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 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 ESTCommuting structure Jacobi operators for real hypersurfaces in complex space forms IIhttps://projecteuclid.org/euclid.tkbjm/1554170419<strong>U-Hang Ki</strong>, <strong>Hiroyuki Kurihara</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 2, 127--154.</p><p><strong>Abstract:</strong><br/>
Let $M$ be a real hypersurface in a complex space form $M_n(c)$, $c \not= 0$. In this paper, we prove that if the structure Jacobi operator $R_\xi$ is $\phi\nabla_{\xi}\xi$-parallel and $R_\xi$ commute with the Ricci tensor, then $M$ is a Hopf hypersurface provided that the mean curvature of $M$ is constant with respect to the structure vector field.
</p>projecteuclid.org/euclid.tkbjm/1554170419_20190401220029Mon, 01 Apr 2019 22:00 EDTThe hypergeometric function for the root system of type A with a certain degenerate parameterhttps://projecteuclid.org/euclid.tkbjm/1554170420<strong>Nobukazu Shimeno</strong>, <strong>Yuichi Tamaoka</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 2, 155--172.</p><p><strong>Abstract:</strong><br/>
We express explicitly the Heckman-Opdam hypergeometric function for the root system of type A with a certain degenerate parameter in terms of the Lauricella hypergeometric function.
</p>projecteuclid.org/euclid.tkbjm/1554170420_20190401220029Mon, 01 Apr 2019 22:00 EDTAn indecomposable continuum as subpower Higson coronahttps://projecteuclid.org/euclid.tkbjm/1554170421<strong>Yutaka Iwamoto</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 2, 173--190.</p><p><strong>Abstract:</strong><br/>
In this paper, we study topological properties of the subpower Higson coronas of proper metric spaces and show that the subpower Higson corona of the half open interval with the usual metric is an indecomposable continuum. Continuous surjections from Higson-type coronas onto a Higson-type compactifications of the half open interval are also constructed.
</p>projecteuclid.org/euclid.tkbjm/1554170421_20190401220029Mon, 01 Apr 2019 22:00 EDTComputation methods of logarithmic vector fields associated to semi-weighted homogeneous isolated hypersurface singularitieshttps://projecteuclid.org/euclid.tkbjm/1554170422<strong>Katsusuke Nabeshima</strong>, <strong>Shinichi Tajima</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 2, 191--231.</p><p><strong>Abstract:</strong><br/>
Methods for computing logarithmic vector fields along a semi-weighted homogeneous hypersurface with an isolated singularity are considered in the context of symbolic computation. The main idea of our approach is based on the concept of polar variety and of algebraic local cohomology. New algorithms are introduced for computing a set of generators of the modules of logarithmic vector fields. The keys of the resulting algorithms are a notion of parametric syzygy system and that of parametric local cohomology system.
</p>projecteuclid.org/euclid.tkbjm/1554170422_20190401220029Mon, 01 Apr 2019 22:00 EDTHigson compactifications of Wallman typehttps://projecteuclid.org/euclid.tkbjm/1554170423<strong>Yasser F. Ortiz-Castillo</strong>, <strong>Artur Hideyuki Tomita</strong>, <strong>Takamitsu Yamauchi</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 2, 233--250.</p><p><strong>Abstract:</strong><br/>
We provide a sufficient condition for a proper metric space in order that its Higson compactification may be of Wallman type.
</p>projecteuclid.org/euclid.tkbjm/1554170423_20190401220029Mon, 01 Apr 2019 22:00 EDTA topological proof of Chen's alternative Kneser coloring theoremhttps://projecteuclid.org/euclid.tkbjm/1554170424<strong>Yasuhiro Hara</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 2, 251--258.</p><p><strong>Abstract:</strong><br/>
Johnson, Holroyd and Stahl [5] conjectured that the circular chromatic number of the Kneser graph is equal to the ordinary chromatic number. Chen completely confirmed the conjecture in [4]. Chen's alternative Kneser coloring theorem is a key lemma in his proof of Johnson-Holroyd-Stahl conjecture. Chen [4] and Chang, Liu and Zhu [3] proved the theorem by using Fan's lemma. In this paper, we prove Chen's alternative Kneser coloring theorem by using cohomology.
