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European Mathematical Society Publishing House
2024-03-29 11:57:51
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=45&iss=4&update_since=2024-03-29
Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
45
2009
4
Existence and Nonexistence of Traveling Waves for a Nonlocal Monostable Equation
Hiroki
Yagisita
Kyoto University, KYOTO, JAPAN
We consider the nonlocal analogue of the Fisher-KPP equation ut = μ ∗ u− u + f(u), where μ is a Borel-measure on ℝ with μ(ℝ) = 1 and f satisfies f(0) = f(1) = 0 and f > 0 in (0, 1). We do not assume that μ is absolutely continuous with respect to the Lebesgue measure. The equation may have a standing wave solution whose profile is a monotone but discontinuous function. We show that there is a constant c∗ such that it has a traveling wave solution with speed c when c ≥ c∗ while no traveling wave solution with speed c when c
Partial differential equations
General
925
953
10.2977/prims/1260476648
http://www.ems-ph.org/doi/10.2977/prims/1260476648
Existence of Traveling Wave Solutions for a Nonlocal Bistable Equation: An Abstract Approach
Hiroki
Yagisita
Kyoto University, KYOTO, JAPAN
We consider traveling fronts to the nonlocal bistable equation ut = μ ∗ u– u + f(u), where μ is a Borel-measure on ℝ with μ(ℝ) = 1 and f satisfies f(0) = f(1) = 0, f< 0 in (0, α) and f > 0 in (α, 1) for some constant α ∈(0, 1). We do not assume that μ is absolutely continuous with respect to the Lebesgue measure. We show that there are a constant c and a monotone function φ with φ(–∞) = 0 and φ(+∞) = 1 such that u(t, x) := φ(x+ct) is a solution to the equation, provided f'(α) > 0. In order to prove this result, we would develop a recursive method for abstract monotone dynamical systems and apply it to the equation.
Partial differential equations
General
955
979
10.2977/prims/1260476649
http://www.ems-ph.org/doi/10.2977/prims/1260476649
Gauss Hypergeometric Functions, Multiple Polylogarithms, and Multiple Zeta Values
Shu
Oi
Waseda University, TOKYO, JAPAN
In this article, we express solutions of the Gauss hypergeometric equation as a series of the multiple polylogarithms by using iterated integral. This representation is the most simple case of a semisimple representation of solutions of the formal KZ equation. Moreover, combining this representation with the connection relations of solutions of the Gauss hypergeometric equation, we obtain various relations of the multiple polylogarithms of one variable and the multiple zeta values.
Special functions
General
981
1009
10.2977/prims/1260476650
http://www.ems-ph.org/doi/10.2977/prims/1260476650
Torsion Points of Abelian Varieties with Values in Infinite Extensions over a p-adic Field
Yoshiyasu
Ozeki
Kyoto University, KYOTO, JAPAN
abelian variety, Galois representation, p-adic Lie group
Let A be an abelian variety over a p-adic field K and L an algebraic infinite extension over K. We consider the finiteness of the torsion part of the group of rational points A(L) under some assumptions. In 1975, Hideo Imai proved that such a group is finite if A has good reduction and L is the cyclotomic ℤp-extension of K. In this paper, first we show a generalization of Imai’s result in the case where A has good ordinary reduction. Next we give some finiteness results when A is an elliptic curve and L is the field generated by the p-th power torsion of an elliptic curve.
Number theory
General
1011
1031
10.2977/prims/1260476651
http://www.ems-ph.org/doi/10.2977/prims/1260476651
On a Curvature Property of Effective Divisors and Its Application to Sheaf Cohomology
Hiroshi
Fuse
Nagoya University, NAGOYA, JAPAN
Takeo
Ohsawa
Nagoya University, NAGOYA, CHIKUSA-KU, JAPAN
Exploring a method of taming the boundary behavior of n-convex exhaustion functions, a curvature property of line bundles associated to effective Cartier divisors is proved. Cohomology vanishing theorems of the Serre type and the Kodaira-Nakano type are obtained as application.
Several complex variables and analytic spaces
General
1033
1039
10.2977/prims/1260476652
http://www.ems-ph.org/doi/10.2977/prims/1260476652
On Hansen’s Version of Spectral Theory and the Moyal Product
Mark
Hennings
Rugby School, RUGBY, UNITED KINGDOM
Daniel
Dubin
Open University, MILTON KEYNES, UNITED KINGDOM
Quantum theory
General
1041
1093
10.2977/prims/1260476653
http://www.ems-ph.org/doi/10.2977/prims/1260476653
Logarithmic Geometry, Minimal Free Resolutions and Toric Algebraic Stacks
Isamu
Iwanari
Tohoku University, SENDAI, JAPAN
In this paper we will introduce a certain type of morphisms of log schemes (in the sense of Fontaine, Illusie and Kato) and study their moduli. Then by applying this we define the notion of toric algebraic stacks, which may be regarded as torus emebeddings in the framework of algebraic stacks and prove some fundamental properties. Also, we study the stack-theoretic analogue of toroidal embeddings.
Algebraic geometry
General
1095
1140
10.2977/prims/1260476654
http://www.ems-ph.org/doi/10.2977/prims/1260476654