bluuebunny/crossref_metadata_2025 huggingface dataset:
Extended Affine Root Systems III (Elliptic Weyl Groups)
Authors: Saito Kyoji , Takebayashi Tadayoshi
Published: January 2008

We give a presentation of an elliptic Weyl group
W
(
R
) (=the Weyl group for an elliptic root system*)
R
) in terms of the elliptic Dynkin diagram
Γ
(
R, G
) for the elliptic root system. The presentation is a generalization of a Coxeter system: the generators are in one to one correspondence with the vertices of the diagram and the relations consist of two groups : i) elliptic Coxeter relations attached to the diagram, and ii) a flniteness condition on the Coxeter transformation attached to the diagram. The group defined only by the elliptic Coxeter relations is isomorphic to the central extension
W
(
R
,
G
) of
W
(
R
) by an infinite cyclic group, called the hyperbolic extension of
W
(
R
). *) an elliptic root system=a 2-extended affine root system (see the introduction and the remark at its end).
Second Order Perturbation Bounds
Authors: Bist Vikas , Vasudeva Harkrishan L.
Published: January 2008

With a view to studying perturbation bounds, the class of functions

f

for which

\Vert df(A)\Vert = \Vert f^{(1)}(A)\Vert

and

\Vert d^{(2)} f(A)\Vert = \Vert f^{(2)}(A)\Vert

, where

d^kf(A)

(respectively

f^{(k)}(A)

) denotes the

k

-th Frechet (ordinary) derivative,

k=1,2

, has been investigated.
On Tuples of Commuting Compact Operators
Authors: Bhattacharyya Tirthankar
Published: January 2008

The joint spectrum of commuting operators, as introduced by Taylor, has been shown by Cho and Takaguchi to be the set of joint eigenvalues in the case of matrices. These joint eigenvalues can be read off from their simultaneous uppertriangularization. We prove here a similar result for compact operators on Banach spaces.
Growth Order of Eigenfunctions of Schrödinger Operators with Potentials Admitting Some Integral Conditions I — General Theory —
Authors: Arai Masaharu , Uchiyama Jun
Published: January 2008

In this paper we consider the sharp estimates of the growth orders of the eigenfunctions of the Schrödinger operators with potentials oscillating violently at infinity. We make use of the modified Kato's method (Comm. Pure Appl. Math., 12 (1959), 403-425) and we apply the ideas of J. Uchiyama and O. Yamada (Publ. RIMS, Kyoto Univ., 26 (1990), 419-449). Applications will be given in the next paper [2] in this issue.
On the K-Theory of Cuntz–Krieger Algebras
Authors: Pask David , Raeburn Iain
Published: January 2008

We extend the uniqueness and simplicity results of Cuntz and Krieger to the countably infinite case, under a row-finite condition on the matrix

A

. Then we present a new approach to calculating the K-theory of the Cuntz–Krieger algebras, using the gauge action of

\mathbf T

, which also works when

A

is a countably infinite

0

-

1

matrix. This calculation uses a dual Pimsner-Voiculescu six-term exact sequence for algebras carrying an action of

\mathbf T

. Finally, we use these new results to calculate the K-theory of the Doplicher–Roberts algebras.
Compact Quantum Groups of Face Type
Authors: Hayashi Takahiro
Published: January 2008

We give a generalization of the compact quantum group theory of S. Woronowicz, or rather its variant due to T. Koornwinder and M. Dijkhuizen. Our framework covers algebras of
L
-operators of lattice models efface type without spectral parameters and "Galois quantum group" of AFD Il1-subfactors of index < 4.
CQ*-Algebras: Structure Properties
Authors: Bagarello Fabio , Trapani Camillo
Published: January 2008

Some structure properties of CQ * -algebras are investigated. The usual multiplication of a quasi *-algebra is generalized by introducing a weak- and strong product. The *-semisemplicity is defined via a suitable family of positive sesquilinear forms and some consequences of this notion are derived. The basic elements of a functional calculus on these partial algebraic structures are discussed.
A Remark on Singular Perturbation Methods via the Lyapunov-Schmidt Reduction
Authors: Taniguchi Masaharu
Published: January 2008

For some reaction-diffusion equations, Lyapunov-Schmidt reduction was shown to be applicable to construct singularly perturbed equilibrium solutions. For this application, it is indispensable to show that some inverse operator are uniformly bounded. In this paper, we give an elementary proof of this fact.
Traces, Unitary Characters and Crossed Products by $ℤ$
Authors: Thomsen Klaus
Published: January 2008

We determine the character group of the infinite unitary group of a unital exact

C^*

-algebra in terms of K-theory and traces and obtain a description of the infinite unitary group modulo the closure of its commutator subgroup by the same means. The methods are then used to decide when the state space

SK_0(A\times_\alpha ℤ)

of the

K_0

group of a crossed product by

ℤ

is homeomorphic to

SK_0(A)_{α_*}

or

T(A)_{α^*}

. We also consider the crossed product

A \times_α G

by a discrete countable abelian group

G

and give necessary and sufficient conditions for the equality

T(A \times_α G) = T(A)_α

to hold.
The Cohomology Rings of Some $p$-Groups
Authors: Chin Angelina Y.M.
Published: January 2008

We determine the

\mathrm{mod}

-

p

cohomology ring and some of the integral cohomology ring structure of a

p

-group expressible as an extension with kernel cyclic of order

p

and quotient

C_{p^m} \oplus C_{p^n}

, where

m, n > 1

.
Global Existence of Small Solutions to Semilinear Schrödinger Equations with Gauge Invariance
Authors: Chihara Hiroyuki
Published: January 2008

