A complete 1H and 13C NMR data assignment for 3-phenylmethylene-1H,3H-naphtho-[1,8-c,d]-pyran-1-one

Complete assignments of the 1H and 13C NMR chemical shifts for 3-phenylmethylene-1H,3H-naphtho-[1,8-c,d]-pyran-1-one were done by means of one- and two-dimensional NMR techniques, including 1H-(1)H COSY, HMQC and HMBC spectra. Ab initio quantum chemistry calculations and a shift prediction by an incremental method provided values close to the proposed assignments. All mid-IR spectral bands are given as reference data. The DRIFT FTIR, ATR FTIR and Raman spectra are given as a Supplementary data in JCAMP-DX format, version 4.24. In addition, a method of compound's synthesis, that has the product yield higher as compared to already known data in the literature, is given.     

Needle-type glucose biosensor with an electrochemically codeposited enzyme in a platinum black matrix

In this study we report the development of a needle-type glucose biosensor for the management of hemorrhagic shock. The immobilization technique depends on the electrophoretic deposition of the glucose oxidase enzyme in an electrochemically grown platinum black matrix. The sensor was coated with Nafion to decrease the effect of interferents. Preliminary tests were carried out to evaluate the sensor performance in vitro. These tests included the measurement of glucose levels in buffer solutions containing various potential physiological interferents, as well as in bovine serum. The preliminary results show the sensor to have inearity up to 33 mM and a diminished response to interferents. The advantages of this technique are its simplicity and high controllability.     

Patterns of spiral wave attenuation by low-frequency periodic planar fronts

There is evidence that spiral waves and their breakup underlie mechanisms related to a wide spectrum of phenomena ranging from spatially extended chemical reactions to fatal cardiac arrhythmias [A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 2001); J. Schutze, O. Steinbock, and S. C. Muller, Nature 356, 45 (1992); S. Sawai, P. A. Thomason, and E. C. Cox, Nature 433, 323 (2005); L. Glass and M. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, 1988); R. A. Gray et al., Science 270, 1222 (1995); F. X. Witkowski et al., Nature 392, 78 (1998)]. Once initiated, spiral waves cannot be suppressed by periodic planar fronts, since the domains of the spiral waves grow at the expense of the fronts [A. N. Zaikin and A. M. Zhabotinsky, Nature 225, 535 (1970); A. T. Stamp, G. V. Osipov, and J. J. Collins, Chaos 12, 931 (2002); I. Aranson, H. Levine, and L. Tsimring, Phys. Rev. Lett. 76, 1170 (1996); K. J. Lee, Phys. Rev. Lett. 79, 2907 (1997); F. Xie, Z. Qu, J. N. Weiss, and A. Garfinkel, Phys. Rev. E 59, 2203 (1999)]. Here, we show that introducing periodic planar waves with long excitation duration and a period longer than the rotational period of the spiral can lead to spiral attenuation. The attenuation is not due to spiral drift and occurs periodically over cycles of several fronts, forming a variety of complex spatiotemporal patterns, which fall into two distinct general classes. Further, we find that these attenuation patterns only occur at specific phases of the descending fronts relative to the rotational phase of the spiral. We demonstrate these dynamics of phase-dependent spiral attenuation by performing numerical simulations of wave propagation in the excitable medium of myocardial cells. The effect of phase-dependent spiral attenuation we observe can lead to a general approach to spiral control in physical and biological systems with relevance for medical applications.     

Ideals of identities of representations of nilpotent lie algebras

Let L be a Lie algebra, nilpotent of class 2, over an infinite field K, and suppose that the centre C of L is one dimensional; such Lie algebras are called Heisenberg algebras. Let ρ:L→hom _KV be a finite dimensional representation of the Heisenberg algebra L such that ρ(C) contains non-singular linear transformations of V, and denote l(ρ) the ideal of identities for the representation ρ. We prove that the ideals of identities of representations containing I(ρ) and generated by multilinear polynomials satisfy the ACC. Let sl ₂(L) be the Lie algebra of the traceless 2×2 matrices over K, and suppose the characteristic of K equals 2. As a corollary we obtain that the ideals of identities of representations of Lie algebras containing that of the regular representation of sl ₂(K) and generated by multilinear polynomials, are finitely based. In addition we show that one cannot simply dispense with the condition of multilinearity. Namely, we show that the ACC is violated for the ideals of representations of Lie algebras (over an infinite field of characteristic 2) that contain the identities of the regular representation of sl ₂(K).     

Non-random fluctuations and multi-scale dynamics regulation of human activity

We investigate if known extrinsic and intrinsic factors fully account for the complex features observed in recordings of human activity as measured from forearm motion in subjects undergoing their regular daily routine. We demonstrate that the apparently random forearm motion possesses dynamic patterns characterized by robust scale-invariant and nonlinear features. These patterns remain stable from one subject to another and are unaffected by changes in the average activity level that occur within individual subjects throughout the day and on different days of the week, since they persist during daily routine and when the same subjects undergo time-isolation laboratory experiments designed to account for the circadian phase and to control the known extrinsic factors. Further, by modeling the scheduled events imposed throughout the laboratory protocols, we demonstrate that they cannot account for the observed scaling patterns in activity fluctuations. We attribute these patterns to a previously unrecognized intrinsic nonlinear multi-scale control mechanism of human activity that is independent of known extrinsic factors such as random and scheduled events, as well as the known intrinsic factors which possess a single characteristic time scale such as circadian and ultradian rhythms.     

Syrian hamster embryo (SHE) assay (pH 6.7) coupled with infrared spectroscopy and chemometrics towards toxicological assessment

The Syrian hamster embryo (SHE) assay (pH 6.7) is an in vitro candidate to replace in vivo carcinogenicity tests. However, the conventional method of visual scoring of foci (non-transformed vs. transformed colonies) can be time-consuming and is open to subjectivity. Infrared (IR) spectroscopy has the potential to provide objective assessment of such SHE colonies with the added advantage of potentially providing mechanistic information. In this study, SHE cells were treated with one of eight different chemical regimens, allowed in culture to attach and form foci on IR-reflective glass slides; these were subsequently interrogated by attenuated total reflection (ATR) Fourier-transform IR (FTIR) spectroscopy. Derived mid-IR spectra (n = 13,406) were subjected to chemometric analysis focusing primarily on the extraction of biochemical information related to test agent treatment and/or morphological transformation. The use of ATR-FTIR spectroscopy with chemometrics to analyze the SHE assay is a novel approach to toxicological assessment.     

The central polynomials for the Grassmann algebra

In this paper we describe the central polynomials for the infinite-dimensional unitary Grassmann algebra G over an infinite field F of characteristic ≠ 2. We exhibit a set of polynomials that generates the vector space C(G) of the central polynomials of G as a T-space. Using a deep result of Shchigolev we prove that if charF = p > 2 then the T-space C(G) is not finitely generated. Moreover, over such a field F, C(G) is a limit T-space, that is, C(G) is not a finitely generated T-space but every larger T-space W ≩ C(G) is. We obtain similar results for the infinite-dimensional nonunitary Grassmann algebra H as well.     

Multivariate holomorphic Hermite polynomials

The Ramanujan Journal - We introduce holomorphic Hermite polynomials in n complex variables that generalize the Hermite polynomials in n real variables introduced by Hermite in the late 19th...