Hilbert’s 6-th problem and principle of completeness in dynamics

The following offers a new axiomatic basis of mechanics and physics in their most important dynamics domain, i.e. a principle (axiom) of completeness intended to generalize Newton’s second law of motion for the case of a non-stationary variable-mass point (system) that varies with time. This generalization leads to hyperdynamic dependencies describing such motion from new accurate qualitative standpoints.

A Bayesian Hurdle Quantile Regression Model for Citation Analysis with Mass Points at Lower Values

Quantile regression presents a complete picture of the effects on the location, scale, and shape of the dependent variable at all points, not just the mean. We focus on two challenges for citation count analysis by quantile regression: discontinuity and substantial mass points at lower counts. A Bayesian hurdle quantile regression model for count data with a substantial mass point at zero was proposed by King and Song (2019). It uses quantile regression for modeling the nonzero data and logistic regression for modeling the probability of zeros versus nonzeros. We show that substantial mass points for low citation counts will nearly certainly also affect parameter estimation in the quantile regression part of the model, similar to a mass point at zero. We update the King and Song model by shifting the hurdle point past the main mass points. This model delivers more accurate quantile regression for moderately to highly cited articles, especially at quantiles corresponding to values just beyond the mass points, and enables estimates of the extent to which factors influence the chances that an article will be low cited. To illustrate the potential of this method, it is applied to simulated citation counts and data from Scopus. Peer Review https://publons.com/publon/10.1162/qss_a_00147

Is Jacobi theorem valid in the singly averaged restricted circular Three-Body-Problem?

C. Jacobi found that in the General N-Body-Problem (including N = 3) for the Lagrangian stability of any solution necessary is the negativity of the total energy of the system. For the restricted three-body-problem, this statement is trivial, since a zero-mass body introduces zero contribution to the energy of the system. If we consider only the equations describing the movement of the zero mass point, then the energy integral disappears. However, if we average the equations over the longitudes of the main bodies, the energy integral appears again. Is the Jacobi theorem valid in this case? It turned out not. For arbutrary large values of total energy, there exist bounded periodic orbits. At the same time the negative energy is sufficient for the boundedness of an orbit in the configuration space.

The Market Trajectory of a Radically New Product: E-Cigarettes

The study analyzes the diffusion of electronic cigarettes as an innovation, as well as how industry, society, and the individual affect its market dynamics. The study is based on five surveys conducted during the years 2017-2019, and including participants of all ages (age 12 to 80 and beyond). The article describes indicators for evaluating the sustainability of a really-new product like electronic cigarettes, following the market trajectory of this product as it sets its dominant design and shapes the use-system for the product type from now onward. This process has two phases: trial and adoption. The probability of each nicotine product type’s adoption is different, depending on the prevalence of trials of that product among the population. The results of e-cigarette trials and additional indicators reveal the point (critical mass-point) where social influence outweighs rational evaluation by the individual regarding nicotine products. By using triers’ prevalence as the indicator for measuring an entry of really-new product into the market, the authors could identify the sustainability of that really-new product at a much early phase. Therefore, the prevalence of triers can be used as a predictor for the diffusion rate of an innovative product in a certain population and should be measured. The authors also propose a regression model that estimates the prevalence of triers based on the extent of users in the population.

Unified theory of classic mechanics and quantum mechanics

In this paper, I review one of the most important and interesting parts of my new book “Fuzzy Systems to Quantum Mechanics” (see Ref. 1). Several conclusions in this part are worth introducing here. First of all, the motion of a mass point in classic mechanics has also waviness and the wave function of the motion of a mass point is composed of wave functions of countably infinite microscopic particles. Secondly, based on the waviness of the motion of a mass point we surely know the new conclusion described as the wave-mass-point dualism in classic mechanics. And thirdly, by using the closed relation between the wave-mass-point dualism in classic mechanics and the wave-particle dualism in quantum mechanics, unified theory of classic mechanics and quantum mechanics is naturally formed.

Study on Torsional Vibration Characteristics of Cross Shaft Universal Coupling

In this work, the ship propulsion shaft system with cruciform universal coupling is studied. First, based on the analysis of the structure and characteristics of the cross-axis universal coupling, the motion relations and expressions between the components of the universal coupling are established by using the coordinate transformation method. Second, the characteristics of the four submodels of the head mass point element, the end mass point element, the universal coupling mass point element, and other mass point elements are discussed, and the corresponding torsional vibration differential equations of the four submodels are established. On this basis, the mathematical model of the propulsion shafting system and the differential equations of torsional vibration are established by using the modularization method and lumped parameter method. Finally, the torsional vibration modes and response characteristics of the shafts are calculated and analyzed by using the system matrix method when the external load driving torques of the universal coupling, propeller, and diesel engine are considered. At the same time, the correctness of the mathematical model and calculation method is verified by the test and comparative analysis of ship propulsion shafts. It lays a theoretical foundation for further research on torsional vibration characteristics and mechanisms of the ship propulsion shafting system based on universal coupling.

High-Precision Plane Detection Method for Rock-Mass Point Clouds Based on Supervoxel

In respect of rock-mass engineering, the detection of planar structures from the rock-mass point clouds plays a crucial role in the construction of a lightweight numerical model, while the establishment of high-quality models relies on the accurate results of surface analysis. However, the existing techniques are barely capable to segment the rock mass thoroughly, which is attributed to the cluttered and unpredictable surface structures of the rock mass. This paper proposes a high-precision plane detection approach for 3D rock-mass point clouds, which is effective in dealing with the complex surface structures, thus achieving a high level of detail in detection. Firstly, the input point cloud is fast segmented to voxels using spatial grids, while the local coplanarity test and the edge information calculation are performed to extract the major segments of planes. Secondly, to preserve as much detail as possible, supervoxel segmentation instead of traditional region growing is conducted to deal with scattered points. Finally, a patch-based region growing strategy applicable to rock mass is developed, while the completed planes are obtained by merging supervoxel patches. In this paper, an artificial icosahedron point cloud and four rock-mass point clouds are applied to validate the performance of the proposed method. As indicated by the experimental results, the proposed method can make high-precision plane detection achievable for rock-mass point clouds while ensuring high recall rate. Furthermore, the results of both qualitative and quantitative analyses evidence the superior performance of our algorithm.

Model of above-ground biomass distribution of Norway spruce (Picea abies L. (Karst.))

Climate change with more frequent extreme weather events and prolonged winter periods with un-frozen, wet soil is causing frequent wind damage events in forests. Trees with higher mass point and heavier weight are more prone to wind damage; however, limited information exists on distribution of biomass under naturally moist conditions. Such information is essential to improve models of wind damage prediction. Therefore, the aim of the present study was to assess the biomass distribution and the parameters important for wind-load of Norway spruce (Picea abies (L.) Karst.). Samples were collected in the year 2019 from 87 trees growing on two different sites, corresponding to freely drained mineral and peaty mineral soils at the age of 55 and 88 years, respectively. Tree diameters at breast height, height, and height of first living branch were measured. Tree stems were pruned and cut into 2-m-long fragments and weighed (fresh weight) afterwards. A biomass distribution model was developed to estimate fresh weight of the stem of Norway spruce using easy measurable tree variables. Relative height of the mass point and height of living branches were higher in peaty mineral soil than on freely drained mineral soil, which was an indicator for higher windthrow risks.