bluuebunny/crossref_metadata_2025 huggingface dataset:
Reaction of children and adults to violence in school
Authors: Plut Dijana , Popadic Dragan
Published: January 2008

The aim of this research is to describe the reaction of pupils and adults who work in school to violence. Reactions to violence, aimed at the child personally, have to be differentiated from the reactions to the violent scenes that the child witnesses. The analyzed data, collected in the questionnaires within the program of fighting violence which was started by UNICEF in 2005, comprise the answers of 25.056 pupils and 4.793 adults from 71 schools in Serbia. The results indicate that the pupils react to violence inconsistently and that in their repertoire they have both constructive and non-constructive ways of reacting. One half of the pupils are ready to seek help from others in case of being in danger, and widespread are also those reactions (answering by aggression or submissiveness) which substantiate further violence. Every tenth pupil who is a violence victim just tolerates and conceals violence. If they witness violence, 11% of the pupils consequently distance themselves from helping. The pupils who are violence victims do not feel abandoned by their peers, 73% of them said that their friends helped them. Although adults themselves estimate highly their own readiness and the ability to react to violence, the measures undertaken by them are not assessed well on the part of pupils. In the conclusion, there is the elaboration of all the measures which can be used to stop self-reproduction of violent behavior in school and the emphasis on the need for the programs for prevention of school violence which would be based on the inclusion of the whole school collective, and especially pupils.
Towards the promotion of reproductive health of the young
Authors: Stankovic Biljana
Published: January 2008

Premature sexual activity of the young, before reaching physical and psycho-social maturity, brings along the risk of jeopardizing their reproductive health, mostly because it can lead to sexually transmitted infections or pregnancy, which is mostly unwanted in adolescence. The starting assumption of the promotion of reproductive health of the young is understanding and acceptance of their sexuality and relevant needs in social environment in which they live. Primarily in the family, the media, healthcare institutions and school. During the period of childhood and youth, school possesses the unique possibility to enable a large number of young people to acquire knowledge and skills related to sexuality and reproductive health and shape their values, attitudes and beliefs. The complexity of the process of making the decision about becoming sexually active, as well as the space for action towards its postponement to older age, are also indicated by the results of the research conducted in Belgrade, on the sample of one hundred and eleven female adolescents aged fourteen to twenty, who became sexually active at the age sixteen and earlier. These are primarily those results which refer to the meaning of love and sex in their value system, motives, feelings and attitudes related to becoming sexually active.
Determinant Formula for Solutions of the Quantum Knizhnik–Zamolodchikov Equation Associated with $U_q(sl_n)$ at $|q| = 1$
Authors: Miwa Tetsuji , Takeyama Yoshihiro , Tarasov Vitaly
Published: January 2008

We construct the hypergeometric solutions for the quantized Knizhnik–Zamolodchikov equation with values in a tensor product of vector representations of

U_q(sl_n)

at

|q| = 1

and give an explicit formula for the corresponding determinant in terms of the double sine function.
Régularité des Ondes élastiques dans la Région Glancing des Ondes $P$
Authors: Morioka Tatsushi
Published: January 2008

In this paper, we show that the outgoing solutions of the isotropic elastic equation with Dirichlet condition at the boundary have the Gevrey 3 regularity in the glancing region of the longitudinal waves, when the dimension of the space is 3, the domain is exterior and the Gaussian curvature is positive. It is an analogy of the work by Lebeau [14] concerning the wave equation, for the isotropic elastic equation.
Large Time Behavior of Solutions for Derivative Cubic Nonlinear Schrödinger Equations
Authors: Hayashi Nakao , Naumkin Pavel , Uchida Hidetake
Published: January 2008

We study the asymptotic behavior in time and scattering problem for the solutions to the Cauchy problem for the derivative cubic nonlinear Schrödinger equations of the following form

\begin{align*}
iu_t+u_{xx} = \mathcal N(u, \bar u, u_x, \bar u_x),\quad t\in \mathbf R,\ x\in \mathbf R;\quad u(0, x) = u_0(x),\quad x \in \mathbf R,\\
\tag{A}    
\end{align*}

where

\begin{align*}
&\mathcal N(u, \bar u, u_x, \bar u_x) = \\
&\quad \mathcal K_1|u|^2 u +
i\mathcal K_2|u|^2 u_x +
i\mathcal K_3 u^2 \bar u_x +
\mathcal K_4|u_x|^2 u +
\mathcal K_5 \bar uu_x^2 +
i \mathcal K_6|u_x|^2 u_x,
\end{align*}

\mathcal K_I = \mathcal K_I(|u|^2)

,

\mathcal K_I(z) \in C^3(\mathbf R^+)

;

\mathcal K_I(z) = λ_I + O(z)

, as

z → +0

,

\mathcal K_1

,

\mathcal K_6

are real valued functions. Here the parameters

λ_1, λ_6 \in \mathbf R

, and

λ_2, λ_3, λ_4, λ_5 \in ℂ

are such that

λ_2 – λ_3 \in \mathbf R

and

λ_4 – λ_5 \in \mathbf R

. If

\mathcal K_5(z) = \frac{λ_5}{1+μz}

and

λ_5 = μ = ∓ 1

,

\mathcal K_1 = \mathcal K_2 = \mathcal K_3 = \mathcal K_4 = \mathcal K_5 = \mathcal K_6 = 0

, equation (A) appears in the classical pseudospin magnet model [9]. We prove that if

u_0 \in H^{3,0} ∩ H^{2,1}

and the norm

‖u_0‖_{3,0} + ‖u_0‖_{2,1} = ε

is sufficiently small, then the solution of (A) exists globally in time and satisfies the sharp time decay estimate

