A new shape function and some specific wormhole solutions in braneworld scenario

Considering an energy density of the form [Formula: see text] (where [Formula: see text] is an arbitrary positive constant with dimension of energy density and [Formula: see text]), a shape function is obtained by using field equations of braneworld gravity theory in this paper. Under isotropic scenario wormhole solutions are obtained considering six different redshift functions along with the obtained new shape function. For anisotropic case, wormhole solutions are obtained under the consideration of five different shape functions along with the redshift function [Formula: see text], where [Formula: see text] is an arbitrary constant. In each case all energy conditions are examined and it is found that for some cases all energy conditions are satisfied in the vicinity of the wormhole throat and for the rest of the cases all energy conditions are satisfied except strong energy condition.

Time-Universal Data Compression

Nowadays, a variety of data-compressors (or archivers) is available, each of which has its merits, and it is impossible to single out the best ones. Thus, one faces the problem of choosing the best method to compress a given file, and this problem is more important the larger is the file. It seems natural to try all the compressors and then choose the one that gives the shortest compressed file, then transfer (or store) the index number of the best compressor (it requires log m bits, if m is the number of compressors available) and the compressed file. The only problem is the time, which essentially increases due to the need to compress the file m times (in order to find the best compressor). We suggest a method of data compression whose performance is close to optimal, but for which the extra time needed is relatively small: the ratio of this extra time and the total time of calculation can be limited, in an asymptotic manner, by an arbitrary positive constant. In short, the main idea of the suggested approach is as follows: in order to find the best, try all the data compressors, but, when doing so, use for compression only a small part of the file. Then apply the best data compressors to the whole file. Note that there are many situations where it may be necessary to find the best data compressor out of a given set. In such a case, it is often done by comparing compressors empirically. One of the goals of this work is to turn such a selection process into a part of the data compression method, automating and optimizing it.

Uniform asymptotic expansions for oblate spheroidal functions II: negative separation parameter λ

In [3], uniform asymptotic expansions were derived for solutions of the oblate spheroidal wave equation (z2 − 1)d2p/dz2 + 2zdp/dz − (λ + μ2/(z2 − 1)) p = 0, for the case where the parameter μ is real and non-negative, the separation parameter λ is real and positive, and γ is purely imaginary (γ = iu). As u → ∞, uniform asymptotic expansions were derived involving elementary, Airy and Bessel functions, these being valid in certain subdomains of the complex z plane. In this paper the complementary case, where λ is real and negative, is considered. Asymptotic expansions are derived which are valid in certain subdomains of the half-plane |arg (z)| ≦ π/2, uniformly valid for u → ∞ with λ /u2 fixed and negative, and 0 ≦ μ/u ≦ − ½λ /u2 − δ, where δ is an arbitrary positive constant. Explicit error bounds are available for all the approximations.

Conical functions with one or both parameters large

SynopsisUniform asymptotic expansions are derived for conical functions, Legendre functions of order µ and degree −½ + iτ, where µ and τ are non-negative real parameters. As τ → ∞, expansions are furnished for the conical functions which involve Bessel functions of order µ. These expansions are uniformly valid for 0 ≦ µ ≦ Aτ (A an arbitrary positive constant), and are also uniformly valid for Re (z) ≧ 0 in the complex argument case, and 0 ≦ z < ∞ in the real argument case. The case µ → ∞ is also considered, and expansions are furnished which are uniformly valid in the same z regions for 0 ≦ τ ≧ Bµ (B an arbitrary positive constant); in the cases where Re(z) ≧ 0 and 1 ≦ z < ∞, the expansions involve Bessel functions of purely imaginary order iτ, and in the case where 0 ≦ z < 1 the expansions involve elementary functions.

Oscillating properties of the solutions of a class of neutral type functional differential equations

The present paper deals with some oscillating and asymptotic properties of the functional differential equations of the formwhere λ is an arbitrary positive constant and τ > 0 is a constant delay.