半群OCK_n的理想的极大子半群

设X_n={1,2,…,n}并赋予自然数序,OCK_n是X_n上的具有核连续的保序变换半群.将考虑OCK_n的理想OCK(n,r)={α∈OCK_n:|imα|≤r}(3≤r≤n-1),并得到了OCK(n,r)的极大子半群的完全分类.     

一类核具有连续横截面变换半群的秩

设X_n={1,2,…,n}并赋予自然数序,MCK_n是X_n上核具有连续横截面保序或反序变换所构成的半群.K_n是MCK_n的最大正则子半群.本文将考虑K_n的理想K(n,r)={α∈K_n:|im(α)|≤r}(3≤r≤n-1).证明了K(n,r)的秩为(n-r+1)(n-r+2)(n-r+3)/6.     

Detection of acetone in the human breath as diabetes biomarker based on PPy/WO3 nanocomposite sensor by FFT continuous cyclic voltammetry method

This research represents a novel detection method of acetone level in the exhaled breath samples (RH=88 %) based on polypyrrole/tungsten oxide (PPy/WO₃) nanocomposite sensor. The PPy/WO₃ sensor was fabricated by the deposition of nanocomposite on/between interdigitated electrodes (IDEs) through electrospray coating and was then characterized by FE-SEM imaging. In this detection method, the coulometric signal of the sensor was calculated using Fast Fourier Continuous Cyclic Voltammetry (FFTCCV), where cyclic voltammetry (CV) was applied to the sensor in the defined potential rang and then charge changes of the sensor was obtained by integration of the current in all scanned potential ranges. FFTCCV method enhances the sensitivity of the sensor when exposed to the gas mixtures containing acetone. In addition to its fast coulometric response time (≤5 s) in the two linear ranges of 0.7–2.8 ppm and 2.8–28.2 ppm (R²=0.99), FFTCCV method provides the low detection limit of 70 ppb, and high sensitivity toward acetone at the optimum values of the parameters. The fabricated sensor showed great selectivity toward acetone when exposed to humid air and some exhaled gas like carbon dioxide, ammonia, methanol, ethanol and alkyl amines. The results were very satisfying as the sensor was capable to detect different acetone levels in human exhaled breath as non-invasive diagnosis of diabetes with a good correlation (R²≃0.9) to the routine blood sugar test taken by different commercial glucometers results.     

Switchable Synthesis of 7- and 14-Membered Cyclic Peptides Containing N-Methyl- and β-Amino Acids Utilizing Microflow Technology

Smaller cyclic peptides containing non-proteinogenic amino acids have garnered much attention for use as drugs, but their chemical synthesis is extremely challenging. In this study, a rapid (60.5 min) synthesis of 7- and 14-membered cyclic peptides containing N-methyl- and β-amino acids was achieved by only switching the concentrations (0.20 M or 0.01 M) of the substrates. The developed approach required neither expensive transition-metals nor expensive coupling agents. As far as we could ascertain, this is the first report of the synthesis of smaller (≤16-membered) cyclic N-methylated peptides via dimerization-cyclization strategy.     

Preparative separation of immunoglobulins from bovine colostrum by continuous divergent-flow electrophoresis

Immunoglobulins in bovine colostrum were separated and fractionated from other proteins using the method and instrumentation developed in our laboratory. The proposed separation was based on bidirectional isotachophoresis/moving boundary electrophoresis with electrofocusing of the analytes in a pH gradient from 3.9 to 10.1. The preparative instrumentation included the trapezoidal non-woven fabric that served as separation space with divergent continuous flow. The defatted and casein precipitate-free colostrum supernatant was loaded directly into the instrument without any additional colostrum pre-preparation. Immunoglobulin G was fractionated from other immune proteins such as bovine serum albumin, β-lactoglobulin, and α-lactalbumin, and was continuously collected in separated fractions over 3 h. The fractions were further processed, and isolated immunoglobulin G in the liquid fractions was confirmed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and by re-focusing in gel isoelectric focusing. Separated immunoglobulin G was detected in seven fractions by sodium dodecyl sulfate-polyacrylamide gel electrophoresis with a gradually decreased concentration in the fractions. Re-focusing of the proteins in the fractions by gel isoelectric focusing revealed multiple separated zones of immunoglobulin G with the isoelectric point values covering the range from 5.4 to 7.2. Each fraction contained distinct zones with gradually increased isoelectric point values and decreased concentrations from fraction to fraction.     

Low‐memory iterative density fitting

A new low‐memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix‐vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15‐fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12‐core CPU workstation. © 2015 Wiley Periodicals, Inc.     

