Comparison of fatty acids, vitamin E and physicochemical properties of Canarium odontophyllum Miq. (dabai), olive and palm oils.

Canarium odontophyllum Miq. fruit (dabai) is an important food and oil resource for the native people in Sarawak, Malaysia. However, there is little information regarding their oil composition. In this paper, fatty acid compositions, vitamin E contents and physicochemical properties of dabai pulp and kernel oils were studied. These parameters were compared with commercial olive and palm oils. The content of total saturated fatty acid was found to be 44.4% in dabai pulp, kernel (60.8%), palm oil (47.9%) and olive (25.5%) oils. Palmitic, myristic, oleic and linoleic acids were detected in dabai pulp oil (36.1, 5.8, 41.5 and 11.8%) dabai kernel oil (46.4, 9.3, 35.1 and 2.8%), palm oil (33.8, 9.2, 39.7 and 10.9%) and olive oil (9.9, 12.9, 64.4 and 5.1%). Vitamin E was not detected in the dabai pulp oil, while palm oil had the highest vitamin E content, followed by dabai kernel oil and olive oil. In addition, the physicochemical characteristics of dabai oils show better quality than the studied commercial oils. The present study also showed that dabai pulp and kernel oils have good fatty acid composition and a high potential to be developed into healthy cooking oils

Neumann Li-Yau gradient estimate under integral Ricci curvature bounds

We prove a Li-Yau gradient estimate for positive solutions to the heat equation, with Neumann boundary conditions, on a compact Riemannian submanifold with boundary ${\bf M}^n\subseteq {\bf N}^n$, satisfying the integral Ricci curvature assumption: \begin{equation} D^2 \sup_{x\in {\bf N}} \left( \oint_{B(x,D)} |Ric^-|^p dy \right)^{\frac{1}{p}} < K \end{equation} for $K(n,p)$ small enough, $p>n/2$, where $diam({\bf M})\leq D$. The boundary of ${\bf M}$ is not necessarily convex, but it needs to satisfy the interior rolling $R-$ball condition

Inverse scattering and solitons in An−1A_{n-1} affine Toda field theories

We implement the inverse scattering method in the case of the $A_n$ affine Toda field theories, by studying the space-time evolution of simple poles in the underlying loop group. We find the known single soliton solutions, as well as additional solutions with non-linear modes of oscillation around the standard solution, by studying the particularly simple case where the residue at the pole is a rank one projection. We show that these solutions with extra modes have the same mass and topological charges as the standard solutions, so we do not shed any light on the missing topological charge problem in these models. We also show that the integrated energy-momentum density can be calculated from the central extension of the loop group.Comment: 28 pages, Latex, 4 figs include

S-duality in Abelian gauge theory revisited

Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function is calculated via zeta-function regularization with special attention to its modular properties. In the compact case, compared with the purely topological result of Witten, we find a non-trivial curvature correction to the modular weights of the partition function. But S-duality can be restored by adding gravitational counter terms to the Lagrangian in the usual way. In the ALF case however we encounter non-trivial difficulties stemming from original non-compact ALF phenomena. Fortunately our careful definition of the partition function makes it possible to circumnavigate them and conclude that the partition function has the same modular properties as in the compact case.Comment: LaTeX; 22 pages, no figure

Fermion-boson duality in integrable quantum field theory

We introduce and study one parameter family of integrable quantum field theories. This family has a Lagrangian description in terms of massive Thirring fermions $\psi,\psi^{\dagger}$ and charged bosons $\chi,\bar{\chi}$ of complex sinh-Gordon model coupled with $BC_n$ affine Toda theory. Perturbative calculations, analysis of the factorized scattering theory and the Bethe ansatz technique are applied to show that under duality transformation, which relates weak and strong coupling regimes of the theory the fermions $\psi,\psi^{\dagger}$ transform to bosons and $\chi,\bar{\chi}$ and vive versa. The scattering amplitudes of neutral particles in this theory coincide exactly with S-matrix of particles in pure $BC_n$ Toda theory, i.e. the contribution of charged bosons and fermions to these amplitudes exactly cancel each other. We describe and discuss the symmetry responsible for this compensation property.Comment: 12 pages, LaTex file with amste

Supergravity solitons and non-perturbative superstrings

A review is given of the implications of supersymmetric black holes for the non-perturbative formulation of toroidally compactified superstrings, with particular emphasis on symmetry enhancement at special vacua and S-duality of the heterotic string.Comment: Latex 8pp. To appear in Procs. of 1995 Trieste Spring Superstring School and Worksho