The solubility of cellulose in liquid ammonia/salt solutions

The dissolution of cellulose in solutions of liquid ammonia and ammonium thiocyanate is discussed. Viscosity measurements on dilute solutions of cellulose in this solvent over a range of shear rates and shear stresses are reported. A four-bulb Ubbelohde suspended level viscometer was used for the measurements. Plots of log [η] versus log M gave Mark-Houwink coefficients of a = 0.95 and K = 6.686 × 10^?5 at 25°C for [η] as dl/g. The Bloomfield equation was used to calculate effective bond lengths (b) from limiting viscosity numbers of cellulose in solutions of ammonia/ammonium thiocyanate and Cuene, respectively. Results indicate that cellulose may have similar configurations in both solvents and also that the ammonia solutions are true cellulose solutions. Miscibility of the cell- ulose/ammonia/ammonium thiocyanate solutions with organic solvents, such as glycerol, is also reported. Further, a few interesting characteristics of the liquid ammonia/ammonium salt solutions, discussed briefly, are the convenient boiling point, the rheological behavior, and the relatively high concentration of cellulose obtainable.     

The anionic coordination polymer {K2[PtII2AgI8(2,2′‐bipyridine)2(O2CCF3)14]}n

The trimetallic compound catena‐poly[dipotassium(I) [bis(2,2′‐bipyridine)di‐μ₃‐trifluoroacetato‐dodeca‐μ₂‐trifluoroacetato‐diplatinum(II)octasilver(I)]], K₂[Pt₂Ag₈(C₂F₃O₂)₁₄(C₁₀H₈N₂)₂], forms an extended structure in the solid state. Electrostatic interactions involving the K⁺ ions play a key role in the formation of the extended structure in three dimensions. The Ag^I ions form one‐dimensional coordination polymers, with alternating Ag₂ and Ag₆ units linked by CF₃CO₂⁻ ligands. Pt...Pt interactions perpendicular to the one‐dimensional polymerization axis provide another element of long‐range order, and electrostatic interactions with K⁺ ions provide connectivity between adjacent polymeric structures.     

Algebraic Theory of Causal Double Products

Corresponding to each “rectangular” double product in the form of a formal power series R[h] with coefficients in the tensor product ?(?)⊙ ? (?) with itself of the Itô Hopf algebra, we construct “triangular” elements T[h] of ?(?) satisfying ΔT[h] = T[h]⁽¹⁾ R[h]T{h]⁽²⁾. In Fock space representations of ?(?) by iterated quantum stochastic integrals when ? is the algebra of Itô differentials of the calculus, these correspond to “causal” double product integrals in a single Fock space.     

MiodesinTM Positively Modulates the Immune Response in Endometrial and Vaginal Cells

Endometriosis presents high prevalence and its physiopathology involves hyperactivation of endometrial and vaginal cells, especially by bacteria. The disease has no cure and therapies aiming to inhibit its development are highly desirable. Therefore, this study investigated whether Miodesin^TM (10 µg/mL = IC₈₀; 200 µg/mL = IC₅₀), a natural compound constituted by Uncaria tomentosa, Endopleura uchi, and astaxanthin, could exert anti-inflammatory and anti-proliferative effects against Lipopolysaccharides (LPS) stimulation in endometrial and Candida albicans vaginal cell lines. VK2 E6/E7 (vaginal) and KLE (epithelial) cell lines were stimulated with Candida albicans (1 × 10⁷ to 5 × 10⁷/mL) and LPS (1 μg/mL), respectively. Miodesin^TM inhibited mRNA expression for Nuclear factor kappa B (NF-κB), ciclo-oxigenase 1 (COX-1), and phospholipase A2 (PLA2), beyond the C–C motif chemokine ligand 2 (CCL2), CCL3, and CCL5 in VK2 E6/E7 cells (p < 0.05). In addition, the inhibitory effects of both doses of Miodesin^TM (10 µg/mL and 200 µg/mL) resulted in reduced secretion of interleukin-1β (IL-1β), IL-6, IL-8, tumor necrosis factor α (TNF-α) (24 h, 48 h, and 72 h) and CCL2, CCL3, and CLL5 (p < 0.05) by VK2 E6/E7 cells. In the same way, COX-1 Miodesin^TM inhibited LPS-induced hyperactivation of KLE cells, as demonstrated by reduced secretion of IL-1β, IL-6, IL-8, TNF-α (24 h, 48 h, and 72 h) and CCL2, CCL3, and CLL5 (p < 0.05). Furthermore, Miodesin^TM also inhibited mRNA expression and secretion of matrix metalloproteinase-2 (MMP-2), MMP-9, and vascular endothelial growth factor (VEGF), which are key regulators of invasion of endometrial cells. Thus, the study concludes that Miodesin^TM presents beneficial effects in the context of endometriosis, positively affecting the inflammatory and proliferative response.     