‖u(t)‖_{2,0, ∞} ≤ Cε(1+|t|)^{-1/2}

, where

‖φ‖_{m,s,p} = ‖(1+x_2)^{s/2}(1−∂_x^2)^{m/2}φ‖_{L^p}

,

H_p^{m,s} =\{φ \in S'; ‖φ‖_{m,s,p} < ∞\}

. Furthermore we prove existence of modified scattering states and nonexistence of nontrivial scattering states. Our method is based on a certain gauge transformation and an appropriate phase function.
Blowing Ups of 3-dimensional Terminal Singularities
Authors: Hayakawa Takayuki
Published: January 2008

We study the blowing up
π
:
X
->
X
of a 3-dimensional terminal singularity
X
of index
m
> 2 such that the exceptional locus of
π
consists of a prime divisor
E
with discrepancy 1/
m
. A complete classification of such blowing ups is given and it is proved that these correspond to weighted blow ups by a certain kind of maximal weights except for the case where
X
is of type (cD/2). We shall treat the (cD/2) case later. These also give examples of contractions of extremal rays which contract a divisor to a point.
The Berezin Calculus
Authors: Robinson Paul Lee
Published: January 2008

We present a canonical account of the Berezin integral and associated Berezin expectation over Hilbert spaces of arbitrary dimension. Our account is illustrated by an extensive discussion of Gaussians, by a Berezinian version of the kernel theorem for generalized functions, and by an extension of the Shale–Stinespring theorem on spin transformations.
Canonical Isomorphism of Two Lie Algebras Arising in $\textit{CR}$-geometry
Authors: Ezhov Vladimir V. , Isaev Alexander V.
Published: January 2008

We show that the maximal prolongation of a certain algebra associated with a non-degenerate Hermitian form on

ℂ^n \times ℂ^n

with values in

ℝ^k

is canonically isomorphic to the Lie algebra of infinitesimal holomorphic automorphisms of the corresponding quadric in

ℂ^{n+k}

. This fact creates a link between different approaches to the equivalence problem for Levi-nondegenerate strongly uniform

\textit{CR}

-manifolds.
Automorphic Forms on the Expanded Symmetric Domain of Type IV
Authors: Aoki Hiroki
Published: January 2008

We introduce a lifting from a given Jacobi form of index 1 to an automorphic form on an expanded domain of type F , introduced by Saito [20, 22]. The method is a generalization of Gritsenko [10, 11] for symmetric domain of type IV. We constract a lifting function satisfying a certain translation formula on the expanded domain.
Generic and $q$-Rational Representation Theory
Authors: Cline Edward , Parshall Brian , Scott Leonard
Published: January 2008

Part I of this paper develops various general concepts in generic representation and cohomology theories. Roughly speaking, we provide a general theory of orders in non-semisimple algebras applicable to problems in the representation theory of finite and algebraic groups, and we formalize the notion of a “generic” property in representation theory. Part II makes new contributions to the non-describing representation theory of finite general linear groups. First, we present an explicipt Morita equivalence connecting

GL_n(q)

with the theory of

q

-Schur algebras, extending a unipotent block equivalence of Takeuchi [T]. Second, we apply this Morita equivalence to study the cohomology groups

H^*(GL_n(q),L)

, when

L

is an irreducible module in non-describing characteristic. The generic theory of Part I then yields stability results for various groups

H^t(GL_n(q),L)

, reminscent of our general theory [CPSK] with van der Kallen of generic cohomology in the describing characteristic case, (in turn, the stable value of such a cohomology group can be expressed in terms of the cohomology of the affine Lie algebra

\widehat{\mathfrak{gl}}_n(ℂ)

.) The arguments entail new applications of the theory of tilting modules for

q

-Schur algebras. In particular, we obtain new complexes involving tilting modules associated to endomorphism algebras obtained from general finite Coxeter groups.
Atomic Positive Linear Maps in Matrix Algebras
Authors: Ha Kil-Chan
Published: January 2008

We show that all of the known generalizations of the Choi maps are atomic maps.
Integral and Theta Formulae for Solutions of $sl_N$ Knizhnik–Zamolodchikov Equation at Level Zero
Authors: Nakayashiki Atsushi
Published: January 2008

The solutions of the sin Knizhnik–Zamolodchikov(KZ) equations at level 0 are studied. We present the integral formula which is obtained as a quasi-classical limit of the integral formula of the form factors of the

SU(N)

invariant Thirring model due to F. Smirnov. A proof is given that those integrals satisfy

sl_N

KZ equation of level 0. The relation of the integral formulae with the chiral Szegö kernel is clarified. As a consequence the integral formula with the special choice of cycles is rewritten in terms of the Riemann theta functions associated with the

Z_N

curve. This formula gives a generalization of Smirnov's formula in the case of

sl_2

.
Spherically Symmetric Dirac Operators with Variable Mass and Potentials Infinite at Infinity
Authors: Schmidt Karl Michael , Yamada Osanobu
Published: January 2008

We study the spectrum of spherically symmetric Dirac operators m three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions. We prove that purely absolutely continuous spectrum covers the whole real line if the potential dominates the mass, or scalar potential, term. In the situation where the potential and the scalar potential are identical, the positive part of the spectrum is purely discrete: we show that the negative half-line is filled with purely absolutely continuous spectrum in this case.
Standard Monomial Theory for Bott–Samelson Varieties of $\textit{GL}(n)$
Authors: Lakshmibai Venkatramani , Magyar Peter
Published: January 2008

We construct an explicit basis for the coordinate ring of the Bott–Samelson variety

Z_i

associated to

G= \textit{GL}(n)

and an arbitrary sequence of simple reflections

\mathbf i

. Our basis is parametrized by certain standard tableaux and generalizes the Standard Monomial basis for Schubert varieties.
On a Solution of a $q$-Difference Analogue of Laurieella's $D$-Type Hypergeometric Equation with $|q| = 1$
Authors: Nishizawa Michitomo
Published: January 2008

