Any natural number can be expressed as an Egyptian fraction, i.e., P 1/ai with a1 < a2 < · · · < a`, where each denominator is the product of three distinct primes.

Spherical linkages, having rotational joints whose axes coincide in a common center point, are sometimes used in multi-degree-of-freedom robot manipulators and in onedegree-of-freedom mechanisms. The forward kinematics of parallel-link robots, the inverse kinematics of serial-link robots and the input/output motion of single-degree-offreedom mechanisms are all problems in displacement analysis....

Let A be a matrix of order n. The properties of the powers A k of A have been extensively studied in the literature. This paper concerns the perturbed powers where the E k are perturbation matrices. We will treat three problems concerning the asymptotic behavior of the perturbed powers. First, determine conditions under which P k ! 0. Second, determine the limiting structure of P k. Third, inve...

A construction of hexagonal shaped 8-point QAM called H8QAM is shown. It is shown that H8QAM constellation outperforms the conventional rectangular constellation and 8-PSK. Further, we construct H8QAM sequences having low peak-to-mean envelope power ratios (PMEPR) from QPSK Golay sequences. Various upper bounds on peak envelope powers of these sequences are evaluated.

We generalize the construction of Doppler-tolerant Golay complementary waveforms by Pezeshki-CalderbankMoran-Howard to complementary code sets having more than two codes. This is accomplished by exploiting numbertheoretic results involving the sum-of-digits function, equal sums of like powers, and a generalization to more than two symbols of the classical two-symbol Prouhet-Thue-Morse sequence.

We generalize the construction of Doppler-tolerant Golay complementary waveforms by PezeshkiCalderbank-Moran-Howard to complementary code sets having more than two codes. This is accomplished by exploiting number-theoretic results involving the sum-of-digits function, equal sums of like powers, and a generalization to more than two symbols of the classical two-symbol Prouhet-Thue-Morse sequence.

Some recursive matrix relations for the geometric analysis, kinematics and dynamics of a 3-RRR symmetric spherical Agile Wrist parallel mechanism are established. The manipulator prototype is a three-degree-offreedom mechanical system with three parallel legs. Controlled by concurrent torques, which are generated by some electric motors, three active elements of the robot have three independent...