Rolling of a non-homogeneous ball over a sphere without slipping and twisting

Consider the problem of rolling a dynamically asymmetric balanced ball (the Chaplygin ball) over a sphere. Suppose that the contact point has zero velocity and the projection of the angular velocity to the normal vector of the sphere equals zero. This model of rolling differs from the classical one. It can be realized, in some approximation, if the ball is rubber coated and the sphere is absolutely rough. Recently, J. Koiller and K. Ehlers pointed out the measure and the Hamiltonian structure for this problem. Using this structure we construct an isomorphism between this problem and the problem of the motion of a point on a sphere in some potential field. The integrable cases are found.      

关于算子方程AX=XAX与AX=XA=XAX

用A的不变子空间作参数，给出了算子方程AX＝XAX的全部解。当A是单射或稠值域时，或者当A是正规算子时，给出了算子方程AX＝XA＝XAX的全部解。我们还给出正规算子X是算子方程AX＝XZ＝XAX的解的充分必要条件。     

Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.     

Comparison of the sensitivity of 11 crosslinked hyaluronic acid gels to bovine testis hyaluronidase

Crosslinked hyaluronan gels are used in various applications where their stability is a prerequisite. The sensitivity of such gels to hyaluronidase can be determined as an index of stability by several approaches: chromatography, electrophoresis, and viscometry. We describe here a test based on the colorimetric determination of the N-acetyl-d-glucosamine released by hyaluronidase in standardized conditions. The sensitivities to bovine testicular hyaluronidase of 11 different gels used to fill skin wrinkles (Restylane; Perlane; Juvéderm 18, 24, 24HV, 30, and 30HV; Surgiderm 18, 24XP, 30, and 30XP) were compared.The method was reproducible, easy to perform, not time-consuming and allowed us to demonstrate that the sensitivity to testicular hyaluronidase was dependent on the degree of crosslinking of the gels and also on their monophasic/biphasic nature. Under our conditions, Surgiderm 30, 24XP and 30XP were the most resistant gels.We propose to retain the hyaluronidase test to predict the in situ stability of a crosslinked gel used to fill skin wrinkles.     

Decomposition of N-cyclopropyl-N-nitrosourea in the presence of reducing agents as a new way of generating the cyclopropyl radical

A new way of generating cyclopropyl radicals in the base-catalyzed decomposition of N-cyclopropyl-N-nitrosourea in the presence of organic reducing agents (1-phenylpyrazolidin-3-one and 4-methoxyphenol) was developed. The cyclopropyl radical generated under these conditions can not only abstract a proton from the substrate to give cyclopropane but also form C-C or C-Br bonds in reactions with aromatic substrates or polybromomethanes. Dedicated to Academician O. M. Nefedov on the occasion of his 75th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1934–1938, November, 2006.     

Cooperation of reducing species for NO reduction over Ag/Al2O3 under oxidizing conditions

Summary The cooperation effect of reducing species for selective reduction of NO over Ag/Al₂O₃ has been investigated in the presence of excess oxygen. When the combinations of propene or propane and ethanol or methanol were used as reducing agents, NO reduction took place over a wider temperature range, compared with a single hydrocarbon as reducing agent.     

新的聚合物支载硼氢负离子还原剂系统研究 3: 聚合物支载还原剂III

硼氢化钠的低分子还原系统研究很多,但其聚合物支载还原剂相对来说就很少,而且仅以强碱型阴离子交换树脂来制备的聚合物试剂。为了寻找用途更广泛的、新的聚合物支载还原剂,我们进行了硼氢负离子的聚合物还原系统的研究;发现能用弱酸型阳离子交换树脂制备出新的聚合物支载还原剂。前文报道了用NaBH_4的水溶液和阴离子交换树脂     

Relative Abundance of Alpha-Amylase/Trypsin Inhibitors in Selected Sorghum Cultivars

