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An approach to the construction of efficient algorithms for the exact computation of distributions of statistics by means of the Markov chains is described. The Pearson statistic, the number of empty cells for random allocations of particles, and the Kolmogorov – Smirnov statistic are considered as examples. Possibilities of extending the approach are discussed, in particular to the computation of the joint distributions of statistics.

An analysis of the appearance of a complex dependence of the echo signal field on the observation conditions was performed. It was demonstrated that it is caused by the interference of electromagnetic fields of the local scattering area (LSA) of a complex object with the spatial coherence of the probe signal generated by the antenna with a limited aperture. Reducing of the variability of the informative features is associated with solving the problem of reducing the interference of the local scattering area, forming the signal reflected by the target. This is possible either by increasing the spatial resolution of the radar system or by averaging the received field over a particular set of parameters. It was demonstrated that the carrier parameter of quasi-monochromatic premises for spectral scanning of the probe signal is an effective parameter for the formation of stable informative features of averaging signal. It follows from the analysis that, for a sufficiently wide band in which the scanning probe is scanned and the object is in an arbitrary spatial location, the phases of the scattered signal are statistically independent and uniformly distributed. It increases robustness of characteristics of scattered signals to the variations in observation parameters due to the decrease of the sensitivity of frequency-averaged parameters to the spatial position of LSA. The criterion of sufficiency of the frequency band for approximate fulfillment of abovementioned statistical independence is provided. It has been demonstrated that the characteristics of complex radio-locative objects obtained utilizing the signal frequency-averaging satisfy the conditions of universality of the description, robustness to the spatial position of LSA, accessibility of their observation, and informativeness.

Context it is caused by the need to search for scientific and technical ways to ensure the effectiveness of protecting ground (surface) objects from high-precision guided missile weapons. Objective it is a necessity to ensure effective self-defense of objects from radar homing means. Method. Electrodynamic modeling of Echo signals from spatially distributed objects, taking into account the features of their design and related operational limitations. Results. Based on the analysis of the shortcomings of the well-known method of protecting stationary objects from radar surveillance and damage, based on the simulation of an effective reflection center outside the physical dimensions of the object, a new method of countering high-precision measurement of coordinates of stationary and mobile ground (surface) objects is proposed. The technique is based on the spatial deformation of the location of the effective target reflection center with dynamics that exceed the inertial capabilities of the auto-observation contour of the attacking missile (projectile). A structural and functional scheme of technical implementation of the methodology based on the first proposed relationship of simple design and technological solutions is proposed and justified. Conclusions. The analytical model of Echo signals of spatially distributed ground (surface) objects was further developed, which takes into account the specifics of their design, and on its basis, for the first time, a universal method of self-defense of objects from radar home-leading devices was developed, which is implemented in a patented method and complex to exclude damage to protected objects.

Let XN be a set of N elements and F1, F2,… be a sequence of random independent equiprobable mappings XN → N. For a subset S0 ⊂ XN, |S0|=m, we consider a sequence of its images St=Ft(…F2(F1(S0))…), t=1,2… An approach to the exact recurrent computation of distribution of |St| is described. Two-sided inequalities forM{|St|||S0|=m} such that the difference between the upper and lower bounds is o(m)for m, t, N → ∞, mt=o(N) are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.

Theorems on the limit distributions of the minimal and maximal distances to the nearest neighbor in a sample of random independent points having a uniform distribution on a metric space are proved. As examples of such spaces a multidimensional torus and a binary cube are considered.

Let 𝓧𝓝 be a set consisting of N elements and F 1,F 2, … be a sequence of random independent equiprobable mappings 𝓧𝓝 → 𝓧𝓝. For a subset S 0 ⊂ 𝓧𝓝, |S 0| = n, we consider a sequence of its images St = Ft (… F 2(F 1(S 0))…), t = 1, 2 … The conditions on n, t, N → ∞ under which the distributions of image sizes |St | are asymptotically connected with the standard normal distribution are presented.

A transient discrete-time Markov chain is considered that describes the evolution of the content of an urn with balls having $n$ different colors. At each step the number of balls of a randomly sel...

It is shown that, with suitable time change, the finite-dimensional distributions of the process formed by successive values of the Pearson statistics for an expanding sample converge to finite-dimensional distributions of the stationary random process, namely, the normalized square of the Bessel process. The results obtained earlier on the limit joint distributions of the Pearson statistics are used to derive explicit formulas for the density of joint distributions of the Bessel process.

