In real semialgebraic geometry it is common to represent a polynomial q which is positive on a region R as a weighted sum of squares. Serious obstructions arise when q is not strictly positive on the region R. Here we are concerned with noncommutative polynomials and obtaining a representation for them which is valid even when strict positivity fails. Specifically, we treat a ”symmetric” polyno...

We consider combinatorial optimization problems arising in radiation therapy. Given a matrix I with non-negative integer entries, we seek a decomposition of I as a weighted sum of binary matrices having the consecutive ones property, such that the total sum of the coefficients is minimized. The coefficients are restricted to be non-negative integers. Here, we investigate variants of the problem...

The segment minimization problem consists of finding a smallest set of binary matrices (segments), where non-zero values in each row of each matrix are consecutive, each matrix is assigned a positive integer weight (a segment-value), and the weighted sum of the matrices corresponds to the given input intensity matrix. This problem has direct applications in intensitymodulated radiation therapy,...

For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study the fluctuations of the matrix elements for the desymmetrized quantum cat map. We present a conjecture for the distribution of the normalized matrix elements, ...

An ideal self-healing matrix composite which is capable of being monitored for damage events in the matrix so that they can be healed in a thermal cycle to restore the material’s performance without negatively affecting the properties is discussed. A novel technique employing a solid-state matrix repair system for a thermosetting resin that has been shown to be capable of healing of its pre-fra...

The structure of orthogonal polynomials on R with the weight function |x1 − x2| |x1x2|1e 2 1+x 2 2)/2 is based on the Dunkl operators of type B2. This refers to the full symmetry group of the square, generated by reflections in the lines x1 = 0 and x1− x2 = 0. The weight function is integrable if k0, k1, k0 +k1 > − 1 2 . Dunkl operators can be defined for polynomials taking values in a module o...

The well characterized castor bean (Rhscm is L*) allergens were Identdfied as the low molecular weight albmin storae protein In the matrix of the protein bodles in the edsp mThe metbods of Idetifcatdon involved molecular weight estbition, amino acid compositon, stabilty at 1000 C, sobulity In various solvents, gel elec rs , and Immunological technbques. The fdinig explains the wide distrbution ...

in this paper, a new method is proposed for the production of mwcnts/pvc (multi-walled carbon nanotubes/ polyvinyl chloride) nanocomposites. in this method, a spray is used to produce layers of carbon nanotubes within a pvc matrix. various parameters influence the production of the nanocomposite and its mechanical properties. these parameters are studied separately and the effect of each of par...

BACKGROUND Identifying transcription factor binding sites (TFBS) in silico is key in understanding gene regulation. TFBS are string patterns that exhibit some variability, commonly modelled as "position weight matrices" (PWMs). Though convenient, the PWM has significant limitations, in particular the assumed independence of positions within the binding motif; and predictions based on PWMs are u...