bluuebunny/crossref_metadata_2025 huggingface dataset:
Quadratic Representations of the Canonical Commutation Relations
Authors: Proksch Martin , Reents George , Summers Stephen J.
Published: January 2008

This paper studies a class of representations (called quadratic) of the canonical commutation relations over symplectic spaces of arbitrary dimension, which naturally generalizes coherent and symplectic (i.e. quasifree) representations and which has previously been heuristically employed in the special case of finite degrees of freedom in the physics literature. An explicit characterization of canonical quadratic transformations in terms of a 'standard form' is given, and it is shown that they can be exponentiated to give representations of the Weyl algebra. Necessary and sufficient conditions are presented for the unitary equivalence of these representations with the Fock representation. Possible applications to quantum optics and quantum field theory are briefly indicated.
Distributions with Exponential Growth and Boehner-Schwartz Theorem for Fourier Hyperfunctions
Authors: Chung Soon-Yeong , Kim Dohan
Published: January 2008

Every positive definite Fourier hyperfunction is a Fourier transform of a positive and infra-exponentially tempered measure, which is the generalized Boehner-Schwartz theorem for the Fourier hyperfunctions. To prove this we characterize the distributions with exponential growth via the heat kernel method.
Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. III. Sutherland Type Systems and their Duals
Authors: Ruijsenaars Simon N. M.
Published: January 2008

We present an explicit construction of an action-angle map for the nonrelativistic

N

- particle Sutherland system and for two different generalizations thereof, one of which may be viewed as a relativistic version. We use the map to obtain detailed information concerning dynamical issues such as oscillation periods and equilibria, and to obtain simple formulas for partition functions. The nonrelativistic and relativistic Sutherland systems give rise to dual integrable systems with a solitonic long-time asymptotics that is explicitly described. We show that the second generalization is self-dual, and that its reduced phase space can be densely embedded in

\mathbf P^{N-1}

with its standard Kähler form, yielding commuting global flows. In a certain limit the reduced action-angle map converges to the quotient of Fourier transformation on

\mathbf C^N

under the standard projection

\mathbf C^N \backslash \{0\} → \mathbf P^{N-1}

.
Automorphisms of the Extended Affine Root System and Modular Property for the Flat Theta Invariants
Authors: Satake Ikuo
Published: January 2008

We define the central extension

\widetilde{\operatorname{Aut}}^+(R)

of the automorphism group

\operatorname{Aut}^+(R)

of the extended affine root system. We give the action of

\widetilde{ \operatorname{Aut}}^+(R)

on the flat theta invariants (theta functions). This describes the modular property for the flat theta invariants.
On Types of Quasifree Representations of Clifford Algebras
Authors: Murakami Toshiki , Yamagami Shigeru
Published: January 2008

The types of von Neumann algebras generated by quasifree representations of infinite dimensional Clifford algebras are studied in terms of spectral properties of positive operators parametrizing quasifree states.
Representations of Unitary Groups and Free Convolution
Authors: Biane Philippe
Published: January 2008

To each finite dimensional representation of a unitary group
U
(
n
) is associated a probability measure on the set of integers, depending on the highest weights which occur in this representation. We show that asymptotically for large
n
and large irreducible representations of
U
(
n
) the measure associated to the tensor product of two representations, or to the restriction of a representation to a subgroup
U
(
m
) with
m
comparable to
n
, can be expressed in terms of the measures associated to the first representations by means of the notion of free convolution (namely additive free convolution for the tensor product problem and multiplicative free convolution for the restriction problem).
Simply Typed Lambda Calculus with First-Class Environments
Authors: Nishizaki Shin-ya
Published: January 2008

We propose a lambda calculus

λ^→_{\mathit{env}}

where it is possible to handle first-class environments. This calculus is based on the idea of
explicit substitution
, that is

λ σ

-calculus. Syntax of

λ^→_{\mathit{env}}

is obtained by merging the class of terms and the one of substitutions. Reduction is made from the weak reduction of

λ σ

-calculus. Its type system also originates in the one of

λ σ

-calculus. Confluence of

λ^→_{\mathit{env}}

is proved by Hardin's
interpretation method
which is originally used for proving confluence of

λ σ

-calculus. We proved strong normalizability of

λ^→_{\mathit{env}}

by reducing it to strong normalizability of a simply typed record calculus. Finally, we propose a type inference algorithm which produced a principal typing for each typable term.
Nonnormal del Pezzo Surfaces
Authors: Reid Miles
Published: January 2008

This paper studies reduced, connected, Gorenstein surfaces with ample-
K
, assumed to be reducible or nonnormal. The normalisation is a union of one or more standard surfaces (scrolls and Veronese surfaces), marked with a conic as double locus. The question is how to glue these together to get a Gorenstein scheme. In characteristic 0, the results amount to a classification of projective surfaces in the style of the 1880s. However, the methods involve a study of the dualising sheaf of a nonnormal variety in terms of Rosenlicht differentials, and there is a subtle pathology in characteristic p due to Mori and S. Goto.
Division Theorems in Spaces of Entire Functions with Growth Conditions and their Applications to PDE of Infinite Order
Authors: Berenstein Carlos A. , Gay Roger , Vidras Alekos
Published: January 2008

It is shown that every entire function

f\in \mathrm{Exp}_0(\mathbf C^n)

,

f(0) ≠ 0

is “slowly decreasing”. As an application of this property, a theorem on analytic continuation of solutions of infinite order differential equations with constant coefficients is proven.
Remarks on the Bifurcation of Two Dimensional Capillary-Gravity Waves of Finite Depth
Authors: Okamoto Hisashi , Shoji Mayumi
Published: January 2008

