A compressible flow characterized by a velocity field u(x)(x, t)=ax/(1+at) is analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook kinetic model. The sign of the control parameter (the longitudinal deformation rate a) distinguishes between an expansion (a>0) and a condensation (a<0) phenomenon. The temperature is a decreasing function of time in the former case, while it is...

A general result on the structure and dimension of the root subspaces of a linear operator under finite rank perturbations is proved: The increase of dimension from the n-th power of the kernel of the perturbed operator to the (n+ 1)-th power differs from the increase of dimension of the corresponding powers of the kernels of the unperturbed operator by at most the rank of the perturbation. Thi...

A space X has the Rothberger property in all finite powers if, and only if, its collection of ω-covers has Ramseyan properties.

Eighty years ago, Ramanujan conjectured and proved some striking congruences for the partition function modulo powers of 5, 7, and 11. Until recently, only a handful of further such congruences were known. Here we report that such congruences are much more widespread than was previously known, and we describe the theoretical framework that appears to explain every known Ramanujan-type congruence.

Regulation of radio began in 1910 when Congress passed modest legislation over the infant wireless communication industry. Following the development of broadcasting and a surge of growth during the 1920s, the Radio Act of 1927 was passed. The act created an independent commission to determine regulatory policy for broadcasting in the United States. The venerable Communications Act of 1934 expan...

We identified a set of four rephasing invariant parameters of the CKM matrix. They are found to exhibit hierarchies in powers of λ 2 , from λ 2 to λ 8. It is shown that, at the present level of accuracy, only the first three parameters are needed to fit all available data on flavor physics.

For a given finite field Fq, we study sufficient conditions to guarantee that the set {θ 1 + θ y 2 : 1 ≤ x ≤ M1, 1 ≤ y ≤ M2} represents all the nonzero elements of Fq. We investigate the same problem for θ 1 − θ y 2 and as a consequence we prove that any element in the finite field of q elements has a representation of the form θ − θ, 1 ≤ x, y ≤ √ 2q whenever θ has multiplicative order at least...

A space X has the Rothberger property in all finite powers if, and only if, its collection of ω-covers has Ramseyan properties.

Article history: Received 20 November 2008 Available online 17 November 2009 Communicated by Peter Webb In memoriam Karl Gruenberg