Numerical Scheme Based on the Implicit Runge-Kutta Method and Spectral Method for Calculating Nonlinear Hyperbolic Evolution Equations

A numerical scheme for nonlinear hyperbolic evolution equations is made based on the implicit Runge-Kutta method and the Fourier spectral method. The detailed discretization processes are discussed in the case of one-dimensional Klein-Gordon equations. In conclusion, a numerical scheme with third-order accuracy is presented. The order of total calculation cost is O(Nlog2N). As a benchmark, the relations between numerical accuracy and discretization unit size and that between the stability of calculation and discretization unit size are demonstrated for both linear and nonlinear cases.

Developing and implementing a new methodology to test the affordability of currently popular weight loss diet meal plans and healthy eating principles

Background Weight loss diets continue to rise in popularity; however, the associated costs are seldom reported. Certain weight loss diets may be unaffordable and differ from their traditional nutrition composition to include non-conventional premium products. In contrast, healthy eating principles such as the Australian Guide to Healthy Eating (AGHE) and the Mediterranean Diet (MedDiet) place an emphasis on fresh produce and staple foods but are sometimes thought to be unaffordable. A new methodology was piloted to assess the cost of weight loss diets using seven meal plans. Methods Seven meal plans were analysed to quantify the absolute grams required of all ingredients across seven days and multiplied by the cost of the ingredient per gram to determine the total cost of each ingredient based on unit size and price. The weekly grocery shopping cost was determined through summation of all ingredients and their entire unit size to compare weekly costs. Results Weekly meal plans (absolute grams) cost between $93-193AUD. The AGHE meal plan was the least expensive and 8 Weeks to Wow was the most expensive. Weekly grocery shopping of entire units cost between $345-$625AUD, over $100AUD greater than the spending of an average Australian ($237AUD/week). Conclusions The financial feasibility for long-term sustainment of weight loss diets may be questionable for groups including low-income earners and low socioeconomic status. Further, when dietary patterns are adapted for weight loss, or followed by consumers, deviations from foundational principles tend to occur which may influence overall cost.

ANALYSIS OF THE ERROR COMPONENTS OF LEVER TYPE FORCE-GENERATING MACHINES

The national standards are the basis of the technical base of the state metrological system. The developing of a na-tional primary standard of force unit solves such tasks as ensuring the uniformity of force measurements, transmitting the size of a unit of force with the required accuracy, metrological support of a large fleet of working standards and measuring instruments used in Ukraine. One of the main stages in the creation of the national standard is the development of a mathematical model of the process of reproducing the unit size of a physical quantity, namely N - Newton. The purpose of this study is to analyze the components of the error of force-generating installations of the multi-lever type, which are part of the national standard. Force generating installations used by calibration laboratories are usually traced to national standards through verification using precision force transducers. Calibration of force measuring instruments will typically be performed on these installations according to a documented procedure, such as ISO 376, and the components of error and uncertainty of calibration results will depend on the calibration and measurement capabilities of the unit size reproduction. Similarly, the uncertainty of the calibration of industrial force measuring in-struments will depend in part on the uncertainty contributing by the force measuring instrument, and the uncertainty of any subsequent force measurement will depend in part on the uncertainty associated with the reproduction of a unit of force, including national standard. It can be seen that the uncertainty of the final strength measurement depends on all previous stages of the measurement, and this work aims to make recommendations on how these contributions can be estimated. The purpose of this study is to analyze the components of the error of power plants of the multi-lever type, which are part of the state standard. The paper analyzes the method of reproduction, storage and transmission of the unit size, lever reinforcement installations, which can be used as reference metrological institutes and calibration laboratories. The basic principles of operation of the above reference installations are considered and the mathematical model of reproduction of the size of unit of force is created.

Searching for continuous phase transitions in 5D SU(2) lattice gauge theory

We study the phase diagram of 5-dimensional SU(2) Yang-Mills theory on the lattice. We consider two extensions of the fundamental plaquette Wilson action in the search for the continuous phase transition suggested by the 4 + ϵ expansion. The extensions correspond to new terms in the action: i) a unit size plaquette in the adjoint representation or ii) a two-unit sided square plaquette in the fundamental representation. We use Monte Carlo to sample the first and second derivative of the entropy near the confinement phase transition, with lattices up to 125. While we exclude the presence of a second order phase transition in the parameter space we sampled for model i), our data is not conclusive in some regions of the parameter space of model ii).

