Iteration scheme for nondensely defined ordinary differential operator equation

An iteration scheme is given for constructing the unique least-squares solution of minimal norm for an ordinary differential operator equation. This operator is subject to generalized two- point boundary conditions and is nondensely defined. The convergence is established in a uniform topology.     

Spliced-fiber mode filter for 1060-nm single-mode transmission

We present a novel mode filter operating for the 1060-nm band, which selectively removes the power of the high-order mode (HOM) from a conventional single-mode fiber (C-SMF) that supports two modes at the short-wavelength band. Our mode filter is fabricated very easily by fusion-splicing a short section of short-wavelength single-mode fiber in the middle of the C-SMF link. By using our spliced-fiber mode filter (SF-MF), a high HOM suppression performance of > 18 dB has been achieved with a low insertion loss of < 0.3 dB over the full band of optical communications from 1050 nm to 1650 nm. We have also developed a new mode power measurement scheme that takes advantage of the bending sensitivity of the HOM guidance. This measurement scheme enabled us to evaluate accurately the performance factors of the fabricated mode filter.     

The monotonic property and stability of solutions of fractional differential equations

In this paper we improve on the monotone property of Lemma 1.7.3 in Lakshmikantham et al. (2009) [5] for the case g(t,u)=λu with a nonnegative real number λ. We also investigate the Mittag-Leffler stability of solutions of fractional differential equations by using the fractional comparison principle.     

Partial Geometric Difference Families

We introduce the notion of a partial geometric difference family as a variation on the classical difference family and a generalization of partial geometric difference sets. We study the relationship between partial geometric difference families and both partial geometric designs and difference families, and show that partial geometric difference families give rise to partial geometric designs. We construct several infinite families of partial geometric difference families using Galois rings and the cyclotomy of Galois fields. From these partial geometric difference families, we generate a list of infinite families of partial geometric designs and directed strongly regular graphs.     

Optimal Wloc2,2-regularity,Pohozhaevʼs identity,and nonexistence of weak solutions to some quasilinear elliptic equations

We begin by establishing a sharp (optimal) $W_{\mathrm{loc}}^{2,2}$-regularity result for bounded weak solutions to a nonlinear elliptic equation with the p-Laplacian, ${\mathrm{\Delta }}_{p}u\stackrel{\mathrm{def}}{=}\mathrm{div}({|\mathrm{?}u|}^{p?2}\mathrm{?}u)$, $1<p<\infty$. We develop very precise, optimal regularity estimates on the ellipticity of this degenerate (for $2<p<\infty$) or singular (for $1<p<2$) problem. We apply this regularity result to prove Pohozhaev?s identity for a weak solution $u\in W^{1,p}(\Omega )$ of the elliptic Neumann problem(P)$?{\mathrm{\Delta }}_{p}u+W^{\prime }(u)=f(x)\text{in}\Omega ;?u/?\nu =0\text{on}?\Omega .$ Here, Ω is a bounded domain in ${\mathbb{R}}^N$ whose boundary ?Ω is a $C^2$-manifold, $\nu \equiv \nu (x_0)$ denotes the outer unit normal to ?Ω at $x_0\in ?\Omega$, $x=(x_1,\dots ,x_N)$ is a generic point in Ω, and $f\in L^{\infty }(\Omega )\cap W^{1,1}(\Omega )$. The potential $W:\mathbb{R}\to \mathbb{R}$ is assumed to be of class $C^1$ and of the typical double-well shape of type $W(s)={|1?{|s|}^{\beta }|}^{\alpha }$ for $s\in \mathbb{R}$, where $\alpha ,\beta >1$ are some constants. Finally, we take an advantage of the Pohozhaev identity to show that problem (P) with $f\equiv 0$ in Ω has no phase transition solution $u\in W^{1,p}(\Omega )$ ($1<p?N$), such that $?1?u?1$ in Ω with $u\equiv ?1$ in ${\Omega }_{?1}$ and $u\equiv 1$ in ${\Omega }_1$, where both ${\Omega }_{?1}$ and ${\Omega }_1$ are some nonempty subdomains of Ω. Such a scenario for u is possible only if $N=1$ and ${\Omega }_{?1}$, ${\Omega }_1$ are finite unions of suitable subintervals of the open interval $\Omega ?{\mathbb{R}}^1$.     

Morphology of Polystyrene Core–dPoly(ethylene oxide) Shell Arborescent Copolymer Micelles from Small-Angle Neutron Scattering Analysis

Arborescent (dendrigraft) copolymers with a branched polystyrene (PS) core grafted at the chain termini with deuterated poly(ethylene oxide) segments (PS-dPEO) were characterized in benzene and acetone by small-angle neutron scattering measurements using the contrast matching technique. While copolymers incorporating a G1 (twice-grafted) PS core aggregated to some extent, the portion of the scattering curve corresponding to non-aggregated copolymer molecules could still be analyzed to determine the shape and segment radial density profile for core and shell. These were derived from the pair distance distribution function P(r) and the scattering length density contrast profile Δρ(r) = ρ(r) ? ρ(solvent), obtained by the indirect Fourier transformation and deconvolution methods. The profiles obtained for the G1 copolymer are consistent with a well-defined PS core–dPEO shell morphology, only observed previously for upper generation (G4) polymers with deuterated PS (dPS) chains grafted randomly on arborescent PS substrates. Detailed morphological analysis could not be carried out for an analogous G3 arborescent PS copolymer terminally grafted with dPEO segments due to extensive aggregation in both solvents.     

The graphs G(n, k) of the Johnson Schemes are unique for n ≥ 20

Let G(n, k) denote the graph of the Johnson Scheme J(n, k), i.e., the graph whose vertices are all k-subsets of a fixed n-set, with two vertices adjacent if and only if their intersection is of size k ? 1. It is known that G(n, k) is a distance regular graph with diameter k. Much work has been devoted to the question of whether a distance regular graph with the parameters of G(n, k) must isomorphic to G(n, k). In this paper, this question is settled affirmatively for n ≥ 20. In fact the result is proved with weaker conditions.     

Influence of SiNx:H film properties according to gas mixture ratios for crystalline silicon solar cells

The Hydrogenated silicon nitride (SiN_x:H) using plasma enhanced chemical vapor deposition is widely used in photovoltaic industry as an antireflection coating and passivation layer. In the high temperature firing process, the SiN_x:H film should not change the properties for its use as high quality surface layer in crystalline silicon solar cells. For optimizing surface layer in crystalline silicon solar cells, by varying gas mixture ratios (SiH₄ + NH₃ + N₂, SiH₄ + NH₃, SiH₄ + N₂), the hydrogenated silicon nitride films were analyzed for its antireflection and surface passivation (electrical and chemical) properties. The film deposited with the gas mixture of SiH₄ + NH₃ + N₂ showed the best properties in before and after firing process conditions.The single crystalline silicon solar cells fabricated according to optimized gas mixture condition (SiH₄ + NH₃ + N₂) on large area substrate of size 156 mm × 156 mm (Pseudo square) was found to have the conversion efficiency as high as 17.2%. The reason for the high efficiency using SiH₄ + NH₃ + N₂ is because of the good optical transmittance and passivation properties. Optimized hydrogenated silicon nitride surface layer and high efficiency crystalline silicon solar cells fabrication sequence has also been explained in this study.     

Some asymptotic results useful in enumeration problems

Suppose one is given two related generating functionsa(x) = a _n x ⁿ andb(x) = b _n x ⁿ , often it is of interest to determine the limiting behaviour of the quantitiesa _n /b _n We survey some earlier results of this nature and give some new ones