Strict Proof Research Articles

A Modeling Framework for Schedulability Analysis of Distributed Avionics Systems

This paper presents a modeling framework for schedulability analysis of distributed integrated modular avionics (DIMA) systems that consist of spatially distributed ARINC-653 modules connected by a unified AFDX network. We model a DIMA system as a set of stopwatch automata (SWA) in UPPAAL to analyze its schedulability by classical model checking (MC) and statistical model checking (SMC). The framework has been designed to enable three types of analysis: global SMC, global MC, and compositional MC. This allows an effective methodology including (1) quick schedulability falsification using global SMC analysis, (2) direct schedulability proofs using global MC analysis in simple cases, and (3) strict schedulability proofs using compositional MC analysis for larger state space. The framework is applied to the analysis of a concrete DIMA system.

Distributed cooperative learning for a group of uncertain systems via output feedback and neural networks

This paper studies the problem of adaptive neural network (NN) output-feedback control for a group of uncertain nonlinear multi-agent systems (MASs) from the viewpoint of cooperative learning. It is assumed that all MASs have identical unknown nonlinear dynamic models but carry out different periodic control tasks, i.e., each agent system has its own periodic reference trajectory. By establishing a network topology among systems, we propose a new consensus-based distributed cooperative learning (DCL) law for the unknown weights of radial basis function (RBF) neural networks appearing in output-feedback control laws. The main advantage of such a learning scheme is that all estimated weights converge to a small neighborhood of the optimal value over the union of all system estimated state orbits. Thus, the learned NN weights have better generalization ability than those obtained by traditional NN learning laws. Our control approach also guarantees the convergence of tracking errors and the stability of closed-loop system. Under the assumption that the network topology is undirected and connected, we give a strict proof by verifying the cooperative persisting excitation condition of RBF regression vectors. This condition is defined in our recent work and plays a key role in analyzing the convergence of adaptive parameters. Finally, two simulation examples are provided to verify the effectiveness and advantages of the control scheme proposed in this paper.

Robust adaptive output feedback tracking control for flexible-joint robot manipulators based on singularly perturbed decoupling

SUMMARYThis paper presents a robust adaptive output feedback tracking controller for the flexible-joint robot manipulators to deal with the unknown upper bounds of parameter uncertainties and external disturbances. With applying the singular perturbation theory and integral manifold concept, the complex nonlinear coupled system of the flexible-joint robot manipulators is divided into a slow subsystem and a fast subsystem. A robust adaptive control scheme based on an improved linear parameterization expression is designed for the slow subsystem, and a saturation function is applied in the robust control term to make the torque output smooth. In the meantime, different from the previous approaches, the second-order derivative term of elastic torque is avoided by using the proposed computed torque method, which simplifies the implementation of the fast control law. Moreover, to carry out the whole control system with only position measurements, an approximate differential filter is involved to generate pseudo velocity signals for links and joint motors. In addition, an explicit but strict stability proof of the control system based on the theory of singularly perturbed systems is presented. Finally, simulation results verify the superior dynamic performance of the proposed controller.

Finite-Time Synchronization for a Class of Fully Complex-Valued Networks With Coupling Delay

In this paper, the problem of synchronization for a class of fully complex-valued networks with coupling delay is investigated by the linear feedback control in a finite time. The state variables, system function, inner coupling matrix, and outer coupling matrix in this model are set as complex values. By decomposing the complex-valued network into real and imaginary parts, an equivalent real-valued system is established. Based on the finite-time stability theory and Lyapunov functional method, linear feedback controllers are constructed to guarantee the synchronization for the complex-valued networks with or without coupling delay in a desired finite time. Then, some sufficient conditions for assurance of finite-time synchronization are given by strict proof. Finally, simulation examples are provided to verify our results.

On Full Duplex Scheduling for Energy Efficiency Maximization in Multi-Hop Wireless Networks

With the rapid innovations in the design of transceiver for full duplex (FD) communications, the benefits of FD for single-hop wireless communications have been widely shown. But in a multi-hop wireless network, the benefits of FD with power control still need to disclose. The goal of this paper is to investigate the energy efficiency (EE) performance of FD scheduling in a multi-hop wireless network. In this paper, we explore FD on EE in multi-hop networks under optimal scheduling through strict mathematical model, formulation and proof. First, an EE model under FD scheduling with power control in multi-hop wireless networks is constructed. Then, through exploiting the reformulation linearization technique to reformulate and piece-wise linearization method to approximate, the nonlinear optimization problem for EE under FD is transformed into a linear one and solved with performance guarantee. Finally, simulation results validate the proposed optimization method to achieve the optimal EE under FD with power control compared to half duplex with power control and FD without power control.

