EULER–LAGRANGE EQUATIONS FOR FUNCTIONALS DEFINED ON FRÉCHET MANIFOLDS

We prove a version of the variational Euler–Lagrange equations valid for functionals defined on Fréchet manifolds, such as the spaces of sections of differentiable vector bundles appearing in various physical theories.     

ULTRASONIC BIOEFFECTS AND SAFETY PROBLEM OF ULTRASONIC CLINICAL DIAGNOSIS

With the rapid development of ultrasonic application in clinical diagnosis,especially inobstetrics,the problem on the safety has been attracting more and more attention of scientists andpublic.In this review a series of problems concerning exposure parameters,data generalization ofultrasonic bioeffects,recommendations on safety threshold,epidemiological studies on the safety ofultrasonic examination in pregnancy and some phenomena expected urgently to be studied aredicussed and several intelligent guide principles which would be accepted for use of ultrasound inobstetrics will be pointed out.     

CALCULATION OF THE SPECIFIC ACOUSTIC RESISTANCE OF THE FINE GRIDS AND ITS APPLICATION

In this paper,the rigorous formula for calculating the specific acoustic resistance of a fine gridis derived by means of the fundamental theory of sound.The corresponding approximate formulasto meet the practical purpose are obtained.Theoretical calculations are compared with experimentalresults.Some suggestions to be valuable to the practical design are discussed.     

ON THE PROBLEM OF THE DUAL CHARGE (MAGNETIC MONOPOLE) OF NON-ABELLAN GROUPS (Ⅱ)

The method of relating the gauge potential to the connection on a spherical surface developed in a previous paper is generalized to the discussion of the potential of an SU(2) magnetic monopole with O(5) symmetry. Expressions for the potential of the monopole with double string singularity or single string singularity are obtained. Finally, by a combined coordinate-gauge transformation, we obtain a string free expression for an SU(2) magnetic monopole with O(5) symmetry.     

ON THE CONTROL OF RINGING NOISE EXCITED BY IMPACT II:THE ENERGY OF RINGING NOISE AND THE BUFFERING OF THE IMPACT

In the first of these two papers,the expression for the total energy of vibration excited by impacthas been obtained.In this paper the energy equation of ringing noise was derived from the resultof the first paper.This energy equation indicates the approaches to control ringing noise.Thebuffering method was discussed here in detail.The experiment which has been conducted was describedalso.     

INVARIANCE OF THE KAUP–KUPERSHMIDT EQUATION AND TRIANGULAR AUTO-BÄCKLUND TRANSFORMATIONS

We report triangular auto-Bäcklund transformations for the solutions of a fifth-order evolution equation, which is a constraint for an invariance condition of the Kaup–Kupershmidt equation derived by E. G. Reyes in his paper titled "Nonlocal symmetries and the Kaup–Kupershmidt equation" [J. Math. Phys. 46 (2005) 073507, 19 pp.]. These auto-Bäcklund transformations can then be applied to generate solutions of the Kaup–Kupershmidt equation. We show that triangular auto-Bäcklund transformations result from a systematic multipotentialization of the Kupershmidt equation.     

CHARACTERISTICS OF THE FLOW RATE AND NOISE RADIATION OF MICROPORE MUFFLER

In the present work,the flow rates and noise radiations of micropore and micropore muffler atdifferent chamber pressures are investigated.When the number of micropores of a micropore muffleris small(the total geometrical area of micropores is,say,less than 1.5 times the cross section area of theexhaust pipe)and the flow is choked at the micropores,the flow rate and noise radiation are proportionalto the number of pores and the back pressure is very low,around 0.1 atmosphere pressure or so.Theflow rate through each micropore is proportional to the chamber pressure(or the stagnation pressureof microjet),but the effective area of micropore is only about 60 percent of its geometrical area.Whenthe total geometrical area of pores is near or greater than 1.5 times the cross section area of the mufflerinlet pipe,the increase of flow rate with the increase of the number of micropores will slow down andfinally the total flow reaches a limit va1ue equal to that of the bare exhaust pipe.The noise radiationof each mi     

THE GENERATOR COORDINATE METHOD AND NUCLEAR COLLECTIVE MOTIONS (Ⅷ) THE CHOICE AND REPRESENTATION OF COLLECTIVE DEGREES OF FREEDOM

The choice and representation of degrees of freedom of collective motions are thoroughly discussed. Starting from the dynamical group of a shematic model, it is pointed out that the number of independent collective degrees of freedom is uniquely determined, although there exist different continuous variable or boson representations. If more collective degrees of freedom were involved, there must be accompanied conditions.     

FM-EVOKED RESPONSES AND FM-TONOTOPIC CHARACTERISTICS IN THE AUDITORY CORTEX OF THE CAT

Averaged FM-evoked responses were recorded from different points on the surface of the AI areain cats and response thresholds(△F_m)for different carrier frequencies(F)were determined.△F_m variedgreatly with Fand with the site of recording.The majority of the △F_m-versus-F curves were markedwith the presence of one or more deep valleys.High,middle and low characteristic-F points of FM-responses intermingled in the AI area,a distribution entirely different from the tonotopic mapping ofthe auditory cortex in tuning responses.This was discussed in view of fine neuro-structural differentia-tion at the cortex level for auditory perception and discrimination.The smallest △F_m obtained incats with the FM-response method was lower than 1%F for F>1000Hz and lower than 10Hz forF<1000Hz.     

