On the solitonic structures of the cylindrical dust-acoustic and dust-ion-acoustic waves with symbolic computation

Dusty plasmas can support the dust-ion-acoustic and dust-acoustic modes, modelled by the cylindrical Korteweg–de Vries equation as proposed. In this Letter, we point out that there exist a couple of problems in the plasma-physics literature on the cylindrical Korteweg–de Vries equation, i.e., the claim of non-existence of exact analytic solutions and omission of varying ambient field, to which we provide our answers. With symbolic computation, we obtain a family of exact analytic, solitonic solutions, of which the previous solutions in plasma physics turn out to be the special cases. With figures, we work out some possibly observable effects for the future plasma experiments, featured by a solitonic pulse aboard the varying ambient field propagating with its varying velocity and amplitude.     

Mechanical theorem proving in differential geometry

An automated reasoning method, based on Wu’s method and calculus of differential forms, is proposed for mechanical theorem proving in local theory of space surfaces in differential geometry. The method has been used to simplify one of Chem’s theorems: “The non-trivial families of isometric surfaces having the same principal curvatures are W-surfaces.” Some other theorems are also tested by this method. The proofs are generally simpler than those in differential geometry textbooks. Project supported partially by the National Natural Science Foundation of China.     

GENERALIZED BOCHNER THEOREM ON LOCALLY CONVEX SPACES

ThisworkissupportedinpartbythePostdoctoralScienceFoundationofChina.1.IntroductionTheclassicalBochnertheoremstatesthatafunctionCiR"-CisthecharacteristicfunctionofaprobabilitymeasureonR"iffCispositivedefinite,C(0)=1andcontinuous.FOrvariousgeneralizationsofthetheoremtoinfinitedimensionspaces,thereaderisreferredto{1]andT3I.Inthemonographl'],MinlostheoremgeneralizestheclassicalBochnertheoremtonuclearspaces,whichcharacterizestheclassofcharacteristicfunctionalsofRadonprobabilitymeasuresonstron…     

Spinless Excitons Implicit in SO(5) Theory

A pair of up-down operators are constructed explicitly for S.C.Zhang‘s SO(5) theory of high Tc superconductivity.From them two good quantum numbers are derived.The up-down operators are related to the spin-independent excitons which are not considered before.``     

Compact diode-pumped Nd:YVO4 intracavity-doubled red laser at 671 nm

A design of diode-pumped high efficiency Nd:YVO₄/LBO laser with a compact linear cavity was reported. Employing a type-II noncritical phase-matched LBO crystal, we generated 520 mW of 671 nm in single transverse mode at 6 W of incident pump power, the optical conversion efficiency being 8.7%.     

GaS multi-walled nanotubes from the lamellar precursor

Inorganic fullerene-like (IF) nanotubes constructed from layered metal chalcogenides are of particular significance because of their excellent physical properties and potential application in wide fields. But very few previous studies were focused on the IF nanotubes of layered III-VI semiconductor. Therefore we investigate the preparation, structure and photoluminescence (PL) properties of GaS nanotube (an important III-VI semiconductor IF nanotube). A simple method is introduced to prepare GaS multi-walled nanotubes for the first time by annealing the natural lamellar precursor in Ar. The reaction temperature is crucial for the formation of nanotube. A suitable temperature range is 500–850 °C. Bulk quantities of GaS nanotubes with diameters of 30–150 nm and lengths up to ten micrometers were produced. Some of these nanotubes show corrugated and interlinked structure and form many segments, demonstrating a bamboo-like structure. As compared to bulk materials, the obvious distinction of the products in PL spectra at liquid nitrogen temperature of 77 K was due to the structure variety. PACS 61.46.+w; 81.07.De; 81.16.Be     

Synchronous multi-scale observations on rock damage and rupture

This paper reports a multi-scale study on damage evolution process and rupture of gabbro under uniaxial compression with several experimental techniques, including MTS810 testing machine, white digital speckle correlation method, and acoustic emission technique. In particular, the synchronization of the three experimental systems is realized for the study of relationship of deformation and damage at multiple scales. It is found that there are significant correlation between damage evolution at small and large length scales, and rupture at sample scale, especially it displays critical sensitivity at multiple scales and trans-scale fluctuations.     

Preparation of magnetic poly(methylmethacrylate–divinylbenzene–glycidylmethacrylate) microspheres by spraying suspension polymerization and their use for protein adsorption

Moderately uniform magnetic poly(methylmethacrylate–divinylbenzene–glycidylmethacrylate) microspheres (poly(MMA–DVB–GMA) microspheres) were prepared by spraying suspension copolymerization of methyl methacrylate, divinylbenzene and glycidyl methacrylate in the presence of Fe₃O₄ magnetic fluid. A protein adsorption assay indicated that these magnetic microspheres could significantly improve the capacity of protein adsorption.     

p-adic Transcendence and p-adic Transcendence Measures for the Values of Mahler Type Functions

We prove the p-adic transcendence and p-adic transcendence measures for the values of some Mahler type functions.     

Growth and oxidation of Cr films on the W(1 0 0) surface

The growth and oxidation of Cr films on the W(1 0 0) surface have been studied with low energy electron microscopy (LEEM) and diffraction (LEED). Cr grows in a Stranski-Krastanov (SK) mode above about 550 K and in a kinetically limited layer-by-layer mode at lower temperature. Stress relief in the highly strained pseudomorphic (ps) Cr film appears to be achieved by the formation of (4 × 4) periodic inclusions during the growth of the third layer between 575 and 630 K and by growth morphological instabilities of the third layer at higher temperature. Kinetic or stress-induced roughening is observed at lower temperature. In the SK regime, three-dimensional (3D) Cr islands nucleate after the growth of three Cr layers. 3D island nucleation triggers dewetting of one layer from the surrounding Cr film. Thus, two ps Cr layers are thermodynamically stable. However, one and two layer ps Cr films are unstable during oxidation. 3D clusters, that produce complex diffraction features and are believed to be Cr₂O₃, are formed during oxidation of one Cr layer at elevated temperature, T ? 790 K. The single layer Cr film remains intact during oxidation at T ? 630 K. 3D bulk Cr clusters are formed predominantly during oxidation of two ps Cr layers.