An estimate on the convergence of Baskakov-Bézier operators

In the present paper we estimate the rate of convergence on functions of bounded variation for the Bézier variant of the Baskakov operators Bn,α(f,x). Here we have studied the rate of convergence of Bn,α(f,x) for the case 0<α<1.     

Die kubischen Phasen Na16(ARb6)Sb7, Verbindungen mit den Anionen A = Rb−, Na−, Au−, I−

The Cubic Phases Na₁₆(ARb₆)Sb₇, Compounds with the Anions A = Rb^?, Na^?, Au^?, I^? The novel compounds Na₁₆(ARb₆)Sb₇ have been synthesized from the elements in sealed Nb ampoules at 873 K (A = Rb) and 823 K (A = I, Na, Au). They form brittle cuboctahedra (silver metallic; A = Rb) and irregular polyhedra (silver metallic lustre; A = Na, I; golden metallic lustre; A = Au). They rapidly decompose in moist air to gray products. Their crystal structures have been determined by single crystal X-ray crystallography (A = Rb: a = 1565.8(2) pm; A = I: a = 1563.3(2) pm; A = Na: a = 1562.6(2) pm; A = Au: a = 1560.7(2) pm). They crystallize cubically in the space group Fm3 m (no. 225) with Z = 4 formula units and are isotypic with Sc₁₁Ir₄. The compounds are ZINTL phases and their structures can be described as an eightfold defect variant of the Li₃Bi type of structure (cF128-8; a = 2a′(Li₃Bi)). The Sb atoms form a network of cuboctahedra, centered alternatingly by a SbNa₈ cube or a ARb₆ octahedron. Main structural features are the anions A^? within the Rb₆ octahedron. Supporting the existence of A^? are the isotypical compounds with the more common anion forming elements (A = Au, I), as well as electrostatic potential considerations together with calculations of the volume increments. The semiconducting properties (E_g = 0.33 eV) of Na₁₆(RbRb₆)Sb₇, as well as the diamagnetism χ_mol = ?508 × 10^?6 cm³ mol^?1, are in accordance with those to be expected from the Zintl concept.     

Efficient nested pricing in the simplex algorithm

We report a remarkable success of nested pricing rules over major pivot rules commonly used in practice, such as Dantzig’s original rule as well as the steepest-edge rule and Devex rule.     

Using volcano plots and regularized-chi statistics in genetic association studies

Labor intensive experiments are typically required to identify the causal disease variants from a list of disease associated variants in the genome. For designing such experiments, candidate variants are ranked by their strength of genetic association with the disease. However, the two commonly used measures of genetic association, the odds-ratio (OR) and p-value may rank variants in different order. To integrate these two measures into a single analysis, here we transfer the volcano plot methodology from gene expression analysis to genetic association studies. In its original setting, volcano plots are scatter plots of fold-change and t-test statistic (or −log of the p-value), with the latter being more sensitive to sample size. In genetic association studies, the OR and Pearson's chi-square statistic (or equivalently its square root, chi; or the standardized log(OR)) can be analogously used in a volcano plot, allowing for their visual inspection. Moreover, the geometric interpretation of these plots leads to an intuitive method for filtering results by a combination of both OR and chi-square statistic, which we term “regularized-chi”. This method selects associated markers by a smooth curve in the volcano plot instead of the right-angled lines which corresponds to independent cutoffs for OR and chi-square statistic. The regularized-chi incorporates relatively more signals from variants with lower minor-allele-frequencies than chi-square test statistic. As rare variants tend to have stronger functional effects, regularized-chi is better suited to the task of prioritization of candidate genes.     

Synthesis,spectroscopic, structural and magnetic studies of new binary Cr(III)–citrate pH-specific structural variants from aqueous media

In an attempt to understand the aqueous interactions of Cr(III) with the low molecular mass physiological ligand citric acid, the pH-specific synthesis in the binary Cr(III)–citrate system was pursued, leading to the new complexes Na₃[Cr(C₆H₅O₇)₂]·8.5H₂O (1) and (Hdmphen)₆[Cr(C₆H₅O₇)₂]·(NO₃)₃·14H₂O (2). Complexes 1 and 2 were characterized by elemental analysis, spectroscopic, structural, thermal, and magnetic susceptibility studies. The structures of 1 and 2 reveal a mononuclear octahedral complex of Cr(III) with two citrate ligands bound to it. Albeit of the same deprotonation state, the disposition of the two citrate ligands with respect to Cr(III) differs between 1 and 2 in the solid state, thus reflecting the presence of pH-structural variants in the requisite binary system. This conformational difference is lifted in aqueous solution, thus providing (a) comparative information on the distribution and diversity of species in the binary Cr(III)–citrate system, and (b) insight into the nature of interactions developing in the binary Cr(III)–hydroxycarboxylate systems in abiotic and biological applications.     

