New Examples of Willmore Surfaces in S n

A surface x: M S ⁿ is called a Willmore surface if it is a criticalsurface of the Willmore functional _M (S – 2H ²)dv, where H isthe mean curvature and S is the square of the length of the secondfundamental form. It is well known that any minimal surface is aWillmore surface. The first nonminimal example of a flat Willmoresurface in higher codimension was obtained by Ejiri. This example whichcan be viewed as a tensor product immersion of S ¹(1) and a particularsmall circle in S ²(1), and therefore is contained in S ⁵(1) gives anegative answer to a question by Weiner. In this paper we generalize theabove mentioned example by investigating Willmore surfaces in S ⁿ (1)which can be obtained as a tensor product immersion of two curves. We inparticular show that in this case too, one of the curves has to beS ¹(1), whereas the other one is contained either in S ²(1) or in S ³(1). In the first case, we explicitly determine the immersion interms of elliptic functions, thus constructing infinetely many newnonminimal flat Willmore surfaces in S ⁵. Also in the latter casewe explicitly include examples.     

Radiation inhibition effects in the coherent-state many-atom Jaynes-Cummings model

Summary Radiation inhibition in the many-atom Jaynes-Cummings model being a consequence of cooperative as well as cavity detuning effects is examined. Numerical solutions for the time evolution of the atomic population inversion exhibiting quasi-stationary behaviour are presented. Furthermore, the cooperative energy shift of these quasi-stationary states is numerically computed by using a special projection operator. The authors of this paper have agreed to not receive the proofs for correction.     

Far infrared surface plasmon propagation

New experimental evidence is presented which shows that, contrary to an earlier report, far-infrared surface plasmons at metal-air interfaces propagate long distances (tens of centimeters or longer).     

近自由面细长体的振荡问题

本文引进细长体的假定,把三维的流体运动问题化成了二维的非定常问题。前面剖面对后面剖面的干扰作用用积分表示,对物体作了适当近似以后,改善了切片理论。根据物面条件把整个问题的求解分解为兴波问题和振荡问题,而振荡问题可由兴波问题的适当组合表示出来。这样,大大简化了问题的求解。作为例子,本文数值计算了细长体的水动力导数,给出了结果。     

Triangle anomaly free weak interaction with two neutral currents

Considering that the neutral interaction is free of triangle anomalies we derive an expression for the most general neutral interaction with two neutral currents. We show that the Bargers version is a special case. We also determine the interaction wheneverZ, D are mass eigen states and show that this differs from the Barger’s version in an essential way.     

A solvent-governed surface state strategy for rational synthesis of N and S co-doped carbon dots with multicolour fluorescence

ABSTRACT

Multicolour emissive carbon dots (CDs) are widely investigated by virtue of their merits on fluorescent properties. Method on heteroatom doping assisted with various solvents has been proved efficient in achieving multiple-colour-emissive CDs, especially long-wavelength emission. Herein, a synthesis of multicolour-emissive CDs by controlled surface function is reported. By tuning the thermal-pyrolysis temperature and molar ratio of reactants, optimal emission of the resulted CDs gradually shifts from blue to yellow light with the assistance of different solvents. According to the emissive relationship dependent on excitation, fluorescence lifetimes, and FT-IR of these CDs, the different surface states participated with S and N elements on the surface of carbogenic core govern fluorescent colours of the CDs. In terms of the applications, blue CDs (B-CDs) exhibits high sensitivity for ion detections of Ag⁺ and Fe³⁺, which is further illustrated to have different quenching mechanisms each other because that these ions have the affinity interaction with different surface groups of the CDs. Moreover, blue and yellow CDs solutions are mixed with PVP water solution to fabricate white-light CDs/PVP film, which exhibits stable fluorescence with a CIE coordinate of (0.32, 0.33) and endows these CDs as potentially fluorescent nanomaterial in the solid state lighting field.     

Multiple phase transitions in the generalized Curie-Weiss model

The generalized Curie-Weiss model is an extension of the classical Curie-Weiss model in which the quadratic interaction function of the mean spin value is replaced by a more general interaction function. It is shown that the generalized Curie-Weiss model can have a sequence of phase transitions at different critical temperatures. Both first-order and second-order phase transitions can occur, and explicit criteria for the two types are given. Three examples of generalized Curie-Weiss models are worked out in detail, including one example with infinitely many phase transitions. A number of results are derived using large-deviation techniques.     

Determination of the content and localization of magnesium in bioapatite of bone

Using x-ray diffraction, electrothermal atomization atomic absorption spectroscopy, and scanning electron microscopy with an x-ray microanalysis, we have studied the phase decomposition of biogenic and synthetic Mg-containing apatite at 900°C with formation of β-tricalcium-magnesium phosphate (β-TCMP). Employing simplified model representations, we obtained a relation that couples the initial Mg concentration with the degree of transformation of apatite into β-TCMP. It is shown that for the β-TCMP contents measured in bioapatite samples and on replacement of calcium by magnesium to about 8% in this phase the calculated range of Mg concentrations coincides with that available in literature sources (0.2–0.6 wt. %). A comparative investigation of the products of decomposition of biogenic and synthetic apatite by the methods of analysis of the composition and structure has established that the formation of β-TCMP is limited by both the insufficient concentration of magnesium and the small sizes of the crystals. The results of the investigations carried out together with the experimental data known from the literature are indicative of the nonuniform distribution of magnesium in the bulk of crystals of biogenic and synthetic apatite, with its predominant localization at the surface sites of the lattice. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 6, pp. 821–826, November–December, 2005.