bluuebunny/crossref_metadata_2025 huggingface dataset:
Systèmes Différentiels Fuchsiens le Long d'une Sous-Variété
Authors: Laurent Yves , Monteiro Fernandes Teresa
Published: January 2008

Let

X

be a complex analytic manifold and let

Y

be a submanifold of

X

. We introduce
the notion of “fuchsian differential System along

Y

”, and we prove that for such Systems
the meromorphic solutions and those with essential singularities are the same. We prove as
well that the formal solutions (along

Y

) always converge. These results are well-known
in the regular holonomic case.

Soit

X

une variété analytique complexe et

Y

une sous-variété lisse de

X

. Nous introduisons la notion de “système différentiel fuchsien le long de

Y

”, et nous montrons que pour de tels systèmes les solutions méromorphes et les solutions à singularités essentielles sont les mêmes. Nous montrons aussi que les solutions formelles (le long de

Y

) sont toujours convergentes. Ces résultats sont bien connus dans le cas holonôme singulier régulier.
On a Stability Theorem for Local Uniformlzation In Characteristic $p^*$
Authors: Moh T.T.
Published: January 2008

A 2nd numerical

d

is bounded under blow-ups.
The Ergodicity of the Convolution $μ*υ$ on a Vector Space
Authors: Okazaki Yoshiaki , Takahashi Yasuji
Published: January 2008

Let

\mathrm G

be a subgroup of a vector space

X

and

μ,υ

be two probability measures on

X

. If

μ

and

υ

are

\mathrm G

-quasi-invariant and

\mathrm G

-ergodic, then the convolution

μ*υ

is also

\mathrm G

-ergodic.
Twisted $\textit{SU}(2)$ Group. An Example of a Non-Commutative Differential Calculus
Authors: Woronowicz Stanisław Lech
Published: January 2008

For any number

ν

in the interval

[-1, 1]

, a

C^*

-algebra

A

, generated by two elements

α

and

γ

satisfying simple (depending on

ν

) commutation relation, is introduced and investigated.

If

ν=1

, then the algebra coincides with the algebra of all continuous functions on the group

\textit{SU}(2)

. Therefore, one can introduce many notions related to the fact that

\textit{SU}(2)

is a Lie group. In particular one can speak about convolution products, Haar measure, differential structure, cotangent boundle, left invariant differential forms. Lie brackets, infinitesimal shifts and Cartan Maurer formulae. One can also consider representations of

\textit{SU}(2)

.

For

ν< 1

, the algebra

A

is no longer commutative, however the notions listed above are meaningful. Therefore,

A

can be considered as the algebra of all “continuous functions” on a “pseudospace

\textit{S}_\nu\textit{U}(2)

” and this pseudospace is endowed with a Lie group structure.

The potential applications to the quantum physics are indicated.
Completely Positive Stochastic Linear Maps Over AFD-Factors and Unitary Mixing on Generating U.H.F.-Subalgebras
Authors: Alberti Peter M.
Published: January 2008

Provided M is a non-finite AFD-factor, it it shown that the action of a completely positive, state-pre-serving linear map (stochastic map) on normal states over M can always be reduced to a unitary mixing mapping with respect to a generating U.H.F.-subalgebra.
Note on the EIlenberg-Moore Spectral Sequence
Authors: Yamaguchi Atsushi
Published: January 2008

In this paper, we prove two theorems on the Eilenberg-Moore spectral sequence. We give a relation between the Bockstein homomorphism in the _E_2-term and the Bockstein homomorphism of the space to which the spectral sequence converges and also relate the homology suspension to the Eilenberg-Moore spectral sequence.
Singular States on Maximal Op*-algebras
Authors: Löffler Frank , Timmermann Werner
Published: January 2008

The paper is devoted to the investigation of singular states on topological *-algebras of unbounded operators defined on (
F
)-domains. There are considered only functionals which are continuous with respect to the so called uniform topology τD. Equivalent characterizations of positive singular functional and a decomposition result for functionals are proved. Analogously to the bounded case positive singular functional can be given with the help of limits on free ultrafilters. Moreover, the state space of the maximal
Op
*-algebra is the
w
*-closed convex hull of vector states (pure states) - despite the fact that the state space is not
w
-compact.
When is a Field a Jacobi-Field? A Characterization of States on Tensor Algebras
Authors: Brüning Erwin
Published: January 2008

In order to analyse the positivity condition for states on the tensoralgebra

\underline E

over certain (function-)spaces

E

more efficiently a representation of the components of the states in terms of a set of “independent parameters” is suggested. For this purpose the concept of a Jacobifield is introduced. In the case of a finite dimensional space

E

every state on

\underline E

is “parametrized” this way. If however the basic space

E

is infinite dimensional additional domain problems arise related to algebras of unbounded operators which are involved naturally. It is analysed to which extent this “parametrization in terms of Jacobi-fields” also works in the general case, and it is shown that for “many” basic spaces

E

which occur in applications “most” of the states admit indeed such a “parametrization”. This then also means a corresponding decomposition for the associated algebra of unbounded operators into “independent components”. Several applications are indicated.
Cyclic Cohomology of $A[X]$ and $A[X,X^{–1}]$
Authors: Masuda Tetsuya
Published: January 2008

Cyclic cohomology of

A

coefficient polynomial algebra

A[X]

and Laurent polynomial algebra

A[X,X^{–1}]

is studied by making use of a deformation of projective resolution and the machinery of A. Connes. The spectral sequence