We consider the problem to determine the two dimensional water waves of permanent configuration. The problem is a bifurcation problem ([16]). In this paper, we define a mapping
G
between two Hilbert spaces and prove that the solutions of the above problem are in one-to-one correspondence to the zeros of the mapping
G
. Our most important contribution in this paper is to clarify the role of the aspect ratio, i.e., the ratio between the mean depth of the flow and the wave length. In particular, we prove that there is no degenerate bifurcation point, whatever the aspect ratio may be.
On the Cones of $α$- and Generalized $α$-Positivity for Quantum Field Theories with Indefinite Metric
Authors: Hofmann Gerald
Published: January 2008

In order to construct a Krein-space theory (i.e., a

*

-algebra of (unbounded) operators which are defined on a common, dense, and invariant domain in a Krein space) the cones of

α

-positivity and generalized

α

-positivity are considered in tensor algebras. The relations between these cones, algebraic

\#

-cones, and involutive cones are investigated in detail.

Furthermore, an example of a

P

-functional

ϕ

defined on

(\mathbf C^2)_\otimes

(tensor algebra over

\mathbf C^2

) not being

α

-positive and yielding a non-trivial Krein-space theory is explicitely constructed. Thus, an affirmative answer to the question whether or not the method of

P

-functionals (introduced by Ôta) is more general than the one of

α

-positivity (introduced by Jakóbczyk) is provided in the case of tensor algebras.
Solvability of Convolution Operators
Authors: Okada Yasunori
Published: January 2008

We study the Surjectivity of convolution operators on the spaces of hyperfunctions and Fourier hyperfunctions. On the space of hyperfunctions, we give a sufficient condition (the kernel is a nonzero ultradistribution), weaker than earlier conditions. On the space of Fourier hyperfunction, we give a new sufficient condition and new necessary conditions for the Surjectivity. Especially in one dimensional case, they become a sufficient and necessary condition. To this aim we use the Fourier analysis as in L. Ehrenpreis [E-2] and T. Kawai [Ka-1].
Fibrewise Hopf Construction and Hoo Formula for Pairings
Authors: Oda Nobuyuki
Published: January 2008

Let
Γ
be a fibrewise co-Hopf space over a topological space
B
. A
ΓB
-suspension space
ΓBX
is a generalization of a fibrewise suspension space
ΣBX
for any fibrewise pointed space
X
over
B
. Making use of
ΓB
-suspension space, we define
ΓB
-Hopf construction and prove a
ΓB
-suspension formula which generalizes the suspension formula of C. S. Hoo. The dual formula is also proved.
A Process Associated with the Radially Symmetric Dirac Equation
Authors: Jefferies Brian
Published: January 2008

The dynamical group associated with the Dirac equation with a radially symmetric potential is represented in terms of integrals with respect to the operator valued set functions associated with the Dirac equation in four space-time dimensions.
Asymptotic Behaviour of Time-Inhomogeneous Evolutions on von Neumann Algebras
Authors: Frigerio Alberto , Grillo Gabriele
Published: January 2008

We consider a sequence

τ_n

of dynamical maps of a von Neumann algebra

\mathcal M

into itself, each of which has a faithful normal invariant state

ω_n

, and we investigate conditions under which the time-evolved

φ_n=φ_0\circ τ_1\circ ⋯\circ τ_n

of an arbitrary normal initial state

φ_0

is such that

\lim_{n→ ∞}|| φ_n-ω_n||=0

. This is proved under conditions on the spectral gap of

τ_n

extended to a contraction on the GNS space of

(\mathcal M, ω_n)

, and on the difference (in a sense to be made precise below) between

ω_n

and

ω_{n-1}

, we do not require detailed balance of

τ_n

w. r. t.

ω_n

. We also give conditions on the sequence of relative Hamiltonians

h_n

between

ω_n

and

ω_{n-1}

ensuring that the result holds. Finally, we prove that the techniques of the present paper do not admit a simple generalization to

C^*

-algebras and non-normal states.
An $r$-Matrix Approach to Nonstandard Classes of Integrable Equations
Authors: Konopelchenko Boris , Oevel Walter
Published: January 2008

Three different decompositions of the algebra of pseudo-differential operators and the corresponding

r

-matrices are considered. Three associated classes of nonlinear integrable equations in

1 +1

and

2 + 1

dimensions are discussed within the framework of generalized Lax equations and Sato's approach. The

2 + 1

-dimensional hierarchies are associated with the Kadomtsev–Petviashvili (KP) equation, the modified KP equation and a Dym equation, respectively. Reductions of the general hierarchies lead to other known integrable

2 + 1

-dimensional equations as well as to a variety of integrable equations in

1 +1

dimensions. It is shown, how the multi-Hamiltonian structure of the

1 +1

-dimensional equations can be obtained from the underlying

r

-matrices. Further, intimate relations between the equations associated with the three different r-matrices are revealed. The three classes are related by Darboux theorems originating from gauge transformations and reciprocal links of the Lax operators. These connections are discussed on a general level, leading to a unified picture on (reciprocal) Bäcklund and auto-Bäcklund transformations for large classes of integrable equations covered by the KP, the modified KP, and the Dym hierarchies.
Pairings in Categories
Authors: Oda Nobuyuki
Published: January 2008

