It is well-recognized that in the presence of singular (and in particular nonisolated) solutions of unconstrained or constrained smooth nonlinear equations, the existence of critical solutions has a ...crucial impact on the behavior of various Newton-type methods. On the one hand, it has been demonstrated that such solutions turn out to be attractors for sequences generated by these methods, for wide domains of starting points, and with a linear convergence rate estimate. On the other hand, the pattern of convergence to such solutions is quite special, and allows for a sharp characterization which serves, in particular, as a basis for some known acceleration techniques, and for the proof of an asymptotic acceptance of the unit stepsize. The latter is an essential property for the success of these techniques when combined with a linesearch strategy for globalization of convergence. This paper aims at extensions of these results to piecewise smooth equations, with applications to corresponding reformulations of nonlinear complementarity problems.
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CEKLJ, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
It is concluded in the literature that the Ellis wormhole is unstable under small perturbations and would either decay to the Schwarzschild black hole or expand away to infinity. While this ...deterministic conclusion of instability is correct, we show that the Ellis wormhole reduces to the Schwarzschild black hole only when the Ellis solution parameter gamma assumes a complex value ?i. We shall then reexamine the stability of Ellis and phantom wormholes from the viewpoint of local and asymptotic observers by using a completely different approach, viz., we adapt Tangherlini's nondeterministic, prequantal statistical simulation about photon motion in the real optical medium to an effective medium reformulation of motions obtained via Hamilton's optical-mechanical analogy in a gravity field. A crucial component of Tangherlini's idea is the observed increase of momentum of the photons entering a real medium. We show that this fact has a heuristic parallel in the effective medium version of the Pound-Rebka experiment in gravity. Our conclusion is that there is a nonzero probability that Ellis and phantom wormholes could appear stable or unstable depending on the location of observers and on the values of gamma, leading to the possibility of ghost wormholes (like ghost stars). The Schwarzschild horizon, however, would always certainly appear to be stable (R=1, T=0) to observers regardless of their location. Phantom wormholes of bounded mass in the extreme limit aarrowright?1 are also shown to be stable just as the Schwarzschild black hole is. We shall propose a thought experiment showing that our nondeterministic results could be numerically translated into observable deterministic signatures of ghost wormholes.
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The famous hoop conjecture by Thorne has been claimed to be violated in curved spacetimes coupled to linear electrodynamics. Hod 1 has recently refuted this claim by clarifying the status and ...validity of the conjecture appropriately interpreting the gravitational mass M. However, it turns out that violations of the conjecture might seemingly occur also in the well known regular curved spacetimes of gravity coupled to nonlinear electrodynamics. Using the interpretation of M in a generic form accommodating nonlinear electrodynamic coupling, we illustrate that the conjecture is not violated even in such curved spacetimes. In the process, we introduce a Hod function summarizing the conjecture and find that it surprisingly encapsulates the transition regimes between “horizon and no horizon” across the critical values determined essentially by the concerned curved geometries.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The nonlinear optical effect of free polarization decay (FPD) in an ultrathin gas cell, the inner thickness of which is less than or on the order of the wavelength of the exciting monochromatic laser ...radiation propagating orthogonally to the plane-parallel walls of this cell, is studied theoretically. The considered coherent FPD signal is emitted immediately after abrupt termination of this comparatively weak stationary radiation. The sub-Doppler resonances appearing at the central frequencies of the studied quantum transitions in the FPD intensity and energy spectra due to the transit-time relaxation of atoms in the gas cell are detected and studied. It is shown that these resonances and the FPD dynamics strongly depend on the ratio between the inner thickness of the gas cell and the wavelength of the exciting monochromatic radiation. The narrow high–contrast sub-Doppler resonances of FPD observed and studied in a linear optical regime can be used in atomic (molecular) high-resolution spectroscopy and as references for compact frequency standards.
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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 method of sub-Doppler fluorescence spectroscopy is proposed and is based on the narrowing behavior with time of the velocity distribution of optically excited atoms (molecules) of a rarefied gas ...medium in a thin cell after exposure to a sufficiently short light pulse. Changes in the established sub-Doppler resonances with time and the essential dependence of these resonances on the gas-cell dimensions are analyzed.
For the classical quadratic penalty, it is known that the distance from the solution of the penalty subproblem to the solution of the original problem is at worst inversely proportional to the value ...of the penalty parameter under the linear independence constraint qualification, strict complementarity, and the second-order sufficient optimality conditions. Moreover, using solutions of the penalty subproblem, one can obtain certain useful Lagrange multipliers estimates whose distance to the optimal ones is also at least inversely proportional to the value of the parameter. We show that the same properties hold more generally, namely, under the (weaker) strict Mangasarian–Fromovitz constraint qualification and second-order sufficiency (and without strict complementarity). Moreover, under the linear independence constraint qualification and strong second-order sufficiency (also without strict complementarity), we demonstrate local uniqueness and Lipschitz continuity of stationary points of penalty subproblems. In addition, those results follow from the analysis of general power penalty functions, of which quadratic penalty is a special case.
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CEKLJ, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
18.
Orbit of the visual binary star 61 Cyg Izmailov, I. S.; Apetyan, A. A.
Astronomische Nachrichten,
January 2024, 2024-01-00, 20240101, Volume:
345, Issue:
1
Journal Article
Peer reviewed
We present the orbit and the mass estimates for the components of the visual binary star 61 Cyg obtained with the positional observations, including the high‐precision Gaia data, and the measurements ...of differences in the radial velocities and the radial accelerations of the components. Since the orbital period of this star significantly exceeds the period of observations, using the radial velocities and the radial accelerations allows us to reduce uncertainty in the determination of the orbital elements and the total mass of the system.
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The potential for spectroscopy in a multilayer cell with rarefied gas medium is theoretically investigated where said cell can be used as a compact analog of a large number of plane-parallel beams of ...atoms (or molecules) in an optically excited quantum level. In particular, this situation occurs for metastable and highly excited long-lived Rydberg states of atoms and molecules. Velocity selection of atoms (molecules) excited to said quantum level by broadband optical pumping was found to be efficient because of their characteristic transit and collisional relaxation in said cell. Sub-Doppler resonances at the optical transition frequencies from a given level were narrow as a result of the selection when the monochromatic probe light beam was absorbed.
The MD simulation package Amber offers an attractive platform to refine crystallographic structures of proteins: (i) state-of-the-art force fields help to regularize protein coordinates and ...reconstruct the poorly diffracting elements of the structure, such as flexible loops; (ii) MD simulations restrained by the experimental diffraction data provide an effective strategy to optimize structural models of protein crystals, including explicitly modeled interstitial solvent as well as crystal contacts. Here, we present the new crystallography module xray, released as a part of the Amber 2023 package. This module contains functions to calculate and scale structure factors (including the contributions from bulk solvent), evaluate the maximum-likelihood-type crystallographic potential, and compute its derivative forces. The X-ray functionality of Amber no longer relies on external dependencies so that the full advantage of GPU acceleration can be taken. This makes it possible to refine in a short time hundreds of crystal models, including supercell models comprised of multiple unit cells. The new automated Amber-based refinement procedure leads to an appreciable improvement in R free (in some cases, by as much as 0.067) as well as MolProbity scores.
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