Polynomials on Banach spaces with unconditional bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.

Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Application of Jacobi algorithm for ISI channels

Here, the Jacobi iterative algorithm is applied to combat intersymbol interference (ISI) caused by frequency-selective channels. The performance bound of the equaliser is analysed in order to gain an insight into its asymptotic behaviour. Because of the error propagation problem, the potential of this algorithm is not reached in an uncoded system. However, its extension to a coded system with the application of the turbo-processing principle results in a new turbo equalisation algorithm, which demonstrates comparable performance with reduced complexity compared with some existing filter-based turbo equalisation schemes; and superior performance compared with some frequency domain solutions, such as orthogonal frequency division multiplexing and single-carrier frequency domain equalisation.

Algorithmic computation of knot polynomials of secondary structure elements of proteins

The classification of protein structures is an important and still outstanding problem. The purpose of this paper is threefold. First, we utilize a relation between the Tutte and homfly polynomial to show that the Alexander-Conway polynomial can be algorithmically computed for a given planar graph. Second, as special cases of planar graphs, we use polymer graphs of protein structures. More precisely, we use three building blocks of the three-dimensional protein structure-alpha-helix, antiparallel beta-sheet, and parallel beta-sheet-and calculate, for their corresponding polymer graphs, the Tutte polynomials analytically by providing recurrence equations for all three secondary structure elements. Third, we present numerical results comparing the results from our analytical calculations with the numerical results of our algorithm-not only to test consistency, but also to demonstrate that all assigned polynomials are unique labels of the secondary structure elements. This paves the way for an automatic classification of protein structures.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Factorial Design of Cement Slurries Containing Limestone Powder for Self-Consolidating Slurry-Infiltrated Fiber Concrete

Slurries with high penetrability for production of Self-consolidating Slurry Infiltrated Fiber Concrete (SIFCON) were investigated in this study. Factorial experimental design was adopted in this investigation to assess the combined effects of five independent variables on mini-slump test, plate cohesion meter, induced bleeding test, J-fiber penetration test and compressive strength at 7 and 28 days. The independent variables investigated were the proportions of limestone powder (LSP) and sand, the dosages of superplasticiser (SP) and viscosity agent (VA), and water-to-binder ratio (w/b). A two-level fractional factorial statistical method was used to model the influence of key parameters on properties affecting the behaviour of fresh cement slurry and compressive strength. The models are valid for mixes with 10 to 50% LSP as replacement of cement, 0.02 to 0.06% VA by mass of cement, 0.6 to 1.2% SP and 50 to 150% sand (% mass of binder) and 0.42 to 0.48 w/b. The influences of LSP, SP, VA, sand and W/B were characterised and analysed using polynomial regression which identifies the primary factors and their interactions on the measured properties. Mathematical polynomials were developed for mini-slump, plate cohesion meter, J-fiber penetration test, induced bleeding and compressive strength as functions of LSP, SP, VA, sand and w/b. The estimated results of mini-slump, induced bleeding test and compressive strength from the derived models are compared with results obtained from previously proposed models that were developed for cement paste. The proposed response models of the self-consolidating SIFCON offer useful information regarding the mix optimization to secure a highly penetration of slurry with low compressive strength

Influence of mix proprtions on rheolgy of cement grouts containing limestone powder

In this paper the parameters of cement grout affecting rheological behaviour and compressive strength are investigated. Factorial experimental design was adopted in this investigation to assess the combined effects of the following factors on fluidity, rheological properties, induced bleeding and compressive strength: water/binder ratio (W/B), dosage of superplasticiser (SP), dosage of viscosity agent (VA), and proportion of limestone powder as replacement of cement (LSP). Mini-slump test, Marsh cone, Lombardi plate cohesion meter, induced bleeding test, coaxial rotating cylinder viscometer were used to evaluate the rheology of the cement grout and the compressive strengths at 7 and 28 days were measured. A two-level fractional factorial statistical model was used to model the influence of key parameters on properties affecting the fluidity, the rheology and compressive strength. The models are valid for mixes with 0.35-0.42 W/B, 0.3-1.2% SP, 0.02-0.7% VA (percentage of binder) and 12-45% LSP as replacement of cement. The influences of W/B, SP, VA and LSP were characterised and analysed using polynomial regression which can identify the primary factors and their interactions on the measured properties. Mathematical polynomials were developed for mini-slump, plate cohesion meter, inducing bleeding, yield value, plastic viscosity and compressive strength as function of W/B, SP, VA and proportion of LSP. The statistical approach used highlighted the limestone powder effect and the dosage of SP and VA on the various rheological characteristics of cement grout

Isotope Shift in the Dielectronic Recombination of Three-Electron ANd57+

Isotope shifts in dielectronic recombination spectra were studied for Li-like ^ANd⁵⁷⁺ ions with A=142 and A=150. From the displacement of resonance positions energy shifts dE^142?150(2s-2p_1/2)=40.2(3)(6)??meV [(stat)(sys)] and dE^142?150(2s-2p_3/2)=42.3(12)(20)??meV of 2s-2p_jtransitions were deduced. An evaluation of these values within a full QED treatment yields a change in the mean-square charge radius of ^142?150d?r²?=-1.36(1)(3)??fm². The approach is conceptually new and combines the advantage of a simple atomic structure with high sensitivity to nuclear size.