Specific Transformation Research Articles

Regularity of the Solution of the Prandtl Equation

Solvability and regularity of the solution of the Dirichlet problem for the Prandtl equation $$\frac{u(x)}{p(x)}-\frac{1}{2\pi}\int_{-1}^1\frac{u'(t)}{t-x}\,dt=f(x)$$ is studied. Here $$p(x)$$ is a positive function on $$(-1,1)$$ such that $$\sup(1-x^2)/p(x)<\infty$$ . We introduce the scale of spaces $$\widetilde H^s(-1,1)$$ in terms of the special integral transformation on the interval $$(-1,1)$$ . We obtain theorems about the existence and uniqueness of the solution in the classes $$\widetilde H^{s}(-1,1)$$ with $$0\le s\le 1$$ . In particular, for $$s=1$$ the result is as follows: if $$r^{1/2}f\in L_2$$ , then $$r^{-1/2}u,r^{1/2}u'\in L_2$$ , where $$r(x)=1-x^2$$ .

Special transformation properties for certain equations with applications in Plasma Physics

Nonlocal transformation properties are derived for a nonlinear system which appears in certain problems in Plasma Physics. Such properties exist since the system admits conservation laws. These conservation laws lead to auxiliary systems which are studied in the point of view of equivalence transformations and Lie point symmetry analysis. The existence of infinite dimensional symmetries, in some cases, leads to the construction of linearizing mappings.

Architectural dominants of the city of Chisinau built in the first years after the Second World War

The first years after the Second World War are characterized by the reconstruction of the cities of the Moldovan Soviet Socialist Republic (MSSR). The development of post-war architecture was dependent on political authorities. The regulations in the field led to special urban transformations. The Soviet urban image is a recognizable one, especially in the development of the main arteries, defined by spatial and volumetric greatness. Another impressive thing is the architecture of Stephen the Great boulevard, whose aesthetics promotes Soviet ideology. It had particular regulations regarding the alignment of the buildings, their height, their proportions, the aesthetics of the facades facing the boulevard, the relationship with the neighboring buildings and others, forming a coherent configuration. The established rules ordered the street front; the buildings often formed “parade courts”, increasing the visibility of the massive facades, called “parade facades”, which became recognizable by decorative exuberance. This article aims at observing the development of the constructions on a certain segment of the main artery of the capital of MSSR - one of the priority preoccupations of the authorities in the given period.

Dynamic interaction of behaviors of time-fractional shallow water wave equation system

In this study, the traveling wave solutions for the time-fractional shallow water wave equation system, whose physical application is defined as the dynamics of water bodies in the ocean or seas, are investigated by [Formula: see text]-expansion method. The nonlinear fractional partial differential equation is transformed to the non-fractional ordinary differential equation with the use of a special wave transformation. In this special wave transformation, we consider the conformable fractional derivative operator to which the chain rule is applied. We obtain complex hyperbolic and complex trigonometric functions for the time-fractional shallow water wave equation system with the help of this technique. New traveling wave solutions are obtained for the special values given to the parameters in these complex hyperbolic and complex trigonometric functions, and the behavior of these solutions is examined with the help of 3D and 2D graphics.

Analysis of heteroscedastic measurement data by the self-refining method of interval fusion with preference aggregation – IF&PA

The newly proposed interval fusion with preference aggregation (IF&PA) procedure, further modified and formalized to improve the accuracy of the fusion result, is presented and applied to process the heteroscedastic data of a real experiment. The experiment consisted in determination of the reference values of the two measurands, DC voltage and resistance, based on the readings of five different models of multimeters. The data heteroscedasticity was ensured by a special transformation of the raw measurements. For comparison, the same data were processed by the method of weighted mean. For the two methods, absolute deviations of the obtained reference values from the nominal values (which are the high-precision calibrator outputs) and reference value uncertainties were estimated. The paper key outcome is that the IF&PA procedure provides a reference value to be very close to nominal value with considerably reduced uncertainty in comparison with traditional weighted mean calculation.

