A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems

In this paper Mei symmetry is introduced for a nonconservative system. The necessary and sufficient condition for a Mei symmetry to be also a Lie symmetry is derived. It is proved that the Mei symmetry leads to a non-Noether conservative quantity via a Lie symmetry, and deduces a Lutzky conservative quantity via a Lie point symmetry.

Homo-& Heteroclinic Orbits in Conservative Systems with 3-wells Potential

Consider the following 2×2 nonlinear system:where f(u): R→R is a, smooth function. Setwhere F’(u)= f(u). Then (1) can be rewritten as an equivalent Hamiltonian system:

About One-Dimensional Conservative Systems with Position Depending Mass

For a one-dimensional conservative system with position depending mass, one deduces consistently a constant of motion, a Lagrangian, and a Hamiltonian for the nonrelativistic case. With these functions, one shows the trajectories on the spaces (x,v) and (x,p) for a linear position depending mass. For the relativistic case, the Lagrangian and Hamiltonian cannot be given explicitly in general. However, we study the particular system with constant force and mass linear dependence on the position where the Lagrangian can be found explicitly, but the Hamiltonian remains implicit in the constant of motion.

Characteristic analysis of 5D symmetric Hamiltonian conservative hyperchaotic system with hidden multiple stability

Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traversal and pseudorandomness. In this work, a novel five-dimensional(5D) Hamiltonian conservative hyperchaotic system is proposed based on the 5D Euler equation. The proposed system can have different types of coordinate transformations and time reversal symmetries. In this work, Hamilton energy and Casimir energy are analyzed firstly, and it is proved that the new system satisfies Hamilton energy conservation and can generate chaos. Then, the complex dynamic characteristics of the system are demonstrated and the conservatism and chaos characteristics of the system are verified through the correlation analysis methods such as phase diagram, equilibrium point, Lyapunov exponent, bifurcation diagram, and SE complexity. In addition, a detailed analysis of the multistable characteristics of the system reveals that many energy-related coexisting orbits exist. Based on the infinite number of center-type and saddle-type equilibrium points, the dynamic characteristics of the hidden multistability of the system are revealed. Then, the National Institute of Standards and Technology(NIST)test of the new system shows that the chaotic sequence generated by the system has strong pseudo-random. Finally, the circuit simulation and hardware circuit experiment of the system are carried out with Multisim simulation software and digital signal processor(DSP) respectively. The experimental results confirm that the new system has good ergodicity and realizability.

Acupuncture therapies in combination with conservative treatments for postoperative ileus:a systematic review and network meta-analysis

Background:Although acupuncture therapies have been widely used in combination with conservative treatments(CT)for postoperative ileus(POI),evidence of their safety and efficacy remains scarce.To evaluate and rank the efficacy of different acupuncture therapies combined with CT for POI.Methods:A comprehensive search was carried out in several databases(Embase,PubMed,Cochrane Library,Chinese National Knowledge Infrastructure,Wanfang Data,VIP Chinese Science and Technology Periodical Database and China Biology Medicine disc)for relevant randomized controlled trials(RCTs)investigating different acupuncture therapies for POI from inception to February 17,2023.The Cochrane risk of bias tool was used to determine the risks of bias of the included RCTs.The primary outcomes included the time to first defecation,time to first flatus,and time to first bowel movement;and the secondary outcome was the response rate.Pairwise meta-analysis was performed by Review Manager 5.3 software,and network meta-analysis was carried out by Stata v.15.0 software.The cumulative ranking curve was obtained with Stata v.15.0 and was utilized to rank the included treatments.Results:29 studies with 2,600 participants were included in this systematic review.This meta-analysis demonstrated that all acupuncture therapies combined with CT were superior to conservative treatments alone in time to first defecation,time to first flatus,time to first bowel movement,and response rate.Among 10 evaluated methods,auricular needle with CT was the most effective treatment to reduce the time to first defecation.Furthermore,moxibustion with CT was the most effective in reducing the time to first flatus,and warm needling with CT most markedly reduced the time to first bowel movement among 9 interventions.Moreover,manual acupuncture with CT showed the largest improvement in response rate.Conclusion:This meta-analysis revealed that all acupuncture therapies are effective and safe for POI,with warm needling+CT being the most effective way to relieve symptoms.These results indicated that acupuncture therapies combined with CT should be considered for POI patients.However,most of the included trials were ranked as moderate quality,and further large-scale,high-quality RCTs are required to confirm the optimal interventions for POI patients.

Input-to-State Stability of Impulsive Switched Systems Involving Uncertain Impulse-Switching Moments

Dear Editor,This letter studies the input-to-state stability(ISS)for a class of impulsive switched systems,where uncertain impulse-switching moments are involved.The robustness of ISS with respect to the perturbations of the occurrence time of impulse-switching moments is revealed by several less conservative dwell-time conditions for the uncertain impulse-switching moments combined with Lyapunov conditions.Moreover,the Lyapunov conditions have multiple coefficients at discrete time so as to handle the hybrid effect of impulse-switching moments,and the case that time derivative of Lyapunov function is indefinite is also taken into account.Finally,a numerical example is proposed to illustrate the effectiveness of the theoretical results.