We present the global existence theorem for semilinear Schrödinger equations satisfying gauge invariance. Combining the local existence results and a priori estimates, we construct global solutions with small initial data.
Minimal Affinizations of Representations of Quantum Groups: the Rank 2 Case
Authors: Chari Vyjayanthi
Published: January 2008

If

U_q (\mathfrak g)

is a finite-dimensional complex simple Lie algebra, an affinization of a finite-dimensional irreducible representation

V

of

U_q (\mathfrak g)

is a finite-dimensional irreducible representation

\hat V

of

U_q (\mathfrak g)

which contains

\hat V

with multiplicity one, and is such that all other

U_q (\mathfrak g)

-types in

\hat V

have highest weights strictly smaller than that of

V

. We define a natural partial ordering

≼

on the set of affinizations of

V

. If

\mathfrak g

is of rank

2

, we show that there is a unique minimal element with respect to this order and give its

U_q (\mathfrak g)

-module structure when

\mathfrak g

is of type

A_2

or

C_2

.
On Boundedness and $\|\cdot \|_p$ Continuity of Second Quantisation
Authors: Araki Huzihiro , Sinha Kalyan B. , Sunder Viakalathur S.
Published: January 2008

In this short note, we determine precisely which operators have the property that their (full, symmetric or antisymmetric) second quantisation is an operator which is bounded or belongs to one of the various Schatten ideals; we also note that in ‘the interior’ of the natural domain, the second quantisation is a continuous map.
The Flow of Weights in Subfactor Theory
Authors: Winsløw Carl
Published: January 2008

We define a Connes-Takesaki type flow of weights for any inclusion of factors. It is shown that Popa's classification of strongly amenable subfactors as well as some new structural results on type III-subfactors can be stated in a unified way using this invariant. The invariant also separates certain "exotic" examples of subfactors which are not covered by that classification.
Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. II. Solitons, Antisolitons, and their Bound States
Authors: Ruijsenaars Simon N. M.
Published: January 2008

We present an explicit construction of an action-angle map for the nonrelativistic Calogero-Moser systems with 1/sh2 and —1/ch2 pair potentials, and for relativistic generalizations thereof. The map is used to obtain extensive information concerning dynamics and scattering. We also discuss the relation between the relativistic
N
-particle systems and the
N
-particle-like solutions of various soliton PDEs, including the sine-Gordon equation.
On the Admissibility of Singular Perturbations in Cauchy Problems II
Authors: Ashino Ryuichi
Published: January 2008

We shall give a new proof of the admissibility of singular perturbations, which was introduced by the author [2], without the assumption on the characteristic roots assumed in [2] using the method introduced by the author in [5, Appendix].
On Unbounded Positive *-Representationson Fréchet-Domains
Authors: Heinrichs Wolf-Dieter
Published: January 2008

Let
D
be a Fréchet-domain from Op*-algebra, abbreviated F-domain. The present paper is concerned with the study of positive *-representations of
L
+(
D
), of the Calkin representation of
L
+(
D
) and of bounded sets in ultrapower
Du
. For this the density property plays an important role. It was introduced by S. Heinrich for locally convex spaces in [2].

In the paper [3] we gave several characterizations of the density property of an F-domain
D
. In this work we give a characterizations of continuity of positive *-representations and Calkin representation of
L
+(
D
) by the density property of
D
. This generalizes the well-known result due to K. Schmiidgen, see [12], Further we describe bounded subsets in ultrapower
Du
. If
D
has the density property, then every bounded set
M
c
Du
has a simple structure: For each bounded set
M c Du
there exists a bounded set
N
c
D
with
M
c'
Nu
. S. Heinrich proved an analogous result for bounded ultrapowers on locally convex spaces.
An Estimate of the Depth from an Intermediate Subfactor
Authors: Wierzbicki Jerzy
Published: January 2008

We show that for a triple

K ⊂ N ⊂ M

of type

\mathrm{II}_1

factors the depth of the inclusion “

K ⊂ M

” is not greater than the maximum of depths of the inclusions “

K ⊂ N

” and “

N ⊂ M

” provided there is such a factor

P

, that the diagram

\begin{smallmatrix}
P & \subset & M\\
\cup & & \cup \\
K& \subset & N
\end{smallmatrix}

is commuting and co-commuting square (or a non-degenerate commuting square) of type

\mathrm{II}_1

factors.
On the Irregularity of Special Non-Canonical Surfaces
Authors: Konno Kazuhiro
Published: January 2008

We consider minimal surfaces of general type whose canonical map is "special" meaning that it is composed of a pencil or its degree is high. We characterize, to some extent, Beauville's examples of irregularity 2 in the pencil case, and show that the irregularity is at most 12 when the canonical degree is 5.
The Structure of Hilbert Flag Varieties
Authors: Helminck Gerard F. , Helminck Aloysius G.
Published: January 2008

In this paper we present a geometric realization of infinite dimensional analogues of the finite dimensional representations of the general linear group. This requires a detailed analysis of the structure of the flag varieties involved and the line bundles over them. In general the action of the restricted linear group can not be lifted to the line bundles and thus leads to central extensions of this group. It is determined exactly when these extensions are non-trivial. These representations are of importance in quantum field theory and in the framework of integrable systems. As an application, it is shown how the flag varieties occur in the latter context.
Yangians and Gelfand–Zetlin Bases
Authors: Nazarov Maxim , Tarasov Vitaly
Published: January 2008

We establish a connection between the modern theory of Yangians and the classical construction of the Gelfand–Zetlin bases for the Lie algebra

\mathfrak{gl}_n

. Our approach allows us to produce the

q

-analogues of the Gelfand–Zetlin formulae in a straightforward way.
Quantization in Polar Coordinates and the Phase Operator
Authors: Dubin Daniel A. , Hennings Mark A. , Smith Thomas B.
Published: January 2008

We review some of the difficulties previously encountered in defining the phase operator for finite quantum systems. We then propose the Wigner–Weyl quantization of the angle function

φ

on phase space as the phase operator, and derive a closed expression for its matrix elements with respect to the Hermite functions. We also determine the quantization of

e^{iφ}

, which turns out to be a weighted shift operator, its spectrum and that of its adjoint.