Chaotic analysis of fractional Willis delayed aneurysm system

The dynamic system of Willis aneurysm (WAS) has played an important role in theoretical and clinical research of cerebral aneurysms. Fractional differential is an effective mathematical tool that can describe the cerebral aneurysm system accurately and profoundly. However, the existing fractional Willis aneurysm system (FWAS) cannot describe the delayed aneurysm rupture of unknown cause in reality. Therefore, by introducing the time-delay factors into the existing fractional Willis aneurysm system as a rational extension, a new fractional Willis aneurysm system with time-delay (FWASTD) is proposed in this paper.First, FWASTD is introduced in the context, and the comparison of time sequences map between FWAS and FWASTD proves that FWASTD is feasible in the depiction of time-delay situations. The bifurcation diagram and the largest Lyapunov exponent diagram as well as the phase diagram of fractional order also confirm the chaotic characteristics of the FWASTD.Then, the classical analysis methods in chaotic dynamics, such as time series diagram, phase diagram and Poincar section are used to analyze FWASTD in detail. When studying the diagrams of time-delay factors for the important physiological parameters of the system, we find that blood flow resistance coefficient can exert a remarkable effect on the system stability under time-delay. Besides, the experimental results show that the FWASTD becomes stable with the increase of blood flow resistance under a certain condition. Usually, promoting thrombosis is a kind of adjunctive therapy in clinic for cerebral aneurysm. The results of this part can accord with the treatment in clinic and has great significance in clinical diagnosis.Finally, as the chaotic state of the time-delay system indicates that cerebral aneurysm is in a dangerous situation, the primary task of the control for this new system is to achieve stability rather than synchronization. The stability theory of fractional time-delayed system is adopted in a strict proof of the uniqueness of solution for the FWASTD. To make FWASTD stable, a corresponding linear controller is designed based on the stability theory of fractional order delay system. The numerical simulation indicates that the linear controller can control the blood flow velocity and speed up the periodic fluctuation within a small range, which illustrates that it is not easy to rupture the cerebral aneurysm. We also make self-synchronization control between FWASTD and FWAS just in case that the coefficients of the system are not clear.The research results in this paper, to some extent, can serve as theoretical guidance for the clinical diagnosis and the treatment of aneurysm.

A numerical algorithm to solve multivariate transcendental equation sets in complex domain and its application in wave dispersion curve characterization

A numerical algorithm that can quantitatively solve transcendental equation sets with multiple independent variables in the complex number domain is presented in this paper. A strict mathematical proof of solving the unary transcendental equation in the real domain is given in detail to show the process of the algorithm, which can be generalized to the equations with two or more variables. The complex variable concerned in this method is treated as two independent variables in real domain that represent the real part and the imaginary part of the variable, respectively. The criterion for choosing the dimension of scanning elements is given to overcome the difficulty in solving the general multivariate equation. Finally, the algorithm is applied in the problem of plotting 3-D dispersion curves in complex wave number and real frequency domains. Three examples are used to illustrate the correctness and effectiveness of the algorithm.

