On the computation of the dipole change arising from vibrational angular momentum and some inter-relationships between the elements of the atomic polar tensor

A programme is developed for the computation of the contribution of the rotation of the dipole moment to vibrational transition moments. It is argued that this return to fundamentals has much in its favour compared with earlier methods based on pseudo isotope calculations. The programme is applied to H₂O. Some discrepancies are noted with the results of the matrix method originally proposed by Biarge, Herranz and Morcillo. The existence of internal relationships between the elements of the APT is demonstrated. Such relationships are of importance in the refinement of the APT to fit experimental transition moments.     

Complemented copies of ℓ<Subscript>p</Subscript> spaces in tensor products

We give sufficient conditions on Banach spaces X and Y so that their projective tensor product X ⊗_π Y, their injective tensor product X ⊗_ɛ Y, or the dual (X ⊗_π Y)^* contain complemented copies of ℓ_p.     

Theoretical treatment of mixed hyperfine interactions resulting from a monochromatic, circularly polarized Mössbauer source

The analytical form of the antisymmetric part of the Mössbauer intensity tensor, directly available in the measurements with circularly polarised source, is derived. The possibility of measurements of the hyperfine magnetic field vector is discussed for the case when quadrupole interaction cannot be neglected.     

The Kato-type spectrum and local spectral theory

Let T ∈ ℒ(X) be a bounded operator on a complex Banach space X. If V is an open subset of the complex plane such that λ-T is of Kato-type for each λ ∈ V, then the induced mapping f(z) ↦ (z-T)f(z) has closed range in the Fréchet space of analytic X-valued functions on V. Since semi-Fredholm operators are of Kato-type, this generalizes a result of Eschmeier on Fredholm operators and leads to a sharper estimate of Nagy’s spectral residuum of T. Our proof is elementary; in particular, we avoid the sheaf model of Eschmeier and Putinar and the theory of coherent analytic sheaves.     

Some Interesting Features for External Region of Spherical Symmetric Mass in New Theory of Gravitation VGM

This paper briefly discusses some interesting features for the external region of the spherical symmetric mass in the new theory of gravitation VGM, Le. The theory of gravitation by considering the vector graviton field and the metric field, such as pseudo-singularity, curvature tensor, static limit, event horizon, and the radial motion of a particle. All these features are different from the corresponding features obtained from general relativity.     

ORIENTATION DISTRIBUTION FUNCTIONS FOR MICROSTRUCTURES OF HETEROGENEOUS MATERIALS (Ⅰ) ──DIRECTIONAL DISTRIBUTION FUNCTIONS AND IRREDUCIBLE TENSORS

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Nonparallelism of the Ricci Tensor of Pseudo-cylindric Metrics

We describe examples of metrics in the conformal class [g] on some conformally flat Riemannian manifolds (M,g]. These metrics have a constant scalar curvature and an harmonic curvature with nonparallel Ricci tensor.     

各向加权异性张力有限元法及其应用

本文利用各向异性张力有限元的特点设计了灵活而有效的各向加权异性有限元算法，采用这种方法，计算了离心叶轮内部准三元流场。     

引力场中的应力张量及其应用

根据引力场和静电场的相似性质，通过类比方法由静电场的麦克斯韦应力张量得出了引力场中的应力张量，并用它计算均质球体内部的万有引力。     

Decompositions of the category of noncommutative sets and Hochschild and cyclic homology

In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.