This is done in the framework of quantization of a certain symbol class of phase space distributions, specialized to those which depend on one variable only. After recalling some results for the position and momentum variables, we apply the scheme to functions of radius or angle. We give necessary and sufficient conditions for operators obtained by quantizing functions of the angle to be elements of

\mathscr L^+ [\mathscr S(\mathbf R)]

and

\mathscr L^+ [\mathscr S (\mathbf R), L^2(\mathbf R)]

, and a sufficient condition for boundedness.

We then consider the associated questions of commutation relations and uncertainties for operators in

\mathscr L^+ [\mathscr S(\mathbf R), L^2(\mathbf R)]

, which we define as bilinear forms. As must be the case, the commutator between our phase operator and the number operator exhibits noncanonical terms. Not surprisingly, the Poisson bracket of their phase space symbols also exhibits a noncanonical term.
A Characterization for Fourier Hyperfunctions
Authors: Chung Jaeyoung , Chung Soon-Yeong , Kim Dohan
Published: January 2008

The space of test functions for Fourier hyperfunctions is characterized by two conditions

\sup |φ (x)| \exp k|x|<∞

and

\sup|\hat φ(ξ) | \exp h|ξ|<∞

for some

h,k>0

. Combining this result and the new characterization of Schwartz space in [1] we can easily compare two important spaces

\mathcal F

and

\mathcal S

which are both invariant under Fourier transformations.
Operators Characterized by Certain Cauchy-Schwarz Type Inequalities
Authors: Watanabe Hideharu
Published: January 2008

A Hilbert space operator

T

satisfying

\begin{align*}
&\text{either } && (**) && |(T ξ, η)|^2 ≤ (|T| _ξ,ξ) (|T| _η,η)\ \text{for all } ξ, η\in \mathcal H, \\
&\text{or } && (*) && |(T ξ, ξ)| ≤ (|(T|_ξ,ξ) \ \text{for all } ξ\in \mathcal H,
\end{align*}

is studied. The condition (

**

) defines a slightly larger class than the hyponormality, and for compact operators (

**

) is equivalent to the normality. The condition (

*

) is characterized by using an operator whose numerical radius is less than 1, and among other things we show that (

*

) and the normality are equivalent for matrices. Moreover, we show that (

*

) and the normality are equivalent for trace class operators in Appendix.
Fibrewise Decomposition of Generalized Suspension Spaces and Loop Spaces
Authors: Oda Nobuyuki
Published: January 2008

We work in the category

\mathbf{Top}^B_B

of fibrewise pointed topological spaces over

B

. Let

Γ

be a co-Hopf space (which need not be co-associative) in

\mathbf{Top}^B_B

. The

Γ_B

-suspension space

Γ_BX

and the

Γ_B

-loop space

Γ^*_BX

of a fibrewise pointed space

X

over

B

are defined as generalization of the usual suspension space

ΣX

and the loop space

ΩX

respectively,

Γ_B

-suspension spaces and

Γ_B

-loop spaces have some properties similar to those of the usual suspension spaces and loop spaces. This is an example of Eckmann–Hilton duality. In this paper, decomposition theorems of

Γ_B

-suspension space

Γ_BX

and

Γ_B

-loop space

Γ^*_BX

are proved. Short exact sequences of homotopy sets involving

Γ_B

-suspension spaces or

Γ_B

-loop spaces are obtained in the category of algebraic loops.
Classical Theta Functions and Quantum Tori
Authors: Weinstein Alan
Published: January 2008

The Schwartz kernel of the multiplication operation on a quantum torus is shown to be the distributional boundary value of a classical multivariate theta function. The kernel satisfies a Schrödinger equation in which the role of time is played by the deformation parameter

ℏ

and the role of the hamiltonian by a Poisson structure. At least in some special cases, the kernel can be written as a sum of products of single variable theta functions.
Generalised Mean Averaging Interpolation by Discrete Cubic Splines
Authors: Shrivastava Manjulata
Published: January 2008

The aim of this work is to introduce for a discrete function, certain discrete integrals which may reduce in particular to usual Riemann Stieltjes integrals. We name them as Discrete Stieltjes integrals. The existence and convergence of a discrete cubic interpolatory spline whose discrete Stieltjes integrals between consecutive meshpoints match with the corresponding integrals of a given periodic discrete function, are studied.
Quantized Radiation States from the Infinite Dicke Model
Authors: Honegger Reinhard , Rieckers Alfred
Published: January 2008

By interpreting infinitely many two-level atoms as a mean field quantum lattice system in a recent paper the time evolution of the Dicke Maser model has been elaborated in terms of operator algebraic methods. Using these results, here the emitted radiation of the infinite Dicke model is investigated. It is shown how the collective behaviour of the atoms influences the quantized radiation, which for large times becomes classically coherent (in the sense of Glauber). The field modes which are (approximately) resonant with the level-splitting energy of the atoms are found to be the essential part of the generated coherent light, and thereby determine its macroscopic nature. Furthermore, the destruction and revival of coherence, the mean number of the emitted photons during the time evolution, as well as their spatial distribution are discussed.
Existence of the Greek Letter Elements in the Stable Homotopy Groups of $E(n)_*$-Localized Spheres
Authors: Shimomura Katsumi , Yokotani Masaaki
Published: January 2008

Let

E_2^{*.*}(X)

denote the

E_2

-term of the Adams–Novikov spectral sequence converging to the homotopy groups of

