Let A denote the mod 2 Steenrod algebra (see Steenrod and Epstein [28]). The problem of computing its cohomology H∗,∗(A) is of great importance in algebraic topology, for this bigraded commutative algebra is the E2 term of the Adams spectral sequence (see Adams [1]) converging to the stable homotopy groups of spheres. But despite intensive investigation for nearly half a century, the structure ...

Dickenstein, A., N. Fitchas, M. Giusti and C. Sessa, The membership problem for unmixed polynomial ideals is solvable in single exponential time, Discrete Applied Mathematics 33 (1991) 73-94. Deciding membership for polynomial ideals represents a classical problem of computational commutative algebra which is exponential space hard. This means that the usual al membership problem which are base...

A basic problem in the representation theory of a compact Lie group is to calculate the restriction of an irreducible representation of K to a closed subgroup. Most classical results on this problem concern connected groups. We’ll recall some of those, and talk about some of the modifications needed to work with disconnected groups. 1. Weight multiplicities Suppose g is a complex semisimple Lie...

Tight connections between leafs languages and strings compressed via straight-line programs (SLPs) are established. It is shown that the compressed membership problem for a language L is complete for the leaf language class defined by L via logspace machines. A more difficult variant of the compressed membership problem for L is shown to be complete for the leaf language class defined by L via ...

we study the problem of reconstructing binary images from four projections data in a fuzzy environment. given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. we provide an iterative algorithm based on fuzzy integer programming and linear membership functions.

We improve several upper bounds to the complexity of the membership problem for languages deened by iterated morphisms (D0L systems). The complexity bounds are expressed in terms of DLOGT IME-uniform circuit families. We prove: 1) For polynomially growing D0L systems the membership problem is contained in AC 0. 2) For arbitrary D0L systems the membership problem is contained in NC 1. 3) The lat...

multi objective quadratic fractional programming (moqfp) problem involves optimization of several objective functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a nite number of extreme points and the denominator part of each of the object...

Data envelopment analysis (DEA) is a method to evaluate the relative efficiency of decision making units (DMUs). In this method, the issue has always been to determine a set of weights for each DMU which often caused many problems. Since the DEA models also have the multi-objective linear programming (MOLP) problems nature, a rational relationship can be established between MOLP and DEA problem...

Z. Takáč in [16] introduced the aggregation operators on any subalgebra of M (set of all fuzzy membership degrees of the type-2 fuzzy sets, that is, the functions from [0,1] to [0,1]). Furthermore, he applied the Zadeh’s extension principle (see [24]) to obtain in [16, 17] a set of aggregation operators on L* (the strongly normal and convex functions of M). In this paper, we introduce the aggre...

We study the Zariski cancellation problem for Poisson algebras in three variables. In particular, we prove those with bracket either being quadratic or derived from a Lie algebra are cancellative. also use various invariants, including Makar–Limanov invariant, divisor subalgebra, and stratiform length, to skew algebras.