Twist Coefficient Research Articles

Manufacturing Processing of Polylactic Acid Braids as Artificial Bone Matrix

In this study, the PLA plied yarn was fabricated by twisting four of PLA yarns together, then PLA plied yarn was used a 16-spindle braid machine to produce the PLA braids. PLA braids were immersed in the suspension of β-tricalcium phosphate (β-TCP), and heat treatment to improve the adhesion of β-TCP particles. PLA/β-TCP composite braids were immersed in simulated body fluid (SBF) to promote bonelike apatite production. The morphology of PLA braids were investigated by scanning electron microscopy (SEM), and the results shown that when twist coefficient was 3 of PLA plied yarn, the concentration of β-TCP suspension was 0.15 wt % and heat treatment at 175 °C for 9 min, we can obtain the optimal conditions of β-TCP particles adhesion.

Instabilities in nematic elastomers in external electric and magnetic fields

In this paper we study the macroscopic behavior of nematic side-chain liquid single crystal elastomers exposed to an external electric or magnetic field. For this purpose we use the framework of a continuum model. The geometries investigated comprise the bend and the twist geometry known from the classical Frederiks transition in low molecular weight liquid crystals. For the bend geometry we find a laterally homogeneous and a two-dimensional undulatory instability, which may compete at onset. In the case of the twist geometry three instabilities can occur at onset, two of which are two dimensional and clearly show undulations. As a major result we propose how the values of the twist coefficient K(2) and the values of the material parameters D(1) and D(2) connected to relative rotations between the director field and the polymer network can be determined from experimental observations. In addition, we explain why a twist experiment is probably the most suitable set-up in order to measure the material parameter D(1).

On the motion of an oscillator with a periodically time-varying mass

The stability of the motion of an oscillator with a periodically time-varying mass is under consideration. The key idea is that an adequate change of variables leads to a newtonian equation, where classical stability techniques can be applied: Floquet theory for the linear oscillator, KAM method in the nonlinear case. To illustrate this general idea, first we have generalized the results of [W.T. van Horssen, A.K. Abramian, Hartono, On the free vibrations of an oscillator with a periodically time-varying mass, J. Sound Vibration 298 (2006) 1166–1172] to the forced case; second, for a weakly forced Duffing’s oscillator with variable mass, the stability in the nonlinear sense is proved by showing that the first twist coefficient is not zero.

The K-theoretic Farrell–Jones conjecture for hyperbolic groups

We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.

Existence and stability of periodic solutions for second-order semilinear differential equations with a singular nonlinearity

It is proved that a periodically forced second-order equation with a singular nonlinearity in the origin with linear growth in infinity possesses a -periodic stable solution for high values of the mean value of the forcing term. The method of proof combines a rescaling argument with the analysis of the first twist coefficient of the Birkhoff normal form for the Poincaré map.

$L^1$ criteria for stability of periodic solutions of a newtonian equation

We develop new criteria for the stability of a periodic solution of a given newtonian equation based on the -norm of the coefficients of the third order approximation, by proving that the twist coefficient is different form zero.

Geometric construction of spinors in orthogonal modular categories

A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations. Quantum dimensions and twist coefficients for 1-graded simple objects (spinors) are calculated. We show that our even orthogonal modular categories admit cohomological refinements and the odd orthogonal ones lead to spin refinements. The relation with the quantum group approach is discussed.

Effect of Gray Fabric Properties on Flame Resistance of Knitted Fabric

In this study, knitted fabrics that have been used extensively in recent years are chosen to investigate the effects of their properties on flame resistance. Physical parameters (fiber type and composition, yarn count, yarn twist coefficient, fabric design, weight per unit area, air permeability, fabric thickness, cover factor, loop density) that affect fabric flammability are defined and an experimental study is designed. The burning behavior of the all fabrics is evaluated using the BS 5438 vertical flammability test method because its results are very similar to real fabric burning behavior and it is more responsive than other test methods. Finally, experimental results are evaluated according to a MANOVA analysis using an SPSS statistical program. How and at which level knitted fabric param eters affect a fabric's burning behavior is defined, and regression models of these parameters are obtained. Using these regression models, the burning behavior of knitted fabrics is evaluated, and it is possible to rank them according to their burning character istics.

THE BEST BOUND ON THE ROTATIONS IN THE STABILITY OF PERIODIC SOLUTIONS OF A NEWTONIAN EQUATION

In most cases, the third order approximation of a scalar Newtonian equation can lead to the Lyapunov stability of a periodic solution through the obtaining of a nonzero twist coefficient. Recently, Ortega obtained the twist property of a periodic solution when the second order coefficient does not change sign and the third one is negative under a crucial limitation to the rotation of the linearization equation. The paper finds that the best bound on the limitation of the rotations is θ 0 * = arccos ( − 1 / 4 ) . .