</p>projecteuclid.org/euclid.tkbjm/1554170424_20190401220029Mon, 01 Apr 2019 22:00 EDTOn an analog of the Arakawa-Kaneko zeta function and relations of some multiple zeta valueshttps://projecteuclid.org/euclid.tkbjm/1554170425<strong>Ryota Umezawa</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 2, 259--294.</p><p><strong>Abstract:</strong><br/>
T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an analog of the Arakawa-Kaneko zeta function of Miyagawa-type (defined by T. Miyagawa) and to obtain relations among Miyagawa-type multiple zeta values. The other is to find a class of zeta functions to which Ito's zeta functions of the case of general index are related.
</p>projecteuclid.org/euclid.tkbjm/1554170425_20190401220029Mon, 01 Apr 2019 22:00 EDTA note on the product of independent random variables with regularly varying tailshttps://projecteuclid.org/euclid.tkbjm/1554170426<strong>Yuji Kasahara</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 2, 295--308.</p><p><strong>Abstract:</strong><br/>
The tail probability of the product of independent random variables is discussed. The class of random variables with regularly varying tails is known to be closed under multiplication and some explicit examples are given by Kifer-Varadhan [2]. We extend them.
</p>projecteuclid.org/euclid.tkbjm/1554170426_20190401220029Mon, 01 Apr 2019 22:00 EDTA formula for the Hurwitz zeta function, Riemann's functional equation and certain integral representationshttps://projecteuclid.org/euclid.tkbjm/1554170427<strong>Yasuyuki Kachi</strong>, <strong>Pavlos Tzermias</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 42, Number 2, 309--334.</p><p><strong>Abstract:</strong><br/>
There is a well-known formula for the Hurwitz zeta function which implies the functional equation for the Riemann zeta function. We give a new proof of that formula and recover certain integral representations for the Hurwitz and Riemann zeta functions.
</p>projecteuclid.org/euclid.tkbjm/1554170427_20190401220029Mon, 01 Apr 2019 22:00 EDTRealizations of inner automorphisms of order four and fixed points subgroups by them on the connected compact exceptional Lie group $E_8$, Part IIhttps://projecteuclid.org/euclid.tkbjm/1571968818<strong>Toshikazu Miyashita</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 1, 1--22.</p><p><strong>Abstract:</strong><br/>
The compact simply connected Riemannian 4-symmetric spaces were classified by J. A. Jiménez according to type of the Lie algebras. As homogeneous manifolds, these spaces are of the form $G/H$, where $G$ is a connected compact simple Lie group with an automorphism $\tilde{\gamma}$ of order four on $G$ and $H$ is a fixed points subgroup $G^\gamma$ of $G$. According to the classification by J. A. Jiménez, there exist seven compact simply connected Riemannian 4-symmetric spaces $G/H$ in the case where $G$ is of type $E_8$. In the present article, we give the explicit form of automorphisms $\tilde{w}_4$, $\tilde{\upsilon}_4$ and $\tilde{\mu}_4$ of order four on $E_8$ induced by the $C$-linear transformations $w_4, \upsilon_4$ and $\mu_4$ of the 248-dimensional vector space $𝔢^C_8$, respectively. Further, we determine the structure of these fixed points subgroups $(E_8)^{w_4}, (E_8)^{\upsilon_4}$ and $(E_8)^{\mu_4}$ of $E_8$. These amount to the global realizations of three spaces among seven Riemannian 4-symmetric spaces $G/H$ above corresponding to the Lie algebras $𝔥 = i \boldsymbol{R} \oplus 𝔰𝔲(8)$, $i\boldsymbol{R} \oplus 𝔢_7$ and $𝔥 = 𝔰𝔲(2) \oplus 𝔰𝔲(8)$, where $𝔥 = \mathrm{Lie}(H)$.
</p>projecteuclid.org/euclid.tkbjm/1571968818_20191024220024Thu, 24 Oct 2019 22:00 EDTExamples of transversally complex submanifolds of the associative Grassmann manifoldhttps://projecteuclid.org/euclid.tkbjm/1571968819<strong>Kanako Enoyoshi</strong>, <strong>Kazumi Tsukada</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 1, 23--36.</p><p><strong>Abstract:</strong><br/>
We consider the Grassmann manifold of associative subspaces in the space of imaginary octonions, which we call the associative Grassmann manifold. It is known that the associative Grassmann manifold is an eight-dimensional compact symmetric quaternionic Kähler manifold. We construct interesting examples of four-dimensional complex submanifolds of the associative Grassmann manifold.
