Poor rich demarcation of Matthew effect on scale-free systems and its application

In a scale-free network,only a minority of nodes are connected very often,while the majority of nodes are connected rarely. However,what is the ratio of minority nodes to majority nodes resulting from the Matthew effect In this paper,based on a simple preferential random model,the poor-rich demarcation points are found to vary in a limited range,and form a poor-rich demarcation interval that approximates to k/m ∈ [3,4]. As a result,the (cumulative) degree distribution of a scale-free network can be divided into three intervals: the poor interval,the demarcation interval and the rich interval. The inequality of the degree distribution in each interval is measured. Finally,the Matthew effect is applied to the ABC analysis of project management.     

Regularity Properties of Perturbed Hille—Yosida Operators and Retarded Differential Equations

In this work we give sufficient conditions on the semigroup (T ₀ (t)) _t\geq0 , generated by the part of a Hille—Yosida operator in the closure of its domain, in order that certain perturbations preserve some regularity properties of (T ₀ (t)) _t\geq0 , like the norm continuity, compactness and differentiability. An application of our abstract results to retarded differential equations is given. May 22, 2000     

Antibacterial and antioxidant properties of mixed linkage beta-oligosaccharides from extracted β-glucan hydrolysed by Penicillium occitanis EGL lichenase

The aim of this study was first to ascertain the chemical composition and the physicochemical properties of cereal extracted β-glucan from barley flour. Secondly, to assess the antioxidant properties and the antibacterial properties of extracted β-glucan hydrolysates. The proximate composition, FT-IR and scanning electron microscopy of extracted β-Glucan were studied. Hydrolysates from extracted β-glucan, obtained by lichenase EG_L from Penicillium occitanis, were a mixed linkage beta-oligosaccharides (MLBO) of trisaccharides and tetrasaccharides. MLBO showed a DPPH radical scavenger with IC50 about 1.8 ± 0.01 mg/mL whereas the IC50 of extracted β-glucan was about 5 ± 0.01 mg/mL. MLBO showed a high antioxidative capacity (175 μmol/mL α-tocopherol equivalents) at 5 mg/mL. The antimicrobial activity was confirmed against all tested bacteria especially at 20 mg/mL of MLBO while no inhibition was observed for all the strains used after the addition of either EG_L or extracted β-glucan.     

Copper(II) complexation with 1-methyl-2-mercaptoimidazole in 7 M HCl

The complexation of copper(II) with 1-methyl-2-mercaptoimidazole in 7 M HCl was potentiometrically studied. The compositions of complexes were determined, and their stepwise formation constants were calculated. The complexes were shown to become less stable with increasing temperature. The thermodynamic functions of complexation were estimated. The copper complexes were shown to surpass the rhenium complexes in stability.     

A Simple Post-Polymerization Modification Method for Controlling Side-Chain Information in Digital Polymers

A three-step post-polymerization modification method was developed for the design of digitally encoded poly(phosphodiester)s with controllable side groups. Sequence-defined precursors were synthesized, either manually on polystyrene resins or automatically on controlled pore glass supports, using two phosphoramidite monomers containing either terminal alkynes or triisopropylsilyl (TIPS) protected alkyne side groups. Afterwards, these polymers were modified by stepwise copper-catalyzed azide–alkyne cycloaddition (CuAAC). The terminal alkynes were first reacted with a model azide compound, and after removal of the TIPS groups, the remaining alkynes were reacted with another organic azide. This simple method allows for quantitative side-chain modification, thus opening up interesting avenues for the preparation of a wide variety of digital polymers.     

Complex impedance spectroscopy studies of (La0.70−xNdx)Sr0.30Mn0.70Cr0.30O3 (x≤0.30) perovskite compounds

The transport properties of Nd-doped perovskite materials (La_0.7−xNd_x)Sr_0.3Mn_0.7Cr_0.3O₃ (x≤0.30) were investigated using impedance spectroscopy techniques over a wide range of temperatures and frequencies. AC conductance analyses indicate that the conduction mechanism is strongly dependent on temperature and frequency. The DC conductance plots can be described using the small polaron hopping (SPH) model, with an apparent reduction of the polaron activation energy below the Curie temperature T_C. Complex impedance plots exhibit semicircular arcs described by an electrical equivalent circuit. Off-centered semicircular impedance plots show that the Nd-doped compounds obey to a non-Debye relaxation process. The conductivity of grains and grain-boundaries has been estimated. The activation energies calculated from the conductance and from time relaxation analyses are comparable. This indicates that the same type of charge carriers is responsible for both the electrical conduction and relaxation phenomena.     

Polynomial and exponential stability for one-dimensional problem in thermoelastic diffusion theory

We consider one-dimensional problem for the thermoelastic diffusion theory and we obtain polynomial decay estimates. Then we show that the solution decays exponentially to zero as time goes to infinity; that is, denoting by E(t) the first-order energy of the system, we show that positive constants C ₀ and c ₀ exist which satisfy E(t) ≤ C ₀ E(0)e ^{?c ₀ t} .     

A weighted Hardy inequality and nonexistence of positive solutions

In this article, we prove that the following weighted Hardy inequality $$\begin{array}{ll}\big(\frac{|{d-p}|}{p}\big)^{p}\, \int\limits_{\Omega}\, \frac{|{u}|^{p}}{|{x}|^{p}}\;d\mu \\ \quad \quad \le \int\limits_{\Omega}\,|{\nabla u}|^{p}\;d\mu+ \big(\frac{|{d-p}|}{p}\big)^{p-1}\,\textrm{sgn}(d-p)\,\int\limits_{\Omega}|{u}|^{p}\,\frac{(x^{t}Ax)^{p/2}}{|{x}|^{p}}\; d\mu \quad \quad \quad (1) \end{array}$$ holds with optimal Hardy constant ${\big(\frac{|d-p|}{p}\big)^{p}}$ for all ${u \in W^{1,p}_{\mu,0}(\Omega)}$ if the dimension d ≥ 2, 1 < p < d, and for all ${u \in W^{1,p}_{\mu,0}(\Omega{\setminus}\{0\})}$ if p > d ≥ 1. Here we assume that Ω is an open subset of ${\mathbb{R}^{d}}$ with ${0 \in \Omega}$ , A is a real d × d-symmetric positive definite matrix, c > 0, and $$ d \mu: = \rho(x) \,dx \qquad \textrm{with} \quad \rho(x) = c \cdot \exp(-\frac{1}{p}(x^{t}Ax)^{p/2}), \quad x \in\Omega.\quad \quad (2) $$ If p > d ≥ 1, then we can deduce from (1) a weighted Poincaré inequality on ${W^{1,p}_{\mu,0}(\Omega \setminus\{0\})}$ . Due to the optimality of the Hardy constant in (1), we can establish the nonexistence (locally in time) of positive weak solutions of a p-Kolmogorov parabolic equation perturbed by a singular potential in dimension d = 1, for 1 < p <  + ∞, and when Ω =  ]0, + ∞[.