We study a categorical generalization of some of the basic results of the homotopy theory which have been obtained in the category of topological spaces with base point. They are some of the results of Gottlieb, Hilton, Hoo, Lim, Varadarajan, Woo and Kim and others. To carry out categorical approach, we define pseudo-product, pseudo-coproduct and homotopy relation in general categories. These concepts enable us to define pairings and copairings in categories. Some of the classical results mentioned above are generalized to the categories with product, coproduct and zero object.
Fourier Hyperfunctions as the Boundary Values of Smooth Solutions of Heat Equations
Authors: Kim Kwang Whoi , Chung Soon-Yeong , Kim Dohan
Published: January 2008

We show that if a

C^∞

-solution

u(x, t)

of heat equation in

\boldsymbol R_+^{n+1}

does not increase faster than

\exp[ε(\frac 1 t+|x|)]

then its boundary value determines a unique Fourier hyperfunction. Also, we prove the decomposition theorem for the Fourier hyper functions. These results generalize the theorems of T. Kawai and T. Matsuzawa for Fourier hyperfunctions and solve a question given by A. Kaneko.
Asymptotic Stability of the Relativistic Maxwellian
Authors: Glassey Robert T. , Strauss Walter A.
Published: January 2008

Solutions of the relativistic Boltzmann equation are studied for all initial data which are periodic in the space variable and near equilibrium. An equilibrium is a relativistic Maxwellian distribution of momenta. Under appropriate conditions on the scattering kernel, this equilibrium is asymptotically stable in a variety of function spaces.
The Word Problem for Groups with Regular Relations – Improvement of the Knuth-Bendix Algorithm
Authors: Hayashi Chuya
Published: January 2008

The Knuth-Bendix algorithm is a practical algorithm which, for a given finite presentation of a group, finds a finite confluent set of relations, if it terminates. From this confluent set we can know a solution of the word problem for the group. In this paper we introduce a concept of a regular confluent set of relations, which also gives a solution of the word problem, and represent a class of groups with such sets in terms of the Cayley graphs of the groups. Furthermore we make an algorithm to find a regular confluent set of relations as an improvement of the Knuth-Bendix algorithm. This new algorithm is a genuine improvement because there are some finite presentation, for which the Knuth-Bendix algorithm does not stop but the new one does.
An Inclusion of Type III Factors with Index 4 Arising from an Automorphism
Authors: Sekine Yoshihiro
Published: January 2008

We consider an inclusion of type

\mathrm{III}

factors with index 4 arising from an automorphism. It has the extended Coxeter–Dynkin diagram

\tilde A

or

A_{∞,∞}

as the principal graph. We show the equivalence between classification of automorphisms and that of the corresponding subfactors, and compute conjugacy invariants for the subfactors. As an application, we show the existence of a pair of type

\mathrm{III}_1

factors which does not split into a type

\mathrm{II}_1

inclusion.
A Class of Extremal Positive Maps in $3 \times 3$ Matrix Algebras
Authors: Osaka Hiroyuki
Published: January 2008

We shall provide a large class of extremal positive maps in

M_3(\mathbf C)

which are neither 2-positive nor 2-copositive and study the algebraic structure of the set of all positive linear maps in

M_3(\mathbf C)

.
Discrete Cubic Interpolatory Splines
Authors: Shrivastava Manjulata
Published: January 2008

In the present paper, existence, uniqueness and convergence properties of a discrete cubic spline which satisfies certain averaging interpolatory condition are established. This type of interpolatory condition has been studies earlier for usual cubic splines in [3]. More precise range for weights involved in the interpolatory condition and sharper error estimates than in [3], are obtained in the present paper.
Goldman's Type Theorem for Index 3
Authors: Izumi Masaki
Published: January 2008

We show a Goldman's type theorem for any inclusions of (not necessarily AFD) factors with the principal graph _A_5. Our main tools are correspondences and sectors.
Itô's Formula for Non-Smooth Functions
Authors: Aebi Robert
Published: January 2008

Let us consider an application of forward local _C_1,ε-semimartingale flows of _C_1-diffeomorphisms. First a change of variable formula is derived and the existence of all moments of the appearing Jacobian is shown. Then as a consequence, Itô's formula holds for continuous functions which first and second order derivatives exist only in the sense of distributions.
Unitarily Invariant Norms under Which the Map $A → |A|$ Is Lipschitz Continuous
Authors: Kosaki Hideki
Published: January 2008

We will characterize the unitarily invariant norms (for compact operators) under which the map

A → |A| = (A^*A)^{1/2}

is Lipschitz-continuous. Although the map is not Lipschitz-continuous for the trace class norm, we will obtain a certain Lipschitz-type estimate by making use of the Macaev ideal.
Quantum Deformation of Classical Groups
Authors: Hayashi Takahiro
Published: January 2008

We construct coordinate algebras of quantum orthogonal, special orthogonal and symplectic groups using M. Jimbo's solutions of the Yang-Baxter equation and determine their Peter-Weyl decompositions. To do this, we study some class of bialgebras and their group-like elements (quantum determinants). A new realization of the universal
R
-matrix is also given.
Pairings and Copairings in the Category of Topological Spaces
Authors: Oda Nobuyuki
Published: January 2008

We prove a theorem which gives a relation between the pairings of homotopy sets induced by pairings and copairings of topological spaces. We obtain many results on commutativity of elements of homotopy sets as immediate consequences of the theorem. As a further application of the theorem, we prove a generalization of a theorem of Sugawara on the existence of inverse element in the homotopy set when the target space is a Hopf space. We also prove the dual result which is a generalization of a theorem of Hilton, Mislin and Roitberg.
Invariants of 3-Manifolds Associated with Quantum Groups and Verlinde's Formula
Authors: Takata Toshie
Published: January 2008

