Polynitro-substitutedN-alkylalkaneimidoyl chlorides

The reaction of 00/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-fluorosubstituted polynitroalkylaldimines with HCl results in replacement of the fluorine atom by a chlorine atom. The hitherto unknown 00/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-chlorosubstituted polynitroalkylaldimines have been obtained, and their X-ray structural investigation has been performed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 440–443, March, 1994.     

In-capillary micro solid-phase extraction and capillary electrophoresis separation of heterocyclic aromatic amines with nanospray mass spectrometric detection

A miniaturised technique to analyse and detect heterocyclic aromatic amines (HAs) using micro solid-phase extraction (00w/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0">SPE) coupled on-line (in-capillary) to capillary electrophoresis (CE) separation with nanospray (nESI) mass spectrometry (MS) detection has been developed. HAs are mutagenic and carcinogenic compounds formed at low levels in protein-rich food during cooking. Due to the low concentrations of HAs and the high complexity of the matrix in which they exist, sensitive and selective analytical methods are required for quantification. 00w/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0">SPE was performed on a packed bed of C₁₈ particles inside the CE capillary, which minimised the dead volume. The on-line coupling of SPE, CE and nESI-MS reduced the time for extraction and identification to less than half an hour, which will allow for screening of several samples per day. The new technique provides short analysis time, low sample and solvent consumption, and HAs in standard solutions were easily detected at 12–17 fmol injections, and in spiked urine samples at 750–810 fmol injections.     

Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.     

The pebbling threshold of the square of cliques

Given an initial configuration of pebbles on a graph, one can move pebbles in pairs along edges, at the cost of one of the pebbles moved, with the objective of reaching a specified target vertex. The pebbling number of a graph is the minimum number of pebbles so that every configuration of that many pebbles can reach any chosen target. The pebbling threshold of a sequence of graphs is roughly the number of pebbles so that almost every (resp. almost no) configuration of asymptotically more (resp. fewer) pebbles can reach any chosen target. In this paper we find the pebbling threshold of the sequence of squares of cliques, improving upon an earlier result of Boyle and verifying an important instance of a probabilistic version of Graham's product conjecture.     

Locally strong endomorphisms of paths

We determine the number of locally strong endomorphisms of directed and undirected paths—direction here is in the sense of a bipartite graph from one partition set to the other. This is done by the investigation of congruence classes, leading to the concept of a complete folding, which is used to characterize locally strong endomorphisms of paths. A congruence belongs to a locally strong endomorphism if and only if the number l of congruence classes divides the length of the original path and the points of the path are folded completely into the l classes, starting from 0 to l and then back to 0, then again back to l and so on. It turns out that for paths locally strong endomorphisms form a monoid if and only if the length of the path is prime or equal to 4 in the undirected case and in the directed case also if the length is 8. Finally some algebraic properties of these monoids are described.     

The influence of water on the memory effect of the amylose tris(3,5-dimethylphenyl carbamate) stationary phase

Acid/base modifiers are sometimes used as additives in normal phase elution on columns packed with CHIRALPAK^® AD^®. These modifiers affect enantioseparations in ways that are not yet fully understood for the lack of systematic studies. Shifts of the selectivity of certain pairs of enantiomers upon exposure of the column to these modifiers is amply documented. Furthermore, once the modifier has been removed from the mobile phase, the modified selectivity remains, which has been named the Memory Effect. After a column has been exposed to an eluent stream containing acidic/basic modifiers, this particular column no longer separates certain enantiomeric pairs with the same selectivity as a modifier naive column. This makes the transfer of developed methods from one to other CHIRALPAK AD columns difficult to predict, if the selectivity needs to be similar between the two columns. We selected four enantiomeric pairs for a systematic study of this Memory Effect. The selectivity of 4-chlorophenylalanine ethyl ester improves after a solution of ethanesulfonic acid (ESA) is percolated through the column. The selectivity of Propranolol and Tröger's base increases after a solution of Diiospropylamine is percolated through the column. The selectivity of Propranolol and Tröger's base enantiomers is inversely affected by percolation of the acid solution. The 4-chlorophenylalanine ethyl ester enantiomers is inversely affected by percolation of the base solution. In contrast, the selectivity of trans-stilbene oxide (TSO) is not affected by either modifier. Analytical studies of the stationary phase suggest that slow protonation/deprotonation of water molecules attached to the carbamate moiety may be responsible for the acid/base Memory Effect. To further the understanding of the effect of water on the Memory Effect, mobile phases – spiked with water (0.01–0.43%) – were used to measure changes in the Memory Effect. Finally, we showed that the influence of water on the Memory Effect can be minimized by percolating through the column a sufficiently concentrated solution of the appropriate base while using dried mobile phases.     

Atomic N00N state generation in distant cavities by virtual excitations

A general scheme of generating N00N states of virtually-excited 2N atoms is proposed. The two cavities are fibre-connected with N atoms in each cavity. Although we focus on the case of N=2, the system can be extended to a few atoms with N>2. It is found that all 2N atoms can be entangled in the form of N00N states if the atoms in the first cavity are initially in the excited states and atoms in the second cavity are all in the ground states. The feasibility of the scheme is carefully discussed, it shows that the N00N state with a few atoms can be generated with good fidelity and the scheme is feasible in experiment.     

How algebra spoiled recreational problems: A case study in the cross-cultural dissemination of mathematics

This paper deals with a sub-class of recreational problems which are solved by a simple memorized rule resulting from an elementary arithmetical or algebraic solution, called proto-algebraic rules. Their recreational aspect is derived from a surprise or trick solution which is not immediately obvious to the subjects involved. Around 1560 many such problems wane from arithmetic and algebra textbooks to reappear in the eighteenth century. Several hypotheses are investigated why popular Renaissance recreational problems lost their appeal. We arrive at the conclusion that the emergence of algebra as a general problem solving method changed the scope of what is considered recreational in mathematics.     

Strongly Supercommuting Self-Adjoint Operators

We introduce the notion of strong supercommutativity of self-adjoint operators on a 004_1233_IEq1.gif" alt="$$\mathbb{Z}_2 $$" align="middle" border="0"> -graded Hilbert space and give some basic properties. We clarify that strong supercommutativity is a unification of strong commutativity and strong anticommutativity. We also establish the theory of super quantization. Applications to supersymmetric quantum field theory and a fermion-boson interaction system are discussed.