Some properties of the riesz charge associated with a δ-subharmonic function

The first property is a refinement of earlier results of Ch. de la Vallée Poussin, M. Brelot, and A. F. Grishin. Let w=u–v with u, v superharmonic on a suitable harmonic space (for example an open subset of R ⁿ ), and let [w]=[u]–[v] denote the associated Riesz charge. If w0, and if E denotes the set of those points of at which the lim inf of w in thefine topology is 0, then the restriction of [w] to E is 0. Another property states that, if e denotes a polar subset of such that the fine lim inf of |w| at each point of e is finite, then the restriction of [w] to e is 0.     

Chern forms,chern numbers and curvature conditions on a Kähler-Einstein surface

In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL ²-norm of (3C ₂ ?C ₁ ² )/C ₁ ² is sufficiently small, whereC ₁ andC ₂ are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C ₂ ?C ₁ ² = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature.     

Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

Fractionation and purification of antioxidant peptides from Chinese sturgeon (Acipenser sinensis) protein hydrolysates prepared using papain and alcalase 2.4L

Protein hydrolysates have the potential to be natural and safer sources of bioactive peptides. In this study, two proteases were used to hydrolyze Chinese sturgeon (Acipenser sinensis) protein, and the hydrolysates were then purified to yield antioxidant peptides. The degree of hydrolysis of 23.56 % and 18.14 % was obtained using papain and alcalase 2.4L, respectivly, and hydrolysates had 96.80 % and 87.24 % total amino acid content, respectivly. The papain hydrolysate (PH) and alcalase 2.4L hydrolysate (AH) showed good antioxidant activity against DPPH^? (IC₅₀ of 3.64 and 3.15 mg/mL) and ABTS^?+ (IC₅₀ of 1.92 and 1.58 mg/mL), respectively. The low-molecular-weight (<1000 Da) fraction of both hydrolysates demonstrated the highest antiradical activity (IC₅₀ of 2.59 and 2.31 mg/mL, DPPH) and (IC₅₀ of 1.54 and 1.36 mg/mL, ABTS), respectively. Nine peptides were separated from both hydrolysates using reverse phase high performance liquid chromatography (RP-HPLC). The IC₅₀ for ABTS^?+ scavenging activity of peptide P5 with valine, glycine and asparagine (MW of 282.13 Da) from PH, and peptide P3 with histidine, glycine and alanine (MW of 302.74 Da) from AH was 0.89 and 0.72 mg/mL, respectively. The fractions and purified peptides obtained from Chinese sturgeon hydrolysates could be utilized as natural antioxidant substitutes in pharmaceuticals and food products.     

Retaining and recovering enzyme activity during degradation of TCE by methanotrophs

To determine if compounds added during trichloroethylene (TCE) degradation could reduce the loss of enzyme activity or increase enzyme recovery, different compounds serving as energy and carbon sources, pH buffers, or free radical scavengers were tested. Formate and formic acid (reducing power and a carbon source), as well as ascorbic acid and citric acid (free radical scavengers) were added during TCE degradation at a concentration of 2 mM. A saturated solution of calcium carbonate was also tested to address pH concerns. In the presence of formate and methane, only calcium carbonate and formic acid had a beneficial effect on enzyme recovery. The calcium carbonate and formic acid both reduced the loss of enzyme activity and resulted in the highest levels of enzyme activity after recovery.     

Conditional solubility versus pO2− of cerium(III) oxide in molten equimolar NaCl+KCl at 727°C

Reactions between cerium trichloride and oxide ions were studied in NaCl+KCl (1/1) at 1000°K, by potentiometry with a calcia-stabilized zirconia membrane electrode. Titration curves clearly demonstrated the existence of soluble cerium oxychloride (CeO⁺) and precipitated cerium oxide (Ce₂O₃), with respective dissociation constants 10^?11 and 10^?30 (molality scale). The corresponding conditional solubility diagram {log S (Ce^III)=f(pO^2?)} is presented and discussed.     

Alkylidinphosphane und -arsane. I [P ≡ C?S]−[Li(dme)3]+ – Synthese und Struktur

Alkylidynephosphanes and -arsanes. I [P ≡ C? S]^?[Li(dme)₃]⁺ – Synthesis and Structure O,O′-Diethyl thiocarbonate and bis(tetrahydrofuran)-lithium bis(trimethylsilyl)phosphanide dissolved in 1,2-dimethoxyethane, react below 0°C to give ethoxy trimethylsilane and tris(1,2-dimethoxyethane-O,O′)lithium 2λ³-phosphaethynylsulfanide – [P≡C? S]^? [Li(dme)₃]⁺ – ( 1a ). Apart from bis(trimethylsilyl)sulfane or carbon oxide sulfide, dark red concentrated solutions of λ³-phosphaalkyne 1 are also obtained from reactions of carbon disulfide with bis(tetrahydrofuran)-lithium bis(trimethylsilyl)phosphanide or with the homologous lithoxy-methylidynephosphane ( 2 ) [1]. The ir spectrum shows two absorptions at 1762 and 747 cm^?1 characteristic for the P≡C and C? S stretching vibrations. The nmr parameters {δ(³¹P) ? 121.3; δ(¹³C) 190.8 ppm; ¹J_CP 18.2 Hz} resemble much more values of diorganylamino-2λ³-phosphaalkynes than those of bis(1,2-dimethoxyethane-O,O′)lithoxy-methylidyne-phosphane ( 2a ). As found by an X-ray structure analysis (P2₁/c; a = 1192.6(16); b = 1239.1(19); c = 1414.8(26) pm; β = 105.91(13)° at ?100 ± 3°C; Z = 4 formula units; wR = 0.064) of pale yellow crystals (mp. + 16°C) isolated from the reaction with O,O′-diethyl thiocarbonate, the solid is built up of separate [P≡C? S]^? and [Li(dme)₃]⁺ ions. Typical bond lengths and angles are: P≡C 155.5(11); C? S 162.0(11); Li? O 206.4(17) to 220.3(20) pm; P≡C? S 178.9(7)°.     

Convergence of multistep methods for Volterra functional differential equations

Summary This paper deals with the convergence of nonstationary quasilinear multistep methods with varying step, used for the numerical integration of Volterra functional differential equations. A Perron type condition (appearing in the differential equations theory) is imposed on the increment function. This gives a generalization of some results of Tavernini ([19–21]).     

On bounds for the range of ordered variates II

Letx ₁, ,x _n be real numbers with ₁ ⁿ x _j =0, |x ₁ ||x ₂ ||x _n |, and ₁ ⁿ f(|x _i |)=A>0, wheref is a continuous, strictly increasing function on [0, ) withf(0)=0. Using a generalized Chebycheff inequality (or directly) it is easy to see that an upper bound for |x _m | isf ^–1 (A/(n–m+1)). If (n–m+1) is even, this bound is best possible, but not otherwise. Best upper bounds are obtained in case (n–m+1) is odd provided either (i)f is strictly convex on [0, ), or (ii)f is strictly concave on [0, ). Explicit best bounds are given as examples of (i) and (ii), namely the casesf(x)=x ^p forp>1 and 0<p<1 respectively.