Experimental and density functional studies on two structurally similar antipyrine derivatives: 4-(2-hydroxy-5-nitrobenzylidene-amino)-1,2-dihydro-1,5-dimethyl-2-phenylpyrazol-3-one and 4-(3-bromo-5-chloro-2-hydroxybenzylideneamino)-1,2-dihydro-1,5-dimethyl-2-phenylpyrazol-3-one

The Schiff base compounds, 4-(2-hydroxy-5-nitr- obenzylideneamino)-1,2-dihydro-1,5-dimethyl-2-phenylpy- razol-3-one and 4-(3-bromo-5-chloro-2-hydroxybenz- ylideneamino)-1,2-dihydro-1,5-dimethyl-2-phenylpyrazol-3-one, have been synthesized and characterized by elemental analysis, IR, and X-ray single crystal determination. Density functional calculations of the structures, natural bond orbitals, and frontier molecular orbitals and Mülliken charge analysis on the compounds were performed at B3LYP/6-31+G(d) level of theory. Vibrational frequencies were also predicted, assigned, and compared with the experimental values, which supported each other.     

Die Perthioborate RbBS3, TIBS3 und TI3B3S10

The Perthioborates RbBS₃, TIBS₃, and Tl₃B₃S₁₀ . RbBS₃ (P2₁/c, a=7.082(2) Å, b=11.863(4) Å, c=5.794(2) Å, β=106.54(2)°) was prepared as colourless, plate-shaped crystals by reaction of stoichiometric amounts of rubidium sulfide, boron, and sulfur at 600°C and subsequent annealing. TlBS₃ (P2₁/c, a=6.874(3) Å, b=11.739(3) Å, c=5.775(2) Å, β=113.08(2)°) which is isotypic with RbBS₃ was synthesized from a sample of the composition Tl₂S · 2 B₂S₃. The glassy product which was obtained after 7 h at 850°C was annealed in a two zone furnace for 400 h at 400→350°C. Yellow crystals of TlBS₃ formed at the warmer side of the furnace. Tl₃B₃S₁₀ (P1 , a=6.828(2) Å, b=7.713(2) Å, c=13.769(5) Å, α=104.32(2)°, β=94.03(3)°, γ=94.69(2)°) was prepared as yellow plates from stoichiometric amounts of thallium sulfide, boron, and sulfur at 850°C and subsequent annealing. All compounds contain tetrahedrally coordinated boron. The crystal structures consist of polymeric anion chains. In the case of RbBS₃ and TlBS₃ nonplanar five-membered B₂S₃ rings are spirocyclically connected via the boron atoms. To obtain the anionic structure of Tl₃B₃S₁₀ every third B₂S₃ ring of the polymeric chains of MBS₃ is to be substituted by a six-membered B(S₂)₂B ring.     

Every large set of equidistant (0, +1, −1)-vectors forms a sunflower

A theorem of Deza asserts that ifH ₁, ...,H _m ares-sets any pair of which intersects in exactlyd elements and ifm ≧s ² −s+2, then theH _i form aΔ-system, i.e. . In other words, every large equidistant (0, 1)-code of constant weight is trivial. We give a (0, +1, −1) analogue of this theorem.     

基于遗传算法的PTP1B抑制剂的二维定量构效关系研究

利用遗传算法,并结合线性回归和交叉验证方法,对一系列43个苯并呋喃/噻吩联二苯类PTP1B抑制剂作了二维定量构效关系的研究.计算得到了一组效果较好的定量构效关系模型.模型不仅具有好的回归能力,而且还具有很好的预测能力.同时,通过分析在遗传优化过程中参数在精华种群中所占的比例,还得到了可能对活性影响较大的成分.计算结果表明,分子的4个参数:lgP(分配系数)、Area（表面积）、MW（分子量）以及Dip（偶极距）是影响化合物活性的最重要的参数,这对抑制剂的设计和改造提供了指导.     

Affine Ebenen und Tupelsysteme

Zusammenfassung Es werden zwei neue Koordinatisierungsmethoden für affine Ebenen gegeben, und zwar durch homogene bzw. stark balancierte Tupelsysteme. Ihre Brauchbarkeit wird u.a. demonstriert an einer Charakterisierung der Kollineationsgruppen einer affinen Ebene mit der Eigenschaft (R) Für alle i l enthält der Stabilisator von i nur Perspektivitäten mit Zentrum i. Außerdem wird der Satz bewiesen: Für eine Elation der geraden Ordnung d in einer projektiven Ebene der Ordnung v gilt 2d|v. Dieses Resultat impliziert schon bekannte Ergebnisse von Hughes (d=2) und Hall.

