Four inequalities for monotone gradient vector fields

We consider vector fields which have realizations as subdifferentials of convex functionals on a Hilbert space. Four inequalities relating the resolvent of the subdifferential to the semigroup flow are known in the literature. In this paper the constant appearing in one of these inequalities is improved, and the resulting four inequalities are shown to be optimal.     

Error Bounds for Hermite Interpolation by Quadratic Splines on an {alpha}-Triangulation

For l, an -triangulation F of a planar domain is such that,for every T F, there holds 1 R_T/2r_T , where R_T (resp. r_T)denotes the radius of the circumscribed (resp. inscribed) circleof the triangle T. When T is varying in F the centre of itsinscribed circle is varying in a compact interior to T and itsorthogonal projections on the sides are varying in compact intervalsinterior to these sides. Precise results are given about thesizes of these compacts and are used for the computation oferror constants in the problem of Hermite interpolation by Powell-Sabinquadratic finite elements, bringing to the fore their dependenceon the parameter .     

Luminescence from Ti2+ ions in LiF crystals

Luminescence of Ti²⁺: LiF crystals in the wavelength range 650–900 nm excited using laser radiation is reported. The values of 10Dq and the Racah B parameter obtained from the present results indicate that in LiF the ¹ E, ¹ T ₂, and ³ T ₂ energy levels are almost at the cross-over point in the Tanabe-Sugano diagram. In consequence photoluminescence from all three energy levels to the ground state is observed. At low temperature (T 14 K) the emission is mainly due to sharp emission lines with weak vibronic structure due to the ¹ E, ¹ T ₂³ T ₁ transitions of Ti²⁺ ions. The ³ T ₂³ T ₁ broad-band emission is weak at low temperature, becoming stronger at 300 K due to a phonon-assisted tunnelling process, similar to that observed in Cr³⁺: garnets [1]. The excitation spectrum of these lines is a broad peak at 590 nm due to absorption in the ³ T ₁³ T ₂ transition.     

A simple method for determining water content in organic solvents based on cobalt(Ⅱ)complexes

A method to determine water content in organic solvents was developed based on the color change of cobalt(Ⅱ) nitrate in different solvents.The color-change mechanism and optimal conditions for determining the water content were investigated.The results showed that there was a good linear relationships between the absorbance of cobalt(Ⅱ) complexes in organic solvents and water contents withγin 0.9989～0.9994.This method has the advantages of low cost,good reproducibility,good sensitivity,simple in operation,fast in detection,friendly to the environment and no limitation on linear range for determining water content.It was used to determine water in samples with a satisfactory recovery in 97.81%～101.24%.     

Optimization of non-ideal multimode interference devices

Multimode interference devices are examined outside of the step-index, paraxial regime. To determine the optimum length of these devices, we maximize the projection of the propagated field in the multimode section onto the desired field profile. By consideration of the orthogonality among the guided modes, this reduces to a criterion of minimum weighted phase errors at the imaging plane, with no dependence on the actual mode field profiles. The results are confirmed by comparison with mode propagation analysis simulations. This analysis is immediately applicable to the design of multimode interference devices in weakly-guiding geometries such as shallow ridge waveguides, weakly-guiding materials systems such as photosensitive glasses and polymers, and waveguides with graded claddings and/or weak index gradients in the core, such as those formed through diffusive processes. The procedure is also used to explain the presence of the recently observed pseudo-self-image, which is not predicted by the standard theory of multimode interference.     

The interrelationship of subglottic air pressure, fundamental frequency, and vocal intensity during speech

In this study we have simultaneously measured subglottic air pressure, airflow, and vocal intensity during speech in nine healthy subjects. Subglottic air pressure was measured directly by puncture of the cricothyroid membrane. The results show that the interaction between these aerodynamic properties is much more complex that previously believed. Certain trends were seen in most individuals, such as an increase in vocal intensity with increased subglottic air pressure. However, there was considerable variability in the overall aerodynamic properties between subjects and at different frequency and intensity ranges. At certain frequencies several subjects were able to generate significantly louder voices without a comparable increase in subglottic air pressure. We hypothesize that these increases in vocal efficiency are due to changes in vocal fold vibration properties. The relationship between fundamental frequency and subglottic pressure was also noted to vary depending on vocal intensity. Possible mechanisms for these behaviors are discussed.     