By using the double sine function, an integral solution of a

q

-difference analogue of Laurieella's

D

-type hypergeometric equation is constructed in the case when

|q| = 1

. Furthermore, its contiguity operators are considered.
Singularities in Fuchsian Cauchy Problems with Holomorphic Data
Authors: Yamane Hideshi
Published: January 2008

It has been proved by Baouendi and Goulaouic that the holomorphic Cauchy problem for a Fuchsian partial differential operator of weight

m-m'

has a unique solution if its characteristic exponents avoid integers

≥m-m'

. In the present paper we consider the singularity of the solution which appears if some of the characteristic exponents take integral values

≥m-m'

.
A Trace Formula for Discrete Schrödinger Operators
Authors: Shirai Tomoyuki
Published: January 2008

We discuss two types of trace formula which arise from the inverse spectral problem for discrete Schrödinger operators as
L
= —Δ +
V
(
x
) where
V
is a bounded potential. One is the relationship between a potential and spectral data, and another is the one between the green function of
L
and periodic orbits of a state space.
Squeezing of Optical States on the CCR-Algebra
Authors: Honegger Reinhard , Rieckers Alfred
Published: January 2008

Squeezing processes are commonly described in terms of quadratic Hamiltonians, which generate unitary implementations of Bogoliubov transformations of the quantized electromagnetic field. Here the behaviour of the quasifree, the classical, and the coherent photon states under general squeezing Bogoliubov transformations is investigated. It is found that there is a great variety of mixed classical states, which remain classical under the squeezing operation, whereas each pure classical state becomes non-classical. Especially, some classical, microscopic first order coherent states remain classical and coherent of first order under one-mode squeezing. This contrasts squeezing of macroscopic coherent states.
A Complex Analytic Study on the Theory of Fourier Series on Compact Lie Groups
Authors: Saburi Yutaka
Published: January 2008

The characterization of Fourier series of real analytic functions and hyperfunctions on compact Lie groups is discussed by means of complex analysis.
Multiple Gamma Functions and Multiple $q$-Gamma Functions
Authors: Ueno Kimio , Nishizawa Michitomo
Published: January 2008

We give an asymptotic expansion (
the higher Stirling formula
) and an infinite product representation (
the Weierstrass canonical product representation
) of the Vigneras multiple gamma functions by considering the classical limit of the multiple

q

-gamma functions.
Finite-Dimensional Representations of Quantum Affine Algebras
Authors: Akasaka Tatsuya , Kashiwara Masaki
Published: January 2008

We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affme algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental representations is completely described by the poles of

R

-matrices. The conjecture is proved in the cases of type

A_n^{(1)}

and

C_n^{(1)}

.
Solvability of Equations for Motion of a Vortex Filament with or without Axial Flow
Authors: Tani Atusi , Nishiyama Takahiro
Published: January 2008

It is known that the motion of a vortex filament with axial flow in a perfect fluid is approximately described by a generalization of the localized induction equation. The unique solvability of the initial value problem for it is first established by parabolic regularization. As the axial flow effect vanishes, its solution converges to that of the localized induction equation. Analogous results are obtained in the spatially periodic case.
Semialgebraic Description of Teichmiiller Space
Authors: Komori Yohei
Published: January 2008

We give a concrete semialgebraic description of Teichmiiller space

T_g

of the closed surface group

Γ_g

of genus

g(≥ 2)

. Our result implies that for any

\textit{SL}_2(\mathbf R)

-representation of

Γ_g

, we can determine whether this representation is discrete and faithful or not by using

4g-6

explicit trace inequalities. We also show the connectivity and contractibility of

T_g

from the point of view of

\textit{SL}_2(\mathbf R)

-representations of

Γ_g

. Previously, these properties of _Tg _had been proved by using hyperbolic geometry and quasi-conformal deformations of Fuchsian groups. Our method is simple and only uses topological properties of the space of

\textit{SL}_2(\mathbf R)

-representations of

Γ_g

.
Monodromy at Infinity and Fourier Transform
Authors: Sabbah Claude
Published: January 2008

Let

f:U→\mathbf C

be a regular function on a smooth quasi-projective variety

U

. We compute the limit mixed Hodge structure (when

t→ ∞

) of the cohomology of the fibers

f= t

in terms of the Fourier transform of the Gauss–Manin system associated to

f

.
A Note on the Approximation Entropies of Certain Shifts
Authors: Nishiuchi Kiichi
Published: January 2008

Voiculescu has proposed several routes to quantum entropies. Among them, the notion of the "approximation entropies" is a group of four entropies with similar definitions, based on two kinds of approximations. The C*-cases are extensions of the classical topological entropy and the W*-cases are those of the measure-theoretic one. In this paper, we will focus on the approximation entropies and investigate the entropies of Powers' binary shifts with some condition and the Jones shifts.
Normal Algebraic Surfaces with Trivial Tricanonical Divisors
Authors: Zhang De-Qi
Published: January 2008

We prove that upto isomorphisms there are at least one and at most three rational log Enriques surfaces of index 3 and Type _A_17.
On Uniqueness of Commutative Rings of Weyl Group Invariant Differential Operators
Authors: Taniguchi Kenji
Published: January 2008

The uniqueness of commutative rings of classical Weyl group invariant differential operators is discussed. We show this uniqueness for trigonometric or elliptic potential cases under some order conditions. For rational potential cases, counter examples are constructed.
Hodge Theory and the Art of Paper Folding
Authors: Kapovich Michael , Millson John J.
Published: January 2008

Using Hodge theory and

L^2

-cohomology we study the singularities and topology of configuration and moduli spaces of polygonal linkages in the 2-sphere. As a consequence we describe the local deformation space of a folded paper cone in

\boldsymbol R^3

.
Plcard-Lefschetz Theory for the Universal Coverings of Complements to Affine Hypersurfaces
Authors: Shimada I.
Published: January 2008

