Enantioselective Synthesis of α-Thiocarboxylic Acids by Nitrilase Biocatalysed Dynamic Kinetic Resolution of α-Thionitriles

The enantioselective synthesis of α-thiocarboxylic acids by biocatalytic dynamic kinetic resolution (DKR) of nitrile precursors exploiting nitrilase enzymes is described. A panel of 35 nitrilase biocatalysts were screened and enzymes Nit27 and Nit34 were found to catalyse the DKR of racemic α-thionitriles under mild conditions, affording the corresponding carboxylic acids with high conversions and good-to-excellent ee. The ammonia produced in situ during the biocatalytic transformation favours the racemization of the nitrile enantiomers and, in turn, the DKR without the need of any external additive base.     

Bei der Elementaranalyse zur Bestimmung von Kohlenstoff und Wasserstoff

Ohne Zusammenfassung     

Computing Zeta Functions of Kummer Curves via Multiplicative Characters

We present a practical polynomial-time algorithm for computing the zeta function of a Kummer curve over a finite field of small characteristic. Such algorithms have recently been obtained using a method of Kedlaya based upon Monsky–Washnitzer cohomology, and are of interest in cryptography. We take a different approach. The problem is reduced to that of computing the L-function of a multiplicative character sum. This latter task is achieved via a cohomological formula based upon the work of Dwork and Reich. We show, however, that our method and that of Kedlaya are very closely related.Dedicated to the memory of Gian-Carlo Rota     

Fish locomotion: kinematics and hydrodynamics of flexible foil-like fins

The fins of fishes are remarkable propulsive devices that appear at the origin of fishes about 500 million years ago and have been a key feature of fish evolutionary diversification. Most fish species possess both median (midline) dorsal, anal, and caudal fins as well as paired pectoral and pelvic fins. Fish fins are supported by jointed skeletal elements, fin rays, that in turn support a thin collagenous membrane. Muscles at the base of the fin attach to and actuate each fin ray, and fish fins thus generate their own hydrodynamic wake during locomotion, in addition to fluid motion induced by undulation of the body. In bony fishes, the jointed fin rays can be actively deformed and the fin surface can thus actively resist hydrodynamic loading. Fish fins are highly flexible, exhibit considerable deformation during locomotion, and can interact hydrodynamically during both propulsion and maneuvering. For example, the dorsal and anal fins shed a vortex wake that greatly modifies the flow environment experienced by the tail fin. New experimental kinematic and hydrodynamic data are presented for pectoral fin function in bluegill sunfish. The highly flexible sunfish pectoral fin moves in a complex manner with two leading edges, a spanwise wave of bending, and substantial changes in area through the fin beat cycle. Data from scanning particle image velocimetry (PIV) and time-resolved stereo PIV show that the pectoral fin generates thrust throughout the fin beat cycle, and that there is no time of net drag. Continuous thrust production is due to fin flexibility which enables some part of the fin to generate thrust at all times and to smooth out oscillations that might arise at the transition from outstroke to instroke during the movement cycle. Computational fluid dynamic analyses of sunfish pectoral fin function corroborate this conclusion. Future research on fish fin function will benefit considerably from close integration with studies of robotic model fins.     

Hydrodynamics of a biologically inspired tandem flapping foil configuration

Numerical simulations have been used to analyze the effect that vortices, shed from one flapping foil, have on the thrust of another flapping foil placed directly downstream. The simulations attempt to model the dorsal–tail fin interaction observed in a swimming bluegill sunfish. The simulations have been carried out using a Cartesian grid method that allows us to simulate flows with complex moving boundaries on stationary Cartesian grids. The simulations indicate that vortex shedding from the upstream (dorsal) fin is indeed capable of increasing the thrust of the downstream (tail) fin significantly. Vortex structures shed by the upstream dorsal fin increase the effective angle-of-attack of the flow seen by the tail fin and initiate the formation of a strong leading edge stall vortex on the downstream fin. This stall vortex convects down the surface of the tail and the low pressure associated with this vortex increases the thrust on the downstream tail fin. However, this thrust augmentation is found to be quite sensitive to the phase relationship between the two flapping fins. The numerical simulations allows us to examine in detail, the underlying physical mechanism for this thrust augmentation.      