X

. We can define the Greek letter elements in

E_2^{*.*}(L_nS^0)

in the same way as those in

E_2^{*.*}(S^0)

. We show that these of

E_2^{*.*}(L_nS^0)

are permanent cycles, though we know little for

E_2^{*.*}(S^0)

.
The $E_7$ Commuting Squares Produce $D_{10}$ as Principal Graph
Authors: Evans David E. , Kawahigashi Yasuyuki
Published: January 2008

We prove that the (two) connections, or commuting squares, on the Coxeter–Dynkin diagram

E_7

produce a subfactor with principal graph

D_{10}

. This was conjectured by J.-B. Zuber in connection with modular invariants in conformal field theory, and solve the last case of computing the flat parts of the connections on Coxeter–Dynkin diagrams with index less than 4.
Filtering Problems for Conditionally Linear Systems with Non-Gaussian Initial Conditions
Authors: Hara Shigeomi
Published: January 2008

We solve the filtering problems for conditionally linear systems, that is, stochastic, partially observable systems which are linear in unobservable processes and nonlinear in observable processes, with non-Gaussian initial conditions. We assume that all coefficients of given SDEs are Lipshitz continuous in the observable processes, and that certain quantities concerning the diffusion coefficients of given SDEs are uniformly nonsingular. But we assume nothing about the initial distribution and allow that a part of the coefficients of the given SDEs are of linear growth order in the observable processes.
Phantom Maps and Monoids of Endomorphisms of $K(\boldsymbol Z,m) \times S^n$
Authors: Shitanda Yoshimi
Published: January 2008

The compositions

hf

,

hg

of phantom pair

f, g

and a phantom map

h

are homotopic. The compositions

hf

,

kf

of phantom pair

h, k

and a phantom map

f

are homotopic. We determine the homotopy set

[K(\boldsymbol Z,m) \times S^n_,K(\boldsymbol Z,m) \times S^n]

and its monoid structure given by the composition of maps for all

m, n ≥ 1

.
Self-avoiding Paths on the Three Dimensional Sierpinski Gasket
Authors: Hattori Kumiko , Hattori Tetsuya , Kusuoka Shigeo
Published: January 2008

We study self-avoiding paths on the three-dimensional pre-Sierpinski gasket. We prove the existence of the limit distribution of the scaled path length, the exponent for the mean square displacement, and the continuum limit. We also prove that the continuum-limit process is a self-avoiding process on the three-dimensional Sierpinski gasket, and that a path almost surely has infinitely fine creases.
Blow up for a Holonomic System
Authors: Neto Orlando
Published: January 2008

We introduce a functor that associates to a holonomic system of microdifferential equations

\mathcal M

on a contact manifold

X

and a closed Lagrangian submanifold

Λ

of

X

a contact manifold

\widetilde X

and a holonomic system

\widetilde{\mathcal M}

on

\widetilde X

. The manifold

\widetilde X

is an open set of the blow up of

X

along a certain ideal of the sheaf of holomorphic functions on

X

. Moreover the restriction of

\mathcal M

to the complementary of

Λ

and the restriction of

\widetilde{\mathcal M}

to the complementary of the exceptional divisor of

\widetilde X

are isomorphic as systems of microdifferential equations.
An Explicit Realization of a GNS Representation in a Krein-Space
Authors: Hofmann Gerald
Published: January 2008

On the tensor-algebra over the basic space

\boldsymbol C^2

, a

P

-functional is constructed. Using methods which are due to J.P. Antoine and S. Ôta, a Krein-space theory (i.e., a *-algebra of operators which are defined on a common, dense, and invariant domain in a Krein-space

\mathcal K

) is obtained via the GNS construction. It is shown that

\mathcal K

does not contain any

π

-invariant dual pairs. This gives an answer to a problem first posed by J.P. Antoine and S. Ôta.

The theory so obtained describes the complex superposition of two harmonic oscillators. With this in mind, the annihilation and creation operators, the operator of total electric charge, and the gauge group are explicitly given.
Remarks on the Shuffling Problem for Finite Groups
Authors: Hora Akihito
Published: January 2008

The shuffling problem is discussed as the asymptotic behavior of random walks on finite groups. We give a new characterization for asymptotic equidistribution of such random walks in terms of representations of the group. As applications, we characterize perfect groups and consider random walks on classical Weyl groups.
On the Regularity of the Partial $O^*$-Algebras Generated by a Closed Symmetric Operator
Authors: Antoine Jean-Pierre , Inoue Atsushi , Trapani Camillo
Published: January 2008

Let be given a dense domain

\mathcal D

in a Hilbert space and a closed symmetric operator

T

with domain containing

\mathcal D

. Then the restriction of

T

to

\mathcal D

generates (algebraically) two partial

{}^*

-algebras of closable operators (called weak and strong), possibly nonabelian and nonassociative. We characterize them completely. In particular, we examine under what conditions they are regular, that is, consist of polynomials only, and standard. Simple differential operators provide concrete examples of all the pathologies allowed by the abstract theory.
Clebsch-Gordan Coefficients for $\mathcal U_q(\mathcal{su}(1,1))$ and $\mathcal U_q(\mathcal{sl}(2))$, and Linearization Formula of Matrix Elements
Authors: Shibukawa Youichi
Published: January 2008

The tensor product of two representations of the discrete series and the limit of the discrete series of

\mathcal U_q(\mathcal{su}(1,1))

is decomposed into the direct sum of irreducible components of

\mathcal U_q(\mathcal{sl}(1,1))

, and the Clebsch–Gordan coefficients with respect to this decomposition are computed in two ways. In some cases, the tensor product of an irreducible unitary representation of

