Search results for "Second derivative"
showing 10 items of 37 documents
The initial boundary value problem for free-evolution formulations of General Relativity
2017
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate primarily on boundaries that are geometrically determined by the outermost normal observer to spacelike slices of the foliation. We present high-order-derivative boundary conditions for the gauge, constraint violating and gravitational wave degrees of freedom of the formulation. Second order derivative boundary conditions are presented in terms of the conformal variables used in numerical relativity simulations. Using Kreiss-Agranovich-Metivier theory we demons…
Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumpi…
2019
We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the metric across this boundary could perhaps present a finite step too. However, we can assume that the metric is ${\cal C}^1$ class everywhere. In such a case, although the partial second derivatives of the metric exhibit finite (no Dirac $\delta$ functions) discontinuities, the Dirac $\delta$ functions will still appear in the conservation equation of the energy-momentum tensor. As a consequence, strictly speaking, the corresponding metric solutions of the …
Automatic program for peak detection and deconvolution of multi-overlapped chromatographic signals
2005
Several interlinked algorithms for peak deconvolution by non-linear regression are presented. These procedures, together with the peak detection methods outlined in Part I, have allowed the implementation of an automatic method able to process multi-overlapped signals, requiring little user interaction. A criterion based on the evaluation of the multivariate selectivity of the chromatographic signal is used to auto-select the most efficient deconvolution procedure for each chromatographic situation. In this way, non-optimal local solutions are avoided in cases of high overlap, and short computation times are obtained in situations of high resolution. A new algorithm, fitting both the origin…
Analytic second derivatives for the spin-free exact two-component theory
2011
The formulation and implementation of the spin-free (SF) exact two-component (X2c) theory at the one-electron level (SFX2c-1e) is extended in the present work to the analytic evaluation of second derivatives of the energy. In the X2c-1e scheme, the four-component one-electron Dirac Hamiltonian is block diagonalized in its matrix representation and the resulting "electrons-only" two-component Hamiltonian is then used together with untransformed two-electron interactions. The derivatives of the two-component Hamiltonian can thus be obtained by means of simple manipulations of the parent four-component Hamiltonian integrals and derivative integrals. The SF version of X2c-1e can furthermore exp…
Development of the H-point standard additions method for coupled liquid chromatography and UV-visible spectrophotometry
1992
Abstract This work establishes the fundamentals of the H-point standard additions method for liquid chromatography for the simultaneous analysis of binary mixtures with overlapped chromatographic peaks. The method was compared with the deconvolution method of peak suppression and the second derivative of elution profiles. Different mixtures of diuretics were satisfactorily resolved.
Comparison of several methods used for the determination of cephalosporins. Analysis of cephalexin in pharmaceutical samples
2002
The precision of UV absorbance of intact and acid degraded cephalosporins, ninhydrin, high performance liquid chromatography and iodometric methods used for analysis of cefoxitin, cefotaxime, cephazolin and cephalexin were compared. To obtain the calibration graphs the analytical signal used were: absorbance, first derivative absorbance, second derivative absorbance and H-point Standard Additions Method by using absorbance values at two selected wavelengths as analytical signal. These methods and calibration graphs were also used for the determination of cephalexin in pharmaceutical samples.
Analytic second derivatives for general coupled-cluster and configuration-interaction models.
2004
Analytic second derivatives of energy for general coupled-cluster (CC) and configuration-interaction (CI) methods have been implemented using string-based many-body algorithms. Wave functions truncated at an arbitrary excitation level are considered. The presented method is applied to the calculation of CC and CI harmonic frequencies and nuclear magnetic resonance chemical shifts up to the full CI level for some selected systems. The present benchmarks underline the importance of higher excitations in high-accuracy calculations.
Anharmonic force fields from analytic CCSD(T) second derivatives: HOF and F2O
1999
The recent implementation of analytic second derivatives for CCSD(T) (coupled cluster theory with single and double excitations augmented by a perturbational treatment of connected triple excitations) has been combined with a numerical finite difference procedure to calculate cubic and semidiagonal quartic force fields. Computational details of this approach are outlined. Applications are reported for HOF and F2O. The CCSD(T) results are in excellent agreement with experiment and represent a substantial improvement over the results obtained from MP2 (Mo/ller–Plesset second-order perturbation theory).
Importance of Triples Contributions to NMR Spin–Spin Coupling Constants Computed at the CC3 and CCSDT Levels
2016
We present the first analytical implementation of CC3 second derivatives using the spin-unrestricted approach. This allows, for the first time, the calculation of nuclear spin–spin coupling constants (SSCC) relevant to NMR spectroscopy at the CC3 level of theory in a fully analytical manner. CC3 results for the SSCCs of a number of small molecules and their fluorine substituted derivatives are compared with the corresponding coupled cluster singles and doubles (CCSD) results obtained using specialized basis sets. For one-bond couplings the change when going from CCSD to CC3 is typically 1–3%, but much higher corrections were found for 1JCN in FCN, 15.7%, and 1JOF in OF2, 6.4%. The changes v…
Simultaneous determination of oxybenzone and 2-ethylhexyl 4-methoxycinnamate in sunscreen formulations by flow injection-isodifferential derivative u…
2001
Abstract A flow injection procedure was developed for the simultaneous determination of two UV filters (oxybenzone and 2-ethylhexyl 4-methoxycinnamate) in sunscreen formulations, based on the isodifferential approach. The use of the second derivative spectra allowed a selective determination of the analytes free from matrix interferences and without pretreatment of samples. Standard solutions of the analytes were analyzed by the proposed procedure in order to select the appropriate wavelengths to solve the mixture. After this, the procedure was validated using commercial sunscreen formulations the concentrations of which were determined by an HPLC procedure. The two procedures gave comparab…