E^*_n

,

n ≥ 1

behaves the same as algebraic

K

-theory.
Jensen Measures and Maximal Functions of Uniform Algebras
Authors: Matsuoka Cho-ichiro
Published: January 2008

Our purpose here is to seek on an arbitrary uniform algebra the class of representing measures which admit a certain maximal function for each log-envelope function defined on the maximal ideal space of the algebra. These maximal functions can be considered as a proper generalization of those that are associated with two-dimensional Brownian motion in the concrete algebras

\boldsymbol R(K)

. Most of the results already obtained from the probabilistic approach, e. g. Burkholder–Gundy–Silverstein inequalities, a weaker form of Fefferman's duality theorem etc., are valid for our maximal functions. The remarkable feature of our class of representing measures is that it is stable under the weak-star limit and the convex combination. In the concrete algebras

\boldsymbol R (K)

, if the harmonic measure and the Keldysh measure for a given point of

K

are different, then our class of representing measures that are supported on the topological boundary of

K

forms an infinite-dimensional weak-star compact convex set in the dual of

\boldsymbol R (K)

.
A Dichotomy for Derivations on $\mathscr O_n$
Authors: Bratteli Ola , Evans David E. , Goodman Frederick , Jorgensen Palle E.T.
Published: January 2008

Let

\mathscr O_n

be the Cuntz algebra generated by

s_1, \cdots ,s_n

, and let

\mathscr P(\mathscr O_n)

be the

{}^*

-subalgebra of

{}^*

-polynomials in the generators. We show that if

\delta

is a gauge-invariant derivation mapping

\mathscr P(\mathscr O_n)

into

\mathscr P(\mathscr O_n)

, and

\delta

is approximately inner, then

\delta

is inner.
Reflection Positivity for the Complementary Series of $\textit{SL}(2n,ℂ)$
Authors: Schrader Robert
Published: January 2008

We apply the concept of reflection positivity in euclidean quantum field theory to the complementary series of

\textit{SL}(2n,ℂ)

as given by Gelfand and Neumark for

n=1

and by Stein for

n>1

. The result is a virtual representation in the sense of Fröhlich, Osterwalder and Seiler or equivalently a strongly continuous representation of a closed subsemigroup by contractions on a new Hilbert space. Analytic continuation gives a unitary representation of a certain dual group of

\textit{SL}(2n,ℂ)

. The possible relation to the theory of noncommuting monodromy matrices appearing in the theory of integrable quantum systems is briefly discussed.
Some Aspects of Normal Quantisation
Authors: Hannabuss Keith C. , Hennings Mark A.
Published: January 2008

A generalisation of the process of normal quantisation is studied which deals with a physical system whose phase space is given by a coadjoint orbit of a locally compact Lie group
G
. Under certain conditions, an algebra structure—implemented by a Fronsdal *-product—is assigned to the family of physical observables in such a way that the normal quantisation provides a representation of the algebra. This method, then, provides a useful means of determining a physically sensible Fronsdal *-product for a given system.
Quantum Mechanics and Nilpotent Groups. I. The Curved Magnetic Field
Authors: Jorgensen Palle E.T. , Klink W. H.
Published: January 2008

The quantum mechanics of massive spinless particles in an external magnetic field polynomial in position variables is shown to be related to nilpotent Lie groups. By using the known representation structure of such groups, the Hilbert spaces of the quantum mechanical systems can be decomposed into irreducible representations of the nilpotent groups. Such a decomposition is given explicitly for constant and curved magnetic fields. Since the Hamiltonian for polynomial magnetic fields is quadratic in the Lie algebra elements, its spectrum can be found using the representation structure of nilpotent groups. The explicit time dependence of the system can also be found by solving the heat equation on nilpotent groups. These ideas are worked out for the constant magnetic field, where the solution is well known, and the curved magnetic field, where it is not. Generalizations to other systems whose interaction terms are polynomial are also given.
On Grothendieck's Problem of Topologies
Authors: Alcántara-Bode Julio
Published: January 2008

Some classes of locally convex spaces

E

and

F

are identified for which not every bounded set of the completed projective tensor product,

E\widehat{\otimes}F

, is contained in the bipolar of some set

A\otimes B

, where

A

is bounded in

E

and

B

is bounded in

F

.
Theory of Symbolic Expressions, II
Authors: Sato Masahiko
Published: January 2008

A new domain S of symbolic expressions is introduced and its structure is studied formally. To study S formally an intuitionistic first order theory, SA, is introduced. SA is a theory adequate for developing elementary metamathematics within it. Gödels second incompleteness theorem is proved formally within SA to show the adequacy. A modified version of Post-Smullyan's formal system is used to define basic concepts in SA. The close relation between formal systems and the logic programming language Qute is also pointed out.
Conditional Probability and A Posteriori States in Quantum Mechanics
Authors: Ozawa Masanao
Published: January 2008

In order to develop a statistical theory of quantum measurements including continuous observables, a concept of a posteriori states is introduced, which generalizes the notion of regular conditional probability distributions in classical probability theory. Its statistical interpretation in measuring processes is discussed and its existence is proved. As an application, we also give a complete proof of the Davies-Lewis conjecture that there are no (weakly) repeatable instruments for non-discrete observables in the standard formulation of quantum mechanics, using the notion of a posteriori states.
Some Applications of Boolean Valued Set Theory to Abstract Harmonic Analysis on Locally Compact Groups
Authors: Nishimura Hirokazu
Published: January 2008

