Twist Coefficient Research Articles

Twisted coefficients on coarse spaces and their corona

To a metric space X we associate a compact topological space ν′(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u '({X})$$\\end{document} called the corona of X. Then a coarse map f:X→Y\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f:X\\rightarrow Y$$\\end{document} between metric spaces is mapped to a continuous map ν′(f):ν′(X)→ν′(Y)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u '({f}):\ u '({X})\\rightarrow \ u '({Y})$$\\end{document} between coronas. Sheaf cohomology assigned to a coarse metric space is preserved and reflected by the corona functor. This work reveals new tools to analyze the Higson corona.

Cofinal Elements and Fractional Dehn Twist Coefficients

Abstract We show that for a surface $S$ with positive genus and one boundary component, the mapping class of a Dehn twist along a curve parallel to the boundary is cofinal in every left ordering of the mapping class group $\operatorname{Mod}(S)$. We apply this result to show that one of the usual definitions of the fractional Dehn twist coefficient—via translation numbers of a particular action of $\operatorname{Mod}(S)$ on $\mathbb{R}$—is in fact independent of the underlying action when $S$ has genus larger than one. As an algebraic counterpart to this, we provide a formula that recovers the fractional Dehn twist coefficient of a homeomorphism of $S$ from an arbitrary left ordering of $\operatorname{Mod}(S)$.

Effect of Yarn Physical Properties on Fiber Migration and Packing Density of Cotton/Acrylic Blended Yarns

In the scope of the study, the effect of fiber blending ratio, yarn count and twist coefficient on fiber migration, packing density and diameter of the cotton/acrylic blended yarns were investigated. The yarn samples with 75-25%, %50-50%, 40-60% cotton-acrylic blending ratios were produced with three different yarn numbers; 20/1 Ne, 24/1 Ne, 30/1 Ne and three twist coefficients; 3.5 α, 4 α, 4.5 α. Thus, totally 27 yarn samples were obtained. The yarn cross-sectional samples were sliced with microtome. The image frames of yarn cross-sections were acquired via digital microscope. The yarn packing density was calculated by using image processing algorithm and the fiber migration was determined via cross-section images. The results were evaluated statistically.

Representation Stability and Finite Orthogonal Groups

In this paper, we prove homological stability results about orthogonal groups over finite commutative rings where 2 is a unit. Inspired by Putman and Sam (2017), we construct a category OrI(R) and prove a local Noetherianity theorem for the category of OrI(R)-modules. This implies an asymptotic structure theorem for orthogonal groups. In addition, we show general homological stability theorems for orthogonal groups, with both untwisted and twisted coefficients.

Equivariant hyperbolization of 3-manifolds via homology cobordisms

The main result of this paper is that any 3-dimensional manifold with a finite group action is equivariantly invertibly homology cobordant to a hyperbolic manifold; this result holds with suitable twisted coefficients as well. The following two consequences motivated this work. First, there are hyperbolic equivariant corks (as defined in previous work of the authors) for a wide class of finite groups. Second, any finite group that acts on a homology 3-sphere also acts on a hyperbolic homology 3-sphere. The theorem has other corollaries, including the existence of infinitely many hyperbolic homology spheres that support free Zp-actions that do not extend over any contractible manifolds, and (from the non-equivariant version of the theorem) infinitely many that bound homology balls but do not bound contractible manifolds. In passing, it is shown that the invertible homology cobordism relation on 3-manifolds is antisymmetric, and thus a partial order.

Lyapunov stability of singular planarsystems related to dispersion-managedsolitons in optical fiber

In this paper, we consider two singular planar differential systems which can describe the evolution of the optical pulse width and chirp for the so-called dispersion-managed solitons. Based on the method of third order approximation in combination with some quantitative information obtained by the upper–lower solutions method and the averaging method, some results on the existence and Lyapunov stability of the periodic solutions are obtained. Moreover, the formula of the first twist coefficient and a stability criterion of a nonlinear differential equation are also established.

