ICTP - The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

List of Abstracts of 1997 Preprints
in Mathematics issued at ICTP

ICTP Preprint No.

IC/97/4

THE USE OF SURVIVAL ANALYSIS TECHNIQUE
IN THE ESTIMATION OF AGE AT FIRST CALVING
OF COWS PARITY DATA
by F.W.O Saporu
ABSTRACT: A survival analysis technique is proposed for estimating the average age at first calving of a herd of cows from their parity data. The details of the method are illustrated with two data sets arising from different livestock management systems. The average age at first calving is estimated for each system. The effects of physiological, haematological and biochemical variables on the age at first calving are also investigated.

ICTP Preprint No.

IC/97/10

ON THE COHOMOLOGY OF REGULAR DIFFERENTIAL FORMS
AND DUALIZING SHEAVES
by Reinhold Hubl and Xiaotao Sun
ABSTRACT: If $Y$ is a local Dedekind scheme and $X/Y$ is a projective Cohen-Macaulay variety of relative dimension $1$, then $R^1 f_*\omega^1_{X/Y}$ is torsion free, if and only if $X/Y$ is arithmetically Cohen-Macaulay for a suitable embedding in $\Bbb P^n_k$. If $X$ is regular then $R^1 f_* \omega^1_{X/Y}$ is torsion free whenever the multiplicity of the special fibre is not a multiple of the characteristic of the residue class field.

ICTP Preprint No.

IC/97/13

VECTOR BUNDLES ON THE PROJECTIVE LINE OVER A DISCRETE VALUATION RING
by Reinhold Hubl and Xiaotao Sun
ABSTRACT: No abstract provided.

ICTP Preprint No.

IC/97/15

ANALYSIS OF SINGULARITIES IN THE NONLINEAR WAVES
FOR QUASILINEAR HYPERBOLIC SYSTEMS
by Kong De-Xing
ABSTRACT: It is well-known that classical solutions of quasilinear hyperbolic system in general have singularities even if their initial data are smooth. In this paper we apply the singularity theory of smooth mapping to show that the singularities of these solutions are in general fold points, and at the points where the shock waves occur initially, the singular points are cusp points. At the same time, we prove that the blow-up points must be on the envelope curve of characteristics in the same family. Finally, we give a clear structure of singularities of the solution for a system with the form of conservation laws.

MODULI OF REGULAR HOLONOMIC $\cal D$-MODULES WITH NORMAL CROSSING SINGULARITIES
by Nitin Nitsure
ABSTRACT: This paper solves the global moduli problem for regular holonomic $\cal D$-modules with normal crossing singularities on a nonsingular complex projective variety. This is done by introducing a level structure (which gives rise to Òpre-$\cal D$-modulesÓ), and then introducing a notion of (semi-)stability and applying Geometric Invariant Theory to construct a coarse moduli scheme for semistable pre-$\cal D$-modules. A moduli is constructed also for the corresponding perverse sheaves, and the Riemann-Hilbert correspondence is represented by an analytic morphism between these moduli spaces.

ICTP Preprint No.

IC/97/21

MODULI OF REGULAR HOLONOMIC $\cal D$-MODULES
WITH NORMAL CROSSING SINGULARITIES
by Nitin Nitsure
ABSTRACT: This paper solves the global moduli problem for regular holonomic $\cal D$-modules with normal crossing singularities on a nonsingular complex projective variety. This is done by introducing a level structure (which gives rise to Òpre-$\cal D$-modulesÓ), and then introducing a notion of (semi-)stability and applying Geometric Invariant Theory to construct a coarse moduli scheme for semistable pre-$\cal D$-modules. A moduli is constructed also for the corresponding perverse sheaves, and the Riemann-Hilbert correspondence is represented by an analytic morphism between these moduli spaces.

ICTP Preprint No.

IC/97/22

EXISTENCE OF DISCRETE GAUGE HOLONOMY EFFECTS
by Brett McInnes
ABSTRACT: Let $G$ be any compact but not necessarily connected Lie group, and let $M$ be any connected paracompact manifold. We give an existence theory for connections on principal $G$-bundles over $M$, requiring the holonomy group to be $G$. That is, we consider the problem of constructing non-trivial ÒdiscreteÓ gauge configurations. Several techniques are explained, and it is also shown that for some simple choices of $G$ and $M$ it is actually {\em impossible} to construct such a configuration.

