We show that the fractional Sobolev inequality for the embedding H̊ s 2 (R ) →֒ L 2N N−s (R ), s ∈ (0, N) can be sharpened by adding a remainder term proportional to the distance to the set of optimizers. As a corollary, we derive the existence of a remainder term in the weak L N N−s -norm for functions supported in a domain of finite measure. Our results generalize earlier work for the non-fract...

In this note we consider the following Sobolev inequality

Random linear network code has to sacrifice part of bandwidth to transfer the coding vectors, thus a head of size k log |T | is appended to each packet. We present a distributed random network coding approach based on the Chinese remainder theorem for general multicast networks. It uses a couple of modulus as the head, thus reduces the size of head to O(log k). This makes it more suitable for s...

We introduce concepts of “recursive polynomial remainder sequence (PRS)” and “recursive subresultant,” along with investigation of their properties. A recursive PRS is defined as, if there exists the GCD (greatest common divisor) of initial polynomials, a sequence of PRSs calculated “recursively” for the GCD and its derivative until a constant is derived, and recursive subresultants are defined...