Birkhoff normal form and twist coefficients of periodic orbits of billiards* *X J is supported in part by the NSF Grant DMS-1854232.

In this paper we study the Birkhoff normal form around elliptic periodic points for a variety of dynamical billiards. We give an explicit construction of the Birkhoff transformation and obtain explicit formulas for the first two twist coefficients in terms of the geometric parameters of the billiard table. As an application, we obtain characterizations of the nonlinear stability and local analytic integrability of the billiards around the elliptic periodic points.

Optimization of the preparation process of electrostatic-solution blow spinning nanofiber yarn using response surface methodology

There are several methods of preparing nanofiber yarns, but little work has been reported using a combination of electrospinning and solution blowing methods (i.e., electrostatic-solution blow spinning) to prepare nanofiber yarns. In this study, a response surface method (RSM) based on Box–Behnken design was used to investigate the relationship between the yarn parameters and yarn diameter, and the process was optimized. The yarn diameter was simulated by electrostatic voltage, air pressure, winding speed and funnel velocity. The correlation coefficients before and after adjustment were 0.97 and 0.95, respectively, through variance analysis, which verified the accuracy of the yarn diameter model. The results showed that the influence of each experimental factor on the yarn diameter was in descending order of winding speed, electrostatic voltage, airflow and funnel velocity, and there were interactions among the factors. The BDD response model was used to obtain the best experimental conditions, which provided a good theoretical reference for the preparation of polyacrylonitrile nanofibers. In addition, the effects of voltage and air pressure on the diameter of the nanofiber and yarn and the effects of the twist coefficient on the shape and mechanical properties of the yarn were studied. The results showed that with the increase of voltage and air pressure, the diameter of the nanofiber decreased, and the yarn diameter decreased first and then increased. When the twist factor was 100, the twist angle of the yarn was 49.91°, the breaking strength was 12.92 MPa and the elongation at break was 81.34%.

Characterizing the temporal rotation and radial twist of the interference pattern of vortex beams

We experimentally and theoretically characterize the temporal rotation and radial twist of the interference pattern of a vortex beam with its conjugate copy. To quantitatively study the temporal rotation and radial twist, we controllably modify the conjugate beam to obtain a frequency or wavefront curvature difference using a movable Mach–Zehnder interferometer. The effects of the physical parameters (i.e., the topological charge, frequency difference and wavefront curvature difference of the vortex beams) on the temporal rotation as well as radial twist are systematically explored. We further measure two parameters, the rotation velocity Ω and twist coefficient α, respectively, to characterize the degree of the temporal rotation and radial twist of the interference pattern. The theory of the interference model on vortex beams has good agreement with the experimental results. This work is helpful for study on the detailed structure of the interference pattern and manipulation of matter with superimposed vortex beams.

On the sharp lower bounds of modular invariants and fractional Dehn twist coefficients

Abstract Modular invariants of families of curves are Arakelov invariants in arithmetic algebraic geometry. All the known uniform lower bounds of these invariants are not sharp. In this paper, we aim to give explicit lower bounds of modular invariants of families of curves, which is sharp for genus 2. According to the relation between fractional Dehn twists and modular invariants, we give the sharp lower bounds of fractional Dehn twist coefficients and classify pseudo-periodic maps with minimal coefficients for genus 2 and 3 firstly. We also obtain a rigidity property for families with minimal modular invariants, and other applications.

