On the sequence n! mod pn! \bmod p

We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(\sqrt{2} + o(1))\sqrt{p}$ distinct residues modulo prime $p$. Moreover, factorials on an interval $\mathcal{I} \subseteq \{0, 1, \dots, p - 1\}$ of length $N > p^{7/8 + \varepsilon}$ produce at least $(1 - o(1))\sqrt{p}$ distinct residues modulo $p$. As a consequence, we obtain a polynomial improvement in the problem of representing a given residue class as a product of seven small factorials.Comment: 9 page

Spin-fluctuation theory beyond Gaussian approximation

A characteristic feature of the Gaussian approximation in the functional-integral approach to the spin-fluctuation theory is the jump phase transition to the paramagnetic state. We eliminate the jump and obtain a continuous second-order phase transition by taking into account high-order terms in the expansion of the free energy in powers of the fluctuating exchange field. The third-order term of the free energy renormalizes the mean field, and fourth-order term, responsible for the interaction of the fluctuations, renormalizes the spin susceptibility. The extended theory is applied to the calculation of magnetic properties of Fe-Ni Invar.Comment: 20 pages, 4 figure

Assessment of the genetic distances between some species of the family Bradybaenidae (Mollusca, Pulmonata)

On the basis of inter-simple sequence repeat (ISSR) loci and the nucleotide sequences of nuclear (18S and ITS-1) and mitochondrial genes (COI and 16S), a phylogenetic analysis of the three species of terrestrial mollusks of the family Bradybaenidae (Mollusca, Pulmonata), Bradybaena fruticum Mull., Bradybaena schrencki Midd., and Bradybaena transbaicalia Shileyko, was conducted to clarify their taxonomic statu

Концепция повышения энергоэффективности автономных локомотивов

The growing attention to the issues of increasing energy efficiency of railway transport results in suggesting various designs of traction rolling stock with the most advanced technical solutions, but, unfortunately, many of them remain only at the development or prototype stage.The analysis of operating experience of existing mainline locomotives is proposed to help to develop fundamental principles of the concept of improving the energy efficiency of autonomous locomotives, aimed at creating a modular locomotive structure that makes it possible to coordinate operational loads with the operating modes of traction equipment to provide the best conditions for converting and transferring energy to wheel sets. Modern on-board systems of locomotives record many parameters that can be used both to determine the energy efficiency of the locomotive, as well as to evaluate new technical solutions aimed at the use of discrete-adaptive control of the modular design of diesel generator sets and traction motors under the operating conditions of mainline locomotives.Implementation of the proposed concept could make it possible to save up to 20 % of diesel fuel during transportation work, which was confirmed during testing a prototype locomotive.Вопросам повышения энергоэффективности железнодорожного транспорта уделяется много внимания, предлагаются различные конструкции тягового подвижного состава с самыми передовыми техническими решениями, но, к сожалению, многие из них так и остаются лишь на стадии разработки или опытного образца.Приведён анализ опыта эксплуатации существующих магистральных локомотивов с целью разработки основополагающих принципов концепции повышения энергоэффективности автономных локомотивов, направленных на создание модульной структуры локомотива, позволяющих согласовывать эксплуатационные нагрузки с режимами работы тягового оборудования, что даёт возможность обеспечить наилучшие условия преобразования и передачи энергии на колёсные пары. Современные бортовые системы локомотивов регистрируют большое количество параметров, которые можно использовать как для определения энергоэффективности работы локомотива, так и для оценки новых технических решений, направленных на применение дискретноадаптивного управления работой модульного исполнения дизель-генераторных установок итяговых электродвигателей в условиях эксплуатации магистральных локомотивов.Реализация предлагаемой концепции позволяет сэкономить до 20 % дизельного топлива при выполнении перевозочной работы, что подтверждено на опытном образце локомотива

New fast algorithm for solution of electrical tomography problem

Electrical Impedance Tomography (EIT) is the most developed approach in electrical tomography that includes the resistance (ERT) and capacitance (ECT) tomography is produced by active electrodes, located outside of investigated domain Ω . It initiates some distribution of the electric potential inside the domain Ω . The measurements of necessary values would be realized on the boundary curve Γ with another, no active electrodes. The physical concept of approach is based on General Ray Principl

Modeling of the HIV-1 Life Cycle in Productively Infected Cells to Predict Novel Therapeutic Targets

