New reductions of integrable matrix PDEs: Sp(m)Sp(m)-invariant systems

We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative mKdV equations and a new integrable variant of the massive Thirring model, in addition to the already known systems. We also discuss integrable semi-discretizations of the obtained systems and present new soliton solutions to both continuous and semi-discrete systems. As a by-product, a new integrable semi-discretization of the Manakov model (self-focusing vector NLS equation) is obtained.Comment: 33 pages; (v4) to appear in JMP; This paper states clearly that the elementary function solutions of (a vector/matrix generalization of) the derivative NLS equation can be expressed as the partial $x$-derivatives of elementary functions. Explicit soliton solutions are given in the author's talks at http://poisson.ms.u-tokyo.ac.jp/~tsuchida

Finite-dimensional representations of twisted hyper loop algebras

We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the classification of the irreducible modules, the definition of the universal highest-weight modules, called the Weyl modules, and, under a certain mild restriction on the characteristic of the ground field, a proof that the simple modules and the Weyl modules for the twisted hyper loop algebras are isomorphic to appropriate simple and Weyl modules for the non-twisted hyper loop algebras, respectively, via restriction of the action

The Plateau de Bure Neutron Monitor: design, operation and Monte-Carlo simulation

This paper describes the Plateau de Bure Neutron Monitor (PdBNM), an instrument providing continuous ground-level measurements of atmospheric secondary neutron flux resulting from the interaction of primary cosmic rays with the Earth's atmosphere. The detector is installed on the Plateau de Bure (Devoluy mountains, south of France, latitude North 44{\deg} 38' 02", longitude East 5{\deg} 54' 26", altitude 2555 m) as a part of the ASTEP Platform (Altitude Single-event effects Test European Platform), a permanent installation dedicated to the study of the impact of terrestrial natural radiation on microelectronics circuit reliability. The present paper reports the neutron monitor design, its operation since August 2008 and its complete numerical simulation using the Monte Carlo codes GEANT4 and MCNPX. We particularly detail the computation of the neutron monitor detection response function for neutrons, muons, protons and pions, the comparison between GEANT4 and MCNPX numerical results and the evaluation of the PdBNM counting rate a function of both the nature and flux of the incident atmospheric particles.Comment: 37 pages, 14 figures, 5 tables; numerical error in GEANT4 particle sourse corrected, section 4.4 was significantly revised. Submitted to IEEE Transactions on Nuclear Scienc

The boundary Riemann solver coming from the real vanishing viscosity approximation

We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The conservative case is, in particular, included in the previous formulation. We suppose that the solutions $v^{\epsilon}$ to these problems converge to a unique limit. Also, it is assumed smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $A$ can be $0$. Second, we take into account the possibility that $B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.Comment: 84 pages, 6 figures. Text changes in Sections 1 and 3.2.3. Added Section 3.1.2. Minor changes in other section

Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem

Schur duality decomposes many copies of a quantum state into subspaces labeled by partitions, a decomposition with applications throughout quantum information theory. Here we consider applying Schur duality to the problem of distinguishing coset states in the standard approach to the hidden subgroup problem. We observe that simply measuring the partition (a procedure we call weak Schur sampling) provides very little information about the hidden subgroup. Furthermore, we show that under quite general assumptions, even a combination of weak Fourier sampling and weak Schur sampling fails to identify the hidden subgroup. We also prove tight bounds on how many coset states are required to solve the hidden subgroup problem by weak Schur sampling, and we relate this question to a quantum version of the collision problem.Comment: 21 page

Regulator constants and the parity conjecture

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p-infinity Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p extension, then the p-parity conjecture holds for twists of E by all orthogonal Artin representations of Gal(K^\infty/Q). We also give analogous results when K/Q is non-abelian, the base field is not Q and E is replaced by an abelian variety. The heart of the paper is a study of relations between permutation representations of finite groups, their "regulator constants", and compatibility between local root numbers and local Tamagawa numbers of abelian varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat

Algebraic volume density property of affine algebraic manifolds

We introduce the notion of algebraic volume density property for affine algebraic manifolds and prove some important basic facts about it, in particular that it implies the volume density property. The main results of the paper are producing two big classes of examples of Stein manifolds with volume density property. One class consists of certain affine modifications of \C^n equipped with a canonical volume form, the other is the class of all Linear Algebraic Groups equipped with the left invariant volume form.Comment: 35 page

The structures of Hausdorff metric in non-Archimedean spaces

For non-Archimedean spaces $X$ and $Y,$ let $\mathcal{M}_{\flat } (X), \mathfrak{M}(V \rightarrow W)$ and $\mathfrak{D}_{\flat }(X, Y)$ be the ballean of $X$ (the family of the balls in $X$), the space of mappings from $X$ to $Y,$ and the space of mappings from the ballen of $X$ to $Y,$ respectively. By studying explicitly the Hausdorff metric structures related to these spaces, we construct several families of new metric structures (e.g., $\widehat{\rho } _{u}, \widehat{\beta }_{X, Y}^{\lambda }, \widehat{\beta }_{X, Y}^{\ast \lambda }$) on the corresponding spaces, and study their convergence, structural relation, law of variation in the variable $\lambda,$ including some normed algebra structure. To some extent, the class $\widehat{\beta }_{X, Y}^{\lambda }$ is a counterpart of the usual Levy-Prohorov metric in the probability measure spaces, but it behaves very differently, and is interesting in itself. Moreover, when $X$ is compact and $Y = K$ is a complete non-Archimedean field, we construct and study a Dudly type metric of the space of $K-$valued measures on $X.$Comment: 43 pages; this is the final version. Thanks to the anonymous referee's helpful comments, the original Theorem 2.10 is removed, Proposition 2.10 is stated now in a stronger form, the abstact is rewritten, the Monna-Springer is used in Section 5, and Theorem 5.2 is written in a more general for