Correlation analysis between fabric structure and color rendering of polyester colored spun woven fabric based on the improved relative discrimination criterion

To clarify the color variation and influencing factors between colored spun yarn and its fabrics with different weave structures, a multi-dimensional spectral feature extraction model integrating distance and shape features is established in this paper. Considering the spectral reflectance of colored spun yarn and its fabric fluctuates randomly, a relative discrimination criterion based on the category separable ratio model is proposed; in addition, the principal component analysis algorithm is applied to the correlation analysis of the colored spun product’s color change. The results show that the established multi-dimensional spectral feature extraction model and relative discrimination criteria can effectively characterize the spectral features of colored spun yarns and fabrics. The difference of spectral features between the plain fabric samples and colored spun yarn samples is the largest, the twill structure is the second, and the difference of satin structure is the smallest. For colored spun fabric samples, the spectral feature fluctuation of the satin structure is the highest; the plain weave is the second, while the twill is the lowest. In addition, the increase in twist coefficient leads to a decrease in the difference of spectral features, but the color variation remains the same. Besides, there is no significant difference in spectral features between yarn and fabric samples using the principal component analysis algorithm. In the visible light range, the high-dimensional spectral features are more suitable for the characterization and analysis of the colored textiles’ color information.

Fabrication of Low-Twist and High-Strength Metallic Fibre Hybrid Spun Yarns

Stainless-steel fibre hybrid spun yarns are becoming increasingly popular due to their wide range of applications. In this aspect, the cost-effective and scalable processing of such yarns is highly important. Stainless-steel staple fibres are relatively heavier and weaker compared to conventional textile fibres. As a result, the staple spinning processing of these fibres showing higher tensile strength and productivity both at the same time is quite challenging. In this manuscript, we explored a number of spinning techniques to find the optimised method of producing low-twist and high-strength stainless-steel fibre hybrid spun yarns offering the advantage of both quality and productivity. Conventional ring spinning, folding and twisting, and advanced ring spinning techniques (ARSTs) such as pneumatic compact ring spinning and pneumatic compact SIRO spinning were employed in this study. Additionally, the plain and SIRO yarns were produced in two forms using the compact spinning method, one with pneumatic suction active (compact plain, compact SIRO) and other with pneumatic suction inactive (noncompact plain, noncompact SIRO). The tensile properties of yarns were tested and analysed. The results reveal that the tensile properties of conventional ring-spun and plied yarns can be enhanced to some extent by increasing the twist coefficient (TC) and the number of yarn plies, respectively. In contrast, by finding optimised spinning parameters, a substantially higher tensile strength (up to 16%) of yarns, produced at ARSTs, was observed even at the minimum level of TC used in experiments. The findings of the study are extremely valuable in terms of scaling up the production of high-quality metallic fibre hybrid spun yarns at a higher productivity level.

Evaluation of Unevenness and Tensile Properties of Open-End Yarns Produced by Recycled Acrylic-Based Textile Wastes from Different Sources

Abstract The classification of acrylic textile wastes based on source is important, because each waste type from different sources greatly affects product quality. This study primarily deals with recycled acrylic fibers obtained from three categories of acrylic-based tops, yarn, and fabric waste through a mechanical recycling method of garneting. With the use of recycled acrylic fiber types as 100 % ratio and in blends with recycled cotton and virgin polyester fibers, open-end yarns in two twist coefficients were produced, and then the effects of these selected materials and twist coefficient on the unevenness (CVm) and tensile properties of the yarns were discussed. The 100 % recycled acrylic yarn type produced from the tops waste type revealed the lowest CVm results and the highest tenacity and breaking elongation results. The blending of the virgin polyester fiber with the recycled acrylic fiber types improved the tenacity results. It can be concluded that tops, yarn, and fabric acrylic wastes have potential to be used as sustainable and low-cost sources of raw material in the production of open yarns of acceptable quality.