We study the global monodromy on the middle homology group of the universal coverings of the complements to non-singular affine hypersurfaces which intersect the hyperplane at infinity transversely. This monodromy can be regarded as a deformation of the monodromy on the middle homology group of the affine hypersurfaces. We show that this representation becomes irreducible when the deformation parameter is generic.
Geometric Construction of $*$-Representations of the Weyl Algebra with Degree 2
Authors: Kurose Hideki , Nakazato Hiroshi
Published: January 2008

Let

\mathcal W_2

denote the Weyl algebra generated by self-adjoint elements

\{p_j,q_j\}_{j=1,2}

satisfying the canonical commutation relations. In this paper we discuss

*

-representations

\{π\}

of

\mathcal W_2

such that

π(p_j)

and

π(q_j)

(j=1, 2)

are essentially self-adjoint operators but

π

is not exponentiable to a representation of the associated Weyl system. We first construct a class of such

*

-representations of

\mathcal W_2

by considering a non-simply connected space

Ω= \boldsymbol R^2\setminus \{\boldsymbol a_1, ⋯, \boldsymbol a_N\}

and a one-dimensional representations of the fundamental group

π_1(Ω)

. Non-exponentiability of those

*

-representations comes from the geometry of the universal covering space

\tilde Ω

of

Ω

. Then we show that our

*

-representations of

\mathcal W_2

are related, by unitary equivalence, with Reeh–Arai's ones, which are based on a quantum system on the plane under a perpendicular magnetic field with singularities at

\boldsymbol a_1, ⋯, \boldsymbol a_N

, and, by doing that, we classify the Reeh–Arai's

*

-representations up to unitary equivalence. We further discuss extension and irreducibility of those

*

-representations. Finally, for the

*

-representations of

\mathcal W_2

, we calculate the defect numbers which measure the distance to the exponentiability.
Growth Order of Eigenfunctions of Schrödinger Operators with Potentials Admitting Some Integral Conditions II — Applications —
Authors: Arai Masaharu , Uchiyama Jun
Published: January 2008

In this paper we give applications of M. Arai and J. Uchiyama [2, Theorems 1.1 and 1.2], which treat the sharp estimates of the growth orders of the eigenfunctions of the Schrödinger operators with potentials oscillating violently at infinity. We can generalize the results of G.B. Khosrovshahi, H.A. Levine and L.E. Payne (Trans. Amer. Math. Soc., 253 (1979), 211-228) and H. Kalf and V.K. Kumar (Trans. Amer. Math. Soc., 275 (1983), 215-229). Also we generalize the result of S. Agmon (J. Analyse Math., 23 (1970), 1-25).
The Mean Ratio Set for $ax + b$ Valued Cocycles
Authors: Dajani Karma , Dooley Anthony H.
Published: January 2008

Let

X=\prod^∞_{\iota =1} Z_{l(\iota)}

be acted upon by the group

Γ=\bigoplus^∞_{\iota =1}Z_{l(\iota)}

of changes in finitely many coordinates and

μ

a

G

-measure on

X

which is nonsingular for the

Γ

-action on

X

. We consider cocycles on

(X, Γ, μ)

taking values in the

ax + b

group. We give a structure theorem for such cocycles, we define the mean ratio set which is a closed subgroup of the

ax + b

group and we exhibit for each closed subgroup a cocycle whose mean ratio set is the given subgroup.
On Localized Weak Precompactness in Banach Spaces
Authors: Matsuda Minoru
Published: January 2008

In this paper we make a study of
K
-weakly precompact sets
A
in Banach spaces. We give various characterizations of such sets by the effective use of the lifting theory, weak*-–
A
*-dentability and a
K
-valued weak*-measurable function constructed in the case where
A
is non-
K
-weakly precompact. These results also can be regarded as generalizations of corresponding ones on Pettis sets and weakly precompact sets.
Asymptotic Behavior of Blowup Solutions of a Parabolic Equation with the $p$-Laplacian
Authors: Fujii Ataru , Ohta Masahito
Published: January 2008

We consider the blowup problem for

u_t = Δ_pu + ∣ u ∣^{p–2}u

(

x\in Ω

,

t > 0

) under the Dirichlet boundary condition and

p > 2

. We derive sufficient conditions on blowing up of solutions. In particular, it is shown that every non-negative and non-zero solution blows up in a finite time if the domain

Ω

is large enough. Moreover, we show that every blowup solution behaves asymptotically like a self-similar solution near the blowup time. The Rayleigh type quotient introduced in Lemma A plays an important role throughout this paper.
Outer Automorphism Group of the Ergodic Equivalence Relation Generated by Translations of Dense Subgroup of Compact Group on its Homogeneous Space
Authors: Gefter Sergey L.
Published: January 2008

We study the outer automorphism group Out_Rr_ of the ergodic equivalence relation_Rr_ generated by the action of a lattice
Γ
in a semisimple Lie group on the homogeneos space of a compact group
K
. It is shown that Out_Rr_ is locally compact. If
K
is a connected simple Lie group, we prove the compactness of 0ut_Rr_ using the D. Witte's rigidity theorem. Moreover, an example of an equivalence relation without outer automorphisms is constructed.
Critères de Complétude des Vecteurs Propres Généralisés d'une Classe d'Opérateurs Non Auto-adjoints Compacts ou à Résolvante Compacte et Applications
Authors: Aimar Marie-Thérèse , Intissar Abdelkader , Paoli Jean-Martin
Published: January 2008

In this work we establish sufficient conditions on thé denseness of thé generalized eigenvectors for a class of compact (or compact résolvent) non self adjoint operators. We can apply our results to operators arising in many fields, particularly in field's theory and in abstract second order differential équations. Our results generalize some results of Aimar and al [1] and [2], Macaev and Keldysh [11] and Dunford-Schwartz [9].
The Feynman Representation for the Dirac Propagator with a Radially Symmetric Potential
Authors: Jefferies Brian
Published: January 2008

