One-dimensional Sections Research Articles

Distorted copulas

In this paper, we deal with the problem of preserving the copula property by means of a transformation called distortion where automorphisms of the real unit interval are involved. A new methodological approach is followed by resorting to a special branch of group theory. The crucial role of absolute continuity of one-dimensional sections of a distorted copula is illustrated. Some necessary and sufficient conditions concerning the automorphisms which preserve the copula property for a large class of bivariate copulas are proved. Several examples are presented.

Analysis of versions of topology of MIMO radars antenna systems with two-dimensional and one-dimensional arrangement of antenna elements

For a MIMO radar with a digital view in azimuth and range, it is of fundamental interest to compare the topology options for the two-dimensional and one-dimensional arrangement of the elements of the antenna system (AS). In this case, the case is theoretically important when the one-dimensional version of the topology of the AS elements is a projection of the two-dimensional version onto the coordinate axis perpendicular to the bisector of the sector of azimuthal coordinates. The aims of investigation are the comparison of the potential resolution of a MIMO radar in range and azimuth for two variants of the topology of the AS elements based on the calculation of the sections of the generalized uncertainty function (GUF) at specific target ranges and azimuths in the case of monopulse multi-frequency radiation of probing signals by the transmitting elements of the AS. For short-range MIMO radars, using theoretical expressions for the GUF in the case of a fixed point target, two-dimensional and one-dimensional sections of the GUF in the “range–azimuth” plane are determined, which are compared for the variants of the two-dimensional and the corresponding one-dimensional arrangement of the transmitting and receiving elements of the MIMO AS. The proposed mathematical technique allows you to quickly identify the degree of equivalence of complex configurations of two-dimensional AS to their one-dimensional counterparts in order to use them in the development and creation of MIMO radars.

Coherent information accumulation from virtual MIMO radars with multiple increase of interelement distances in the real MIMO radar

To reduce the number of air carriers when using MIMO radars, it is advisable to reduce the number of transmitting and receiving elements (TLE and RTE) of real MIMO radars, as well as the use of virtual MIMO radars. The reduction in the number of TLE and RTE can be achieved by increasing the distances between them to values significantly exceeding the average radiation wavelength. In this case, it is necessary to theoretically estimate the spatial resolution and accuracy of the measured coordinates in the selected system of virtual MIMO radars corresponding to real MIMO radars with spatially highly rarefied TLE and RTE. For short-range MIMO radars, using theoretical expressions for the generalized uncertainty function (GUF) in the case of a fixed point target, two-dimensional and one-dimensional sections of GUF in the “range–azimuth” plane are determined, which are compared for variants of moderate and highly rarefied two-dimensional arrangements of TLE and RTE of real and virtual MIMO antennas. The proposed mathematical technique allows you to quickly evaluate the resolution in range and azimuth in the development and creation of real and virtual MIMO radars with increased inter-element distances.

Investigation of the stability of one difference equation with complex coefficients

We study the stability of a linear autonomous difference equation with two (generally speaking, complex) coefficients. The starting point of the study is the Schur-Kohn theorem on the location of the roots of the characteristic equation with respect to the unit disk in the complex plane. To construct the domain of exponential stability in the parameter space, we use the D decompodition method, which consists in constructing curves (or surfaces) such that the number of roots of the characteristic equation outside the unit disk changes when passing through the curves; then the area is determined, which corresponds to the zero number of such roots; this is the area of stability. We implement this scheme for the above difference equation: geometric stability criteria are found and the domains of exponential stability in a four-dimensional space of coefficients are described, as well as their three-dimensional, two-dimensional and one-dimensional sections. The Lyapunov stability is studied separately, which is corresponded by the domain of exponential stability supplemented by a part of its boundary. To describe Lyapunov stability exactly we use a "multiplicity curve", which is a line such that all its points correspond to multiple roots of the characteristic equation. In addition, we find and construct a domain of absolute stability with respect to one of the parameters of the initial equation. For this domain, we formulate criteria of exponential stability and Lyapunov stability.The results obtained can be applied to the study of processes in physics, technology, economics, biology, which are modeled using discrete models in the form of difference equations.

