Statistical analysis of the data series from 1856 to 2000 for the annual global and hemispheric surface air temperature anomalies is completed. Statistically significant correlations are found between global and hemispheric temperature anomalies and solar and geomagnetic indices. The temperature anomalies in the Northern and Southern hemispheres show similar statistical relations with the solar and geomagnetic indices. The c ross-correlation analysis shows no statistically significant global temperature lag behind the sunspots as well as behind aa-indices. The correlation between the temperature anomalies and the geomagnetic indices is about two times higher than the correlation between the temperature anomalies and the solar indices. These results support the suggestion that the geomagnetic forcing predominates over the solar activity forcing on the global and hemispheric surface air temperatures.

We have used data for 45 countries with a population of over 30 millions in which 85.8% of the world's population lives. The statistical relationships of total COVID-19 Cases and Deaths per million populations in these countries with 10 demographic, economic and social indicators (indices) were studied. These indicators are Life Expectancy, Median Age, Growth Rate, Population Density, GDP PPP per capita, Human Development Index (HDI), Gini index of income equality, Intelligence Quotient (IQ), Corruption Perceptions Index (CPI) and Democracy Index. Statistically significant relationships were found with all indicators excluding Gini index and Population Density. We have found that the closest is the relationship of Deaths per million population and total Cases per million population with correlation coefficient R = 0.926. Therefore, it is clear statistically that the more are Cases per million in a country the more are Deaths per million. This confirms the correctness of the timely and effective introduction of the necessary pandemic restrictions in the countries. It is interesting that the close correlations were found of Cases and Deaths per 1 million with a purely economic index like GDP PPP per capita, where R = 0.687 and R = 0.660, respectively. Even more close correlations were found of Cases and Deaths per 1 million with a composite index HDI, where the correlation coefficients reach 0.724 and 0.680, respectively. This paradoxical results show that the richest and well-being countries are most seriously affected by the COVID-19 pandemic. The most probable reason for this is the large percentage of aging population, comorbidity of population with severe chronic diseases and obesity in countries with high GDP and HDI. No less important reason appears the delayed and/or insufficiently effective pandemic restrictions in these countries, which have underestimated the danger of a pandemic in early stage. Other indicators (excluding Gini index and Population Density) also show statistically significant correlations with Cases and Deaths per 1 million with correlation coefficients from 0.432 to 0.634. The countries that deviates the most from the regression lines were shown. Surprisingly, there was no statistically significant correlation between Cases and Deaths with Population Density. The statistical significance of the found correlations determined using Student's t-test was p <0.0001. The countries that deviate the most from both sides of the regression line were shown. It has been shown that the correlations of COVID-19 cases and Deaths with the studied indicators decrease with time. Key words: COVID-19 pandemic; statistics; cases and deaths per million; demographic, economic and social indicators

The ratio between the proton and electron masses is shown to be close to the ratio between the strong and electromagnetic interaction coupling constants at Extremely Low Energy (ELE). Based on the experimental data, this relation has been extended for the weak and gravitational interactions, too. Thus, a mass relation has been found, according to which the rest mass of the Lightest Free Massive Stable Particle (LFMSP), acted upon by a particular interaction, is proportional to the coupling constant of the respective interaction at ELE. On the basis of this mass relation, the electron neutrino and graviton masses have been approximately estimated to 2.1 × 10 -4 eV/c 2 and 2.3 × 10 -34 eV/c 2 , respectively. The last value is of the order of the magnitude of 2 c H h , where H is the Hubble constant.It is worth noting that this value has been obtained by fundamental constants only, without consideration of any cosmological models. PACS n

The recent astronomical observations indicate that the expanding universe is homogeneous, isotropic and asymptotically flat. The Euclidean geometry of the universe enables to determine the total gravitational and kinetic energy of the universe by Newtonian gravity in a flat space. By dimensional analysis, we have found the mass of the universe close to the Hoyle-Carvalho formula M ∼ c 3 /(GH). This value is independent from the cosmological model and infers a size (radius) of the universe close to Hubble distance. It has been shown that almost the entire kinetic energy of the universe ensues from the cosmological expansion. Both, the total gravitational and kinetic energies of the universe have been determined in relation to an observer at an arbitrary location. The relativistic calculations for total kinetic energy have been made and the dark energy has been excluded from calculations. The total mechanical energy of the universe has been found close to zero, which is a remarkable result. This result supports the conjecture that the gravitational energy of the universe is approximately balanced with its kinetic energy of the expansion.