Gorenstein liaison of 0-dimensional schemes

 The theory of Gorenstein liaison has been developed during the last 3 years to generalize liaison theory of codimension 2 schemes to schemes of codimension ≥ 3 in a projective space. One of the main open questions in Gorenstein liaison theory is whether any arithmetically Cohen-Macaulay subscheme of ℙ ⁿ is in the Gorenstein liaison class of a complete intersection. In this paper we prove that any set of general points lying on a rational normal scroll surface is in the Gorenstein liaison class of a complete intersection. Received: 21 November 2001 Published online: 24 April 2003 Mathematics Subject Classification (2000): 14M06, 14C20, 14M05     

On 0-dimensional schemes with all permissible conductor degrees

IfX is a set of distinct points in ℙ² with given graded Betti numbers, we produce a new set of pointsY with the same graded Betti numbers asX which admits all possible conductor degrees according to the graded Betti numbers. Moreover, for such schemes we can compute the conductor degree for each point. We conclude by generalizing the construction of these schemes, obtaining again the same results.     

A variety of exact travelling wave solutions for the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation

In this paper the (2 + 1)-dimensional Boiti-Leon-Pempinelli (BLP) equation will be studied. The tanh-coth method will be used to obtain exact travelling wave solutions for this equation. The Exp-function method will also be applied to the BLP equation to derive a new variety of travelling wave solutions with distinct physical structures.     

Two theorems on imbeddings of 0-dimensional groups

In the class of 0-dimensional groups with infinite weight, the universal group is constructed. We prove that a 0-dimensional group can be imbedded into a multiplicative subgroup of a topological ring.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1594–1596, November, 1994.     

Reducibility of minimax to minisum 0–1 programming problems

We consider 0–1 programming problems with a minimax objective function and any set of constraints. Upon appropriate transformations of its cost coefficients, such a minimax problem can be reduced to a linear minisum problem with the same set of feasible solutions such that an optimal solution to the latter will also solve the original minimax problem.Although this reducibility applies for any 0–1 programming problem, it is of particular interest for certain locational decision models. Among the obvious implications are that an algorithm for solving a p-median (minisum) problem in a network will also solve a corresponding p-center (minimax) problem.It should be emphasized that the results presented will in general only hold for 0–1 problems due to intrinsic properties of the minimax criterion.     

Construction of some families of 2-dimensional crystalline representations

We construct explicitly some analytic families of étale (,)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and extend some results (of Deligne, Edixhoven, Fontaine and Serre) on the representations arising from modular forms.Mathematics Subject Classification (2000): 11F80, 11F33, 11F85, 14F30     

New families of Q-polynomial association schemes

In this paper, we construct the first known infinite family of primitive Q-polynomial schemes which are not generated by distance-regular graphs. To construct these examples, we introduce the notion of a relative hemisystem of a generalized quadrangle with respect to a subquadrangle.     

Reducibility for a Class of Analytic Multipliers on the Dirichlet Space

It is proved that if \(\phi \) is a finite Blaschke product with four zeros, then \(M_\phi \) is reducible on the Dirichlet space with norm \(\Vert \ \Vert \) if and only if \(\phi =\phi _1\circ \phi _2\), where \(\phi _1, \phi _2\) are Blaschke products and \(\phi _2\) is equivalent to \(z^2\). Also, the same reducibility of \(M_\phi \) with finite Blaschke product \(\phi \) on the Dirichlet space under the equivalent norms \(\Vert \ \Vert _1\) and \(\Vert \ \Vert _0\) is given.     

Concatenating construction of the multisymplectic schemes for 2+1-dimensional sine-Gordon equation

In this paper, taking the 2+1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The-method is to discretizee independently the PDEs in different directions with symplectic schemes, so that the multisymplectic schemes can be constructed by concatenating those symplectic schemes. By this method, we can construct multisymplectic schemes, including some widely used schemes with an accuracy of any order. The numerical simulation on the collisions of solitons are also proposed to illustrate the efficiency of the multisymplectic schemes.     

Techniques for the study of singularities with applications to resolution of 2-dimensional schemes

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.     

Albanese homomorphism of the Chow group of 0-cycles of a real Algebraic variety

We study a certain homomorphism of the Chow group of 0-cycles of degree zero of a real algebraic variety into the group of real points of the Albanese variety; this homomorphism is obtained from the Albanese mapping for the corresponding variety. The kernel of this homomorphism is calculated and estimates for the kernel of the mapping of the torsion groups are obtained. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 76–83, January, 1999.     

Arithmetic families of smooth surfaces and equisingularity of embedded schemes

This article deals with the foundations of a theory of equisingularity for families of zero-dimensional sheaves of ideals on smooth algebraic surfaces, in the arithmetic context, i.e., where one works with schemes defined over Dedekind rings. Here, different equisingularity conditions are analyzed and compared, based on one of the following requirements: 1) each member of the the family has the same desingularization tree, 2) the family admits a simultaneous desingularization, 3) a naturally associated family of curves is equisingular. Similar conditions had been investigated, in the context of Complex Local Analytic Geometry, by J. J. Risler. Received: 17 November 1997 / Revised version: 19 April 1999     

Geometric families of 4-dimensional Galois representations with generically large images

We study compatible families of four-dimensional Galois representations constructed in the étale cohomology of a smooth projective variety. We prove a theorem asserting that the images will be generically large if certain conditions are satisfied. We only consider representations with coefficients in an imaginary quadratic field. We apply our result to an example constructed by Jasper Scholten (A non-selfdual 4-dimensional Galois representation, , 1999), obtaining a family of linear groups and one of unitary groups as Galois groups over . Research partially supported by MEC grant MTM2006-04895.     

Quasi-positive families of continuous Darcy-flux finite volume schemes on structured and unstructured grids

New families of flux-continuous control-volume distributed finite volume schemes are presented for the general full-tensor pressure equation arising in porous media and formulated for structured and unstructured grids. These schemes offer the practical advantage of being flux-continuous while only depending on one degree of freedom per control-volume, unlike rival approximations such as the Mixed Finite Element method. M-matrix bounds are presented, quasi QM-matrices are defined and an optimal quadrilateral scheme is identified. Anisotropy favoring triangulation is also shown to yield an optimal scheme. The new schemes prove to be relatively robust for the cases tested, including strongly anisotropic full tensor fields. Strong oscillations encountered with the earlier formulations, are removed or minimized.     

Structure of the cycle map for Hilbert schemes of families of nodal curves

We study the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension, via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the discriminant locus, which consists of cycles with multiple points. We determine the structure of certain projective bundles called node scrolls which play an important role in the geometry of Hilbert schemes.