ANALYSIS FOR THE BEZOUT IDENTITY OF GENERALIZED SYSTEMS

The state space representation of the Bezout identity for generalized systems proposed by (Wang and Balas, 1989) is discussed again. A more concise way of description and proof is presented and the physical significance of the result in is also analyzed. Thus, our work is of independent interest.

Existence of Solutions to a Generalized System

In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity and extend Minty’s lemma for the generalized system. And using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for the generalized system with monotonicity in real reflexive Banach spaces. As the continuation of existing studies, our paper present a series of extended results based on existing corresponding results.

Design of Protograph LDPC-Coded MIMO-VLC Systems with Generalized Spatial Modulation

This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain(SiD) symbols and the spatial-domain(SpD) light emitting diode(LED)-index patterns are coded by a protograph low-density parity-check(P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating(SSER) method for constructing a type of novel generalized spatial modulation(GSM) constellations, referred to as SSERGSM constellations, so as to boost the performance of the BICGSM-ID MIMO-VLC systems.Moreover, by applying a modified PEXIT(MPEXIT) algorithm, we further design a family of rate-compatible P-LDPC codes, referred to as enhanced accumulate-repeat-accumulate(EARA) codes,which possess both excellent decoding thresholds and linear-minimum-distance-growth property. Both analysis and simulation results illustrate that the proposed SSERGSM constellations and P-LDPC codes can remarkably improve the convergence and decoding performance of MIMO-VLC systems. Therefore, the proposed P-LDPC-coded SSERGSM-mapped BICGSMID configuration is envisioned as a promising transmission solution to satisfy the high-throughput requirement of MIMO-VLC applications.

Generalized autoencoder-based fault detection method for traction systems with performance degradation

Fault diagnosis of traction systems is important for the safety operation of high-speed trains.Long-term operation of the trains will degrade the performance of systems,which decreases the fault detection accuracy.To solve this problem,this paper proposes a fault detection method developed by a Generalized Autoencoder(GAE)for systems with performance degradation.The advantage of this method is that it can accurately detect faults when the traction system of high-speed trains is affected by performance degradation.Regardless of the probability distribution,it can handle any data,and the GAE has extremely high sensitivity in anomaly detection.Finally,the effectiveness of this method is verified through the Traction Drive Control System(TDCS)platform.At different performance degradation levels,our method’s experimental results are superior to traditional methods.

Necessary and Sufficient Conditions for Oscillations of the Generalized Liénard Systems

In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.

Multiparameter generalized universal characters and multiparameter generalized B-type universal characters

We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functions are derived.Furthermore,we introduce two integrable systems known as the generalized UC(GUC)hierarchy and the generalized Btype UC(GBUC)hierarchy satisfied by the generalized universal character and the generalized B-type universal character,respectively.Based on infinite sequences of complex numbers,we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character,which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy,respectively.

Determinants of generalized anxiety and construction of a predictive model in patients with chronic obstructive pulmonary disease

BACKGROUND Patients with chronic obstructive pulmonary disease(COPD)frequently experience exacerbations requiring multiple hospitalizations over prolonged disease courses,which predispose them to generalized anxiety disorder(GAD).This comorbidity exacerbates breathing difficulties,activity limitations,and social isolation.While previous studies predominantly employed the GAD 7-item scale for screening,this approach is somewhat subjective.The current literature on predictive models for GAD risk in patients with COPD is limited.AIM To construct and validate a GAD risk prediction model to aid healthcare professionals in preventing the onset of GAD.METHODS This retrospective analysis encompassed patients with COPD treated at our institution from July 2021 to February 2024.The patients were categorized into a modeling(MO)group and a validation(VA)group in a 7:3 ratio on the basis of the occurrence of GAD.Univariate and multivariate logistic regression analyses were utilized to construct the risk prediction model,which was visualized using forest plots.The model’s performance was evaluated using Hosmer-Lemeshow(H-L)goodness-of-fit test and receiver operating characteristic(ROC)curve analysis.RESULTS A total of 271 subjects were included,with 190 in the MO group and 81 in the VA group.GAD was identified in 67 patients with COPD,resulting in a prevalence rate of 24.72%(67/271),with 49 cases(18.08%)in the MO group and 18 cases(22.22%)in the VA group.Significant differences were observed between patients with and without GAD in terms of educational level,average household income,smoking history,smoking index,number of exacerbations in the past year,cardiovascular comorbidities,disease knowledge,and personality traits(P<0.05).Multivariate logistic regression analysis revealed that lower education levels,household income<3000 China yuan,smoking history,smoking index≥400 cigarettes/year,≥two exacerbations in the past year,cardiovascular comorbidities,complete lack of disease information,and introverted personality were significant risk factors for GAD in the MO group(P<0.05).ROC analysis indicated that the area under the curve for predicting GAD in the MO and VA groups was 0.978 and 0.960.The H-L test yieldedχ^(2) values of 6.511 and 5.179,with P=0.275 and 0.274.Calibration curves demonstrated good agreement between predicted and actual GAD occurrence risks.CONCLUSION The developed predictive model includes eight independent risk factors:Educational level,household income,smoking history,smoking index,number of exacerbations in the past year,presence of cardiovascular comorbidities,level of disease knowledge,and personality traits.This model effectively predicts the onset of GAD in patients with COPD,enabling early identification of high-risk individuals and providing a basis for early preventive interventions by nursing staff.

