We construct a one-parameter family of generalized Mathieu functions, which are reduced quaternion-valued functions pair real variables lying in an ellipse, and we call λ-reduced quaternionic functions. prove that the λ-RQM kernel Moisil-Teodorescu operator D+λ (D is Dirac λ∈R∖{0}), form complete orthogonal system Hilbert space square-integrable λ-metamonogenic with respect to L2-norm over conf...

The notions of symbolic matrix system and λ-graph system for a subshift are generalizations of symbolic matrix and λ-graph (= finite symbolic matrix) for a sofic shift respectively ([Doc. Math. 4(1999), 285-340]). M. Nasu introduced the notion of textile system for a pair of graph homomorphisms to study automorphisms and endomorphisms of topological Markov shifts ([Mem. Amer. Math. Soc. 546,114...

Red-shifted bioluminescent emitters allow improved in vivo tissue penetration and signal quantification, and have led to the development of beetle luciferin analogues that elicit red-shifted bioluminescence with firefly luciferase (Fluc). However, unlike natural luciferin, none have been shown to emit different colors with different luciferases. We have synthesized and tested the first dual-col...

In case of sequence of matrices we define the characteristic exponent ( ) ( ) N n n ∈ Δ = Δ ( ) Δ λ as a exponent of ( ) ( ) N n n ∈ Δ . It is well known [2] that the set of all Lyapunov exponents of system (1) contains at most s elements, say ) ( ... ) ( ) ( 2 1 A A A r λ λ λ < < < and the set { } ) ( ),..., ( 1 A A r λ λ is called the spectrum of (1). The greatest and the smallest exponent of...

and Applied Analysis 3 to be of the limit point or limit circle type is given in 4, 43 . These two papers seem to be the only ones on time scales which are devoted to the Weyl-Titchmarsh theory for the second order dynamic equations. Another way of generalizing the Weyl-Titchmarsh theory for continuous and discrete Hamiltonian systems was presented in 3, 5 . In these references the authors cons...

We present results for a galaxy formation model which includes a simple treatment for the disruption of dwarf galaxies by gravitational forces and galaxy encounters within galaxy clusters. This is implemented a posteriori in a semi–analytic model by considering the stability of the cluster dark matter haloes at z = 0. We assume that a galaxy whose dark matter substructure has been disrupted wil...