We consider a nonlinear Volterra integral equation with local and/or integral loads on the desired solution given by the Stieltjes integral. The equation contains a bifurcation parameter and has the ...trivial solution for any of the parameter values. Necessary and sufficient conditions are obtained for those values of the parameter (bifurcation points) in the vicinity of which the equation has nontrivial continuous real solutions. The leading terms of the asymptotics of the solution branches are constructed, and a method for their refinement is indicated. Illustrative examples are given. A linearization principle is established that permits one to find bifurcation points using only information about the linear part of the nonlinear equation with a vector load and a vector bifurcation parameter.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Abstract
In this paper, the nonlinear shallow water wave equation is illustrated. The famous semi-analytical method, homotopy analysis method (HAM) is applied for solving this equation. The main ...novelty, of this study is to validate the numerical results using the stochastic arithmetic, the CESTAC method and the CADNA library. Based on this method, we can find the optimal iteration of the HAM, optimal approximation of the shallow water wave equation and optimal error. The main theorem of the CESTAC method is proved. Based on this theorem, we can show that the number of common significant digits for two successive approximations are almost equal to the number of common significant digits for exact and approximate solutions. Thus instead of traditional absolute error to show the accuracy of method we can apply the new termination criterion depends on two successive approximations. In order to find the convergence region of the HAM, several ħ-curves are demonstrated.
We study the time-domain system of equations of a traveling wave tube (TWT) with delayed feedback. Under conditions of low-depth feedback, we find the self-mode-locking operation regimes ...characterized by the generation of correlated sequences of ultrashort pulses. The existence of these regimes is verified within 3-D simulations of an experimentally implemented <inline-formula> <tex-math notation="LaTeX">{W} </tex-math></inline-formula>-band TWT using the particle-in-cell method. With increasing beam current, the regimes of generation of pulse sequences with duration of about 380, 180, 130, and 80 ps, duty factor of about 25%, and peak efficiency of about 14% are obtained.
Filamentation of ultrashort laser pulses in the atmosphere offers unique opportunities for long-range transmission of high-power laser radiation and standoff detection. With the critical power of ...self-focusing scaling as the laser wavelength squared, the quest for longer-wavelength drivers, which would radically increase the peak power and, hence, the laser energy in a single filament, has been ongoing over two decades, during which time the available laser sources limited filamentation experiments in the atmosphere to the near-infrared and visible ranges. Here, we demonstrate filamentation of ultrashort mid-infrared pulses in the atmosphere for the first time. We show that, with the spectrum of a femtosecond laser driver centered at 3.9 μm, right at the edge of the atmospheric transmission window, radiation energies above 20 mJ and peak powers in excess of 200 GW can be transmitted through the atmosphere in a single filament. Our studies reveal unique properties of mid-infrared filaments, where the generation of powerful mid-infrared supercontinuum is accompanied by unusual scenarios of optical harmonic generation, giving rise to remarkably broad radiation spectra, stretching from the visible to the mid-infrared.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
Numerical simulation is applied to study the features of a low-frequency (55 and 137 Hz) acoustic field and its recording by linear horizontal and vertical arrays in a shallow-water waveguide with a ...depth of ≈30 m and an inhomogeneous bottom. The area where the sound speed in the bottom is close that in water is considered. For calculations, we used the spatial distribution of the sound speed in the Kara Sea bottom sediments, obtained during engineering seismic survey, as well as test drilling data. It is shown that an inhomogeneous bottom not only affects the depth-averaged loss during sound propagation, which can be detected by a vertical array, but also leads to horizontal refraction of acoustic waves, which manifests itself during beamforming at an extended horizontal array. The maximum effects are observed for a low frequency (55 Hz): the decrease in transmission losses reaches 5 dB, and the bias in the maximum response of the array is 3.4°.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The chemical reactions and mechanism of the pyrolytic decomposition of the isolated methylsilane molecule in the gas phase were theoretically studied. The thermodynamic parameters of the chemical ...reactions of decomposition of methylsilane (the changes in the energy, enthalpy, Gibbs energy, and entropy) were calculated by a nonempirical method using the second-order Móller–Plesset perturbation theory and the basis set of atomic orbitals 6-31G including additional polarization functions. It was determined that the chemical reactions that occur by the 1,2-elimination mechanism are preferred.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Abstract
Integral equations play the important role in applied mathematics, related to many areas of theory, especially applications. In this article, we consider the numerical method for solving ...Volterra integral equations for the fractional order of integration. The error of this method is
O(1/N)
.
We obtain sufficient conditions for the existence of a principal solution of a nonlinear Volterra integral equation of the second kind on the half-line and on a finite interval. We suggest a method ...for computing the boundary of an interval outside which the solution can blow up.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Aim
To compare hemorrhagic safety of ticagrelor and clopidogrel in patients with ST-segment elevation acute coronary syndrome (STEACS) after thrombolytic therapy (TLT).
Material and methods
...This nonrandomized study included 183 patients followed up for 30 days. Hemorrhagic safety was compared in a group of patients with STEACS (n=71) after a thrombolytic treatment with alteplase and early ticagrelor treatment (180 mg followed by switching to 90 mg twice daily) and in a group of patients (n=112) with STEACS receiving TLT with alteplase and clopidogrel (loading dose, 600 mg followed by switching to 75 mg daily). Primary endpoint was hemorrhage associated with TLT; patients were followed up for 30 days.
Results
During the follow-up period, TLT-associated hemorrhages were observed in 11.3% of patients in the ticagrelor treatment group and in 10.7% of patients in the clopidogrel treatment group (p=0.9; odds ratio, 1.06 at 95 % confidence interval, from 0.41 to 2.73). Intracranial hemorrhages and fatal hemorrhages were absent in both groups.
Conclusion
There were no significant differences in hemorrhagic safety between patients with STEACS after the TLT treatment with alteplase and early treatment with ticagrelor or clopidogrel.
—A broadband (35–1000 Hz) sound field formed by a point source in a shelf zone with inhomogeneous bottom sediment structure is studied using numerical modeling. The shelf depth is about 30 m and the ...maximum distance is 10 km. The transitional zone from the bottom with a sound speed of 1400 m/s to the bottom with a speed of 1600 m/s is chosen as the model inhomogeneity. The normal mode theory and wide-angle parabolic equations are used for sound field calculations. Numerical experiments show that the manifestation of horizontal refraction is noticeable at low frequencies (below 100 Hz). It leads to an increase in the amplitude of the low-frequency sound pulse propagating along the transitional zone by more than 10 dB in comparison with a similar waveguide with a homogeneous bottom. At frequencies above 100 Hz, the dominant effect is the mode coupling, causing the appearance of quasi-periodic oscillations of modal amplitude in the frequency domain. The conclusions from the simplified model are confirmed by calculations for the real structure of bottom sediments in the Kara Sea.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
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