Mathematical Deduction Research Articles

A new model for contact angle hysteresis of superhydrophobic surface

Contact angle hysteresis (CAH) is essential to characterize the wetting properties of a surface. But its underlying causes are not yet understood. A model relating to CAH is presented through mathematical deduction. The calculation results coincide well with several experimental data from previous findings in literatures. Factors affecting CAH are investigated. This study offers new insight into the understanding of CAH and offers useful guidance for the preparation of superhydrophobic surfaces.

The Lorentz transformations and one observation in the perspective of fractional calculus

The Lorentz transformations are a key element in the Special Relativity Theory. Their deduction is a consequence of three physical principles, namely, relativity, homogeneity and isotropy, although this issue is commonly omitted. In the first part of the paper, we provide a rigorous mathematical deduction for the formula of Lorentz transformations, including a generalization for accelerated frames. In a second part, we establish a relationship between the formulations in the perspective of integer and Fractional Calculus. We examine when a magnitude (measured as an integral from the point of view of one observer) can be computed as a fractional integral from the point of view of the other observer. Finally, we compute the velocity in a relativistic travel from the solution of a given fractional integral equation.

The Design of Looped-Synchronous Mechanism With Duplicated Spatial Assur-Groups

The looped-synchronous mechanism (LSM) is a special one degree-of-freedom (DOF) closed chain of transmission with a large number of duplicated units that synchronizes the motion of many output links. This kind of mechanism can be found in many applications such as stator blade adjusting mechanisms for various aero-engines. The LSMs are composed of a large number of links and joints and must be designed by specific means. Spatial Assur-group, which is a concept extended from traditional Assur-group(in planar scope), and usually with a little number of parts and joints, is used in this work to design LSM. First, based on the formula of DOF of spatial Assur-group, all possible combinations are listed and two feasible combinations are chosen as the main body of each unit of LSM, combining with a prime mover to meet the requirement to be inexpandable and adjustable. Second, the condition for transmission ratio of the used Assur-group to be 1 is distilled for being synchronous and looped under the situation that all units of LSM have the same topology. To meet the condition, the needed dimensional conditions are researched and mathematical deduction is used to figure out the possibilities. Third, after confirming that it is impossible to meet the condition strictly, an optimization method in the environment of Simulink is used to approach the condition as close as possible. Finally, numerical and dynamic simulations are carried out to verify the effectiveness of the mentioned methods.

A novel unified method for the fast computation of discrete image moments on grayscale images

We proposed a new method to compute the discrete image moments in this paper. By simple mathematical deduction, the discrete image moments can be transformed into first-order moments. Therefore, the fast algorithm for first-order moments’ calculation can be used to compute discrete image moments. We also design an efficient computation structure based on systolic array to implement this approach. Since our method does not use the moment kernel polynomials’ properties in the calculation process, the proposed method can be used to compute any discrete image moments in the same way. The presented algorithm has several advantages such as regular and simple computation structure, without multiplication, independent of the image’s intensity distribution, applicable to any discrete moment family. Various experiments demonstrate the effectiveness of the proposed algorithm in comparison with some state-of-the-art methods.

Mathematical Base and Deduction of Security Region for Distribution Systems With DER

This paper presents the mathematical definition and deduction for distribution system security region (DSSR), which lays a foundation for the DSSR theory. The DSSR is the set of all the N-1 secure operating points in the state space of a distribution system. First, this paper proposes the strict mathematical definition of DSSR, which defines that a set can be called a “region” only if three mathematical conditions are satisfied. Then, the N-1 security is deducted, based on which DSSR is proved existing and is mathematically deducted. As a basic feature of the future smart distribution system with distributed energy resources, the bidirectional power flow is fully considered in the deduction. In the conclusion, the observation and mathematical deduction both show the existence of security region for any distribution system.

Super-resolution Geometry Processing Technology for Ill-sampled Astronomical Images

In order to improve the cell sensitivity or to satisfy the needs of a large field of view, a large size CCD pixel is usually chosen as detection unit in optical imaging systems. However, this methodology cannot meet the Nyquist sampling theorem, and thus generate ill-sampling images. In other words, the geometric resolution of images in optical diffraction limited systems is directly restricted by the size of CCD pixel. In this paper, a carefully designed optical mask is implemented to ensure loseless images before CCD sampling. By applying spatial spectral filtering technology, we can acquire images with appropriate resolution. The method presented in this paper significantly abates the resolution decline due to ill-sampling. By mathematical deduction and simulation, the geometric super resolution images can be achieved.