We obtain a projectively linear representation of

\mathit{SL}(2, \boldsymbol Z)

from invariants defined by Reshetikhin and Turaev and prove ‘Verlinde's formula’ for

\mathit{SU}(2)

based on the computation of invariants. Using an algebra associated with ‘Ising model’, we constract invariants of links and 3-manifolds.
Quotients of Local Banach Algebras are Local Banach Algebras
Authors: Schmitt Lothar M.
Published: January 2008

We show that quotients of local Banach algebras are local Banach algebras. This solves a problem posed by B. Blackadar in his book on
K
-Theory [BLA1]. Furthermore our techniques allow to prove additional density Theorems for the
K
-Theory of normed algebras stable under inverses and logarithms.
Application of Fusion Rules to Classification of Subfactors
Authors: Izumi Masaki
Published: January 2008

By the technique of Longo's sector, the following two results are obtained. (1) A proof is given to Ocneanu's announcement about the non-existence of paragroups for Coxeter graphs _E_7 and _D_odd. (2) Subfactors of the type III1 AFD factor with index 3 are classified.
Integral Solutions of Trigonometric Knlzhnik-Zamolodchikov Equations and Kac-Moody Algebras
Authors: Cherednik Ivan
Published: January 2008

We use Kac-Moody algebras to get some integral solutions for trigonometric
r
-matrix Knizhnik-Zamolodchikov equations of type
Xl
(1) generalizing those in the case of Yang's
r
-matrix, where our construction gives a new interpretation and a short proof of Schechtman, Varchenko theorem.
New $R$ Matrices Associated with Cyclic Representations of $U_q(A_2^{(2)})$
Authors: Date Etsuro , Jimbo Michio , Miki Kei , Miwa Tetsuji
Published: January 2008

New

R

matrices are constructed as intertwiners of

N

-dimensional representations of

U_q(A_2^{(2)})

at

q^{\bar N}=1

. Analogous construction for

U_q(A_1^{(1)})

reproduces the chiral Potts model.
On Ground State Degeneracy of $Z_2$ Symmetric Quantum Spin Models
Authors: Matsui Taku
Published: January 2008

We consider a class of

\boldsymbol Z_2

symmetric quantum spin Hamiltonians. Anisotropic spin

1/2

Heisenberg models are typical examples.

Proof of groound state degeneracy (

\boldsymbol Z_2

symmetry breaking), construction of pure gournd states are given in a systematic way.
The Structure and Represenation of a $\mathrm C^*$-Algebra Associated to the Super-Poincaré Group
Authors: Hannabuss Keith C. , Weiss Winfried R.E.
Published: January 2008

The representation theory of a class of algebras associated to certain graded Lie groups is investigated. To a group whose even part is central is associated a natural involutive algebra all of whose

{}^*

-representations factor through a quotient algebra of continuous Clifford algebra-valued fields. The irreducible representations of crossed products of the algebra by a Lie algebra, such as the super-Poincaré group, are then constructed by Takesaki's method. It is then shown that they may also be constructed by Rieffel's

\mathrm C^*

-algebraic induction. Tensor product decompositions are briefly discussed.
Decompositions of Regular Representations of the Canonical Commutation Relations
Authors: Schaflitzel Reinhard
Published: January 2008

Every cyclic regular representation of the canonical commutation relations over any inner product space
V
can be decomposed into a direct integral of irreducible regular representations, where the fibers are representations over subspaces of
V
. An example using the so-called direct-product representations shows that generally the irreducible representations cannot be defined over the whole
V
. So we get a new type of decomposition having no equivalent in the decompositions of locally compact groups.
Quadratic Forms for Singular Perturbations of the Laplacian
Authors: Teta Alessandro
Published: January 2008

Singular perturbations of — Δ in _L_2(_R_3) supported by points, regular curves and regular surfaces are considered. Using a renormalization technique the corresponding quadratic forms are constructed and a complete characterization of the domain and the action of the operators is given, together with explicit expressions for the resolvent.
Representations of Graph Temperley-Lieb Algebras
Authors: Martin Paul P.
Published: January 2008

We define graph Temperley-Lieb algebras, which are certain generalisations of Temperley-Lieb algebras including those appropriate for building the transfer matrices for lattice models in arbitrary dimensions. We construct various representations for these algebras, which are parameterised by a scalar
Q
. In particular we give the generically irreducible representations associated with statistical mechanical models. These representations are well defined for all
Q
, whereas the representations coming directly from physical models are typically only defined for certain values of
Q
. We also give representations with bases derived from the partitions of n distinguishable objects (
n
is the number of nodes in the graph). We show how to compute the dimensions of these epresentations by a diagrammatic technique.
Partial *-Algebras of Closable Operators. I. The Basic Theory and the Abelian Case
Authors: Antoine Jean-Pierre , Inoue Atsushi , Trapani Camillo
Published: January 2008

This paper, the first of two, is devoted to a systematic study of partial *-algebras of closable operators in a Hilbert space (partial Op*-algebras). After setting up the basic definitions, we describe canonical extensions of partial Op*-algebras by closure and introduce a new bounded commutant, called quasi-weak. We initiate a theory of abelian partial *-algebras. As an application, we analyze thoroughly the partial Op*-algebras generated by a single closed symmetric operator.
The Super-Toda Lattice Hierarchy
Authors: Ikeda Kaoru
Published: January 2008

The super-Toda lattice (STL) hierarchy is introduced. The equivalence between the Lax representation and Zakharov–Shabat representation of the STL hierarchy is shown. Introducing the Lie superalgebra

\mathrm{osp}(∞ | ∞)

