‘Universal’ inequalities for the eigenvalues of the Hodge de Rham Laplacian

We obtain ‘universal’ inequalities for the eigenvalues of the Laplacian acting on differential forms of a Euclidean compact submanifold. These inequalities generalize the Yang inequality concerning the eigenvalues of the Dirichlet Laplacian of a bounded Euclidean domain.      

Positive muon diffusion in mixed Nb‐hydrides, NbHxDy

Positive muons have been used to monitor the proton and deuteron mobilities in mixed, concentrated NbH_xD_y hydrides, with x+y= constant. The mobility of the muons decreases linearly with increasing D‐content, which is expected if the protons and the deuterons move in an uncorrelated fashion. Combined with other evidence which suggests that such correlations exist, the present observation may be interpreted as due to a destruction of a correlated motion of H’s or D’s in the vicinity of the muons. This revised version was published online in August 2006 with corrections to the Cover Date.     

Supercritical carbon dioxide extraction and gas chromatography–mass spectrometry analysis of Gymnema sylvestre R.Br. roots

Supercritical fluid extraction (SFE) achieves a wide range of applications since the past decade as a sustainable green technology. The present study investigates the process for producing high yield by supercritical carbon dioxide (Sc-CO₂) extraction form Gymnema sylvestre R.Br. roots. The effect of temperature and pressure on the percentage of accumulative yield is demonstrated. It is found that the highest yield is obtained at the temperature of 60°C and the pressure of 10?MPa. A proper review showed that there is a lack in the study of Sc-CO₂ extraction of this plant especially for optimization of SFE process which makes this study useful and valuable. For more benefit, the extract which achieves highest percentage is subjected to gas chromatography–mass spectrometry to study its chemical composition and detect the active principle compounds which present with high concentration and expected to be responsible of the pharmaceutical properties of the extract.     

Colloidal stability of aqueous nanofibrillated cellulose dispersions

Cellulose nanofibrils constitute an attractive raw material for carbon-neutral, biodegradable, nanostructured materials. Aqueous suspensions of these nanofibrils are stabilized by electrostatic repulsion arising from deprotonated carboxyl groups at the fibril surface. In the present work, a new model is developed for predicting colloidal stability by considering deprotonation and electrostatic screening. This model predicts the fibril-fibril interaction potential at a given pH in a given ionic strength environment. Experiments support the model predictions that aggregation is induced by decreasing the pH, thus reducing the surface charge, or by increasing the salt concentration. It is shown that the primary mechanism for aggregation upon the addition of salt is the surface charge reduction through specific interactions of counterions with the deprotonated carboxyl groups, and the screening effect of the salt is of secondary importance.     

A Reilly inequality for the first Steklov eigenvalue

Let M be a compact submanifold with boundary of a Euclidean space or a Sphere. In this paper, we derive an upper bound for the first non-zero eigenvalue p₁ of Steklov problem on M in terms of the r-th mean curvatures of its boundary ∂M. The upper bound obtained is sharp.     

Asymptotics of periodic subelliptic operators

We establish that heat diffusion with periodic conductivity is governed by two scales. The small time diffusion is described by the geodesic distance but the large time behaviour is dictated by the distance associated with an homogenized system obtained by a suitable averaging process. Our methods are quite general and apply to diffusion on a stratified Lie group.     

Relative locality of derivations

Let H and K be symmetric linear operators on a C¹-algebra $\text{U}$ with domains D(H) and D(K). H is defined to be strongly K-local if $\text{ω(K(A)}{}^1\text{K(A)) = 0}$ implies $\text{ω(H(A)}{}^1\text{H(A)) = 0}$ for A?D(H) ∩ D(K) and ω in the state space of $\text{U}$, and H is completely strongly K-local if $\text{Ω(K(A)}{}^1\text{K(A))=0}$ implies $\text{Ω(H(A)}{}^1\text{H(A))=0}$ for A ∈ D(H) ∩ D(K) and Ω in the state of $\text{U}$, and H is cpmpletely strongly K-local if $\text{H??}{}_{\mathrm{n}}$ is $\text{K??}{}_{\mathrm{n}}$-local on U?M_n for all n ? 1, where $\text{1}$_n is the identity on the n × n matrices M_n. If $\text{U}$ is abelian then strong locality and complete strong locality are equivalent. The main result states that if τ is a strongly continuous one-parameter group of ¹-automorphisms of $\text{U}$ with generator δ₀ and δ is a derivation which commutes with τ and is completely strongly δ₀-local then δ generates a group α of ¹-automorphisms of $\text{U}$. Various characterizations of α are given and the particular case of periodic τ is discussed.