High-power continuous-wave operation of a diode-pumped laser at

The continuous-wave laser properties of an efficient diode-pumped Nd:GdVO₄ crystal operating at formed with a simple plane-concave cavity have been studied. With the incident pump power of 21 W, an output power of 6.9 W was obtained, giving an optical conversion efficiency of 32.8% and a slope efficiency of 35.3%. The laser characterization of two different Nd³⁺-doped concentration of Nd:GdVO₄ crystals were studied.     

Studies on the conformation of α-arylcinnamic acids and their esters: Crystal structures of methyl (E)-2,3-bis(3,4-dimethoxyphenyl)propenoate and methyl (Z)-2,3-bis(3,4-dimethoxyphenyl)propenoate

The conformations of stereoisomers of -arylcinnamic acids and their esters are discussed based on crystal structures of the E and Z forms of 2,3-bis(3,4-dimethoxyphenyl)propenoic acid and its methyl ester. In the E forms of the cinnamic acid and the cinnamic acid ester, the plane of the -aryl substituent is approximately perpendicular to that of the rest of the molecule. In the Z forms the plane of the carboxyl or methoxycarbonyl group is approximately perpendicular to that of the ethylenic group, and both the aromatic group planes are significantly twisted out of the ethylenic group plane. Crystal structures of methyl (E)-2,3-bis(3,4-dimethoxyphenyl)propenoate (space group P2₁/n with a = 8.1697(5), b = 11.3882(9), c = 19.7766(9) Å, = 90.058(4)°, V = 1840.0(2) ų, and Z = 4), monoclinic methyl (Z)-2,3-bis(3,4-dimethoxyphenyl)propenoate (space group P2₁/n with a = 11.183(2), b = 5.640(2), c = 29.737(7) Å, = 99.19(2)°, V = 1851.4(9) ų, and Z = 4), and orthorhombic methyl (Z)-2,3-bis(3,4-dimethoxyphenyl)propenoate (space group P2₁2₁2₁ with a = 8.849(4), b = 24.288(9), c = 8.734(3) Å, V = 1877(1) ų, and Z = 4) are reported.     

σ-多项式的根

§ 1　IntroductionAll graphs considered are finite and simple.Undefined notation and terminology willconform to those in[1 ] .Let V(G) ,E(G) and Gdenote the vertex set,edge set and complement of a graph G,respectively. Let P(G,x) andσ(G,x) denote the chromatic polynomial andσ-polynomialof G,respectively.The log-concavity property of the chromatic polynomial andσ-polyno-mial of G has a close relation to their roots,which were well studied in[2 ,3] .Results onthe study of the roots of…     

An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.     

On the convergence of modified Noor iterations with errors for asymptotically nonexpansive mappings

In this paper, several weak and strong convergence theorems are established for a modified Noor iterative scheme with errors for three asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type, and Noor-type iterations are covered by the new iteration scheme. Our results extend and improve the recently announced ones [B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453; Y.J. Cho, H. Zhou, G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004) 707-717] and many others.     

The ideal property, the projection property, continuous fields and crossed products

Let A be the C^∗-algebra associated to an arbitrary continuous field of C^∗-algebras. We give a necessary and sufficient condition for A to have the ideal property and, if moreover A is separable, we give a necessary and sufficient condition for A to have the projection property. Some applications of these results are given. We also prove that “many” crossed products of commutative C^∗-algebras by discrete, amenable groups have the projection property, generalizing some of our previous results.     

beta-Barrel transmembrane proteins: Geometric modelling, detection of transmembrane region, and structural properties

The location of the membrane lipid bilayer relative to a transmembrane protein structure is important in protein engineering. Since it is not present on the determined structures, it is essential to automatically define the membrane embedded protein region in order to test mutation effects or to design potential drugs. beta-Barrel transmembrane proteins, present in nature as outer membrane proteins (OMPs), comprise one of the two transmembrane protein fold classes. Lately, the number of their determined structures has increased and this enables the implementation and evaluation of structure-based annotation methods and their more comprehensive study. In this paper, we propose two new algorithms for (i) the geometric modelling of beta-barrels and (ii) the detection of the transmembrane region of a beta-barrel transmembrane protein. The geometric modelling algorithm combines a non-linear least square minimization method and a genetic algorithm in order to find the characteristics (axis, radius) of a shape with axial symmetry which best models a beta-barrel. The transmembrane region is detected by profiling the external residues of the beta-barrel along its axis in terms of hydrophobicity and existence of aromatic and charged residues. TbB-Tool implements these algorithms and is available in . A non-redundant set of 22 OMPs is used in order to evaluate the algorithms implemented and the results are very satisfying. In addition, we quantify the abundance of all amino acids and the average hydrophobicity for external and internal beta-stranded residues along the axis of beta-barrel, thus confirming and extending other researchers' results.     

Precoloring extension on unit interval graphs

In the precoloring extension problem a graph is given with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper k-coloring of the graph. Answering an open question of Hujter and Tuza [Precoloring extension. III. Classes of perfect graphs, Combin. Probab. Comput. 5 (1) (1996) 35-56], we show that the precoloring extension problem is NP-complete on unit interval graphs.     

Riemann theta functions periodic wave solutions and rational characteristics for the nonlinear equations

In this paper, based on a multidimensional Riemann theta function, a lucid and straightforward generalization of the Hirota-Riemann method is presented to explicitly construct multiperiodic Riemann theta functions periodic wave solutions for nonlinear equations such as the Caudrey-Dodd-Gibbon-Sawada-Kotera equation and (2+1)-dimensional breaking soliton equation. Among these periodic waves, the one-periodic waves are well-known cnoidal waves, their surface pattern is one-dimensional, and often they are used as one-dimensional models of periodic waves. The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional so that they have two independent spatial periods in two independent horizontal directions. A limiting procedure is presented to analyze in detail, asymptotic behavior of the multiperiodic waves and the relations between the periodic wave solutions and soliton solutions are rigorously established. This generalized Hirota-Riemann method can also be demonstrated on a class variety of nonlinear difference equations such as Toeplitz lattice equation.