Vibrational spectra,normal coordinate analyses,and molecular configurations of crystalline propionic acid

Temperature dependence of the IR spectra of crystalline propionic acid were examined in the temperature range 242–50 K. The intensities of most absorption bands increased on lowering the temperature, but some bands diminished until they disappeared at temperatures lower than about 120 K. Normal coordinate analyses indicate that the former bands are due to the stable cis dimer and the latter due to the less stable trans dimer which would be produced from the cis dimer by simultaneous proton transfer along two hydrogen bonds.     

Gradient of the ZAPT2 energy

 An explicit expression for the analytical first derivative of the Z-averaged perturbation theory taken to second order energy, due to Lee and Jayatilaka, is presented for application to high-spin systems described by a restricted open-shell Hartree–Fock wavefunction. The use of frozen core orbitals is incorporated into the derivation. Received: 23 April 2001 / Accepted: 31 August 2001 / Published online: 9 January 2002     

Based on MFe2O4 (M=Co,Cu, and Ni): Magnetically recoverable nanocatalysts in synthesis of heterocyclic structural scaffolds

Abstract

Catalysis research under magnetically recoverable nanocatalysts is a well-known topic in organic synthesis. In recent times, catalysis research has clearly experienced a renaissance in the area of utility of ferrite nanoparticles based on their ability to recovery and reusability. In this review, the focus is on the fabrication, characterization and of application the MFe₂O₄ (M=Co, Cu, and Ni) nanocatalysts in synthesis of heterocyclic structural scaffolds.     

Berechnung des ?quivalenzpunktes potentiometrischer Titrationen

Ohne Zusammenfassung

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Calculation of the equivalence point of potentiometric titrations

     

Rearrangement during cyclisation of some 3-(2-pyrrolyl) propionic acids and related compounds

Cyclisation of the title compounds leads to mixtures of the expected 4H-cyclopental[b]pyrrol-4-ones (1), the corresponding 6-ones (3) by a single rearrangement, and the cyclopenta[c]pyrrol-4-ones (4) by a double rearrangement, the proportions depending upon the substituents.The ¹H NMR spectra of 2-methyl-4H-cyctopenta[b]thiophen-6-one (3f) shows 6J long range $\text{CH}{}_3\text{CH}{}_2$ coupling, but this is absent in the corresponding pyrroles (3c,d). The ¹³C spectra of 1 and 3 cannot be interpreted on the basis of substituent chemical shifts in pyrroles and thiophens, and are clearly -CH = CH-X (X = NMe, NPh, S) bridged derivatives of cyclopent-2-enone.     

Nonalkaloid Constituents from Stemona japonica

Five new nonalkaloid constituents, a neolignan, japonin A ( 1 ), a macrocyclic lactone, japonin B ( 2 ), a (phenylethyl)benzoquinone, japonin C ( 3 ), a phenanthraquinone, japonin D ( 4 ), as well as a dihydrostilbene, stilbostemin M ( 5 ), were isolated from the roots of Stemona japonica, together with eight known compounds. Their structures were established by spectroscopic analyses.     

The Discrete Approximation of Continuous-state Nonlinear Branching Processes in Lévy Random Environments北大核心CSCD

In this paper, we establish the discrete approximation of continuous-state nonlinear branching processes in Lévy random environments by using tightness and convergence sequence in infinite dimensional product space via stochastic differential equations. Taking α-stable branching as an example, the conditions which are given to discretize continuous-state nonlinear branching processes in Lévy random environments are verified. © 2022 Chinese Academy of Sciences. All rights reserved.     

Relationship between tetrahedron shape measures

Tetrahedron shape measures are used for evaluating the quality of tetrahedra in finite element meshes. Three shape measures, theminimum solid angle _min theradius ratio , and themean ratio , are discussed in this paper. A new formula for the computation of a solid angle of tetrahedron is derived. For different shape measures andv (with values 1), we establish a relationship between andv of the form wherec ₀,c ₁,e ₀, ande ₁ are positive constants. This means that if one measure approaches zero for a poorly-shaped tetrahedron, so does the other. Combined with the property that each measure attains a maximum value only for the regular tetrahedron, this means that the shape measures are equivalent.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Rates of convergence and optimal spectral bandwidth for long range dependence

Summary For a realization of lengthn from a covariance stationary discrete time process with spectral density which behaves like ^1–2H as 0+ for 1/2<H<1 (apart from a slowly varying factor which may be of unknown form), we consider a discrete average of the periodogram across the frequencies 2j/n,j=1,..., m, wherem andm/n0 asn. We study the rate of convergence of an analogue of the mean squared error of smooth spectral density estimates, and deduce an optimal choice ofm.