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— One approach to obtain a cryptographically strong encryption gamma is to use linear-feedback shift registers defined by primitive polynomials. The ability to quickly select the appropriate polynomial can provide the required degree of security of the stream cipher. Currently, primitive polynomials for sufficiently large degrees are known, but usually these are so-called sparse polynomials. To increase the correlational stability, it is necessary to be able to quickly generate new primitive polynomials of the given degrees, which is the focus of this study.

Background Epidemiological studies have shown deterioration in dental health accompanying the ageing process. Tooth loss increases with age. Chewing ability is closely correlated with number of natural teeth present: there is a threshold of 20–21 teeth, below which chewing ability declines. The government of Israel is currently considering adding dental treatment for elderly to the basket of services of the National Health Insurance Law. Information on the influence of elderly’s dental health on nutrition and general health status can contribute to the decision making process. Methods Secondary analysis of data collected on a subsample ( N  = 1776) of the cross-sectional Mabat Zahav - National Health and Nutrition Survey of the Elderly was done. Intakes of energy, fiber, protein, fruits and vegetables, associations with dental visits, dentures presence and functional ability were analyzed. Linear regression adjusted for confounders was performed. Results Statistically significant differences in dietary intake of energy, fiber, protein and vegetables were found between elderly who visited a dentist in the last year and those who did not. Elderly who possessed dentures had lower dietary intakes than their dentate counterparts. Elderly with functional problems such as impaired chewing had worse dietary intakes than the others. This was so after controlling for education, degree of interest in the relationship between nutrition and health and reading the nutrition label. Conclusions The findings in our study suggest that those who visited a dentist in the last year, had natural teeth and no denture/s and reported no chewing problems had better dietary intake. The results emphasize the importance of maintaining adequate dental health, preserving natural teeth and regular dental visits in the elderly to assure adequate nutrient status in this age group.

Plane gravitational waves in the Riemann space of General Relativity is considered. The criterion of plane gravitational waves is used based on the analogy between plane gravitational and electromagnetic waves. The Theorem is proved that the action of the Lie derivative on the plane wave curvature 2-form in the direction of the vector generating the invariance group of this wave in the Riemann space is equal to zero. It is justified that the gravitational waves can be used to transmit information in the Riemann space.

The Trautman problem determines the conditions under which GWs transfer the information contained in them in an invariant manner. According to the analogy between plane gravitational and electromagnetic waves, the metric tensor of a plane gravitational wave is invariant under the five-dimensional group , which does not change the null hypersurface of the plane wave front. The theorems are proven on the equality to zero for the result of the action of the Lie derivative on the curvature 2-form of a plane GW in Riemann and Riemann–Cartan spaces in the direction determined by the vector generating the group . Thus the curvature tensor of a plane gravitational wave can invariantly transfer the information encoded in the source of the GW.

The early evolution of a supernova (SN) can reveal information about the environment and the progenitor star. When a star explodes in vacuum, the first photons to escape from its surface appear as a brief, hours-long shock-breakout flare 1 , 2 , followed by a cooling phase of emission. However, for stars exploding within a distribution of dense, optically thick circumstellar material (CSM), the first photons escape from the material beyond the stellar edge and the duration of the initial flare can extend to several days, during which the escaping emission indicates photospheric heating 3 . Early serendipitous observations 2 , 4 that lacked ultraviolet (UV) data were unable to determine whether the early emission is heating or cooling and hence the nature of the early explosion event. Here we report UV spectra of the nearby SN 2023ixf in the galaxy Messier 101 (M101). Using the UV data as well as a comprehensive set of further multiwavelength observations, we temporally resolve the emergence of the explosion shock from a thick medium heated by the SN emission. We derive a reliable bolometric light curve that indicates that the shock breaks out from a dense layer with a radius substantially larger than typical supergiants. Using ultraviolet data as well as a comprehensive set of further multiwavelength observations of the supernova 2023ixf, a reliable bolometric light curve is derived that indicates the heating nature of the early emission.

We present a solution methodology for dynamic problems of the theory of elasticity based on the fundamental (F)-solutions approach for layers and semilayers containing cavities. Under the proposed solution framework boundary-value problems for three-dimensional cylindrical bodies are reduced to well-studied systems of one-dimensional singular integral equations. With the aid of the integral Fourier transform in time, we study the problem of impulse loading at the sides of cavities. We also demonstrate how the combination of the proposed methodology with the approach of reflections can be used for the solution of analogous problems for semi-infinite layers.

Multi-frequency and multi-component extra-deep azimuthal resistivity measurements with depth of investigation of a few tens of meters provide advanced possibilities for mapping of complex reservoir structures. Inversion of the induction measurements set becomes an important technical problem. We present a regularized Levenberg–Marquardt algorithm for inversion of resistivity measurements in a 2D environment model with pixel-based resistivity distribution. The cornerstone of the approach is an efficient parallel algorithm for computation of resistivity tool signals and its derivatives with respect to the pixel conductivities using volume integral equation method. Numerical tests of the suggested approach demonstrate its feasibility for near real time inversion.

Extra-deep azimuthal resistivity measurements improve the depth of investigation up to 30 m from the wellbore. Interpretation of electromagnetic logging data in the neighbourhood of a well becomes an important technical problem. We present an efficient parallel method for computation of induction tool responses with multiple transmitter-receiver configurations in 2D pixel-based anisotropic model crossed by an arbitrary well trajectory. The cornerstone of the approach is volume integral equation method. We consider the conductivity distribution as a sum of background and anomalous conductivities. Background conductivity is 1D-layered. Anomalous conductivity has arbitrary 2D distribution. Electromagnetic fields are the superposition of background and anomalous fields. Background fields are calculated exactly using rigorous analytical solution for 1D-layered background model. With this approach, the 2D pixel-based model is treated as an extension of the 1D-layered model. The anomalous fields are required only in pixels with conductivity different from the conductivity of the 1D-layered model. Anomalous fields are calculated using convergent series of integral operators [1]. The approach takes into account conductivity anisotropy and allows obtaining both the exact solution and the fast approximate one. The convergence of approximate solution is investigated on some synthetic examples.

The relationships between the main tectonic features in the north of central and western Siberia are analyzed on the basis of the available geologic and geophysical data. The chain of troughs and syneclises, including the Yenisei-Khatanga Foredeep, the Lena-Anabar Trough, and the Ust-Yenisei and Yamal-Gydan syneclises are bounded in the north and south by systems of swells of approximately the same size and age. It is suggested that these swells, having appeared simultaneously with the troughs, were eroded subsequently and then buried beneath the Mesozoic-Cenozoic sediments.[PUBLICATION ABSTRACT]