ВИКОРИСТАННЯ ГІС ПРИ ДОСЛІДЖЕННІ ГОРИЗОНТАЛЬНИХ ЗМІЩЕНЬ РУСЛА РІЧКИ СІРЕТ

The aim of the work is to study the horizontal displacements of the Siret riverbed from the settlement of Stara Zhadova to the village of Cherepkivtsi. Methodology: GIS analysis methods, mathematical data processing, analysis of Siret riverbed displacements were used to solve the issues raised in the work on horizontal displacements of the Siret riverbed. Semi-automatic digitization of the Siret riverbed on the scale maps: 1:75 000, 1:50 000, 1:25 000, 1:28000 was carried out and the lengths and coefficients of tortuosity were determined. Areas with the most pronounced meandering and changes in horizontal displacements of the channel are selected. The result of the study: For the study, the course of the river Siret was digitized from space images in 2016, which allowed to establish the coefficient of tortuosity, which is 1.52. Due to the vectorization of the water body on the topographic map of 1987 at a scale of 1:50 000, it was determined that the coefficient of tortuosity increased to 1.57. The military-topographic map of the Austro-Hungarian Empire was linked to the territory of the western part of Ukraine in 1889 and the coefficient of tortuosity along the digitized riverbed equal to 1.75 was calculated. The raster image was also digitized with the formation of vectorized layers on a 1957 map at a scale of 1:25 000 and the twist coefficient was determined to be 1.7. The study used the Austrian military topographic map of Galicia and Bukovina in 1861-1864 in modern western Ukraine, which calculated the coefficient of tortuosity at 1.9, which is the highest value for the entire observation period. The general overlay analysis showed that during the whole period of observations the channel was straightened, which led to a decrease in meandering processes along the entire length of the water body. Areas with the most pronounced meandering and areas with the greatest changes in horizontal displacements of the channel were identified: near the villages of Nova Zhadova, Cherepkivtsi, Kamyanka, Klynivka, and the town of Storozhynets. Scientific novelty: GIS analysis of horizontal displacements of the Siret riverbed during the 152-year observation period was carried out, which allowed to identify the main characteristic parts of the riverbed. Practical significance: the results of the study can be used in organizations and departments, in hydraulic services, in institutions involved in the design of river crossings, in regional and district water departments, as well as in research institutions.

MacPherson’s Conjecture via Hörmander’s Estimate

Abstract In this note, we reprove MacPherson’s conjecture on $L^2-(n,q)$-cohomology through Demailly’s formulation of Hörmander’s estimate. This approach allows us to prove the MacPherson’s conjecture of twisted coefficient bundle endowed with a singular hermitian metric. As applications, we study the MacPherson type problem for pluri-canonical bundles.

Optimization of Draft and Twist Values for Improvement of Breaking Strength and Elongation Properties of Dual-Core Yarns

Dual-core yarns, which are developed to have high elasticity and strength properties at the same time in the yarn structure, have been the focus of interest in yarn sector. Considering the purpose of developing dual-core yarns, it is obvious that the breaking strength and elongation performances expected from these yarns are very important. In this paper, the twist coefficient and PET (Polyethylene terephthalate)/Elastane draft ratios of dual-core yarns were optimized by Taguchi Method for improved of breaking strength and elongation performance. The signal to noise ratio (SNR) was calculated for each output and optimum levels were determined over these ratios. As a result of the study, it was determined that PET draft was the most effective parameter for both outputs. Considering the individual optimum levels determined for each output, common factor-level combinations covering both outputs were determined. Consequently, optimal common combination for the multi-performances was found as 4.2 twist coefficient, 1.15 PET draft ratio and 3.8 elastane ratio.

Texture Representation and Application of Colored Spun Fabric Using Uniform Three-Structure Descriptor

Abstract The local binary pattern (LBP) and its variants have shown their effectiveness in texture images representation. However, most of these LBP methods only focus on the histogram of LBP patterns, ignoring the spatial contextual information among them. In this paper, a uniform three-structure descriptor method was proposed by using three different encoding methods so as to obtain the local spatial contextual information for characterizing the nonuniform texture on the surface of colored spun fabrics. The testing results of 180 samples with 18 different color schemes indicate that the established texture representation model can accurately express the nonuniform texture structure of colored spun fabrics. In addition, the overall correlation index between texture features and sample parameters is 0.027 and 0.024, respectively. When compared with the LBP and its variants, the proposed method obtains a higher representational ability, and simultaneously owns a shorter time complexity. At the same time, the algorithm proposed in this paper enjoys ideal effectiveness and universality for fabric image retrieval. The mean Average Precision (mAP) of the first group of samples is 86.2%; in the second group of samples, the mAP of the sample with low twist coefficient is 89.6%, while the mAP of the sample with high twist coefficient is 88.5%.

