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One-dimensional quasilattices, namely, the geometrical objects to represent quasicrystals, are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes. For every MLD class, we can choose a self-similar member as its representative, and a non-self-s...

The new low-dimensional ternary chalcogenide, Nb(1+x)V(1-x)S(5) (x = 0.18), has been prepared and characterized. This compound crystallizes in the monoclinic space group, C2(2h)-P2(1)/m with two formula units in a cell with dimensions a = 9.881(4) A, b = 3.329(1) A, c = 8.775(3) A, and beta = 114.82(3) degrees. The layer is composed of two unique chains of face-sharing Nb-centered bicapped trig...

We show that superlattices can be formed in the ternary and quaternary ln(GaAl)As alloys on InP by molecular beam epitaxy without mechanical shuttering. Periodic ordering is produced by rotation of the substrate through the naturally nonuniform distribution of beam fluxes at the rotating substrate. The growth rate and substrate rotation rate together determine the superlattice period which is m...

In the year 1971, W. G. Lister [14] introduced the notion of ternary ring. Later in the year 2014, J. R. Castillo and Jocelyn S. ParaderoVilela [2] introduced the notion of krasner ternary hyperring. In [6] we introduce the notion of multiplicative ternary hyperring. In this paper we study prime hyperideals in a multiplicative ternary hyperring. We obtain some Characterizations of prime hyperid...

We solve the problem of one-dimensional peg solitaire. In particular, we show that the set of configurations that can be reduced to a single peg forms a regular language, and that a linear-time algorithm exists for playing the game.

The SEIR model for the transmission dynamics of measles is extended by the addition of second-order space derivatives to enable the geographic spread of the disease in a population which has not been vaccinated against it. The resulting system of three reaction-diffusion equations is solved by a convergent finite-difference technique which is second-order accurate in space and time. A parallel ...

• For a discrete RV the mass function is pX(x) = P (X = x). The continuous analog is the probability density function (pdf) that may be interpreted as fX(x) ≈ P (x < X < x+ ∆)/∆ as 0 < ∆→ 0. • The cumulative distribution function (cdf) FX(x) = P (X ≤ x) is the probability that X is less than or equal to a specific value. In the continuous case we have fX(x) = dFX(x)/dx and FX(x) = ∫ x −∞ fX(r)d...