Robust multi-product inventory optimization under support vector clustering-based data-driven demand uncertainty set

A robust multi-product inventory optimization approach is developed with an uncertainty set constructed from the available data using support vector clustering (SVC). The multi-product inventory problem is subject to demand uncertainties in a newsvendor setting with the historical demand data as the only available information. By using SVC, the uncertainty set to which the uncertain demands belong is constructed with a certain confidence in a data-driven approach. The associated robust counterpart model is then developed using the absolute robustness criterion. Through mathematical deduction, the proposed counterpart model is transformed into a tractable linear programming model which can be solved efficiently. The transformed and the original models are proved to be mathematically equivalent. Numerical studies are conducted to illustrate the effectiveness and practicality of the proposed SVC-based data-driven robust optimization approach for dealing with demand uncertainties. The results show that the robust optimization approach under the proposed SVC-based uncertainty set outperforms those under the traditional, i.e., the box and the ellipsoid, uncertainty sets. These results provide evidences that the proposed data-driven robust optimization approach can better hedge against demand uncertainties in multi-product inventory problems.

Stability analysis of spinning missiles induced by seeker disturbance rejection rate parasitical loop

This paper focuses on the dynamic stability of spinning missiles equipped with two-loop autopilot considering the seeker disturbance rejection rate parasitical loop (DRRPL) effect induced by attitude disturbance of projectile. The representative mathematical model of spinning missiles in the non-spinning coordinate system is established, and the cross-coupling effect between the pitch and yaw induced by the rotation motion of missile body is analyzed and decoupled. The two-loop acceleration autopilot for each channel is designed with the conventional design method, and the relationship between the autopilot gains and the expected design indexes is deduced. A proportional navigation guidance (PNG) system model with consideration for the seeker DRRPL is further proposed in the form of complex summation. After strict mathematic deduction, the sufficient and necessary condition of the dynamic stability for spinning missiles is obtained. Numerical simulations and discussions under different cases are conducted to demonstrate the validity of stability condition. The results indicate that the stability of a spinning missile is closely related to the amplitude of the seeker DRR, the rolling rate, and the autopilot design indices. The stable region of the autopilot design frequency is obtained by solving the dynamic stability condition. To meet the requirement of stable controlling at a constant spinning rate, it was found to be effective to decrease the amplitude of the seeker DRR for spinning missiles, employ the lead angle decoupling approach to the commands for the servo system, and guarantee that the autopilot design frequency is lower than the critical value. The dynamic stability condition derived in this paper is useful for evaluating the stability of a spinning missile with consideration for the seeker DRRPL, and the conclusions obtained can provide guidance for the autopilot design of spinning missiles.

A Sensorless Rotor Position Estimation Method Based on the Field Current Harmonic for an LCI-Fed EESM

In this paper, a sensorless rotor position estimation method based on the field current harmonic for a load-commutated inverter (LCI)-fed electrically excited synchronous motor (EESM) operating at zero or low speed is proposed. A detailed theoretical analysis and mathematical deduction are presented. The field current harmonic is used instead of the extra high-frequency signal injection. A reasonable harmonic frequency is selected, and a realizable field current control method is given. To simplify the complex signal processing and improve the measurement accuracy, a specific bandpass filter and a normalized quadrature phase-locked loop are designed. The phase change caused by the filters is compensated properly. The proposed approach is demonstrated through the simulation and experiment with a 15-kW LCI-fed EESM drive platform, confirming its feasibility and accuracy.

Strategy Determined Partnerships for Innovation: A Triple Helix Analysis of the Dynamics of Partnership Conditions with Evidence from an Emerging Economy

Systems emerge, grow and evolve. Triple helix relations are not immune to such conditions. We theoretically review three hypothesis that we believe play a major role in the strategic decision making of individual agents within innovation networks. Using simple mathematical deductions, we show that cluster tendencies in conjunction with knowledge levels vis-í -vis projected benefits influence the partnership formation. Using Games Theory, we further show the possible adopting strategies that agents may activate to maximize benefits.