Theoretical Modeling of Piezoelectric Cantilever MEMS Loudspeakers

Piezoelectric microelectromechanical system (MEMS) loudspeakers have received extensive attention in recent years. In particular, the piezoelectric cantilever MEMS loudspeaker, which uses multilayer piezoelectric cantilever actuators (MPCAs), has attracted attention because of its small size, low cost, ease of manufacture, and desirable piston movement. However, owing to the complex driving principles of MPCAs, no adequately efficient and appropriate method currently exists that can be used to analyze and predict the performance of piezoelectric cantilever MEMS loudspeakers. In this study, the equivalent circuit method (ECM) is adopted to theoretically model piezoelectric cantilever MEMS loudspeakers, and an ECM model with a special MPCA transformer for electromechanical conversion is proposed. With the proposed ECM model, the performance characteristics of piezoelectric cantilever MEMS loudspeakers, such as the displacement and sound pressure response, can be calculated efficiently and conveniently. To verify the accuracy of the ECM model, the finite element method is adopted for simulation, and the simulated results are compared with those of the ECM models. A satisfactory agreement was found, which verifies the accuracy of the proposed ECM model.

On the conformal symmetry of exceptional scalar theories

The DBI and special galileon theories exhibit a conformal symmetry at unphysical values of the spacetime dimension. We find the Lagrangian form of this symmetry. The special conformal transformations are non-linearly realized on the fields, even though conformal symmetry is unbroken. Commuting the conformal transformations with the extended shift symmetries, we find new symmetries, which when taken together with the conformal and shift symmetries close into a larger algebra. For DBI this larger algebra is the conformal algebra of the higher dimensional bulk in the brane embedding view of DBI. For the special galileon it is a real form of the special linear algebra. We also find the Weyl transformations corresponding to the conformal symmetries, as well as the necessary improvement terms to make the theories Weyl invariant, to second order in the coupling in the DBI case and to lowest order in the coupling in the special galileon case.

An Adaptive Method for Numerical Differentiation of Difficult-to-Compute Functions

An adaptive approach to the numerical differentiation of difficult-to-compute functions is considered. Complex dependencies, which are the result of multiple superpositions of functions or the product of various algorithmic processes, are knowingly difficult to study directly. To establish the nature of the behavior of such dependencies, one has to resort to numerical analysis. One of the important characteristics of functions is a derivative, which indicates the direction and rate of change of a dependence. However, with difficult-to-compute functions, the available a priori information is not always sufficient to achieve the appropriate accuracy of the solution by known means. The loss of accuracy occurs due to the accumulation of round-off errors that grow in proportion to the number of calculated values of a function. In this case, it is necessary to pass on to the posterior approach in order to determine the behavior of the function and move away from the scheme of equidistant nodes, relying on an adaptive way of studying the local situation in the domain of the function. This paper implements an adaptive method for finding derivatives of a function with a minimum of restrictive requirements for the class of functions and the form of their assignment. Due to this, the costs of calculating the function have been significantly reduced with the result that their number has been brought to almost the optimal level. At the same time, the amount of RAM used has sharply decreased. There is no need for a preliminary analysis of the problem of establishing the class of the function under study, in the involvement of special functions or transformation of initial conditions for using standard tables of weight coefficients, etc. For research, it is enough to assign a continuous and bounded function on a fixed segment and a minimum step, which is indirectly responsible for ensuring the required accuracy of differentiation. The effectiveness of the proposed method is demonstrated on a number of test examples. The developed method can be used in more complex problems, for example, in solving some types of differential and integral equations, as well as for a wide range of optimization problems in a wide variety of areas of applied analysis and synthesis.

Massless fermions in planar Bianchi-type-I universes: exact and approximate solutions

Based upon the exact formal solutions of the Weyl–Dirac-equation in anisotropic planar Bianchi-type-I background spacetimes with power law scale factors, one can introduce suitable equivalence classes of the solutions of these models. The associated background spacetimes are characterized by two parameters. It is shown that the exact solutions of all models of a given equivalence class can be generated with the help of a special transformation of these two parameters, provided one knows a single exact solution of an arbitrary member of this class. The method can also be utilized to derive approximate solutions, i.e. solutions which exhibit the correct behavior at early and at late times as well. This is explicitly demonstrated for the case of the anisotropic Kasner background with axial symmetry.

