Disruption of the three-body gravitational systems: Lifetime statistics

We investigate statistics of the decay process in the equal-mass three-body problem with randomized initial conditions. Contrary to earlier expectations of similarity with "radioactive decay", the lifetime distributions obtained in our numerical experiments turn out to be heavy-tailed, i.e. the tails are not exponential, but algebraic. The computed power-law index for the differential distribution is within the narrow range, approximately from -1.7 to -1.4, depending on the virial coefficient. Possible applications of our results to studies of the dynamics of triple stars known to be at the edge of disruption are considered.Comment: 13 pages, 2 tables, 3 figure

Mixed stochastic delay differential equations

We consider a stochastic delay differential equation driven by a Holder continuous process and a Wiener process. Under fairly general assumptions on its coefficients, we prove that this equation is uniquely solvable. We also give sufficient conditions for finiteness of its moments and establish a limit theorem

Annotated imports

Presented simple extensions to scala language related to import statements: exported imports, which provide ability to reuse sequence of import clauses in composable form and default rewriters, which provide mechanism for pluggable macro-based AST transformation of overall compilation unit, activated by import of library object. Using these facilities not only allows more compact code, it prevents application programmer from producing certain type of errors too and allows to implement local language extension as libraries on top of standard compiler. Part of discussed extensions is submitted to scala language committee as pre-sip \cite{ai-presip} and can be used as first step for refining imports semantics in the future version of scala language

Division intensification according to fineness and dehydration of raw materials at the new way of vibroshock grating

Наведено результати експериментальних досліджень нового методу віброударного грохочення з використанням для інтенсифікації розпушення крупних часток. Отримано залежності вологості надрешітного і та вмісту класів у продуктах від співвідношення крупних часток до мілких та питомого навантаження.Приведены результаты экспериментальных исследований нового метода виброударного грохочения с использованием для интенсификации разрыхления крупных частиц. Получены зависимости влажности надрешетного и содержания классов в продуктах от соотношения крупных частиц к мелким и удельной нагрузки.Results of pilot studies of a new method of a vibroshock screening with use for an intensification of a loosening of large particles are given. Dependences of humidity above deck and the maintenance of classes in products from a ratio of large particles to small and specific loading are received

Direct regulation of Treslin by cyclin-dependent kinase is essential for the onset of DNA replication

Treslin, a TopBP1-interacting protein, is necessary for deoxyribonucleic acid (DNA) replication in vertebrates. Association between Treslin and TopBP1 requires cyclin-dependent kinase (Cdk) activity in Xenopus laevis egg extracts. We investigated the mechanism and functional importance of Cdk for this interaction using both X. laevis egg extracts and human cells. We found that Treslin also associated with TopBP1 in a Cdk-regulated manner in human cells and that Treslin was phosphorylated within a conserved Cdk consensus target sequence (on S976 in X. laevis and S1000 in humans). Recombinant human Cdk2–cyclin E also phosphorylated this residue of Treslin in vitro very effectively. Moreover, a mutant of Treslin that cannot undergo phosphorylation on this site showed significantly diminished binding to TopBP1. Finally, human cells harboring this mutant were severely deficient in DNA replication. Collectively, these results indicate that Cdk-mediated phosphorylation of Treslin during S phase is necessary for both its effective association with TopBP1 and its ability to promote DNA replication in human cells