</p>projecteuclid.org/euclid.tkbjm/1571968819_20191024220024Thu, 24 Oct 2019 22:00 EDTA scalar Calabi-type flow in the almost Hermitian geometryhttps://projecteuclid.org/euclid.tkbjm/1571968820<strong>Masaya Kawamura</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 1, 37--54.</p><p><strong>Abstract:</strong><br/>
We define a parabolic flow of almost Hermitian metrics which evolves an initial metric along the second derivative of the Chern scalar curvature. We show that the flow has a unique shorttime solution and also show a stability result when the background metric is quasi-Kähler with constant scalar curvature.
</p>projecteuclid.org/euclid.tkbjm/1571968820_20191024220024Thu, 24 Oct 2019 22:00 EDTCurves on weighted K3 surfaces of degree two with symmetric Weierstrass semigroupshttps://projecteuclid.org/euclid.tkbjm/1571968821<strong>Jiryo Komeda</strong>, <strong>Makiko Mase</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 1, 55--69.</p><p><strong>Abstract:</strong><br/>
Let $C$ be a curve on the weighted projective plane $\mathbf{P}(1, 1, 4)$ which is of Fermat type or almost Fermat type. We construct K3 surfaces which are double covers of $\mathbf{P}(1, 1, 4)$ and which contain pointed curves with symmetric Weierstrass semigroups which are double covers of $C$.
</p>projecteuclid.org/euclid.tkbjm/1571968821_20191024220024Thu, 24 Oct 2019 22:00 EDTRegular prehomogeneous vector spaces for valued Dynkin quivershttps://projecteuclid.org/euclid.tkbjm/1571968822<strong>Tomohiro Kamiyoshi</strong>, <strong>Yoshiteru Kurosawa</strong>, <strong>Hiroshi Nagase</strong>, <strong>Makoto Nagura</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 1, 71--111.</p><p><strong>Abstract:</strong><br/>
We introduce regular prehomogeneous vector spaces associated with an arbitrary valued Dynkin graph $(\Gamma, \boldsymbol{v})$ having a fixed oriented modulation $(𝔐, \Omega)$ over the ground field $K$. Here $K$ is of characteristic zero, but it may not be algebraically closed. We will construct a fundamental theory of such prehomogeneous vector spaces.
Each generic point of a regular prehomogeneous vector space corresponds to a hom-orthogonal partial tilting $\Lambda$-module, where $\Lambda$ is the tensor $K$-algebra of $(𝔐, \Omega)$. We count the number of isomorphism classes of hom-orthogonal partial tilting $\Lambda$-modules of type $\mathbf{B}_n$, $\mathbf{C}_n$, $\mathbf{F}_4$ and $\mathbf{G}_2$. As a consequence of our theorem, we estimate lower and upper bounds for the number of basic relative invariants of regular prehomogeneous vector spaces for any valued Dynkin quiver.
</p>projecteuclid.org/euclid.tkbjm/1571968822_20191024220024Thu, 24 Oct 2019 22:00 EDTParaholomorphic cohomology groups of hyperbolic adjoint orbitshttps://projecteuclid.org/euclid.tkbjm/1585706449<strong>Nobutaka Boumuki</strong>, <strong>Tomonori Noda</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 2, 113--143.</p><p><strong>Abstract:</strong><br/>
For a paracomplex manifold, we construct certain cohomology groups. The main purpose of this paper is to clarify a link between such cohomology groups of hyperbolic adjoint orbits and the de Rham cohomology groups of real flag manifolds. That establishes relation between a paraholomorphic invariant and a topological invariant.
</p>projecteuclid.org/euclid.tkbjm/1585706449_20200331220052Tue, 31 Mar 2020 22:00 EDT48 dimensional even unimodular nearly extremal lattices.https://projecteuclid.org/euclid.tkbjm/1585706450<strong>Michio Ozeki</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 2, 145--189.</p><p><strong>Abstract:</strong><br/>
In this paper we introduce the notion of an even unimodular nearly extremal lattice in the case of 48 dimension. We prove two basic properties of such lattices $L$. First we prove that any nearly extremal lattice $L$ is generated by the vectors of norm 4 and norm 6 in $L$. Next we prove that the Siegel theta series of degree 2 associated with an even unimodular nearly extremal lattice is determined by the Fourier coefficients which are connected with the vectors of norm 4.