A [formula omitted]-dressing approach to the Kundu-Eckhaus equation

Starting from a local 2×2 matrix ∂¯-equation with non-normalization boundary conditions, the spatial and time spectral problems associated with the Kundu-Eckhaus (KE) equation are derived via two linear constraint equations. The gauge equivalence among the KE equation, NLS equation and Heisenberg chain equation are given. A KE hierarchy with source is proposed by using recursive operator. The N-solitions of the KE equation are constructed based the ∂¯-equation by choosing a special spectral transformation matrix. Further the explicit one- and two-soliton solutions are obtained.

Applying Program Transformations for Deductive Verification of the List Reverse Program

The program transformation methods to simplify the deductive verification of programs with recursive data types are investigated. The list reversion program is considered as an example. A source program in the C language is translated to the cP functional language which includes no pointers. The resulting program is translated further to the WhyML language to perform deductive verification of the program. The cP language includes the same constructs of the C language except pointers. In the C program, all actions that include pointers are replaced by the equivalent fragments without pointers. These replacement are performed by the special transformations using the results of the program dataflow analysis. Three variants of deductive verification of the transformed list reverse program in the Why3 verification platform with SMT solvers (Z3 4.8.6, CVC3 2.4.1, CVC4 1.7) are performed. First, the recursive WhyML program supplied with specifications was automatically verified successfully using only SMT solvers. Second, the recursive program was translated to the P predicate language. Correctness formulae were constructed for the P program and translated further to the why3 specification language. The formulae proving correctness were easy like the first variant. But correctness formulae for the first and second variants were different. Third, the "imperative" WhyML program that included while loop with additional invariant specifications was verified. The proving was easy but not automatic. So, for deductive verification, recursive program variant appears to be more preferable against imperative program variant.

Mathematical model of transition of a production enterprise to a circular economy

In the published article, a mathematical model of an enterprise is proposed, the production activity of which is described by two production functions. The main production function converts resources into the products of an enterprise, the additional production function turns resources into its waste, which are usually included in costs. Enterprises of a waste-free circular economy organize their own production so that the waste of an enterprise becomes new production factors and is completely converted into additional useful products. The process of transition in time of an enterprise of an ordinary economy to an enterprise of a waste-free circular economy is described using a special dimensionless transformation function, which varies from zero to one. Two variants of the peculiarities of changes in the economic indicators of an enterprise that arise during the transition to waste-free production are considered. In the first case, a one-factor manufacturing enterprise was investigated, which in its production activity uses only one resource, which integrates the volumes of factors of production consisting of fixed capital, production assets involved in the production of labor resources, used in the production of materials, applied technologies, of various kinds innovation. In the second case, a two-factor manufacturing enterprise has been investigated, which in its production activity uses two resources, the first of which is fixed capital and production assets, the second production factor includes labor resources involved in production. Regularities have been established for changes in the time of production, waste, profits and costs of an enterprise when introducing waste-free technologies for the case of one-factor production. Anumerical analysis of the obtained economic and mathematical model shows that the maximum value of the enterprise's profit changes over time and corresponds to the level of the introduced circular technologies.

Dbar-dressing method for the Gerdjikov–Ivanov equation with nonzero boundary conditions

We apply the Dbar-dressing method to study a Gerdjikov–Ivanov (GI) equation with nonzero boundary at infinity. A spatial and a time spectral problem associated with GI equation are derived with a asymptotic expansion method. The N-soliton solutions of the GI equation are constructed based the Dbar-equation by choosing a special spectral transformation matrix. Further the explicit one- and two-soliton solutions are obtained.