Calculation of the Absolute Breaking Load of Twisted Polypropylene Film Fibres

The Belitsin equation cannot be used for calculation of the breaking load of twisted PP film fibres of different linear density as a function of the twist value because of the large difference from the real breaking load. New coefficients of the change in the breaking load as a function of the twist value and twist coefficient for corrugated PP film fibres with a linear density of 55, 115, and 230 tex are derived using a single-factor experiment design; it can be used to calculate the breaking load with a minimum error. A universal coefficient for the change in the breaking load as a function of the twist value and linear density is obtained for 55-230 tex PP film fibres, and the difference between the real and theoretical breaking load does not exceed 4% as a result of using it.

Semiclassical limits for the hyperbolic plane

We study the concentration properties of high-energy eigenfunctions for the Laplace-Beltrami operator of the hyperbolic plane with special consideration of automorphic eigenfunctions. At the center of our investigation is the microlocal lift of an eigenfunction to SL(2;ℝ) introduced by S. Zelditch. The microlocal lift is based on S. Helgason's Fourier transform and has a straightforward description in terms of the Lie algebra sl(2;ℝ). We begin with an elementary demonstration of Zelditch's exact differential equation for the microlocal lift. Further, for a sequence of suitably bounded eigenfunctions with eigenvalues tending to infinity, we show that the limit of microlocal lifts is a geodesic-flow-invariant positive measure. Our main consideration is the microlocal lifts of the elementary eigenfunctions constructed from the Macdonald-Bessel functions. We find that with a scaling of auxiliary parameters the corresponding high-energy limit converges to the positive Dirac measure for the lift to SL(2;ℝ) of a single geodesic on the upper half-plane. In particular, at high energy the microlocal lift of a Macdonald-Bessel function is concentrated along the lift of a single geodesic. We further find that the convergence is uniform in parameters, and thus our considerations can be applied to study automorphic eigenfunctions, in particular, the Maass cusp forms for certain cofinite subgroups of SL(2;ℝ). A formula is presented for the microlocal lift of a cusp form as an integral of a family of Dirac measures and a measure given directly by sums of products of the classical Fourier coefficients of the cusp form. The formula establishes that questions on quantum chaos for automorphic eigenfunctions are equivalent to classically stated questions on twisted sums of coefficients. In particular, we find that the uniform distribution for the microlocal limit is equivalent to a uniform distribution for the limit of twisted coefficient sums. We extend the considerations to the case of the nonholomorphic Eisenstein series for the modular group. We find that a result of W. Luo and P. Sarnak is equivalent to a limit-sum formula involving the Riemann zeta-function and the elementary divisor function. The formula is suggestive of a formula of S. Ramanujan.

Extraction of higher twists from electron-proton inclusive data at large Bjorkenx

We extract the power corrections to the ``scaling'' proton structure function ${F}_{2}{(x,Q}^{2})$ by using QCD moments obtained from the world's inclusive lepton-proton scattering data. As opposed to previous analyses, we take particular account of data at large Bjorken $x(x>0.75)$ which are dominated by nucleon resonances and which make up most of the structure function at low ${Q}^{2}{(Q}^{2}<~4 {\mathrm{GeV}}^{2}).$ We discuss possible improvements on the determination of the magnitude of the higher twist coefficients that could be obtained from a new set of measurements of the nucleon structure functions at large x and moderate ${Q}^{2}.$

Tubed incompressible surfaces in knot and link complements

We prove that the complements of all knots and links in S 3 which have a 2n-plat projection with absolute value of all twist coefficients bigger than 2 contain closed embedded incompressible non-boundary parallel surfaces. These surfaces are obtained from essential planar meridional surfaces by tubing to one side along the knot or link. In the case of a knot it follows that these surfaces stay incompressible in all manifolds obtained by non-trivial surgery on the knot.

Semi-localization of a one pointed Kan complex

First we give a course in semi-simplicial homotopy theory. Then we construct the non-simple Postnikov tower for a one pointed Kan complex. This is done by means of twisted coefficient transgression theory. Then we develope a twisted coefficient obstruction theory for non-simple complexes. Finally we extend the notion of P-localization to an arbitrary one pointed Kan complex, where P is a collection of prime integers. We show that if X is a one pointed Kan complex there exists a map f: X $\to$ X$\sb{p}$ of one pointed Kan complexes such that $f\sb*$: $\pi\sb1$(X) $\to$ $\pi\sb1$(X$\sb{p}$) is an isomorphism, and $f\sb{k}$: $\pi\sb{k}$(X) $\to$ $\pi\sb{k}$(X$\sb{p}$) is P-localization for all k $>$ 1. The Appendix contains a theorem computing the twisted cohomology groups for the models L$\sb\pi$(G, n).