</p>projecteuclid.org/euclid.tkbjm/1585706450_20200331220052Tue, 31 Mar 2020 22:00 EDTShimura and Shintani liftings of certain cusp forms of half-integral and integral weightshttps://projecteuclid.org/euclid.tkbjm/1585706451<strong>Manish Kumar Pandey</strong>, <strong>B. Ramakrishnan</strong>, <strong>Anup Kumar Singh</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 2, 191--210.</p><p><strong>Abstract:</strong><br/>
In [4], W. Kohnen constructed explicit Shintani lifts from the space of cusp forms of weight $2k$ on $Γ_0(N)$, which are mapped into the plus space $S^+_{k+1/2}(Γ_0(4N))$, where $N$ is an odd integer. This lifting is adjoint to the (modified) Shimura map defined by him with respect to the Petersson scalar product. Using this construction along with the theory of newforms on $S^+_{k+1/2}(Γ_0(4N))$ (where $N$ is an odd square-free natural number) developed in [3], he derived explicit Waldspurger theorem for the newforms belonging to the space $S^+_{k+1/2}(Γ_0(4N))$. Further in this work, Kohnen considered the $\pm 1$ eigen subspaces corresponding to the Atkin-Lehner involution and showed that the intersection of this $\pm$ spaces with the corresponding newform spaces are isomorphic under the Shimura correspondence. A natural question is whether a similar result can be obtained for the intersection of this $(\pm1)$ subspaces with the space of oldforms. In this direction, S. Choi and C. H. Kim [2] considered the case where $N$ is an odd prime $p$ and constructed similar Shimura and Shintani maps between subspaces of forms of half-integral and integral weights. The subspaces considered by Choi and Kim are nothing but $+1$ eigenspace under the Fricke involution. In this paper, we generalise the work of Choi and Kim to the case where $N$ is an odd square-free natural number.
</p>projecteuclid.org/euclid.tkbjm/1585706451_20200331220052Tue, 31 Mar 2020 22:00 EDTTilting complexes for group graded self-injective algebrashttps://projecteuclid.org/euclid.tkbjm/1585706452<strong>Andrei Marcus</strong>, <strong>Shengyong Pan</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 2, 211--222.</p><p><strong>Abstract:</strong><br/>
We construct derived equivalences between group graded self-injective algebras, starting from equivalences between their 1-components, obtained via a construction of J. Rickard and S. Al-Nofayee.
</p>projecteuclid.org/euclid.tkbjm/1585706452_20200331220052Tue, 31 Mar 2020 22:00 EDTTime-space $L^2$-boundedness for the 2D Navier-Stokes equations and hyperbolic Navier-Stokes equationshttps://projecteuclid.org/euclid.tkbjm/1585706453<strong>Takayuki Kobayashi</strong>, <strong>Masashi Misawa</strong>, <strong>Kenji Nakamura</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 2, 223--239.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the Cauchy problem for the two dimensional Navier-Stokes equations and hyperbolic Navier-Stokes equations. We show the time-space $L^2$-boundedness of the solutions for initial data in $L^1$ space. The $L^2$-boundedness of solutions which proved in this paper gives better decay order in time than known results.
</p>projecteuclid.org/euclid.tkbjm/1585706453_20200331220052Tue, 31 Mar 2020 22:00 EDTOn a combination of the cyclic Nimhoff and subtraction gameshttps://projecteuclid.org/euclid.tkbjm/1585706454<strong>Tomoaki Abuku</strong>, <strong>Masanori Fukui</strong>, <strong>Ko Sakai</strong>, <strong>Koki Suetsugu</strong>. <p><strong>Source: </strong>Tsukuba Journal of Mathematics, Volume 43, Number 2, 241--249.</p><p><strong>Abstract:</strong><br/>
In this paper, we study a combination (called the generalized cyclic Nimhoff) of the cyclic Nimhoff and subtraction games. We give the $\mathscr{G}$-value of the game when all the $\mathscr{G}$-value sequences of the component subtraction games have a common $h$-stair structure.
</p>projecteuclid.org/euclid.tkbjm/1585706454_20200331220052Tue, 31 Mar 2020 22:00 EDT