In this paper we give a combinatorial proof of an addition formula for weighted partial Motzkin paths. The addition formula allows us to determine the LDU decomposition of a Hankel matrix of the polynomial sequence defined by weighted partial Motzkin paths. As a direct consequence, we get the determinant of the Hankel matrix of certain combinatorial sequences. In addition, we obtain an addition...

We present the logic analysis, circuit implementation and verification of a novel selftimed adder scheme based on Carry Select (CS) logic. The preliminary analysis of the variabletime behavior of CS logic justifies the design of self-timed CS adders, and identifies the best choice for the block size to optimize the average performance. Hence we describe the logic design and full-custom circuit ...

For three particles P,Q,R travelling on a straight line, let vPQ be the (relative) velocity of P as measured by Q, and define vQR, vPR similarly. According to classical mechanics, the velocity v of a particle moving on a line can be any real number, and relative velocities add by the simple formula vPR = vPQ + vQR. On the other hand, the special theory of relativity says velocities are restrict...

We give two parametrizations of points on Edwards curves that omit the X coordinate. The first parametrization leads to a differential addition formula that has the cost 5M + 4S, a doubling formula that has the cost 5S and a tripling formula that costs 4M+7S. The second one yields a differential addition formula with cost 5M + 2S and a doubling formula with cost 5S both even on generalized Edwa...