The main purpose of this paper is to extend Takeuti's [23] Boolean valued treatment of abstract harmonic analysis on locally compact abelian groups to locally compact groups (neither abelian nor compact in general). The distinctive feature of our approach, compared with traditional treatments of the subject, is that we can establish many important theorems without resort to direct integrals or to the theory of Banach algebras. By way of illustration, we will give such a proof of renowned Bochner's theorem. This paper is not intended to be exhaustive at all but hopefully to be suggestive. How far we can proceed in this direction yet remains to be seen.
Some Infinite Dimensional Groups and Bundles
Authors: Carey Alan L.
Published: January 2008

The group O of Bogoliubov automorphisms of the infinite dimensional Clifford algebra, implementable in a Fock representation, the analogous group of automorphisms of the canonical commutation relations and various generalisations are discussed. Their homotopy type is determined in a topology naturally defined by the spin and metaplectic representations. A theorem of Araki and Evans on a 2-index for certain projections is generalised using our "mod 2" index for ???. Connections with _K_1 of certain Banach algebras are described.
On an Abstract Analog of the Bellmann-Gronwall Inequality
Authors: Bainov D. D. , Myshkis A. D. , Zahariev A. I.
Published: January 2008

The paper considers one of the possible generalizations of the Volterra equations in the case when the independent variable belongs to an arbitrary compact metric space and, as a corollary of the obtained results, an abstract analog of the Bellman-Gronwall inequality is proved.
Coarse Moduli Space for Polarized Compact Kähler Manifolds
Authors: Fujiki Akira
Published: January 2008

Using the results of our previous papers [5] [8] [9] we shall construct the coarse moduli space for non-uniruled polarized compact Kahler manifolds as a separated complex space.
An Approach to the Dimension Theory of Continous Geometry from the Standpoint of Boolean Valued Analysis
Authors: Nishimura Hirokazu
Published: January 2008

Recently Boolean valued analysis (i.e., analysis based on Boolean valued set theory) has been extensively studied by G. Takeuti [14-16]. The main purpose of this paper is to show, by using this technique, that any continuous geometry can be viewed as an irreducible continuous geometry in its center valued set theory. This makes the transition from irreducible continuous geometries to reducible ones automatic.
On an Abstract Differential Equation and Its Application to Positive Eigenvalues of Schrödinger Operators
Authors: Wong Man W.
Published: January 2008

A second order differential equation in Hilbert space is shown to have only trivial solutions. This functional analytic result is then used to derive an upper bound for the set of positive eigenvalues of the one-body Schrödinger operator.
Time-Orthogonal Unitary Dilations and Noncommutative Feynman-Kac Formulae, II
Authors: Hudson Robin L. , Ion P. D.F. , Parthasarathy K. R.
Published: January 2008

In a previous paper [6] it was shown that a certain two-parameter dilation of a given strongly continuous self-adjoint contraction semigroup, called the time-orthogonal unitary dilation, gives rise to noncommutative Feynman-Kac formulae through the mechanism of Boson second quantisation in Fock space. This paper explores the modifications of this theory which arise firstly by using Fermion rather than Boson second quantisation, and secondly by using Boson second quantisation based on extremal universally invariant states of the CCR algebra. In the second case it is found that the programme is successful if and only if the infinitesimal generator of the original semigroup is of trace class.
Completeness of Noncompact Analytic Spaces
Authors: Ohsawa Takeo
Published: January 2008

Let
X
be a reduced paracompact complex analytic space of dimension
n
. It is proved that if
X
has no compact irreducible branches of dimension
n
, then
X
is
n
-complete, and if
X
has finitely many compact irreducible branches of dimension
n
,
X
is
n
-pseudoconvex, both in the sense of Andreotti-Grauert. Applying Andreotti-Grauert's finiteness theorem (resp. Barlet's theorem on the Steinness of cycle spaces) we deduce from our result Siu's theorem on analytic sheaf cohomology groups of noncompact complex spaces (resp. the Steinness of the space of (
n
—1) cycles of analytic spaces whose
n
-dimensional irreducible branches are non-compact).
Turbulence and Singularity of the Velocity Field
Authors: Kida Shigeo
Published: January 2008

The small-scale properties of turbulence are related to the singularity of the velocity field in the inviscid limit. The energy spectrum in the inertial range is expressed in terms of the fractal dimension and Holder's exponent of the singularity. It is pointed out that the entrainment process is important in the dynamics of active eddies in the
β
-model theory of turbulence.
Pattern Formation in Competition-Diffusion Systems in Nonconvex Domains
Authors: Matano Hiroshi , Mimura Masayasu
Published: January 2008

We deal with a weakly-coupled system of semilinear parabolic equations, namely a competition-diffusion system, and prove the existence of a stable spatially-inhomogeneous equilibrium solution on the assumption that the spatial domain is far from being convex and that the corresponding system of ODEs in the absence of diffusion posesses at least two distinct asymptotically stable equilibria. We also consider a non-weakly coupled system of competition type involving cross-diffusion terms, which leave the system quasilinear but no longer semilinear. The point of interest is to see how the shape of the spatial domain or the presence of cross-diffusion terms contributes to the occurrence of pattern formation.
A Method for Evaluation of the Error Function of Real and Complex Variable with High Relative Accuracy
Authors: Mori Masatake
Published: January 2008

