Approximate Calculation Research Articles

Approximate Voigt function formula for laser-induced breakdown spectroscopy fitting.

Accurate and rapid spectrum fitting is very important for quantitatively analyzing laser-induced breakdown spectroscopy (LIBS). The Voigt function is often used to fit LIBS spectral lines. We propose a new approximate Voigt function formula. Based on the classic Lorentz-Gauss linear combination formula, a summation term was added that contained a specific convolution operation to improve the Voigt function's calculation and fitting accuracy. This formula can be used for the approximate calculation of the Voigt function with an overall accuracy of 0.31% and a full width at half-maximum internal accuracy of 0.25% when the ratio of Lorentzian linewidth to Gaussian linewidth is 1:1. The formula was then applied to LIBS data processing to fit four element spectral lines of calcium (Ca-393.37, 396.85, and 422.67 nm) and potassium (K-766.49 nm). The fitting results showed that this new approximate formula could fit at least seven data points, and compared with the complex plane partition method and the classic linear combination formula, the new formula had better fitting speed and accuracy.

A dynamic approach for updating the optimal approximation of rough set

The approximate representation and calculation of target concept on approximate space are the foundation of rough set model study. For dynamic attribute reduction and related tasks, it is often necessary to update the approximation of the target concept of rough set theory, and most existing updating approaches are based on the lower and upper approximations of target concepts. This paper presents a dynamic approach for updating the optimal set when a single object is added into the decision table. Aiming at the dynamic change of condition class and decision class caused by the incremental object, the paper discusses the updating mechanisms of optimal approximation set in four different cases and then the dynamic updating algorithm of optimal approximation set is obtained. Finally, the experiments on different data sets from UCI show that the time complexity of optimal approximate updating of decision classes are different for four different cases and the incremental methods are feasible and efficient for decision systems of added one single object.

APPLICATION OF THE THEORY OF NEW INFORMATION OPERATORS IN CONDUCTING RESEARCH IN THE FIELD OF INFORMATION TECHNOLOGIES

Due to the rapid development and implementation of the latest information technologies in many fields of science and technology significant changes have taken place. In particular, new mathematical theories have emerged; they can be effectively used in building and improving existing mathematical models of various phenomena and objects. Mathematical modeling is currently one of the main methods in scientific research of technological, social, economic processes and natural phenomena. No research thesis is complete without the use of mathematical methods and algorithms. In view of this it is important to acquaint young scientists with modern trends in mathematical modeling during their training for PhD degree, in particular. The development of information technology has contributed to the emergence of new approaches to obtaining, processing and analyzing information in scientific research. In this way, the theory of new information operators, which is widely used in mathematical modeling, was created. The analysis of the existing research reveals the need to consider the theoretical basics of new information operators and their application to the numerical integration of several variables functions. The example of the problem of numerical integration of two variables functions shows the way how to create cubature formulas depending on the type of the input information about function. The paper presents new cubature formulas for the approximate calculation of double integrals, in the case when the information is given by the set of traces on lines and values of the function at points. The proposed formulas have high accuracy but use much less input information compared to classical formulas for numerical integration of double integrals. All the results are supported by numerous examples made in the computer mathematics system Mathcad. The implementation of the developed methodology of using new information operators in scientific research has shown its efficacy during seminars with Master and PhD students.

Mathematical Model for the Kinetics of Heterogeneous Reaction of Carbonates Dissociation in the Process of Roasting in the Presence of Temperatures Gradients in Phosphate Raw Material

The paper deals with the investigation of the parameters for the structural and kinetic rate equation of the carbonates dissociation reaction, in accordance with the obtained results of the nonisothermic experiment, in the conditions of gradient temperature presence in the investigated samples. The most significant is the study of physicochemical transformations kinetic laws, which degree of completeness effects the quality of intermediate products directly, that is decarbonization and sintering. The main part of the process, when phosphorites are heated, takes place in a solid phase. The feature of topochemical reactions is their localization in the aria between a solid phase surface of the initial substance and the reaction products. This surface is formed and changed, as a result of chemical and power technological process for roasting, determining the dependence of the reaction rate on time. The method of thermal analytical experiments is used. The reverse kinetic problem is solved in the temperatures range of the chemical–technological process for roasting phosphate raw materials on conveyor indurating machines. The authors propose a method of approximate calculation for the parameters of kinetic equations which allows to reduce errors, caused by the heat exchange processes in a measuring cell, significantly. The obtained results and their accuracy are suitable for the practical application.

