Shear buckling modes of cylindrical sandwich shells under external pressure, tension-compression of bearing layers with unequal forces, and inhomogeneous across-the-thickness temperature

Equations are set up for describing, in a correct statement and with an accuracy sufficient in actual practice, the shear buckling modes (BMs) of cylindrical sandwich shells with a transversely soft core of arbitrary thickness. Based on them, solutions are obtained to a number of problems on the buckling instability according to shear modes under some force and thermal loadings. It is found that the BMs occur in the shell along the circumferential and axial directions if, in the precritical state, a normal compressive stress arises in the transverse direction. It is shown that this condition is fulfilled in the following cases: in axial tension of the shell with unequal forces applied to the end faces of bearing layers (the parameter of critical load is maximum if the tensile forces are equal); under external (internal) pressure; on cooling the outer and heating the inner layers. The results obtained are presented in the form of simple analytical formulas for determining the corresponding critical parameters of the force and thermal actions.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 37–48, January–February, 2005.     

模糊一致体

定义了模糊一致体概念,研究了它与模糊拓扑体的关系及它与模糊一致空间的关系;给出了借助于体的模糊子集族对模糊一致体的刻画,还引入了模糊一致子体,模糊一致商体与模糊一致体的直积;并讨论了它们的分离性.     

Modern proton‐detected 1D 1H–15N NMR experiments. Application to the measurement of 1H,15N coupling constants at natural abundance

Non‐selective and selective versions of several proton‐detected 1D NMR experiments to be applied to ¹⁵N are proposed. Clean, artifact‐free 1D spectra are easily obtained by the effective coherence selection by pulsed‐field gradients and the attainable sensitivity is maximized using modern pulse schemes. Despite the low sensitivity inherent to ¹⁵N NMR spectroscopy, the successful application of these experiments is demonstrated for resonance assignments and accurate measurement of both one‐bond and long‐range proton–nitrogen coupling constants on a model tripeptide at natural abundance. Copyright © 2001 John Wiley & Sons, Ltd.     

Extension of the Coherent Gradient Sensor (CGS) to the Combined Measurement of In-Plane and Out-of-Plane Displacement Field Gradients

The Coherent Gradient Sensor (CGS) is extended to the optical differentiation of specular, diffracted wave fronts leading to the combined measurement of in- and out-of-plane displacement field gradients. A derivation of the underlying optical interference principles is presented along with an analysis of the effective instrument sensitivity. In order to demonstrate the capabilities of the technique, experimental measurements of crack-tip deformation fields were conducted under various loading conditions corresponding to mode-I, mode-II, and mixed mode near-tip crack fields. The experimental procedures and results of these tests are presented as validation of the technique.     

Gribov ambiguity in gauge theories

Gribov ambiguity in gauge field theories is discussed and it is shown that such an ambiguity exists even for Abelian theories in covariant gauge at finite temperature. Both geometric and algebraic proofs are presented. In view of the importance of non-perturbative methods, some special gauges are given in which such ambiguities do not exist or are not relevant. The significance of these in the study of confinement in QCD is pointed out.     

On the moduli space of deformations of bihamiltonian hierarchies of hydrodynamic type

We investigate the deformation theory of the simplest bihamiltonian structure of hydrodynamic type, that of the dispersionless KdV hierarchy. We prove that all of its deformations are quasi-trivial in the sense of B. Dubrovin and Y. Zhang, that is, trivial after allowing transformations where the first partial derivative ∂u of the field is inverted. We reformulate the question about deformations as a question about the cohomology of a certain double complex, and calculate the appropriate cohomology group.     

High performance polymer field‐effect transistors based on polythiophene derivative with conjugated side chain

Poly(3‐[2‐(5‐hexyl‐2‐thienyl) ethenyl]‐2,2′‐bithiophene) ( P2 , see Scheme 1 ) with conjugated thienylvinyl side chain was synthesized by copolymerization of the thiophene units with and without conjugated side chain with Pd‐catalyzed Stille coupling method. For comparison, P1 with the hexyl side chain instead of conjugated side chain was also synthesized. P2 film shows broad absorption in the visible region with absorption edge at about 700 nm. The solution‐processed polymer field‐effect transistors were fabricated and characterized with bottom gate/top contact geometry. The organic field‐effect transistors (OFET) based on P2 showed an average hole mobility of about 0.034 cm²/Vs (the highest value reached 0.061 cm²/Vs) upon annealing at about 180 °C for 30 min, with a threshold voltage of ?1.15 V and an on/off ratio of 10⁴ with n‐octadecyltrichlorosilane (OTS) modified SiO₂ substrate. In comparison, the OFET based on P1 displayed a hole mobility of 8.9 × 10^–4 cm²/Vs and an on/off ratio of 10⁴ with OTS modified SiO₂ substrate. The results indicate that the polythiophene derivative with conjugated thienylvinyl side chain is a promising polymer for the application in polymer field‐effect transistors. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5304–5312, 2009     

Laplaza sets, or how to select coherence diagrams for pseudo algebras

We define a general concept of pseudo algebras over theories and 2-theories. A more restrictive such a notion was introduced in [Po Hu, Igor Kriz, Conformal field theory and elliptic cohomology, Adv. Math. 189 (2) (2004) 325-412, http://www.math.lsa.umich.edu/~ikriz/], but as noticed by M. Gould, did not capture the desired examples. The approach taken in this paper corrects the mistake by introducing a more general concept, allowing more flexibility in selecting coherence diagrams for pseudo algebras.     

Quadratic Actions in Dependent Fields and the Action Principle

General field theories are considered, within the functional differential formalism of quantum field theory, with interaction Lagrangian densities L _I (x;λ), with λ a generic coupling constant, such that the following expression ∂ L _I (x;λ)/∂ λ may be expressed as quadratic functions in dependent fields but may, in general, be arbitrary functions of independent fields. These necessarily include, as special cases, present renormalizable gauge theories. It is shown, in a unified manner, that the vacuum-to-vacuum transition amplitude (the generating functional) may be explicitly derived in functional differential form which, in general, leads to modifications to computational rules by including such factors as Faddeev–Popov ones and modifications thereof which are explicitly obtained. The derivation is given in the presence of external sources and does not rely on any symmetry and invariance arguments as is often done in gauge theories and no appeal is made to path integrals.     

ARC INTERFACE CRACK IN A THREEPHASE PIEZOELECTRIC COMPOSITE CONSTITUTIVE MODEL

An in-depth investigation is made on the problem of an arc-shaped interface insulating crack in a three-phase concentric circular cylindrical piezoelectric composite constitutive model. An exact solution in series form is derived by employing the complex variable method. In addition, the distribution of physical quantities such as stresses, strains, electric displacements and electric fields in the whole field and along the interface is also presented. Explicit expressions for crack opening displacement, jump in electric potential on the crack surface and the electro-elastic field intensity factors at the crack tips are obtained. Specific calculations demonstrate that the convergence of the series form solution is satisfactory and that the outer phase (composite phase) will exert a significant effect on the electro-mechanical coupling response of the composite system. Owing to the fact that stresses and electric displacements still possess conventional inverse square root singularities, the oscillating singularities near the crack tip under plane strain conditions will be absent and, as a result, no unphysical interpenetration phenomenon of the two crack surfaces will occur. In conclusion, the elastic solution obtained is also based on a solid physical foundation. Project supported by the National Natural Science Foundation of China (No.59635140), and the Doctorate Foundation of Xi'an Jiaotong University.