We present the initial experimental results obtained using a two-part receive/transmit (Rx/Tx) radiofrequency (RF) coil design for small animals magnetic resonance imaging at 7 T. The assembly uses a butterfly-type coil tuned to 300 MHz for scanning the 1H nuclei and a non-resonant antenna with a metamaterial-inspired resonator tunable over wide frequency range for X-nuclei. 1H, 31P, 23Na and 13C are selected as test nuclei in this work. Coil simulations show the two parts of the RF-assembly to be efficiently operating at the required frequencies. Simulations and phantom imaging show sufficiently homogeneous transverse transmit RF fields and tuning capabilities for the pilot heteronuclear experiments.

This work aims to provide a way of performing parallel imaging with a single-channel variable-frequency resonant device. Different spatial sensitivity profiles required for SENSE reconstruction are achieved by switching between the device eigenmodes. A device capable of such switching is manufactured and several k-spaces are acquired using the device different eigenmodes. The k-spaces are then subject to downsampling to obtain the sensitivity profiles of each eigenmode and then - to perform SENSE-based reconstruction of the unaliased images with different acceleration factors.

Summary It is proposed to determine the direction of the “main stress” based on the study of the deformation and acoustic properties of full-size core samples with its subsequent binding to the side of the world using the paleomagnetic method. The methodology of the experiments, the equipment used for this purpose, and the results obtained are described.

Summary Within the promising areas identified in the regional forecast of the oil and gas potential of the Bazhenov formation, according to well survey data, it is proposed to identify potentially productive rocks in its section, determine their total thickness and build a map of their total thickness within the selected territory. Examples of tectonophysical modeling are considered using seismic data, on the basis of which a predictive-structural scheme for the distribution of local productive zones of various categories of prospect is maked.

Summary Two main types of the Bazhenov suite are distinguished, differing by the degree of catagenetic transformation. The first type is common in low-temperature areas and is characterized by weak thermal transformation, and the second, on the contrary, occurs in high-temperature areas exposed to tectono-hydrothermal effects, and therefore the organic matter that is part of the Bazhenov suite is here thermally transformed and metamorphosed to various degrees metamorphosed bitumen. Various ways of developing the Bazhenov suite in low-temperature and high-temperature areas are proposed.

Summary The results of hydrothermal modeling of the formation of secondary reservoirs (hydrothermal silicites) in siliceous limestones in the H2O-CO2 system are considered. Equilibrium mineral associations were established for various values of temperature and CO2 content in the composition of the hydrothermal fluid. The causes of silicification of the surface of siliceous limestone specimens have been identified. The most stable and, on the contrary, the most unstable minerals in hydrothermal conditions that are part of siliceous limestones have been established. The sizes of secondary voids of hydrothermal origin are determined. On the basis of the obtained data, it was concluded that the resulting hydrothermal silicites, due to the predominance of small voids in them, will contain large amounts of residual water.

Summary The main types of organisms involved in the accumulation of sedimentary and organic materials in the composition of the Bazhenov formation are considered. It has been proven that at present there are mainly bitumen as well as hydrocarbons and hetero compounds in the composition of the Bazhenov formation. In various lithological types of rocks, naphthids are present, having different group and hydrocarbon composition, due to the processes of their generation and migration. Nafthis of a similar composition to that obtained from the Bazhenov formation oil, are contained in siliceous and carbonate lithological types of rocks.

Обсуждаются результаты экспериментов с известным пакетом статистических критериев NIST, предназначенным для проверки гипотезы о равновероятности и независимости элементов двоичных последовательностей. В частности, рассмотрены условия на параметры чередования отрезков двух линейных рекуррентных последовательностей, при которых полученная последовательность успешно проходит все тесты пакета NIST.

Summary Based on the analysis of seismic data, the main types of anticlinal structures present in the sedimentary cover of the West Siberian oil and gas basin are established. Using the opticalpolarization and tectono-sedimentation methods, the modeling of the process of their formation was carried out. The mechanism of formation of zones of subsidence or decompression of sediments above growing elevations of various shapes is explained, the most likely areas of secondary tectonogenic fracturing in competent formations, including silicon-carbonate deposits of the Bazhen-Abalak complex, are identified

We propose and investigate new algorithms permitting to find an identical object in the database using the number of operations not depending on the volume of the database. One algorithm requires memory size that depends linearly on the database volume in the average.

Let all vertices of a complete binary tree of finite height be independently and equiprobably labeled by the elements of some finite alphabet. We consider the numbers of pairs of identical tuples of labels on chains of subsequent vertices in the tree. Exact formulae for the expectations of these numbers are obtained. Convergence to the compound Poisson distribution is proved.

Let an urn contain balls of white and black colors. After each step with probabilities equal to 1 2 ${1 \over 2}$ either the number of white balls is increased by the number of black balls or the number of black balls is increased by the number of white balls. Formulas for the first two moments of the total number of balls in an urn are derived and it is shown that the limiting distribution function of the proportion of the number of white balls in an urn coincides with the Minkowski number-theoretic function.