Приближенное представление дилогарифмами решения одной вариационной краевой задачи для круга при граничном условии Неймана

It is known that boundary value problems for the Laplace and Poisson equations are equivalent to the problem of the calculus of variations – the minimum of an integral for which the given partial differential equation is the Euler – Lagrange equation. For example, the problem of the minimum of the Dirichlet integral in the unit disc centered at the origin on some admissible set of functions for given values of the normal derivative on the circle is equivalent to the Neimann boundary value problem for the Laplace equation in this domain. An effective approximate dilogarithm representation of the solution of the above equivalent variational boundary value problem is constructed on the basis of the known exact solution of the Neumann Boundary value problem for a circle using a special approximate formula for the Dini integral. The approximate formula is effective in the sense that it is quite simple in numerical implementation, stable, and the error estimation, which is uniform over a circle, allows calculations with the given accuracy. A special quadrature formula for the Dini integral has a remarkable property – its coefficients are non-negative. Quadrature formulas with non-negative coefficients occupy a special place in the theory of approximate calculations of definite integrals and its applications. Naturally, this property becomes even more significant when the coefficient are not number, but some functions. The performed numerical analysis of the approximate solution confirms its effectiveness.

INCREASING SENSITIVITY OF EDDY CURRENT NON-DESTRUCTIVE TESTING OF DELAMINATION IN CARBON-FIBER REINFORCED PLASTICS

The paper is concerned with increasing sensitivity of eddy current nondestructive testing of most dangerous delamination in carbon-fiber reinforced plastics (CFRP). Increased sensitivity is achieved by separate registration and comparison of eddy current signals obtained from a set of stratifications of carbon fibers with the same orientation. The separation of eddy current signals is possible due to pronounced anisotropy of the electrical conductivity of the layers dominant in the direction of the fibers of the corresponding layer. Eddy-current signals are registered by eddy current probes with maximum sensitivity in a given angular direction. Prior to the scan eddy current signals of the probe are leveled on a defect-free area. The influence of the working gap on the difference between the eddy current signals of the probe is suppressed by normalizing it according to one of the signals. The analysis of the registered signals from delamination has been performed using an approximate calculation model. The reliability of the obtained results has been confirmed by comparison with experimental results and calculations using the finite element method.

Proposals for the construction of overpass structures and transport hubs for the high-speed highway in St. Petersburg

Background: As part of student research at St. Petersburg architectural-construction University continues to develop alternative proposals for the creation of a circumferential highway at the boundaries of communication areas of St. Petersburg and Leningrad region. The article presents the results of research works on optimization of routing highways, according to the architectural layout of buildings, transport hubs, to study the effects the pre-tension of the puffs and the guys at the reduction of efforts and deformations of the main elements of the highway, the calculations of the designs of the most high and loaded sea area. The construction of the 8-high-speed transport highway was upgraded due to restrictions related to the reconstruction of Levashovo and Pulkovo airports, the transfer of the capital of the Leningrad region to Gatchina, and linking to the promising metro stations Strelna, Yanino and Kudrovo. The upgraded scheme of the highway is proposed in the form of an open polygon with transport and interchange nodes in the corners and is based on load-bearing trestle structures of arched-cable design that provide the necessary functionality, reliability and safety.
 Aim: development of a district high-speed transport system on the borders of St. Petersburg and the Leningrad region, based on the widespread use of electric transport, with passenger traffic comparable to the metro line.
 Materials and Methods: trestle structures are designed for combinations of operating loads, forces and impacts, including consideration of dynamic aspects and non-linearity, using the "SCAD Office" software package. 
 Results: based on the results of variant design, an arch-cable-stayed version with spans of 180 m and 360 m was adopted as a supporting structure according to the metal consumption criterion, which became the basic one for building a highway of overpass design. From an approximate calculation, it follows that the cost of building a highway on land plots (two-track scheme) compared to the construction of the metro, it is expected to be 5-6 times lower, and on the sea sections 3-4 times lower due to high pylons and deep pile foundations. 
 Conclusion: the estimated volume of passenger traffic per day for the two-track high-speed and two-track high-speed highways will be 208 thousand passengers, and 76 million passengers per year, which is quite comparable to this indicator for the metro line.