Stability of ion triplets in ionic liquid/lithium salt solutions: Insights from implicit and explicit solvent models and molecular dynamics simulations

Binding energies of ion triplets formed in ionic liquids by Li⁺ with two anions have been studied using quantum‐chemical calculations with implicit and explicit solvent supplemented by molecular dynamics (MD) simulations. Explicit solvent approach confirms variation of solute‐ionic liquid interactions at distances up to 2 nm, resulting from structure of solvation shells induced by electric field of the solute. Binding energies computed in explicit solvent and from the polarizable continuum model approach differ largely, even in sign, but relative values generally agree between these two models. Stabilities of ion triplets obtained in quantum‐chemical calculations for some systems disagree with MD results; the discrepancy is attributed to the difference between static optimized geometries used in quantum chemical modeling and dynamic structures of triplets in MD simulations. © 2015 Wiley Periodicals, Inc.     

A Three‐Minute Synthesis and Purification of Ibuprofen: Pushing the Limits of Continuous‐Flow Processing

In a total residence time of three minutes, ibuprofen was assembled from its elementary building blocks with an average yield of above 90 % for each step. A scale‐up of this five‐stage process (3 bond‐forming steps, one work‐up, and one in‐line liquid–liquid separation) provided ibuprofen at a rate of 8.09 g h^?1 (equivalent to 70.8 kg y^?1) using a system with an overall footprint of half the size of a standard laboratory fume hood. Aside from the high throughput, several other aspects of this synthesis expand the capabilities of continuous‐flow processing, including a Friedel–Crafts acylation run under neat conditions and promoted by AlCl₃, an exothermic in‐line quench of high concentrations of precipitation‐prone AlCl₃, liquid–liquid separations run at or above 200 psi to provide solvent‐free product, and the use of highly aggressive oxidants, such as iodine monochloride. The use of simple, inexpensive, and readily available reagents thus affords a practical synthesis of this important generic pharmaceutical.     

Effects of GC temperature and carrier gas flow rate on on‐line oxygen isotope measurement as studied by on‐column CO injection

Although deemed important to δ¹⁸O measurement by on‐line high‐temperature conversion techniques, how the GC conditions affect δ¹⁸O measurement is rarely examined adequately. We therefore directly injected different volumes of CO or CO–N₂ mix onto the GC column by a six‐port valve and examined the CO yield, CO peak shape, CO–N₂ separation, and δ¹⁸O value under different GC temperatures and carrier gas flow rates. The results show the CO peak area decreases when the carrier gas flow rate increases. The GC temperature has no effect on peak area. The peak width increases with the increase of CO injection volume but decreases with the increase of GC temperature and carrier gas flow rate. The peak intensity increases with the increase of GC temperature and CO injection volume but decreases with the increase of carrier gas flow rate. The peak separation time between N₂ and CO decreases with an increase of GC temperature and carrier gas flow rate. δ¹⁸O value decreases with the increase of CO injection volume (when half m/z 28 intensity is <3 V) and GC temperature but is insensitive to carrier gas flow rate. On average, the δ¹⁸O value of the injected CO is about 1‰ higher than that of identical reference CO. The δ¹⁸O distribution pattern of the injected CO is probably a combined result of ion source nonlinearity and preferential loss of C¹⁶O or oxygen isotopic exchange between zeolite and CO. For practical application, a lower carrier gas flow rate is therefore recommended as it has the combined advantages of higher CO yield, better N₂–CO separation, lower He consumption, and insignificant effect on δ¹⁸O value, while a higher‐than‐60 °C GC temperature and a larger‐than‐100 µl CO volume is also recommended. When no N₂ peak is expected, a higher GC temperature is recommended, and vice versa. Copyright © 2015 John Wiley & Sons, Ltd.     

Chemical Evolution of a Bacterial Proteome

We have changed the amino acid set of the genetic code of Escherichia coli by evolving cultures capable of growing on the synthetic noncanonical amino acid L ‐β‐(thieno[3,2‐b]pyrrolyl)alanine ([3,2]Tpa) as a sole surrogate for the canonical amino acid L ‐tryptophan (Trp). A long‐term cultivation experiment in defined synthetic media resulted in the evolution of cells capable of surviving Trp→[3,2]Tpa substitutions in their proteomes in response to the 20 899 TGG codons of the E. coli W3110 genome. These evolved bacteria with new‐to‐nature amino acid composition showed robust growth in the complete absence of Trp. Our experimental results illustrate an approach for the evolution of synthetic cells with alternative biochemical building blocks.