Dowodzenie związku przyczynowo-skutkowego w sprawach o zakażenia szpitalne

wiązek przyczynowo-skutkowy jest jedną z przesłanek odpowiedzialności świadczeniodawcy za zakażenie szpitalne. Jednakże trudności dowodowe występujące w sprawach o naprawienie szkody wyrządzonej pacjentowi z powodu zakażenia szpitalnego stanowią ważną, a zarazem wciąż problematyczną kwestię. Ustawodawca przyjął precyzyjną definicję, w myśl której zakażenie szpitalne pozostaje w funkcjonalnym i adekwatnym związku przyczynowo-skutkowym z udzielaniem świadczenia medycznego. W procesie cywilnym to poszkodowany musi uprawdopodobnić i udowodnić powstanie związku przyczynowego między winą podmiotu leczniczego a zaistniałą szkodą. W procesach medycznych sąd może, po rozważeniu całokształtu okoliczności sprawy, uznać za wystarczający wysoki stopień prawdopodobieństwa, nie wymagając ścisłego i pewnego udowodnienia, jaką drogą organizm został zainfekowany, taki bowiem dowód – ze względu na właściwości procesów biologicznych – często nie jest możliwy do przeprowadzenia. Zatem jeżeli brak możliwości ścisłego udowodnienia związku przyczynowo-skutkowego pomiędzy zakażeniem a szkodą w postaci rozwoju choroby, będący wynikiem obecnego stanu wiedzy medycznej, winien zostać rozważony na płaszczyźnie art. 6 i art. 361 § 1 k.c. Powyższe ograniczenia dowodowe i charakter spraw, w których występują, skutkują także swoistym przemieszczeniem ciężaru dowodu. W przypadku nierealnego wymogu ścisłego udogodnienia, jakimi drogami infekcja przedostała się do organizmu, jeżeli strona pozwana twierdzi, iż mimo ustalonego stanu rzeczy infekcja pochodzi z innych źródeł, ciężar dowodu przesuwa się na pozwanego, czyli podmiot leczniczy.

Jammed systems of oriented needles always percolate on square lattices.

Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Several studies have recently conjectured that in the RSA of rectangular needles, or k-mers, on a square lattice, percolation is impossible if the needles are sufficiently long (k of order of several thousand). We refute these claims and present rigorous proof that in any jammed configuration of nonoverlapping, fixed-length, horizontal, or vertical needles on a square lattice, all clusters are percolating clusters.

Self-supported Gd-doped ceria films for electromechanical actuation: Fabrication and testing

In this study, we explored the feasibility of employing Gd-doped ceria (GDC) thin films (1–2μm) as functional, mechanically reliable material for microelectromechanical systems (MEMS). Self-supported structures, based on microscopic-scale GDC membranes, bridges, and cantilevers, were fabricated using Si-compatible processes and materials. With voltages of different amplitudes and frequencies and a variety of metal electrodes, we monitored structural stability and device response. The membrane-based structures displayed much higher stability under voltage and better mechanical robustness than those based on bridges or cantilevers. At low frequencies (a few Hz), the use of Ti contacts resulted in observable displacement of the membranes in the presence of moderately low voltage (≤10V/1.6μm), while Al, Cr, and Ni contacts did not provide such functionality. Although for all contact metals tested, formation of a blocking layer at room temperature is evident, for the case of Ti, the barrier height is much lower. In view of the fact that the crystallographic space group of weakly doped GDC is Fm-3m, the electromechanical response of the microfabricated GDC membranes is most likely electrostrictive, but a strict proof is not yet available. At high frequencies (>100kHz), the membranes produce lateral displacement as large as several microns due to Joule heating, i.e., a thermo-electromechanical response.

Max–Min Weighted Downlink SINR With Uplink SINR Constraints for Full-Duplex MIMO Systems

In this paper, we investigate a max–min weighted signal-to-interference-plus-noise-ratio (SINR) problem in a full-duplex multiuser multiple-input-multiple-output system, where a full-duplex-capable base station (BS) equipped with multiple antennas communicates with multiple half-duplex downlink and uplink users under the same system resources. Specifically, we consider a practical scenario where the downlink minimum weighted SINR is maximized under specific SINR constraints for uplink users. Moreover, the optimization is conducted by jointly considering the BS transmit power, the transmit power of uplink users, and BS transmit and receive beamforming. This optimization problem is, therefore, subject to multiple uplink SINR constraints and multiple transmit power constraints. Due to the SINR constraints, negative matrix components arise and hence the optimization problem cannot be directly solved by the standard approach, i.e., Perron–Frobenius theory. We have provided an explicit iterative scheme to solve this joint optimization problem with a strict proof. The proposed algorithm is proved to converge to Karush–Kuhn–Tucker points. Simulation results show that our proposed algorithm has a fast convergence rate and leads to a better performance compared with other optimization techniques that do not jointly consider all parameters.

Synchronization analysis of fractional-order neural networks with time-varying delays via discontinuous neuron activations

Abstract In this paper, we study the drive-response synchronization for a class of fractional-order delayed neural networks with discontinuous activations(FDNNDAs). Under the framework of Filippov solutions, the concept of fractional-order Filippov solution for the initial value problem of FDNNDAs is introduced. The global existence of Filippov solutions to FDNNDAs is guaranteed by the given growth condition and strict mathematical proof. State feedback controller and adaptive controller are designed respectively to ensured the global synchronization of the FDNNDAs. Based on the nonsmooth analysis and the Razumikhin-type stability theorem, several new synchronization conditions are derived. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.

