Kolmogorov complexity and computably enumerable sets

We study the computably enumerable sets in terms of the:     

Cup and cap products in intersection (co)homology

We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincaré duality in intersection (co)homology which is similar in spirit to the usual proof for ordinary (co)homology of manifolds.     

Some stable homology calculations and Occam's razor for Hodge structures

Motivated by motivic zeta function calculations, Vakil and Wood in [10] made several conjectures regarding the topology of subspaces of symmetric products. The purpose of this note is to prove two of these conjectures and disprove a strengthening of one of them.     

On the Lipschitz equivalence of self‐affine sets

Recently Lipschitz equivalence of self‐similar sets on has been studied extensively in the literature. However for self‐affine sets the problem is more awkward and there are very few results. In this paper, we introduce a w‐Lipschitz equivalence by repacing the Euclidean norm with a pseudo‐norm w. Under the open set condition, we prove that any two totally disconnected integral self‐affine sets with a common matrix are w‐Lipschitz equivalent if and only if their digit sets have equal cardinality. The main methods used are the technique of pseudo‐norm and Gromov hyperbolic graph theory on iterated function systems.     

Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.     

The survival probability of critical and subcritical branching processes in finite state space Markovian environment

Let ${\left(Z_n\right)}_{n\ge 0}$ be a branching process in a random environment defined by a Markov chain ${\left(X_n\right)}_{n\ge 0}$ with values in a finite state space $\mathbb{X}$. Let ${\mathbb{P}}_i$ be the probability law generated by the trajectories of ${\left(X_n\right)}_{n\ge 0}$ starting at $X_0=i\in \mathbb{X}.$ We study the asymptotic behaviour of the joint survival probability ${\mathbb{P}}_i\left(Z_n>0,X_n=j\right)$, $j\in \mathbb{X}$ as $n\to +\infty$ in the critical and strongly, intermediate and weakly subcritical cases.     

高龄老年男性腰椎骨密度独立相关因素的研究

目的 通过分析高龄老年（≥80岁）男性腰椎骨密度（LBMD）的独立相关因素,寻找提高高龄老年男性LBMD 的方法。方法 对1066例高龄老年男性进行LBMD测定、血液生化、骨代谢和生殖激素等指标的检测,运用多元回归分析筛选高龄老年男性LBMD 的独立相关因素。结果 高龄老年男性LBMD的独立相关因素有体重指数（β=0.018,P＜0.01）、I型胶原羧基端肽β特殊序列（β=-0.226,P＜0.01）、慢性阻塞性肺疾病（β=-0.047,P＜0.01）、雌二醇（β=0.002,P＜0.01）。结论 维持合理的体重指数和雌二醇水平,降低血清I型胶原羧基端肽β特殊序列水平,积极防治慢性阻塞性肺疾病,可能是提高高龄老年男性LBMD的重要方法。     

Physicochemical Studies on an All-Purpose Pesticide Spray Adjuvant-(APSA-80)

APSA-80, an useful pesticide spray adjuvant is a mixture of 2-[2-(4-nonylphenoxy) ethoxy] ethanol, 1-butanol and tall oil fatty acids. It is strongly surface active and can decrease the surface tension of water to ～20 mNm^?1 at its critical micelle concentration (CMC) of 0.006 g%. APSA-80 itself and its binary mixtures, (APSA-80 + water) and (APSA-80 + isopropylmyristate [IPM]) and ternary mixtures (APSA-80 + water +IPM) can undergo a number of physical changes with rise in temperature; the main changes are in color, turbidity and phases. The ternary mixtures of APSA-80/water/IPM with changing compositions can form mono-, bi-, and triphasic solutions as well as gels and viscous solutions. The gel and viscous phases show characteristic rheological properties of both shear thinning and thickening types. They also show permeation of hydrophilic and oleophilic dyes through them. SEM and optical microscopic measurements have shown interesting surface morphologies of the gels and their vertical projections in three-dimensional pictorial mode. Salts like LiCl, NaCl, KCl, CsCl, MgSO₄, and Al₂(SO₄)₃ can have both minor and major effects on the gel consistencies. The alkanols like ethanol, propanol, and isopropanol are also mild to fairly large gel influencing co solvents. The antibacterial properties of APSA-80 have been studied with two Gram positive bacteria and a yeast; the activities found were moderate.     

Design and In Vitro Evaluation of Solid-Lipid Nanoparticle Drug Delivery for Aceclofenac

Solid-lipid nanoparticles (SLNs) are an interesting nanoparticulate delivery system. The present work was carried out with the aim to develop a prolonged release solid-lipid nanoparticulate system for the drug using aceclofenac. Aceclofenac-loaded solid-lipid nanoparticles (ACSLNs) was prepared by hot high pressure homogenization technique. Tripalmitin was used as the lipid core. Surfactants (Poloxamer 188, Tween 80, and soya lecithin) and co-surfactant (sodium tauro glycholate) were used in the formulations. The prepared ACSLN formulations were characterized for encapsulation efficiency (EE), photon correlation spectroscopy (PCS), scanning electron microscopy (SEM), and x-ray diffraction (XRD). From these studies, mean particle diameter of the formulation prepared with combination of surfactants (Poloxmer 188 and Tween 80) was about 200 nm with spherical morphology and amorphous nature. Higher EE was obtained with SLNs prepared using combination of soya lecithin and poloxmer 188. The organization and distribution of the ingredients in the nanoparticulate system were studied by differential scanning calorimetry (DSC) and the results showed that the drug is incorporated into the solid matrix. The prepared formulations demonstrated favorable in vitro prolonged release characteristics. Experimental in vitro release data were substituted in available mathematical models to establish the release kinetics of ACSLNs and it was found to follow first-order kinetics and Higuchi diffusion mechanism. Our results suggest that these SLN formulations could constitute a promising approach for the drug delivery of aceclofenac.     

Catalytic solid substrate-room temperature phosphorimetry for the determination of trace As(V) based on oxidising reaction between hydrogen peroxide and fullerenol using tween-80 as sensitizer

A new catalytic solid substrate-room temperature phosphorimetry (SS-RTP) for the determination of trace arsenic(V) has been established. It is based on the fact that fullerenol (F-ol) emitted strong and stable room temperature phosphorescence (RTP) on nitric acid cellulose membrane (NCM) substrate. H₂O₂ could oxidise F-ol to cause the quenching of RTP. As(V) could catalyse H₂O₂ to oxidise F-ol and decrease the RTP signal of F-ol sharply. After adding tween-80 in the system, its ΔI _p enhanced 7.7 times compared with the without-tween-80 levels. Under the optimum conditions, the linear dynamic range of this method was 0.016?11.2 ag spot^?1 with a detection limit (LD) of 9.3 zg spot^?1 (corresponding concentration: 2.3 × 10^?17 g mL^?1). This sensitive, simple and selective method has been successfully applied to the determination of trace As(V) in human hair and tea samples. The reaction mechanism for SS-RTP is also discussed.