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 EDTDense chaos and densely chaotic operatorshttp://projecteuclid.org/euclid.tkbjm/1358777004<strong>Xinxing Wu</strong>, <strong>Peiyong Zhu</strong><p><strong>Source: </strong>Tsukuba J. Math., Volume 36, Number 2, 367--375.</p><p><strong>Abstract:</strong><br/>
The aim of this paper is to study dense chaos and densely chaotic operators on Banach
spaces. First, we prove that a dynamical system is densely δ-chaotic for some
δ > 0 if and only if it is densely chaotic and sensitive. Meanwhile, we also show
that for general dynamical systems, Devaney chaos and dense chaos do not imply each other.
Then, by using these results, we have that for a operator defined on a Banach space, dense
chaos, dense δ-chaos, generic chaos and generic δ-chaos are equivalent and
they are all strictly stronger than Li-Yorke chaos.
</p>projecteuclid.org/euclid.tkbjm/1358777004_Mon, 21 Jan 2013 09:03 ESTMon, 21 Jan 2013 09:03 ESTOn the Fourier coefficients of Hilbert modular forms of
half-integral weight over arbitrary algebraic number fieldshttp://projecteuclid.org/euclid.tkbjm/1373893402<strong>Hisashi Kojima</strong><p><strong>Source: </strong>Tsukuba J. Math., Volume 37, Number 1, 1--11.</p><p><strong>Abstract:</strong><br/>
In Theorem 2.5 in previous paper [4], we determined the Fourier coefficients of the image
of Shimura correspondence of modular forms f of half integral weight over arbitrary
algebraic number fields in terms of those of f . It seems that there is a gap in the
proof. We give a correct proof of Theorem 2.5 in [4]. Moreover, we deduce useful formulas
between the product of Fourier coefficients of f and the central value of quadratic
twisted L -series associated with the image of Shimura correspondence of f
.
</p>projecteuclid.org/euclid.tkbjm/1373893402_Mon, 15 Jul 2013 09:03 EDTMon, 15 Jul 2013 09:03 EDTHochschild cohomology ring of the generalized quaternion
algebrashttp://projecteuclid.org/euclid.tkbjm/1373893403<strong>Takao Hayami</strong><p><strong>Source: </strong>Tsukuba J. Math., Volume 37, Number 1, 13--25.</p><p><strong>Abstract:</strong><br/>
We will give an efficient bimodule projective resolution of the generalized quaternion
Z algebra Γ. As a main result, we will determine the ring structure of the
Hochschild cohomology HH *(Γ) by calculating the Yoneda products using this
resolution.
</p>projecteuclid.org/euclid.tkbjm/1373893403_Mon, 15 Jul 2013 09:03 EDTMon, 15 Jul 2013 09:03 EDTInteractive infinite Markov particle systems with jumpshttp://projecteuclid.org/euclid.tkbjm/1373893404<strong>Seiji Hiraba</strong><p><strong>Source: </strong>Tsukuba J. Math., Volume 37, Number 1, 27--50.</p><p><strong>Abstract:</strong><br/>
In [2] we investigated independent infinite Markov particle systems as measure-valued
Markov processes with jumps, and we gave sample path properties and martingale
characterizations. In particular, we investigated the exponent of Hölder-right
continuity in case that the motion process is absorbing α-stable motion on
(0,∞) with 0 < α < 2, that is, time-changed absorbing Brownian
motions on (0,∞) by the increasing α/2-stable Lévy processes.In the
present paper we shall extend the results to the case of simple interactive infinite
Markov particle systems. We also consider the absorbing stable motion on a half space
H = R d −1 × (0,∞) as a motion
process.
</p>projecteuclid.org/euclid.tkbjm/1373893404_Mon, 15 Jul 2013 09:03 EDTMon, 15 Jul 2013 09:03 EDTPeriodicity and eigenvalues of matrices over quasi-max-plus
algebrashttp://projecteuclid.org/euclid.tkbjm/1373893405<strong>Horst Brunotte</strong><p><strong>Source: </strong>Tsukuba J. Math., Volume 37, Number 1, 51--71.</p><p><strong>Abstract:</strong><br/>
We extend the notion of a max-plus algebra and study periodicity and eigenvalues of
matrices over this new structure thereby generalizing some well-known results on matrices
over a max-plus algebra.
