Singularity-Free Lie Group Integration and Geometrically Consistent Evaluation of Multibody System Models described in terms of Standard Absolute Coordinates

A classical approach to the MBS modeling is to use absolute coordinates, i.e. a set of (possibly redundant) coordinates that describe the absolute position and orientation of the individual bodies w.r.t. to an inertial frame (IFR). A well-known problem for the time integration of the equations of motion (EOM) is the lack of a singularity-free parameterization of spatial motions, which is usually tackled by using unit quaternions. Lie group integration methods were proposed as alternative approach to the singularity-free time integration. Lie group integration methods, operating directly on the configuration space Lie group, are incompatible with standard formulations of the EOM, and cannot be implemented in existing MBS simulation codes without a major restructuring. A framework for interfacing Lie group integrators to standard EOM formulations is presented in this paper. It allows describing MBS in terms of various absolute coordinates and at the same using Lie group integration schemes. The direct product group SO(3)xR3; and the semidirect product group SE(3) are use for representing rigid body motions. The key element of this method is the local-global transitions (LGT) transition map, which facilitates the update of (global) absolute coordinates in terms of the (local) coordinates on the Lie group. This LGT map is specific to the absolute coordinates, the local coordinates on the Lie group, and the Lie group used to represent rigid body configurations. This embedding of Lie group integration methods allows for interfacing with standard vector space integration methods.

CLASSIFICATION OF WEARABLE ELECTRONIC DEVICES

Background. Today smart watches, fitness bracelets, smart rings are must-have accessory for everyone who cares about their health. It is projected that the average annual growth of the wearable device market in 2021–2026 will be 18 %, which is respectively reflected in this segment of the Ukrainian market. Well-known electronics stores use different approaches to group the range of wearable devices, as there are no single standards to classify these products. The aim of this article is to develop a classification of wearable devices and to identify the classification featuresfor smart watches and fitness bracelets based on the analysis of the assortment presented in online stores. Materials and methods. Methods of logical analysis, generalization of scientific literature, statistical data of export and import of wearable devices were applied. Data on their assortment and grouping in well-known retail chains were used to create a classification. Results. Based on the analysis of the world market of electronic goods and the assortment of well-known retail chains, the authors propose a classification of goods related to wearable devices. In particular, there is a division of wearable devices into 7 groups (wrist devices, head devices, smart clothes, smart shoes, smart jewelry, wearable devices, medical devices), these groups include subgroups, categories and subcategories. Only a few types of wearable devices are sold on the Ukrainian market – smart watches, fitness bracelets, virtual reality glasses and smart rings. However, only two retail chains allocate these products separately in the product group "Wearable Products", the others form a large product group "Gadgets…", which according to the authors is not entirely correct, as the latter differ significantly in purpose and characteristics. Since the range of smart watches and fitness bracelets is quite wide and includes hundreds of types, it is proposed to use a number of classification features that clearly distinguish them by their functionality. Conclusion. With the COVID-19 pandemic, the wearable devices market seg­ment will continue to grow. Restrictions on mobility and an individual’s desire to monitor vital signs of their health during a pandemic will be the main factors that will influence the market for these devices. The classification of goods related to wearable devices has been developed. The classification features for smart watches and fitness bracelets, the range of which includes hundreds of types, are proposed. It is established that the main difference between smart watches and a fitness bracelets is a wider functionality of the first and a much longer battery life of the latter.

Effects of Ephedrine-Containing Products on Weight Loss and Lipid Profiles: A Systematic Review and Meta-Analysis of Randomized Controlled Trials