The dynamical group associated with the Dirac equation with a radially symmetric potential in four space-time dimensions is represented in terms of integrals with respect to operator valued set functions associated with the free Dirac operator. In coordinates in which

c = ℏ = 1

, the class of potentials treated includes Coulomb potentials

-a/r

with

|a| < 1

.
Reduced Free Products of Completely Positive Maps and Entropy for Free Product of Automorphisms
Authors: Choda Marie
Published: January 2008

The reduced free product of unital completely positive maps is defined. An invariant state on a
C
*-algebra for an automorphism (based on the free shift) is the composition of a state of a subalgebra with the reduced free product of expectations. Entropies for the reduced free product and the tensor product of an automorphism
γ
with the free shift coincide with the entropy of
γ
.
Quantization of Contact Manifolds
Authors: Kashiwara Masaki
Published: January 2008

We show the existence of the stack of micro-differential modules on an arbitrary contact manifold, although we cannot expect the global existence of the ring of micro-differential operators.
On the Solvability of Convolution Equations in Beurling's Distributions
Authors: Pahk Dae Hyeon , Sohn Byung Keun
Published: January 2008

Let

\mathscr D'_w

be the space of Beurling's generalized distributions on

\mathbf R^n

and

\mathscr E'_w

the spaces of generalized distributions which has compact support. We show that, for

S\in \mathscr E'_w

,

S \ast \mathscr D'_w = \mathscr D'_w

is equivalent to the following: Every generalized distribution

u\in \mathscr E'_w

with

S \ast u\in \mathscr D_w

is in

\mathscr D_w

.
High-energy Behavior of the Scattering Amplitude for a Dirac Operator
Authors: Ito Hiroshi T.
Published: January 2008

We study the high-energy behavior of the scattering amplitude and the total scattering cross section for a Dirac operator with a 4 x 4 matrix-valued potential. Moreover, in the electro-magnetic case, it is shown that the electric potential and the magnetic field can be reconstructed from the high-energy behavior of the scattering amplitude. The study of the high-energy behavior of the resolvent estimates is crucial for our proof.
Galilei Invariant Molecular Dynamics
Authors: Jäkel Christian D. , Hörmann Günther
Published: January 2008

We construct a model for a chemical reaction in the Heisenberg representation. The time evolution exists in the thermodynamic limit, independent of the particle density and the initial state. In mathematical terms, we establish a C*-dynamical system. Thus we can benefit from general results in algebraic quantum statistical mechanics, showing, for example, that equilibrium states exist. Galilei invariance of our nonrelativistic model is demonstrated by defining it directly on the Galilean space-time manifold, without reference to any coordinate system. PACS 05.30.Fk, 03.70.+ k, ll.10.Cd, 11.15.Tk
The Topological Structure of Polish Groups and Groupoids of Measure Space Transformations
Authors: Danilenko Alexandre I
Published: January 2008

It is proved that the groupoid of nonsingular partial isomorphisms of a Lebesgue space

(X,μ)

is weakly contractible in a “strong” sense: we present a contraction path which preserves invariant the subgroupoid of

μ

-preserving partial isomorphisms as well as the group of nonsingular transformations of

X

. Moreover, let

\mathcal R

be an ergodic measured discrete equivalence relation on

X

. The full group

[\mathcal R]

endowed with the uniform topology is shown to be contractible. For an approximately finite

\mathcal R

of type

\mathit{II}

or

\mathit{III}_λ

,

0≤λ<1

, the normalizer

N[\mathcal R]

of

\mathcal R

furnished with the natural Polish topology is established to be homotopically equivalent to the centralizer of the associated Poincaré flow. These are the measure theoretical analogues of the resent results of S. Popa and M. Takesaki on the topological structure of the unitary and the automorphism group of a factor.
The Quantum Weak Coupling Limit (II): Langevin Equation and Finite Temperature Case
Authors: Accardi Luigi , Frigerio Alberto , Lu Yun G.
Published: January 2008

We complete the program started in [4] by proving that, in the weak coupling limit, the matrix elements, in the collective coherent vectors, of the Heisenberg evolved of an observable of a system coupled to a quasi-free reservoir through a laser type interaction, converge to the matrix elements of a quantum stochastic process satisfying a quantum Langevin equation driven by a quantum Brownian motion. Our results apply to an arbitrary quasi-free reservoir so, in particular, the finite temperature case is included.
Circle Actions and Higher Elliptic Genera
Authors: Hara Yasuhiro
Published: January 2008

For a manifold with an _S_1-action, we define generalized elliptic genera by using the orbit map and generalize Hirzebruch-Slodowy's formula in [9]. As a result, we have vanishing theorems of higher elliptic genera and higher twisted Â-genera. We also generalize elliptic genera of level
N
for stable almost complex manifolds and have a similar vanishing theorem.
Symmetric Flat Connections, Triviality of Loi's Invariant and Orbifold Subfactors
Authors: Goto Satoshi
Published: January 2008

We define a notion of symmetric connections on subfactors and get a sufficient condition for a subfactor to have a symmetric connection. We also give a necessary and sufficient condition for Loi's invariant of a non-strongly outer automorphism of a subfactor to be trivial in the case with a symmetric connection. We apply this result to non-AFD
SU
(_n_k subfactors and construct orbifold subfactors of non-AFD
SU
(_n_k subfactors as well as the AFD case, as conjectured in our previous work. This generalizes constructions of Evans-Kawahigashi and Xu.
Hermitian and Positive $C$-Semigroups on Banach Spacest
Authors: Li Yuan-Chuan , Shaw Sen-Yen M.
Published: January 2008

Two classes of operator families, namely

n

-times integrated

C

-semigroups of hermitian and positive operators on Banach spaces, are studied. By using Gelfand transform and a theorem of Sinclair, we prove some interesting special properties of such

C

-semigroups. For instances, every hermitian nondegenerate

n

-times integrated

C

-semigroup on a reflexive space is the

n

-times integral of some hermitian

C

-semigroup with a densely defined generator; an exponentially bounded

C

-semigroup on

L^p(μ)

(

1 < p < ∞

) dominates

C

(a positive injective operator) if and only if its generator

A

is bounded, positive , and commutes with

C

; when

C

has dense range, the latter assertion is also true on

L^p(μ)

and

C_0(Ω)

.
Classification of Paragroup Actions on Subfactors
Authors: Kawahigashi Yasuyuki
Published: January 2008

We define “a crossed product by a paragroup action on a subfactor” as a certain commuting square of type

\mathrm{II}_1

factors and give their complete classification in a strongly amenable case (in the sense of S. Popa) in terms of a new combinatorial object which generalizes Ocneanu's paragroup.