Hacia una explicación de las coaliciones: una taxonomía de modelos formales de formación y colapso de los Gobiernos

CCoalition theory is one of the fields that has extensively benefited from formal modelling in political science. Since the publication of William Riker’s (1962) seminal book, a variety of coalition models has been developed to explain government formation and breakdown. Nevertheless, despite the diversity of models, the literature seems to judge their predictability solely in terms of empirical tests, usually deriving hypotheses from their propositions and testing via statistics. In this work, I survey classical and more recent formal models in coalition theory, demonstrating how they serve different purposes. I build a taxonomy of models that acknowledges these purposes, and, more importantly, the roles they play in building explanations about coalitions. I identify three types of models: conceptual models, whose conceptual and theoretical value relies on the mathematical deductions entailed in the model; quasi-conceptual models, which formalise explanations of regularities in the real world; and extrapolative models, which allow for an empirical test of formal models via a variety of statistical methods. All of these types of models coexist, generating explanations and setting research agendas.

Interval Tree and Its Application in Integer Factorization

The paper first puts forward a way to study odd integers by placing the odd integers in a given interval on a perfect full binary tree, then makes an investigation on the odd integers by means of combining the original properties of the integers with the properties of the binary trees and obtains several new results on how an odd integer's divisors distribute on a level of a binary tree. The newly discovered law of divisors' distribution that includes common divisors between two symmetric nodes, genetic divisors between an ancestor node and its descendant node can provide a new and simple approach to factorize odd composite integers. Based on the mathematical deductions, numerical experiments are designed and demonstrated in the Maple software. All the results of the experiments are conformance to expectation and validate the validity of the approach.

An Adaptive Estimation of Distribution Algorithm for Multipolicy Insurance Investment Planning

Insurance has been increasingly realized as an important way of investment and risk aversion. Fruitful insurance products are launched by insurers, but there is little research on how to make a proper insurance investment plan for a specific policyholder given different kinds of policies. In this paper, we aim to propose a practical approach to multipolicy insurance investment planning with a data-driven model and an estimation of distribution algorithm (EDA). First, by making use of the insurance data accumulated in the modern financial market, an optimization model about how to choose endowment and hospitalization policies is built to maximize the yearly profit of insurance investment. With the model parameters set according to the real data from insurance market, the resulting plan is practical and individualized. Second, as the optimal solution cannot be achieved by mathematical deduction under this data-driven model, an EDA is introduced. To adapt the EDA for the considered problem, the proposed EDA is mixed with both the continuous and discrete probability distribution models to handle different kinds of variables. In addition, an adaptive scheme for choosing suitable distribution models and an efficient constraint handling strategy are proposed. Experiments under different conditions confirm the effectiveness and efficiency of the proposed model and method.

Terminal computing for Sylvester equations solving with application to intelligent control of redundant manipulators

Sylvester matrix equations are widely used in many engineering fields. When referred to the time-varying Sylvester, the computational time increases sharply because of the heavy burden calculations for not satisfying the computational requirement. Recently, a type of asymptotic neural networks called Zhang neural network (ZNN) has been proposed to achieve astonished convergent speed for Sylvester computing problems as long as the time goes to infinity. How to make the convergent rate to finite time is worth to think about, which induces us to find a finite-time method to accelerate the convergent speed. To tackle this problem, two types of recurrent neural models named terminal computing neural dynamics (TCND) and its accelerated form (ATCND), which are of terminal attraction characteristics are constructed. The proposed neural dynamics are developed not only to accelerate the convergent speed, but also to improve the convergent accuracy of the dynamic error generated by time-varying systems. The upper bound of the convergent time is given via mathematical deduction. In addition, simulation performances of time-varying Sylvester equations are evaluated by TCND, ATCND and ZNN for comparison. Furthermore, a repeatable trajectory motion scheme based on TCND is derived for the solution of trajectory planning with redundant manipulators. Experimental results validate the effectiveness of the novel neural solving dynamics.

Ground Attack Strategy of Cooperative UAVs for Multitargets

Humans have a fundamental ability, that is, to share vision among each other to fulfill common goals, which cooperative UAVs do not have. The difficulties mainly lie in the homologous mathematical description of humans and elusive experimental practice. This paper proposed a parallel multiview splicing on clouds, which first review both theory and practice studies in UAVs. These terms are then reconsidered from humans’ vision sharing. Next, a conceptual model of parallel multiview splicing on clouds is proposed and the mathematical deduction if fulfilled. Furthermore, an experimental cooperative UAVs platform is built to practically implement the algorithms. Both the simulated and practiced results have validated the feasibility of our method. Finally, a general discussion and proposals for addressing future issues are given.

