COVID-19 immunization threshold(s): an analysis

2AbstractAs COVID-19 vaccine research efforts seem to be yielding the first tangible results, the proportion of individuals needed to reap the benefits of herd immunity is a key element from a Public Health programs perspective.This magnitude, termed the critical immunization threshold (q), can be obtained from the classical SIR model equilibrium equation, equaling (1 − 1/R0)/ ϵ, where R0 is the basic reproduction number and ϵ is the vaccine efficacy. When a significant proportion of the population is already immune, this becomes (n − 1/R0)/ ϵ, where n is the proportion of non-immune individuals. A similar equation can be obtained for short-term immunization thresholds(qt), which are dependent on Rt.qs for most countries are between 60-75% of the population. Current qt for most countries are between 20-40%.Therefore, the combination of gradual vaccination and other non-pharmaceutical interventions will mark the transition to the herd immunity, providing that the later turns out to be a feasible objective. Nevertheless, immunization through vaccination is a complex issue and many challenges might appear.

SPECTRAL and FOCAL PARAMETERS of NORTHERN CAUCASUSEARTHQUAKES

Dynamic sources parameters of 21 earthquakes of the North Caucasus for 2014 with КР=9.5–11.5, determined from 44 S-wave amplitude spectra are analyzed. Records of three regional digital seismic stations, “Anapa”, “Kislovodsk” and “Sochi”, located no more than 300 km from the sources are used. For the environment near these stations, the values of the frequency-dependent Q-factor, necessary for recalculating the station spectra to the focal ones, were obtained earlier by O.V. Pavlenko. In 2014, the majority of earthquakes studied were located in the Eastern Caucasus. The dependence between log M0 and КР for this zone was constructed using the data for 2010–2013. Compared to the similar equation for the entire Caucasus (Riznichenko et all., 1976), this dependence is in a good agreement with respect to the free term, but differs by the slope.

SPECTRAL and SOURCE EARTHQUAKE PARAMETERS on NORTHERN CAUCASUS

The dynamic parameters of of 18 earthquakes sources in the North Caucasus for 2013 with КР=10.0–12.9, determined from 64 amplitude spectra of S-waves are given. Records of three regional digital seismic sta-tions, “Anapa”, “Kislovodsk” and “Sochi” are used. They are located no more than 300 km from the sources. The records of the “Makhachkala” station were used in a test mode. For the environment near these stations, the values of the frequency-dependent Q-factor, necessary for recalculating the station spectra to the focal ones, were obtained earlier. In 2013, the largest number of studied earthquakes was located in the Eastern Caucasus. The dependence of log M0 and КР for this zone was established with use of the data ob-tained in 2010–2013. Compared to the similar equation of world average dependence (Riznichenko, 1976), our dependence is in a good agreement with it by the slope, but the free term exceeds the same in the world average dependence by almost two units.

Improving the tie force method for progressive collapse design of RC frames

Purpose The purpose of this paper is to recover the deficiency of existing tie force (TF) methods by considering the decrease in section strength due to cracking and by selecting limit state of collapse according to section properties. Design/methodology/approach A substructure is selected by isolating the connected beams from the entire structure. For interior joints, the TFs in the orthogonal beams are obtained by catenary action. For corner joints, the TFs are assessed by beam action. For edge joints, however, the resistance is gained by greater of the resistance under catenary action for periphery beams and beam action for all the connecting beams in both directions. For catenary action, the TF capacities must satisfy Equation (20). On the other hand, for beam action, the TF must satisfy Equation (16), while R is calculated from Equation (17). In the case where the length of the connecting beams is similar, Equation (19) can be used. Findings Closed form solutions are available for TFs on both beam and catenary stages. Originality/value The proposed formulation makes designing more practical and convenient. However, the proposed formulation had good agreement with experimental results.

Morse simulation of the global monopole equation in flat spacetime

We show that a Morse-type potential simulates an analytic solution for the highly nonlinear global monopole field equation in three and higher-dimensional flat spacetimes. Owing to the fact that in the flat space limit the similar equation remains intact, we wish to borrow the curved space terminology of global monopole also in flat spacetime. This may provide a compelling example that can be used effectively in different nonlinear theories such as flat space [Formula: see text] as well as in curved spacetimes.