</p>projecteuclid.org/euclid.tkbjm/1373893405_Mon, 15 Jul 2013 09:03 EDTMon, 15 Jul 2013 09:03 EDTPropriété d'extension pour les compacts et
rétractes absolushttp://projecteuclid.org/euclid.tkbjm/1373893406<strong>Robert Cauty</strong><p><strong>Source: </strong>Tsukuba J. Math., Volume 37, Number 1, 73--84.</p><p><strong>Abstract:</strong><br/>
We prove that a σ-compact metric space having the compact extension property is an
AR. This solves the problem ANR 13 of West's list [5].
</p>projecteuclid.org/euclid.tkbjm/1373893406_Mon, 15 Jul 2013 09:03 EDTMon, 15 Jul 2013 09:03 EDTThe Iwasawa decomposition and the Bruhat decomposition of the
automorphism group on certain exceptional Jordan algebrahttp://projecteuclid.org/euclid.tkbjm/1373893407<strong>Akihiro Nishio</strong><p><strong>Source: </strong>Tsukuba J. Math., Volume 37, Number 1, 85--119.</p><p><strong>Abstract:</strong><br/>
Let J 1 be the real form of a complex simple Jordan algebra such that
the automorphism group is F 4(−20) . By using some orbit types of
F 4(−20) on J 1 , for F 4(−20) ,
explicitly, we give the Iwasawa decomposition, the Oshima-Sekiguchi's
K ε -Iwasawa decomposition, the Matsuki decomposition, and the
Bruhat and Gauss decompositions.
</p>projecteuclid.org/euclid.tkbjm/1373893407_Mon, 15 Jul 2013 09:03 EDTMon, 15 Jul 2013 09:03 EDTDouble points of the slowness surface of the system of crystal
acoustics for tetragonal crystalshttp://projecteuclid.org/euclid.tkbjm/1373893408<strong>Claudio Melotti</strong><p><strong>Source: </strong>Tsukuba J. Math., Volume 37, Number 1, 121--152.</p><p><strong>Abstract:</strong><br/>
The aim of this paper is to study the location and the geometrical properties of the
double points of the slowness surface associated to the system of linear
crystal-elasticity in three space dimensions for tetragonal crystals. It will turn out
that compared with the case of cubic crystals, the location of these double points is more
involved. Moreover, for some specific choices of the “so-called” stiffiness
constants, a new type of singularities namely “biplanar” ones, will
appear.
</p>projecteuclid.org/euclid.tkbjm/1373893408_Mon, 15 Jul 2013 09:03 EDTMon, 15 Jul 2013 09:03 EDTThe number of arrows in the quiver of tilting modules over a path
algebra of Dynkin typehttp://projecteuclid.org/euclid.tkbjm/1373893409<strong>Ryoichi Kase</strong><p><strong>Source: </strong>Tsukuba J. Math., Volume 37, Number 1, 153--177.</p><p><strong>Abstract:</strong><br/>
Happel and Unger defined a partial order on the set of basic tilting modules. The tilting
quiver is the Hasse diagram of the poset of basic tilting modules. We determine the number
of arrows in the tilting quiver over a path algebra of Dynkin type.
</p>projecteuclid.org/euclid.tkbjm/1373893409_Mon, 15 Jul 2013 09:03 EDTMon, 15 Jul 2013 09:03 EDTSome transformations on ( LCS ) n -manifoldshttp://projecteuclid.org/euclid.tkbjm/1407938669<strong>Absos Ali Shaikh</strong>, <strong>Helaluddin Ahmad</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 1, 1--24.</p><p><strong>Abstract:</strong><br/>
The present paper deals with a study of certain transformations on an ( LCS ) n -manifold. It is shown that an ( LCS ) n -manifold remains invariant under a D -homothetic deformation. We also study an infinitesimal CL -transformation on an ( LCS ) n -manifold and obtain a necessary and sufficient condition for such an infinitesimal transformation to be a Killing or a conformal Killing vector field. Finally, we study CL -transformation on an ( LCS ) n -manifold and obtained a new tensor field, called CL-curvature tensor field , which is invariant under such a transformation.