Ponton (flow) bridges from metal polyethylene pipes

The object of the study is a pontoon link, where the role of the bearing structure is performed by non-standard pipes. Construction of surface bridges is widely used in bridge construction and is an essential part of the development of transport infrastructure of our country and abroad. In the case where it is not possible to build capital or low-water bridges, surface bridges or ferry crossings are used. Built-up bridges are very convenient to use in the construction of capital bridges, when the main course of the route is blocked instead of temporary stationary bridges. In order to compare the application of the developed solution, an approximate calculation of the cost of the pontoon was made. Analysis of costs in the market of analogues showed that the cost of only the bearing structure of a pontoon of similar load capacity based on plastic pipes, will be much higher than the cost of pantone out of non-standard. The study examined the possibility of using non-standard pipes for the construction of weld bridges. Non-standard pipes are a promising material for construction of weld bridges due to buoyancy, low cost, such pipes are easily available raw materials.

METHOD FOR APPROXIMATE CALCULATION OF FUNCTIONAL CHARACTERISTICS OF GAS PUMPING UNITS

Is described the method of approximate calculation of the functional characteristics of gas-pumping units and the method of diagnostics of the value of the impairment of the working wheel of the central center of the main gas pipelines is described. It is clear that the deposits are inflated with the impairment of productivity and productivity, and that is efficiency factor of superchargers. The architecture of the program complex is described, as well as the necessary system and technical facilities for carrying out the transfer for fragmentation at the warehouse of the automatic transmission system of the gas transmission system. Experimentally, the accuracy of the value of the radial prominence in the gaps of the working wheel on the buttstock of the "Demag" 655 P2 type was verified. The revision of the growth rates from the results of the straight lines to the open flow part was not shifted 0.15 mm. Descriptions of the method of implementation by a complex of programs, allow to carry out the development of the main indicators of the functional and technical mill of the VCN GPA: vitreous-pressure, forceful, polytropic KKD characteristics. These indicators are used for the purpose of determining the overall performance of the energy efficiency of the robotic skin GPU: the effective effort of the gas turbines, the vitrates of the fired gas from the of the coated gas pump, which is displayed in the real demand. The economics of the robotics of compressor stations, the supply of the pumped gas, the confirmation of the plans for the supply of gas to the residents and the safe functioning of the gas transportation system (GTS) of Ukraine, a significant world of possessing the functional To this, it is of particular importance to build up the development of new methods and to provide diagnostics, to ensure that the actual FCS possesses an assessment. At present, there is evidence of the actual state of possession of a more efficient operation of the plant in the transition from a traditional technical service to a resource-saving one. The obtained results show that the calculation of the actual characteristics of the VCN using the proposed method allows to take into account the influence of seal wear on the actual parameters of the regime over the entire range of workloads of single-stage and multistage superchargers.

Theoretical analysis of casing collapse in locally expansive mudstone

Expansion of mudstone through absorbing water can increase local stress in information, which is one of the main reasons for casing damage in mudstone. To establish a reasonable mechanical model of local stress increase is the key problem for casing damage in locally expansive mudstone. Many models of uniform stress or linear stress are established to simulate the local stress increase. However, the accuracy and scientificity for those models are insufficient. In this paper, a study on casing strength in locally expansive mudstone is carried out based on theoretical analysis and numerical calculation. Firstly, a mechanical model of casings under parabolic-like loads is established to simulate the local stress increase. Then, an analytical solution of casings is obtained based on the stress function method. Next, a finite element calculation of casings under the same boundary condition is carried out. In the end, the comparisons between analytical solution and finite element method (FEM) are conducted. The results reveal that the theoretical solutions are in good agreement with the FEM. In addition, a novel predicting method of the casing stress in locally expansive mudstone is presented. Finally, our theoretical analysis can be the standard for numerical and approximate calculations. It is helpful to explore the casing damage mechanism in mudstone layer and reduce the casing collapse in complex underground environment.

Analysis of the Resonator Element in Different Positions in the Circular Patch Microstrip Antenna

Abstract In this article, a circular patch microstrip antenna with a metamaterial resonator for 4G applications is proposed. For the design of the circular antenna patch, an approximate calculation was performed. The circular resonator is inserted into the patch for some antennas, in different positions for a parametric study. When incorporating the resonator, the performance of the antenna is improved and analyzed through some parameters, when compared with the antenna without the resonator. To verify the influence of the resonator and validate its performance, simulated results were performed with the ANSYS HFSS® software and compared with the experimental results, through prototypes, in which they showed a good agreement.