The NMR spectra of porphyrins: 22—Ring current effects in chlorins versus porphyrins

The proton NMR spectra of tetraphenylporphyrin, octaethylporphyrin and the analogous chlorins (7,8-dihydroporphyrins) are presented, and the chemical shift changes on chlorin formation are interpreted using a ring current model. In these compounds a general 10% reduction in the ring current occurs upon chlorin formation. Similar comparison of the chemical shifts of the corresponding dications and also of the protonated form of 2-vinylphylloerythrin methyl ester with the corresponding chlorin, methyl pyropheophorbide-a, shows that chlorin formation now has a much larger effect on the ring current, this reflecting the increased steric effects within the macrocycle which occur upon protonation. Variable temperature studies on the porphyrins and chlorins examined show clearly the effect of NH exchange processes and, in particular, novel intermolecular exchange processes with trifluoroacetic acid in the protonated species are recorded.     

Application of density functional theory to the investigation of polymer degradation: Example of cross-linked ethylene–vinyl acetate–vinyl alcohol (EVA-OH) terpolymer de-acetylation

We report on the application of Density Functional Theory (DFT) methodologies to investigate the degradation of polymer materials and provide new insights into the effects of degradation on molecular geometry. The temperature- and radiation-assisted degradation of a cross-linked ethylene–vinyl acetate–vinyl alcohol (EVA-OH) elastomer was studied both experimentally and theoretically, in order to correlate observable parameters with theoretically calculated electronic properties. Experiments showed ‘yellowing’ of the material, outgassing of acetic acid, and attenuated IR deformation modes upon exposure to increased levels of gamma radiation or increased temperatures, consistent with the de-acetylation model in which acetic acid is abstracted from the vinyl acetate group via a molecular rearrangement involving the displacement of a hydrogen atom from the ethylene backbone toward the acetyl group, and the propagation of the mechanism to adjacent vinyl acetate groups, forming polyenes in the polymer backbone. DFT modeling predicted the molecular structures of the cross-linked EVA-OH polymer for various degrees of de-acetylation, with corresponding IR and UV–visible absorption spectra. Theoretical attenuated IR deformation modes matched experimental observations, and the theoretical absorption spectrum of polyenes with 5 double bonds matched the optical absorption data, shedding light onto the final chemical structure of the polymer fragment. In addition, DFT unveiled precise and local effects of de-acetylation on the geometry of both the remaining polymer chain and cross-linker, which could only be detected as methylene deformation mode reflectance changes by IR spectroscopy.     

络合滴定法连续测定钨镍铜合金中的镍和铜

拟定了用络合滴定法连续测定钨镍铜合金中镍和铜的方法.在两份试液中,一份控制pH≈8,以疏代硫酸钠掩蔽Cu(Ⅱ),氟离子掩蔽W(Ⅵ),用EDTA标准溶液直接滴定Ni(Ⅱ),求得镍含量.另一份在过量氨水介质中,用EDTA标准溶液滴定Ni(Ⅱ)、Cu(Ⅱ),求得镍-铜合量,铜含量由差减法求得.指示剂为紫脲酸铵.方法简便、快速,结果准确可靠.     

A New Cycloartane Triterpene Glycoside from Souliea vaginata

Souliea vaginata (Maxim.) Franch. (Ranunculaceae) is widely distributed in the southwest and northwest of China. It possesses anti-inflammatory analgesic functions as a well-known Chinese folk medicine. Its rhizomes or the whole plant are used to treat conjunctivitis, stomatitis, pharyngitis, enteritis, and diarrhea1. Previously, we have reported the isolation and structural elucidation of suolieasides A-C from the ethanol extract of the rhizomes of this plant2. In our further investigation…