A Damping-Tunable Snap System: From Dissipative Hyperchaos to Conservative Chaos

A hyperjerk system described by a single fourth-order ordinary differential equation of the form x⃜=f(x⃛,x¨,x˙,x) has been referred to as a snap system. A damping-tunable snap system, capable of an adjustable attractor dimension (DL) ranging from dissipative hyperchaos (DL<4) to conservative chaos (DL=4), is presented for the first time, in particular not only in a snap system, but also in a four-dimensional (4D) system. Such an attractor dimension is adjustable by nonlinear damping of a relatively simple quadratic function of the form Ax2, easily tunable by a single parameter A. The proposed snap system is practically implemented and verified by the reconfigurable circuits of field programmable analog arrays (FPAAs).

Derivation of Yarn Package Radius Measuring System for Yarn Winding Machines

Decreasing waste materials through recycle has in the recent contributed to sustainable manufacturing in many textile industries for better resource utilization in textile mills. This has been given first priority in manufacturing, processing and finishing operations. Most of the time the yarn manufacturing and proper utilization of this material didn’t give attention in most companies. Especially yarn length variation of packages, weaving beams and copes have very critical impact on those companies which manufacture and utilize yarn products. This variation problem has great impact on their productivity and profitability. This paper describes the application of a new formula in the yarn packaging process and it is accomplished by derivation a new formula that can determine the radius of any package. The formula has integrated the basic characteristics of yarn and fiber including yarn diameter, yarn/ fiber density and mass of the yarn coiled on the cop. Finally we have concluded that package radius is the quadratic function of yarn density and package mass on the cope.

Use of discriminant function analysis for forecasting crop yield

The present paper deals with use of discriminant function analysis for developing wheat yield forecast model for Kanpur (India). Discriminant function analysis is a technique of obtaining linear/Quadratic function which discriminates the best among populations and as such, provides qualitative assessment of the probable yield. In this study, quantitative forecasts of yield have been obtained using multiple regression technique taking regressors as weather scores obtained through discriminant function analysis. Time series data of 30 years (1971-2000) have been divided into three categories: congenial, normal and adverse, based on yield distribution. Taking these three groups as three populations, discriminant function analysis has been carried out. Discriminant scores obtained from this have been used as regressors in the modelling. Various strategies of using weekly weather data have been proposed. The models have been used to forecast yield in the subsequent three years 2000-01 to 2002-03 (which were not included in model development). The approach provided reliable yield forecast about two months before harvest.

Predicting Logarithm of Real Numbers to any Real Number Base

This paper aims to propose an algorithm that can predict the values of logarithmic function for any domain and for any bases with minimum possible error using basic mathematical operations. It talks about a univariate quadratic function that overlaps with the graph of the common logarithmic function to some extent, and using this resemblance to fullest advantage. It proposes a formula and certain algorithms based on the same formula.

Minimizing uncertainty in complete automation of Douglas-Peucker Algorithm for geospatial mapping

It is qualitatively evident that the greater the map scale change, the greater the optimal distance threshold of the Douglas-Peucker Algorithm, which is used in polyline simplification. However, no specific quantitative relationships between them are known by far, causing uncertainties in complete automation of the algorithm. To fill this gap, the current paper constructs quantitative relationships based on the spatial similarity theories of polylines. A quantitative spatial similarity relationship model was proposed and evaluated by setting two groups of control experiments and taking <C, T> as coordinates. In order to realize the automatic generalization of the polyline, we verified whether these quantitative relationships could be fitted using the same function with the same coefficients. The experiments revealed that the unary quadratic function is the best, whether the polylines were derived from different or the same geographical feature area(s). The results also show that using the same optimal distance threshold is unreasonable to simplify all polylines from different geographical feature areas. On the other hand, the same geographical feature area polylines could be simplified using the same optimal distance threshold. The uncertainties were assessed by evaluating the automated generalization results for position and geometric accuracy perspectives using polylines from the same geographic feature areas. It is demonstrated that in addition to maintaining the geographical features, the proposed model maintains the shape characteristics of polylines. Limiting the uncertainties would support the realization of completely automatic generalization of polylines and the construction of vector map geodatabases.