As applications, we show that the subfactor

N ⊂ M

of Goodman–de la Harpe–Jones with index

3 + \sqrt 3

is not conjugate to its dual

M ⊂ M_1

by showing the fusion algebras of

N

-

N

bimodules and

M

-

M

bimodules are different, although the principal graph and the dual principal graph are the same. We also make an analogue of the coset construction in RCFT for subfactors in our settings.
The Chern Character of the Symmetric Space $\textit{El}$
Authors: Watanabe Takashi
Published: January 2008

The purpose of this paper is to describe the Chern character homomorphism of the compact symmetric space

\textit{El}

.
Euler–Poincaré Characteristic and Polynomial Representations of Iwahori–Hecke Algebras
Authors: Duchamp Gérard H. E. , Krob Daniel , Lascoux Alain , Leclerc Bernard , Scharf Thomas , Thibon Jean-Yves
Published: January 2008

The Hecke algebras of type

A_n

admit faithful representations by symmetrization operators acting on polynomial rings. These operators are related to the geometry of flag manifolds and in particular to a generalized Euler–Poincaré characteristic denned by Hirzebruch. They provide

q

-idempotents, together with a simple way to describe the irreducible representations of the Hecke algebra. The link with Kazhdan–Lusztig representations is discussed. We specially detail the case of hook representations, and as an application, we investigate the hamiltonian of a quantum spin chain with

U_q(\mathfrak{su}(1/1))

symmetry.
General Existence Theorems for Orthonormal Wavelets, an Abstract Approach
Authors: Baggett Larry , Carey Alan L. , Moran William , Ohring Peter
Published: January 2008

Methods from noncommutative harmonic analysis are used to develop an abstract theory of orthonormal wavelets. The relationship between the existence of an orthonormal wavelet and the existence of a multi-resolution is clarified, and four theorems guaranteeing the existence of wavelets are proved. As a special case of the fourth theorem, a generalization of known results on the existence of smooth wavelets having compact support is obtained.
Perturbation Formulas for Traces on $C^*$-algebras
Authors: Hansen Frank , Pedersen Gert K.
Published: January 2008

We introduce the Frechet differential of operator functions on

C^*

-aIgebras obtained via spectral theory from ordinary differentiate functions. In the finite-dimensional case this differential is expressed in terms of Hadamard products of matrices. A perturbation formula with applications to traces is given.
Representations of Witt Algebras
Authors: Rao Senapathi Eswar
Published: January 2008

In this paper we construct new families of representations for the Lie-algebra of diffeomorphisms of the torus
Td
and describe its sub representations.
Indecomposable Restricted Representations of Quantum $\textit{sl}_2$
Authors: Chari Vyjayanthi , Premet Alexander
Published: January 2008

We construct and classify all the indecomposable restricted representations of

U_q(\textit{sl}_2)

when

q

is a root of unity.
Riemann–Hilbert Factorizations and Inverse Scattering for the AKNS-Equation with $L^1$-Potentials I
Authors: Dorfmeister Josef , Szmigielski Jacek
Published: January 2008

A detailed group theoretic approach is developed for the

2 \times 2

AKNS system with potentials supported on the half-line. This approach uses consistently Riemann–Hilbert splittings interpreted as factorizations in certain Banach Lie groups. In particular, it is shown how meromorphic splittings introduced by Beals and Coifman can be replaced with regular Riemann–Hilbert splittings leading to the group theoretic notion of a scattering data.
Free Convolution and the Random Sum of Matrices
Authors: Speicher Roland
Published: January 2008

We show that the spectral measure of the sum of two selfadjoint matrices is 'almost surely' given by the free convolution (in the sense of Voiculescu) of the spectral measures of the two matrices if their size tends to infinity.
Subcoercive and Subelliptic Operators on Lie Groups: Variable Coefficients
Authors: ter Elst A. F.M. , Robinson Derek W.
Published: January 2008

Let

a_1, \ldots, a_{d'}

 be an algebraic basis of rank

r

in a Lie algebra

\mathfrak g

of a connected Lie group

G

and let

A_τ

be the left differential operator in the direction

a_i

on the

L_p

-spaces with respect to the left, or right, Haar measure, where

p\in [1, \infty]

. We consider

m

-th order operators

H= Σ c_αA^α

with complex variable bounded coefficients 

c_α

which are subcoercive of step

r

, i.e., for all

g\in G

the form obtained by fixing the 

c_α

at

g

is subcoercive of step

r

and the ellipticity constant is bounded from below uniformly by a positive constant. If the principal coefficients are

m

-times differentiate in

L_∞

in the directions of  

a_1, \ldots, a_{d'}

we prove that the closure of

H

generates a consistent interpolation semigroup

S

which has a kernel. We show that

S

is holomorphic on a non-empty

p

-independent sector and if

H

is formally self-adjoint then the holomorphy angle is

π/2

. We also derive ‘Gaussian’ type bounds for the kernel and its derivatives up to order

m-1

.
Topes of Oriented Matroids and Related Structures
Authors: Handa Keiichi
Published: January 2008

An oriented matroid can be viewed as a combinatorial abstraction of the facial incidence relations of the polyhedral cones induced by a finite arrangement of oriented hyperplanes in