ASYMPTOTIC FREEDOM AND THE WAVE FUNCTIONS AT THE ORIGIN AND THE ENERGY LEVELS OF THE J/ψ AND THEY

On the basis of phenomenological quantum chromodynamics (QCD), a nonre-lativistic linear and Coulomb-like potential describtion of the strong interaction be-tween quarks is assumed and it is considered that the effective quark-gluon coup-ling constant approaches the asymptotically free limit of QCD. The cloice of thepotential parameters is so made as to fit the experimental values of the wave func-tions at the origin as well as the masses of the J/ψ and the γ Following the calcu-lation referring to the ψ′and the γ′, we acquire a consistent explanation for boththe relative values of the wave functions at the origin and the experimental mass asdifferences of these particles.     

RECURRENT FORMULA FOR α-ROW PARTITION AND THE CALCULATIONS OF THE MULTIPLICITIES OF COUPLING STATES IN SHELL-MODEL

In this paper, a recurrent formula for α-row partition is given. Using this formula, we get the multiplicities of all sorts of coupling states in shell-model. It has been proved to be very efficient in simplifying the ealculations concerned.     

THE OVERLAP OF MAGNETIZATION AND THE COUPLING OF IMPURITIES WI丁H LATTICE FOR DM SPIN GLASS

The overlap of magnetization of the giound state in a RKKY spin glass system with the Dzyaloshinsky-Moriya interaction is studied based on the theory of infinite number of order parameter. It is shown that the nonmagnetic impurities are coupled with the host lattice.The results are in good agreement with experiments.     

PARTIAL RESTORATION OF THE CHIRAL SYMMETRY AND THE π CONDENSATION IN NUCLEAR MATTER

From the relativistic semiclassieal theory of π condensation[1], we deduced that, in the σ model, because of the variation of the radius of the magic circle with nuclear density, the π condensation in nuclear matter is possible. The calculated critical density is slightly higher than that of the normal ground state nuclear matter.     

ON THE NONLOCAL SYMMETRIES OF THE μ-CAMASSA–HOLM EQUATION

The μ-Camassa–Holm (μCH) equation is a nonlinear integrable partial differential equation closely related to the Camassa–Holm and the Hunter–Saxton equations. This equation admits quadratic pseudo-potentials which allow us to compute some first-order nonlocal symmetries. The found symmetries preserve the mean of solutions. Finally, we discuss also the associated μCH equation.     

A TRIAL OF ESTABLISHING THE DYNAMICAL METHODOLOGY FOR ESTIMATING THE STATE OF LINEAR STRUCTURE VIBRATION THROUGH THE OBSERVATIONS OF RADIATED NOISE POWER AND ITS SIMULATION EXPERIMENT

This paper describes a methodological trial from a basic viewpoint based on the system theoryand its simulation for the environmental noise and vibration problems.The state estimation of non-stationarily vibratory structure system through the observation of radiated noise accompanied withundesirable other vibration and background noise is discussed here.The recursive estimation algo-rithm is newly derived by expanding the so-called Bayes'theorem in the form of an orthogonal expan-sion series.Consequently,any kinds of statistics of state variables can be derived from this estimatedprobability density function.The validity and the effectiveness of proposed method are confirmedespecially by means of digital simulation,since the present study is yet in an early stage and focussedon only the methodological viewpoint in this paper.     

THE DETECTION OF SIGNALS AND ESTIMATION OF PARAMETERS IN A RANDOMLY SPACE-TIME VARIANT CHANNEL

The detection performance of matched filter will be degraded and the errors of estimated para-meters of matched filter will be increased in a randomly space-time variant channel.The paperdiscussed this effect.The architecture and performance of optimum space-time processor are givenin this case.The way to construct a practical system is discussed.This paper corrects some am-biguous concepts on scatter function expression of partial coherence channel in some papers.     

G2 PREDICTION OF THE ENTHALPIES OF FORMATION FOR SOME DIATOMIC CATIONS AND NEUTRALS

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WAVE FRONT SOL盯IONS AND STABILITY PROBLEM OF A MODEL DESCRIBING TISSUE GROWTH

A biological model describing tissue growth under the inhibition of chalones is investigated. Wave solutions and their stability properties are worked out.     

ESSENTIAL WORK OF FRACTURE AND THE PHASE TRANSFORMATION IN β-iPP

The possibility of phase transformation toughening is demonstrated by the example of the β-modification isotactic polypropylene (β-iPP), which undergoes the β–α transformation (i.e., from hexagonal to monoclinic) during mechanical loading. The β–α recrystallization was examined on essential work of fracture (EWF) specimens with two processing conditions. Differential scanning calorimetry and wide-angle x-ray diffraction demonstrate the occurrence of this β–α transformation. Some structural changes can be identified in EWF specimens by using nano-indentation machine. Toughness of the α- and β-iPP is studied and compared with the EWF concept by using static-loaded deeply double-edge-notched tensile specimens. The main effect of the β–α transformation is a large increase in the specific plastic work consumed in the necked zone.