Crystal structure of cyanocalix[4]arene methyl ether

The title compound has been prepared by the addition of bromocalix[4]arene methyl ether to CuCN in N-methylpyrrolidone. The crystals belong to the monoclinic space groupP2₁/n witha=13.591(3),b=24.778(5),c=11.057(3)Å,=93.58(2)°, andD _c=1.09 g cm^–3 forZ=4. Refinement based on 1118 observed reflections led to a finalR value of 0.085. The molecule exhibits the partial cone conformation.     

Functional integral representations of the Pauli-Fierz model with spin 1/2

A Feynman-Kac-type formula for a Lévy and an infinite-dimensional Gaussian random process associated with a quantized radiation field is derived. In particular, a functional integral representation of e−tHPF generated by the Pauli-Fierz Hamiltonian with spin 1/2 in non-relativistic quantum electrodynamics is constructed. When no external potential is applied HPF turns translation-invariant and it is decomposed as a direct integral . The functional integral representation of e−tHPF(P) is also given. Although all these Hamiltonians include spin, nevertheless the kernels obtained for the path measures are scalar rather than matrix expressions. As an application of the functional integral representations energy comparison inequalities are derived.     

Error Correcting Sequence and Projective De Bruijn Graph

Let X be a finite set of q elements, and n, K, d be integers. A subset C ⊂ X ⁿ is an (n, K, d) error-correcting code, if #(C) = K and its minimum distance is d. We define an (n, K, d) error-correcting sequence over X as a periodic sequence {a _i } _i=0,1,... (a _i ∈ X) with period K, such that the set of all consecutive n-tuples of this sequence form an (n, K, d) error-correcting code over X. Under a moderate conjecture on the existence of some type of primitive polynomials, we prove that there is a error correcting sequence, such that its code-set is the q-ary Hamming code with 0 removed, for q > 2 being a prime power. For the case q = 2, under a similar conjecture, we prove that there is a error-correcting sequence, such that its code-set supplemented with 0 is the subset of the binary Hamming code [2 ^m  − 1, 2 ^m  − 1 − m, 3] obtained by requiring one specified coordinate being 0. Received: October 27, 2005. Final Version received: December 31, 2007     

Donor-acceptor distance-dependence of photoinduced electron-transfer rate in flavoproteins

Ultrafast fluorescence quenching of flavin in flavodoxin from Megasphaera elsdenii was investigated by means of a fluorescence up-conversion method. Fluorescence lifetimes of flavodoxin from M. elsdenii were estimated to be tau(1) approximately 165 fs (0.97%) and tau(2) approximately 10 ps (0.03%). Correlation of photoinduced electron-transfer rates (k(ET)) with averaged distances (D(av)) between isoalloxazine and nearby tryptophan or tyrosine was examined and obtained an empirical equation of ln k(ET) vs D(av) by means of a nonlinear least-squares method using reported data together with flavodoxin from M. elsdenii. The values of D(av) were calculated from X-ray structures of the flavoproteins. The ln k(ET) was approximately linear at D(av) shorter than 7 A. The model free empirical equation was expressed as ln k(ET) = 29.7 + (-0.327 D(av) + 2.84 x 10(-5))/(0.698 - D(av)(2)). We also analyzed the observed values of ln k(ET) with Marcus theory, but could not obtain reasonable results. Our analysis suggests that the average distance, rather than the shortest (edge to edge) distance or interplanar angles between the aromatics rings, is the key factor in the process of the photoinduced electron transfer in these flavoproteins.     