Investigation on the fractal characteristic of asphalt pavement texture roughness incorporating 3D reconstruction technology

<abstract> <p>The textural roughness of asphalt pavement surface is an important indicator to characterize pavement skid resistance. In this paper, multi-visual technology was applied to capture the surface image of asphalt pavement which was transformed into a visualized 3D point cloud model. Then, based on the principle of the digital elevation model (DEM), the disordered 3D point cloud is rasterized and projected into a 2D matrix which contains generalized point cloud elevation information. Meanwhile, the 2D matrix is transformed into grayscale to build the equivalent grayscale image. Furthermore, the fractal dimensions were calculated in terms of one-dimensional pavement section profile, two-dimensional grayscale, and equivalent grayscale to characterize the pavement roughness. The results showed that the fractal dimensions are positively correlated with the mean texture depth (MTD), and the fractal dimension of equivalent grayscale has the best correlation with MTD. It should be highlighted that the equivalent grayscale image is directly transformed by the reconstruction of the three-dimensional point cloud, and the grayscale value of each point can represent the elevation of different pavement surfaces. Therefore, the equivalent grayscale image can better reflect the real roughness of the pavement surface. Meanwhile, the proposed method in this paper can effectively reduce the influence of some factors (e.g., light and color, etc..) on the texture detection of the pavement surface.</p> </abstract>

Altai earthquake (2003) fault zone velocity structure - case study

This paper presents the results of seismic surveys in the epicentral zone of the Alaty earthquake (2003), conducted in the summer of 2021. The object of research was a fractured zone, which on the surface manifests itself as a rupture of the earth's surface with a width of 3-5, a depth of up to 1 and a length of about 200 meters. The main objective of the 2021 research was to study changes in the structure of the velocity section in the rupture zone, presumably associated with the degradation of the permafrost. As a result of processing records of refracted waves, a seismotomographic model for P-waves was obtained, and a seismic boundary was identified by the GRM method. As a result of processing surface wave recordings by MASW, one-dimensional S-wave sections were obtained for the left and right parts of the section. Interpretation of the results showed the presence of a huge unfrozen zone with a thickness of about 30 meters, which indicates an active process of degradation of the permafrost in this area.

Sequence stratigraphic interpretation in marginal marine settings by the approach of parasequence-thickness-to-sandstone-fraction ratio: Case studies of the Gallup and Ferron outcrops in the Western Interior Basin, U.S.A.

ABSTRACTThe parasequence-thickness-to-sandstone-fraction ratio (TSF) is a simple but potentially powerful tool to identify stratal stacking patterns and associated systems tracts in siliciclastic paralic sequences. Parasequence thickness (T) reflects accommodation, and the sandstone fraction (SF) may serve as a proxy for the rate of sediment supply. Although previous research shows the effectiveness of applying TSF techniques to sequence stratigraphic analyses in siliciclastic depositional environments, constraints and analytical procedures of the technique are still not clearly illustrated. The paleogeography and sequence stratigraphy of the Cretaceous Gallup system and Ferron Notom deltaic complex in the Western Interior Basin have been extensively studied, providing an opportunity to explore the applicability and detailed workflow of the TSF method. TSF analyses are conducted first on two representative measured sections from the Gallup and the Ferron outcrops, respectively. The TSF analyses of the two one-dimensional (1D) sections are capable of identifying transgressive–regressive (T-R) cycles of the two deltas. However, the 1D sections can reflect the accommodation and sediment supply change only at single locations, which limits their usefulness in identification of stratigraphically consecutive parasequences and composite bounding surfaces. The utility of TSF analyses on cross sections is then tested on a depositional-dip transect of the Gallup delta, as well as dip-oblique and strike-oblique cross sections of the Ferron Notom delta. Parameters of T and SF are acquired from measured sections as well as interpolated virtual sections. For both the Gallup system and the Ferron Notom deltaic complex, the cross-sectional TSF analyses are more effective in recognizing systems tracts and associated bounding surfaces than the TSF analyses in 1D sections. Because dip-oriented cross sections usually encompass both proximal and distal parts of parasequences, and preserve stratigraphically continuous successions, they can provide more complete information for TSF interpretations than strike-oriented cross sections. Above all, TSF analysis via both measured and virtual sections along a depositional-dip profile is inclined to result in sequence stratigraphic categories that best match those based on the full set of geological observations.TSF analyses can also be used to identify general direction of shoreline trajectories in both the Gallup and Ferron Notom deltas. Parameterization of T, SF, and maximum progradation distance for both the Gallup and Ferron Notom parasequences are used to indicate shelf gradients throughout their deposition. The prominent differences of the shelf gradients between different deltaic parasequences indicate differences in allogenic and autogenic controls on the development of T-R sequences in these two deltas.

