Geological and hydrogeological investigation in West Malaysia

The author has identified the following significant results. The broad synoptic view of the images allowed easy identification of circular features and major fault traces in low lying areas. Sedimentary units were delineated in accordance with the prevailing rock types and where applicable the folding characteristics. Igneous units could easily be differentiated by tone, degree of fracturing, texture, and drainage pattern. The larger fold structures, anticlinoriums and synclinoriums, of the younger sediments on the eastern edge of the central belt could also be easily delineated

Correlations and Event-by-Event Fluctuations in High Multiplicity Events Produced in 208^{208}Pb-208^{208}Pb Collisions

Analysis of high multiplicity events produced in 158A GeV/c $^{208}$Pb-$^{208}$Pb collisions is carried out to study the event-by-event fluctuations. The findings reveal that the method of scaled factorial moments can be used to identify the events having densely populated narrow phase space bins. A few events sorted out adopting this approach are individually analyzed. It is observed that these events do exhibit large fluctuations in their pseudorapidity, $\eta$ and azimuthal angle, $\phi$ distributions arising out due to some dynamical reasons. Two particle $\Delta\eta$-$\Delta\phi$ correlation study applied to these events too indicates that some complex two-dimensional structure of significantly high magnitude are present in these events which might have some dynamical origin. The findings reveal that the method of scaled factorial moments may be used as an effective triggering for events with large dynamical fluctuations.Comment: 20 pages, 7 figures (Accepted for publication in Advances in High Energy Physics

Dispersion-engineered silicon nitride waveguides for mid-infrared supercontinuum generation covering the wavelength range 0.8-6.5 mu m

We numerically demonstrate the generation of a mid-infrared supercontinuum (SC) through the design of an on-chip complementary metal oxide semiconductor (CMOS) compatible 10-mm-long air-clad rectangular waveguide made using stoichiometric silicon nitride (Si 3 N 4 ) as the core and MgF 2 glass as its lower cladding. The proposed waveguide is optimized for pumping in both the anomalous and all-normal dispersion regimes. A number of waveguide geometries are optimized for pumping at 1.55 μ m with ultrashort pulses of 50-fs duration and a peak power of 5 kW. By initially keeping the thickness constant at 0.8 μ m, four different structures are engineered with varying widths between 3 μ m and 6 μ m. The largest SC spectral evolution covering a region of 0.8 μ m to beyond 6.5 μ m could be realized by a waveguide geometry with a width of 3 μ m. Numerical analysis shows that increasing width beyond 3 μ m by fixing thickness at 0.8 μ m results in a reduction of the SC extension in the long wavelength side. However, the SC spectrum can be enhanced beyond 6.5 μ m by increasing the waveguide thickness beyond 0.9 μ m with the same peak power and pump source. To the best of our knowledge, this is first time report of a broad SC spectral evolution through numerical demonstration in the mid-infrared region by the silicon nitride waveguide. In the case of all-normal dispersion pumping, a flatter SC spectra can be predicted with the same power and pump pulse but with a reduced bandwidth spanning 950–2100 nm

Extremal GG-invariant eigenvalues of the Laplacian of GG-invariant metrics

The study of extremal properties of the spectrum often involves restricting the metrics under consideration. Motivated by the work of Abreu and Freitas in the case of the sphere $S^2$ endowed with $S^1$-invariant metrics, we consider the subsequence $\lambda_k^G$ of the spectrum of a Riemannian manifold $M$ which corresponds to metrics and functions invariant under the action of a compact Lie group $G$. If $G$ has dimension at least 1, we show that the functional $\lambda_k^G$ admits no extremal metric under volume-preserving $G$-invariant deformations. If, moreover, $M$ has dimension at least three, then the functional $\lambda_k^G$ is unbounded when restricted to any conformal class of $G$-invariant metrics of fixed volume. As a special case of this, we can consider the standard O(n)-action on $S^n$; however, if we also require the metric to be induced by an embedding of $S^n$ in $\mathbb{R}^{n+1}$, we get an optimal upper bound on $\lambda_k^G$.Comment: To appear in Mathematische Zeitschrif

Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds

We give upper bounds for the eigenvalues of the La-place-Beltrami operator of a compact $m$-dimensional submanifold $M$ of $\R^{m+p}$. Besides the dimension and the volume of the submanifold and the order of the eigenvalue, these bounds depend on either the maximal number of intersection points of $M$ with a $p$-plane in a generic position (transverse to $M$), or an invariant which measures the concentration of the volume of $M$ in $\R^{m+p}$. These bounds are asymptotically optimal in the sense of the Weyl law. On the other hand, we show that even for hypersurfaces (i.e., when $p=1$), the first positive eigenvalue cannot be controlled only in terms of the volume, the dimension and (for $m\ge 3$) the differential structure.Comment: To appear, London Math Societ

Geological and hydrogeological investigations in west Malaysia

The author has identified the following significant results. Large structures along the east coast of the peninsula were discovered. Of particular significance were the circular structures which were believed to be associated with mineralization and whose existence was unknown. The distribution of the younger sediments along the east coast appeared to be more widespread than previously indicated. Along the Pahang coast on the southern end, small traces of raised beach lines were noted up to six miles inland. The existence of these beach lines was unknown due to their isolation in large coastal swamps