A data process of human knee joint kinematics obtained by motion-capture measurement

BackgroundThe motion capture has been used as the usual method for measuring movement parameters of human, and most of the measuring data are obtained by partial manual process based on commercial software. An automatic kinematics data process was developed by programming on MATLAB software in this paper.MethodsThe motion capture measurement of healthy volunteers was carried out and the MATLAB program was used for data process. Firstly, the coordinate data of markers and anatomical points on human lower limb measured by motion capture system were read and repaired through the usual and the patch program. Meantime, the local coordinate systems of human femur and tibia were established with anatomical points. Then flexion/extension, abduction/adduction and internal/external rotation of human knee tibiofemoral joint were obtained by special coordinate transformation program.ResultsUsing the above methods, motion capture measurements and batch data processing were carried out on squatting and climbing stairs of 29 healthy volunteers. And the motion characteristics (flexion/extension, internal/external rotation and adduction/abduction) of the knee joint were obtained. For example, the maximum internal/external rotation in squatting and climbing stairs were respectively was 30.5 degrees and 14 degrees, etc. Meantime, the results of this paper also were respectively compared with the results processed by other research methods, and the results were basically consistent, thus the reliability of our research method was verified. After calibration processing, the compiled MATLAB program of this paper can directly be used for efficient batch processing and avoiding manual modeling one by one.ConclusionA novel Patch Program of this paper has been developed, which can make reasonable compensation for missing and noise signals to obtain more complete motion data. At the same time, a universal data processing program has also been developed for obtaining the relative movement of various components of the human body, and the program can be modified for detail special analysis. These motion capture technologies can be used to judge whether the human body functions are abnormal, provide a reference for rehabilitation treatment and design of rehabilitation equipment, and evaluate the effectiveness before and after surgery.

An operation health status monitoring algorithm of special transformers based on BIRCH and Gaussian cloud methods

The health status monitoring of special transformers is of great significance to ensure the secure operation of the distribution network and the power quality of special transformer users. Given this background, an operation health status monitoring algorithm of special transformers is proposed in this paper based on balanced iterative reducing and clustering using hierarchies (BIRCH) and Gaussian Cloud methods (GCM). The algorithm is composed of two parts, i.e., the offline and online parts. For the offline part, the operating indexes of special transformers are extracted based on historical operating data, and Gaussian clouds of normal operating conditions of the special transformers are determined by BIRCH clustering and Gaussian cloud methods. For the online part, Gaussian clouds of real-time operating conditions of special transformers are determined by BIRCH clustering and Gaussian cloud methods based on real-time operation data. Then, the monitoring results of operating health status are determined by the distance between the standard Gaussian clouds and the real-time Gaussian clouds of special transformers. Finally, case studies for actual special transformers are performed to verify the proposed method, and the results show that the proposed model can effectively identify the abnormal operation of the special transformer.

Analysis of the Possibility of Ice Melting Intensity Monitoring by Direct Current in High-Voltage Electrical Systems

The Rostov nuclear power plant is the largest energy center in the South of Russia. Electricity from the nuclear power plant is transmitted to nodal substations across the territory of the Southern region, the climatic conditions of which contribute to the formation of ice deposits on power lines, this determines the urgency of the problem of ice melting. Existing systems for early detection of ice and melting it on wires of 110-500 kV overhead lines allow preventing wire breakage and destruction of supports. In modern methods ice melting is performed with alternating and direct current using special transformers and rectifiers with a melting voltage of 10 kV and a melting current of up to 3600 A, currents and voltages to prevent overheating of contacts in melting circuits and compliance with melting parameters. In circuits using direct current, there is no reliable method for controlling its magnitude. The paper considers the possibility of using a fiber-optic current sensor with a measurement range from 1 to 3600 A.

A Strategy for judging real-time and active reporting outage based on the power consumption information acquisition system

To optimize the energy structure, smart grids are constructed rapidly. The optimization of the power consumption information acquisition system helps to eliminate outages caused by device quality failures, and makes the processing of outages more efficient. A reasonable outage reporting strategy can detect and handle outage faults on the low-voltage side in time, reducing the safety threats to people and devices caused by continuous faults. Therefore, given all the technical means mastered and the shortcomings of the original outage analysis strategy, an outage judgment strategy is established in this paper to make outage judgments for each level. First, the outage judgment strategy of the collection devices is used to analyze the information about outages reported by the collection devices (i.e., special transformer terminals, public transformer terminals, type I concentrators, type II concentrators, and smart meters), and create corresponding outage analysis units; Second, the outage judgment strategy of the outage analysis unit is used to determine the area where outages occurred. A display interface of the master station is designed in this paper based on the function of the strategy. Combined with the results of the actual application, the outage judgment strategy analyzes and judges each outage faults. The outage area in transformer terminals, station areas, and low-voltage branch lines are determined and the corresponding alarms are sent to the emergency maintenance platform to realize power recovery.