Research on Road Dangerous Goods Transport System Risk Evaluation Method: Based on Translation-Corrected Entropy Weight Method

In order to evaluate the road dangerous goods transportation system risk (RDGTSR) objectively, we divided the system into four sub-systems including Human (H), Machine (M1), Environment (E) and Management (M2), used the happened road dangerous goods transport accidents number and translation-corrected Entropy Weight Method (EWM) to calculate coupling coordination degree (CCD), established a new RDGTSR evaluation approach. We introduced the information loss tolerance coefficient (ILTC) to control the data information loss in a reasonable range when we applied the translation-corrected EWM to obtain the weight, the strict mathematical proof and case study results show that the smaller of the ILTC, the final weight is closer to the weight without translation-corrected. Also the case study results show that three-factors coupling degree is higher than both two-factors and four-factors coupling degree, higher coupling degree means higher risk to cause dangerous goods transport accidents. Meanwhile, CCD is higher during January to June than the value during July to December, higher CCD means better development of road dangerous goods transport system, higher degree of system harmony and orderliness degree, and easy to cause a road dangerous goods transport accident.

Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control

Considering the fact that time delays are unavoidable in the control of practical systems, this paper considers globally exponential synchronization of complex-valued complex dynamical networks with multiple time-varying delays and stochastic perturbations by designing a time-delayed impulsive control scheme. By taking the advantage of Lyapunov method in complex field and utilizing an impulsive inequality with delays, several synchronization criteria are obtained through strict mathematical proofs. Our results are general which extend some existing ones concerning impulsive synchronization. A numerical example is given to illustrate the effectiveness of theoretical results.

Flaws in classical proofs of vector Kirchhoff integral theorem and its new strict proof

The vector Kirchhoff integral theorem (VKI) is an important formula in electromagnetic (EM) theory,especially it is a basis of the optical diffraction theory.Recently,it has been found that there exist some flaws in the proofs presented in the literature.There are mainly two types of methods to prove the VKI.The first type of method is to employ the vector analysis to prove the VKI directly.Some flaws of this type of proof presented in the literature have been found and pointed out in this paper.The second type of method is to employ the scalar Kirchhoff Integral (SKI) to directly obtain the VKI. The SKI was first derived by Kirchhoff (1882).In spite of its mathematical inconsistency and its physical deficiencies, the SKI works remarkably well in the optical domain and has been the basis of most of the work on diffraction.However, the proofs for SKI usually need the scalar radiation conditions.The scalar radiation condition was first proposed by Sommerfeld to ensure the uniqueness of the solution of certain exterior boundary value problems in mathematical physics. But whether the scalar radiation conditions were suitable for the EM was not sure.In fact,for electromagnetic field,we have another vector radiation conditions which have been verified to be adaptable for all the radiation and scattering fields.It is difficult to obtain the scalar radiation conditions directly by just separating three Cartesian directions from the vector one,because the different scalar components are coupled together after the rotation and cross product operation.Actually,few strict proofs could be found to support the fact that EM satisfies the scalar radiation condition. So as the supplementary,the scalar radiation conditions will be derived in detail with far-field approximation method in this paper.To avoid using the scalar radiation condition which may bring some non-rigorousness,we perform a new strict proof for the VKI by using the vector analysis identities. The rest of this paper is organized as follows.In Section 2,the different proofs presented in the classical books will be analyzed in detail.The flaws existing in these proofs will be pointed out.After that,in Section 3,based on the Stratton-Chu formula,a new strict proof will be given with using the vector identities.In Section 4,a sensitivity analysis is numerically performed to confirm our demonstration.Finally,the conclusions are drawn from the present study in Section 5.The scalar radiation conditions will be discussed in the appendix.