Азимутальная анизотропия Саяно-Байкальской складчатой области по приемным функциям далеких землетрясений

The purpose of the work is the determination of a detailed velocity structure of the earth's interior of the seismically active Sayan-Baikal fold region, including the identification of the azimuths and depths in the vicinity of the observation points with anisotropic properties. The source data for the study is the long-term observations by five broadband seismic stations in the Sayano-Baikal fold region. The proposed methodology for identifying the depths and directions of the earth's interior with anisotropic properties is based on the longitudinal receiving function method. The receiving functions for all possible directions of each observation point have been selected from the tele-seismic records. The azimuthal boundaries are identified in relation to the observing station where the receiving functions change significantly, which means a change in the velocity structure when crossing these conditional boundaries. Within the azimuth ranges (BAZ) with homogeneous receiving functions, velocity models (V S ) have been calculated by inverting the functions. The models take into account the relationship between the depth of medium sounding (h) and the corresponding distance from the seismic station (d). Based on the one-dimensional velocity sections for different azimuths, circular models V S (h,BAZ,d) have been constructed with the account of the seismic drift. The models visualize the velocity structure in relation to all observation points at the depths up to 70 km and 270 km. As a result of the study, a set of models reflecting the detailed deep-seated velocity structure of the Sayano-Baikal folded region has been obtained. The velocities of the seismic waves V S ( h ) have been determined within the earth's crust with an average depth step of 1 km, and within the mantle, with a step of 5-10 km. The circular models V S (h,BAZ,d) clearly demonstrate the velocity heterogeneity in various directions from the observation point and allow one to identify the anisotropy of the medium. The latter is manifested as the presence of a symmetry axis in the circular models, which on average has a northwest-southeast orientation, but varies with the depth.

Log-gases on quadratic lattices via discrete loop equations and q-boxed plane partitions

We study a general class of log-gas ensembles on (shifted) quadratic lattices. We prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are Gaussian with a universal covariance. We apply our general results to analyze the asymptotic behavior of a q-boxed plane partition model introduced by Borodin, Gorin and Rains. In particular, we show that the global fluctuations of the height function on a fixed slice are described by a one-dimensional section of a pullback of the two-dimensional Gaussian free field.Our approach is based on a q-analogue of the Schwinger–Dyson (or loop) equations, which originate in the work of Nekrasov and his collaborators, and extends the methods developed by Borodin, Gorin and Guionnet to quadratic lattices.

Development of a New Simulation Tool Coupling a 2D Finite Volume Overland Flow Model and a Drainage Network Model

Numerical simulation of mixed flows combining free surface and pressurized flows is a practical tool to prevent possible flood situations in urban environments. When dealing with intense storm events, the limited capacity of the drainage network conduits can cause undesirable flooding situations. Computational simulation of the involved processes can lead to better management of the drainage network of urban areas. In particular, it is interesting to simultaneuously calculate the possible pressurization of the pipe network and the surface water dynamics in case of overflow. In this work, the coupling of two models is presented. The surface flow model is based on two-dimensional shallow water equations with which it is possible to solve the overland water dynamics as well as the transformation of rainfall into runoff through different submodels of infiltration. The underground drainage system assumes mostly free surface flow that can be pressurized in specific situations. The pipe network is modeled by means of one-dimensional sections coupled with the surface model in specific regions of the domain, such as drains or sewers. The numerical techniques considered for the resolution of both mathematical models are based on finite volume schemes with a first-order upwind discretization. The coupling of the models is verified using laboratory experimental data. Furthermore, the potential usefulness of the approach is demonstrated using real flooding data in a urban environment.

