Linear preservers of extremes of rank inequalities over semirings: Term rank and zero-term rank

We characterize linear operators on matrices over semirings that preserve the extremal cases in the bounds on term and zero-term ranks of sums and products of matrices. __________ Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 2, pp. 3–21, 2004.     

Vehicle Fleet Composition

In this paper we consider the problem of determining the optimal composition of a vehicle fleet (i.e. the best fleet size and the best fleet mix). A literature review is given and a new formulation of the problem is presented.     

Multiplicative properties of generalized matrix functions

We consider scalar-valued matrix functions for n×n matrices A=(a_ij) defined by Where G is a subgroup of S_n the group of permutations on n letters, and χ is a linear character of G. Two such functions are the permanent and the determinant. A function (1) is multiplicative on a semigroup S of n×n matrices if d(AB)=d(A)d(B) AB∈S.

With mild restrictions on the underlying scalar ring we show that every element of a semigroup containing the diagonal matrices on which (1) is multiplicative can have at most one nonzero diagonal(i.e., diagonal with all nonzero entries)and conversely, provided that χ is the principal character(χ≡1).     

Supercomputers and OR

This paper presents a literature survey on the use of supercomputers in operational research.     

Linear preservers of matrices of rank-2

Let T be a linear operator on the space of all m×n matrices over any field. we prove that if T maps rank-2 matrices to rank-2 matrices then there exist nonsingular matrices U and V such that either T(X)=UXV for all matrices X, or m=n and T(X)=UX^tV for all matrices X where X^t denotes the transpose of X.     

Investigating the interactions of the first 17 amino acid residues of Huntingtin with lipid vesicles using mass spectrometry and molecular dynamics

The first 17 amino acid residues of Huntingtin protein (Nt17 of htt) are thought to play an important role in the protein's function; Nt17 is one of two membrane binding domains in htt. In this study the binding ability of Nt17 peptide with vesicles comprised of two subclasses of phospholipids is studied using electrospray ionization ‐ mass spectrometry (ESI‐MS) and molecular dynamics (MD) simulations. Overall, the peptide is shown to have a greater propensity to interact with vesicles of phosphatidylcholine (PC) rather than phosphatidylethanolamine (PE) lipids. Mass spectra show an increase in lipid‐bound peptide adducts where the ordering of the number of such specie is 1,2‐dioleoyl‐sn‐glycero‐3‐phosphocholine (DOPC) > 1‐palmitoyl‐2‐oleoyl‐glycero‐3‐phosphocholine (POPC) > 1‐palmitoyl‐2‐oleoyl‐sn‐glycero‐3 phosphoethanolamine (POPE). MD simulations suggest that the compactness of the bilayer plays a role in governing peptide interactions. The peptide shows greater disruption of the DOPC bilayer order at the surface and interacts with the hydrophobic tails of lipid molecules via hydrophobic residues. Conversely, the POPE vesicle remains ordered and lipids display transient interactions with the peptide through the formation of hydrogen bonds with hydrophilic residues. The POPC system displays intermediate behavior with regard to the degree of peptide‐membrane interaction. Finally, the simulations suggest a helix stabilizing effect resulting from the interactions between hydrophobic residues and the lipid tails of the DOPC bilayer.     

Metal-insulator crossover in high T c cuprates: A gauge field approach

A metal-insulator crossover appears in the experimental data for in-plane resistivity of underdoped cuprates and a range of superconducting cuprates in the presence of a strong magnetic field suppressing superconductivity. We propose an explanation for this phenomenon based on a gauge field theory approach to the t-J model. In this approach, based on a formal spin-charge separation, the low energy effective action describes gapful spinons (with a theoretically derived doping dependence of the gap m _s ² ∼ δ| ln δ|) and holons with finite Fermi surface (ɛF ∼ tδ) interacting via a gauge field whose basic effect on the spinons is to bind them into overdamped spin waves, shifting their gap by a damping term linear in T, which causes the metal-insulator crossover. The presence of a magnetic field perpendicular to the plane acts by increasing the damping, in turn producing a big positive transverse in-plane magnetoresistance at low T, as experimentally observed.     

Linear transformations on matrices: the invariance of sets of ranks

Let R_E denote the set of all m × n matrices over an algebraically closed field F whose ranks lie in the set E, where E is a subset of {1,2,…,m}. Let T be a linear transformation which maps R_E into itself. Under some restrictions on E, or when T is nonsingular, there are nonsingular matrices U and V such that T(A) = UAV for every m × n matrix A.     

Regular matrices and their strong preservers over semirings

An m×n matrix A over a semiring is called regular if there is an n×m matrix G over such that AGA=A. We study the problem of characterizing those linear operators T on the matrices over a semiring such that T(X) is regular if and only if X is. Complete characterizations are obtained for many semirings including the Boolean algebra, the nonnegative reals, the nonnegative integers and the fuzzy scalars.     

A heuristic for the circle packing problem with a variety of containers

In this paper we present a heuristic algorithm based on the formulation space search method to solve the circle packing problem. The circle packing problem is the problem of finding the maximum radius of a specified number of identical circles that can be fitted, without overlaps, into a two-dimensional container of fixed size. In this paper we consider a variety of containers: the unit circle, unit square, rectangle, isosceles right-angled triangle and semicircle. The problem is formulated as a nonlinear optimization problem involving both Cartesian and polar coordinate systems.Formulation space search consists of switching between different formulations of the same problem, each formulation potentially having different properties in terms of nonlinear optimization. As a component of our heuristic we solve a nonlinear optimization problem using the solver SNOPT.Our heuristic improves on previous results based on formulation space search presented in the literature. For a number of the containers we improve on the best result previously known. Our heuristic is also a computationally effective approach (when balancing quality of result obtained against computation time required) when compared with other work presented in the literature.