\mathcal U_q(\mathcal{sl}(2))

and a representation of the discrete series of

\mathcal U_q(\mathcal{su}(1,1))

is decomposed into the direct sum of irreducible components of

\mathcal U_q(\mathcal{sl}(2))

, and the Clebsch–Gordan coefficients with respect to this decomposition are calculated, too. Making use of these coefficients, the linearization formula of the matrix elements is obtained.
Quantum Lorentz Group Having Gauss Decomposition Property
Authors: Woronowicz Stanisław Lech , Zakrzewski S.
Published: January 2008

A new deformation of

\mathit{SL}(2, \mathbf C)

(considered as a real Lie group) is constructed and shown to have a Gauss type decomposition. The groups entering this decomposition are identified as

E_μ(2)

and its Pontryagin dual

Ê_μ(2)

. The whole group is the double group built over

E_μ(2)

.
On Algebraic $\#$-Cones In Topological Tensor-Algebras, I. Basic Properties and Normality
Authors: Hofmann Gerald
Published: January 2008

The concept of algebraic

\sharp

-cones (alg-

\sharp

cones) in topological tensor-algebras

E_\otimes[τ]

is introduced. It seems to be useful because the well-known cones such as the cone of positivity

E_\otimes^+

, the cone of reflection posilivity (Osterwalder–Schrader cone), and some cones of

α

-positivity in QFT with an indefinite metric are examples of alg-

\sharp

cones.

It is investigated whether or not the known properties of

E_\otimes^+

(e.g.,

E_\otimes^+

is a proper and generating cone not satisfying the decomposition property) apply to alg-

\sharp

cones. For proving deeper results, the structure of the elements of alg-

\sharp

cones is analyzed, and certain estimations between the homogeneous components of those elements are proven. Using them, a detailed investigation of the normality of alg-

\sharp

cones is given.

Furthermore, the convex hull of finitely many alg-

\sharp

cones is also considered.
An Algorithm for Computing a Nondegenerate Hysteresis Point
Authors: Okamoto Hisashi
Published: January 2008

We propose an algorithm for computing nondegenerate hysteresis points arising in bifurcation problems with two parameters such as

G:\boldsymbol R^2 \times \boldsymbol R^N → \boldsymbol R^N

. A combination of methods in [5] and [7] requires finding zeros of an extended system of

4N+3

variables. Shintani and Kanda [6] proposes another algorithm, in which computation of extended system of

3N+3

variables is sufficient. On the contrary, in our algorithm, we should find zeros of another extended system of

3N+2

variables.
Representation Theoretical Meaning of the Initial Value Problem for the Toda Lattice Hierarchy II
Authors: Takebe Takashi
Published: January 2008

The Toda lattice hierarchy is shown to have the virtual Bruhat decomposition of the

A_∞

group as its parameter space, instead of the Grassmann manifold for the
KP
hierarchy. The small cells of the Bruhat decomposition are examined. The parametrization of the
KP
hierarchy is utilized for this purpose with the help of the Miura transformation.
The Moyal Product and Spectral Theory for a Class of Infinite Dimensional Matrices
Authors: Hansen Frank
Published: January 2008

We study tempered distributions that are multipliers of the Schwartz space relative to the Moyal product. They form an algebra
N
under the Moyal product containing the polynomials. The elements of
N
are represented as infinite dimensional matrices with certain growth properties of the entries. The representation transforms the Moyal product into matrix multiplication. Each real element of
N
allows a resolvent map with values in tempered distributions and an associated spectral resolution. This giaes a tool to study distributions associated with symmetric, but not necessarily self-adjoint operators.
Construction of Gelfand–Tsetlin Basis for $\mathcal U_q(\textit{gl}(N+1))$-modules
Authors: Ueno Kimio , Takebayashi Tadayoshi , Shibukawa Youichi
Published: January 2008

The Gelfand-Tsetlin basis for irreducible

\mathcal U_q(\textit{gl}(N+1))

-modules of finite dimensions is constructed by means of the lowering operators.
The General Form of non-Fock Coherent Boson States
Authors: Honegger Reinhard , Rieckers Alfred
Published: January 2008

Specifying their (normally ordered) characteristic functions we determine all states of the boson
C
*-Weyl algebra which satisfy Glauber's coherence condition and are not realizable as density operators in Fock space. The pure ones are shown to be just the eigenstates of the annihilation operators in their GNS-representations (in contrast to the Fock case) and are characterized in many equivalent manners. The central decomposition of an arbitrary coherent state has the macroscopic phase variable as parameter and is supported by the pure coherent states, which is in fact the only way for a maximal decomposition. The set of all coherent states with the same absolute factorizing function is proven to be a Bauer simplex. The appearence of a classical coherent field part is studied in detail in the GNS-representations and shown to correspond to an enlargement of the set of one boson states by just one additional mode.
On the Maunder Type Theorems in the Ex-homotopy Category
Authors: Shitanda Yoshimi
Published: January 2008

We study the homotopy theory of comma category and define the cell structure and Postnikov system in the ex-homotopy category. By using these structures we give the four types of spectral sequences and show that Maunder type theorems hold for these spectral sequences.
Orbital Stability of the Periodic Solutions of Autonomous Systems with Impulse Effect
Authors: Simeonov Pavel S. , Bainov D. D.
Published: January 2008

In the present paper the orbital asymptotic stability of the periodic solutions of autonomous systems with impulse effect is investigated. An analogue of the theorem of Andronov-Vitt is proved.
Fundamental Groups for Ergodic Actions and Actions with Unit Fundamental Groups
Authors: Gefter Sergey L. , Golodets Valentin Ya.
Published: January 2008

Fundamental groups of ergodic dynamical systems with invariant measure are considered. For a given countable subgroup

\Lambda⊂\boldsymbol R^*_+

, an ergodic dynamical system is constructed whose fundamental group is countable and contains

\Lambda

. G.A. Margulis and D. Sullivan revealed that the orthogonal group contains a dense countable subgroup with the proprety T. The fact is applied to construct ergodic actions with a unit fundamental group. The group of outer automorphisms of these actions has also been completely calculated. The proofs are based on the results of studies of the properties of action centralizers.

