Mathematical Deduction Research Articles

Event-Triggered Iterative Learning Containment Control of Model-Free Multiagent Systems

A new event-triggered iterative learning control method is proposed for handling the distributed containment control problem of model-free multiagent systems under a fixed directed graph. The designed controller merely uses the input and output signals, controlled model information is not required. At first, the unknown dynamic is transformed into the linearization model upon the base of pseudo partial derivative. Secondly, the novel distributed containment controller is proposed for each follower by use of iterative learning algorithm. Moreover, a new trigger mechanism is designed to save energy of the systems, such that the updating number of the proposed controller can be reduced greatly. Mathematical deduction shows that the controller can render the outputs of the followers converge to a convex hull formed by the outputs of leaders. Finally, simulation examples are given for verifying the significance of proposed method.

A Mathematical Model about Neo-Classical Economy

We live in the era of market economy. Market and government intervention is tapering gradually. Classical planned economy has no longer adapted to the society instead of the private market in the neo-classical economic model. This paper use uses mathematics as a powerful tool, with specific examples of mathematical deduction, at the same time with graphic example, we have study the neo-classical economic model, solved the neatly and a non-equilibrium market evolve toward equilibrium.

Quantitative aging assessment method for cellulose pressboard based on the interpretation of the dielectric response mechanism

Cellulose pressboard is used as a key element in various power equipment insulation structures and determines the operational safety of electric equipment and power systems. This paper aims to increase the application of a pressboard aging assessment method based on frequency domain spectroscopy, a promising nondestructive method for power equipment diagnosis, through in-depth theoretical analysis and accurate data fitting. To achieve this purpose, first, based on classic theoretical models in the field of dielectric physics, a mathematical deduction is proposed to separate each dielectric process in the overlapping frequency band. Second, a novel analysis approach that considers both the pressboard dielectric response and the thermally stimulated current is proposed and demonstrated to be effective in determining the physical meaning of pressboard microscopic dielectric processes. Third, a function model based on a specific microscopic mechanism is established to fit the frequency domain spectra of pressboard samples with different aging degrees. Based on this approach, the variations in charge carrier motion characteristics in the frequency domain with increasing pressboard aging degree are clarified. Moreover, the function model provides characteristic parameters that are clearly related to the degree of polymerization of the material, which represents a quantitative method for evaluating the aging degree of cellulose pressboard by indirectly obtaining its frequency response curve.

An effective averaging theory for fractional neutral stochastic equations of order [formula omitted] with Poisson jumps

This paper, focusing on the fractional neutral stochastic differential equations (FNSDEs) in the Euclidean space Rn, successfully provides the first evidence of a new fractional averaging theorem via rigorous mathematical deductions. With the help of integration by part, the fractional term is handled simply and ingeniously. Based on this new idea, we show that the mild solutions of two fractional systems before and after averaging are equivalent in mean square sense. The study here gives a general approach to come up with the Khasminskii averaging principle for FNSDEs.

On the Pedigree of Hurwicz’s Economic Thought and Its Methodology

The mechanism design theory founded by Hurwicz is the inheritance and development of neoclassical economics. Hurwicz’s research did not deviate from Eggertsson’s statement of the hard core of neoclassical economics, but there were new developments in the theoretical framework and research methods by Hurwicz. On the one hand, he broke the old thinking framework that regarded system and mechanism as exogenous and nonadjustable variables. He introduced mechanism design into economic analysis, which deepened the understanding of the essence, change and choice of institution. On the other hand, he introduced game theory, a tool of mathematical analysis, into the study of market economy theory, especially the process of economic exchange and the theory of economic resource allocation. Although the core of game theory is still the utility maximization of rational economic man based on individual standard advocated by neoclassical economics, it also reveals the potential damage to the overall utility caused by the promotion of individual rationality lacking the spirit of cooperation. The economic theory innovation of Hurwicz is of great practical significance to the innovation and development of economics in China and the deepening of the market-oriented reform and opening-up in the new era.This paper provides the following conclusions through a literature survey of Hurwicz’s writings. Firstly, the mechanism design theory originated from the controversy over plan and market in the 1920s and 1930s and gradually extended to the core proposition of the relationship between government and market. Hurwicz established a pedigree of economic thought with inherent logic incorporating economic freedom, decentralized decision-making, information efficiency and incentive compatibility. Secondly, Hurwicz’s economic methodology focuses on the axiomatic logical analysis method of deductive reasoning. That is to say, it intends to interpret the economic world through functional relationship between digitized economic variables, mathematical logical deduction of axiomatic propositions and the equilibrium state in mechanical sense, emphasizes logical deduction over historical induction in research, reveals the logical mechanism from both holistic and individual points of view, and thus demonstrates the mechanism optimization of the real world.To sum it up, this paper extends the existing researches from three aspects. Firstly, it investigates Hurwicz’s economic thought in the context of the overall development of modern economics in the middle and late 20th century, and deconstructs the core propositions and basic elements in the pedigree of his thought. Secondly, it captures the logical substance and main characteristics of Hurwicz’s economic research methodology through a review of his academic track and achievements. Thirdly, based on the analysis of Hurwicz’s economic thought pedigree and its methodology, this paper sums up the implications for China’s further promotion of economic theory innovation and market-oriented reform deepening.