Homogenization Method in the Problem of Long Wave Propagation from a Localized Source in a Basin over an Uneven Bottom

In the framework of the linearized shallow water equations, the homogenization method for wave type equations with rapidly oscillating coefficients that generally cannot be represented as periodic functions of the fast variables is applied to the Cauchy problem for the wave equation describing the evolution of the free surface elevation for long waves propagating in a basin over an uneven bottom. Under certain conditions on the function describing the basin depth, we prove that the solution of the homogenized equation asymptotically approximates the solution of the original equation. Model homogenized wave equations are constructed for several examples of one-dimensional sections of the real ocean bottom profile, and their numerical and asymptotic solutions are compared with numerical solutions of the original equations.

SURVEY OF INDUSTRIAL WASTE LANDFILL BY MEANS OF GEOPHYSICAL METHODS

The paper shows the possibility of geophysical methods to find scrap metal burial sites on an example of inspection of industrial waste landfill in the Middle Urals Mountains. The research tasks included conducting a magnetic and electrometric survey of industrial landfill territory for revealing of anomalies, and electromagnetic (audiomagnetotellurics) soundings — for definition of occurrence depth of anomalous objects. A brief description of research methods, techniques of fieldwork and features of data processing is given. As a result of electric profiling by the method of VLF-R, a map of apparent resistivity was created. The result of the magnetic survey was a map of the total vector of the Earth's magnetic field and its vertical gradient. Analysis of the anomalies of apparent resistances and vertical gradient of the magnetic field has allowed identifying scrap of ferrous and nonferrous metals from the difference in physical properties. The audiomagnetotellurics soundings data was processed by means of the one-dimensional (1D) and two-dimensional (2D) inversion software. One-dimensional geoelectric sections are presented by the elementary models within the framework of the equivalence principle and do not reflect the true structure of the landfill. The most authentic are the 2D-geoelectric sections gained by the joint inversion of data for two modes and possessing more information concerning to local conductors. The zone structure of landfill in the shape of a «puff cake», consisting of several electrically conductive structural levels divided by isolating horizons was revealed. The surfaces of the sections are close to horizontal, which corresponds to sequential change of materials and gradual increase in the landfill. Based on the results of geophysical explorations, promising places for the development of scrap metal have been identified. One of the places coincided with trial dredging of the ground where a waste of copper-smelting manufactures was found.

One-dimensional sections of exotic spacetimes with superconducting circuits

We introduce analogue quantum simulations of 1 + 1 dimensional sections of exotic 3 + 1 dimensional spacetimes, such as Alcubierre warp-drive spacetime, Gödel rotating universe and Kerr highly-rotating black hole metric. Suitable magnetic flux profiles along a SQUID array embedded in a superconducting transmission line allow to generate an effective spatiotemporal dependence in the speed of light, which is able to mimic the corresponding light propagation in a dimensionally-reduced exotic spacetime. In each case, we discuss the technical constraints and the links with possible chronology protection mechanisms and we find the optimal region of parameters for the experimental implementation.

