## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (204.217 recursos)

Tokyo Journal of Mathematic

1. #### On the Plus and the Minus Selmer Groups for Elliptic Curves at Supersingular Primes

KITAJIMA, Takahiro; OTSUKI, Rei
Let $p$ be an odd prime number, and $E$ an elliptic curve defined over a number field. Suppose that $E$ has good reduction at any prime lying above $p$, and has supersingular reduction at some prime lying above $p$. In this paper, we construct the plus and the minus Selmer groups of $E$ over the cyclotomic $\mathbb Z_p$-extension in a more general setting than that of B.D. Kim, and give a generalization of a result of B.D. Kim on the triviality of finite $\Lambda$-submodules of the Pontryagin duals of the plus and the minus Selmer groups, where $\Lambda$ is the...

2. #### Geometric Aspects of $p$-angular and Skew $p$-angular Distances

Corresponding to the concept of $p$-angular distance $\alpha_p[x,y]:=\left\lVert\lVert x\rVert^{p-1}x-\lVert y\rVert^{p-1}y\right\rVert$, we first introduce the notion of skew $p$-angular distance $\beta_p[x,y]:=\left\lVert \lVert y\rVert^{p-1}x-\lVert x\rVert^{p-1}y\right\rVert$ for non-zero elements of $x, y$ in a real normed linear space and study some of significant geometric properties of the $p$-angular and the skew $p$-angular distances. We then give some results comparing two different $p$-angular distances with each other. Finally, we present some characterizations of inner product spaces related to the $p$-angular and the skew $p$-angular distances. In particular, we show that if $p>1$ is a real number, then a real normed space $\mathcal{X}$ is an...

3. #### On the Semi-simple Case of the Galois Brumer-Stark Conjecture for Monomial Groups

ROBLOT, Xavier-François
In a previous work, we stated a conjecture, called the Galois Brumer-Stark conjecture, that generalizes the (abelian) Brumer-Stark conjecture to Galois extensions. Other generalizations of the Brumer-Stark conjecture to non-abelian Galois extensions are due to Nickel. Nomura proved that the Brumer-Stark conjecture implies the weak non-abelian Brumer-Stark conjecture of Nickel when the group is monomial. In this paper, we use the methods of Nomura to prove that the Brumer-Stark conjecture implies the Galois Brumer-Stark conjecture for monomial groups in the semi-simple case.

4. #### On the Unique Solvability of Nonlinear Fuchsian Partial Differential Equations

BACANI, Dennis B.; LOPE, Jose Ernie C.; TAHARA, Hidetoshi
We consider a singular nonlinear partial differential equation of the form $$(t\partial_t)^mu= F \Bigl( t,x,\bigl\{(t\partial_t)^j \partial_x^{\alpha}u \bigr\}_{(j,\alpha) \in I_m} \Bigr)$$ with arbitrary order $m$ and $I_m=\{(j,\alpha) \in \mathbb{N} \times \mathbb{N}^n \,;\, j+|\alpha| \leq m, j0 \}$. In this case, the equation is said to be a nonlinear Fuchsian partial differential equation. We show that if $F(t,x,0)$ vanishes at a certain...

5. #### A Sufficient Condition That $J(X^*)=J(X)$ Holds for a Banach Space $X$

KOMURO, Naoto; SAITO, Kichi-Suke; TANAKA, Ryotaro
It is shown that the James constant of the space $\mathbb{R}^2$ endowed with a $\pi/2$-rotation invariant norm coincides with that of its dual space. As a corollary, we have the same statement on symmetric absolute norms on $\mathbb{R}^2$.

6. #### Weak-type Estimates in Morrey Spaces for Maximal Commutator and Commutator of Maximal Function

GOGATISHVILI, Amiran; MUSTAFAYEV, Rza; AǦCAYAZI, Müjdat

KODAMA, Shun

KODAMA, Shun
We study concentration phenomena of the least energy solutions of the following nonlinear Schrödinger equation: $h^2 \Delta u - V(x) u + f( u ) = 0 \quad \text{in} \ \mathbb{R}^N, \ u>0, \ u \in H^1(\mathbb{R}^N)\,,$ for a totally degenerate potential $V$. Here $h>0$ is a small parameter, and $f$ is an appropriate, superlinear and Sobolev subcritical nonlinearity. In~[16], Lu and Wei proved that when the parameter $h$ approaches zero, the least energy solutions concentrate at the most centered point of the totally degenerate set $\Omega = \{ x \in \mathbb{R}^N \mid V(x) = \min_{ y \in... 19. #### Harmonic Analysis on the Space of$p$-adic Unitary Hermitian Matrices, Mainly for Dyadic Case HIRONAKA, Yumiko We are interested in harmonic analysis on$p$-adic homogeneous spaces based on spherical functions. In the present paper, we investigate the space$X$of unitary hermitian matrices of size$m$over a${\mathfrak p}$-adic field$k$mainly for dyadic case, and give the unified description with our previous papers for non-dyadic case. The space becomes complicated for dyadic case, and the set of integral elements in$X$has plural Cartan orbits. We introduce a typical spherical function$\omega(x;z)$on$X$, study its functional equations, which depend on$m$and the ramification index$e$of$2$in$k$, and give its... 20. #### Harmonic Analysis on the Space of$p$-adic Unitary Hermitian Matrices, Mainly for Dyadic Case HIRONAKA, Yumiko We are interested in harmonic analysis on$p$-adic homogeneous spaces based on spherical functions. In the present paper, we investigate the space$X$of unitary hermitian matrices of size$m$over a${\mathfrak p}$-adic field$k$mainly for dyadic case, and give the unified description with our previous papers for non-dyadic case. The space becomes complicated for dyadic case, and the set of integral elements in$X$has plural Cartan orbits. We introduce a typical spherical function$\omega(x;z)$on$X$, study its functional equations, which depend on$m$and the ramification index$e$of$2$in$k\$, and give its...

Aviso de cookies: Usamos cookies propias y de terceros para mejorar nuestros servicios, para análisis estadístico y para mostrarle publicidad. Si continua navegando consideramos que acepta su uso en los términos establecidos en la Política de cookies.