Colin Maclaurin (1698–1746) and his contemporaries on wind and water: the local and the universal

This paper explores the issue of geographical and social place in the community of mathematicians in the generation following Isaac Newton (1642–1727). It is informed by the approach of historical geographers to work in the field, and those studying the communication of mathematics in a broad sense. It considers Colin Maclaurin's circumstances in what he regarded as a remote location, arguing that he was not disadvantaged with respect to other Newtonian mathematicians and the rational mechanics of the period. Like his contemporaries, he communicated throughout Europe by means of the republic of letters, and also like them he had access to a particular local environment. Using the subject of water and wind power, a number of questions are posed regarding the efficacy of fluxions, the relative attention given to experiment and mathematical deduction, and changes in these emphases over time and place. While definite answers require further work, it has been possible, using a brief comparison with a few contemporaries, to reach the conclusion that different localities and social situations provided different opportunities, but that those of Maclaurin in Scotland were not impediments to the development of his mathematics or its applications.

Research on Mutual Inductance Prediction of Resonant Magnetic Coupling Wireless Power Transmission System Based on Recursive Least Square Method

In this paper, based on recursive least square algorithm and resonant magnetic coupling wireless power transmission technology, the magnetic coupling mutual inductance value, which is a significant factor affecting the transmission power and efficiency of wireless transmission system, is predicted. According to the characteristics of the system, a mathematical model of LCC-P-type topology structure is established. Through mathematical deduction and analysis, combined with MATLAB/Simulink simulation results are obtained, and its feasibility is verified by experimental results.

Volterra Expansion Based Intra Channel Nonlinear Effect Equalization Method for Optical OFDM/OQAM Systems

Optical orthogonal frequency-division multiplexing offset quadrature amplitude modulation (O-OFDM/OQAM) system relaxes the orthogonal condition of the sub-carriers from the complex domain to the real field. Inter-symbol-interference (ISI) and inter-carrier-interference (ICI) could be suppressed by using filter banks with promising time-frequency-localization (TFL) properties. Therefore, cyclic prefix (CP) inserted between consecutive OFDM blocks could be removed for O-OFDM/OQAM system to improve system spectral efficiency. When passing through fiber channel, O-OFDM/OQAM faces serious intrinsic imaginary interference (IMI) induced by chromatic dispersion (CD), and fiber nonlinear effect, which would deteriorate system performance evidently. Fiber nonlinear effect induced interference is a great impairment for long haul transmission O-OFDM/OQAM system, and can not be equalized directly by using nonlinear equalization method designed for traditional optical OFDM. There is still much room for improvement of nonlinear equalization method for O-OFDM/OQAM. In this paper, we systematically study Volterra expansion based nonlinear equalization method (VENE) for O-OFDM/OQAM. We theoretically deduce simplified Volterra series expansion nonlinear transmission matrix (SVEM) for O-OFDM/OQAM based on mathematic deduction. With SVEM, intra channel nonlinear effect induced distortions could be modeled and estimated. By using specially designed pilot blocks, we obtain approximate solution of SVEM and perform effective VENE with very limited complexities. As shown in multiple Montel Carlo simulation results, nonlinear robustness for O-OFDM/OQAM has been improved significantly thanks to VENE, with various transmission distances and system parameters.

A Novel Fault Detection Method for Running Gear Systems Based on Dynamic Inner Slow Feature Analysis

Process and sensor noise often affect the monitoring of slowly changing faults in high-speed trains, which seriously increases the difficulty of slow-change fault detection (FD). By introducing the idea of dynamic inner into the framework of multiple statistics, a novel dynamic inner slowness feature analysis (DISFA) is proposed in this article. This method considers both dynamic and static conditions and improves the detection speed of slow-change faults of running gears, and improves the detection rate of slow-change faults. Compared with other traditional methods, this method is more sensitive to slow changes, can effectively analyze fault-related data, and improve the detection efficiency of slow-changing faults. First, the validity of the method proposed in this article is proved by mathematical deduction, then it is verified by actual operation devices.