A method for evaluation of the error function of real and complex variable by means of a trapezoidal sum with a correction term is proposed. This method gives a result with high relative accuracy with small number of operations. A precise upper bound of the relative error of the approximation for real variable is given.
Transformation Theory for Anti-Self-Dual Equations
Authors: Ueno Kimio , Nakamura Yoshimasa
Published: January 2008

An infinite-dimensional Lie algebra acting on solutions to the anti-self-dual equations on a four-dimensional Euclidean space is derived by means of the Riemann–Hilbert problem. Three types of Backlund transformations are considered in the framework of the Riemann–Hilbert problem.
Convergence of Martingales on a Riemannlan Manifold
Authors: Darling Richard W.R.
Published: January 2008

When the scalar quadratic variation of a martingale on a Riemannian manifold is finite almost surely, then the martingale converges almost surely in the one-point compactification of the manifold. A partial converse due to Zheng Wei-an is also proved. No curvature conditions on the manifold are required.
A Proof Description Language and Its Reduction System
Authors: Hagiya Masamichi
Published: January 2008

The normalization of a natural deduction proof of a closed existential formula

∃xA

gives a term

t

and a proof of

A_x[t]

. This allows us to regard a proof as a program (Goad [9] [10] etc.). But it is not always necessary to completely normalize the given proof to obtain

t

. We analyze the situation by introducing the notions called

minimal

I

-reduct, proper reduction

etc.; in a word, we define the
normal order
of proof reduction and study its proof-theoretical property. Then, we present an experimental proof-checker-reducer system that actually uses those principles. In designing a proof-checker (or rather a
proof description language
), we focussed our attention on the readability of proofs.
On Quasi-equivalence of Quasifree States of the Canonical Commutation Relations
Authors: Araki Huzihiro , Yamagami Shigeru
Published: January 2008

A necessary and sufficient condition for two quasifree states of CCR's (the canonical commutation relations) to yield quasi-equivalent representations is obtained, in the most general setting where states are non gauge-invariant in general and the symplectic form defining CCR might be degenerate (either from the start or after completion relative to the topology induced by states). The criterion consists of the following two conditions: (1) The induced topologies on the test function space are equivalent (2) operators

\tilde S

and

\tilde S'

on the completed test function space (completion relative to the induced topology, after taking quotient by the kernel of the representation) giving the two point functions

S

and

S'

(relative to any common inner product giving rise to the induced topology) are such that

\tilde S^{1/2} - \tilde S^{\prime 1/2}

is in the Hilbert Schmidt class.
Finite Element Approximations Applied to the Nonlinear Boundary Value Problem $Δu = bu^2$
Authors: Ishihara Kazuo
Published: January 2008

In this paper, we consider finite element approximations for the nonlinear boundary value problem

Δu = bu^2

, based on piecewise linear polynomials, and discuss iterative methods associated with the finite element schemes. Error estimates are obtained, which imply that the approximate solutions converge uniformly to the exact solution. Finally, we give some numerical examples indicating the effectiveness of our results.
A Product Formula and Its Application to the Schrödinger Equation
Authors: Ichinose Takashi
Published: January 2008

A product formula is given which represents the unitary group for the form sum of a pair of nonnegative selfadjoint operators in a Hilbert space.
On a Certain Semilinear Parabolic System Related to the Lotka-Volterra Ecological Model
Authors: Mimura Masayasu , Nishida Takaaki
Published: January 2008

A mathematical model proposed to explain the horizontal structure of prey and predator populations is represented by a semilinear parabolic system of equations. In this paper some mixed problems for this kind of system, Lotka-Volterra system, are considered and asymptotic behaviors of the solutions are investigated by use of Energy Method. A remarkable fact is that, in opposition to Steele's conjecture (see [3]), the solution in the case of the Neumann boundary condition is asymptotically spatially homogeneous but does not tend to any constant steady state solution.
On Limiting Gibbs States of the Two-Dimensional Ising Models
Authors: Higuchi Yasunari
Published: January 2008

We consider limiting Gibbs states in the two-dimensional ferromagnetic Ising model at sufficiently low temperatures. We prove that every limiting Gibbs state corresponding to a boundary condition such that

N^+/N^– < θ < 3/5

on every boundary is

μ^–

, where

N^+

is the number of up-spins on the boundary and

N^-

is that of down-spins. We also prove that for each

θ > 3/5

, there exists a boundary condition such that

3/5 < N^+/N^– ≤ θ

on every boundary, and the limiting Gibbs state corresponding to this boundary condition is

μ^+

.
A Finite Element Method for Solving the Two Phase Stefan Problem in One Space Dimension
Authors: Mori Masatake
Published: January 2008

A finite element method based on time dependent basis functions is presented for solving a two phase Stefan problem for the heat equation in one space dimension. The stability and the convergence of the method are studied, and a numerical example is given.
On Invariants $G(σ)$ and $Γ(σ)$ for an Automorphism Group of a von Neumann Algebra
Authors: Ikunishi Akio , Nakagami Yoshiomi
Published: January 2008

An invariant

Γ

for an automorphism group of a factor given by Connes is generalized to a general von Neumann algebra and the relation between

Γ

and a characterization of an inner automorphism group of a von Neumann algebra due to Borchers are discussed.
Derivations Determined by Multipliers on Ideals of a C*-Algebra
Authors: Elliott George A.
Published: January 2008