Development of Methodology for Calculation of Discontinuous Circular Welds in Torsion

The main criterion for the performance of welds is the strength. The least durable ones are the corner joints used to perform various types of welded joints. In the literature, the methods of calculating the strength of welded joints with solid welds are considered in sufficient details. Methods of calculation of connection interrupted sutures absent. In this case, the greatest difficulty is the calculation of connections using circular intermittent welds, which are often performed in welded drums and pulleys; they work on torsion. Therefore, the development of methods for calculating circular intermittent welds for torsion is quite important.Shear stresses in welds from torque are determined depending on the value of the polar moment of resistance of its dangerous section. When determining the polar moment of resistance of the dangerous section of a circular discontinuous weld, it was represented by a set of sections in the form of a sector of a circular ring. The method of calculation of the polar moment of resistance of the rotated dangerous section of a circular discontinuous weld, which takes into account the relative length of the weld areas and their number, as well as the method of accurate and approximate calculation of shear stresses in the weld.

МЕТОД ФИКТИВНЫХ РЕАКЦИЙ В МОДЕЛИРОВАНИИ КОНТАКТНОЙ ПОВЕРХНОСТИ НА ПРИМЕРЕ ФЛАНЦЕВЫХ СОЕДИНЕНИЙ

An iterative method for calculating flanged connections in the finite element formulation is proposed. The essence of the proposed method is to separate the contact problem into a separate localized process that depends only on the initial distribution of forces from the main load on the flange connection. In the initial matrix of stiffness of unrelated bodies, a binding matrix of contact with elements of high rigidity is added. The calculation is performed in two phases: the first phase determines the movement of the actual loads on the second, through a vector of dummy reactions, iterative specified voltage at the contact surfaces. The results obtained by the proposed method are compared with the experimental results and with the approximate calculation method.

ОПТИМИЗАЦИЯ ФЕРМЕННЫХ КОНСТРУКЦИЙ С ПОЯСАМИ СТУПЕНЧАТО-ПЕРЕМЕННЫХ СЕЧЕНИЙ ИЗ ПРЯМОУГОЛЬНЫХ ТРУБ

The article describes the regularity of the optimization calculation of unification zones in relation to beam chords of step-variable cross-sections with the determination of their design coefficients. The rationality of the formation of these chords in truss structures made of rectangular pipes is shown due to the difference not in the heights of the sections, but in their thicknesses with welded joints on the longitudinal slits.The engineering method for calculating such joints, as well as their load-bearing capacity, has been tested by tensile strength tests of the samples.The universality of the technical solution of welded joints with slits ensures their use in structures made of tubular and rolled profiles, and it preserves the accepted layout of standardized trusses with assemblies and flanged connections. The significant reduction in structural material (steel) in standardized trusses made of bent-welded profiles was revealed when chords of uniform cross-sections were replaced with chords of step-variable cross-sections. The article also gives the comparative calculation of the design coefficients and the averaged coefficients of chord elements use when the lengths of the unification zones and the belt panels coincide. Sufficient correctness of the approximate calculation method for solving optimization problems and variant design of load-bearing structures is confirmed.

Distinct late Pleistocene subtropical-tropical divergence revealed by fifteen low-copy nuclear genes in a dominant species in South-East China

In East Asia, genetic divergence is usually considered to be correlated to different floristic regions, however, subtropical-tropical divergence is largely ignored, compared to widely explored temperate-subtropical divergence. Lindera aggregata (Lauraceae), a dominant species in South-East China was selected to address this issue. Fifteen low-copy nuclear genes (LCGs) and four chloroplast DNA (cpDNA) fragments were used to detect its evolutionary history. In LCGs, STRUCTURE and dated Bayesian phylogeny analyses detect distinct subtropical-tropical divergence since late Pleistocene. Approximate Bayesian calculation (ABC) further supports the distinct subtropical-tropical divergence, and close related Taiwan and South China populations are diverged at the last interglacial. Isolation by distance, isolation by environment and isolation by resistance analyses suggest the current climatic difference rather than geographical distance contributes to the genetic differentiation. Principle component analysis shows populations of tropical cluster occur in warmer area with higher precipitation. Ancestral area reconstruction based on Bayesian phylogeny indicates that ancestral L. aggregata populations are distributed in tropical region. In cpDNA, although unique haplotypes are found in tropical region, distinct subtropical-tropical divergence is absent. In conclusion, distinct late Pleistocene subtropical-tropical divergence of L. aggregata is triggered by climate. It is likely that L. aggregata is originated in Southwest-South China and experienced hierarchical dispersal from south to north. The South China Sea land bridge has dual role in connecting or isolating Taiwan and mainland populations since the last glaciation.