Time-Dependent Deformation Mechanism for Swelling Soft-Rock Tunnels in Coal Mines and Its Mathematical Deduction

AbstractThe floor heave and the inward movement of sidewalls are often encountered in the excavation of tunnels with swelling rock properties. However, the deformation mechanism for swelling soft-r...

Component damping evaluation in sub‐synchronous oscillation based on transient energy flow method

In recent years, sub-synchronous oscillations have occurred frequently. Torsional interactions may cause oscillations in turbo-generator rotor shafts and thus huge losses. Conventional studies focus on the damping of system oscillation modes, but little on the damping of components, which could aid in finding out the source of a poorly damped or undamped oscillation. This study aims at a quantitative evaluation method of the damping characteristics of each component in torsional interaction. The transient energy flow method successfully applied in component damping evaluation and source location of low-frequency and ultra-low-frequency oscillations is further developed for that of sub-synchronous oscillation. The transient energy flow method evaluates the damping of a component by its dissipation rate of transient energy. A method of computing the transient energy flow in sub-synchronous oscillation is proposed. It is found that the rate of energy flow is relevant to the difference between the super-synchronous and sub-synchronous powers. The relation between the transient energy dissipation and the damping of a component is validated by both mathematical deduction and simulation results. The transient energy flow method can evaluate component damping and therefore locate oscillation sources effectively in sub-synchronous oscillation.

No-overflowing Magnification Scheme in Redundant CORDIC algorithm and its implementation in FPGA

In this paper, normalization and magnification methods to maintain the calculating accuracy of CORDIC algorithm for small amplitude inputs are discussed, especially the overflowing boundaries are analyzed through mathematical deduction and the correctness has been proven by simulation. Finally, the FPGA implementations of different methods are conducted, which shows that the proposed magnification factor chosen scheme has an effective reduction on hardware resources consumption compared with the conventional normalization method.

A novel POD reduced-order model based on EDFM for steady-state and transient heat transfer in fractured geothermal reservoir

A new proper orthogonal decomposition reduced-order model (POD-ROM) for fluid flow and heat transfer processes in a fractured geothermal reservoir is proposed. First, the primary governing equations are established based on the embedded discrete fracture model. Second, the POD-ROM is developed by projecting the discrete matrix equations instead of the primary governing equations onto the low-dimensional space spanned by the pressure and temperature basis functions. Compared with the typical POD modeling method, the new model reduction technique can easily deal with mass and energy transfer between the matrix and fractures, thus ensuring the mass and energy conservation of the whole system in the projection process. The new model does not require complex mathematical deduction and is easy to implement in practical applications. The accuracy and robustness of the model were carefully studied for three complex heat transfer cases. Calculation results indicated that the computational efficiency can be improved by at least 10–15 times while high reconstruction and prediction accuracy is maintained.

Real-Time Pricing of Smart Grid Based on Piece-Wise Linear Functions

Abstract In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption; cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility, and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal; they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.

Depiction of Physiological Homeostasis by Self-Coupled System and Its Significance.

The negative feedback system (NFS) was regarded as the basic unit of regulation of physiological homeostasis for more than 70 years. However, NFS-based depiction possesses some limitations. The self-coupled system (SCS), a non-stop system in which the output of the current moment becomes the input of the next moment, can also be utilized to depict homeostasis. In SCS-based depiction, all of the related regulatory mechanisms of a homeostasis are regarded as an entity. Then, homeostatic dynamics can be expressed by simple mathematical language. A new disease group was revealed and some useful inferences were obtained through mathematical deduction. They were supported by published studies. SCS-based depiction of homeostasis should be a requisite supplement to medical knowledge systems based on NFS.

