广义Birkhoff系统分数阶最优控制问题的Noether定理

探讨了广义Birkhoff系统分数阶最优控制问题的Noether定理。首先,基于Caputo分数阶导数提出广义Birkhoff系统的分数阶最优控制问题,并运用分数阶变分方法得到了广义Birkhoff系统的分数阶最优控制问题的极值条件。然后,运用分数阶微积分和分数阶变分方法讨论了泛函在无穷小变换群作用下的不变性,分别给出了其时间不变和时间变化情况下的分数阶最优控制问题的Noether定理。最后,应用实例显示方法的有效性。

Grindability Evaluation of Ultrasonic Assisted Grinding of Silicon Nitride Ceramic Using Minimum Quantity Lubrication Based SiO_(2)Nanofluid

Minimum quantity Lubrication(MQL)is a sustainable lubrication system that is famous in many machining systems.It involve the spray of an infinitesimal amount of mist-like lubricants during machining processes.The MQL system is affirmed to exhibit an excellent machining performance,and it is highly economical.The nanofluids are understood to exhibit excellent lubricity and heat evacuation capability,compared to pure oil-based MQL system.Studies have shown that the surface quality and amount of energy expended in the grinding operations can be reduced considerably due to the positive effect of these nanofluids.This work presents an experimental study on the tribological performance of SiO_(2)nanofluid during grinding of Si_(3)N_(4)ceramic.The effect different grinding modes and lubrication systems during the grinding operation was also analyzed.Different concentrations of the SiO_(2)nanofluid was manufactured using canola,corn and sunflower oils.The quantitative evaluation of the grinding process was done based on the amount of grinding forces,specific grinding energy,frictional coefficient,and surface integrity.It was found that the canola oil exhibits optimal lubrication performance compared to corn oil,sunflower oil,and traditional lubrication systems.Additionally,the introduction of ultrasonic vibrations with the SiO_(2)nanofluid in MQL system was found to reduce the specific grinding energy,normal grinding forces,tangential grinding forces,and surface roughness by 65%,57%,65%,and 18%respectively.Finally,regression analysis was used to obtain an optimum parameter combinations.The observations from this work will aid the smooth transition towards ecofriendly and sustainable machining of engineering ceramics.

Some Indicators of the Water Regime in Some Varieties Belonging to the Monarda didyma L. Genus in the Conditions of Tashkent (Uzbekistan)

In this article, the names of 3 varieties of Monarda didyma L., which are considered to be introduced species, some indicators of the water regime in the climatic conditions of Uzbekistan: the amount of water in the leaves, water deficit, water storage capacity were studied in spring and summer, and seasonal changes were determined. According to these indicators of the water regime, the studied varieties belong to the labile water regime, high green mass (centner), seed yield (how many grams), resistance to diseases and pests have been determined, which shows that it is promising for introduction in the conditions of our republic. Therefore, it is recommended to breed these varieties in the foothills and hilly regions of Uzbekistan, where the amount of precipitation is more than 400 - 500 mm.

Perceptions of Bark Beetle Landscape Disturbance Effects on Natural Resources and Drinking Water: Assessing Communication and Knowledge Exchange in the Rocky Mountain Region, USA

Widespread changes to forested watersheds affected by the mountain pine beetle (Dendroctonus ponderosae Hopkins) epidemic across western North America raised concerns about the effects of this climate-induced disturbance on drinking water and natural resources. Effective communication and knowledge exchange across scientists and stakeholders (i.e., drinking water managers) is essential for constructively responding to such landscape scale disturbances, providing improved adaptive capacity through knowledge sharing. An assessment of stakeholder knowledge levels, information needs, primary concerns, and suggested communication strategies were conducted via an online elicitation survey and World Science Café workshops. Knowledge levels, assessed via a survey of local water managers and experts, were relatively low with approximately half of the respondents reporting little to no knowledge of the effects of mountain pine beetle on drinking water quality and quantity, thereby indicating limited knowledge exchange between scientists and drinking water stakeholders. Increased accessibility and dissemination of research findings pertinent to the mountain pine beetle epidemic’s effects on drinking water quality and quantity is necessary for natural resource management. Recommendations for improved communication among scientists and drinking water stakeholders in particular and forest health in general include dispersal of non-academic research summaries, information exchange through existing media and community resources, demonstration projects, and information clearinghouses. This information provides a better understanding of the challenges, concerns, and first-hand experience of stakeholders of a landscape disturbance issue to apply this knowledge to enhance land management practice and how researchers on this overall project enhanced science communication efforts.