Hybrid Control Scheme for Three-Phase Multilevel Unidirectional Rectifier Under Unbalanced Input Voltages

In this paper, a hybrid control scheme for three-phase Y-connected multilevel bridgeless rectifier (TMBR) under unbalanced input voltages is presented, based on the mathematical model of the TMBR topology, with the emphasis on the discussion for power fluctuation suppression, dc-link capacitor voltages balancing and input current zero-crossing distortion elimination. With the hybrid control scheme, the power fluctuation can be suppressed and three-phase input currents can flow with a purely sinusoidal waveform, besides, three-phase dc-link capacitor voltages can be controlled to be equal to each other under unbalanced input voltages. Moreover, the proposed hybrid control scheme is applicable to all other three-phase three wire multilevel unidirectional rectifiers under unbalanced input voltages. The validity of the proposed control scheme is demonstrated by the mathematical deduction. The simulations and experimental results verify that, with the proposed control scheme, TMBR can stably operate not only under balanced input voltages but also under unbalanced input voltages.

Unmanned Aerial Vehicle Perception System Following Visual Cognition Invariance Mechanism

Humans have a fundamental ability that is fulfilling visual perception with complex brain functions, while intelligent sensors onboard UAVs do not have. The difficulties mainly lie in the inexhaustive study of brain science and the homologous mathematical description. In this paper, a visual cognition invariance mechanism has been proposed, which first review studies in brain research, moving from theoretical to practical. These terms are then reconsidered from brain pathways of visual perception. Next, a conceptual model of visual cognition invariance mechanism is proposed and the mathematical deduction is fulfilled. Furthermore, an experimental unmanned aerial vehicle is built to practically implement the proposed algorithm. The simulation results and experimental practices have validated the effectiveness and celerity of our method. Finally, a general discussion and proposals for addressing future issues are given.

Drivers to equity valuation: Perpetuities or annuities approach? An application to the main European stock markets

Academics and practitioners have been applying equity valuation methods mainly based on discount cash flow models, residual income models or dividend discount models combined with balance sheet and income statement multiples of market comparables to analyse share price and to provide price targets for investors or even base for transactions such as mergers and acquisitions (M&A). Most of those methods rely on mathematical deductions of growing or constant perpetuities or near perpetuities (such as annuities) to attain market values. However, it is of the outmost relevance for valuation to verify how the theoretical models relate with real values and what is its relationship with companies’ firm past age. Beyond stating a non-linear relationship for valuation models and ascertain important valuation drivers, using a sample of more than 3400 European companies with cross section data, this paper contributes to the improvement of valuation model’s effectiveness by inducing non-explicit period valuation modifications to long term annuities and perpetuities considering class age intervals. This paper’s originality is supported by the study of the relation of past company age with predicted annuities, the proof of non-compliance of perpetuity-based valuation models and the contribution with new value drivers for valuation purposes.

An Impedance Measurement Method at Controlled Frequency Band for Both Traction Power System and Electric Train

Abstract Electric railway systems occur instability and oscillation frequently for the mismatched impedances between the traction power system (TPS) and the voltage-source-converter (VSC)-based electric train. However, the parameters of both TPS and electric train (hereinafter TPS-train) are not fully known so that utilizing the mathematical deduction to quantify the impedances is difficult. This paper gives a method to measure the impedances at controlled frequency band. A chirp-PWM signal is introduced and utilized to drive the insulated gate bipolar transistor (IGBT) modules of disturbance circuit, which can produce a desired broad spectral excitation at controlled frequency band. The impedances can be then calculated with the corresponding response voltages and currents after connecting the disturbance to the tested system. Then, the stability and oscillations can be identified using the measured TPS and electric train impedances. The proposed method is easy to implement with its simple hardware structure and software control, and also it gives a high measurement accuracy. Simulations verify the effectiveness of this method.

Finite-Time Stability of a Time-Delay Fractional-Order Hydraulic Turbine Regulating System

Finite-time terminal sliding mode control of a time-delay fractional-order hydraulic turbine regulating system (HTRS) is studied. First, an improved Adams–Bashforth–Moulton algorithm is introduced to solve the fractional-order nonlinear system with a time delay. Then, given the unique advantage of fractional calculus and the great influence that time delay has on system stability, a time-delay fractional-order HTRS is introduced. Moreover, by means of a frequency distribution model, the transformation of the fractional-order HTRS is realized. To stabilize the system under the influence of a random disturbance, a novel terminal sliding surface and a controller are proposed, and the detailed mathematical deduction for system stability is given. Finally, the simulation results, compared with traditional proportional-integral-derivative control and the conventional sliding mode control in the existing literature, demonstrate the validity and significant advantages of the proposed finite-time control scheme.