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…

VDP::Mathematics and natural science: 400::Chemistry: 440Silica gelnear infrared spectroscopyVDP::Technology: 500::Chemical engineering: 560Near-infrared spectroscopyInorganic chemistryGeneral EngineeringAnalytical chemistryAdvanced materialssecond derivative profileschemistry.chemical_compoundAdsorptionchemistrysilanol groupsMethanolmethanol
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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…

VibrationRenner–Teller effectChemistryExcited stateHarmonicPhysics::Chemical PhysicsPhysical and Theoretical ChemistryAtomic physicsGround stateRotation (mathematics)ExcitationSecond derivativeTheoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta)
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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. …

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyMathematical optimizationControl and Optimization02 engineering and technology01 natural sciences020901 industrial engineering & automationJacobi fieldSingularity0101 mathematicsorbit transferMathematicsSecond derivativeJacobi fieldsecond-order intrinsic derivative010102 general mathematicsConjugate pointsattitude control49K15 49-04 70Q05[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Optimal controlComputational MathematicsFlow (mathematics)Control and Systems EngineeringTrajectoryconjugate pointLagrangian singularity[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Orbit (control theory)
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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

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyPhysics::General Physics010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]02 engineering and technology01 natural sciences020901 industrial engineering & automationExponential mappingCaustic (optics)[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematicsBang bangBang–bang controlSmoothingMathematicsConjugateSecond derivative
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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.

medicine.medical_specialtybusiness.industryUltrasoundmedicine.diseaseSignalmedicine.anatomical_structurePhotoplethysmogramOcclusionArterial stiffnessMedicineWaveformsense organsRadiologybusinessArterySecond derivativeBiomedical engineeringSPIE Proceedings
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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…

second derivative profileschemistry.chemical_compoundAdsorptionMaterials scienceVDP::Mathematics and natural science: 400::Chemistry: 440chemistryChemical engineeringsilanol groupsadsorption NIR spectroscopySilica gelGeneralLiterature_REFERENCE(e.g.dictionariesencyclopediasglossaries)International Journal of Engineering and Technology
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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.

viscosity solutionsintegrability of second derivativesType (model theory)01 natural sciencesDivergencelocal C1ViscosityMathematics - Analysis of PDEsFOS: Mathematicspartial differential equations0101 mathematicsMathematicsMathematical physicsosittaisdifferentiaaliyhtälötα regularityApplied Mathematics010102 general mathematicsta111p-Laplacianlocal C1α regularityviskositeettiDegenerate equation35J60 35B65 35J92010101 applied mathematicsviscosityp-LaplacianAnalysisAnalysis of PDEs (math.AP)Journal of Differential Equations
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