In the Supplement we introduce the concept of a fundamental group for ergodic actions of continuous groups. It will be shown by means of results of the R. Zimmer's rigidity theory that any finite measure-preserving action of the lattice of the simple Lie group, whose real rank is not less 2, has a unit fundamental group.
Additivity of Quadratic Maps
Authors: Friedman Yaakov , Hakeda Josuke
Published: January 2008

The set of observables of a Quantum Mechanical System need only be closed under a "quadratic" product. It is shown that an additive structure of this set (whose existence is less natural) is uniquely determined by this multiplicative structure.
Equivariant Phantom Maps
Authors: Oda Nobuyuki , Shitanda Yoshimi
Published: January 2008

This paper contains a study of the characterization of the equivariant phantom maps by means of the equivariant localization and the equivariant completion. The equivariant integral approximation and the equivariant Miller-Zabrodsky theorem will be used to describe the homotopy set of the equivariant phantom maps by the equivariant cohomology groups.
Fredholm Determinants and the $τ$ Function for the Kadomtsev–Petviashvili Hierarchy
Authors: Pöppe Ch. , Sattinger D. H.
Published: January 2008

The “dressing method” of Zakharov and Shabat is applied to the theory of the

τ

function, vertex operators, and the bilinear identity obtained by Sato and his co-workers. The vertex operator identity relating the

τ

function to the Baker–Akhiezer function is obtained from their representations in terms of the Fredholm determinants and minors of the scattering operator appearing in the Gel'fand–Levitan–Marchenko equation. The bilinear identity is extended to wave functions analytic in a left half plane and is proved as a consequence of the inversion theorem and the convolution theorem for the Laplace transform.
Spectral Analysis in Krein Spaces
Authors: Nakagami Yoshiomi
Published: January 2008

For a bounded #-unitary, the existence of a Tomita's triangular matrix representation is equivalent to the existence of an invariant maximal nonnegative subspace due to Pontrjagin, Krein et al. In other words, if a bounded #-unitary
u
has such an invariant subspace, its spectral analysis can be reduced to the following three cases: (i)
u
is #-spectral; (ii)
u
is quasi-#-spectral; and (iii)
u
is represented in the form of a Tomita's triangular matrix.
Canonical Forms of Unbounded Unitary Operators in Krein Spaces
Authors: Gheondea Aurelian
Published: January 2008

The canonical forms of bounded unitary operators in Krein spaces, with respect to fundamental decompositions, are generalized to the case of unbounded unitary operators. In connection with this there are also investigated unbounded selfadjoint projections and unbounded symmetries in Krein spaces.
Heyting Valued Set Theory and Fibre Bundles
Authors: Nishimura Hirokazu
Published: January 2008

Takeuti and Titani [15] have demonstrated that, given a manifold

B

with topology

Ω = \mathcal O(B)

, the internal notion of an apartness vector space in

V^{(Ω)}

and the external notion of a vector bundle over

B

are no more than two representations of the same entity. The principal objective of this paper is, first of all, to internalize fibre bundles on the lines of Takeuti and Titani [15], and then to establish various internal-external interconnections around this. For example, we show that the external notion of integration over the fibre corresponds to the usual integration on internalized manifolds within

V^{(Ω)}

. The paper attains its climax as we discuss the internal and external aspects of an internalized version of celebrated Stokes theorem.
Notes on Some Inequalities for Hilbert Space Operators
Authors: Kittaneh Fuad
Published: January 2008

Several inequalities for Hilbert space operators are extended. These include results of Furuta, Halmos, and Kato on the mixed Schwarz inequality, the generalized Reid inequality as proved by Halmos and a classical inequality in the theory of compact non-self-adjoint operators which is essentially due to Weyl. Some related inequalities are also discussed.
On Operator Inequalities due to Ando–Kittaneh–Kosaki
Authors: Fuji Jun Ichi , Fuji Masatoshi
Published: January 2008

Operator norm inequalities due to Ando–Kittaneh–Kosaki for positive operators

A, B

and a non-negative operator monotone function

f

on

[0,∞)

are discussed: Main inequality is

\Vert f(A) – f (B)\Vert ≤ \Vert f(|A–B|)\Vert

. It is shown that the equality holds for invertible

A, B

and non-linear

f

if and only if

A = B

and

f(0) = 0

. Similarly, from the Kittaneh–Kosaki inequality, we show that 

\Vert f(A) – f(B)\Vert = f'(t)\Vert A–B\Vert

for

A, B≥ t> 0

and nonlinear

f

 if and only if

A = B

.
Continuous Dependence on the Initial Condition of the Solution of a System of Differential Equations with Variable Structure and with Impulses
Authors: Dishliev A. B. , Bainov D. D.
Published: January 2008

In the paper an initial value problem is considered for a system of ordinary differential equations with variable structure and impulses. Sufficient conditions are found under which there exists a solution of such system for

t≥τ_0

where

τ_0

is a real constant. Sufficient conditions are presented for continuous dependence of the solution of the initial condition.
Outer Conjugacy for Actions of Continuous Amenable Groups
Authors: Golodets Valentin Ya. , Sinelshchikov Sergey D.
Published: January 2008