, the ortho-symplectic (OSp)-STL hierarchy is defined as well. These equations are solved through the Riemann-Hilbert decomposition of corresponding infinite dimensional Lie supergroups. An explicit representation of solutions is given by means of the super-

τ

field.
Dirichlet Forms on Fractals and Products of Random Matrices
Authors: Kusuoka Shigeo
Published: January 2008

The author studies Dirichlet forms on fractals. He constructs some local Dirichlet forms on abstract fractal sets by using products of random matrices. Also, he studies the martingale dimension of the associated diffusion processes and its self-similarity.
Proofs and Programs: A Naïve Approach to Program Extraction
Authors: Nakahara Hayao
Published: January 2008

In this paper, we examine a naive but precise relation between verification proofs of iterative programs with recursions and proofs in a predicate logic. For that purpose, a logic of total correctness of programs is introduced, which is an extension of a predicate logic and a variant of Pratt's dynamic logic equipped with program variables. Then it is shown that correctnes proofs of programs are regarded as proofs in a predicate logic. Conversely we show how programs and their correctness proofs can be obtained from proofs of their specifications. These methods provide means to examine how difference among algorithms reflects difference among proofs and vice verse. Using them, we can replace processes of programming by processes of proving specifications. Our method does not depend on specific concrete theories, so we can use our method to problem solving on abstract domain.
Endomorphisms of Certain Operator Algebras
Authors: Price Geoffrey L.
Published: January 2008

In this paper we study

C(X)

-endomorphisms of

C(X, \mathfrak B(\mathfrak H))

, for

X

a compact space. The local structure of these endomorphisms is analyzed. We prove the existence of a

C(X)

-shift, not all of whose fibers are shifts on

\mathfrak B(\mathfrak H)

.
Remarks on Functional Integral Representations of Quantum Evolutions for Systems with Electromagnetic Fields
Authors: Papiez Lech S.
Published: January 2008

The solutions of Schrödinger equation in the form of the Dyson series are used as the starting point for functional integral representations of wave functions. Quantum systems in the presence of the external electromagnetic fields are discussed in this respect. The results on measure theoretic approach to functional integral representations of quantum states are proved and related to the appropriate mathematical formulations of Feynman path integrals.
Microfunctions at the Boundary and Mild Microfunctions
Authors: Schapira Pierre , Zampieri Giuseppe
Published: January 2008

Let

X

be a real manifold,

\mathscr F

an object of

D^b(X)

, the derived category of the category of bounded complexes of sheaves of abelian groups on

X

. The functor

μ\hom (\cdot,\cdot)

, defined in [3], appears to be a useful tool especially in the theory of boundary value problems for partial differential equations. The aim of the present paper is to calculate the stalk of

RΓ_zμ\hom(\boldsymbol N_Ω, \mathscr F)

, when

Ω

is a convex (up to diffeomorphism) and open subset of a closed submanifold

M

of

X

, and

Z

is a closed convex proper cone of

T^*X

. As an application we show how to recover in a short and functorial way, the theory of mild microfunctions by Kataoka [5].
Discrete Cubic $\mathscr X$-Splines
Authors: Rana Surendra Singh
Published: January 2008

In the present paper, we introduce the discrete cubic

\mathscr X

-splines and study the existence, uniqueness and convergence properties of such

\mathscr X

-splines which interpolate given functional values at the mesh points. An optimal interpolating discrete cubic

\mathscr X

-spline and splines of special interest have also been discussed.
Symbol Theory of Microlocal Operators
Authors: Uchikoshi Keisuke
Published: January 2008

Let
u
(
x
,
x'
)
dx'
be an arbitrary microlocal operator. We define the symbol function
û
(
x
,
ξ
of
u
(
x
,
x'
)
dx'
, and give a characterization of such symbol functions. Symbol formulae for adjoint operators and for composite operators are given.
Heyting Valued Considerations on Some Fundamental Existence Theorems in Modern Analysis
Authors: Nishimura Hirokazu
Published: January 2008

Following the honorable tradition of Rousseau's [6] treatment of Weierstrass theorems in several complex variables, we give some other specimens of transfer from intuitionistic theorems to classical ones. The classical theorems which we deal with in this paper include the implicit function theorem and Cauchy's local existence theorem in ordinary differential equations.
On Factor Decomposition of an Ergodic Groupoid
Authors: Yamagami Shigeru
Published: January 2008

Factor decomposition of cocycle regular representations of ergodic groupoids whose stabilizer groups are uniformly abelian is studied.
Gevrey Well-Posedness of an Abstract Cauchy Problem of Weakly Hyperbolic Type
Authors: D'Ancona Piero
Published: January 2008

We consider here a general second order Cauchy problem of hyperbolic type, with coefficients Holder continuous in the time variable and of Gevrey class in the space variables, in the abstract setting of Hilbert spaces. Some global and local existence results are proved to hold.
A New Method Using the Circles of Curvature for Solving Equations in $R^1$
Authors: Park Bong-kyu , Hitotumatu Sin
Published: January 2008

In this paper, we propose a numerical method using
the circles of curvature
for solving the equations in

R^1

, whose order of convergence is cubic. Some numerical examples are given, for which the method works well, while there is shown an example failed by means of
the Newton–Raphson's method
.
Sur les Classes Caractéristiques des Sous-Feuilletages
Authors: Domínguez Demetrio
Published: January 2008