\mathrm R^d

through the origin. “Topes” of an oriented matroid correspond to maximal polyhedral cones. This paper discusses three structures related to topes of oriented matroids, namely, acycloids,

L^1

-systems and median systems. It is shown that

L^1

-systems are closely related to convex geometries. Median systems are introduced as an equivalent notion of median graphs, and they are, in particular, applied to characterize median graphs. Perturbations of acycloids and

L^1

-systems are studied.
Finiteness of Mordell-Weil Groups of Kuga Fiber Spaces of Abelian Varieties
Authors: Saito Masa-Hiko
Published: January 2008

In this paper, we will study Mordell-Weil groups of Kuga fiber spaces of abelian varieties associated to the standard symplectic representation classified by Satake. We will show the finiteness theorem for them with a few exceptions by using the Hodge theory and Borel-Wallach's vanishing theorem.
Projection Maps for Tensor Products of $\mathcal{gl}(\mathcal r, \boldsymbol C)$-Representations
Authors: Benkart Georgia , Britten Daniel , Lemire Frank
Published: January 2008

We investigate the tensor product

\mathscr T =V(λ^1)\otimes ⋯ \otimes V(λ^m)

of the finite dimensional irreducible

\mathscr G = \mathcal{gl}(\mathcal r, \boldsymbol C)

modules labelled by partitions

λ^1,⋯,λ^m

of

m

not necessarily distinct numbers

n_1,⋯,n_m

respectively. We determine the centralizer algebra

\textit{End}_{\mathscr G}(\mathscr T)

and the projection maps of

\mathscr T

onto its irreducible

\mathscr G

-summands and give an explicit construction of the corresponding maximal vectors. In the special case that

n_i = 1

for

i = 1,⋯,m

, the results reduce to the well-known results of Schur and Weyl.
Operator Representations of $\boldsymbol R_q^2$
Authors: Schmüdgen Konrad
Published: January 2008

We study the operator relation
ab
=
qba
, where |q| = 1, for self-adjoint operators.
On Orthogonality of Two Subfactors Constructed from Factor Maps
Authors: Sano Takashi
Published: January 2008

Two subfactors constructed from two factor maps are considered. A characterization is given for the angles between two subfactors to become trivial.
Algebraic Aspects in Modular Theory
Authors: Yamagami Shigeru
Published: January 2008

Algebraic features of modular theory in von Neumann algebras are discussed with the help of Haagerup's
Lp
-theory and some notational devices.
Complex Quantum Groups and Their Real Representations
Authors: Podlés Piotr
Published: January 2008

We define

\ast

-Hopf algebras

\mathit{Fun}(\mathit{SL}_q(N, ℂ; ε_1,…, ε_N))

,

\mathit{Fun}(O_q(N, ℂ; ε_1,…, ε_N))

and

\mathit{Fun}(\mathit{Sp}_q(n, ℂ; ε_1,…, ε_{2n}))

as the real complexifications of

\ast

-Hopf algebras

\mathit{Fun}(\mathit{SU}_q(N, ℂ; ε_1,…, ε_N))

,

\mathit{Fun}(O_q(N, ℂ; ε_1,…, ε_N))

and

\mathit{Fun}(\mathit{Sp}_q(N, ℂ; ε_1,…, ε_{2n}))

of [RTF] (for

q > 0

). Such construction can be done for each coquasitriangular (CQT)

\ast

-Hopf algebra

\mathbf A

. The obtained object

\mathbf A^{ℂℝ}

is also a CQT

\ast

-Hopf algebra. We describe the theory of corepresentations of

\mathbf A^{ℂℝ}

in terms of such a theory for

\mathbf A

.
Principal Fiber Bundle Interpretation of the KP-Hierarchy
Authors: Dorfmeister Josef , Szmigielski Jacek
Published: January 2008

The Grassmannian and the Lax pair approaches to the Kadomtsev-Petviashvili (KP) hierarchy are analyzed in the framework of (formal) principal fiber bundles. The underlying factorization problem is formulated as a local triviality condition. In particular the common object in the two approaches — the Baker function — coordinatizes the base space, the fiber consists of certain generalized differential operators. An example is constructed to show that despite the apparent similarity to the splitting in [8], the local triviality condition cannot be given a group theoretic interpretation.
Some Descriptive-Set-Theoretical Problems in Complexity Theory
Authors: Tanaka Hisao
Published: January 2008

We bring some descriptive-set- theoretical problems into complexity theory. We here deal with the imiformization problem and the separation problem. It is shown that 1) there exists an oracle

A

such that for some set

S\in \mathbf P[A]

the uniformizator

U

, is not in

\mathbf{NP}[A]

, 2) there is an oracle

A

such that

\mathrm{Sep} ( \mathbf{NP}[A]

) does not hold and hence so does not

\mathrm{Unif} ( \mathbf{coNP}[A])

, and 3) there is an oracle

A

such that

\mathrm{Sep}( \mathbf{NEXT}[A]

) does not hold and hence so does not

\mathrm{Unif}( \mathbf{coNEXT}[A]

).
Multiple Solutions for a Class of Non-local Problems for Semilinear Elliptic Equations
Authors: Chabrowski Jan H.
Published: January 2008

The purpose of this papers is to investigate the solvability of a class of non-local problems in the sense of Bitsadze-Samarskii (see (_N_1)). We prove the existence of multiple solutions under the assumptions of the Ambrosetti-Prodi type on a nonlinear function
g
.
Orientations of $\textit{Spin}$ Bundles and Symplectic Cobordism
Authors: Gorbunov Vassily , Ray Nigel
Published: January 2008

We analyse certain cofibrations of projective spaces in terms of Thorn complexes of

\textit{Spin}

bundles, and by applying the symplectic cobordism functor we are able to deduce new relations amongst the elements