A Local Macroscopic Conservative(LoMaC)Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics

In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method.

Physico-chemical properties and macrofauna of soils under various farming systems of cold arid region in Balochistan,Pakistan

Barshore is a small village in the Pishin District,Balochistan,Pakistan,with dry summers and cold rainy winters.This is an agrarian region,mostly with orchards of various fruit trees.This study investigated the physico-chemical properties and macrofauna of soils under various agricultural management practices of this region.The concentrations of soil organic matter(SOM),soil organic carbon(SOC),nutrients,pH,electrical conductivity,soil texture,and the abundance and number of species of soil macrofauna of the agricultural fields were measured.Fifteen agricultural fields were sampled.Fourteen fields were orchards of apple,apricot or the mixture of apple and apricot trees and one field was a cropland,cultivated with wheat as a monocrop.The orchards were under conservation agricultural practices;whereas,the cropland was under conventional management.These agricultural lands were 2-26 years old.The concentration of soil organic matter(SOM)in the upper 0-10 cm depth of these field sites ranged from 11.6 g kg^(-1)to 32.8 g kg^(-1)soil.As compared to cropland,orchards had significantly higher concentration of SOM and SOC.A total of 18 soil macrofauna species were found and the most common and abundant were ants(Monomorium minimum,Camponotus pennsylvanicus,Solenopsis invicta,and Lasius niger)followed by Arion ssp.(Brown Slug)and earthworm Lumbricus terrestris.Regression analysis revealed non-significant relationship of the age and the concentration of SOM with the number of macrofauna species and with the concentrations of total mineral nitrogen,bioavailable phosphorus and clay.The existence of ants had no relationship with the concentration of SOM;whereas,existence of Lumbricus terrestris tended to had a positive relationship with the concentration of SOM.The field of tree-based intercropping system was 2 years of age since the land was converted from rangeland to a cropland,had two ant species coexisting.This indicates the positive influence of crop diversification on soil macrofauna.

Spatiotemporal variations of ecosystem services and driving factors in the Tianchi Bogda Peak Natural Reserve of Xinjiang,China

Nature reserves play a significant role in providing ecosystem services and are key sites for biodiversity conservation.The Tianchi Bogda Peak Natural Reserve(TBPNR),located in Xinjiang Uygur Autonomous Region,China,is an important ecological barrier area in the temperate arid zone.The evaluation of its important ecosystem services is of great significance to improve the management level and ecological protection efficiency of the reserve.In the present study,we assessed the spatiotemporal variations of four ecosystem services(including net primary productivity(NPP),water yield,soil conservation,and habitat quality)in the TBPNR from 2000 to 2020 based on the environmental and social data using the Integrated Valuation of Ecosystem Services and Trade-offs(InVEST)model.In addition,the coldspot and hotspot areas of ecosystem services were identified by hotspot analysis,and the trade-off and synergistic relationships between ecosystem services were analyzed using factor analysis in a geographic detector.During the study period,NPP and soil conservation values in the reserve increased by 48.20%and 25.56%,respectively;conversely,water yield decreased by 16.56%,and there was no significant change in habitat quality.Spatially,both NPP and habitat quality values were higher in the northern part and lower in the southern part,whereas water yield showed an opposite trend.Correlation analysis revealed that NPP showed a synergistic relationship with habitat quality and soil conservation,and exhibited a trade-off relationship with water yield.Water yield and habitat quality also had a trade-off relationship.NPP and habitat quality were affected by annual average temperature and Normalized Difference Vegetation Index(NDVI),respectively,while water yield and soil conservation were more affected by digital elevation model(DEM).Therefore,attention should be paid to the spatial distribution and dynamics of trade-off and synergistic relationships between ecosystem services in future ecological management.The findings of the present study provide a reference that could facilitate the sustainable utilization of ecosystem services in the typical fragile areas of Northwest China.

Secondary Hyperparathyroidism in Dialysis Patients: Short- and Long-Term Outcomes of Conservative Parathyroidectomy

Secondary hyperparathyroidism (HPT) is frequent in dialysis patients. Parathyroidectomy (PTX) is indicated for patients who failed medical therapy. We reviewed the data from 184 dialysis patients who underwent PTX between January 2015 and January 2023. We aimed to evaluate the short and long term outcomes of PTX in dialysis patients, comparing the conservative 3/4 versus 7/8 techniques in this population.166 dialysis patients with secondary HPT were included. A conservative subtotal PTX (sPTX) 7/8 was performed in 72% of patients and sPTX 3/4 in 28% of them. Severe postoperative hypocalcaemiaocurred in 45 patients (27%). Hypocalcaemia was significantly more frequent in the sPTX 7/8 group (p = 0.012). One case of persistent HPT (0.6%) and 20 cases of recurrence (12%) were diagnosed. Recurrence was more frequent in the sPTX 3/4 group (15%). No deaths were reported during the perioperative period.