The purpose of this paper is twofold. First, we compute thé cohomology algebras
H
(
W
(
g
,_H_1; and second, we study some properties of subfoliations, in order to give a geometric interpretation for certain secondary characteristic classes of subfoliations, in particular, Godbillon-Vey's classes of a subfoliation. We also construct examples of subfoliations with non-trivial Godbillon-Vey classes.
An Unbounded Generalization of the Tomita-Takesaki Theory II
Authors: Inoue Atsushi
Published: January 2008

An unbounded generalization of the fundamental concepts of the Tomita-Takesaki theory such as modular automorphism groups and Radon-Nikodym derivatives is considered.
Aspects of Integrability In Self-Dual Einstein Metrics and Related Equations
Authors: Takasaki Kanehisa
Published: January 2008

The nonlinear system describing self-dual Einstein metrics and its generalizations are discussed from the point of view of integrability. It is shown that these nonlinear systems share a variety of remarkable features (such as the existence of a linear scattering problem, a group-theoretical solution technique similar to the Riemann-Hilbert problem, and a geometric interpretation as dynamical motion in an infinite dimensional Grassmann manifold) with nonlinear integrable systems known until now. Differences of the relevant group-theoretical structures between these two classes of nonlinear systems are also pointed out. These results lead to the conclusion that the nonlinear systems in question do form a new class of nonlinear integrable systems.
Smooth Cores of Lipschitz Flows
Authors: Robinson Derek W.
Published: January 2008

We prove that the smooth elements of an abelian
C
*-dynamical system constitute a core of the associated Lipschitz flows.
Heyting Valued Set Theory and Sato Hyperfunctions
Authors: Nishimura Hirokazu
Published: January 2008

Following the lines of Takeuti and Titani [16] as well as Rousseau [9], this paper shows that Sato hyperfunctions with holomorphic parameters can be viewed as those without parameters in an appropriately chosen intuitionistic universe, where we establish, as an application of this idea, de Rham and Dolbeault theorems with hyperfunctional coefficients.
The Completion of the Maximal Op*-Algebra on a Frechet Domain
Authors: Kürsten Klaus-Detlef
Published: January 2008

This paper investigates the completion of the maximal Op*-algebra
L
+ (
D
) of (possibly) unbounded operators on a dense domain
D
in a Hilbert space. It is assumed that
D
is a Frechet space with respect to the graph topology. Let
D
+ denote the strong dual of
D
, equipped with the complex conjugate linear structure. It is shown that the completion of
L
+ (
D
) (endowed with the uniform topology) is the space of continuous linear operators ??? (
D
, <7>D+) . This space is studied as an ordered locally convex space with an involution and a partially defined multiplication. A characterization of bounded subsets of
D
in terms of self-adjoint operators is given. The existence of special factorizations for several kinds of operators is proved. It is shown that the bounded operators are uniformly dense in
L
+ (
D
).
Dressing Transformations and Poisson Group Actions
Authors: Semenov-Tian-Shansky Michael A.
Published: January 2008

Poisson properties of dressing transformations in soliton theory are explained.
On Central Limit Theorems in Probability Gage Spaces
Authors: Ekhaguere G.O.S.
Published: January 2008

Some limit theorems in probability gage spaces over semifinite
W
*-algebras are proved In particular, a Levy-Khinchine type of representation for the Fourier transforms of limit probability gages is established. The results are obtained by exploiting some of the algebraic and topological properties of certain sets of operators, called the decomposability algebraic structures, associated with probability gages. This work has a number of points of contact with aspects of (Euclidean) Quantum Field Theory.
Decompositions of Linear Maps Into Non-Separable $C^*$-Algebras
Authors: Huruya Tadasi
Published: January 2008

We study positive decompositions of bounded linear maps between

C^*

-algebras. A characterization of commutative injective

C^*

-algebras is given in terms of positive decompositions with certain norm condition of linear maps. We also provide under the Continuum Hypothesis a completely bounded map into the Calkin algebra which admits no positive decomposition.
Covariant Markov Dilations of Quantum Dynamical Semigroups
Authors: Frigerio Alberto
Published: January 2008

We develop a general theory of unitary dilations of quantum dynamical semigroups, satisfying a Markov property; and we construct explicit examples by means of the noncommutative stochastic calculus of Hudson and Parthasarathy.
Cramer-type Formula for the Polynomial Solutions of Coupled Linear Equations with Polynomial Coefficients
Authors: Sasaki Tateaki
Published: January 2008

This paper derives a determinant form formula for the general solution of coupled linear equations with coefficients in

K[x_1,\ldots , x_n]

, where

K

is a field of numbers, the number of unknowns is greater than the number of equations, and the solutions are in

K(x_1,\ldots, x_{n–1})[x_n]

. The formula represents the general solution by the minimum number of generators, and it is a generalization of Cramer's formula for the solutions in

K(x_1,\ldots , x_n)

. Compared with another formula which is obtained by a method typical in algebra, the generators in our formula are represented by determinants of quite small orders.
A Simple Proof of Kwapien's Theorem
Authors: Yamasaki Yasuo
Published: January 2008

The purpose of the present note is to prove in a self-contained way Kwapien's theorem that gives a criterion for Hilbertizability of normed spaces. Original proof [1], [2] has required much more complicated discussions. Many authors have investigated [3, 6] relating problems, but their researches are based on mutual quotations, thus it is difficult to follow their studies for readers not so familiar in the topic. So the author believes that a self-contained proof has some meaning.
On the Locality Ideal In the Algebra of Test Functions for Quantum Fields
Authors: Yngvason Jakob
Published: January 2008