ICTP Preprint No.

IC/97/35

PHOTON DISTRIBUTION FUNCTION
FOR STOCKS WAVE STIMULATED RAMAN SCATTERING
by O.V. Man'ko and N.V. Tcherniega
ABSTRACT: New time-dependent integrals of motion are found for stimulated Raman scattering. Explicit formula for the photon-number probability distribution as a function of the laser-field intensity and the medium parameters is obtained in terms of Hermite polynomials of two variables.

ICTP Preprint No.

IC/97/36

EXISTENCE OF PARALLEL SPINORS OF NON-SIMPLY-CONNECTED
RIEMANNIAN MANIFOLDS
by Brett McInnes
ABSTRACT: It is well known, and important for applications, that Ricci-flat Riemannian manifolds of non-generic holonomy always admit a parallel [covariant constant] spinor if they are simply connected. The non-simply-connected case is much more subtle, however. We show that a parallel spinor can still be found in this case {\em provided} that the [real] dimension is not a multiple of four, and {\em provided} that the spin structure is carefully chosen.

ICTP Preprint No.

IC/97/39

FORMATION OF SINGULARITIES
IN ONE-DIMENSIONAL HYDROMAGNETIC FLOW
by Kong De-Xing
ABSTRACT: Two results on the formation of singularities in solutions to the system of one-dimensional hydromagnetic dynamics under various assumptions on the initial data are presented. In particular, it is shown that a smooth periodic solution will develop shocks in a finite time if the initial amounts of entropy and the Òmagnetic fieldÓ in each period is smaller than that of sound waves. We also give a quantitative estimate of the blow-up time.

ICTP Preprint No.

IC/97/42

BIGEBROIDES DE LIE
ET EQUATION DE YANG-BAXTER DYNAMIQUE CLASSIQUE
by Momo Bangoura
ABSTRACT: Lie bialgebroids introduced by K.Mackenzie and P.Xu [M.X] are natural generalisations of Lie bialgebras. On the other hand, the classical dynamical Yang-Baxter equation (CDYBE) is a generalisation of the classical Yang-Baxter equation (CYBE). We show that, just as the solutions of CYBE yield Lie bialgebra structures, the solutions of CDYBE correspond to Lie bialgebroid structures.

ICTP Preprint No.

IC/97/47

HIGHER CLASS GROUPS OF ORDERS
AND INTEGRAL GROUP RINGS
by Aderemi O. Kuku
ABSTRACT: No abstract provided

ICTP Preprint No.

IC/97/48

HIGHER K-THEORY OF ORDERS AND GROUP RINGS
OF FINITE GROUP OVER INTEGERS
IN NUMBER THEORY
by Aderemi O. Kuku
ABSTRACT: No abstract provided.

ICTP Preprint No.

IC/97/51

MAXIMAL ELEMENTS
OF SUPPORT AND COSUPPORT
by Siamak Yassemi
ABSTRACT: We introduce a set that is tightly closed to the set of the Jacobson radical of module (the intersection of all maximal elements in support). In the last section, it is proved that the set of zero divisors of a module is equal to the union of the maximal elements of the support of module if the module in finitely generated and injective.

ICTP Preprint No.IC/97/52 EQUIVARIANT HIGHER K-THEORY
FOR COMPACT LIE GROUP ACTIONS
by Aderemi O. Kuku
ABSTRACT: No abstract provided.

ICTP Preprint No.IC/97/53 PRIMITIVE COMPACT FLAT MANIFOLDS
WITH HOLONOMY GROUP $Z_2 \oplus Z_2$
by Paulo A. Tirao
ABSTRACT: In this paper we determine and classify all compact flat manifolds with holonomy group isomorphic to ${\bold z}_2\oplus{\bold z}_2$ and first Betti number zero.

ICTP Preprint No.IC/97/55 THE DUAL NOTION OF PRIME SUBMODULES
by Siamak Yassemi
ABSTRACT: In this paper the concept of the second submodule (the dual notion of prime submodule) is introduced.

ICTP Preprint No.IC/97/57 NONLINEAR WAVES FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW
THROUGH POROUS MEDIA
by Liu Fa-gui and Kong De-xing
ABSTRACT: By using the Maximum principle the authors give a fair complete result for the global existence and for the blow-up phenomena of classical solutions to the Cauchy problem for the system of compressible adiabatic flow through porous media.

