A fundamental relationship between the relaxation spectra and the tangent distribution function in the theory of linear viscoelasticity

The tangent distribution function (TDF) is analyzed within the theory of linear viscoelasticity on mechanical properties. A proof is given that both the relaxation and retardation spectra can be derived from the TDF, through a Fredholm integral equation. Furthermore, the relaxation strength can be calculated as a consequence of this relationship. Finally, as an example, the relationship is applied to discrete spectra.     

The Closed Orbits of a Class of Cubic Vector Fields in R3

In this paper, we investigate the isolated closed orbits of two types of cubic vector fields in R₃ by using the idea of central projection transformation, which sets up a bridge connecting the vector field X(x) in R₃ with the planar vector fields. We have proved that the cubic vector field in R₃ can have two isolated closed orbits or one closed orbit on the invariant cone. As an application of this result, we have shown that a class of 3-dimensional cubic system has at least 10 isolated closed orbits located on 5 invariant cones, and another type of 3-dimensional cubic system has at least 26 isolated closed orbits located on 13 invariant cones or 26 invariant cones.     

Dielectric Measurements of CVD Diamonds at Millimeter Wavelength Using a Fabry-Perot Open Resonator

Precise dielectric property measurements at a millimeter wave frequency band are attractive. A Fabry-Perot open resonator consisting of hemispherical and plane mirrors, coupling holes is designed by the use of analytic theories and a numerical simulation code. HFSS. Dielectric constant measurements on CVD diamonds are performed by a frequency variation method. Measurements show that permittivity and loss tangent range from 5.59 to 6.46, and from 1.1 × 10⁻³, to 5.3 × 10⁻². respectively, in the frequency range of 95–100 GHz depending on sample preparation of the CVD diamonds.     

Earthquake曲线切向量上的范数

本文研究了定义在earthquake曲线切向量上的范数，首先证明了一条earthquake曲线ht上初始切向量的范数等价于earthquake测度σ的Thurston范数．其次证明了当t→∞时，ht的切向量Vt的范数增长渐近等于O(||→||The^Ct||σ||Th)，其中C是正的万有常数，||σ||Th是σ的Thurston范数，而O所代表的常数是渐近万有的，也即当t||σ||Th充分大时它是万有的．此外，附带证明了定义在Zygmund有界函数上的两种交比范数是等价的．     

Second-Order Conditions for Efficiency in Nonsmooth Multiobjective Optimization Problems

In this paper, we are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. We introduce a second-order constraint qualification, which is a generalization of the Abadie constraint qualification and derive second-order Kuhn-Tucker type necessary conditions for efficiency under the constraint qualification. Moreover, we give some conditions which ensure the constraint qualification holds.     

Asymptotic behaviour of the loss probability of theM/G/1/K andG/M/1/K queues

This paper investigates the asymptotic behaviour of the loss probability of theM / G/1/K and G/M/1/K queues as the buffer size increases. It is shown that the loss probability approaches its limiting value, which depends on the offered load, with an exponential decay in essentially all cases. The value of the decay rate can be easily computed from the main queue parameters. Moreover, the close relation existing between the loss behaviour of the two examined queueing systems is highlighted and a duality concept is introduced. Finally some numerical examples are given to illustrate on the usefulness of the asymptotic approximation.     

The Exact Solutions for the Benjamin-Bona-Mahony Equation

The Benjamin-Bona-Mahony (BBM) equation represents the unidirectional propagation of nonlinear dispersive long waves, which has a clear physical background, and is a more suitable mathematical and physical equation than the KdV equation. Therefore, the research on the BBM equation is very important. In this article, we put forward an effective algorithm, the modified hyperbolic function expanding method, to build the solutions of the BBM equation. We, by utilizing the modified hyperbolic function expanding method, obtain the traveling wave solutions of the BBM equation. When the parameters are taken as special values, the solitary waves are also derived from the traveling waves. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The modified hyperbolic function expanding method is direct, concise, elementary and effective, and can be used for many other nonlinear partial differential equations.     

Stability of Frobenius pull-backs of tangent bundles and generic injectivity of Gauss maps in positive characteristic

For a smooth projective variety X of dimension n in a projective space defined over an algebraically closed field k, the Gauss mapis a morphism from X to the Grassmannian of n-plans in sending to the embedded tangent space .The purpose of this paper is to prove the generic injectivity of Gauss mapsin positive characteristic for two cases; (1) weighted complete intersectionsof dimension of general type; (2) surfaces or 3-folds with -semistable tangent bundles; based on a criterion of Kaji by looking atthe stability of Frobenius pull-backs of their tangent bundles. The first result implies that a conjecture of Kleiman--Piene is true in case X is of general type of dimension . The second result is a generalization of the injectivity for curves.     

Mass Spectra of 2- and 6-Substituted-3-Pyrones: Competition Between “RETRO-DIELS-ALDER” Fragmentation and Substituent Loss

The mass spectra of a series of 6-hydroxy-3-pyrones and their derivatives showed a marked dependence upon the nature of the substituent. The “retro-Diels-Alder” reaction is the primary decomposition observed for the parent compounds, while the α-cleavage (substituent loss) competes with the “retro-Diels-Alder” reaction for their derivatives. An interpretation of this difference based on the charge location and the thermochemical data is proposed.     

Surface composition of alloys

The practical importance of alloy surfaces in catalysis, corrosion andother aspects of materials performance is widely recognized. What is needed now is sufficient knowledge of the relationship between externally controllable factors — alloy composition, temperature, environment — and surface properties — composition, structure, chemical activity — to control materials performance in these applications. Our purpose here is to review progress in determining and predicting the relationship between one surface property, composition, and certain externally controllable variables: overall composition, temperature, environment and physical form.We find that theoretical treatments of metal alloy surface composition now include essentially all significant physical effects and can predict values for most parameters of interest. Though improvements are still possible, the accuracy of predictions is more often limited by uncertainties or absence of the basic data for the calculations (e.g., thermochemical values) than by the models themselves.Alloy surface composition can now be measured well. The first monolayercomposition of large alloy slabs can be determined quantitatively over a wide temperature range in ultra-high vacuum. Difficulties with specimens of practical interest still challenge experimentalists. Among these are supported catalysts, surfaces under chemisorbed layers and composition of layers below the first. Significant progress is being made and we expect the next few years will see success.