Sakai's theorem that every derivation of a simple C*-algebra is determined by a multiplier is generalized, in the class of separable approximately finite-dimensional C*-algebras, as follows. It is shown that, in such a C*-algebra, any derivation can be approximated arbitrarily closely in norm by a derivation which is determined by a multiplier on a nonzero closed two-sided ideal. It is shown, moreover, that the multiplier may be chosen to have norm bounded by fixed multiple of the norm of the derivation.
On the Periods of Certain Pseudorandom Sequences
Authors: Sato Masahiko
Published: January 2008

In [1], Rader et al. gave a fast method for generating pseudorandom sequences. Concerning these sequences, Moriyama et al. [2] made a research including the computational results by computers. In this paper we shall study the periods of these sequences, and give an affirmative answer to the following conjecture presented in [2]: "Let
k
(
n
) be the maximum period of
n
-bit pseudorandom sequences generated by the Rader's method. Then
k
(2_n_) = 2_k_(
n
) for all_n_." We shall also prove a number of algebraic properties of the periods, and give an efficient algorithm for computing
k
(
n
). We remark here that in this paper we are interested only in the algebraic properties of these sequences and not in the randomness of these sequences.
Bargmann's Inequalities In Spaces of Arbitrary Dimension
Authors: Seto Noriaki
Published: January 2008

An inequality is derived which gives an upper bound of the number of bound states in the

l

th partial wave (

l = 0,  1,…

) of the two-body Schrödinger equation with a spherically symmetric potential function in the

n

-dimensional space (

n = 1, 2,…

). This is a generalization of Bargmann’s inequality for the case

n = 3

. The generalization is straightforward for the case

l ≥ 1

with 

n = 2

and

l ≥  0

with 

n ≥ 3

. After a mathematically rigorous justification of his heuristic argument, Schwinger’s method in his simple proof of Bargmann’s inequality is employed here. Newton’s result for the case

l = –\frac 1 2

,  

n = 3

, which is equivalent to the case

l = 0

,

n = 2

, is reobtained.
On Derivation Trees of Indexed Grammars – An Extension of the uvwxy-Theorem
Authors: Hayashi Takeshi
Published: January 2008

In this paper, the uvwxy-theorem of context-free languages is extended to the case of indexed languages. Applying the extended theorem, it is shown that the finiteness problem for the indexed languages is solvable and certain languages such as

\{a^{n!} ∣ n ≥ 1\}

and

\{(\text{\textdollar}w)^{|w|}| w \in
\{a, b\}^*\}

are not indexed languages.
On the Definition of C*-algebras
Authors: Araki Huzihiro , Elliott George A.
Published: January 2008

It is shown that conditions

\Vert x y\Vert ≤ \Vert x\Vert \Vert y\Vert

and

\Vert x^*\Vert= \Vert x\Vert

follow from the other axioms for

C^*

-algebras.
A Remark on Bures Distance Function Remark on Bures Distance Function
Authors: Araki Huzihiro
Published: January 2008

An inequality between the norm of the difference of two vector states of a
W
* -algebra and the infimum distance between vectors representing the states in a fixed representation is derived.
Measures on infinite dimensional vector spaces
Authors: Umemura Yasuo
Published: January 2008

This paper consists of three chapters. In Chap. I, using a modification of Weil's theorem on invariant measures on groups, we shall give another proof of non-existence of translationally quasi-invariant measure on infinite dimensional vector spaces, which was firstly proved by Sudakov [6]. In Chap. II, we shall prove Minlos' theorem for nuclear spaces. The original Minlos' theorem [10] required more restrictions, but actually only the nuclearity condition is necessary. In Chap. Ill, we shall discuss infinite dimensional Gaussian measures, and prove that we can characterize a rotationally invariant measure as a superposition of Gaussian ones. For this fact, infinite dimensionality is essential. Some applications are stated in "Introduction".
Reflection of $\mathrm{C}^∞$ Singularities for a Class of Operators With Multiple Characteristics
Authors: Chazarain Jacques
Published: January 2008

Let

P,

a partial differential operator with real principal part and constant multiplicity characteristics. We have shown in some previous works [1], [2] that several results about operators with simple characteristics can be generalized to these operators with multiple characterics if we add an hypothesis, named Levi's condition, on the lower order terms. For instance, there is still propagation along bicharacteristics for the singularities of distributions

u

such that

Pu\in \mathrm{C}^∞(Ω)

; if moreover the principal part of

P

is hyperbolic, the Cauchy problem is well posed in the

\mathrm{C}^∞

setting.

In this paper, we shall give a generalization to such operators of the theorem of Lax–Nirenberg [6] concerning the reflection at the boundary

∂ Ω

of the singularities of distributions

u

satisfying

Pu\in \mathrm{C}^∞(\bar Ω)

. In order to get a more precise result of regularity up to the boundary, we shall differ from Nirenberg's proof in the details, but the principle will be the same. That is, we factorise micro locally

P

in an elliptic and two hyperbolic factors satisfying the Levi condition; then the proof of the theorem will be reduce to the study of micro local regularity results for elliptic and hyperbolic boundary problems.
Singularities and Newton Polygons
Authors: Kantor Jean-Michel
Published: January 2008

It was conjectured by V. I. Arnold that it should be possible to express all "reasonable" invariants associated to a holomorphic function, in terms of its Newton polygon, at least for "almost all" functions with a given polygon. This conjecture has been worked out in many cases by the joint results of Arnold's school (D. Bernstein, A. Kouchnirenko, A. Varchenko, A. Xovanski). Their results will be the subject of this talk. In particular, the work of Varchenko concerning monodromy and oscillatory integrals should be of great interest in relation with the theory of b-functions.
Discontinuity Formula and Sato's Conjecture
Authors: Kawai Takahiro , Stapp Henry P.
Published: January 2008