</p>projecteuclid.org/euclid.tkbjm/1407938669_20140813100430Wed, 13 Aug 2014 10:04 EDTGoldie extending modules and generalizations of quasi-continuous moduleshttp://projecteuclid.org/euclid.tkbjm/1407938670<strong>Yosuke Kuratomi</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 1, 25--37.</p><p><strong>Abstract:</strong><br/>
A module M is said to be quasi-continuous if it is extending with the condition ( C 3 ) (cf. [7], [10]). In this paper, by using the notion of a G -extending module which is defined by E. Akalan, G. F. Birkenmeier and A. Tercan [1], we introduce a generalization of quasi-continuous “a GQC (generalized quasicontinuous)-module” and investigate some properties of GQC-modules. Initially we give some properties of a relative ejectivity which is useful in analyzing the structure of G -extending modules and GQC-modules (cf. [1]). And we apply them to the study of direct sums of GQC-modules. We also prove that any direct summand of a GQC-module with the finite internal exchange property is GQC. Moreover, we show that a module M is G -extending modules with ( C 3 ) if and only if it is GQC-module with the finite internal exchange property.
</p>projecteuclid.org/euclid.tkbjm/1407938670_20140813100430Wed, 13 Aug 2014 10:04 EDTPartially ordered ringshttp://projecteuclid.org/euclid.tkbjm/1407938671<strong>Yoshimi Kitamura</strong>, <strong>Yoshio Tanaka</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 1, 39--58.</p><p><strong>Abstract:</strong><br/>
We shall consider partially ordered rings as a generalization of ordered rings. We give properties or related matters of partially ordered rings, using convex ideals or non-negative semicones. Also, we consider order-preserving isomorphisms between residue class rings which are partially ordered rings.
</p>projecteuclid.org/euclid.tkbjm/1407938671_20140813100430Wed, 13 Aug 2014 10:04 EDTNon-fiber preserving actions on prism manifoldshttp://projecteuclid.org/euclid.tkbjm/1407938672<strong>John Kalliongis</strong>, <strong>Ryo Ohashi</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 1, 59--73.</p><p><strong>Abstract:</strong><br/>
In this paper we classify the finite groups of isometries which act on a prism manifolds M ( b,d ) and do not preserve any fibering. We construct nine distinct finite groups of isometries which act on M (1,2), and do not preserve any fibering. We then show that if a finite group of isometries G acts on M ( b,d ) and does not preserve any fibering, then M ( b,d ) = M (1,2) and G is conjugate to one of these nine groups which are: Z 3 × T , T , O , S 3 × O , Z 3 ∘ O , S 3 × T , Z 3 × O , Z 3 × I , and S 3 × I , where T , O , I and S 3 are the tetrahedral, octahedral, icosahedral, and symmetric groups respectively.
</p>projecteuclid.org/euclid.tkbjm/1407938672_20140813100430Wed, 13 Aug 2014 10:04 EDTSpheres, symmetric products, and quotient of hyperspaces of continuahttp://projecteuclid.org/euclid.tkbjm/1407938673<strong>Enrique Casta;ñeda-Alvarado</strong>, <strong>Javier Sánchez-Martínez</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 1, 75--84.</p><p><strong>Abstract:</strong><br/>
A continuum means a nonempty, compact and connected metric space. Given a continuum X , the symbols F n ( X ) and C 1 ( X ) denotes the hyperspace of all subsets of X with at most n points and the hyperspace of subcontinua of X , respectively. If n > 1, we consider the quotient spaces SF 1 n ( X ) = F n ( X )/ F 1 ( X ) and C 1 ( X )/ F 1 ( X ) obtained by shrinking F 1 ( X ) to a point in F n ( X ) and C 1 ( X ), respectively. In this paper, we study the continua X such that SF 1 n ( X ) is homeomorphic to C 1 ( X )/ F 1 ( X ) and we analyze when the spaces F n ( X ) and SF 1 n ( X ) are homeomorphic to some sphere.
</p>projecteuclid.org/euclid.tkbjm/1407938673_20140813100430Wed, 13 Aug 2014 10:04 EDTA method for finding a minimal point of the lattice in cubic number fieldshttp://projecteuclid.org/euclid.tkbjm/1407938674<strong>Kan Kaneko</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 1, 85--121.</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/1407938674_20140813100430Wed, 13 Aug 2014 10:04 EDTOn the range of self-interacting random walks on an integer intervalhttp://projecteuclid.org/euclid.tkbjm/1407938675<strong>Kazuki Okamura</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 38, Number 1, 123--135.</p><p><strong>Abstract:</strong><br/>
We consider the range of a one-parameter family of selfinteracting walks on the integers up to the time of exit from an interval. We derive the weak convergence of an appropriately scaled range. We show that the distribution functions of the limits of the scaled range satisfy a certain class of de Rham's functional equations. We examine the regularity of the limits.
</p>projecteuclid.org/euclid.tkbjm/1407938675_20140813100430Wed, 13 Aug 2014 10:04 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 EDT