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[en] We conjecture explicit evolution formulas for Khovanov polynomials, which for any particular knot are Laurent polynomials of complex variables q and T, for pretzel knots of genus g in some regions in the space of winding parameters n,…,n. Our description is exhaustive for genera 1 and 2. As previously observed Anokhina and Morozov (2018), Dunin-Barkowski et al. (2019), evolution at T≠−1 is not fully smooth: it switches abruptly at the boundaries between different regions. We reveal that this happens also at the boundary between thin and thick knots, moreover, the thick-knot domain is further stratified. For thin knots the two eigenvalues 1 and λ=qT, governing the evolution, are the standard T-deformation of the eigenvalues of the R-matrix 1 and −q. However, in thick knots’ regions extra eigenvalues emerge, and they are powers of the “naive” λ, namely, they are equal to λ,…,λ. From point of view of frequencies, i.e. logarithms of eigenvalues, this is frequency doubling (more precisely, frequency multiplication) – a phenomenon typical for non-linear dynamics. Hence, our observation can signal a hidden non-linearity of superpolynomial evolution. To give this newly observed evolution a short name, note that when λ is pure phase the contributions of λ,…,λ oscillate “faster” than the one of λ. Hence, we call this type of evolution “nimble”.
[en] We propose a solution method for studying relativistic spin-0 particles. We adopt the Feshbach–Villars formalism of the Klein–Gordon equation and express the formalism in an integral equation form. The integral equation is represented in the Coulomb–Sturmian basis. The corresponding Green’s operator with Coulomb and linear confinement potential can be calculated as a matrix continued fraction. We consider Coulomb plus short range vector potential for bound and resonant states and linear confining scalar potentials for bound states. The continued fraction is naturally divergent at resonant state energies, but we made it convergent by an appropriate analytic continuation. (author)
[en] We analyze BI-extended model in a complete form and compare the predictions with that of Starobinsky model. Under the parameter constraints in Planck 2018, we find that the dynamics of the whole inflation process described by BI-extended and Starobinsky models are nearly the same, even though there are some differences in the regions out of inflation. We also find the scales of parameters in BI-extended model and inflaton values at the first horizon crossing required to implement inflation. The changes of fingerprints of BI-extended model and that of evolutions of inflaton field due to the variations of relevant parameters are also investigated.
[en] The present work aims to show the functionality of a Monte Carlo simulator for neutron transport currently in development at the Federal University of Rio Grande do Sul. To this end a neutron shielding problem is simulated. Results for the neutron flux in both lightweight and heavyweight cement mixture are found. A purely absorption scenario is also simulated and its result is presented to be in good agreement to its analytical solution. Finally the computational costs of these simulations are shown. (author)
[en] Inherently UWB (Ultra Wideband) communication systems comes with interference problem with some if the existing narrowband communication systems. These bands are stopped with the help of band-stop filter in order to reduce electromagnetic interference However, the complexity and limitations are increased due to these filters, hence this solution is turned down in those applications where design complications and complexity is of concern. Introducing various slots of specific shapes and exact dimensions however, have solved this issue for the researchers around the world. This paper presents a hexagonal PMA (Printed Monopole Antenna) with triple stop bands. The antenna is used for UWB application. The antenna is stopped the WiMAX (Worldwide Interoperability for Microwave Access), WLAN (Wireless Local Area Network) and ITU (International Telecommunication Union) bands. The antenna dimensions are 30x28x16 mm3. FR4 is used between ground and radiating patch with relative permittivity of 4.4. The VSWR (Voltage Standing Wave Ratio) is less than 2 between 3-11 GHz except WiMAX (3.1-3.7 GHz), WLAN (5.1-5.8 GHz) and the ITU frequency band (7.95-8.4 GHz). The antenna is design in CST software. (author)
[en] The big data revolution has led to the emergence of many technologies for processing the enormous volume, high velocity and variety of data sources. The capabilities provided by high-performance computing (HPC) have had a substantial impact in supporting this revolution through the integration of heterogeneous hardware and crafting software and algorithms that exploit the parallelism of HPC. However, big data platforms, written in high-level programming languages, and their architectures differ from HPC languages and architectures. This misalignment has resulted in the underutilization of HPC resources and capabilities for big data problems. In this paper, we highlight and evaluate many of the techniques used in the HPC environment based on the most critical factors influencing performance and resource utilization: load balancing and data locality, job scheduling strategies, topology awareness, decomposition techniques and programming models. We recommend establishing a research roadmap that considers these influential factors in the field of resource and job management within HPC environments for big data computing.(author)
[en] The SePaC and BC methods are used for fractal analysis of mixed events containing incomplete fractals. Reconstruction of the distribution of events by dimension DF is studied. The procedures for analyzing incomplete fractals and correcting the determination of DF of combined fractals by the SePaC method are proposed. We find that the SePaC method fully reconstructs incomplete fractals and suppresses background, separation of incomplete fractals and background by the BC method depends on the basis of the formation of the fractal. The distribution of events by value of DF is more accurately reconstructed by the SePaC method in comparison with the BC method.
[ru]В работе использовались SePaC- и BC-методы для фрактального анализа смешанных событий, содержащих различные виды полных, неполных фракталов и примеси. Предложена процедура анализа SePaC-методом неполных фракталов, а также способ коррекции в определении размерности DF для фракталов с комбинированным делением частей. Установлено, что SePaC-методом полностью реконструируются неполные фракталы и подавляется фон, а разделение фракталов и фоновых событий BC-методом зависит от основания образования фракталов. Показано, что с помощью SePaC-метода более точно восстанавливается распределение фракталов по размерности DF по сравнению с BC-методом.
[en] This work tackles an inverse boundary value problem for a p-Laplace type partial differential equation parametrized by a smoothening parameter . The aim is to numerically test reconstructing a conductivity type coefficient in the equation when Dirichlet boundary values of certain solutions to the corresponding Neumann problem serve as data. The numerical studies are based on a straightforward linearization of the forward map, and they demonstrate that the accuracy of such an approach depends nontrivially on and the chosen parametrization for the unknown coefficient. The numerical considerations are complemented by proving that the forward operator, which maps a Hölder continuous conductivity coefficient to the solution of the Neumann problem, is Fréchet differentiable, excluding the degenerate case that corresponds to the classical (weighted) -Laplace equation. (paper)