The
S
-matrix discontinuity formulas are used to show that in neighborhoods of many physical points the
S
-matrix is a holonomic microfunction.
Quantum Field Theory in Terms of Fourier Hyperfunctions
Authors: Nagamachi Shigeaki , Mugibayashi Nobumichi
Published: January 2008

The Wightman axioms are extended to the quantum field theory in terms of Fourier hyperfunctions. The support concept of hyperfunctions is crucial for the formulation of locality and spectral condition. The complete equivalence is proved between modified Wightman axioms for relativistic theory and modified Osterwalder–Schrader axioms for Euclidean theory.
Complex-dimensional Integral and Light-cone Singularities
Authors: Nakanishi Noboru
Published: January 2008

The notion of a complex-dimensional integral is introduced in the complex
n
-dimensional Minkowski space. Its basic properties, such as Lorentz invariance, are investigated. Complex-dimensional invariant delta functions
Δn
(_x,m_2),
Δ(1)n
(_x,m_2), etc. are explicitly calculated in position space. It is proposed to define products of singular functions in the ordinary Minkowski space by analytically continuing the corresponding
n
-dimensional ones to
n
=4. The light-cone singularities of [
Δ
(_x,m_2)]2,
Δ
(_x,m_2) x
Δ
(1)(_x,m_2)]2 and
Δ
(1)(_x,m_2)]2 are shown to be unambiguously determined in this way.
Existence and Continuation of Holomorphic Solutions of Partial Differential Equations
Authors: Pallu de la Barrière Ph.
Published: January 2008

Necessary conditions and sufficient conditions are given for the existence and the continuation of holomorphic solutions of partial differential equations near the characteristic boundary of an open subset of

\boldsymbol C^n

.
Ultradifferentiable Fundamental Kernels of Linear Partial Diﬀerential Operators on Non-quasianalytic Classes of Roumieu Type
Authors: Albanese Angela A. , Bonet José
Published: January 2008

Let

P

be a linear partial differential operator with coeffcients in the Roumieu class

\mathcal E_{\{ω\}}(Ω)

. We prove that if

P

and its transposed operator

{}^tP

are

\{ω\}

-hypoelliptic in

Ω

and surjective on the space

\mathcal E_{\{ω\}}(Ω)

, then

P

has a global two-sided ultradifferentiable fundamental kernel in

Ω

, thus extending to the Roumieu classes the well-known analogous result of B. Malgrange in the

C^∞

class. This result is new even for Gevrey classes.
Simply Laced Extended Affine Weyl Groups (A Finite Presentation)
Authors: Azam Saeid , Shahsanaei Valiollah
Published: January 2008

Extended affine Weyl groups are the Weyl groups of extended affine root systems. Finite presentations for extended affine Weyl groups are known only for nullities

≤ 2

, where for nullity

2

there is only one known such presentation. We give a ﬁnite presentation for the class of simply laced extended affine Weyl groups. Our presentation is nullity free if rank

> 1

and for rank

1

it is given for nullities

≤ 3

. The generators and relations are given uniformly for all types, and for a given nullity they can be read from the corresponding ﬁnite Cartan matrix and the semilattice involved in the structure of the root system.
Estimates of Kato–Temple Type for $n$-dimensional Spectral Measures
Authors: Kuroda S. T.
Published: January 2008

The Kato–Temple estimate for an isolated eigenvalue of a selfadjoint operator is extended to spectral measures on

\mathbf R^n

, or equivalently, a commuting set of

n

selfadjoint operators. The proof depends on a general variational characterization of the spectrum. In the case of normal operators this corresponds to Rayleigh bounds applied to resolvents. It is also shown that the obtained estimate has a certain invariance property under an inversion of the space.
Magnetic Pseudodifferential Operators
Authors: Iftimie Viorel , Măntoiu Marius , Purice Radu
Published: January 2008

In previous papers, a generalization of the Weyl calculus was introduced in connection with the quantization of a particle moving in

ℝ^n

under the inﬂuence of a variable magnetic ﬁeld

B

. It incorporates phase factors deﬁned by

B

and reproduces the usual Weyl calculus for

B = 0

. In the present article we develop the classical pseum dodifferential theory of this formalism for the standard symbol classes

S^m_{ρ,δ}

. Among others, we obtain properties and asymptotic developments for the magnetic symbol multiplication, existence of parametrices, boundedness and positivity results, properties of the magnetic Sobolev spaces. In the case when the vector potential

A

has all the derivatives of order

≥ 1

bounded, we show that the resolvent and the fractional powers of an elliptic magnetic pseudodifferential operator are also pseudodifferential. As an application, we get a limiting absorption principle and detailed spectral results for self-adjoint operators of the form

H = h(Q, Π^A)

, where

h

is an elliptic symbol,

Q

denotes multiplication with the variables

Π^A = D − A

,

D

is the operator of derivation and

A

is the vector potential corresponding to a short-range magnetic ﬁeld.
Galois Covers of Degree $p$ and Semi-Stable Reduction of Curves in Mixed Characteristics
Authors: Saïdi Mohamed
Published: January 2008

In this paper we study the degeneration of a Galois cover

f : \mathcal Y →\mathcal X

of degree

p

above a proper and smooth curve

\mathcal X

over a complete discrete valuation ring of mixed characteristics

(0, p)

. We exhibit geometric and combinatorial
degeneration data
which describe the geometry of the special ﬁber of a minimal semi-stable model of