Some basic properties of the locality ideal in Borchers's tensor algebra are established. It is shown that the ideal is a prime ideal and that the corresponding quotient algebra has a faithful Hilbert space representation. A topology is determined for which the positive cone in the quotient algebra is normal, and it is shown that every
n
-point distribution satisfying the locality condition is a linear combination of positive functional which also satisfy that condition.
Biquadratic Spline Approximations
Authors: Sakai Manabu , Usmani Riaz A.
Published: January 2008

We shall consider two kinds of spline approximations over a uniform mesh. The first of them is mid-point spline interpolation and the second is histospline approximation. Our methods don't need any knowledge of derivative values, that is, end conditions are homogeneous ones dealing with function values. The linear systems for computing approximations may be conveniently and rapidly solved using the simple algorithm. Some numerical results are given which closely correspond with the prediction of the theory.
Ortho-Independent States of the C. C. R. Algebra
Authors: Lindsay J. M.
Published: January 2008

We determine all states of the C.C. R.
C
* algebra [1] which have a certain independence property relative to a family of von Neumann sub-algebras indexed by subspaces of the test function space.
Functional Dependence between the Hamiltonian and the Modular Operator Associated with a Faithful Invariant State of a $W^*$-Dynamical System
Authors: de Cannière J.
Published: January 2008

Let

H

and

\Delta

be the hamiltonian, resp. the modular operator associated with an invariant faithful normal state

ω

of a

W^*

-dynamical system

(A, α)

. Then

Δ = f(h)

for some decreasing function

f

if and only if (roughly speaking)

ω

is 2-passive with respect to

α

. It follows that under certain conditions a 3-passive state is an equilibrium (i.e. KMS) state.
A Note on a Theorem of A. Connes on Radon-Nikodym Cocycles
Authors: Masuda Tetsuya
Published: January 2008

We give an alternative proof of a theorem of A. Connes that every unitary cocycle (relative to a modular automorphism of a weight _φ_0) is a Radon-Nikodym unitary cocycle (
Dφ
:_Dφ_0)
t
for some faithful normal semifinite weight
φ
.
On Positive Semigroups
Authors: Robinson Derek W.
Published: January 2008

We prove versions of the Feller-Miyadera-Phillips theorem characterizing the generators of positive _C_0- and _C_0*-semigroups on ordered Banach spaces, for which the norm and dual norm are monotonic. Two proofs are given. The first is based on half-norm theory whilst the second exploits the existence of an equivalent Riesz norm. This latter norm exists if, and only if, the positive cone is normal and generating.
Central Limits of Product Mappings between CAR-Algebras
Authors: Fannes Mark , Quaegebeur Johan
Published: January 2008

Product mappings between CAR-algebras are introduced. This notion is used to state and prove that generalised free completely positive mappings between CAR-algebras arise as central limits of general ones.
L'Existence d'une Fonction Analytique sur une Variété Analytique Complexe à Dimension Quelconque
Authors: Nishino Toshio
Published: January 2008

Dans le mémoire précédent [3], on a vu, pour une variété analytique complexe compacte ou bien pseudoconvexe à deux dimensions, que
l'existence d'une surface générique nous permet de former une fonction analytique sur toute la variété
. Cet énoncé peut être généralisé sans difficulté au cas de dimension quelconque. Le but de cette note est de l'indiquer dans les grandes lignes. Comme on peut le facilement voir, quelques énoncés établits pour le cas de deux dimensions dans [3] sont valables pour le cas général au prix de quelques modifications de leurs démonstrations. Ils seront donc utilisés dans cette note sans faire l'objet de démonstration. Quelques notions et quelques notations imposées seront aussi utilisées sans répéter leurs définitions.
Extensions of Quasi-Free Derivations on the CAR algebra
Authors: Price Geoffrey L.
Published: January 2008

We classify all of the infinitesimal generator extensions of a particular quasi-free derivation δ_A_ on the CAR (canonical anticommutation relations) algebra, where
A
is an unbounded symmetric operator on a Hilbert space having deficiency indices (1,1). We show that each of these extensions generates a strongly continuous one-parameter group of Bogoliubov transformations of the CAR algebra.
High Temperature Behaviour of Quantum Mechanical Thermal Functional
Authors: Combe Ph. , Rodriguez R. , Sirugue M. , Sirugue-Collin M.
Published: January 2008

We derive a representation of thermal functionals as expectation with respect to a Markov process in phase space of classical quantities. We prove also that the above quantities have a classical behaviour for high temperature.
Positive Cones and $L_p$-Spacesfor von Neumann Algebras
Authors: Araki Huzihiro , Masuda Tetsuya
Published: January 2008

The

L_p

-space

L_p (M, \eta)

for a von Neumann algebra

M

with reference to its cyclic
and separating vector

\eta

in the standard representation Hilbert space

H

of

M

is constructed either as a subset of

H

(for

2\leq p \leq \infty

), or as the completion of

H

(forl

1\leq p <2

) with an explicitly defined

L_p

-norm. The Banach spaces

L_p (M, \eta)

for different reference vector

\eta

(with the same

p

) are isomorphic.

Any

L_p

element has a polar decomposition where the positive part

L^+_p(M, \eta)

is defined to be either the intersection with the positive cone

V_\eta^{1/(2p)}

(for

2\leq p \leq \infty

) or the completion of the positive cone

V_\eta^{1/(2p)}

(for

1\leq p <2

). Any positive element has an interpretation as the

(1/p)

th power

\omega^{1/p}

of an

\omega \in M^+_*

with its

L_p

-norm given by

\|\omega\|^{1/p}

.

Product of an

L_p

element and an

L_q

element is explicitly defined as an

L_r

element
with

r^{-1}=p^{-1} +q^{-1}

provided that

1\leq r

, and the Hölder inequality is proved.