Assessing Adherence to Antihypertensive Medication by Means of Dose-Dependent Reference Plasma Concentration Ranges and Ultra-High Performance Liquid Chromatography-Ion Trap Mass Spectrometry Analysis

Poor adherence to antihypertensive drug therapy is a well-recognized problem and can be assessed by mass spectrometry-based analyses of body fluids. However, contrary statements exist whether drug quantification in blood or qualitative screening in urine is more suitable. The present pilot study aimed to further elucidate the power of blood plasma drug concentrations for adherence monitoring by developing and validating a quantification procedure for nine antihypertensive drugs (amlodipine, bisoprolol, candesartan, canrenone, carvedilol, metoprolol, olmesartan, torasemide, and valsartan) in blood plasma using liquid–liquid extraction and an ultra-high-performance liquid chromatography-ion trap mass spectrometry analysis. The procedure should then be used for an adherence assessment and compared with the results of an established qualitative urine screening. Selectivity, carryover, matrix effect, accuracy, precision, dilution integrity, and stability were successfully validated, except for amlodipine. The applicability was demonstrated by analyzing 19 plasma samples containing 28 antihypertensive drugs and comparing the measured concentrations with calculated dose-dependent reference plasma concentration ranges. The interpretation of plasma concentrations was found to be more sophisticated and time-consuming than that of urine screening results, and adherence could not be assessed in two cases (10%) due to measured plasma concentrations below the lower limit of quantification. However, 14 out of 19 subjects were classified as adherent (75%) and three as nonadherent (15%), in contrast to 19 (100%) that were claimed to be adherent based on the results of the qualitative urine screening. Nevertheless, further data is needed to estimate whether plasma quantification is superior in terms of assessing adherence to antihypertensive medication.     

Photo‐biocatalytic One‐Pot Cascades for the Enantioselective Synthesis of 1,3‐Mercaptoalkanol Volatile Sulfur Compounds

The synthesis of enantiomerically pure 1,3‐mercaptoalkanol volatile sulfur compounds through a one‐pot photo‐biocatalytic cascade reaction is described. Two new KRED biocatalysts with opposite enantioselectivity were discovered and proved to be efficient on a wide range of substrates. The one‐pot cascade reaction combining photocatalytic thio‐Michael addition with biocatalytic ketoreduction in an aqueous medium provides a green and sustainable approach to enantiomerically pure 1,3‐mercaptoalkanols in high yields with excellent enantioselectivity.     

Hensel lifting and bivariate polynomial factorisation over finite fields

This paper presents an average time analysis of a Hensel lifting based factorisation algorithm for bivariate polynomials over finite fields. It is shown that the average running time is almost linear in the input size. This explains why the Hensel lifting technique is fast in practice for most polynomials.

     

Deformation Theory and The Computation of Zeta Functions

We present a new approach to the problem of computing the zetafunction of a hypersurface over a finite field. For a hypersurfacedefined by a polynomial of degree d in n variables over thefield of q elements, one desires an algorithm whose runningtime is a polynomial function of dⁿ log(q). (Here we assumed 2, for otherwise the problem is easy.) The case n = 1 isrelated to univariate polynomial factorisation and is comparativelystraightforward. When n = 2 one is counting points on curves,and the method of Schoof and Pila yields a complexity of , where the function C_d depends exponentiallyon d. For arbitrary n, the theorem of the author and Wan givesa complexity which is a polynomial function of (pdⁿ log(q))ⁿ,where p is the characteristic of the field. A complexity estimateof this form can also be achieved for smooth hypersurfaces usingthe method of Kedlaya, although this has only been worked outin full for curves. The new approach we present should yielda complexity which is a small polynomial function of pdⁿ log(q).In this paper, we work this out in full for Artin–Schreierhypersurfaces defined by equations of the form Z^p – Z= f, where the polynomial f has a diagonal leading form. Themethod utilises a relative p-adic cohomology theory for familiesof hypersurfaces, due in essence to Dwork. As a corollary ofour main theorem, we obtain the following curious result. Letf be a multivariate polynomial with integer coefficients whoseleading form is diagonal. There exists an explicit deterministicalgorithm which takes as input a prime p, outputs the numberof solutions to the congruence equation f = 0 op, and runs in bit operations, for any >0. This improves upon the elementary estimate of bit operations, where n is the number of variables,which can be achieved using Berlekamp's root counting algorithm.2000 Mathematics Subject Classification 11Y99, 11M38, 11T99.     

Polynomials with Odd Orthogonal Multiplicity

Let theorthogonal multiplicityof a monic polynomialgover a field be the number of polynomialsfover , coprime togand of degree less than that ofg, such that all the partial quotients of the continued fraction expansion off/gare of degree 1. Polynomials with positive orthogonal multiplicity arise in stream cipher theory, part of cryptography, as the minimal polynomials of the initial segments of sequences which have perfect linear complexity profiles. This paper focuses on polynomials which have odd orthogonal multiplicity; such polynomials are characterized and a lower bound on their orthogonal multiplicity is given. A special case of a conjecture on rational functions over the finite field of two elements with partial quotients of degree 1 or 2 in their continued fraction expansion is also proved.