Uncertainty Principle for Space–Time Algebra-Valued Functions

In this paper, we present a set of important properties of the special relativistic Fourier transformation (SFT) on the complex space–time algebra $${\mathcal {G}}{(3,1)}$$ , such as inversion property, the Plancherel theorem, and the Hausdorff–Young inequality. The main objective of this article is to introduce the concept of the vector derivative in geometric algebra and using it together with the notion of the space–time split to derive the Heisenberg–Pauli–Weyl inequality. Finally, we apply the SFT properties for proving the Donoho–Stark uncertainty principle for $${\mathcal {G}}{(3,1)}$$ multi-vector functions.

A novel reduced-dimensional beamspace unitary ESPRIT algorithm for monostatic MIMO radar

In this paper, a novel direction of arrival (DOA) estimation algorithm is proposed for monostatic multiple-input multiple-output (MIMO) radar. Due to redundancy of the received data of monostatic MIMO radar, the computational complexity of the inversion of the covariance matrix is increased. In order to reduce the large computational complexity of existing subspace-based algorithms, we perform two reduced-dimensional operations. First, the high-dimensional received data is transformed the low-dimensional received data through a special transformation matrix. Second, the low-dimensional received data is transformed into beamspace. The receive beamspace filter is designed using convex optimization, and it can flexibly control the bandwidth and limit the sidelobe level. To ensure that the converted noise is Gaussian white noise, the prewhitening process is performed. Based on the above precondition, the reduced-dimensional beamspace technique can be effectively combined with the unitary ESPRIT model. Finally, the Cramer-Rao bound (CRB) on angle estimation in element space and reduced-dimensional beamspace is calculated for performance analysis. Numerical simulations verify the effectiveness of the proposed algorithm.

Operation State Identification Method for Converter Transformers Based on Vibration Detection Technology and Deep Belief Network Optimization Algorithm

The converter transformer is a special power transformer that connects the converter bridge to the AC system in the HVDC transmission system. Due to the special structure of the converter transformer, it is necessary to test its operation state during its manufacture and processing to ensure the safety of its future connection to the grid. Numerous studies have shown that vibration signals in transformers can reflect their operating state. Therefore, in order to achieve an effective identification of the operation state of the converter transformer, this paper proposes a method for identifying the operation state of the converter transformer based on vibration detection technology and a deep belief network optimization algorithm. This paper firstly describes the background, principle and application of vibration detection technology, using vibration measurement systems with piezoelectric acceleration sensors, piezoelectric actuators and data acquisition instruments to collect vibration signals at different measurement points on the converter transformer in states of no-load and on-load. By analyzing the time-frequency characteristics of the vibration signals, fast Fourier transform (FFT), wavelet packet decomposition (WPD) and time domain indexes (TDI) are combined into a fused feature extraction method to extract the eigenvalues of the vibration signals, so that the fused eigenvectors of the signals can be constructed. Considering the excellent performance of deep learning in classification, the deep belief network is used to classify the signals’ eigenvectors. To effectively improve the network classification efficiency, the sparrow search algorithm was introduced to build a mathematical model based on the behavioral characteristics of sparrow populations and combine the model with a deep belief network, so as to achieve adaptive parameter optimization of the network and accurate classification of the signals’ eigenvectors. The proposed method is applied to a 500 kV converter transformer for experimental verification. The experimental results show that the fused feature extraction method was able to fully extract the features of the vibration signal, and the deep belief network optimization algorithm had higher classification accuracy and better operational efficiency, and was able to effectively achieve accurate identification of the operation state of the converter transformer. In addition, the method achieved a precision response to the detection results of the vibration sensors, contributing to future improvements in converter transformer manufacturing technology.