Sorghum is of growing interest and considered as a safe food for wheat related disorders. Besides the gluten, α-amylase/trypsin-inhibitors (ATIs) have been identified as probable candidates for these disorders. Several studies focused on wheat-ATIs although there is still a lack of data referring to the relative abundance of sorghum-ATIs. The objective of this work was therefore to contribute to the characterization of sorghum ATI profiles by targeted proteomics tools. Fifteen sorghum cultivars from different regions were investigated with raw proteins ranging from 7.9 to 17.0 g/100 g. Ammonium bicarbonate buffer in combination with urea was applied for protein extraction, with concentration from 0.588 ± 0.047 to 4.140 ± 0.066 mg/mL. Corresponding electrophoresis data showed different protein profiles. UniProtKB data base research reveals two sorghum ATIs, {"type":"entrez-protein","attrs":{"text":"P81367","term_id":"3913899","term_text":"P81367"}}P81367 and {"type":"entrez-protein","attrs":{"text":"P81368","term_id":"3913900","term_text":"P81368"}}P81368; both reviewed and a targeted LC–MS/MS method was developed to analyze these. Quantifier peptides ELAAVPSR ({"type":"entrez-protein","attrs":{"text":"P81367","term_id":"3913899","term_text":"P81367"}}P81367) and TYMVR ({"type":"entrez-protein","attrs":{"text":"P81368","term_id":"3913900","term_text":"P81368"}}P81368) were identified and retained as biomarkers for relative quantification. Different reducing and alkylating agents were assessed and combination of tris (2 carboxyethyl) phosphine/iodoacetamide gave the best response. Linearity was demonstrated for the quantifier peptides with standard recovery between 92.2 and 107.6%. Nine sorghum cultivars presented up to 60 times lower ATI contents as compared to wheat samples. This data suggests that sorghum can effectively be considered as a good alternative to wheat.     

Comparative evaluation of Fe(III) reducing power-based antioxidant capacity assays in the presence of phenanthroline, batho-phenanthroline, tripyridyltriazine (FRAP), and ferricyanide reagents

The chemical diversity of antioxidants in complex matrices such as plant extracts makes it difficult to separate and quantify antioxidants from these solutions. Therefore it is desirable to establish methods that can measure the total antioxidant capacity (TAC) levels directly from plant extracts. Iron(III)-based TAC assays, especially the most widely used FRAP (ferric-reducing antioxidant power), play an important role in this regard. However, many problems have been reported in the application of the FRAP assay, the most serious one being the incomplete oxidation of a number of antioxidants during the time protocol of the assay. Thus, six different ferric ion-based total antioxidant capacity (TAC) assays have been comparatively tested, modified, and improved so as to obtain more sensitive and precise results for complex mixtures, namely: 1,10-phenanthroline (o-phen) method (with incubation), batho-phenanthroline method (with incubation), original FRAP method, modified FRAP method (with incubation), original ferricyanide method, and modified ferricyanide method (with incubation). Two new assays in this regard (i.e., o-phen and batho-phen) have been established, and the existing assays (FRAP and ferricyanide) have been modified so as to let the oxidation reactions of antioxidants reach completion. The molar absorptivity for a variety of antioxidants was highest for modified FRAP, batho-phen, and original FRAP methods. The absorption maximum wavelength shifted batochromically to a higher extent for modified ferricyanide, FRAP, and batho-phen procedures, decreasing the possibility of interferences due to organics absorbing in the near-UV range of the visible spectrum where most antioxidant assays are performed. The linear concentration ranges were shown to be further extended and linear correlation coefficients improved with respect to the most widely used ferric-based assay, FRAP. Of the six assays tested and developed, only the modified ferricyanide procedure gave high intercept values and low addivitity of TAC values of constituents in complex mixtures, requiring further attention of method optimization. Thus, it was shown that the most widely used FRAP could be effectively modified, and o-phen, batho-phen, and ferricyanide methods constitute cheaper alternatives to FRAP under certain conditions, with partly improved molar absorptivity (and thus sensitivity) for antioxidants, lower intercept values (and higher precision), broader linear range (and higher flexibility), and better additivity of TAC values of antioxidant constituents in mixtures.     

Use of isothermal microcalorimetry in pharmaceutical preformulation studies

Excipient compatibility of a new chemical entity was assessed using an isothermal microcalorimeter. Mixtures of an active pharmaceutical ingredient with a primary amine group and excipients were prepared in a 1:1 ratio and compatibility monitored by exposing to 50, 60 and 70°C in presence of 200 mL of water. The new chemical entity, a primary amine, reacted with reducing sugars such as lactose and resulted in a brown discoloration. This reaction is the Maillard type condensation reaction between amines and reducing sugars. The rate of reaction was dependent on the temperature with rapid degradation at higher temperatures. No other incompatibility was apparent between the primary amine and other excipients This revised version was published online in July 2006 with corrections to the Cover Date.