On asymptotic convergence of the block-iterative Fisher scoring algorithm

This short paper studies convergence properties, particularly asymptotic convergence, of the block-iterative Fisher scoring (BFS) algorithms recently proposed by Ma and Hudson (2008). While applicable in other inverse problem domains (e.g. astronomy, geophysics, signal processing or remote sensing), this class of algorithms was designed for tomographic image reconstruction from projections in medicine. A BFS algorithm is used to reconstruct the patient’s internal structural or functional activity from collected projection data. We briefly introduce the BFS algorithm and a general convergence result provided in Ma and Hudson (2008). This result is used to prove the asymptotic convergence of two specific BFS algorithms under new conditions.     

Calculus In Enveloping Algebras

Motivated by, but independent of, some recent work in quantumstochastic calculus, a theory of differential and integral calculusis developed which is intrinsic to the universal envelopingalgebra of a Lie algebra whose Lie bracket is obtained by takingcommutators in an associative algebra. The differential mapsatisfies a generalisation of Leibniz' formula called the Leibniz–Itôformula, which involves the associative multiplication. Thereis an analogue of the Taylor–Maclaurin expansion. Throughpassing to formal power series, a theory of product integralsis developed; such integrals are characterised by a group-likeproperty with respect to the coproduct.     

On runs of consecutive quadratic residues and quadratic nonresidues

Based on results of Weil and of Burgess, we have obtained a boundK(l) such that all primesp K(l) have a sequence of at leastl consecutive quadratic residues and a sequence of at leastl consecutive nonresidues in the interval [1,p – 1]. The bound forl=9 being 414463, we have computed, for primes less than 420000, the lengths of the longest sequences of consecutive residues and of nonresidues. We present these data and make some observations concerning them. One of the observations is that there is an observed difference in the length of the maximal sequence between primes congruent to 1 (mod 4) and primes congruent to 3 (mod 4).     

Extension of a theorem of Cauchy and Jacobi

Let q and p be prime with q = a² + b² ≡ 1 (mod 4), a ≡ 1 (mod 4), and p = qf + 1. In the nineteenth century Cauchy (Mém. Inst. France17 (1840), 249–768) and Jacobi (J. für Math.30 (1846), 166–182) generalized the work of earlier authors, who had determined certain binomial coefficients (mod p) (see H. J. S. Smith, “Report on the Theory of Numbers,” Chelsea, 1964), by determining two products of factorials given by Π_kkf! (mod p = qf + 1) where k runs through the quadratic residues and the quadratic non-residues (mod q), respectively. These determinations are given in terms of parameters in representations of p^h or of 4p^h by binary quadratic forms. A remarkable feature of these results is the fact that the exponent h coincides with the class number of the related quadratic field. In this paper C. R. Mathews' (Invent. Math.54 (1979), 23–52) recent explicit evaluation of the quartic Gauss sum is used to determine four products of factorials (mod p = qf + 1, q ≡ 5 (mod 8) > 5), given by Π_kkf! where k runs through the quartic residues (mod q) and the three cosets which may be formed with respect to this subgroup. These determinations appear to be considerably more difficult. They are given in terms of parameters in representations of 16p^h by quaternary quadratic forms. Stickelberger's theorem is required to determine the exponent h which is shown to be closely related to the class number of the imaginary quartic field Q(i√2q + 2a√q), q = a² + b² ≡ 5 (mod 8), a odd.     

Inferring phase equations from multivariate time series

An approach is presented for extracting phase equations from multivariate time series data recorded from a network of weakly coupled limit cycle oscillators. Our aim is to estimate important properties of the phase equations including natural frequencies and interaction functions between the oscillators. Our approach requires the measurement of an experimental observable of the oscillators; in contrast with previous methods it does not require measurements in isolated single or two-oscillator setups. This noninvasive technique can be advantageous in biological systems, where extraction of few oscillators may be a difficult task. The method is most efficient when data are taken from the nonsynchronized regime. Applicability to experimental systems is demonstrated by using a network of electrochemical oscillators; the obtained phase model is utilized to predict the synchronization diagram of the system.