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We give two new coordinatization methods for affine planes by means of homogeneous (resp. strong balanced) tuple systems. Their usefulness is demonstrated by proving a characterization of collineation groups of an affine plane with the property (R): The stabilizer of every i l contains only perspectivities with centre i. Besides, we prove: If a projective plane of order v contains an elation of even order d then 2d|v. This implies known results of Hughes (d=2) and Hall.

     

Matrix summability and a generalized Gibbs phenomenon

Letf be a real-valued function sequence {f _k } that converges to on a deleted neighborhoodD of . If there is a subsequence {f _k(j) } and a number sequencex such that lim _j x _j = and either lim _j f _k(j) (x _j )>lim sup _x (x) or lim _j f _k(j) (x _j ) x (x), thenf is said to display theGibbs phenomenon at . IfA is a (real) summability matrix, thenAf is a function sequence given by(Af) _n (x)= _k=0 a _n,k f _k (x). IfAf displays the Gibbs phenomenon wheneverf does, thenA is said to beGP-preserving. By replacingf _k (x) withf _k (x _j )F _k,j , the Gibbs phenomenon is viewed as a property of the matrixF, andGP-preserving matrices are determined by properties of the matrix productAF. The general results give explicit conditions on the entries {a _n,k } that are necessary and/or sufficient forA to beGP-preserving. For example: if(x)0 thenF displaysGP iff lim _k,j F _k,j 0, and ifA isGP-preserving then lim _n,k A _n,k 0. IfA is a triangular matrix that is stronger than convergence, thenA is notGP-preserving. The general results are used to study the preservation of the Gibbs phenomenon by matrix methods of Nörlund, Hausdorff, and others.     

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.     

Investigations of the local distortions and EPR parameters for Cu2+ in xNa2O‐(30–x)K2O‐70B2O3 (5 ≤ x ≤ 25 mol%) glasses

The local distortions and electron paramagnetic resonance parameters for Cu²⁺ in the mixed alkali borate glasses xNa₂O‐(30–x)K₂O‐70B₂O₃ (5 ≤ x ≤ 25 mol%) are theoretically studied with distinct modifier Na₂O compositions x. Owing to the Jahn–Teller effect, the octahedral [CuO₆]¹⁰⁻ clusters show significant tetragonal elongation ratios p ~19% along the C₄ axis. With the increase of composition x, the cubic field parameter Dq and the orbital reduction factor k exhibit linearly and quasi‐linearly decreasing tendencies, respectively, whereas the relative tetragonal elongation ratio p has quasi‐linearly increasing rule with some fluctuations, leading to the minima of g factors at x = 10 mol%. The composition dependences of the optical spectra and the electron paramagnetic resonance parameters are suitably reproduced by the linear or quasi‐linear relationships of the relevant quantities (i.e., Dq, k, and p) with x. The above composition dependences are analyzed from mixed alkali effect, which brings forward the modifications of the local crystal‐fields and the electronic cloud distribution around Cu²⁺ with the variation of the composition of Na₂O.     

血清瘦素水平在评估慢性病毒性肝炎肝纤维化程度中的意义

目的探讨血清瘦素(LEP)水平与慢性乙肝（CHB）和慢性丙肝（CHC）患者肝纤维化程度之间的关系。方法采用ELISA方法检测65例CHB、41例CHC患者血清LEP浓度，同期25例健康体检者作为对照。所有入选患者均经肝脏穿刺病理学检查评估肝纤维化程度。结果与对照组相比，CHB与CHC患者LEP水平明显增高（P＜0.05或0.01），CHB和CHC患者血清LEP水平在纤维化程度较高者均明显高于纤维化程度较低者（均P＜0.01），且CHC组血清LEP水平显著高于相同纤维化分期CHB患者（P＜0.05或0.01）。结论血清LEP水平与慢性病毒性肝炎肝纤维化程度相关，血清LEP水平可作为慢性病毒性肝炎患者肝纤维化程度监测指标之一。     

Convexifactors,generalized convexity and vector optimization

In this article we study a recently introduced notion of non-smooth analysis, namely convexifactors. We study some properties of the convexifactors and introduce two new chain rules. A new notion of non-smooth pseudoconvex function is introduced and its properties are studied in terms of convexifactors. We also present some optimality conditions for vector minimization in terms of convexifactors.