Digital fountain is a new class of the forward error correction technology. One of the most important features is the characteristic called rateless, which allows encoders to generate codewords unlimitedly. As the first practical implementation of digital fountain, LT codes have been widely utilized in many areas, including multimedia streaming, long-distance communication, broadcasting systems...

The purpose of the present expository paper is to give an account of the recent progress and present status of the classification of solvable Lie groups admitting an Einstein left invariant Riemannian metric, the only known examples so far of noncompact Einstein homogeneous manifolds. The problem turns to be equivalent to the classification of Ricci soliton left invariant metrics on nilpotent L...

This paper studies the normalized Ricci flow on surfaces with conical singularities. It’s proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes good geometric sense. For some simple surfaces of this kind, for example, the tear drop and the football, it’s shown that they admit Ricci soliton metric. MSC 2...

In the context of paracontact geometry, η-Ricci solitons are considered on manifolds satisfying certain curvature conditions: R(ξ,X) · S = 0, S · R(ξ,X) = 0, W2(ξ,X) · S = 0 and S · W2(ξ,X) = 0. We prove that on a para-Kenmotsu manifold (M,φ, ξ, η, g), the existence of an η-Ricci soliton implies that (M, g) is quasi-Einstein and if the Ricci curvature satisfies R(ξ,X) · S = 0, then (M, g) is Ei...

This paper introduces three coding strategies for using the Luby Transform (LT) code in a relay aided power-line communication scheme. In the first method, the relay decodes the received packets and re-encodes them for transmission towards the destination. In the second method, the relay only forwardes a random linear combination of its received packets towards the destination, while in the thi...

In this paper, we present a method to provide unequal error protection (UEP) for distributed sources in a two-source single-sink relay network scenario. A simple yet efficient technique to decompose the Robust Soliton Distribution (RSD) into two entirely different distributions by utilizing the concept of deconvolution is presented and these two different distributions are used at two different...

This paper deals with Fountain codes, and especially with their encoding matrices, which are required here to be invertible. A result is stated that an encoding matrix induces a permutation. Also, a result is that encoding matrices form a group with multiplication operation. An encoding is a transformation, which reduces the entropy of an initially high-entropy input vector. A special encoding ...

In the present article we consider Weierstrass representations of spheres in R. An existence of a global Weierstrass representation for any compact oriented surface of genus g ≥ 1 has been established in [19, 20] and this proof, in fact, works for spheres also. Being mostly interested in relations of these representations to the spectral theory and in possibilities to apply the spectral theory ...

The three-dimensional Heisenberg group H3 has three left-invariant Lorentz metrics g1 , g2 and g3 as in [R92] . They are not isometric each other. In this paper, we characterize the left-invariant Lorentzian metric g1 as a Lorentz Ricci soliton. This Ricci soliton g1 is a shrinking non-gradient Ricci soliton. Likewise we prove that the isometry group of flat Euclid plane E(2) has Lorentz Ricci ...

We prove that the asymptotic field of a Skyrme soliton of any degree has a non-trivial multipole expansion. It follows that every Skyrme soliton has a well-defined leading multipole moment. We derive an expression for the linear interaction energy of well-separated Skyrme solitons in terms of their leading multipole moments. This expression can always be made negative by suitable rotations of o...