Probing band-center anomaly with the Kernel polynomial method

We investigate the anomalous behavior of localization length of a non-interacting one-dimensional Anderson model at zero temperature. We report numerical calculations of the Thouless expression of localization length, based on the Kernel polynomial method (KPM), which has an computational complexity, where N is the system size. The KPM results show excellent agreement with perturbative results in a large system size limit, confirming the validity of the Thouless formula. In the perturbative regime, we show that the KPM approximation of the Thouless expression produces the correct localization length at the band center in the thermodynamic limit. The Thouless expression relates localization length in terms of density of states in a one-dimensional disordered system. By calculating the KPM estimates of the density of states, we find a cusp-like behavior around the band center in the perturbative regime. This cusp-like singularity can not be obtained by approximate analytical calculations within the second-order approximations, reflects the band-center anomaly.

Решение задач оптимального управления аэрокосмическим самолетом

The paper overviews works on methods for solving problems of aerospace aircraft control and aims to solve the remaining problems. The purpose of the study was to obtain reference optimal control and its approximation in the guidance functions. When stating the problem, we took into account all essential physical factors; we selected the solution techniques and computational coordinate system, developed a mathematical model, methods and automated procedures for end-to-end optimization relying on the maximum principle, the formation and optimization of guidance functions. In addition to the well-known methods for solving boundary value problems, methods of analytical calculation of the initial approximation and the search for the convergence region were developed. The results of numerical studies contain nominal and perturbed optimal trajectories in which an aerospace aircraft is boosted by an accelerator, performs global spatial maneuvers, and enters orbit. Having analyzed extremals, compared and evaluated the effectiveness of the guidance functions, we drew certain conclusions taking into account the perturbations.

Formulas for Approximate Calculation of the Chebyshev Coefficients

Formulas for Approximate Calculation of the Chebyshev Coefficients

МИКРОКЛИМАТ В ЗДАНИЯХ ИЗ ОБЪЕМНЫХ БЛОКОВ

Providing the necessary parameters of the microclimate is one of the necessary conditions in the modern construction. For these purposes, there is a set of measures and microclimate support systems applicable in all types of the structural design of buildings. But the features of houses form the modular blocks allow us to move away from standard solutions and use energy-efficient construction technologies, namely, walls with a ventilated interlayer. This design allows us to provide the necessary air exchange in the premises while providing the necessary inlet air temperature. Walls with a ventilated interlayer complement the central ventilation systems or even make it possible to abandon their use. In this article the issue of using walls with ventilated interlayers in the modular blocks, with the use of additional heating of the incoming air in the cold season by using film infrared heaters was considered. The question of the integration of this design with the system of “smart home” was also considered, which will lead to the possibility of creating an energy-efficient building by ensuring cellular regulation of the microclimate parameters. The result of the research is the data required for an approximate calculation of walls with ventilated interlayers and infrared film heating systems, and the possibilities of creating active buildings were also considered. To ensure the energy efficiency of the building, it is proposed to control air exchange and temperature. The control will be carried out directly as follows: in the ventilated walls, at the holes, sensors are installed that will control the speed and temperature of the supply air; a radiant heating film and a recuperator plate that heats the supply air are mounted in the inner heating layer of the wall panel. If the plate temperature is insufficient, the heating film is switched on, which increases the temperature of the supply air masses to the desired temperature.

A New Method for determining Added Mass and Damping Coefficients of Floating Objects in Infinite Water Depth: Residue Integration of Singular Free Surface Term

It has been the case that the added mass and damping coefficients of a floating body are determined differently depending on the water depth condition which is finite or infinite. In the present study, Green functions for the finite and infinite depth conditions are compared, and a new method based on residue integration technique is proposed to determine the singular integral of the free surface term in the Green function of infinite water depth. The new method is semi-analytic in that it does not depend on any approximate transcendental functions or numerical calculations as generally appeared in the existing methods. Hence, it can be more advantageous in both accuracy and calculation time. The method is numerically implemented to a floating hemisphere. The results are compared with those of existing numerical studies, and they showed nice agreements. The depth criterion to judge whether to use finite or infinite water depth is discussed as well. Keywords: floating structures, added mass coefficient, radiation damping coefficient, singularity distribution method, Green function