The paper introduces a cohomological approach to the outer conjugacy problem in ergodic theory. Specifically, the following fact is proved: up to an isomorphism of an approximately finite type II ergodic full group there exists only one cohomological class of cocycles with dense range in a given amenable group. This result is used to establish outer conjugacy for strictly outer actions of continuous unimodular amenable subgroups of the normalizer of the full group generated by an ergodic type II automorphism. As a special case we show that outer conjugacy of compact groups reduces merely to conjugation. Besides that the correlation is established between the automorphisms of a principal groupoid with continuous orbits and ones of its discrete reduction. Also the correspondence is found between the automorphisms of groupoids with continuous orbits and those of the associated von Neumann algebras.
Non-translation Invariant Product States of Classical Lattice Systems
Authors: Fannes Mark
Published: January 2008

The notion of symmetric states is extended in such a way as to include the description of non-translation invariant mean field systems. A complete characterization of such states is given by means of non-translation invariant product states.
Some Connections between Heyting Valued Set Theory and Algebraic Geometry —Prolegomena to Intuitionistic Algebraic Geometry—
Authors: Nishimura Hirokazu
Published: January 2008

Rousseau [10] has shown that classical or standard function theory of
n
variables is no other than intuitionistic function theory of one variable over

\boldsymbol C^{n–1}

. Similar works have been done by Nishimura [9] in the realm of Sato hyperfunctions and by Takeuti and Titani [16] in the realm of complex manifolds. The main purpose of this paper is to pursue similar results in the arena of algebraic geometry. Since we would like to do so in an intuitionistically valid manner, we reconstruct some rudiments of algebraic geometry, using the complete Heyting algebra of radical ideals in place of the space of prime ideals with Zariski topology as the starting point of our scheme theory.
Undecidability of Free Pseudo-Complemented Semilattlces
Authors: Idziak Pawel M.
Published: January 2008

Decision problem for the first order theory of free objects in equational classes of algebras was investigated for groups (Malcev [10]), semigroups (Quine [12]), commutative semigroups (Mostowski [11]), distributive lattices (Ershov [6]) and several varieties of rings (Lavrov [9]). Recently this question was solved for all varieties of Hilbert algebras and distributive pseudo-complemented lattices (see [7], [8]). In this paper we prove that the theory of all finitely generated free pseudo-complemented semilattices is undecidable.
On the Brownian Curve and its Circumscribing Sphere
Authors: Adelman Omer
Published: January 2008

The number of points the image of [0,
t
] under a planar Brownian motion has in common with its circumscribing circle does
not
have a zero-one law: it can be either two or three, both with a strictly positive probability. (This contradicts an assertion made by Paul Levy.)
Fermion Ito's Formula II: The Gauge Process in Fermion Fock Space
Authors: Applebaum David
Published: January 2008

The stochastic calculus constructed in [2] for fermion Brownian motion is augmented through the inclusion of stochastic integration with respect to the gauge process. The solutions of certain non-commutative stochastic differential equations are used to construct dilations of contraction semigroups on a Hilbert space

\mathfrak h_0

and of uniformly continuous, completely positive semigroups on

\boldsymbol B(\mathfrak h_0)

. Finally we construct a fermion analogue of the classical Poisson process and investigate some of its properties.
The Radon–Nikodym theorem for $L^p$-spaces of $W^*$-algebras
Authors: Schmitt Lothar M.
Published: January 2008

We prove an analogue of Sakai's [15] Radon–Nikodym theorem for

L^p

-spaces of

W^*

-algebras. Following Takesaki [20] we characterize the Radon–Nikodym derivatives by analytic extensions of modular automorphism groups. Finally we relate the facial structure in

L^p

-spaces of

W^*

-algebras to Connes' [2] unitary Radon–Nikodym cocycles.
Completely Positive Linear Maps in a Concept of Majorization on Certain Operator Algebras
Authors: Alberti Peter M.
Published: January 2008

Some concepts of Majorization in the state spaces of certain operator algebras are discussed and the interrelations among them are established. The main case considered deals with the class of non-finite AFD-factor vN-algebras.
Integral Decomposition of Partial *-Algebras of Closed Operators
Authors: Mathot Françoise D.
Published: January 2008

A method of direct integral decomposition for very general classes of unbounded closed operators is developed. This method is applied to the reduction theory of partial *-algebras and Op*-algebras. As a consequence, representations of partial *-algebras are decomposed into irreducible ones and some states are decomposed into extremal states.
The Homology of Double Loop Spaces of Complex Stiefel Manifolds
Authors: Yamaguchi Atsushi
Published: January 2008

The Hopf algebra structure of

H_*(Ω^2\mathit{SU}(n+1)/\mathit{SU}(m+1)\ : \boldsymbol F_p)

and the action of the Steenrod algebra on it are determined.
Passive Quasi-free States of the CAR Algebra with Discrete Hamiltonians
Authors: Batty Charles J.K.
Published: January 2008

The spectrally passive, gauge-invariant, quasi-free stases

ω

on the C*-algebra of anticommutation relations with respect to a one-parameter quasi-free action

τ

are described. If the one-particle Hamiltonian

H

is discrete, the precise condition on the one-particle density

Q

of 

ω

is combinatorial, but if the Connes spectrum of  

τ

is non-zero, it implies that

Q = (I+e^{β (H+T)})^{–1}

for some

β ≥ 0

and some operator

T

of bounded trace norm, apart from some degenerate possibilities. If

H

has both discrete and continuous parts, these results can be combined with those of de Cannière for the purely continuous case.
Radonification Problem for Cylindrical Measures on Tensor Products of Banach Spaces
Authors: Elezovic Neven
Published: January 2008

An operator

w_1\otimes w_2

is said to be

p

-Radonifying if it maps every cylindrical measure of type

p

, defined on the tensor product

E\otimes F

of two Banach spaces, into a Radon probability cf order

p

on the completion of some normed product

G\otimes_α H

. In this paper we prove that

w_1\otimes w_2

is

p

-Radonifying,

1<p<∞

if and only if it is

\tilde p

-summing.
Linear Radon-NIkodym Theorems for Linear Radon-NIkodym Theorems for on JEW and W* Algebras
Authors: Iochum Bruno , Kosaki Hideki
Published: January 2008

