A rigorous formalism of information transfer between dynamical system components. I. Discrete mapping

We put the concept of information transfer on a rigorous footing and establish for it a formalism within the framework of discrete maps. The resulting transfer measure possesses a property of directionality or transfer asymmetry as emphasized by Schreiber [T. Schreiber, Measuring information transfer, Phys. Rev. Lett. 85 (2) (2000) 461]; it also verifies the transfer measure for two-dimensional systems, which was obtained by Liang and Kleeman [X.S. Liang, R. Kleeman, Information transfer between dynamical system components, Phys. Rev. Lett. 95 (24) (2005) 244101] through a different avenue. Connections to classical formalisms are explored and applications presented. We find that, in the context of the baker transformation, there is always information flowing from the stretching direction to the folding direction, while no transfer occurs in the opposite direction; we also find that, within the Hénon map system, the transfer from the quadratic component to the linear component is of a simple form as expected on physical grounds. This latter result is unique to our formalism.     

Comparative adsorption of methylene blue by magnetic baker’s yeast and EDTAD-modified magnetic baker’s yeast: Equilibrium and kinetic study

Magnetic baker’s yeast (MB) was prepared using glutaraldehyde cross-linking method and chemical modification with ethylenediaminetetraacetic dianhydride (EDTAD). The fabricated EDTAD-modified magnetic baker’s yeast (EMB) was then employed to remove methylene blue. Comparative adsorption of methylene blue by EMB and MB was systematically investigated with respect to pH, contact time, initial concentration and reaction temperature. The mechanism of methylene blue adsorption by EMB and MB was investigated by SEM, FTIR and Special surface area using methylene blue method. The results revealed that Fe₃O₄ nanoparticles were steadily cross-linked/incorporated with baker’s yeast biomass and the EDTA was modified on the surface of the magnetic baker’s yeast. The equilibrium adsorption data were fitted better by Langmuir isotherm, and the specific surface areas were 42.953–226.07 m²/g for MB and 94.972–499.85 m²/g for EMB, respectively. Kinetic studies suggested that the pseudo-second-order model was suitable to describe the adsorption process. Thermodynamic studies indicated that the adsorption was feasible, spontaneous and endothermic. The recovery efficiencies were above 80% by using 0.1 M HCl.     

The orthosomycin family of antibiotics—I : The constitution of flambamycin

The antibiotic, flambamycin, is shown to have the novel oligosaccharide structure (1) associated with two orthoester linkages. It is proposed that flambamycin (1), the everninomicins (28), curamycin, avilamycin, destomycin A (29a), destomycin C (29b), destomycin B (30), hygromycin B (29c), the antibiotics A-396-I (29d) and SS-56C (29e), belong to a new family of antibiotics called the orthosomycins.     

Computing partial information out of intractable: Powers of algebraic numbers as an example

We consider an algorithmic problem of computing the first, i.e., the most significant digits of n² (in base 3) and of the nth Fibonacci number. While the decidability is trivial, efficient algorithms for those problems are not immediate. We show, based on Baker's inapproximability results of transcendental numbers that both of the above problems can be solved in polynomial time with respect to the length of n. We point out that our approach works also for much more general expressions of algebraic numbers.     

A convenient Baker yeast accelerated,one-pot synthesis of pentasubstituted thiopyridines

Here we report a novel Baker yeast catalyzed one pot cyclocondensation, performed at room temperature in ethanol for obtaining high yields of polyfunctionalized pyridines, 2-amino-4-aryl-3,5-dicyano-6-phenylthiopyridines. The developed protocol obeys certain green principles and is scalable and cost effective.     

大麻药中两个新异戊烯基黄酮的高速逆流色谱分离制备

应用高速逆流色谱分离制备大麻药的化学成分,以石油醚∶乙酸乙酯∶乙醇∶水(1∶1.2∶1.2∶1,V/V)为两相溶剂系统,上相为固定相,下相为流动相,流速2.0 mL/min,主机转速800 r/min,分离温度30℃,检测波长280 nm。以此分离条件经一步洗脱从400 mg大麻药粗提物中制备得到95.3 mg和84.5 mg的两个单体化合物,经理化反应和光谱分析分别鉴定为(2S)-5,2′,6′-三羟基-8-异戊烯基-6,7-(3-异戊烯基-2,2-二甲基-1-酮-环己二烯)-二氢黄酮(1)和(2S)-5,2′,6′-三羟基-8-异戊烯基-6,7-(3-异戊烯基-2,2-二甲基吡喃)-3′,4′-(2,2-二甲基-1-酮-环己二烯)-二氢黄酮(2)。所得的化合物1和2均为新化合物。     

Common values of a class of linear recurrences

Let $\left(a_n\right),\left(b_n\right)$ be linear recursive sequences of integers with characteristic polynomials $A\left(X\right),B\left(X\right)\in \mathbb{Z}\left[X\right]$ respectively. Assume that $A\left(X\right)$ has a dominating and simple real root $\alpha$, while $B\left(X\right)$ has a pair of conjugate complex dominating and simple roots $\beta ,\stackrel{?}{\beta }$. Assume further that $\alpha ,\beta ,\alpha /\beta$ and $\stackrel{?}{\beta }/\beta$ are not roots of unity and $\delta =log\left|\beta \right|/log\left|\alpha \right|\in \mathbb{Q}$. Then there are effectively computable constants $c_0,c_1>0$ such that the inequality $|a_n?b_m|>{\left|a_n\right|}^{1?\left(c_0{log}^{2}n\right)/n}$holds for all $n,m\in {\mathbb{Z}}_{\ge 0}^2$ with $max\{n,m\}>c_1$. We present $c_0$ explicitly.