\mathcal Y

.
On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces
Authors: Ferrer Jesús
Published: January 2008

We show constructively that every homogeneous polynomial that is weakly continuous on the bounded subsets of a real Banach space whose dual is not weak

{}^∗

-separable admits a closed linear subspace whose dual is not weak

{}^∗

-separable either where the polynomial vanishes. We also prove that the same can be said for vectorvalued polynomials. Finally, we study the validity of this result for continuous 2-homogeneous polynomials.
Asymptotic Behavior of the Semigroup Associated with the Linearized Compressible Navier–Stokes Equation in an Inﬁnite Layer
Authors: Kagei Yoshiyuki
Published: January 2008

Asymptotic behavior of solutions to the linearized compressible Navier–Stokes equation around a given constant state is considered in an inﬁnite layer

\mathbf R^{n−1} × (0, a)

,

n ≥ 2

, under the no slip boundary condition for the momentum. The

L^p

decay estimates of the associated semigroup are established for all

1 ≤ p ≤ ∞

. It is also shown that the time-asymptotic leading part of the semigroup is given by an

n − 1

dimensional heat semigroup.
Numerical Solutions of Serrin’s Equations by Double Exponential Transformation
Authors: Hamada Shinsuke
Published: January 2008

We consider Serrin’s equations, which describe a steady ﬂow of the incompressible viscous ﬂuid caused by an interaction between a vortex ﬁlament and a planar wall. They are integro-diﬀerential equations with a singularity at an end point. By means of the double exponential transformation, we numerically solve their solutions with high accuracy, and compute a sufficient condition on the uniqueness of the solution.
Poisson Equations with Nonlinear Source Terms on Networks
Authors: Chung Soon-Yeong , Kim Dohan , Lee Nam Kee
Published: January 2008

C. Berenstein and the ﬁrst author introduced an elliptic operator

∆_ω

and an

ω

-harmonic function on graphs, with its physical interpretation as a diffusion equation on graphs, which models electric networks. They also proved the solvability of the problems such as the Dirichlet and Neumann boundary value problems for the Laplace equation and the Poisson equation on networks. In this paper, we consider the Poisson equation with nonlinear source term on networks and show the existence and the uniqueness of a solution with suitable source term.
On Holomorphic $L^2$ Functions on Coverings of Strongly Pseudoconvex Manifolds
Authors: Brudnyi Alexander
Published: January 2008

In this paper we answer an important question posed in the paper [GHS] by Gromov, Henkin and Shubin on existence of sufficiently many holomorphic

L^2

functions on arbitrary coverings of strongly pseudoconvex manifolds.
A Note on Embeddings of $S_4$ and $A_5$ into the Two-dimensional Cremona Group and Versal Galois Covers
Authors: Bannai Shinzo , Tokunaga Hiro-o
Published: January 2008

In this article, we prove that two versal Galois covers for

S_4

and

A_5

introduced in [17], [18] and [19] are birationally distinct to each other. As a corollary, we obtain two non-conjugate embeddings of

S_4

and

A_5

into

\mathrm{Cr}_2 (ℂ)

.
Dynamical Yang–Baxter Maps with an Invariance Condition
Authors: Shibukawa Youichi
Published: January 2008

By means of left quasigroups

L = (L, \cdot)

and ternary systems, we construct dynamical Yang–Baxter maps associated with

L

,

L

, and

(\cdot)

satisfying an invariance condition that the binary operation

(\cdot)

of the left quasigroup

L

deﬁnes. Conversely, this construction characterize such dynamical Yang–Baxter maps. The unitary condition of the dynamical Yang–Baxter map is discussed. Moreover, we establish a correspondence between two dynamical Yang–Baxter maps constructed in this paper. This correspondence produces a version of the vertex-IRF correspondence.
Training in Psychiatry: An Examination of Trainee Perceptions. Part 1
Authors: Kozlowska Kasia , Nunn Kenneth , Cousens Pennelope
Published: January 2008

Objective: To look at the perceptions of New South Wales (NSW) psychiatric trainees in relation to their training experiences and the role and quality of the consultant registrar relationship.

Methods: A self-report questionnaire was developed to probe trainee perceptions of the consultant–trainee relationship in all those who had completed at least 1 year of training in psychiatry (n = 138) in NSW, as well as all consultants who had completed their training in the last 5 years (n = 95). Test-retest reliability was assessed at 3 months for each of the subscales (r = 0.70–0.89) and found to be acceptable. Validity issues are discussed.

Results: The results are discussed with special reference to the perceived competence, availability, breadth of knowledge and willingness to accept responsibilities of the supervising consultant. Consultant competence as a clinician was consistently rated as more important than being emotionally supportive.

Conclusion: In addressing these issues, we aim to increase the degree of self-consciousness and reflectiveness of the profession of psychiatry within the Australian context. If there is to be a substantial shift for the better in trainees' perceptions of consultants, it is likely that the general consultant experience will have to be improved rather than providing small amounts of exposure to high quality consultants.
Gender, Race and Poverty: Bringing the Sociopolitical into Psychotherapy
Authors: Krawitz Roy , Watson Christine
Published: January 2008

Objective: To explore the modification of traditional psychotherapy to provide a more relevant service for non-dominant groups including women, Maori and the poor.

Method: The philosophy and practice of a psychotherapy service that made overt sociopolitical issues for women, Maori and the poor was analysed and linked with literature on psychotherapy for non-dominant groups.

