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.

Polynomial Functions and the Riesz Interpolation Property

Building on a proof by D. Handelman of a generalisation of an example due to L. Fuchs, we show that the space of real-valued polynomials on a non-empty set X of reals has the Riesz Interpolation Property if and only if X is bounded.

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.

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

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 .

The conjugacy problem for two-by-two matrices over polynomial rings

We give an effective solution of the conjugacy problem for two-by-two matrices over the polynomial ring in one variable over a finite field.

Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.