Monitoring of transferrin isoforms in biological samples by capillary electrophoresis

Work dealing with the monitoring of transferrin isoforms in human serum and other body fluids by capillary electrophoresis is reviewed. It comprises capillary zone electrophoresis and capillary isoelectric focusing efforts that led to the exploration and use of assays for the determination of carbohydrate‐deficient transferrin as a marker for excessive alcohol intake, genetic variants of transferrin, congenital disorders of glycosylation and β‐2‐transferrin, which is a marker for cerebrospinal fluid leakage. This paper provides insight into the development, specifications, strengths, weaknesses, and routine use of the currently known capillary electrophoresis based assays suitable to detect transferrin isoforms in body fluids. The achievements reached so far indicate that capillary zone electrophoresis is an attractive technology to monitor the molecular forms of transferrin in biological specimens as the assays do not require an elaborate sample pretreatment and thus can be fully automated for high‐throughput analyses on multicapillary instruments. Assays based on capillary isoelectric focusing are less attractive. They require immunoextraction of transferrin from the biological matrix and mobilization after focusing if instrumentation with a whole‐column imaging detector is not available. Interactions of the carrier ampholytes with the iron of transferrin may prevent iron saturation and thus provide more complicated isoform patterns.     

On the ordering in new low gap semiconductors: PtSnS, PtSnSe, PtSnTe. Experimental and DFT studies

The crystallographic and electronic structures of PtSnS, PtSnSe and PtSnTe were investigated by X-ray structure analysis and density functional theory (DFT) calculations. Conductivity measurements and diffraction patterns show semiconducting ordered pyrite type related compounds containing SnX (X=S, Se, Te) entities. A scheme is presented to model ordered variants according to the relative orientation of the XY dumbbells. It represents the ullmannite, the cobaltite and a new rhombohedral structure type. The scheme allows for a systematic investigation of ordering preferences from first principles. According to the total electronic energy PtSnTe and PtSnSe prefer the cobaltite, PtSnS the rhombohedral structure type. The structural and electronic properties agree with experimental results. The three compounds are predicted to be narrow gap indirect semiconductors from conductivity measurements and band structure calculations.     

Dual-detection approach for a charge variant analysis of monoclonal antibody combination products using imaged capillary isoelectric focusing

The clinical benefits of treatments with a combination of two or more therapeutic monoclonal antibodies (mAbs) have emerged in recent years. Imaged capillary isoelectric focusing is a frequently used technology in the biopharmaceutical industry for charge variant analysis of protein therapeutics. However, with the wide concentration ranges of combination products, one component may fall within the linear detection range, whereas the other does not. Here, we report a novel methodology to explore charge variants of mAb mixtures using multiple detection techniques simultaneously. We use ultraviolet absorbance to monitor the charge variants of the high-concentration component and native fluorescence (FL) to monitor the variants of the low-concentration one. Charge variants of mixtures that span 40-fold in ratio differences can be accurately quantified with this approach. In contrast to the conventional methods, it is not necessary to prepare and analyze two samples at different concentrations and combine the results for combination product testing. Additionally, the use of FL detection enables the charge variant analysis of highly potent/low abundant mAbs in a mixture. This methodology is more quality-control friendly and efficient for the charge variant analysis of combination products with wide ratios.     

Evaluation of an icIEF-MS system for comparable charge variant analysis of biotherapeutics with rapid peak identification by mass spectrometry

Protein therapeutics are usually produced in heterogeneous forms during bioproduction and bioprocessing. Heterogeneity results from post-translational modifications that can yield charge variants and require characterization throughout product development and manufacturing. Isoelectric focusing (IEF) with UV detection is one of the most common methods to evaluate protein charge heterogeneity in the biopharmaceutical industry. To identify charge variant peaks, a new imaged microfluidic chip-based isoelectric focusing (icIEF) system coupled directly to mass spectrometry was recently reported. Bridging is required to demonstrate comparability between existing and new technology. As such, here we demonstrate the comparability of the pI value measurement and relative charge species distributions between the icIEF-MS system and the control data from a frequently utilized methodology in the biopharmaceutical industry for several blinded development-phase biopharmaceutical monoclonal antibodies across a wide pI range of 7.3–9.0. Hyphenation of the icIEF system with mass spectrometry enabled direct and detailed structural determination of a test molecule, with masses suggesting acidic and basic shifts are caused by sialic acid additions and the presence of unprocessed lysine residues. In addition, MS analysis further identified several low-abundance glycoforms. The icIEF-MS system provides sample quantification, characterization, and identification of mAb proteoforms without sacrificing icIEF quantification comparability or speed.     

Concise Large-Scale Synthesis of Tomatidine,A Potent Antibiotic Natural Product

Tomatidine has recently generated a lot of interest amongst the pharmacology, medicine, and biology fields of study, especially for its newfound activity as an antibiotic agent capable of targeting multiple strains of bacteria. In the light of its low natural abundance and high cost, an efficient and scalable multi-gram synthesis of tomatidine has been developed. This synthesis uses a Suzuki–Miyaura-type coupling reaction as a key step to graft an enantiopure F-ring side chain to the steroidal scaffold of the natural product, which was accessible from low-cost and commercially available diosgenin. A Lewis acid-mediated spiroketal opening followed by an azide substitution and reduction sequence is employed to generate the spiroaminoketal motif of the natural product. Overall, this synthesis produced 5.2 g in a single pass in 15 total steps and 15.2% yield using a methodology that is atom economical, scalable, and requires no flash chromatography purifications.