ϕ_i

in the symplectic bordism ring.
Monodromy Representations for Generalized Knizhnik-Zamolodchikov Equations and Hecke Algebras
Authors: Cherednik Ivan
Published: January 2008

In the paper generalizations of the Knizhnik-Zamolodchikov equation with symmetries in Weyl groups for arbitrary classical r-matrices are studied. Their monodromy representations are calculated explicitly in terms of Hecke algebras and affine Hecke algebras for basic examples.
A Characterization of Pettis Sets in Dual Banach Spaces
Authors: Matsuda Minoru
Published: January 2008

In this paper, we give a characterization of Pettis sets in dual Banach spaces in terms of δ-Rademacher trees. This is a generalization of our Theorem 1 in [1].
Partial *-Algebras of Closable Operators. II. States and Representations of Partial *-Algebras
Authors: Antoine Jean-Pierre , Inoue Atsushi , Trapani Camillo
Published: January 2008

This second paper on partial Op*-algebras is devoted to the theory of representations. A new definition of invariant positive sesquilinear forms on partial *-algebras is proposed, which enables to perform the familiar GNS construction. In order to get a better control of the corresponding representations, we introduce and study a restricted class of partial Op*-algebras, called partial GW*-algebras, which turn up naturally in a number of problems. As an example, we extend Powers' results about the standardness of GNS representations of abelian partial *-algebras.
A Generalization of Eichler Integrals and Certain Local Systems over Spin Riemann Surfaces
Authors: Saito Kyoji
Published: January 2008

Let

(X, K_X^{1/2})

be a spin Riemann surface – a Riemann surface together with a halfcanonical bundle (4.1) – of genus

≥ 2

. By using infinite dimensional representations of the fundamental group of

X

, we obtain many local systems on

X

, which taken together define

a resolution of the halfcanonical ring of

X

and indicate a

non-abelian theory of abelian integrals on

X

. The work has a root in a study of the complex structure on the Fricke moduli space [14].
High-order Uniform Convergence Estimation of Boundary Solutions for Laplace's Equation
Authors: Hayakawa Kantaro , Iso Yuusuke
Published: January 2008

Treated in this paper is Laplace's equation with the Neumann condition. Uniform convergence estimation of boundary element methods for this problem was done by Iso [1]. The aim of this paper is to improve the estimates given in [1] and to show high-order uniform convergence of the boundary element scheme.
Stochastic Integration on the Full Fock Space with the Help of a Kernel Calculus
Authors: Speicher Roland
Published: January 2008

We develop a stochastic integration theory with respect to creation, annihilation and gauge operators on the full Fock space. This is done by using a kernel representation for a large class of bounded operators on the full Fock space. It is shown that the kernels form a Banach algebra. Having established the definition of processes and stochastic integrals we go on to prove an Ito formula and use this for examining stochastic evolutions and constructing dilations of special completely positive semigroups. Explicit solutions of the corresponding stochastic differential equations are given.
A Basis of Symmetric Tensor Representations for the Quantum Analogue of the Lie Algebras $B_n$, $C_n$ and $D_n$
Authors: Nakashima Toshiki
Published: January 2008

We give a basis of the finite dimensional irreducible representation of

U_q(X_n)

(

X=B,C,D

) with highest weight

N\Lambda_1

(

N\in ℤ_{ ≥ 0}

), which we call “symmetric tensor representation”.

This basis is orthonormal and consists of weight vectors. The action of

U_q(X_n)

is given explicitly.
On a Theorem by Florek and Slater on Recurrence Properties of Circle Maps
Authors: Lohöfer Georg , Mayer Dieter
Published: January 2008

An obviously little known result by Florek and Slater about the exact recurrence times of the sequence

mβ \mod 1

with respect to an arbitrary connected interval

I

in the unit interval is generalized to disconnected intervals

I_{\overgroup{a,b}} = [0, a)∪(b, 1)

when

b= 1-a

,

a < 1/2

. It is shown that the formula of Florek and Slater expressing the possible recurrence times in terms of the interval

I

is valid also in our case. This let us expect that this formula is valid also for general intervals of the form

I_{\overgroup{a,b}}

. The relation of this result to the recurrence properties of integrable Hamiltonian systems with two degrees of freedom is obvious.
Uniform Convergence Theorems of Boundary Solutions for Laplace's Equation
Authors: Iso Yuusuke
Published: January 2008

The numerical treatments for two-dimensional Laplace's equation with the Neumann condition are dealt with. The author gives a new numerical scheme for the boundary element methods to solve this problem. In this scheme, approximation for the domain is taken account of. The author gives also the uniform convergence theorem for this new scheme, and proves it rigorously. This new scheme is both mathematical and practical.
High Energy Resolvent Estimates for Generalized Many-Body Schrödinger Operators
Authors: Jensen Arne
Published: January 2008

We prove high energy resolvent estimates for a class of generalized many-body Schrödinger operators. The proofs are based on an extension of Mourre's commutator method.
Fubini Products of $C^*$-algebras and Applications to $C^*$-exactness
Authors: Huruya Tadasi , Kye Seung-Hyeok
Published: January 2008

For

C^*

-algebras

A

and

B

, we investigate necessary and sufficient conditions for which the Fubini product

A\otimes_F B

coincides with the ordinary minimal tensor product

A\otimes B

. As an application of our methods, we also give several necessary and sufficient conditions for

C^*

-exactness.
Minimizing Indices of Conditional Expectations onto a Subfactor
Authors: Hiai Fumio
Published: January 2008

For a pair of factors

M⊇N

, let

\mathcal E (M, N)

be the set of all conditional expectations from

M

onto

N

. We characterize

E_0 \in \mathcal E (M, N)

whose index is the minimum of

\{\mathrm{Index}\ E:\ E\in \mathcal E (M, N)\}

. When

M⊇N

are

\mathrm{II}_1

factors, we establish the relation between

\mathrm{Index}\ E_0

and

[M:N]

.