Effect of Ambient Lighting on Frequency Dependence in Transcranial Electrical Stimulation-Induced Phosphenes

Inconsistencies have been found in the relationship between ambient lighting conditions and frequency-dependence in transcranial electric current stimulation (tECS) induced phosphenes. Using a within-subjects design across lighting condition (dark, mesopic [dim], photopic [bright]) and tECS stimulation frequency (10, 13, 16, 18, 20 Hz), this study determined phosphene detection thresholds in 24 subjects receiving tECS using an FPz-Cz montage. Minima phosphene thresholds were found at 16 Hz in mesopic, 10 Hz in dark and 20 Hz in photopic lighting conditions, with these thresholds being substantially lower for mesopic than both dark (60% reduction) and photopic (56% reduction), conditions. Further, whereas the phosphene threshold-stimulation frequency relation was linear in the dark (increasing with frequency) and photopic (decreasing with frequency) conditions, a quadratic function was found for the mesopic condition (where it followed the linear increase of the dark condition from 10-16 Hz, and the linear decrease of the photopic condition from 16-20 Hz). The results clearly demonstrate that ambient lighting is an important factor in the detection of tECS-induced phosphenes, and that mesopic conditions are most suitable for obtaining overall phosphene thresholds.

A quadratic analytical solution of root pressure generation provides insights about bamboo and other species

We derived a steady-state model of whole root pressure generation through the combined action of all parallel segments of fine roots. This may be the first complete analytical solution for root pressure, which can be applied to complex roots/shoots. The osmotic volume of a single root is equal to that of the vessel lumen in fine roots and adjacent apoplastic spaces. Water uptake occurs via passive osmosis and active solute uptake (J_s^*, osmol s-1), resulting in the osmolal concentration Cr (mol·kg-1 of water) at a fixed osmotic volume. Solute loss occurs via two passive processes: radial diffusion of solute Km (Cr-Csoil), where Km is the diffusional constant and Csoil is the soil-solute concentration) from fine roots to soil and mass flow of solute and water into the whole plant from the end of the fine roots. The proposed model predicts the quadratic function of root pressure P_r^2+bP_r+c=0, where b and c are the functions of plant hydraulic resistance, soil water potential, solute flux, and gravitational potential. The present study investigates the theoretical dependencies of Pr on the factors detailed above and demonstrates the root pressure-mediated distribution of water through the hydraulic architecture of a 6.8-m-tall bamboo shoot.

ALGORITHM FOR DETERMINATION OF BRAKE EFFICIENCY OF INDUSTRIAL RAILWAY TRAINS

The main differences between the operating conditions of industrial railway transport from the main-line ones, which feature the performance of technological transportation, i.e., the transportation of goods within the local boundaries of enterprises (domestic technological transportation), and import (export) of goods to other modes of transport (external transportation). Industrial railway transport plays an important role at mining enterprises, as the working conditions of these enterprises are not constant and getting continuously more complicated during the entire period of field development. In this regard, one of the most important factors in ensuring the train safety is the braking efficiency. The calculation of the braking efficiency of a quarry train is performed according to special rules, and the parameters of the braking process that affect the braking distance are set by coefficients. As an estimated characteristic of braking efficiency for industrial railway transport, the maximum speed is taken, at which the braking distance should be no more than 300 m, regardless of the magnitude of the slope of the railway track. For the first time it is proposed to determine the allowable speed by the iterative method using a correction factor, the choice of which is due to the fact that the relationship between speed and braking distance is described by a quadratic function. The calculation showed that in five iterations the difference between the calculated and normative values of the braking distance of 0.01 m (1 cm) is achieved, which indicates the efficiency effect of the proposed determination procedure. The software allows you to automatically perform calculated studies for a given range of values of the slopes. The results of the train calculation in a specified range of slope values are given, as well as an analytical expression for determining the maximum speed for a given arbitrary slope value. Key words: allowable speed, braking distance, iterative process, correction factor, algorithm.