Multiple Solutions for a Class of Singular Boundary Value Problems of Hadamard Fractional Differential Systems with p-Laplacian Operator

This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.

Systemic lupus erythematosus in a 15-year-old female with multiple splenic nodules:A case report

BACKGROUND Systemic lupus erythematosus(SLE)is a chronic inflammatory disease primarily affecting young females.SLE can invade any organ,and various forms of splenic invasion have been reported.Manifestations include splenomegaly and splenic infarction,rupture,and calcification.The study encountered a rare case of splenic involvement,with nodules of various sizes without calcifications or ruptures.CASE SUMMARY A 15-year-old girl presented with arthralgia,weight loss,fever,increased levels of inflammatory markers,and positive antinuclear antibody test results.The patient was diagnosed with SLE.She was asymptomatic while taking steroids and hydroxychloroquine.Ten months after discharge,the patient developed a fever and abdominal pain.Lupus enteritis was suspected,and abdominopelvic computed tomography(AP-CT)was performed.There were no specific findings in the gastrointestinal tract,but multiple splenic nodules were observed.Infection or hemangioma was considered;however,no specific radiological findings were observed.A biopsy of the spleen was performed to determine the possibility of malignancy.The histological findings of the spleen included extensive periarteriolar necrosis with hematoxylin bodies and numerous karyorrhectic debris.Based on the biopsy results,the patient was diagnosed with an SLE flare-up and was maintained on high-dose steroids and immunosuppressants.CONCLUSION As disease activity increased,multiple nodules in the spleen that were previously unseen were observed using AP-CT and histologically confirmed.Spleen invasion by SLE can appear in multiple nodular forms and patterns.Therefore,physicians should consider these findings when differentiating these nodules from infections and malignancies.

Carbon efficiency evaluation method for urban energy system with multiple energy complementary

Urban energy systems(UESs)play a pivotal role in the consumption of clean energy and the promotion of energy cascade utilization.In the context of the construction and operation strategy of UESs with multiple complementary energy resources,a comprehensive assessment of the energy efficiency is of paramount importance.First,a multi-dimensional evaluation system with four primary indexes of energy utilization,environmental protection,system operation,and economic efficiency and 21 secondary indexes is constructed to comprehensively portray the UES.Considering that the evaluation system may contain a large number of indexes and that there is overlapping information among them,an energy efficiency evaluation method based on data processing,dimensionality reduction,integration of combined weights,and gray correlation analysis is proposed.This method can effectively reduce the number of calculations and improve the accuracy of energy efficiency assessments.Third,a demonstration project for a UES in China is presented.The energy efficiency of each scenario is assessed using six operational scenarios.The results show that Scenario 5,in which parks operate independently and investors build shared energy-storage equipment,has the best results and is best suited for green and low-carbon development.The results of the comparative assessment methods show that the proposed method provides a good energy efficiency assessment.This study provides a reference for the optimal planning,construction,and operation of UESs with multiple energy sources.

Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems

This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional(LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.

TWO ALGORITHMS FOR SYMMETRIC LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES

In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple right-hand sides, and show how to incorporate deflation to drop converged linear systems using a natural convergence criterion, and present an adaptive block Lanczos algorithm. We propose also a block version of Paige and Saunders’ MINRES method for iterative solution of symmetric linear systems, and describe important implementation details. We establish a relationship between the block Lanczos algorithm and block MINRES algorithm, and compare the numerical performance of the Lanczos algorithm and MINRES method for symmetric linear systems applied to a sequence of right hand sides with that of the block Lanczos algorithm and block MINRES algorithm for multiple linear systems simultaneously.[WT5,5”HZ]

Multiple Periodic Solutions for Some Classes of First-Order Hamiltonian Systems

Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.

Exponential Stability of Large-Scale Non-Linear Systems with Multiple The Delays

The problem of stabilizing a class of large-scale non-linear multiple delay systems is considered.The complicated system is decomposed into several subsystems; each function of them is expressed by a set of components of the overall state vector,with interconnections between them, and the subsystems are coupled by the delayed state. In this paper, a method is devised to be a suitable choice of state feedback controls of every subsystems, moreover, it is proved that the large-scale system is exponential stable.

Stability criteria for linear systems with multiple time-varying delays

New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast time-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature. Keywords Stability - Delay-independent criteria - Delay-dependent criteria - Linear time-delay systems - Multiple time-varying delays This work was supported by NSFC Key-Project (No. 60334010) and Guangdong Province Natural Science Foundation of China (No. 31406).

Dynamic Consensus of High-order Multi-agent Systems and Its Application in the Motion Control of Multiple Mobile Robots

In this paper, the leader-following consensus problem for multi-agent linear dynamic systems is considered. All agents and leader have identical multi-input multi-output （MIMO） linear dynamics that can be of any order, and only the output information of each agent is delivered throughout the communication network. When the interaction topology is fixed, the leader-following consensus is attained by Ho~ dynamic output feedback control, and the sufficient condition of robust controllers is equal to the solvability of linear matrix inequality （LMI）. The whole analysis is based on spectral decomposition and an equivalent decoupled structure achieved, and the stability of the system is proved. Finally, we extended the theoretical results to the case that the interaction topology is switching. The simulation results for multiple mobile robots show the effectiveness of the devised methods.

BLOCK BIDIAGONALIZATION METHODS FOR MULTIPLE NONSYMMETRIC LINEAR SYSTEMS

The symmetric linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. The aim of this paper is to consider the block bidiagonalization methods derived from a symmetric augmented multiple linear systems and make a comparison with the block GMRES and block biconjugate gradient methods.