Comparative study on the transversal/lengthwise thermal failure propagation and heating position effect of lithium-ion batteries

Because of the multi-layer structure and the diversified connection modes of most battery modules, systematically investigating the thermal failure propagation principles and mechanisms of lithium-ion batteries is critical to provide early warnings and protection for thermal runaway. In this work, a series of experimental studies and mathematical deductions were conducted to investigate the propagation behavior of thermal failures within two types of cells under various heating modes, and their heat transfer mechanisms were analyzed. In general, the thermal runaway phenomenon in Li (Ni1/3Co1/3Mn1/3) O2 cells is more severe than that in LiCoO2 cells. For different heating modes, lengthwise thermal failure propagation is more unlikely to occur in comparison with transversal thermal failure propagation; however, the former involves a more violent combustion. For different heating positions, heating near the positive pole results in the most violent phenomena. Additionally, a higher Tmax of 185.6 °C was obtained via middle heating in comparison with that obtained via heating on the poles. The temperature rising rate also varied, taking 1619, 1578, and 1699 s for the temperature to rise from 20 °C to 168.9 °C, 185.6 °C, and 173.4 °C through bottom, middle, and top heating, respectively. These phenomena were consequently ascribed to the different heat transfer rates along different directions inside the cells, including transversal/lengthwise propagation, and positive-pole-directional/negative-pole-directional propagation. These encouraging results may raise concerns about developing more precise and suitable surveillance and control measures to further enhance the thermal safety performance of cells/modules from both external and internal perspectives.

Bridgeless Buck-Boost PFC Rectifier with Positive Output Voltage

A bridgeless buck-boost power-factor-correction (PFC) rectifier with positive output voltage is proposed herein. This PFC rectifier operates in the discontinuous conduction mode (DCM). Owing to the DCM, a good performance on PF is easily achieved as well as no reverse recovery currents being generated from the diodes. By means of output voltage sensing along with the traditional voltage-follower control, a proper control force is created to drive the switches. By doing so, not only the output voltage is stably controlled at a given value, but also the input current tracks the input voltage as tightly as possible. In addition, the accompanying harmonic distortion meets the requirements of the IEC6100-3-2 Class C harmonics standard, and accordingly, the proposed rectifier is suitable for the AC-DC LED driver. Finally, via mathematical deductions and experimental results, the effectiveness of the proposed bridgeless buck-boost PFC rectifier is verified.

Electromechanical Transient Modeling and Control Strategy of Decentralized Hybrid HVDC Systems

This paper studies the electromechanical transient model and the control strategy of line commutated converter (LCC) and modular multilevel converter (MMC) based decentralized hybrid High Voltage Direct Current (HVDC) Transmission systems. The decentralized hybrid HVDC system is a new type of topology, and the related electromechanical transient model and control strategy have not been studied well. In this paper, the electromechanical transient model of a decentralized hybrid HVDC system is devloped through mathematical deduction. This model can be easily implemented in electromechanical transient simulation software and meet the time domain simulation requirements of large-scale systems. Then, in order to ensure the safe absorption of the DC power under various conditions, an optimal power flow model considering the decentralized hybrid HVDC system is proposed. Finally, the electromechanical transient model proposed in this paper is verified by the electromagnetic transient model, and the control strategy is validated in a modified New England 39-bus system.

Detection of a Semi-Rough Target in Turbulent Atmosphere by an Electromagnetic Gaussian Schell-Model Beam

The interaction of an electromagnetic Gaussian Schell-model beam with a semi-rough target located in atmospheric turbulence was studied by means of a tensor method, and the corresponding inverse problem was analyzed. The equivalent model was set up on the basis of a bistatic laser radar system and a rough target located in a turbulent atmosphere. Through mathematical deduction, we obtained detailed information about the parameters of the semi-rough target by measuring the beam radius, coherence radius of the incident beam and the polarization properties of the returned beam.

Mathematical deduction of a new model for calculation of heat transfer by condensation inside pipes

This paper presents a mathematical deduction of a new improved model for heat transfer during condensation inside tubes. This new model has been developed with the aid of the Gaussian Equation for an infinite straight line, considering this relation with the differential equations that govern the heat transfer process. The proposed model was verified by comparison with available experimental data of 22 different fluids, including various refrigerants, water, and organic substances, which condense inside vertical, inclined and horizontal tubes. The proposed model is valid for an reduced pressure values ranging from 0.0008 to 0.91, values of Reynolds number for single-phase between 68 and 84,827 and for Reynolds number for two-phase between 900 and 59,4373, a range of internal diameters ranging from 2 to 50 mm, vapor quality from 0.01 to 0.99, Pr values for single-phase from 1 to 18 and mass flux rates in the ranges of 3 to 850 kg/(m2s). The mean deviation found for the analyzed data for horizontal tubes was 11.8%, while for the vertical and inclined tubes data the mean deviation was 13.0%. In all cases, the agreement of the proposed model is good enough to be considered satisfactory for practical design.