Search results for "Second derivative"
showing 7 items of 37 documents
Near infrared spectroscopic study on the adsorption of methanol on silica gel
2013
Author's version of an article in the journal: Advanced Materials Research. Also available from the publisher at: http://dx.doi.org/10.4028/www.scientific.net/AMR.650.150 The silanol groups on Silica gel surface are sites for adsorption of polar molecules. Alcohols and other polar molecules are easily adsorbed by forming hydrogen bondings with OH groups on silica gel surface. A study on the adsorption of methanol on silica gel was carried out by using NIR spectroscopy in combination with ssecond derivative techniques. Four of the well characterised silica gel samples were used in this study. Each of the silica gel (0.25g) samples with different surface areas and silanol number was pressed i…
Analytic UHF-CCSD(T) second derivatives: implementation and application to the calculation of the vibration-rotation interaction constants of NCO and…
1998
An implementation of analytic open-shell UHF-CCSD(T) second derivatives is presented. To demonstrate applicability and test the accuracy of the UHF-CCSD(T) approach for the determination of spectroscopical parameters, vibration-rotation interaction constants were calculated for the ground (12Π) and first electronically excited (12Σ) states of the NCO and NCS radicals. In addition, harmonic vibrational frequencies for both states, the Renner-Teller parameter for the ground state, as well as the 12Π→12Σ excitation energy are reported. While the computed values are in good agreement with reliable experimental information for NCO, most of the data presented for NCS are predictions of quantities…
Second order optimality conditions in the smooth case and applications in optimal control
2007
International audience; The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions of Order Two and COnjugate times), available on the web, and apply it to the minimal time problem of orbit transfer, and to the attitude control problem of a rigid spacecraft. …
Conjugate times for smooth singular trajectories and bang-bang extremals
2003
Abstract In this paper we discuss the problem of estimating conjugate times along smooth singular or bang-bang extremals. For smooth extremals conjugate times can be defined in the generic case by using the intrinsic second order derivative or the exponential mapping. An algorithm is given which was implemented in the SR-case to compute the caustic [1] or in recent applied problems [5],[9]. We investigate briefly the problem of using this algorithm in the bang-bang case by smoothing the corners of extremals
Usability of photoplethysmography method in estimation of conduit artery stiffness
2011
Three channel photoplethysmography (PPG) signal waveform studies of leg conduit arteries during a provocative occlusion test were performed. PPG waveform second derivative amplitude ratio and arterial pulse wave velocity values showed significant correlations with ultrasound (US) reference method of local and regional arterial stiffness (AS), showing the ability to use PPG for AS change quantitative assessment.
Effect of Heat on the Adsorption Properties of Silica Gel
2012
Published version of an article in the journal: International Journal of Engineering and Technology. Also available from the publisher at: http://www.ijetch.org/papers/416-T886.pdf Open access. Adsorption properties of silica gel have been attributed to the surface hydroxyl groups of silica gel. Some hydroxyl groups are free standing and called free silanol groups. Some are hydrogen bonded to neighbouring silanol groups. Christy has shown that a high silanol number and a balanced concentration proportionality between these two different types of hydroxyl groups is necessary for effective adsorption of water molecules. Thermal treatment of silica gel samples alters the proportions of these g…
Remarks on regularity for p-Laplacian type equations in non-divergence form
2018
We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.