A retrospective of the long life and numerous accomplishments of eminent mathematician B. A. Sevast'yanov, who passed away on August 30, 2013.

We present here a brief description of the drilling operations in the deep 5G hole at the Russian Vostok Station with more detailed account of the final stage of this long-term project successfully ended on February 5, 2012 with the first Lake Vostok unsealing. Relevant information on the borehole design and the technical characteristics of the downhole and surface drilling equipment is given. The peculiarities of the drilling process are discussed in connection with changing properties of the penetrated ice. The data analysis allows defining the main factors that influence the efficiency of the electromechanical drill system at great depths. It is shown that the elevated temperature of ice and its coarse-crystalline texture are mainly responsible for the significant for the showing-down of ice coring in the bottom sections of ice sheets observed at Vostok and at other drilling sites in Antarctica and Greenland as well. Based on the large amount of experimental data obtained in the course of the deep drilling at Vostok, we discuss the processes which occur in the borehole during the ice drilling and unsealing the sub-ice water bodies. In particular, we investigate the conditions for occurrence of hydraulic fracturing in the hole and the possible effect of the hydrofrac on the height of the water column that have risen in hole 5G after the Lake Vostok unsealing. Finally we formulate the drill equipment requirements and process specifications that would ensure the best performance of an electromechanical drill and trouble-free drilling operations at different depths in a borehole up to the bottom of ice sheet.

Let the vertices of a complete q-ary tree be assigned independent random marks having uniform distribution on a finite alphabet. We consider pairs of identically marked embeddings of a given subtree template. An asymptotic formula for the expectation of the number of such pairs is obtained and the Poisson limit theorem for this number is proposed.

Methodological apparatus optimizing operational and tactical requirements to models of weapons and military equipment to determine their compliance with the requirements of a higher level on the basis of the methodology of the theory of complex systems is considered. The dynamics of the relationship of strategic and tactical requirements, due to the development of scientific and practical foundation for constructing specific models (systems) weapons and military equipment and their operation, which is reflected by feedback between tactical and strategic requirements is shown.

Numerical experiments are used to plan the development of diamond-based microwave FETs with an output power of 2.5 W per 1 mm of the gate width at a frequency of 15 GHz. A family of the I–V characteristics of the Schottky-barrier FET with gate length LG = 50 nm and width W = 1 mm is calculated. Bases on analogy with a TGF2023-20 GaN HEMT, the topology of the high-power diamond transistor (parallel cells with gate widths W = 1.2 mm and 24 elementary gates per cell) is constructed.

The main idea of the article is a solution to the problem of the self-guided missiles to the ground target at alternating sign of the target and background contrast based on the objective coordinator that implements the method of multi-spectral processing radar information.

Steel 08Kh18N10T deformation resistance under hot upsetting conditions is studied in the Gleeble-3800 research unit. The test material is two batches of cylindrical specimens 8 mm in diameter and 12 mm high, cut from a centrifugally-cast pipe billet in longitudinal and transverse directions. It is shown that with a high strain rate (10 sec–1) in the region of high strains transverse specimens have a higher strengthening factor compared with longitudinal specimens.

We present a new form and a short complete proof of explicit two-sided estimates for the distribution function $F_{n,p}(k)$ of the binomial law with parameters $n,p$ from [D. Alfers and H. Dinges, Z. Wahrsch. Verw. Geb., 65 (1984), pp. 399--420]. These inequalities are universal (valid for all values of parameters and argument) and exact (namely, the upper bound for $F_{n,p}(k)$ is the lower bound for $F_{n,p}(k+1)$). Such estimates allow to bound any quantile of the binomial law by two subsequent integers that it contains.

Explicit formulas for the distributions of gaps between successive local maxima in stationary sequences of random variables (independent or dependent ones) are given. Multidimensional asymptotic normality of frequencies of gaps of different lengths is proved. The dependence of distribution of gaps on the structure of random sequence is shown.

Leonhard Euler is one of the creators of methods of calculus. Together with rigorous mathematical (deductive) proofs, Euler extensively used empirical methods (induction) and “likely” arguments. Euler developed methods of calculus largely with the purpose of solving particular mathematical and applied problems. Euler made a large contribution to various domains of mathematics, including combinatorics. The combinatorial results of Leonhard Euler, which are somewhat aside of the main scope of his work, have made it possible to better evaluate both the versatility of his talent and his inclination to use analytical methods. The term “combinatorial mathematics” is understood differently by different authors. Since the ancient Greeks, the principal mathematical abstraction has been infinity (which appears in the infinite series of positive integers, the unbounded divisibility of a line interval, the unboundedness of space, etc.). Somewhat exaggerating, one might say that, unlike almost all other domains of mathematics, which are related, in some way, to studying properties of infinite objects (unbounded or consisting of infinitely many elements), combinatorial calculus studies problems related to properties of objects finite in all senses. In what follows, we give a brief review of Euler’s studies in the directions which are now called graph theory, the theory of Latin squares, and enumerative combinatorics. We discuss methods used by Euler and some more recent results in these directions related to Euler’s work.