Fertilization and Soil Ploughing Practices under Changing Physical Environment Lead to Soil Organic Carbon Dynamics under Conservation Agriculture in Rice-Wheat Cropping System: A Scoping Review

Ploughing and fertilization practices in rice-wheat system have deteriorated the soil carbon (C) pools. Conservation agriculture (CA) based management approaches have proven to enhance C sequestration and reverse the loss of soil-organic-carbon (SOC), which further enhances soil fertility. Different fractions of SOC pools react to the alterations in management practices and indicate changes in SOC dynamics as compared to total C in the soil. Higher SOC levels in soil have been observed in case of reduced/no-till (NT) practices than conventional tillage (CT). However, between CT and zero tillage/NT, total SOC stocks diminished with an increase in soil depth, which demonstrated that the benefits of SOC are more pronounced in the topsoil under NT. Soil aggregation provides physical protection to C associated with different-sized particles, thus, the improvement in soil aggregation through CA is an effective way to mitigate soil C loss. Along with less soil disturbance, residual management, suitable crop rotation, rational application of manures and fertilizers, and integrated nutrient management have been found to be effective in not only improving soil C stock but also enhancing the soil health and productivity. Thus, CA can be considered as a potential method in the build-up of SOC of soil in rice-wheat system.

Research Progress on Conservative Treatment of Lumbar Disc Herniation

Lumbar disc herniation(LDH)is a common orthopedic disease in clinical practice,with main symptoms of varying degrees of pain and functional impairment,seriously affecting the quality of work and life of patients,and also causing a certain degree of economic burden to the patient's family and society.At present,there are various conservative treatment methods for LDH in clinical practice.Conservative treatment has the characteristics of small trauma and high safety,which can achieve symptom relief and cure for most patients in clinical practice.This article aims to provide a scientific reference for the selection of treatment plans for LDH patients by reviewing relevant literature on conservative treatment of LDH that has been publicly reported both domestically and internationally in recent years.

Exploration and Application Practice of Energy Conservation Theory and Method in Steel Manufacturing Process System

This article briefly discusses the theoretical basis and overall goals of energy conservation in the steel manufacturing process system.It is proposed that in the process of implementing system energy conservation,it is necessary to fully recognize and utilize the characteristics and functional advantages of the steel manufacturing process,pay more attention to energy quality,firmly grasp the overall goal of system optimization,focus on the integrated optimization of gas,steam,and waste heat systems,and propose the idea of constructing a"steel chemi-cal gas electricity heating cooling multi generation system".Based on practice,the main principles,models,and effects of implementing systematic energy conservation in steel enterprises have been proposed.

Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems

In this paper,we investigate the long-time near-conservations of energy and kinetic energy by the widely used exponential integrators to highly oscillatory conservative systems.The modulated Fourier expansions of two kinds of exponential integrators have been constructed and the long-time numerical conservations of energy and kinetic energy are obtained by deriving two almost-invariants of the expansions.Practical examples of the methods are given and the theoretical results are confirmed and demonstrated by a numerical experiment.

Non-Noether symmetries and Lutzky conservative quantities of nonholonomic nonconservative dynamical systems

Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally, an example is given to illustrate these results.

Symmetries and exact solutions of discrete nonconservative systems

Based on the property of the discrete model entirely inheriting the symmetry of the continuous system,we present a method to construct exact solutions with continuous groups of transformations in discrete nonconservative systems.The Noether's identity of the discrete nonconservative system is obtained.The symmetric discrete Lagrangian and symmetric discrete nonconservative forces are defined for the system.Generalized quasi-extremal equations of discrete nonconservative systems are presented.Discrete conserved quantities are derived with symmetries associated with the continuous system.We have also found that the existence of the one-parameter symmetry group provides a reduction to a conserved quantity;but the existence of a two-parameter symmetry group makes it possible to obtain an exact solution for a discrete nonconservative system.Several examples are discussed to illustrate these results.

A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrdinger system

We derive a new method for a coupled nonlinear Schr/Sdinger system by using the square of first-order Fourier spectral differentiation matrix D1 instead of traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove the proposed method preserves the charge and energy conservation laws exactly. In numerical tests, we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of soliton collisions. Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws. These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm.

Conformal invariance and conserved quantities of non-conservative Lagrange systems by point transformations

This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.

Equivalentness Between Controllability and Stabilizability for Conservative Systems and Applications

Controllability and stabilizability are a pair of important topics in control theory for distributed parameter systems. In the present note we show the equivalentness between controllability and stabilizability for conservative systems as well as necessary and sufficient

The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems

This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of systems are deduced, is generalized to the case of including the time variational. The requirement for an invariant group transformation is defined to be the Lie symmetry and the criterion when the Noether conserved quantities may be obtained from Lie symmetries is also presented. An example is discussed for applications of the results.