A NEW ANALYZING APPROACH TO MODELING SLOTTED MULTIPLE ACCESS SYSTEMS

In this paper, the analyzing approaches proposed by Zhao Dongfeng, et al.(1997) have been extensively studied. The average cyclic times of the slotted multiple access systems are analyzed by using the average cycle method. Analytic formulae for mean values of a successful period and a colliding period and an idle period are derived. The upper bounds of the system throughput with capture effect and collision resolution are provided. Finally, the simulation results of the slotted multiple access channels are given.

Delay-dependent robust control for uncertain stochastic systems with Markovian switching and multiple delays

The exponential stability in mean square and stabiliza- tion problems for It＆ stochastic switched systems with multiple time-delays are investigated. The system possesses the norm- bounded uncertainties and Markovian jumping parameters. By using an effective descriptor model transformation of the system and applying Ito＇s differential formula and Moon＇s inequality for bounding cross terms, a new delay-dependent sufficient condi- tion is derived in terms of linear matrix inequalities, and its states feedback controller is designed. Numerical examples are given to illustrate the efficiency and less conservation of the results.

Multiple Solutions for a Class of Concave-Convex Quasilinear Elliptic Systems with Nonlinear Boundary Condition

In this paper, a quasilinear elliptic system is investigated, which involves concave-convex nonlinearities and nonlinear boundary condition. By Nehari manifold, fibering method and analytic techniques, the existence of multiple nontrivial nonnegative solutions to this equation is verified.

Design and Optimization of Multiple Interconnected Utility Systems in An Integrated Refining and Petrochemical Complex

In an integrated refining and petrochemical complex,a centralized utility system(CUS)is introduced to integrate the steam demands of production plants.Besides,two sub-utility systems(SUSs)located inside the alkene and refinery plants,respectively,can satisfy the shaft demands.It is difficult to determine the steam production of the CUS because the steam demands of the alkene and refinery plants also depend on the design and operation of the SUSs.To explore the complicated interaction between the CUS and SUSs,we proposed a mixed-integer nonlinear programming(MINLP)model for the design and optimization of multiple interconnected utility systems to minimize the total annualized cost(TAC).An extended superstructure was suggested to contain multiple inter-plant connected steam pipe alternatives between the CUS and SUSs.A more accurate model of the complex steam turbine was proposed.Then the proposed MINLP framework is applied to a new integrated refining and petrochemical complex.Two scenarios are investigated in the case study to explore the effect of steam main temperatures on system configurations and operating parameters.By optimizing the main temperatures,a TAC of$2.7 million can be saved.Judging from the results of the two scenarios,the feasibility and effectiveness of the proposed framework for the design and optimization of multiple interconnected utility systems have been demonstrated.

Novel sensitivity analysis method and dynamics optimization for multiple launch rocket systems

This study establishes the launch dynamics method,sensitivity analysis method,and multiobjective dynamic optimization method for the dynamic simulation analysis of the multiple launch rocket system(MLRS)based on the Riccati transfer matrix method for multibody systems(RMSTMM),direct differentiation method(DDM),and genetic algorithm(GA),respectively.Results show that simulation results of the dynamic response agree well with test results.The sensitivity analysis method is highly programming,the matrix order is low,and the calculation time is much shorter than that of the Lagrange method.With the increase of system complexity,the advantage of a high computing speed becomes more evident.Structural parameters that have the greatest influence on the dynamic response include the connection stiffness between the pitching body and the rotating body,the connection stiffness between the rotating body and the vehicle body,and the connection stiffnesses among 14^(#),16^(#),and 17^(#)wheels and the ground,which are the optimization design variables.After optimization,angular velocity variances of the pitching body in the revolving and pitching directions are reduced by 97.84%and 95.22%,respectively.

Delay-dependent observer-based stabilizing controller design for linear multiple state-delayed systems

This article concerns a coupled LMIs approach to delay-dependent observer-based output feedback stabilizing controller design for linear continuous-time systems with multiple state delays. The advantage of our proposed delay-dependent coupled LMIs criterion lies in that: ( 1 ) it can optimize one of multiple time delays with others selected properly, and at the same time, the feedback-gain and observer-gain can be obtained, respectively. (2) it is less conservative than the existing delay-independent ones in the literature. Algorithm to solve the coupled LMIs is also given. Numerical examples illustrate the effectiveness of our method. Keywords Delay-dependent criterion - Time-delay system - Multiple time-delay - Observer-based controller - Linear matrixinequality (LMI)

Multiple attractors and generalized synchronization in delayed Mackey-Glass systems

Nonlinear dynamics of the time-delayed Mackey-Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincare section. Synchronizations of the drive-response Mackey-Glass oscillators are investigated. The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour. We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers, i.e., more resonance peaks can be found.

Researted FOM for Multiple Shifted Linear Systems

The seed method is used for solving multiple linear systems A (i)x (i) =b (i) for 1≤i≤s, where the coefficient matrix A (i) and the right-hand side b (i) are different in general. It is known that the CG method is an effective method for symmetric coefficient matrices A (i). In this paper, the FOM method is employed to solve multiple linear sy stems when coefficient matrices are non-symmetric matrices. One of the systems is selected as the seed system which generates a Krylov subspace, then the resi duals of other systems are projected onto the generated Krylov subspace to get t he approximate solutions for the unsolved ones. The whole process is repeated u ntil all the systems are solved.

Adaptive switching control of a class of nonlinear systems based on mixed multiple models

The transient behaviors of traditional adaptive control may be very poor in general. A practically feasible approach to improve the transient performances is the adoption of adaptive switc- hing control. For a typical class of nonlinear systems disturbed by random noises, mixed multiple models consisting of adaptive model and fixed models were considered to design the switching con- trol law. Under certain assumptions, the nonlinear system with the switching control law was proved rigorously to be stable and optimal A simulation example was provided to compare the performance of the switching control and the traditional adaptive control.