VOLUME AND TAPER EQUATIONS FOR COMMERCIAL STEMS OF Nothofagus obliqua AND N. alpina

ABSTRACT Timber volume of standing trees is essential information for management decisions. The increasing need to optimize the potential capacity of forests maintaining their conservation, requires the quantification of the different potential possible timber products. The aim was to adjust taper equations to determine volumes of different timber products for commercial stems of Nothofagus alpina and N. obliqua. Trees of both species were randomly selected in harvesting areas of Lanin National Park (Argentina). Trees were felled and cut into commercial logs, measuring diameter with bark at different heights up to the beginning of the crown, and for each tree the diameter at breast height and total height. Five taper equations were selected and non-linear regression processes were employed for the fittings. We obtained the volume through the integration of the stem profile equation and the rotation in the space thereof through solid of revolution. The Bennet and Swindel (1972) model was selected for both Nothofagus species, obtaining similar equation parameters and differences were observed at the top of the stems of larger trees. For this the use of an integrated model is not recommended. With the obtained equations it is possible to: (i) estimate volume at different heights and for different commercial diameters, and (ii) predict the height at which both species reach to a certain diameter. The model presented some statistical limitations (e.g. multicollinearity), however, the fitting of the equation and the easy understanding of the outputs support it as a useful tool in a broad range of forest applications.

Study on the Rainfall Similar of Soil Erosion on Loess Slope

A lot of research about soil erosion similarity have done and obtained rich achievements. However, strictly speaking, it need to do a lot of deep study about to establish the ratio scale model of soil erosion, the problems unsolved include of does not establish the similar equation system about soil erosion and sediment yield entities simulation. we did some experiment, the date shows: the raindrop speed mainly at 0.6-5m/s in 10min, the wave crest was 1m/s and 4.2m/s. At the same times, the 0.125mm grain diameter raindrop speed was about at 0.6-1.4m/s, the 0.25mm grain diameter raindrop speed was about at 1-1.4m/s, the 0.375mm grain diameter raindrop speed was about at 1-1.4m/s, the 0. 5mm grain diameter raindrop speed was about at 1-3.4m/s, the 0.75mm grain diameter raindrop speed was about at 3.4m/s, the 1mm grain diameter raindrop speed was about at 4.2m/s, the 1.25mm grain diameter raindrop speed was about at4.2-5m/s, the 1.5mm grain diameter raindrop speed was about at5m/s.

Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments

In this paper, we propose the study of an integral equation, with deviating arguments, of the typey(t)=ω(t)-∫0∞‍f(t,s,y(γ1(s)),…,y(γN(s)))ds,t≥0,in the context of Banach spaces, with the intention of giving sufficient conditions that ensure the existence of solutions with the same asymptotic behavior at∞asω(t). A similar equation, but requiring a little less restrictive hypotheses, isy(t)=ω(t)-∫0∞‍q(t,s)F(s,y(γ1(s)),…,y(γN(s)))ds,t≥0.In the case ofq(t,s)=(t-s)+, its solutions with asymptotic behavior given byω(t)yield solutions of the second order nonlinear abstract differential equationy''(t)-ω''(t)+F(t,y(γ1(t)),…,y(γN(t)))=0,with the same asymptotic behavior at∞asω(t).

Numerical Analysis of Double Contacts of Similar Elastic Materials

A fast numerical method based on the Cauchy singular integral equations is presented to determine the contact pressure and extents for the contact of two-dimensional similar isotropic bodies when the contact area consists of two separate regions. The partial-slip problem is then solved to determine shear tractions using an equivalence principle. The extents of the contact are not all independent but related to a compatibility equation constraining the displacements of an elastic body in contact with an equivalent rigid body. A similar equation is found for the extents of the stick zones in partial-slip problems. The effects of load history are incorporated into the shear solution. The method is applicable to a wide range of profiles and it provides significant gains in computational efficiency over the finite element method (FEM) for both the pressure and partial-slip problems. The numerical results obtained are compared with that from the FEM for a biquadratic indenter with a single concavity and showed good agreement. Lastly, the transition behavior from double to single contacts in biquadratic profiles is investigated.