Classification of colored spun fabric structure based on wavelet decomposition and hierarchical hybrid classifier

In view of the difficulty in extracting the feature parameters of colored spun fabric structure, this article proposes an automatic classification algorithm based on wavelet decomposition and hierarchical hybrid classifier. Based on HSV color space, the algorithm uses the wavelet function to perform multi-resolution decomposition and parameter feature extraction of colored spun fabric image. At the same time, it uses BP network and naive Bayes to build hierarchical hybrid classifier, and realizes the classification of the structure feature parameters. The experimental results show that the extracted fabric weave features not only have the ability of multi-resolution texture information representation, but also the constructed hybrid classifier has the characteristics of cascade enhancement. The average classification accuracy of 176 colored spun fabric structure with different dyeing fiber blending coefficient and twist coefficient is 96.67%, which proves the effectiveness and robustness of the method. The research in this article has important guiding significance to construct stable and effective colored spun fabric design and production system.

Functional Antibacterial Nanometer Zinc Ion Yarns: Manufacturing Technique and Antimicrobial Efficacy against Escherichia coli

People are no longer satisfied with only comfortable textile clothing with advanced technology and elevated standard of living and, thus, are gradually preferring functional textiles. In the meanwhile, the spread of medical knowledge has educated the public about the antimicrobial concept. In this study, composed of different twist coefficients and different numbers of plies, the zinc ion twisted yarns are made into knitted fabrics. Next, the knitted fabrics are examined for water vapor transmission rate and antimicrobial efficacy. The test results indicate that the water vapor transmission rate is 1013 g/m2/day for 2Zn-0C-K and 981 g/m2/day for 3Zn-0C-K. However, a rise in the twist coefficient adversely affects the water vapor transmission rate. The fabric 2Zn-3C-K exhibits the maximal air permeability of 265 cm3/cm2/s and 3Zn-3C-K 186 cm3/cm2/s. Regardless of whether it is at OD600, colony count observation, or antibacterial rate, 3Zn-5C-K exhibits the maximal antibacterial rate with the value being 0.45 at OD600 and the optimal antimicrobial efficacy being 85%. To sum up, based on the interest of the test results, production cost, and manufacturing process evaluation, 2Zn-5C-K is the optimal nonwoven fabric that achieved the maximal effects.

STUDY OF THE INFLUENCE OF CONSTRUCTION AND MODE PARAMETERS ON THE HYDRODYNAMICS OF A HOLLOW VORTEX APPARATUS

The research was to determine the more efficient design of the swirler from the point of view of hydrodynamics and heat and its optimal parameters. Various swirl designs were manufactured and tested. After preliminary studies conducted on a laboratory installation with a glass working apparatus, several swirlers were selected taking into account their hydraulic resistance, the structure of the swirling gas-liquid flow, and the amount of liquid entrainment by gas. The results of an experimental study of the hydrodynamics of a hollow vortex apparatus with one and two tangential and axial swirlers. Hydraulic losses in the channel and in the swirls during the direct downward movement of gas and gas-liquid flow are determined. In addition, studies of the hydraulic resistance of a vortex-type device allow us to determine the energy consumption of this device for conducting complex processes of dust collection and absorption or contact heat exchange. The hydraulic resistance in the presence of a liquid film is higher than in the case of a single-phase gas flow. The pressure drop in the studied vortex apparatus does not exceed the resistance of high-performance cyclones and vortex-type devices of other designs. The effect of the twist coefficient of gas swirlers, gas velocity, and liquid flow on the pressure drop in the vortex apparatus is established