Primal-dual accelerated gradient methods with small-dimensional relaxation oracle

In this paper, a new variant of accelerated gradient descent is proposed. The pro-posed method does not require any information about the objective function, usesexact line search for the practical accelerations of convergence, converges accordingto the well-known lower bounds for both convex and non-convex objective functions,possesses primal-dual properties and can be applied in the non-euclidian set-up. Asfar as we know this is the rst such method possessing all of the above properties atthe same time. We also present a universal version of the method which is applicableto non-smooth problems. We demonstrate how in practice one can efficiently use thecombination of line-search and primal-duality by considering a convex optimizationproblem with a simple structure (for example, linearly constrained)

3,5-Bis(4-chloro­benzyl­idene)-1-methyl­piperidin-4-one

In the title mol­ecule, C20H17Cl2NO, the central heterocyclic ring adopts a flattened boat conformation. The dihedral angles between the planar part of this central heterocyclic ring [maximum deviation = 0.004 (1) Å] and the two almost planar side-chain fragments [maximum deviations = 0.015 (1) and 0.019 (1) Å], that include the aromatic ring and bridging atoms, are 18.1 (1) and 18.0 (1)°. In the crystal, pairs of weak inter­molecular C—H⋯O hydrogen bonds link mol­ecules into inversion dimers that form stacks along the a axis. The structure is further stabilized by weak inter­molecular C—H⋯π inter­actions involving the benzene rings

1-Benzyl-3,5-bis­(4-chloro­benzyl­idene)piperidin-4-one

The title compound, C26H21Cl2NO, crystallizes with two symmetry-independent mol­ecules (A and B) in the asymmetric unit. In both mol­ecules, the central heterocyclic ring adopts a sofa conformation. The dihedral angles between the planar part of this central heterocyclic ring [maximum deviations of 0.011 (1) and 0.036 (1) Å in mol­ecules A and B, respectively] and the two almost planar [maximum deviations of 0.020 (1) and 0.008 (1) Å in A and 0.007 (1) and 0.011 (1) in B] side-chain fragments that include the aromatic ring and bridging atoms are 20.1 (1) and 31.2 (1)° in mol­ecule A, and 26.4 (1) and 19.6 (1)° in mol­ecule B. The dihedral angles between the planar part of the heterocyclic ring and the benzyl substituent are 79.7 (1) and 53.2 (1)° in mol­ecules A and B, respectively. In the crystal, weak inter­molecular C—H⋯O hydrogen bonds link the two independent mol­ecules into dimers

Short-distance regularity of Green's function and UV divergences in entanglement entropy

Reformulating our recent result (arXiv:1007.1246 [hep-th]) in coordinate space we point out that no matter how regular is short-distance behavior of Green's function the entanglement entropy in the corresponding quantum field theory is always UV divergent. In particular, we discuss a recent example by Padmanabhan (arXiv:1007.5066 [gr-qc]) of a regular Green's function and show that provided this function arises in a field theory the entanglement entropy in this theory is UV divergent and calculate the leading divergent term.Comment: LaTeX, 6 page

Investigative study of the radiation damage on fuel clad of miniature neutron source reactor using computational tools

Core conversion requires some evaluation of the reactor safety. Changes to the reactivity worth, shutdown margin, power density and material properties are crucial to the proper functioning of the reactor. The focus of this article is to study the neutron flux distribution in the reactor core and radiation damage on candidate clads. The Ghana Research Reactor-1 (GHARR-1) operates at maximum power of 30 kW in order to attain a flux of 1.0? 1012 n·cm–2·s for the high enriched uranium core. Using the GHARR-1 core geometry, considering 348 fuel pins, the multiplication factor (Keff) is calculated at enrichments of 10%, 12.5%, 16%, 20%, 30% and 90.2%. The spectrum of neutron flux generated in the 26 group is also calculated at the specified enrichments. The ion/particle interactions with the targets (clad) were studied in the Stopping and Range of Ion in Matter code to establish the best clad material based on recorded defects and vacancies generated. From the calculations and simulations, the best choice from the candidate clads based on the assessment is SiC. The calculation of the fuel campaign length gives 7.5 years. The defects sustained by the prospective clad showed low susceptibility to swelling and other forms of deformation

Criteria of ecological plasticity, stability, and adaptability of potato varieties based on yield

The influence of the physiological and biochemical parameters of the leaves of 12 potato varieties on the formation, plasticity, and stability of the potato crop has been studied. The experiments were carried out on the territory of the Samara Research Institute of Agriculture – branch of the SamSRC RAS (53°03’ N, 49°25’ E) in the period 2019-2022. Average potato yields varied in the range of 14.2-25.7 t/ha. The highest yield was the first planting year. With an increase in the duration of reproduction, yield losses ranged from 25 to 50% due to a decrease in the mass of tubers. The coefficient of variation in yield varied in the range of 24-60% depending on the genotype. Criteria of ecological plasticity and stability of potato of different genetic origin are such indicators as leaf dryness or its hydration, the content of phenolic compounds in the leaves, the content of lipid oxidation products, and the state of the membranes. The amplitudes of variation of leaf indicators can serve as a measure of plasticity. Adaptive capacity is related to the content of proline, the ratio of membrane lipids and proteins, and the number of stomata

Resonance effects due to the excitation of surface Josephson plasma waves in layered superconductors

We analytically examine the excitation of surface Josephson plasma waves (SJPWs) in periodically-modulated layered superconductors. We show that the absorption of the incident electromagnetic wave can be substantially increased, for certain incident angles, due to the resonance excitation of SJPWs. The absorption increase is accompanied by the decrease of the specular reflection. Moreover, we find the physical conditions guaranteeing the total absorption (and total suppression of the specular reflection). These conditions can be realized for Bi2212 superconductor films.Comment: 17 pages, 3 figure