On the Extension of Isometries between Unit Spheres of E and C（Ω）

In this paper,we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E),then under some condition,every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended to be a real linearly isometric map V of E onto C(Ω).From this resultwe also obtain some corollaries. This is the first time we study this problem on different typical spaces,and the method of proof is also very different too.     

On the Action of a Groupoid on a Manifold

In this paper,some properties of reduction for symplectic F-spaces are discussed.The properties of stable subgroups are discussed.We find that the symplectic action of a symplectic groupoid on a symplectic manifold can induce a symplectic map between reduced symplectic manifolds.This symplectic action can be characterized by the action of its induced symplectic groupoid on a symplectic manifold.Lastly,we shall discuss Poisson reduction and give a Poisson reduction theorem.     

QUALITATIVE THEORY OF THE KUKLES SYSTEMS:(Ⅰ) NUMBER OF CRITICAL POINTS

The special cubic system (a natural and simPlest generaIization of thequadratic system of C1ass (l) to cubic system)f.'x = yl y = --x 6y a,x' a2xy a,y' a#x' a,x'y a.xy' a,y' (1)was first studied by the Russian Mathematician I.S.KukIes [ll on the Ilecessaryand sufficient conditions fot O(0,0) to be a ccnter of (1). After [ll, the sameproblem and also the order of O as a fine fOcus were also studied iIl [2--l0] and[13-19], so (l) is now called as a "Kukles system". In l988-…     

Correlation of substituent effects and energy levels of the two lowest excited states of the azulenic chromophore

[structure: see text] Experimental and calculated data show that the relative energy levels of the two lowest excited states of azulene are sensitive to the nature and position of substituents on the nonalternant hydrocarbon. Extending such investigations led to a rational explanation for some of the baffling data on azulenic bacteriorhodopsin analogues in the literature.     

Target strength of an oily deep-water fish, orange roughy (Hoplostethus atlanticus). II. Modeling

Orange roughy consist of approximately 18% lipids by weight, mostly as wax esters, and the lipids must be taken into account when modeling target strength. A deformed cylinder model incorporating the effect of temperature and pressure on sound speed through wax ester was used to scale experimental measurements of target strength to the temperatures and pressures where orange roughy live (approximately 6 degrees C, depths approximately 800-1300 m). The effect of decreasing temperature and increasing pressure is to increase the sound speed in orange roughy lipids. Modeling shows that the net effect of this is to reduce tilt-averaged target strength, 'TS', by approximately 2 dB. Adjusting experimental results to compensate for temperature and pressure effects gives a predicted 'TS' for a 35-cm orange roughy of -48.3 dB. Adjusting in situ estimates of orange roughy 'TS' for avoidance behavior [McClatchie et al., J. Acoust. Soc. Am. 106, 131-142 (1999)] suggests the correct 'TS' is approximately -47.5 dB, rather than -50 dB as previously reported [Kloser et al., ICES J. Mar. Sci. 54, 60-71 (1997)]. We conclude that experimental and in situ estimates now converge at a 'TS' of approximately -48 dB for a 35-cm fish.     

Enhancement and inhibition of acoustic radiation in spherical cavities

Acoustic radiation from a source located inside layered cavities is studied using the transfer matrix method. It is shown that the radiation can be either enhanced or inhibited, depending on the characteristics and the material composition of the cavities. The analysis predicts well-defined spectral peaks and nodes in some cavities. It is found that significant enhancement and inhibition are possible by varying acoustic parameters. The results also show that the strength of the radiating source can be significantly modified due to the presence of layered structures. The link to the similar phenomena in the optical cavities is discussed.     

Real three-dimensional microstructures fabricated by photopolymerization of resins through two-photon absorption

Effective energy windows for two-photon absorption (TPA) photopolymerization of resins were investigated and, with a properly selected laser pulse energy, exquisite three-dimensional (3D) microstructures with submicrometer spatial resolution were achieved. The results show the inherent utility of TPA in the fabrication of real 3D patterns. In particular, we propose and utilize a resin pre-exposure technique by which freely movable components affixed to an axle are built, demonstrating a new application of TPA in laser microfabrication.     

Quantification of cerebral blood flow by bolus tracking and artery spin tagging methods

This study deals with perfusion quantification in healthy volunteers using two types of dynamic magnetic resonance imaging (MRI) methods. Absolute cerebral blood flow (CBF) measurements were performed in 11 subjects by applying both bolus tracking of exogenous contrast agent and non-invasive arterial spin labeling MRI techniques. Both methods produced CBF images with good tissue contrast and CBF values are in good agreement with literature data. The correlation between cerebral blood volume (CBV) and CBF is also discussed.     

Spin-locking mechanism of spin I = 3/2 quadrupolar nuclei undergo magic angle spinning

The spin-locking mechanism of the spin I=3/2 quadrupolar nuclei under magic angle spinning (MAS) has been theoretically and experimentally investigated, and the criterion of adiabatic passage around zero-crossings of the quadrupole splitting was inferred from the time-dependent Shrödinger equation in this article. The theory, numerical simulations, and experiments conducted in this work all indicated that second-order quadrupole interaction and off-resonance play important roles in the spin-locking of the quadrupolar nuclei, and they were responsible for the great loss of the spin-locking signals. The spin-locking for a spin I=3/2 nucleus might be achieved by minimizing the effect of the second-order quadrupole interaction by using a radio frequency (RF) offset. This offset was realized by setting the RF to the opposite position of the isotropic second-order quadrupolar shift of single quantum coherences.     

Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb

We demonstrate a great simplification in the long-standing problem of measuring optical frequencies in terms of the cesium primary standard. An air-silica microstructure optical fiber broadens the frequency comb of a femtosecond laser to span the optical octave from 1064 to 532 nm, enabling us to measure the 282 THz frequency of an iodine-stabilized Nd:YAG laser directly in terms of the microwave frequency that controls the comb spacing. Additional measurements of established optical frequencies at 633 and 778 nm using the same femtosecond comb confirm the accepted uncertainties for these standards.