The

L_p

-space constructed here is isomorphic to those defined by Haagerup, Hilsum, and Kosaki.

As a corollary, any normal state of

M

is shown to have one and only one vector representative in the positive cone

V^\alpha_\eta

for each

\alpha\in [0, 1 /4 ]

.
Linear Radon-Nikodym Theorems for States on a von Neumann Algebra
Authors: Kosaki Hideki
Published: January 2008

Several linear Radon-Nikodym theorems for states on a von Neumann algebra are obtained in the context of a one parameter family of positive cones introduced by H. Araki. Among other results, we determine when a normal state
ϕ
admits a linear Radon-Nikodym derivative with respect to a distinguished normal faithful state _ϕ_0 in the sense of Sakai, that is,
ϕ
= _h ϕ_0 + _ϕ_0
h
with a positive
h
in the algebra.
Extended Landau Variety and the Singularity Spectrum of Position-Space Feynman Amplitudes
Authors: Kawai Takahiro
Published: January 2008

It is shown that the singularity spectrum of (generalized)
position-space
Feynman amplitude Δ_D_(
x
; λ) is confined to the extended Landau variety (introduced by Kashiwara-Kawai [8], [9] and Kashiwara-Kawai-Stapp [11](0)) associated with the Feynman diagram 
D
(0), which is obtained by replacing all the masses associated with the internal lines of 
D
with zero, at least under the assumption that the diagram 
D
is external.
An IMT-Type Double Exponential Formula for Numerical Integration
Authors: Mori Masatake
Published: January 2008

A quadrature formula for evaluation of improper integrals over

(−1,1)

is presented, which is obtained in such a way that the interval of integration

(−1, 1)

is transformed into

(−∞, ∞)

by

x=\tanh(A \sinh 2Bu / (1 − u^2))

and that the trapezoidal rule with an equal mesh size is subsequently applied to the transformed integral. Asymptotic error analysis is made by means of the method of contour integral and a comparison with the IMT-rule and the double exponential formula is given along with some numerical examples.
Theory of Division Games
Authors: Yamasaki Yohei
Published: January 2008

Lehman [9] generalized the Shannon's switching games to those on Boolean functions. We discuss in this paper, the theory of division games which contain Lehman's games and their reverse games. The theory of Lehman's games is analyzed and rearranged in this paper. Our results for division games contain naturally those for the classical ones as Hex, Bridg-it and their reverse games. Especially for the reverse games, we introduce several concepts dual to those introduced before, and obtain concise reformulations. The most significant feature of this paper is that we adopt the notion "assignment" to deal with generalized games in which the principle of alternate move does not necessarily hold. The classical results will be accordingly purified and divided into four theorems, i. e., Theorems 2, 3, 4 and 5, which indicate the dualities about points and about assignments, with respect to signature and to players. It is also a virtue of this generalization that we can characterize in a game theoretical argument the triple systems and the block designs _W_11 and _W_12 whose automorphism groups are Mathieu groups _W_11 and _W_12.
A Mixed Finite Element Method for the Biharmonic Eigenvalue Problems of Plate Bending
Authors: Ishihara Kazuo
Published: January 2008

In this paper, we obtain error estimates of a finite element solution by means of the mixed method for the biharmonic eigenvalue problem of plate bending. Some numerical examples are also given.
On the Fixed Point Algebra of a UHF Algebra under a Periodic Automorphism of Product Type
Authors: Kishimoto Akitaka
Published: January 2008

We study the fixed point algebra &" of a UHF algebra 21 under a periodic automorphism a of product type. We show an example of

la which is simple and has more than two tracial states and we characterize the case where 91* has only one tracial state. Next we show that

iff is a UHF algebra if and only if 21 is generated by an infinite family of mutually commuting a-invariant type IP subfactors whose fixed point algebras are abelian and by a UHF subalgebra of 21" which commutes with the former (where p denotes the period of a).
Relative Entropy of States of von Neumann Algebras
Authors: Araki Huzihiro
Published: January 2008

Relative entropy of two states of a von Neumann algebra is defined in terms of the relative modular operator. The strict positivity, lower semicontinuity, convexity and monotonicity of relative entropy are proved. The Wigner-Yanase-Dyson-Lieb concavity is also proved for general von Neumann algebra.
Propagation of Micro-analyticity for Solutions of Pseudo-differential Equations, I
Authors: Miwa Tetsuji
Published: January 2008

Propagation of micro-analyticity is studied for a solution
u
of a pseudo-diiferential equation
P
(
x
,
D
)
u
= 0 of a certain class whose characteristics are not necessarily of constant multiplicity.
Orbit Computation in Celestial Mechanics by Urabe's Method
Authors: Van Dooren René
Published: January 2008

The numerical computation of orbits in celestial mechanics can be performed by applying Urabe's method for the Galerkin procedure. High order Galerkin approximations are computed for two examples: Hill's variation orbit of the moon and the orbit of an artificial earth satellite. Excellent agreement with known results is obtained.
On Quasifree States of the Canonical Commutation Relations (I)
Authors: Araki Huzihiro , Shiraishi Masafumi
Published: January 2008

A self-dual CCR algebra is defined and arbitrary quasifree state is realized in a Fock type representation of another self-dual CCR algebra of a double size as a preparation for a study of quasi-equivalence of quasifree states.
On Quasifree States of the Canonical Commutation Relations (II)
Authors: Araki Huzihiro
Published: January 2008

A necesssary and sufficient condition for the quasi-equivalence of two quasifree primary representations of the canonical commutation relations is derived.