F. John's stability conditions vs. A. Carasso's SECB constraint for backward parabolic problems

In order to solve backward parabolic problems F. John [{\it Comm. Pure. Appl. Math.} (1960)] introduced the two constraints "$\|u(T)\|\le M$" and $\|u(0) - g \| \le \delta$ where $u(t)$ satisfies the backward heat equation for $t\in(0,T)$ with the initial data $u(0).$ The {\it slow-evolution-from-the-continuation-boundary} (SECB) constraint has been introduced by A. Carasso in [{\it SIAM J. Numer. Anal.} (1994)] to attain continuous dependence on data for backward parabolic problems even at the continuation boundary $t=T$. The additional "SECB constraint" guarantees a significant improvement in stability up to $t=T.$ In this paper we prove that the same type of stability can be obtained by using only two constraints among the three. More precisely, we show that the a priori boundedness condition $\|u(T)\|\le M$ is redundant. This implies that the Carasso's SECB condition can be used to replace the a priori boundedness condition of F. John with an improved stability estimate. Also a new class of regularized solutions is introduced for backward parabolic problems with an SECB constraint. The new regularized solutions are optimally stable and we also provide a constructive scheme to compute. Finally numerical examples are provided.Comment: 15 pages. To appear in Inverse Problem

Multi-split intra-articular fractures of the distal humeral metaepiphysis in children

Background: The need to minimize the immobilization of the elbow joint in multifragmental fractures of the distal metaepiphysis of the humerus is confirmed by a number of factors, including the complexity of its anatomical structure, the uniqueness of biomechanics, as well as the limited ability of hyaline cartilage to regenerate. The restoration of the motor potential of the limb in multifragmentary fractures of the distal metaepiphysis of the humerus determines the priority of the treatment technique, which allows the patient to return to his usual lifestyle in the near future.Objective: Demonstration of the effectiveness of percutaneous spinal osteosynthesis with wires in fractures of distal metaepiphysis of the humerus in adolescent children.Clinical cases: This paper describes two clinical cases in adolescent children with multifragmentary fractures (open and closed) of the distal part of humerus (12В and 13С according to the AO classification). In both cases, the treatment consisted of sequential application of skeletal traction, for fragments traction and their mobility increase, then closed reposition of fragments under the control of electron-optical converter with metal osteosynthesis with wires. Moreover, taking into consideration the U- and T-shape nature of the fractures, the first stage of reposition included stabilization and fixation of the distal fragments to each other and then to the proximal fragment.Conclusion: In our opinion, it is the combination of traditional methods of treatment (application of skeletal traction system), modern technologies (EOC control), alternative (atypical) options for using metal structures that allow achieving good functional treatment results in this category of patients

New limit on the mass of 9.4-keV solar axions emitted in an M1 transition in 83^{83}Kr nuclei

A search for resonant absorption of the solar axion by $^{83}\rm{Kr}$ nuclei was performed using the proportional counter installed inside the low-background setup at the Baksan Neutrino Observatory. The obtained model independent upper limit on the combination of isoscalar and isovector axion-nucleon couplings $|g_3-g_0|\leq 1.69\times 10^{-6}$ allowed us to set the new upper limit on the hadronic axion mass of $m_{A}\leq 130$ eV (95\% C.L.) with the generally accepted values $S$=0.5 and $z$=0.56.Comment: 5 pages, 2 figures, Proceedings of the 10th Patras Workshop on Axions, WIMPs and WISP 29 June - 4 July 2014, CERN, Geneva, Switzerlan