ICTP Preprint No.IC/97/60 PSEUDO-KAHLER QUANTIZATION ON FLAG MANIFOLDS
by Alexander V. Karabegov
ABSTRACT:A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kahler structure is proposed. In particular cases we arrive at Berezin's quantization via covariant and contravariant symbols.

ICTP Preprint No.IC/97/66 ON THE DELIGNE-LUSZTIG CURVE ASSOCIATED TO THE SUZUKI GROUP
by Fernando Torres
ABSTRACT: We give a characterization of the Deligne-Lusztig curve associated to the Suzuki group $Sz(q)$ based on the genus and the number of ${\Bbb F}_q$-rational points of the curve.

ICTP Preprint No.IC/97/72 STEEPEST DESCENT METHOD FOR A CLASS OF NONLINEAR EQUATIONS
by C.E. Chidume and Chika Moore
ABSTRACT: Let E be a real uniformly smooth Banach space and let $A:D(A) \subseteq E\mapsto E$ be a $\psi$-strongly quasi-accretive operator such that the equation $Ax=f$ has a solution $x^{*}\in D(A)$. We introduce a general steepest descent method and prove that it converges strongly to $x^{*}$. Our iteration parameters are independent of the geometry of $E$. We also establish the stability of our methods and obtain explicit convergence rates. Furthermore, we provide an affirmative answer to a question raised by Li-Shan Liu (see Math. Review 96f:47107). Related results deal with the iterative approximation of fixed points of $\psi$-strong pseudocontractions and quasi-nonexpansive maps.

ICTP Preprint No.IC/97/73 STRONG CONVERGENCE AND STABILITY OF FIXED POINT ITERATION PROCESSES
by Chika Moore
ABSTRACT: Let $K$ be a bounded closed convex nonempty subset of a real uniformly smooth Banach space $E$. Let $T:K\mapsto K$ be a strongly pseudocontractive mapping. It is proved that fixed point iteration processes of the Mann and Ishikawa types converge strongly to the fixed point of $T$ and are $T$-stable. Related results deal with strong convergence and stability of the iteration processes for certain nonlinear operator equations.

ICTP Preprint No.IC/97/74 ITERATIVE SOLUTION OF NONLINEAR EQUATIONS IN ARBITRARY BANACH SPACES
by Chika Moore
ABSTRACT: Let $E$ be an arbitrary real Banach space and let $K$ be a proximinal subset of $E$ with a nonempty interior $K^o$. Let $T: K\mapsto E$ be a uniformly continuous strongly accretive operator such that the operator equation $Tx=f$ has a solution $x^*\in K^o$. It is proved that modified iteration processes of the Mann and Ishikawa types converge strongly to $x^*$. If $E$ is reflexive and $T$ is locally uniformly continuous with an open domain $D(T)$, similar results are obtained. Related results deal with the solution of the operator equation $x+Tx=f$ and the approximation of fixed points of strong pseudocontractions. Explicit convergence rates are also given. The technique of the proof is of independent interest.

ICTP Preprint No.IC/97/78 QUASI-BIGEBRES JACOBIENNES
QET ALGEBRES QUASI-BATALIN-VILKOVISKY
by Momo Bangoura
ABSTRACT: To follow in due course.

ICTP Preprint No.IC/97/79 COCHAIN ALGEBRAS OF L-S CATEGORY 1
by Bitjong Ndombol
ABSTRACT: To follow in due course.

ICTP Preprint No.IC/97/80 INERTIA AND TWISTED TENSOR PRODUCTS
by Bitjong Ndombol
ABSTRACT: To follow in due course.

ICTP Preprint No.IC/97/81 A MODEL OF THE FIBER OF A FIBRATION
AS THE FIBER OF A MODEL
by Bitjong Ndombol
ABSTRACT: To follow in due course.

ICTP Preprint No.IC/97/98 IRREDUCIBLE NON-ZERO LEVEL MODULES
WITH FINITE-DIMENSIONAL WEIGHT SPACES
FOR AFFINE LIE ALGEBRAS
by V. Futorny and A. Tsylke
ABSTRACT: To follow in due course.

ICTP Preprint No.IC/97/106 IMAGINARY VRMA MODULES
FOR TOROIDAL LIE ALGEBRAS
by Vyacheslav Futorny and Iryna Kashuba
ABSTRACT: To follow in due course.