Lacunary Measures and Self-similar Probability Measures in Function Spaces

The paper deals with multifractal quantities for some types of Radon measures,especiallyself-similar probability measures,and their relations to Besov spaces.     

Symmetries of Itô and Stratonovich Dynamical Systems and Their Conserved Quantities

A new definition for the symmetries of Itô and Stratonovich dynamicalsystem is given. Determining systems of symmetries for Itô andStratonovich systems have been obtained, and their relation has beendiscussed. It has been shown that some of the Lie point symmetries ofthe Fokker–Planck equation can be constructed using the symmetries ofItô dynamical systems. Conserved quantities can be found from thesymmetries of stochastic dynamical systems which do not arise from aHamiltonian. The results have been applied to an example.     

Lie Symmetry and Conserved Quantities for Nonholonomic Vacco Dynamical Systems

In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity and the Lutzky conserved quantity deduced from the symmetry are obtained.     

中心—焦点区分问题的I l'yashenko算法

对二维平面系统的二维系统的中心焦点区分问题 ,I l'yashenko曾建议一个算法 ,本文给出此法的详细证明 .据此 ,我们讨论了区分问题在 Arnold意义下的代数可解性与不可解性     

新疆产12种中草药中微量金属元素的测定

本文测定了新疆产新疆党参,新疆元胡等１２种中草药中十种微量金属元素的含量．结果表明这些中草药中具有显著生理活性的Ｚｎ、Ｆｅ、Ｃｕ、Ｍｎ等元素．它们的含量除了个别样品外均大于或接近于国内其它地区所产的同种中草药、根据冠心病病因的Ｚｎ／Ｃｕ值假说和微量金属元素的含量关系,新疆产１２种中草药也可用于防治冠心病．     

Conductivity Studies of <Emphasis Type="Italic">n</Emphasis>-Tetrabutylammonium Tetraphenylborate in 3-Pentanone in the Temperature Range from 283.15 to 329.15 K

The molar conductivities (Λ) of solutions of n-tetrabutylammonium tetraphenylborate (NBu₄BPh₄) in 3-pentanone have been measured in the temperature range from 283.15 to 329.15 K. The conductance data have been analyzed using the Lee-Wheaton conductivity equation with the distance parameter (a) set at Bjerrum’s pairing distance, and the limiting molar conductivities (Λ_o) and the association equilibrium constants (K _A) have been derived. The limiting ion conductivities (λ_±^o) have been evaluated according to the method of Krumgalz. The λ₊ ^o values have been compared with λ₊ ^o values calculated from the empirical equation of Gill. The thermodynamic functions, Gibbs energy (Δ G _A ^o), enthalpy (Δ H _A ^o) and entropy (Δ S _A ^o) for the process of ion-pair formation as well as the activation energy of the ionic movement (ΔH ^∗) have been evaluated. The obtained results are discussed in terms of ion-ion and ion-solvent interactions.     

Noether-Mei Symmetry of Mechanical System in Phase Space

In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e., a Noether-Mei symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the Mei conserved quantity deduced from the Noether-Mei symmetry of the system are obtained. Finally, two examples are given to illustrate the application of the results.     

Non-Noether Conserved Quantity of Poincaré-Chetaev Equations of a Generalized Classical Mechanics

In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré-Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced. Finally, an example is given to illustrate the application of the results.     

An Interacting Gauge Field Theoretic Model for Hodge Theory: Basic Canonical Brackets

We derive the basic canonical brackets amongst the creation and annihilation operators for a two （1 ＋ 1）- dimensional （2D） gauge field theoretic model of an interacting Hodge theory where a U（1） gauge field （Aμ） is coupled with the fermionic Dirac fields （ψ and ψ）. In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries （and the concept of their generators） that are present in the theory. We do not use the definition of the canonical conjugate momenta （corresponding to the basic fields of the theory） anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries （and corresponding generators） provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.     

Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed,the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.