Linear Radon-Nikodym theorems for states on a von Neumann algebra are obtained in the context of a one parameter family of positive cones. Especially, necessary and sufficient conditions for existence of linear Radon-Nikodym derivatives are investigated. In the natural cone case we consider Jordan Banach algebras.
Boolean Valued Decomposition Theory of States
Authors: Nishimura Hirokazu
Published: January 2008

Boolean valued analysis (i.e., analysis based on Boolean valued set theory) enables us to introduce a natural framework for decompositions of states over
C
*-algebras with identity. The development apparently runs parallel with the traditional approach originating in von Neumann's reduction theory, but our logical approach succeeds in getting rid of separability restrictions that have haunted the traditional approach.
Partial *-Algebras of Closed Linear Operators In Hilbert Space
Authors: Antoine Jean-Pierre , Karwowski W.
Published: January 2008

Given a dense domain

\mathcal D

of a Hilbert space, we consider the class of all closed operators which, together with their adjoint, have

\mathcal D

in their domain. A partial

*

-algebra of operators on

\mathcal D

is a subset of that class, stable under suitable operations of involution, addition and multiplication, the latter when it is defined. We present two types of such objects and study their properties, both algebraic and topological.
Groupoid Dynamical Systems and Crossed Product, II — The Case of $C^*$-Systems
Authors: Masuda Tetsuya
Published: January 2008

By analogy with

C^*

-dynamical system, we define a

C^*

-groupoid dynamical system

(A,
\Gamma, \rho)

where

A

is a

C^*

-algebra,

\Gamma

is a locally compact groupoid, and

\rho \to \mathrm{Aut}(A)

is a continuous groupoid homomorphism. The groupoid crossed product

A\times_\rho \Gamma

is defined and is shown to have similar properties as the case of a group action. As a special case of this situation, if

\rho

is a continuous homomorphism from

\Gamma

to a locally compact group

G

, we obtain groupoid dynamical system

(C_0 (G), \Gamma, \rho)

. In this case, there exists a co-action

\hat \rho

of

G

on

C^*(\Gamma)

and the groupoid crossed product

C_0 (G) \times \Gamma

is isomorphic to the co-crossed product

C^*(\Gamma) *_{\hat\rho} G

of

C^*(\Gamma)

by

G

. The results in this paper is obtained by the analogy with our previous results for the case of

W^*

-systems.
On the $XY$-Model on Two-Sided Infinite Chain
Authors: Araki Huzihiro
Published: January 2008

The

XY

-model on the one-dimensional lattice, infinitely extended to both directions,is studied by a method of

C^*

-algebras. Return to equilibrium is found for any vector state in the cyclic representation of the equilibrium state. A known relation between the algebras of Pauli spins and the algebra of canonical anticommutation relations (CARs) is used to obtain an explicit solution. However the

C^*

-algebras generated by the two sets of operators become dissociated in the thermodynamic limit of an infinite one-dimensional lattice extending in both directions (in contrast to onesided chain) and this causes a mathematical complication. In particular, we find three features different from the case of one-sided infinite chain: (1) There are no non-trivial constant observables. (2) The (twisted) asymptotic abelian property holds only partially and not in general. (3) Return to equilibrium occurs for all values of the parameter γ and is proved by a method different from the case of one-sided chain.
A Posteriori Improvement of Cubic Spline Approximate Solution of Two-Point Boundary Value Problem
Authors: Sakai Manabu
Published: January 2008

We consider the numerical solution of two-point boundary value problem by collocation method using cubic spline. We derive asymptotic expansions of the errors which are a posteriori determined with little additional computation. The applications of these asymtotic expansions to a posteriori improvement of the approximate solution and adaptive mesh selection strategy (chopping procedure) are discussed. Some numerical results which closely correspond with the predicted theory are given.
Weak and Strong Solutions of the Navier-Stokes Initial Value Problem
Authors: Giga Yoshikazu
Published: January 2008

This paper reviews the existence, uniqueness and regularity of weak and strong solutions of the Navier-Stokes system. For this purpose we emphasize semigroup theory and the theory of the Stokes operator. We use dimensional analysis to clarify the meaning of the results for the solutions.
A Formal System for Specification Analysis of Concurrent Programs
Authors: Hirose Ken , Takahashi Makoto
Published: January 2008

A formal system

\textit{FL}_{m, n}

is proposed to analyze the specification of concurrent programs. The soundness theorem for

\textit{FL}_{m, n}

is also proved.
Recent Development of the Theory of Completely Bounded Maps between $C^*$-Algebras
Authors: Tomiyama Jun
Published: January 2008

Recent development of the theory of completely bounded maps between

C^*

-algebras such as those results by Wittstock, Smith, Paulsen and Huruya are reviewed and discussed as well as the author's results.
A Semi-Group Theoretical Analysis of a Finite Element Method for a Linearized Viscous Shallow-Water System
Authors: Ushijima Teruo
Published: January 2008

A finite element step-by-step time integration scheme of a model linear viscous shallow-water system is analyzed by the approximation theory for semi-groups of linear operators. Strong convergence and
0
(
h
+τ) error estimate in _L_2-sense are established.
Justification of Partially-Multiplicative Averaging for a Class of Functional-Differential Equations with Impulses
Authors: Milusheva S. D. , Bainov D. D.
Published: January 2008

The authors obtain a justification of the method of partially-multiplicative averaging for a class of functional-differential equations with impulses and a transformed argument, dependent on the time and the unknown function.