Ephedrine, the main active ingredient of mahuang, may lead to weight loss; however, it can also induce cardiovascular side effects. As ephedrine use remains controversial, this study aimed to systematically review previous studies on ephedrine-containing products and perform meta-analysis of the existing evidence on weight, blood pressure (BP), heart rate, and lipid change effects of ephedrine-containing products. We searched for placebo-controlled randomized studies in PubMed, Web of Science, and EMBASE until July 2021 using the following search terms: (ephedr* OR mahuang) AND (“weight loss” OR obes* OR overweight). Mean differences (MDs) and 95% confidence intervals (CIs) were calculated to evaluate the effects of ephedrine-containing products on weight, BP, heart rate, and lipid profiles. A total of 10 articles were included. Compared with the placebo group, the ephedrine-containing product group was associated with greater weight loss, with an MD of −1.97 kg (95% CI: −2.38, −1.57). In the ephedrine-containing product group, the mean heart rate was 5.76 beats/min higher than in the placebo group (95% CI: 3.42, 8.10), whereas intergroup differences in systolic and diastolic BP were not statistically significant. The ephedrine-containing product group had a significantly higher mean high-density lipoprotein cholesterol level (MD: 2.74 mg/dL; 95% CI: 0.94, 4.55), lower mean low-density lipoprotein cholesterol level (MD: −5.98 mg/dL; 95% CI: −10.97, −0.99), and lower mean triglyceride level (MD: −11.25 mg/dL; 95% CI: −21.83, −0.68) than the placebo group. Compared with placebo, the ephedrine-containing products showed better effects on weight loss and lipid profiles, whereas they caused increased heart rate. The ephedrine-containing products may be beneficial to obese or overweight patients; however, close monitoring is needed, especially heart rate monitoring.

Inner Product Groups and Riesz Representation Theorem

In this paper, we introduce an inner product on abelian groups and, after investigating the basic properties of the inner product, we first show that each inner product group is a torsion-free abelian normed group. We give examples of such groups and describe the norms induced by such inner products. Among other results, Hilbert groups, midconvex and orthogonal subgroups are presented, and a Riesz representation theorem on divisible Hilbert groups is proved.

Analysis of Methodological Approaches Towards Assessing Conditions of International Commodity Markets Convergence

To analyze different methodological approaches to determining the marketing attractiveness of international markets and their convergence assessing. Develop an indicators system for assessing the convergence of international markets to determine their marketing attractiveness for domestic agricultural enterprises. The international markets have been rated on the basis of summing the ranks of indicators of attractiveness method of their business environment for Ukrainian farmers by the product group «1008 Buckwheat, millet and other cereals» in order to identify more favorable conditions for doing business. The application of this approach allowed to develop a target portfolio for further targeting the implementation of the internationalization strategy by domestic producers of the product group «1008 Buckwheat, millet and other cereals». The methodological basis of the study are general and special research methods: epistemological and systems analysis - in the study of «economic convergence» definition; systems theory and systems analysis - to analyze of process determining the marketing attractiveness of international markets and assessing their convergence; statistical analysis, synthesis and comparison ‒ to identify trends in the entry of agricultural enterprises of Ukraine to international markets; comprehensive assessment of the convergence of agricultural enterprises of Ukraine under the conditions of international diversification. It has been proved that in the expert assessment of convergence indicators the markets of foreign countries, the indicators of which are as close as possible to the economy of Ukraine, should be singled out. It has been determined that the markets of Austria and Nigeria are promising for domestic agricultural enterprises, producers of the commodity group «1008 Buckwheat, millet and other cereals», with the possibility of overcoming a significant gap in certain indicators, namely: the market of Austria, Nigeria where there is low quality regulation and also unfavorable investment conditions. The scientific and methodological approach to the complex assessment of the convergence of new international markets for domestic agricultural enterprises under the conditions of international diversification has been substantiated and developed. The result of the evaluation allowed to come up to the conclusions about the marketing opportunities of domestic agricultural enterprises under the conditions of entering the markets of these countries. As a result of the proposed approach, it is possible to identify foreign markets that demonstrate favorable conditions for doing business in them, which indicates the presence of convergent conditions, which is a prerequisite for the entry of goods of domestic agricultural enterprises in the markets of these countries. As a result of the proposed approaches, there were identified new international markets, that demonstrated favorable conditions for doing business in them by domestic agricultural enterprises producing the product group «1008 Buckwheat, millet and other cereals». It has beed developed in the study a target portfolio for further targeting the strategy implementation of internationalization domestic producers of the product group «1008 Buckwheat, millet and other cereals».