There are many studies that model the within-host population dynamics of Human Immunodeficiency Virus Type 1 (HIV-1) infection. However, the within-infected-cell replication of HIV-1 remains to be not comprehensively addressed. There exist rather few quantitative models describing the regulation of the HIV-1 life cycle at the intracellular level. In treatment of HIV-1 infection, there remain issues related to side-effects and drug-resistance that require further search “...for new and better drugs, ideally targeting multiple independent steps in the HIV-1 replication cycle” (as highlighted recently by Tedbury & Freed, The Future of HIV-1 Therapeutics, 2015). High-resolution mathematical models of HIV-1 growth in infected cells provide an additional analytical tool in identifying novel drug targets. We formulate a high-dimensional model describing the biochemical reactions underlying the replication of HIV-1 in target cells. The model considers a nonlinear regulation of the transcription of HIV-1 mediated by Tat and the Rev-dependent transport of fully spliced and singly spliced transcripts from the nucleus to the cytoplasm. The model is calibrated using available information on the kinetics of various stages of HIV-1 replication. The sensitivity analysis of the model is performed to rank the biochemical processes of HIV-1 replication with respect to their impact on the net production of virions by one actively infected cell. The ranking of the sensitivity factors provides a quantitative basis for identifying novel targets for antiviral therapy. Our analysis suggests that HIV-1 assembly depending on Gag and Tat-Rev regulation of transcription and mRNA distribution present two most critical stages in HIV-1 replication that can be targeted to effectively control virus production. These processes are not covered by current antiretroviral treatments

Modeling of a single-cycle current generator while forming a quasi-sinusoidal current

The paper presents the results of investigation of the influence of the output voltage magnitude on the operating frequency of the switch in the single-cycle quasi-sinusoidal current generator circuit. Analytical expressions for calculating the time parameters for transients in the circuit under given assumptions have been obtained. The results presented in the paper can be used in the design of converters of this type

Condition of hard tissues of teeth and oral fluid in athletes-swimmers

Objective: to determine the state of dental hard tissues and saliva parameters changing in competitive swimmers, before and after a 2­hour training session in the chlorinated water swimming pool.Materials and methods: saliva parameters of competitive swimmers trained in the sport club “Grifon”, city of St. Petersburg, Russia (n = 21), age of participants 18.1 ± 3.5 years, qualifications (1 category­Master of Sports) and track and field athletes of the sports schools “Nevsky district” and “Orlyonok”, city of St. Petersburg, Russia (n = 18), age of participants 18.80 ± 4.54 years, qualifications (1 category — Master of Sports), have been analyzed by various tests include a study of calcium (Ca), phosphorus (P), fluorine (F) levels, and pH before and after training sessions. All athletes in the experimental and control groups have passed an examination by dentist, including: examination of the oral cavity with the determination of the KPU index (the sum of carious, filled and removed permanent teeth in the subject), examination of the most common places of occurrence of dental enamel erosion (medical binoculars) and filling out specially designed questionnaires.Results: there was a tendency to decrease of the average saliva pH in competitive swimmers’ group after a training session, varying from 6.9 ± 0.1 (before training) to 6.5 ± 0.1 (after training) (p > 0.05). In track and field athletes, saliva pH did not change significantly (7.1 ± 0.2 before training and 7.0 ± 0.1 after training) (p < 0.05). The competitive swimmers showed a statistically significant increase in Calcium (Ca) levels (1.25 ± 0.15 mmol/L before exercise and 1.56 ± 0.11 mmol/L after exercise) and Fluorine (F) (0.0010 ± 0.0003 mmol / L before exercise and 0.0090 ± 0.0004 mmol / L after training session) in saliva. The Phosphorus (P) level in saliva was significantly reduced after the training session (from 6.09 ± 0.39 to 3.89 ± 0.46 mmol / L) (p > 0.05). In track and field athletes, there were no significant changes in Ca, F and P levels before and after a training session. As a result of the dentist’s examination, competitive swimmers were found to have 3 athletes (14.3 %) with lesions of the teeth enamel, corresponding to dental erosion and caused by localized demineralization. In the control group of athletes, no such pathologies were revealed.Conclusion: discovered saliva parameters changing in competitive swimmers (decrease in free salivation, pH level, and increase in the level of Ca and F in saliva) can contribute to the demineralization of tooth enamel. Timely and controlled use of fluorides (as part of mouth rinses, application gels, fluoride varnishes), regular preventive dental examinations, in order to prevent the loss of mineral composition of the teeth when swimming in chlorinated pools, will minimize the risk of staining and dental enamel erosions

Dental status of persons engaged in sports swimming

To date, information on the problem is contradictory and ambiguous. It is difficult to trace cause – effect relationships between the condition of hard dental tissues, oral fluid, the dental status of swimmers, and the characteristics of the water environment of training pools. The article presents an analysis and systematization of literature on the dental condition in swimming athletes, as well as formulates modern ideas on the subject and highlights topics for further research

Prof. I.I. Pototsky – 120th birth anniversary

It is reported on the creative path of Professor Ivan Ivanovich Pototsky, who for a long time (from 1939 to 1974) headed the departments of dermatology of the Khabarovsk, Kuban, Kiev GIDUV and Kiev medical institutes and created a scientifi c school of dermatovenerologists (48 Ph.D. and doctoral dissertations), which prepared for Rostov Medical University 2 Heads of the department