Searching for an Optimal Hexagonal Shaped Enumeration Unit Size for Effective Spatial Pattern Recognition in Choropleth Maps

Thoughtful consideration of the enumeration unit size in choropleth map design is important to ensure the correct communication of spatial information. However, the enumeration unit size and its influence on pattern conveying in choropleth maps have not yet been the subject of in-depth empirical studies. This research aims to address this gap. We focused on the issue concerning whether the ability to recognize spatial patterns on an Equal Area Unit Map is related to the hexagonal enumeration unit size, defined by the number of pixels. The aim is to indicate the range of the enumeration unit sizes, namely, at what point the upper and lower borders of the range where the spatial patterns start, and where the end is visible and recognizable by users. To address this problem, we conducted an empirical study with 488 users. The results show that the enumeration unit size has an impact on the users’ spatial pattern recognition abilities. Choropleth maps with enumeration unit sizes of 26, 52, and 104 pixels were, in the majority, indicated by participants as those most suitable for indicating spatial patterns. This was in contrast to choropleth maps with enumeration unit sizes of 1664 and 3328 pixels, which users indicated as not being useful. However, there were some exceptions to this general finding. Thus, determining the optimal enumeration unit size is a challenging task, and requires further insightful investigations.

Mathematical Relationships between Motoneuron Properties Derived by Empirical Data Analysis: Size Determines All Motoneuron Properties

Our understanding of the behaviour of motoneurons (MNs) in mammals partly relies on our knowledge of the relationships between MN membrane properties, such as MN size, resistance, rheobase, capacitance, time constant, axonal conduction velocity and afterhyperpolarization period. Based on scattered but converging evidence, current experimental studies and review papers qualitatively assumed that some of these MN properties are related. Here, we reprocessed the data from 27 experimental studies in cat and rat MN preparations to empirically demonstrate that all experimentally measured MN properties are associated to MN size. Moreover, we expanded this finding by deriving mathematical relationships between each pair of MN properties. These relationships were validated against independent experimental results not used to derive them. The obtained relationships support the classic description of a MN as a membrane equivalent electrical circuit and describe for the first time the association between MN size and MN membrane capacitance and time constant. The obtained relations indicate that motor units are recruited in order of increasing MN size, muscle unit size, MN rheobase, unit force recruitment thresholds and tetanic forces, but underlines that MN size and recruitment order may not be related to motor unit type.

Examining the Moderating Effects of Work Unit Size and Task Analyzability in the Relation Between Leader’s Communication Style and Leader-Member Exchange

There is a consensus regarding the impact of the leader’s communication on the relationship with their followers and on the achievement of organizational outcomes. This study seeks to contribute to clarifying the impact that contextual factors have on the leader’s communication in order to know how leaders should adjust their communication style, depending on the job characteristics, to build high quality relationships with their followers. Therefore, the current research examines the moderating role of two context factors in the effectiveness of leaders’ communication in generating the leader-member relationship. Through a moderation analysis on a sample of 149 white-collar workers, this research study analyzes how work unit size and task analyzability interact regarding six dimensions of leader communication style in relation to LMX. Results suggest that the work unit size moderates the relationship between two dimensions of leader’s communication style (preciseness and verbal aggressiveness) and LMX. Specifically, the positive effect of preciseness on LMX smooths as the work unit size increases. The negative effect of verbal aggressiveness on LMX becomes more intense as work unit size increases. Furthermore, task analyzability moderates the positive relationship between emotionality and LMX for low levels of task analyzability. As a result, this study contributes by deepening on why leaders’ communicative behaviors can have favorable/unfavorable results in specific contexts and on how a leader can modulate his/her communication style according to the context, in order to improve the LMX. Implications are discussed.

Risk of COVID-19 Disease, Dialysis Unit Attributes, and Infection Control Strategy among London In-Center Hemodialysis Patients

Background Patients receiving in-center hemodialysis treatment face unique challenges during the COVID-19 pandemic, specifically the need to attend for treatment that prevents self-isolation. Dialysis unit attributes and isolation strategies that might reduce dialysis center COVID-19 infection rates have not been previously examined. Methods We explored the role of variables including community disease burden, dialysis unit attributes (size, layout) and infection control strategies, on rates of COVID-19 among patients receiving in center hemodialysis in London, UK, between March 2nd 2020 and May 31st 2020. The two outcomes were defined as (i) a positive test for infection or admission with suspected COVID19 and (ii) admission to the hospital with suspected infection. Associations were examined using a discrete-time multi-level time-to-event analysis. Results Data on 5,755 patients, dialysing in 51 units were analysed. 990 (17%) tested positive and 465 (8%) were admitted with suspected COVID-19 between 2nd March and 31st May 2020. Outcomes were associated with age, diabetes, local community COVID-19 rates and dialysis unit size. Greater number of available side rooms and introduction of mask policies for asymptomatic patients were inversely associated with outcomes. No association was seen with sex, ethnicity, or deprivation indices nor with any of the different isolation strategies. Conclusions Rates of COVID-19 in the in center-hemodialysis population relate to individual factors, underlying community transmission, unit size and layout.