PHASE EQUILIBRIA IN SYSTEM (LiF)2 – (NaCl)2 – Na3FSO4

The liquidus surface of the quasi-triple system LiF–NaCl–Na3FSO4 was studied by a differential-thermal method of physicochemical analysis. As a result of the studies, the crystallization temperature (554 °C) and the composition of the three-component eutectic, which can be used as a heat accumulator in thermal energy storage devices, are determined. When designing plants based on renewable energy sources, it is necessary to provide storage tanks for the concentration of thermal energy, so that the stored heat energy can be used even in the period of absence of solar radiation. The most suitable for thermal accumulation are salt eutectic mixtures. Priority in this respect is research devoted to the development of compositions as possible with large values of the latent heat of the solid-liquid phase transition. The experiment was carried out on the synchronous thermal analysis unit STA 449 F3 Phoenix, the company Netzsch, designed to operate in the temperature range from room temperature to 1500 ° C in an atmosphere of inert gases (argon). All facet triangle (LiF)2 – (NaCl)2 – Na3FSO4: stable diagonal (LiF)2 – (NaCl)2 of the triple mutual system Li, Na // F, Cl and quasibinary systems: LiF–Na3FSO4; NaCl – Na3FSO4 is of the eutectic type, therefore it can be assumed that a triple eutectic is formed in the system. To determine the thermo physical characteristics of the eutectic composition, the experiment is planned in accordance with the general rules of the projection-thermographic method. The one-dimensional polythermal section AB located in the crystallization field of lithium fluoride, where A is 50% (LiF)2+ 50% Na3FSO4, B is 50% (LiF)2+ 50% (NaCl)2 was experientally studied. The study of the AB section reveals the direction to the triple eutectic, from the poles of lithium fluoride crystallization, i.e. the study of this section revealed a constant ratio of sodium chloride and sulfate-sodium fluoride in the triple eutectic. At the point showing a constant ratio of the two initial components in the eutectic, the thermal effects of the secondary and tertiary crystallizations are combined, and the primary crystallization is fixed at 657 °C. This composition is the starting point for the investigation of the next section. The content of lithium fluoride in the eutectic is determined by studying the polythermal section of lithium fluoride from the crystallization pole and passing through the projection Ē to the side of the triangle (NaCl)2 – Na3FSO4. As a result of the studies, the crystallization temperature and the concentration of the initial salts in the triple eutectic have been established. The detected eutectic composition (EΔ) crystallizes at 554 °C and contains eq. %: (LiF)2 – 26; (NaCl)2 – 23; Na3FSO4 – 51.Forcitation:Omarova S.M., Verdieva Z.N., Alkhasov A.B., Magomedbekov U.G., Arbukhanova P.A., Verdiev N.N. Phase equilibria in system (LiF)2 – (NaCl)2 – Na3FSO4. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2017. V. 60. N 10. P. 4-8

A Heat and Mass Transfer Model of a Silicon Pilot Furnace

The most common technological route for metallurgical silicon production is to feed quartz and a carbon source (e.g., coal, coke, or charcoal) into submerged-arc furnaces, which use electrodes as electrical conductors. We develop a mathematical model of a silicon furnace. A continuum approach is taken, and we derive from first principles the equations governing the time evolution of chemical concentrations, gas partial pressures, velocity, and temperature within a one-dimensional vertical section of a furnace. Numerical simulations are obtained for this model and are shown to compare favorably with experimental results obtained using silicon pilot furnaces. A rising interface is shown to exist at the base of the charge, with motion caused by the heating of the pilot furnace. We find that more reactive carbon reduces the silicon monoxide losses, while reducing the carbon content in the raw material mixture causes greater solid and liquid material to build-up in the charge region, indicative of crust formation (which can be detrimental to the silicon production process). We also comment on how the various findings could be relevant for industrial operations.

The influence of one-dimensional velocity sections on determining the key parameters of the earthquake sources in Azerbaijan

The paper addresses the construction of one-dimensional (1D) velocity models in the seismogenic regions of Azerbaijan taken individually and the analysis of implications of these models for estimating the key parameters of earthquake sources in Azerbaijan. We considered and analyzed the seismological data from the local earthquakes, the arrival times of the P-, P-g, Pn-, S-, Sg-, and Sn-waves recorded by the network of telemetry stations during the period from 2005 to 2014 with ml ≥ 2.5. For constructing the models, we used the VELEST program which calculates 1D velocity models from travel times of seismic waves. As a result, the 1D models were built for ten regions of Azerbaijan; the key parameters of the hypocenters of the earthquakes were recalculated; and the corrections to the body-wave arrival times at the observation stations were obtained, which increased the accuracy of locating the hypocenter of earthquakes.