Results: Traditional psychotherapy, with its focus on the intrapsychic, has not addressed the condition of marginalised groups such as the poor, ethnic minorities including Maori, and some women, whose mental health difficulties have major contributions from external sources. The service analysed, and much of the literature, used social analysis as a therapeutic tool to break the cycle of self-blame and doubt and to contextualise intrapsychic experience. As non-dominant groups lack power, power differences in the therapy relationship should be lessened to avoid retrauma-tising the patient.

Conclusion: It is possible for psychotherapy to broaden its traditional base to include a sociopolitical viewpoint. This would make it more available and meaningful to a wider range of people, especially those with the double disadvantage of adverse intrapsychic and sociopolitical factors.
Comparative Levels of Psychological Distress in a Pre-Migratory Refugee Population
Authors: McKelvey Robert S. , Webb John A.
Published: January 2008

Objective: This study compares levels of psychological distress in a pre-migratory sample of Vietnamese Amerasians with those in a like-aged, non-migratory sample of Vietnamese living in Ho Chi Minh City, Vietnam.

Method: Subjects were assessed using two measures developed and validated for Vietnamese clinical populations in the United States: the Hopkins Symptom Checklist-25 and the Vietnamese Depression Scale.

Results: Amerasians had significantly higher symptom levels on the depression scale of the Hopkins Symptom Checklist-25, but not on the other measures utilised.

Conclusions: Amerasians' higher levels of depressive symptoms are probably a result of their traumatic lives in Vietnam, but may also reflect acute situational factors or selection bias.
Depressive Symptoms in Patients with HIV Infection: A Further Exploration
Authors: Judd Fiona , Mijch Anne , McCausland Jean , Cockram Alex
Published: January 2008

Objective: The aim of this study was to assess the frequency and severity of depressive symptoms, to determine the rate of depressive disorder, to explore possible reasons for the development of depressive symptoms and to examine the effects of depression in a group of human immunodeficiency virus (HIV)-positive patients.

Method: HIV-positive patients attending an outpatient treatment facility were assessed by the research psychologist and completed a number of questionnaires: the Beck Depression Inventory (BDI); the Life Event Inventory (LEI); the Core Bereavement Item (CBI-17) questionnaire; and the Psycho social Adjustment to Illness Scale (PAIS). Patients scoring 2 14 on the BDI were seen by the psychiatrist for further assessment, and where appropriate, diagnoses were made according to DSM-III-R criteria.

Results: One hundred and ninety-two patients participated in the study; 95 scored ≥ 14 on the BDI and one-third of these were found to have a depressive disorder. Factors significantly predictive of a BDI score ≥ 14 were: an LEI score ≥ 77; a diagnosis of acquired immunodeficiency syndrome (AIDS); being on sickness benefits or a pension; no current relationship; and a past history of depression. Few differences were demonstrated between those with a depressive disorder and those with a BDI score ≥ 14 but no diagnosis of depressive disorder. Both groups had high mean PAIS scores indicating significant illness effects in multiple areas of function.

Conclusions: Depressive symptoms are common among patients with HIV infection. Few factors differentiate between patients with a depressive disorder and those whose depressive symptoms do not meet diagnostic criteria. Substantial disability is present in both groups.
Molecular Biology and the Major Psychoses
Authors: Lloyd Andrew , Dixon Gavin , Huang Xu Feng , Ward Phillip , Catts Stan , Hickie Ian , Wakefield Denis
Published: January 2008

Objective:To highlight the potential role of molecular biological studies in examining the expression of genes of interest in brain tissue to elucidate the pathophysiological basis of the major psychoses.

Method:To review the principles underlying the available techniques for expression studies.

Results:Detection of messenger RNA by in situ hybridisation and quantitation by Northern analysis are powerful tools to detect abnormalities in gene expression in brain tissue.

Conclusion:The availability of simple techniques to examine the expression of RNA and protein products of individual genes, including examination at the level of individual cells, offers a clear opportunity to define the molecular basis of the major psychoses.
Utilising Molecular Biological and Histopathological Techniques to Study the Dopaminergic System in Patients with Melancholia
Authors: Hickie Ian , Lloyd Andrew , Dixon Gavin , Wakefield Denis , Halliday Glenda , McRitchie Deborah , Scott Elizabeth , Mitchell Philip
Published: January 2008

Objective:To describe the rationale for investigating the dopaminergic system in patients with melancholia by applying molecular biological (notably, in situ hybridisation) and histopathological techniques in postmortem brain tissue.

Method:Relevant advances in the functional neuroanatomy of frontostriatal circuits, as well as insights from clinical neuroimaging studies in primary and secondary depressive disorders, are presented. These are integrated with developments in the pharmacological and molecular characteristics of dopamine receptor subtypes and recognition of their selective anatomical distribution.

Results:Converging data from the basic and clinical neurosciences suggest that the pathophysiology of depressive disorders characterised by psychomotor phenomena, such as melancholia, may involve dysregulation of dopaminergic mechanisms within complex frontostriatal circuits.

Conclusions:The key feature of in situ hybridisation is its capacity to test for variations in the functional components of designated biochemical systems within highly specific anatomical regions. We utilise this approach, in combination with relevant histopathological techniques, to test the structural and functional integrity of the dopaminergic system within key fronto-striatal circuits in patients who had exhibited psychomotor phenomena. The same approach can also be used to study the integrity of other relevant biochemical systems, such as the serotoninergic and noradrenergic systems, in patients with other mood disorders.