Fixed point theorems for mixed monotone operators with PPF dependence

In this paper, fixed point theorems for mixed monotone operators are investigated by weakening the requirements in the contractive assumption and strengthening the metric space utilized with a partial order, taking the domain space C[[a,b],E]$C[[a,b],E]$ different from the range E$E$ and using the method of reflection operators.     

Fixed-point theorems in partially ordered metric spaces for operators with PPF dependence

In this paper, fixed point theorems of a nonlinear operator are developed, where the domain space C[[a,b],E]$C[[a,b],E]$ is different from the range, E$E$, which is a metric space with partial order. An application of the fixed point theorem to a periodic boundary value problem with delay is also given.     

Quasilinearization for functional differential equations with retardation and anticipation

The technique of generalised quasilinearization is developed, using the method of lower and upper solutions and the monotone iterative technique (MIT), to prove the existence of unique solutions for functional differential equations (FDE) with retardation and anticipation.     

[1, 2]-sets in graphs

A subset S⊆V$S\subseteq V$ in a graph G=(V,E)$G=(V,E)$ is a [j,k]$[j,k]$-set if, for every vertex v∈V?S$v\in V?S$, j≤|N(v)∩S|≤k$j\le |N\left(v\right)\cap S|\le k$ for non-negative integers j$j$ and k$k$, that is, every vertex v∈V?S$v\in V?S$ is adjacent to at least j$j$ but not more than k$k$ vertices in S$S$. In this paper, we focus on small j$j$ and k$k$, and relate the concept of [j,k]$[j,k]$-sets to a host of other concepts in domination theory, including perfect domination, efficient domination, nearly perfect sets, 2-packings, and k$k$-dependent sets. We also determine bounds on the cardinality of minimum [1, 2]-sets, and investigate extremal graphs achieving these bounds. This study has implications for restrained domination as well. Using a result for [1, 3]-sets, we show that, for any grid graph G$G$, the restrained domination number is equal to the domination number of G$G$.     

Linearization and minimization of cyclic error with heterodyne laser interferometry

We present a method for the linearization and minimization of interferometer cyclic error. We utilize a polynomial curve fitting and resampling algorithm to correct for nonlinear mirror displacement. In the frequency domain, this algorithm compresses cyclic error into a single-frequency component and enables the precise measurement of cyclic error in a noise-dominated environment. We have applied the technique to determine the cyclic error for a range of interferometer components. In addition, we have used these measurements to optimize interferometer configuration and performance such that we routinely achieve a cyclic error of ～50 pm for our custom Glan-Laser interferometer and ～100 pm for a commercial interferometer.     

Electronic surface resonances and crystal surface structure

A new method of determination of the lateral structure of crystal surfaces is presented. The method is based on earlier work showing the existence of resonances in the elastic scattering of low-energy electrons at crystal surfaces. The method consists of: (a) Measurement of the surface resonance band structure Ek_∥E, k_∥ respectively denote the electron energy and surface-parallel momentum for which resonances occur) and (b) Interpretation of E(k_∥) to determine the lateral variation of the effective potential acting on electrons at the surface.The surface resonance band structure is measured by a net-current electron reflection method. The measurement method is basically the same as used previously but here its precision is greatly enhanced by the use of digital methods of data handling including a digital filter to remove background due to inelastic and non-resonance elastic scattering. The surface resonance band structure is interpreted by a two-dimensional nearly-free electron scheme. In this scheme the interaction elements are Fourier coefficients of an effective potential which is an average of a pseudopotential with respect to the depth distribution of electron density in a surface resonance — the surface-weighted pseudopotential. Experimental surface resonance band structure for Ni(001), Ni(001) p(2 × 2)O and two different Ni(001) c(2 × 2)O surfaces (one of them with an oxygen-saturated Ni substrate) are presented for E = 1–30 eV and k_∥ running halfway from $\text{}\text{?}$gG towards H? in the surface Brillouin zone for Ni(001). The experimental results are fitted, using the nearly-free electron scheme, to determine the Fourier coefficients of the surface-weighted pseudopotential. Surface potential variations synthesized from the above data are discussed in comparison with the atomic arrangements known from LEED. It is demonstrated that the new method can give a correct picture of the lateral structure of surfaces. It is emphasized that these results are obtained without costly equipment or computations called for by other methods.     

Phase of reflection of very low energy electrons at crystal surfaces

The amplitude coefficients of electron reflection at crystal surfaces are complex numbers, each of which may be characterized by a reflection intensity (the squared modulus of the coefficient) and a phase. The phase of reflection of very low energy (? 10 eV) electron reflection is described on the basis of existing theory, and experimental approaches to phase determination are reviewed. Theoretical properties of the phase are described on the basis of the two-beam dynamical theory of diffraction. The model considered is an idealized substrate crystal with an attached selvedge (surface region). The indirect effect of inelastic scattering (absorption) is included by going to complex values of the electron energy or of the surface-normal component K of the propagation vector. In the absence of a selvedge the phase is determined solely by the band structure of the substrate crystal. If a selvedge is present there are large additional effects on the phase associated with zeros of the amplitude coefficient of reflection on the complex K plane. The experimental approaches considered are: (1) measurement of the kinetic energy distributions of ions produced in the field ion microscope, and (2) measurement of the periodic deviations from the Schottky line in field-assisted thermionic emission and photo-emission. Recent results of phase determination for W (011) surface by method (1) are summarized and compared with theoretical expectations.     

FREE RADICALS DETECTED BY ESR FROM PHENYLHEPTATRIYNE IN LIPOSOMES IRRADIATED WITH UV-A

Abstract— When irradiated with UV-A liposome bilayers composed of distearoyl phosphatidylcholine and containing phenylheptatriyne produced a free radical signal detected by electron spin resonance spectroscopy. The spectrum contained one broad peak characterized by a linewidth of 19 G and a g value of 2.0017. The rate of formation of the signal amplitude was dependent upon light intensity, concentration of PHT within the bilayer and concentration of the PHT-liposome suspension. Enhancement of the signal under an anaerobic atmosphere indicated a non-photodynamic mechanism for free radical formation. Once formed however, the free radical was stable to the presence of oxygen and decayed very slowly with a half-life of 8 h. Formation of the free radical species was demonstrated to be dependent upon a highly ordered lipid environment since incorporation of lysophosphatidylcholine, stearoyl which perturbs lipid packing, decreased the levels of the free radical species. On the other hand, when PHT was present in a liposome with a more fluid bilayer such as egg yolk phosphatidylcholine, the levels of free radical species were even lower. Conversely, the levels increased when cholesterol which increases lipid order, was incorporated into the egg yolk phosphatidylcholine liposomes. Cells of E. coli, B , containing PHT, produced a similar free radical signal upon irradiation demonstrating in vivo generation of free radicals from PHT.