The refinement equation f(x) = ∑N k=0 ck f(2x− k) plays a key role in wavelet theory and in subdivision schemes in approximation theory. This paper explores the relationship of the refinement equation to the mapping τ(x) = 2x mod 1. A simple necessary condition for the existence of an integrable solution to the refinement equation is obtained by considering the periodic cycles of τ . Another si...

Let a and b be reals. We consider the compactly supported solutions φ :R→R of the twocoefficient dilation equation φ(x) = aφ(2x)+bφ(2x−1). In this paper, we determine sets Ba,b , Ca,b , and Za,b defined in the following way: let x ∈ [0,1]. We say that x ∈ Ba,b (resp., x ∈ Ca,b , x ∈ Za,b) if the zero function is the only compactly supported solution of the two-coefficient dilation equation, whi...

Myosin V is a dimeric molecular motor that moves processively on actin, with the center of mass moving approximately 37 nanometers for each adenosine triphosphate hydrolyzed. We have labeled myosin V with a single fluorophore at different positions in the light-chain domain and measured the step size with a standard deviation of <1.5 nanometers, with 0.5-second temporal resolution, and observat...

We present a resonating-valence-bond theory of superconductivity for the Hubbard-Heisenberg model on an anisotropic triangular lattice. Our calculations are consistent with the observed phase diagram of the half-filled layered organic superconductors, such as the beta, beta', kappa, and lambda phases of (BEDT-TTF)2X [bis(ethylenedithio)tetrathiafulvalene] and (BETS)2X [bis(ethylenedithio)tetras...

Alterations within the penicillin-binding domain of penicillin-binding protein (PBP) genes pbp1a, pbp2b, and pbp2x were determined for 15 Canadian isolates of Streptococcus pneumoniae. All penicillin-nonsusceptible S. pneumoniae isolates showed a variety of PBP 2X substitutions and contained a Thr445-Ala change after the PBP 2B SSN motif. Only isolates for which penicillin MICs were > or =0.5 m...

In this paper, we present the HyersUlamRassias stability of quartic functional equation f(2x + y) + f(2x – y) = 4.f(x + y) + 4f(x – y) + 24f(x) ( 6f(y) in Random 2Normed space . References 1. A. Alotaibi, S.A. Mohiuddine; On the stability of a cubic functional equation in random 2-normed spaces, Advances in Difference Equations, 1,39 (2012) pp. 1-10. 2. D.H. Hyers; On the stability of the linea...

Using angle-resolved photoemission, we have observed sharp quasiparticlelike peaks in the prototypical layered manganite La(2-2x)Sr(1+2x)Mn(2)O(7) (x=0.36,0.38). We focus on the (pi,0) regions of k space and study their electronic scattering rates and dispersion kinks, uncovering bilayer-split bands, the critical energy scales, momentum scales, and strengths of the interactions that renormalize...

We demonstrate that photon antibunching observed for individual nanocrystal quantum dots (NQDs) can be transformed into photon bunching characterized by super-Poissonian statistics when they are coupled to metal nanostructures (MNs). This observation indicates that, while the quantum yield of a biexciton (Q(2X)) is lower than that of a single exciton (Q(1X)) in freestanding NQDs, Q(2X) becomes ...

and Applied Analysis 3 For each complex number x,ΨP x define a linear mapping of C|N| into C. If anyNj is zero, Ψ i,j P is the empty matrix for all i and the corresponding column of matrices in ΨP is absent. If Nj 0 for all j,ΨP x is defined to be the unique linear mapping of {0} C0 into C; its matrix representation is then the empty matrix. In particular consider ΨP x ( x4 2x2 1 − 2x 3x4 2x 4x3 )

Motivated by the research and analysis of new materials for photovoltaics and by the possibility of tailoring their optical properties for improved solar energy conversion, we have focused our attention on the (GaAs)(1-x)Ge(2x) series of alloys. We have investigated the structural properties of some (GaAs)(1-x)Ge(2x) compounds within the local-density approximation to density-functional theory,...