Poisson Theory of Generalized Birkhoff Systems

To study the Poisson theory of the generalized Birkhoff systems, the Lie algebra and the Poisson brackets were used to establish the Poisson theorem. The generalized Poisson condition for the first integral and the generalized Poisson theorem of the generalized Birkhoff systems are obtained. An example is given to illustrate the application of the result.

Symmetries and conserved quantities of generalized Birkhoffian systems

Three kinds of symmetries and their corresponding conserved quantities of a generalized Birkhoffian system are studied. First, by using the invariance of the Pfaffian action under the infinitesimal transformations, the Noether theory of the generalized Birkhoffian system is established. Secondly, on the basis of the invariance of differential equations under infinitesimal transformations, the definition and the criterion of the Lie symmetry of the generalized Birkhoffian system are established, and the Hojman conserved quantity directly derived from the Lie symmetry of the system is given. Finally, by using the invariance that the dynamical functions in the differential equations of the motion of mechanical systems still satisfy the equations after undergoing the infinitesimal transformations, the definition and the criterion of the Mei symmetry of the generalized Birkhoffian system are presented, and the Mei conserved quantity directly derived from the Mei symmetry of the system is obtained. Some examples are given to illustrate the application of the results.

Application of Generalized Predictive Adaptive Control Algorithm in the Design of Missile Control System

To study the application of the generalized predictive adaptive control algorithm in missile control system, the algorithm is presented based on the recursive least square estimation, and a controller of the pitch channel of a missile is designed by using this algorithm. The simulations verify that the designed controller can meet the demands of the task well.

Generalized system function analysis of resonant behavior of electromagnetic open systems

Abstract The generalized system function, H（s）, directly associated with the radiated or scattered fields is presented to effectively analyze the special resonant behavior of electromagnetic open systems in this paper, which is adaptively constructed by using the model-based parameter estimation （MBPE） technique in the complex frequency domain. By analyzing the characteristics of complex zeros, poles and residues of H（s） in a finite operational frequency band, we can effectively determine resonant frequencies and resonant intensity of electromagnetic open systems. It is known that an analysis of Q-factor of antenna and scattering systems has been an interesting and challenging problem. Based on H（s） and the complex frequency w theories, a complex frequency method for Q-factor of electromagnetic open systems is presented in this paper. Some examples of the practical antenna arrays are given to illustrate the applications and validity of the generalized system function theory proposed by this paper.

Close-formed bound on generalized distributed antenna system capacity

The composite channel models of the generalized distributed antenna system （GDAS） such as Rayleigh-lognormal fading are studied. Then comparisons are performed between the GDAS and the traditional multiple-input multiple-output （MIMO） system to analyze the ergodic capacity of the GDAS and make conclusions that it is impossible to achieve an analytical expression for the ergodic capacity of the GDAS. Moreover, in order to evaluate the performance of the ergodic capacity of the GDAS conveniently, the analytical lower bound and upper bound of the ergodic capacity of the GDAS are derived by using the results from multivariate statistics and matrix inequalities, under the scenarios of Rayleigh-lognormal fading and equal power allocation scheme at transmitter. Finally, the analytical bounds are verified by comparisons with the numerical results.

Generalized projective synchronization of chaotic systems via adaptive learning control

In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.

Generalized projective synchronization of a class of chaotic （hyperchaotic） systems with uncertain parameters

In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.

A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics

The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics axe studied. The exact inwriant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invaxiant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invaxiant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invaxiant. An example is also given to illustrate the application of the results.

Bifurcation for the generalized Birkhoffian system

The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered.

Linear generalized synchronization of chaotic systems with uncertain parameters

A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.

Skew-gradient representation of generalized Birkhoffian system

The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of the skew-gradient system are used to study the properties, especially the stability, of the generalized Birkhoffian system. Some examples are given to illustrate the application of the result.

Generalized canonical transformation for second-order Birkhoffian systems on time scales

The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.