On the Origin of Charge-Asymmetric Matter. III. Properties of Autolocalized Dirac Waveforms

This paper continues the author’s work [1] [2], where a novel framework of the matter-induced physical geometry was built and an intrinsic nonlinearity of the Dirac equation was discovered. The previous analysis of solitary waveforms’ properties [2] is extended to the four-component Dirac field. It is found that the internal spherical symmetry of the Dirac waveforms is broken to the axial one. The nonlinear Dirac equation is solved and the localized configurations are found analytically. A strict proof that the proper time slowdown is the major mechanism of autolocalization is presented. The previous qualitative conjecture regarding stability or instability of the two types of the waveforms and the origin of cosmological charge asymmetry is supported by detailed analysis. A solution of the problem of mapping between the matter-induced geometry of autolocalized waveforms and the geometry of an ambient Minkowski space is proposed. These results resolve the longstanding puzzle of how the physical Dirac field of real matter becomes a finite-sized particle.

TJET: Ternary Join-Exit-Tree Based Dynamic Key Management for Vehicle Platooning

Vehicle platooning, which is formed by a group of vehicles traveling in close proximity to one another, nose-to-tail, at highway speeds, has received considerable attention in recent years. However, though it brings many opportunities in self-driving, the security of vehicle platooning is still challenging. In this paper, to secure vehicle platooning, particularly to secure communication and efficient key updating for vehicles in a platoon, we first present the notion of ternary join exit tree. A ternary join exit tree consists of main tree, join tree, and exit tree. The users join in the join tree and leave from exit tree. Then, we propose a new dynamic ternary join-exit tree-based dynamic key management scheme, called TJET, for vehicle platooning, which is characterized by providing efficient key updating for not only vehicle joining and leaving, but also platoon merging and splitting. Specifically, based on the structure of ternary join-exit tree, we devise concrete algorithms for vehicle joining, vehicle exiting, platoon merging, and splitting. Moreover, we also analyze the capacities and activation conditions of join tree and exit tree based on strict mathematical proofs. Detailed security analysis show that our proposed TJET holds desirable security properties including forward security, backward security, and resistance to key control. In addition, performance evaluations via extensive simulations demonstrate the efficiency of TJET.

Strict Proof of the Perfection of the First 98 Masks (Solution to the “X-Problem of the Number 3”)

The proof of the perfection for the first 91 normal Masks in one dimension and for the seven normal Masks in two dimensions is completed (all the centrally symmetric masks are not differentiated and are counted as one). A method is indicated for proving the Perfection of (presumably) any appropriate Mask (which is Perfect).

Ponovljenje parnice po odredbama Zakonika o građanskom sudskom postupku iz 1865. godine

The article sheds light on provisions of legislation from 1865 concerning retrial as sole extraordinary legal remedy, its amendments and supplements, as well as judicial practice regarding repetition of judicial proceedings. Party in a civil lawsuit entitled to remedy was the plaintiff who had been considering himself aggrieved by a court decision from which no appeal was longer allowed, and who came into possession of new and important matter of evidence. It is necessary that, at the time when a decision was passed, that evidence, after the exercise of due dilligence, was not within his knowledge or could not be produced by him. Party might apply for a retrial only if there is strict proof for such allegation. Otherwise, when it appears to the court that there was not sufficient ground for a retrial, application would be rejected. Besides additional evidence, the paper also deals with other reasons to apply for a retrial, such as errors in judicial procedure and unlawfulnesses in court decisions. The author emphasizes that, according to provisions of Code from 1865, retrial could not had been granted without previous notice to the opposite party; nor could be retried lawsuit that had been adjusted by lawful agreement or compromise, with notably rare exceptions. This aforementioned restrictions in application of legal remedy were vitally important for preserving judicial authority, court efficiency and principle of legal certainty.

PQ decoupled 3-phase numerical observability analysis and critical data identification for distribution systems

Summary Emerging active distribution systems are operated under more complicated and uncertain conditions. Because of frequent topology changes or temporary malfunctions of data acquisition, the network may lose observability and in turn may lead to the failure of distribution system state estimation. Without distribution system state estimation, the distribution system operator may not be able to make secure decisions, and the system may face with risk of serious damages. In this paper, a new real/reactive (PQ) decoupled 3-phase numerical observability analysis method and a new critical data identification method for distribution systems are proposed. The methods can efficiently identify all unobservable branches and critical data in a non-iterative manner. In addition to the 3-phase decoupling, the normal equation is also PQ decoupled, and the computation burden is greatly reduced. Furthermore, all entries in the Jacobian matrix are non-negative integers and the proposed methods present good numerical performance. Strict theoretical proofs on the performance of the proposed methods are provided and numerical results on different scales of test systems illustrate their validities.