in arbitrary genus is finitely generated. Indeed enough elements to generate it are given. The latter result is applied to obtain a minimal set of generators of the ring in genus two.
</p>projecteuclid.org/euclid.tkbjm/1541559648_20181106220130Tue, 06 Nov 2018 22:01 ESTConstant negative Gaussian curvature tori and their singularitieshttps://projecteuclid.org/euclid.tkbjm/1541559651<strong>Tatsumasa Ura</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 1, 65--95.</p><p><strong>Abstract:</strong><br/>
We construct constant negative Gaussian curvature tori with one family of planar curvature lines in Euclidean 3-space. We show that these tori are wave fronts. The singularities of these tori are studied.
</p>projecteuclid.org/euclid.tkbjm/1541559651_20181106220130Tue, 06 Nov 2018 22:01 ESTAssociated binomial inversion for unified Stirling numbers and counting subspaces generated by subsets of a root systemhttps://projecteuclid.org/euclid.tkbjm/1541559652<strong>Tomohiro Kamiyoshi</strong>, <strong>Makoto Nagura</strong>, <strong>Shin-ichi Otani</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 1, 97--125.</p><p><strong>Abstract:</strong><br/>
We introduce an associated version of the binomial inversion for unified Stirling numbers defined by Hsu and Shiue. This naturally appears when we count the number of subspaces generated by subsets of a root system. We count such subspaces of any dimension by using associated unified Stirling numbers, and then we will also give a combinatorial interpretation of our inversion formula. In particular, the well-known explicit formula for classical Stirling numbers of the second kind can be understood as a special case of our formula.
</p>projecteuclid.org/euclid.tkbjm/1541559652_20181106220130Tue, 06 Nov 2018 22:01 EST