Multiple enzyme linked immunosorbent assay system on a capillary-assembled microchip integrating valving and immuno-reaction functions

Gastrodin is a bioactive constituent of rhizome in Gastrodia elata Blume (Orchidaceae) The aim of this study is to develop a rapid and sensitive liquid chromatographic method coupled to microdialysis sampling system to measure the unbound of gastrodin in rat blood, brain and bile. Microdialysis probes were simultaneously inserted into the jugular vein, brain striatum and bile duct of each anesthetized rat for sampling after the administration of gastrodin (100 or 300 mg kg⁻¹) through the femoral vein. Separation of unbound gastrodin from various biological fluids was applied to an RP-select B column (250 mm × 4.6 mm i.d., 5 μm). The mobile phase consisted of acetonitrile–50 mM potassium dihydrogen phosphate buffer–triethylamine (5:95:0.1, v/v/v, adjusted to pH 2.5 with orthophosphoric acid) with a flow rate of 1 mL min⁻¹. The UV detector wavelength was set at 221 nm. Fifteen minutes after the administration, the gastrodin reached the peak concentration in brain and bile. In addition, the results indicate that gastrodin penetrates the blood-brain barrier (BBB) and goes through hepatobiliary excretion.     

Remarks on a posteriori error estimation for finite element solutions

We utilize the classical hypercircle method and the lowest-order Raviart–Thomas H(div)$H(\mathrm{div})$ element to obtain a posteriori error estimates of the _P1$P_1$ finite element solutions for 2D Poisson's equation. A few other estimation methods are also discussed for comparison. We give some theoretical and numerical results to see the effectiveness of the methods.     

Unidirectional crystallization of charged colloidal silica due to the diffusion of a base

Dilute aqueous dispersions of charged colloidal silica (particle volume fraction = approximately 0.03-0.04, particle diameter = 110 nm) exhibit unidirectional crystal growth due to the diffusion of a weak base, pyridine (Py). Similar diffusion-crystallization is enabled by a salt of a weak acid and a strong base, sodium hydrogen carbonate (NaHCO3). The resulting crystals consist of columnar (or cubic) crystal grains with a maximum height of a few centimeters and a maximum width of 1 cm. The crystal growth process is attributed to a combination of (i) the diffusion of Py or NaHCO3 accompanied by a charging reaction of the silica particles and (ii) the charge-induced crystallization of the silica colloids. Theoretical growth curves based on the reaction-diffusion model for the case of Py were in good agreement with the observed curves. We also report the immobilization of the resulting large crystals by using a polymer hydrogel matrix.     

Selective ion binding by protein probed with the statistical mechanical integral equation theory

Selective ion binding by human lysozyme and its mutants is probed with the three-dimensional interaction site model theory which is the statistical mechanical integral equation theory. Preliminary and partial results of the study have been already published (Yoshida, N. et al. J. Am. Chem. Soc. 2006, 128, 12042-12043). The calculation was carried out for aqueous solutions of three different electrolytes, CaCl2, NaCl, and KCl, and for four different mutants of the human lysozyme: wild type, Q86D, A92D, and Q86D/A92D, which have been studied experimentally. The discussion of this article focuses on the cleft that consists of amino acid residues from Q86 to A92. For the wild type of protein in the aqueous solutions of all the electrolytes studied, there are no distributions observed for the ions inside the cleft. The Q86D mutant shows essentially the same behavior with that of the wild type. The A92D mutant shows strong binding ability to Na+ in the recognition site, which is in accord with the experimental results. There are two isomers of the Q86D/A92D mutant, e.g., apo-Q86D/A92D and holo-Q86D/A92D. Although both isomers exhibit the binding ability to the Na+ and Ca2+ ions, the holo isomer shows much greater affinity compared with the apo isomer. Regarding the selective ion binding of the holo-Q86D/A92D mutant, it shows greater affinity to Ca2+ than to Na+, which is also consistent with the experimental observation.     

An optical system for measuring the eccentricity of glass wool pipe — for industrial use

An optical system for measuring the eccentricity of the glass wool pipe has been developed for an industrial use. The system consists of a contact sensor, a photo light sensor and a signal processing system with a logic circuit. The system is simple, fast and efficient for practical use; it allows implementation of on-line process monitoring and alarm warning signals for unacceptable pipe eccentricity during manufacturing.