The λ-complete multigraphs

Let E₁……E_m be the edges of a hypergraph. Assume each element in the union of the edges occurs in at least two of E₁……E_m. Assume further that every pair of distinct edges, E₁, and E₁, intersect in at most one element and that for each such pair there are exactly λ other edges E_k such that E₁ and E₁ both intersect E_k. We characterize the hypergraphs for which each |E₁| ≤ 2. These are the λ-complete multigraphs.     

Global stability of stationary solutions of reaction-diffusion systems

We give a condition which implies that the trivial solution, U ≡ 0, of a class of reaction-diffusion systems with homogeneous Dirichlet boundary conditions, is a global attractor for all nonnegative solutions. In certain cases, this condition, which relates the diffusion matrix and the domain to a parameter which depends on the nonlinear term, significantly improves similar conditions which can be obtained from energy estimates. Applications are given to equations arising in mathematical ecology.     

Reflected radical classes

Acta Mathematica Hungarica -     

T-odd momentum correlation in radiative β decay

The triple-product correlations observable in ordinary neutron or nuclear beta decay are all naively T violating and can connect, through an assumption of CPT invariance, to constraints on sources of CP violation beyond the Standard Model. They are also spin dependent. In this context the study of radiative beta decay opens a new possibility, in that a triple-product correlation can be constructed from momenta alone. Consequently its measurement would constrain new spin-independent sources of CP violation. We will describe these in light of the size of the triple momentum correlation in the decay rate arising from electromagnetic final-state interactions in the Standard Model. Our expression for the corresponding T-odd asymmetry is exact in ${\cal O}(\alpha)$ up to terms of recoil order, and we evaluate it numerically under various kinematic conditions. We consider the pattern of the asymmetries in nuclear β decays and show that the asymmetry can be suppressed in particular cases, facilitating searches for new sources of CP violation in such processes.     

Structural and Functional Consequences of the Weak Binding of Chlorin e6 to Bovine Rhodopsin

The chlorophyll‐derivative chlorin e6 (Ce6) identified in the retinas of deep‐sea ocean fish is proposed to play a functional role in red bioluminescence detection. Fluorescence and ¹H NMR spectroscopy studies with the bovine dim‐light photoreceptor, rhodopsin, indicate that Ce6 weakly binds to it with μm affinity. Absorbance spectra prove that red light sensitivity enhancement is not brought about by a shift in the absorbance maximum of rhodopsin. ¹⁹F NMR experiments with samples where ¹⁹F labels are either placed at the cytoplasmic binding site or incorporated as fluorinated retinal indicate that the cytoplasmic domain is highly perturbed by binding, while little to no changes are detected near the retinal. Binding of Ce6 also inhibits G‐protein activation. Chemical shift changes in ¹H‐¹⁵N NMR spectroscopy of ¹⁵N‐Trp labeled bovine rhodopsin reveal that Ce6 binding perturbs the entire structure. These results provide experimental evidence that Ce6 is an allosteric modulator of rhodopsin.     

Luminescence characteristics of InAlP---InGaP heterostructures having native-oxide windows

Data are presented on the luminescence characteristics of InGaP/InAlP heterostructures with oxidized InAlP cladding layers grown by metalorganic chemical vapor deposition. The structures are grown on GaAs substrates and consist of either a 20 nm thick In_0.5Ga_0.5P quantum well or a 0.75 μm InGaP layer sandwiched between two InAlP bulk barriers or between two 10-period In_0.5Al_0.5P/In_xGa_1−xP strain-modulated superlattice heterobarriers, where x varies from 0.5 to 0.45 and the period of the superlattice is 3 nm. The top InAlP cladding layer of the InAlP/InGaP heterostructures is oxidized for 2–5.5 h at 500°C in an ambient of H₂O vapor saturated in a N₂ carrier gas. Photoluminescence and time-resolved photoluminescence studies at room temperature show that, as a result of the oxidation of a portion of the top InAlP cladding layer, the photoluminescence emission intensity and lifetime from the InGaP QWs increase significantly.