巧用梯形中位线证线段a=b+c一例

例(2010江苏省徐州市)如图1,将边长为4cm的正方形纸片ABCD沿EF折叠(点E、F分别在边AB、CD上),使点B落在AD边上的点M处,点C落在点N处,MN与     

这道题可以推广

一、原题《中学生数学》2011(3)·P9《由角平分线的性质想到的辅助线》中例题:如图1,△ABC中,∠ABC=100°.∠ACB的平分线交AB于E,在AC上取点D,使∠CBD=20°,连接DE,求∠CED的度数.二、推广如图2,△ABC中,∠ACB的平分线交AB     

Bounding the sum of powers of the Laplacian eigenvalues of graphs

For a non-zero real number α, let s _α (G) denote the sum of the αth power of the non-zero Laplacian eigenvalues of a graph G. In this paper, we establish a connection between s _α (G) and the first Zagreb index in which the Hölder’s inequality plays a key role. By using this result, we present a lot of bounds of s _α (G) for a connected (molecular) graph G in terms of its number of vertices (atoms) and edges (bonds). We also present other two bounds for s _α (G) in terms of connectivity and chromatic number respectively, which generalize those results of Zhou and Trinajsti? for the Kirchhoff index [B Zhou, N Trinajsti?. A note on Kirchhoff index, Chem. Phys. Lett., 2008, 455: 120–123].     

Geometric realization of Adams maps

Let G/P be a homogenous space with G a compact connected Lie group and P a connected subgroup of G of equal rank. As the rational cohomology ring of G/P is concentrated in even dimensions, for an integer k we can define the Adams map of type k to be l _k : H*(G/P, ℚ) → H*(G/P, ℚ), l _k (u) = k ⁱ u, u ∈ H ²ⁱ (G/P, ℚ). We show that if k is prime to the order of the Weyl group of G, then l _k can be induced by a self map of G/P. We also obtain results which imply the condition that k is prime to the order of the Weyl group of G is necessary.     

Some sufficient conditions for tunnel numbers of connected sum of two knots not to go down

In this paper, we show the following result: Let K _i be a knot in a closed orientable 3-manifold M _i such that (M _i ,K _i ) is not homeomorphic to (S ₂ ×S ₁, x ₀ ×S ₁), i = 1, 2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(K _i ) is less than the difference of one and twice of the tunnel number of K _i . Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive.     

The Fractional Derivatives of a Fractal Function

The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Weierstrass function.     

Vertical and Smooth, etching of InP by Cl2／CH4／Ar Inductively Coupled Plasma at Room Temperature

We study the room-temperature dry, etching of InP by inductively coupled plasma (ICP) using C12/CH4/Ar mixtures. Etches were characterized in terms of anisotropy and surface roughness by scanning electron microscopy and atomic force microscopy, respectively. It is found that the flow ratio between C12 and Ctt4, ICP power, rf chuck power, and table temperature can greatly influence the, etching results. By adjusting, etching parameters,vertical sidewall and smooth surface can be obtained simultaneously, together with a moderate, etch rate and a good select ratio. The root-mean-square surface roughness is measured to be as low as 0.27nm. To the best of our knowledge, this is the best result for InP to date. The, etch rate is 855nm/min, and the selectivity ratio overSi02 is estimated to be higher than 15:1. The stoichiometry of the, etched surface has also been investigated by Auger electron spectroscopy. The, etched surface is found to manifest a slight P deficiency, and the ratio between P and In reaches the stoichiometric value within about 0.75nm depth into the surface.     

单一元件交流电路相位差的定性分析

电容、电感、电阻是三个基本电路元件．它们各自和正弦交流电源连接，分别构成纯电容、纯电感、纯电阻交流电路．它们都是理想的电路模型．纯电容电路中电压uc滞后电流icπ/2，纯电感电路中电压uL超前电流iLπ/2，     

一种标记物中的蛋白质测定

随着生物医学研究的迅速发展，在其相应的研究领域中也出现了许多新技术，蛋白质连接技术即是其一。本实验以自行合成时间分辨荧光免疫分析[TRFIA]双功能螯合剂4，7-二氯磺酰基苯基-1，10-菲绕啰啉-2，9-二羧酸（BCPDA）进行蛋白质连接技术研究，发现BCPDA在280nm处有比蛋白质更强的吸收，严重干扰了蛋白质测定。结合BCPDA标记牛血清白蛋白（BSA）实验，采用考马斯亮蓝染色建立了测定蛋白质方法。