Limitations on using the operator product expansion at small values of x

Limits on the regions of Q 2 and x where the operator product expansion can be safely used, at small values of x are given. For a fixed large Q 2 there is an x 0( Q 2) such that for Bjorken x-values below x 0 the operator product expansion breaks down with significant nonperturbative corrections occurring in the leading twist coefficient and anomalous dimension functions due to diffusion of gluons to small values of transverse momentum.

Applications of simplicial 𝑀-sets to proper and strong shape theories

In this paper we have tried to reduce the classical classification problems for spaces and maps of the proper category and of the strong shape category to similar problems in the homotopy category of simplicial sets or in the homotopy category of simplicial M M -sets, which M M is the monoid of proper selfmaps of the discrete space N \mathbb {N} of nonnegative integers. Given a prospace (prosimplicial set) Y Y , we have constructed a simplicial set P ¯ R Y {\overline {\mathcal {P}} ^R}Y such that the Hurewicz homotopy groups of P ¯ R Y {\overline {\mathcal {P}} ^R}Y are the Grossman homotopy groups of Y Y . For the case of the end prospace Y = ε X Y = \varepsilon X of a space X X , we obtain Brown’s proper homotopy groups; and for the Vietoris prospace Y = V X Y = VX (introduced by Porter) of a compact metrisable space X X , we have Quigley’s inward groups. The simplicial subset P ¯ R Y {\overline {\mathcal {P}} ^R}Y of a tower Y Y contains, as a simplicial subset, the homotopy limit lim R Y {\lim ^R}Y . The inclusion lim R Y → P ¯ R Y {\lim ^R}Y \to {\overline {\mathcal {P}} ^R}Y induces many relations between the homotopy and (co)homology invariants of the prospace Y Y . Using the functor P ¯ R {\overline {\mathcal {P}} ^R} we prove Whitehead theorems for proper homotopy, prohomotopy, and strong shape theories as a particular case of the standard Whitehead theorem. The algebraic condition is given in terms of Brown’s proper groups, Grossman’s homotopy groups and Quigley’s inward groups, respectively. In all these cases an equivalent cohomological condition can be given by taking twisted coefficients. The "singular" homology groups of P ¯ R Y {\overline {\mathcal {P}} ^R}Y provide homology theories for the Brown, Grossman and Quigley homotopy groups that satisfy Hurewicz theorems in the corresponding settings. However, there are other homology theories for the homotopy groups above satisfying other Hurewicz theorems. We also analyse the notion of P ¯ \overline {\mathcal {P}} -movable prospace. For a P ¯ \overline {\mathcal {P}} -movable tower we prove easily (without lim 1 {\lim ^1} functors) that the strong homotopy groups agree with the Čech homotopy groups and the Grossman homotopy groups are determined by the Čech (or strong) groups by the formula G π q = P ¯ π ˇ q ^G{\pi _q} = \overline {\mathcal {P}} \check {\pi }_q . This implies that the algebraic condition of the Whitehead theorem can be given in terms of strong (Čech) groups when the condition of P ¯ \overline {\mathcal {P}} -movability is included. We also study homology theories for the strong (Steenrod) homotopy groups which satisfy Hurewicz theorems but in general do not agree with the corresponding Steenrod-Sitnikov homology theories.

Viscosity Coefficients and Elastic Constants of Nematic Solutions of a Side-Chain Polymer

Abstract Nematic solutions of a side-chain mesomorphic polymer in a commercially available eutectic mixture (E7) were characterised by electric field dynamic light scattering (EDLS). Results are presented for twist and splay viscosity coefficients and elastic constants along with dielectric constants and refractive indices. For the polymer solutions, the measured twist viscosity was greater than the splay viscosity, and the elastic constants reduced relative to E7 in a manner consistent with slight disruption of the nematic order by the polymer backbone.

The Equivariant Serre Spectral Sequence

For spaces with a group action, we introduce Bredon cohomology with local (or twisted) coefficients and show that it is invariant under weak equivariant homotopy equivalence. We use this new cohomology to construct a Serre spectral sequence for equivariant fibrations.

The equivariant Serre spectral sequence

For spaces with a group action, we introduce Bredon cohomology with local (or twisted) coefficients and show that it is invariant under weak equivariant homotopy equivalence. We use this new cohomology to construct a Serre spectral sequence for equivariant fibrations.

The twist coefficient of periodic solutions of a time-dependent Newton's equation

This paper gives sufficient conditions for the existence of periodic solutions of twist type of a time-dependent differential equation of the second order. The concept of periodic solution of twist type is defined in terms of the corresponding Birkhoff normal form and, in particular, implies that the solution is Lyapunov stable. Some applications to nonlocal problems are given.