We describe a device to study reactions relevant for the Single Event Effect (SEE) in microelectronics by means of 200A and 300AMeV, inverse kinematics, Si + H and Si + D reactions. The work is foc ...

Decontamination of ice cores is a critical issue in phylogenetic studies of glacial ice and subglacial lakes. At the Vostok drill site, a total of 3650 m of ice core have now been obtained from the East Antarctic ice sheet. The ice core surface is coated with a hard-to-remove film of impure drilling fluid comprising a mixture of aliphatic and aromatic hydrocarbons and foranes. In the present study we used 16S rRNA gene sequencing to analyze the bacterial content of the Vostok drilling fluid sampled from four depths in the borehole. Six phylotypes were identified in three of four samples studied. The two dominant phylotypes recovered from the deepest (3400 and 3600 m) and comparatively warm (−10°C and −6°C, respectively) borehole horizons were from within the genus Sphingomonas, a well-known degrader of polyaromatic hydrocarbons. The remaining phylotypes encountered in all samples proved to be human- or soil-associated bacteria and were presumed to be drilling fluid contaminants of rare occurrence. The results obtained indicate the persistence of bacteria in extremely cold, hydrocarbon-rich environments. They show the potential for contamination of ice and subglacial water samples during lake exploration, and the need to develop a microbiological database of drilling fluid findings.

Deep drilling into the ice sheet at Vostok station, Antarctica, was started by specialists of the Leningrad Mining Institute (since 1991, St Petersburg State Mining Institute) in 1970. Five deep holes were cored: hole No. 1 to 952 m; hole No. 2 to 450.4 m; hole No. 3G (3G-1, 3G-2) to 2201.7 m; hole No. 4G (4G-1, 4G-2) to 2546.4 m; and hole No. 5G (5G-1) to 3650.2 m depth. Drilling of hole 5G-1 is not yet complete. The deep drilling at Vostok station has had successes and problems. All the deep holes at Vostok have undergone at least one offset drilling operation because of problems with lost drills. These deviations were made successfully using a thermal drilling technique. Several drilling records have been achieved at Vostok station. The deepest dry hole, No. 1 (952 m), was made during Soviet Antarctic Expedition (SAE) 17 in 1972. The deepest fluid-filled hole, No. 5G-1, made by a thermal drill (TBZS-132), reached 2755 m during SAE 38 in 1993. The deepest fluid-filled hole in ice, No. 5G-1, was drilled with a KEMS-132 electromechanical drill and was stopped above Vostok Subglacial Lake at 3650.2 m depth during Russian Antarctic Expedition (RAE) 51 in 2006.

Let N be a set of N elements and F

A complex method for detection of genetic markers of N. gonorrhoeae resistance to penicillin was developed. Mutations in penA and ponA genes were detected by minisequencing reaction with subsequent detection of reaction products by MALDI-TOF mass spectrometry. This approach was tested on 31 clinical strains of N. gonorrhoeae with minimum inhibitory concentration of penicillin from 0.03 to 8 microg/ml and higher. Mutations in penA and ponA genes in moderately resistant strains were shown (minimum inhibitory concentration up to 0.5 microg/ml) and mutations in penA, ponA, and penB genes in resistant strains (minimum inhibitory concentration more than 1.0 microg/ml). beta-Lactamase genes were detected in 4 strains with high resistance (minimum inhibitory concentration 4-8 and more microg/ml). Correlation between microbiological resistance and presence of respective mutations in the studied locuses was detected.

Many known mechanisms of drug resistance in microorganisms have genetic markers, which are specific genomic changes, mostly single-nucleotide polymorphisms (SNPs). A search for new methods of detecting SNPs is necessary for more efficient identification of resistant strains. A new method was proposed for SNP detection on the basis of minisequencing and/or sequencing with subsequent matrix-assisted laser desorption/ionization time of flight (MALDI-TOF) mass spectrometry. The method was tested with a set of Neisseria gonorrhoeae clinical isolates in experiments on detecting the gyrA and parC SNPs that are markers of fluoroquinolone resistance. The results fully coincided with data previously obtained by gold-standard methods (sequencing and gel electrophoresis of sequencing products). Sequencing of short DNA fragments with MALDI-TOF mass spectrometry is of special interest. The new method considerably improves the efficiency of identification and genotyping of microorganisms and determination of their drug resistance markers.