Assessing between and within Product Group Variance of Environmental Efficiency of Swiss Agriculture Using Life Cycle Assessment and Data Envelopment Analysis

Food production systems can contribute to the degradation of the environment; thereby endangering the very resource, they depend on. However, while overall large, the environmental impacts of individual agricultural products are disparate. Therefore, in order to gain a better understanding of the impact different food production systems have on the environment, we should start at the produce level. In this study, we combine life cycle assessment (LCA) methodology and data envelopment analysis to calculate environmental efficiency scores (i.e., agricultural output divided by environmental impacts) for eight product groups (Milk, Cattle, Pig fattening, Cereals, Beets, Potatoes, Vegetables, Fruits) in Switzerland. First, LCA is used to calculate “cradle to farm-gate” environmental impacts. These impacts are then used as inputs in a data envelopment analysis, with the amount of produced agricultural products as outputs. The resulting environmental efficiency scores reflect the relative efficiency (i.e., related to the best-observed performance) of the observed product groups. We find large differences in environmental impacts and environmental efficiency score distribution between the product groups. While we find some variability of environmental efficiency between farming systems (Organic and Proof of Ecological Performance) within a product group (difference in coefficient of variation between farming systems: Fruits = 48%, Vegetables = 13%, Cereals, Potatoes = 8%), we did not find any significant differences in environmental efficiency between organic and integrated farming systems for any of the considered product groups. Furthermore, we did not find a negative effect of multifunctionality of Swiss farms (i.e., multiple simultaneously produced product groups), but found a small positive effect for Milk in the presence of other product groups. However, the high within product group variance of environmental efficiency suggests the potential for improvements (notably >40% for Fruits and >30% for Cattle and Potatoes).

Singularity-Free Lie Group Integration of Multibody System Models Described in Absolute Coordinates

A classical approach to the modeling of multibody systems (MBS) is to use absolute coordinates, i.e. a set of (redundant) coordinates that describe the absolute position and orientation of the individual bodies w.r.t. to an inertial frame (IFR). A well-known problem for the time integration of the equations of motion (EOM) is the lack of a singularity-free parameterization of spatial motions, which is usually tackled by using unit quaternions. Lie group integration methods were proposed as alternative approach to the singularity-free time integration. Lie group methods are inherently coordinate free and thus incompatible with any absolute coordinate description. In this paper, an integration scheme is proposed that allows describing MBS in terms of arbitrary absolute coordinates and at the same using Lie group integration schemes, which allows for singularity-free time integration. Moreover, the direct product group SO (3) × ℝ3 as well as the semidirect product group SE (3) can be use for representing rigid body motions, which is beneficial for constraint satisfaction. The crucial step of this method, which renders the underlying Lie group integration scheme applicable to EOM in absolute coordinates, is the update of the (global) absolute coordinates in terms of the (local) coordinates on the Lie group by means of a local-global transitions (LGT) transition map. This LGT map depends on the used absolute coordinates and the local coordinates on the Lie group, but also on the Lie group itself used to represent rigid body configurations (respectively the deformation field of flexible bodies), i.e. the geometry of spatial frame motions. The Lie group formulation is thus embedded, which allows interfacing with standard vector space integration methods.

A comparison of tobacco product prevalence by different frequency of use thresholds across three US surveys

Background With the increasing changes in tobacco use patterns, “current use” definition and the survey used may have important implications for monitoring population use trends. Methods Using three US surveys (2014/15 TUS-CPS, NHIS and PATH), we compared the adult (age 18+) prevalence of four product groups (cigarettes, other combustibles, smokeless tobacco, and e-cigarettes) based on three past 30-day frequency of use thresholds: 1+, 10+, and 25+ days. We also examined mutually exclusive single, dual, and polytobacco users as a percentage of total users for each product group. Results Regardless of threshold or product, the prevalence was higher in PATH followed by NHIS and TUS-CPS, in some cases by large percentages. The differences in cigarette and smokeless tobacco use prevalence in going from the 1+ to 10+ days and to the 25+ days threshold were minimal. Applying different frequency thresholds had the largest impact on other combustibles prevalence, with a 60% reduction with the 10+ days threshold and a 80% reduction with the 25+ days threshold, compared to the 1+ days threshold, followed by e-cigarettes with 40 and 60% reductions, respectively. The proportion of dual and polytobacco users decreased considerably when using the 10+ vs. the 1+ days threshold and polytobacco use was almost non-existent with the 25+ days threshold. Conclusion The estimated prevalence of each tobacco product use depends largely on the survey and frequency of use threshold adopted. The choice of survey and frequency threshold merits serious consideration when monitoring patterns of tobacco use.