In this paper we shall present a parametrization of all symmetric, possibly nonsquare minimal factorizations of a positive semidefinite rational matrix function. It turns out that a pole-pair of such a nonsquare factor is the same as a pole pair for a specific square factor. The location of the zeros is then determined by a solution to a certain algebraic Riccati inequality. We shall also consi...

The routing efficiency in Mobile Ad Hoc Networks (MANETs) suffers from frequent battery drains, mobility and large variation of received signal strength. Thus, nodes and links in MANETs become more vulnerable and unstable. Multicast routing in MANETs for group communication requires establishment of reliable links between neighbouring nodes called as reliability pair beginning from the source a...

A graph-pair of order t is two non-isomorphic graphs G and H on t non-isolated vertices for which G ∪ H ∼= Kt for some integer t ≥ 4. Given a graph-pair (G,H), we say (G,H) divides some graph K if the edges of K can be partitioned into copies of G and H with at least one copy of G and at least one copy of H . We will refer to this partition as a (G,H)multidecomposition of K. In this paper, we c...

The properties of the ground state of liquid He are studied using a correlated basis function of the form ∏ i<j ψ(rij). Here, ψ(r) is chosen as the exact solution of the Schrödinger equation for two He atoms. A hard-sphere plus an attractive square well is used as the interaction potential between He atoms. The pair distribution function is calculated using approximate integral methods, namely ...

A dynamic analysis method is firstly presented to make up the present methods for calculating the strength of the cylindrical gear pair. The transient stress distribution and variation in the process of gear meshing can be obtained by dynamic simulation, the maximum bending stress, the maximum tooth contact stress and the corresponding worst meshing locations of the gear pair can be also accura...

Motivated by a conjecture of Frid, Puzynina, and Zamboni, we investigate infinite words with the property that for infinitely many n, every length-n factor is a product of two palindromes. We show that every Sturmian word has this property, but this does not characterize the class of Sturmian words. We also show that the Thue–Morse word does not have this property. We investigate finite words w...

We generate photon pairs in a-Si:H microrings using a CW pump, and find the Kerr coefficient of a-Si:H to be 3.73 ± 0.25 × 10-17m2/W. By measuring the Q factor with coupled power we find that the loss in the a-Si:H micro-rings scales linearly with power, and therefore cannot originate from two photon absorption. Theoretically comparing a-Si:H and c-Si micro-ring pair sources, we show that the h...

We consider a discounted dynamic program in which the spaces of states and actions are smooth (in a sense that is suitable for the problem at hand) manifolds. We give conditions that insure that the optimal policy and the value function are smooth functions of the state when the discount factor is small. In addition, these functions vary in a Lipschitz manner as the reward function-discount fac...