A Poincar\`{e} invariant, local scalar field theory in which the Lagrangian and equation of motion contain only up to second-order derivatives fields is called generalized Galileon. The covariant version it four dimensions Horndeski theory, has been vigorously studied applications inflation dark energy. In this paper, we study a class multi-field extensions Galileon theory. By imposing shift $S...

An arithmetic or with-carry analog of Blahut’s theorem is presented. This relates the length of the smallest feedback with carry shift register to the number of nonzero classical Fourier coefficients of a periodic binary sequence.

Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng, Han and He (2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive σ-LFSRs of a given order over a finite field, and it generalizes a known formula for the number of primitive LFSRs, which...

Shift work exerts major influences on the physiological functions of the human body. These are primarily mediated by the disruption of circadian rhythms since most body functions are circadian rhythmic. Next to the disturbances caused by changes in the circadian system, shift work has also been suggested to be related to a number of other health disorders. The present study summarizes recently ...

Let s = (s 1 ; s 2 ; : : : ; s n) be a sequence of characters where s i 2 Z p for 1 i n. One measure of the complexity of the sequence s is the length of the shortest feedback shift register that will generate s, which is known as the maximum order complexity of s 17, 18]. We provide a proof that the expected length of the shortest feedback register to generate a sequence of length n is less th...