Evaluating soil acidification risk and its effects on biodiversity–ecosystem multifunctionality relationships in the drylands of China

Background:Soil acidifcationn caused by anthropogenic activities may aft soil biochemical cydling,bidiversity,productivity,and multiple eosystem-related functions in drylands.However,to date,such information is lacking to support this hypothesis.Methods Based on a transect survey of 78 naturally assembled shrub communities,we caloulated acid deposition flux in Northwest China and evaluated its likely ecological ffets by testing three altemnative hypotheses,namely:.nidche complementarity,mass ratio,and vegetation quantity hypotheses Rao's quadratic entopy and community-weighted mean traits were employed to represent the complementary aspect of niche complementarity and mass ratio effects,respectively.Resulbs:We observed that in the past four decades,the concentrations of exchangeable base cations in soil in Northwest China have decreased significantly to the extent of having faced the risk of depletion,whereas changes in the calium carbonate content and pH of soil were not significant.Adid deposition primani ly increased the aboweground biomass and shrub density in shrublands but had no sigmificant effect on shrub richness and ecasystem multifunctionality(EMF),indicating that acid deposition had positive but weak ecological effects on dryland ecosystems.Community wd ghted mean of functional traits(representing the mass ratio hypothesis)correlated negatively with EMF,whereas both Rao's quadratic entropy(representing the niche complementarity hypothesis)and aboveground biomass(representing the vegetation quantity hypothesis)correlated positively but insignifcantly with EMF.These biodiversity-EMF relationships highlight the fragility and instability of drylands relative to forest ecasystems.Concuions:The findings from this study serve as important reference points to understand the ris of soil acidification in arid regions and its impacts on biodiversity-EMF relationships.

The Effect of Mineral Composition and Quantity of Fines on the Atterberg Limits and Compaction Characteristics of Soils

Because of the various elements that come into play in natural soil formation, the impact of varied proportions of mineral composition and fines amount on Atterberg limits and compaction characteristics of soils is not well known. Three distinct soil samples were used in this investigation. The findings indicated the effect of varied mineral composition proportions and fines amount on the liquid limit, plastic limit, and plasticity index as assessed by the Casagrande test and hand-rolling method. The fluctuation of maximum dry density and optimal moisture content with these three soils has also been studied. Furthermore, correlations were established to indicate the compaction parameters and the amount of minerals and particles in the soil. The data show that the mineral content of the soil has a direct impact on the Atterberg limits and compaction characteristics. Soils containing larger percentages of expansive minerals, such as montmorillonite, have more flexibility and volume change capability. Mineral composition influences compaction parameters such as maximum dry density, ideal water content, axial strain, and axial stress. Soils with a larger proportion of fines, such as Soil 2 and Soil 3, have stronger flexibility and lower compaction qualities, with higher ideal water content and lower maximum dry density. Soil 1 has moderate flexibility and intermediate compaction qualities due to its low fines percentage. The effect of different mineral compositions and fines on the Atterberg limits and compaction characteristics of soils can be used to predict the behavior of compacted soils encountered in engineering practices, reducing the time and effort required to assess soil suitability for engineering use.

Research on Construction of Bill of Quantities of Prefabricated Buildings Based on BIM

Building Information Model(BIM)Technology can be widely used in various construction fields.The construction quality and project cost of the prefabricated construction industry based on BIM can be effectively controlled.Based on BIM Technology,the integration of bill of quantities can effectively control the cost of prefabricated construction and improve competitiveness in the bidding process.Based on this,the characteristics and advantages of bill of quantities pricing based on BIM were expounded in this paper.Besides,the structure and content construction of bill of quantities were analyzed,followed by an analysis of pricing control strategy based on BIM were analyzed for assembly building quantities for reference.

Lie Symmetries and Conserved Quantities of Holonomic Mechanical Systems in Terms of Quasi-Coordinatee

Aim To study the Lie symmetries and conserved quantities of holonomic mechanical systems in terms of qnasi-coordinates. Methods The definition of an infinitesimal generator for the holonomic mechanical systems in terms of quasi-coordinates was given. Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equations of the Lie symmetries of holonomic mechanical systems in terms of quassi-coordinates are established. The structure equation and the form of conserved quantities are obtained. An example to illustrate the applicaiton of the result is given.

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.

Lie Symmetries and Conserved Quantities of Holonomic Systems with Remainder Coordinates

Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.

Lie Symmetries and Conserved Quantities of Systems of Relative Motion Dynamics

Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.

Conformal invariance and Hojman conserved quantities of first order Lagrange systems

In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Conformal invariance and conserved quantities of dynamical system of relative motion

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

基于混合遗传算法的OFDMA资源分配方法

现有的OFDMA资源分配算法无法在保障公平度阈值的前提下有效地最大化系统和速率。针对上述问题,提出了一种基于混合遗传算法的OFDMA资源分配方法。首先将遗传算法的种群个体进行分组并为个体分组设置个体更新量,然后在此基础上采用贪婪子载波分配初始化种群个体,并通过个体更新量降低个体的待优化的维度数量,充分发挥遗传算法的寻优能力。仿真结果表明,所提出的方法能够在等功率的子载波分配阶段即可实现所要求的公平度阈值并能最大化系统和速率,证明了所提出方法的有效性。

New conserved quantities of Noether-Mei symmetry of mechanical system in phase space

This paper studies two new types of conserved quantities deduced by Noether Mei symmetry of mechanical system in phase space. The definition and criterion of Noether Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether- Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether Mei symmetry of mechanical system can be obtained.

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.

The construction of conserved quantities for linearly coupled oscillators and study of symmetries about the conserved quantities

In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.

Conformal invariance,Noether symmetry,Lie symmetry and conserved quantities of Hamilton systems

In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.

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.

Conformal invariance and conserved quantities of Appell systems under second-class Mei symmetry

In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system＇s conformal invariance and Mei symmetry are discussed. And Appell system＇s conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.