Twisted homology for the mirabolic nilradical

The notion of derivatives for smooth representations of GL(n, ? _p ) was defined in [BZ77]. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations in [Sah89] and called the “adduced” representation. In [AGS] derivatives of all orders were defined for smooth admissible Fréchet representations (of moderate growth).A key ingredient of this definition is the functor of twisted coinvariants with respect to the nilradical of the mirabolic subgroup. In this paper we prove exactness of this functor and compute it on a certain class of representations. This implies exactness of the highest derivative functor, and allows to compute highest derivatives of all monomial representations.In [AGS] these results are applied to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations.     

Determination of volatile biogenic amines in muscle food products by ion mobility spectrometry

The extent of spoilage of muscle food products was determined through measurement of volatile biogenic amines that emanated from food samples. The release of the amines was enhanced by addition of a few drops of an alkaline solution and the amines were monitored by ion mobility spectrometry (IMS). The limit of detection of the method for trimethylamine (TMA) was 2 ng and the measurement was completed within <2 min with short and long term reproducibility of 15 and 25%, respectively, for replicate samples. The method provides qualitative information as it distinguishes between different amines, as well as quantitative data for the key compounds. A good correlation was found between the IMS results and the microorganism populations in microbiological cultures. The effects of storage time and temperature and of the type of meat on the formation of biogenic amines were examined, and as expected, the higher the storage temperature the faster the spoilage. Thus, this pilot study shows that the measurement of biogenic amines can serve as an indicator for food spoilage or freshness.     

Rearrangement of fine particles in porous media causing reduction of permeability and formation of preferred pathways of flow: Experimental findings and a conceptual model

The rearrangement of matrix configuration due to the redistribution of clay particles was studied by introducing different suspensions into porous media. Clay (kaolinite) with low CEC (cation exchange capacity) and small flocs of high CEC clay (smectite) accumulated in regions of slow flow. In some experiments this was followed by rapid accumulation in regions of high velocity, impairing flow to a considerable degree. Clay with high CEC formed more voluminous structures which could bridge over a passage and impair the flow.In either case, whether small or large units of clay are involved, the final flow occurred mainly through open, preferred pathways. Such processes of redistribution and appearance of flow pathways may occur in subsurface porous media aquifers where forced gradients exist (e.g. in aquifers near the perforation of pumping wells and in places where large quantity of water are naturally or artificially recharged and in producing gas and oil fields).     

Quantifying chemical composition from two-dimensional data arrays

Many analytical instruments (e.g., videofluorimeter and liquid chromatographs with spectrometric detectors) can produce two-dimensional data arrays. Rank-annihilation factor analysis enables chemical composition to be quantified from such an array. Solution by this method requires a search for a minimum value of an eigenvector which cannot be calculated even iteratively. The problem is presented here as a generalized eigenvalue problem and a direct solution is found by using singular value decomposition.     

Equilibrium first-order melting and second-order glass transitions of the vortex matter in Bi2Sr2CaCu2O8

The thermodynamic phase diagram of Bi2Sr2CaCu2O8 was mapped by measuring local equilibrium magnetization M(H,T) in the presence of vortex shaking. Two equally sharp first-order magnetization steps are revealed in a single temperature sweep, manifesting a liquid-solid-liquid sequence. In addition, a second-order glass transition line is revealed by a sharp break in the equilibrium M(T) slope. The first- and second-order lines intersect at intermediate temperatures, suggesting the existence of four phases: Bragg glass and vortex crystal at low fields, glass and liquid at higher fields.     

The chemistry of THPC–urea polymers and relationship to flame retardance on wool and wool-polyester blends. I. Chemistry of THPC–urea polymers

Polymer formation from THPOH-urea, THPOH-dichloropropanol-urea, and THPC-urea was studied. Order and rate of urea addition were shown to influence insoluble polymer yields as well as polymer structure. The polymers were characterized by elemental analyses and infrared spectroscopy, and predominant structures proposed. The structures were correlated with thermogravimetric and differential scanning calorimetry data and probable thermal decomposition paths.     

Splines with maximal zero sets

Consider a spline s(x) of degree n with L knots of specified multiplicities R₁, …, R_L, which satisfies r sign consistent mixed boundary conditions in addition to s⁽ⁿ⁾(a) = 1. Such a spline has at most n + 1 ?r + ∑_{j = 1}^LR_j zeros in (a, b) which fulfill an interlacing condition with the knots if s(x) ? = 0 everywhere. Conversely, given a set of n ?r + ∑_{j = 1}^LR_j zeros then for any choice η₁ < ··· < η_L of the knot locations which fulfills the interlacing condition with the zeros, the unique spline s(x) possessing these knots and zeros and satisfying the boundary conditions is such that s⁽ⁿ⁾(x) vanishes nowhere and changes sign at η_j if and only if R_j is odd. Moreover there exists a choice of the knot locations, not necessarily unique, which makes $\text{¦s}{}^{\mathrm{(n)}}\text{(x)¦ ≡ 1}$. In particular, this establishes the existence of monosplines and perfect splines with knots of given multiplicities, satisfying the mixed boundary conditions and possessing a prescribed maximal zero set. An application is given to double-precision quadrature formulas with mixed boundary terms and a certain polynomial extremal problem connected with it.