Bosonic lasing and trapping of a dressed photon fluid in InGaN at room temperature

The generation of a quantum fluid of dressed photons at room temperature is experimentally demonstrated in an InGaN microcavity which is divided into two- and one-dimensional sections, resulting in single- and switchable multilevel coherent light emission. Ultra-low-threshold operation is attributed to the slight but robust excitonic fraction of the photonic condensate representing a bosonic laser working below the Mott transition (polariton laser). In contrast to equilibrium Bose-Einstein condensates, the nonequilibrium driven-dissipative nature enables the population of higher orbitals if any confinement potential is present to induce enhanced quantum correlations. Trapping inside microwire spacers leads to a polariton harmonic oscillator resulting in discrete states in an equidistant ladder of photonic orbitals. Level occupation and selection of a specific wave function is managed via optical control, mimicking a quantum emitter on a macroscopic level. It shows that exotic states of matter can be realized in rather simple structures at room temperature directly visible to the human eye. It represents also an excellent opportunity to study basic many-body dynamics in one-dimensional bosonic matter by simultaneously settling an optimized fabrication technique for devices enabling practical Boolean quantum logic gates for optical computing.

Research on the Low Frequency Broadband Piezoelectric-Magnetostrictive Hybrid Transducer

The effective ways for underwater transducer to lower its operating frequency, to broaden its bandwidth, and to develop its miniaturization are investigated. According to the theory of coupled multimode vibrations, a novel Hybrid transducer is developed. Different from the traditional Hybrid transducer, the improved point is the low frequency vibration controlled by the zigzag piezoelectric section and the high frequency vibration controlled by the one-dimensional magnetostrictive section. Through building the equivalent circuit model and finite element model, the performances of transducer will be predicted. The analysis shows that FEM is suitable for analyzing such a Hybrid underwater transducer within 5% deviation. The corresponding tests show that the volume and weight of the Hybrid transducer undergo a sharp drop after improvement. The novel Hybrid transducer has a distinct advantage in low frequency, bandwidth, and miniaturization. The prototype has the resonance at 1.82 kHz and 3.76 kHz. It can be used effectively in the bandwidth of 1.5 kHz to 5 kHz. Its main body has an external diameter of 54 mm. The whole prototype is 235 mm long and weighs 2.61 kg.

On syzygies of linear sections

In this paper, we study how the minimal free resolution of a closed subscheme X ⊂ P r X \subset \mathbb {P}^r relates to that of a linear section X ∩ Λ ⊂ Λ = P s X \cap \Lambda \subset \Lambda = \mathbb {P}^s ( 0 > s > r ) (0 > s >r) . Our main result implies that the shape of the final non-zero row of the Betti diagram of X X is preserved under taking the zero-dimensional and one-dimensional linear sections.

The geometry of the moduli space of odd spin curves

The spin moduli spaceSg is the parameter space of theta characteristics (spin structures) on stable curves of genus g. It has two connected components, S g andS + g , depending on the parity of the spin structure. We establish a complete birational classication by Kodaira dimension of the odd componentS g of the spin moduli space. We show thatS g is uniruled for g < 12 and even unirational for g 8. In this range, introducing the concept of cluster for the Mukai variety whose one-dimensional linear sections are general canonical curves of genus g, we construct new birational models ofS g . These we then use to explicitly describe the birational structure of S g . For instance, S 8 is birational to a locally trivial P 7 -bundle over the moduli space of elliptic curves with seven pairs of marked points. For g 12, we prove thatS g is a variety of general type. In genus 12, this requires the construction of a counterexample to the Slope Conjecture on eective divisors on the moduli space of stable curves of genus 12.