Longest Paths and Cycles in Connected Claw-Free Graphs

A graph is called claw-free if it does not contain a claw as its induced subgraph. In this paper, we prove the following results : 1 ) If G is a 2-connected claw-free graph on n vertices, then for any vertex υ and any two distinct vertices x and y in V(G) - |υ| , G has a path containing v and all neighbors of v and connecting x and y;2) Let C be the longest cycle in a 3-connected claw-free graph G and H a component of G - C,and if H is connected but not 2-connected, then there exist nonadjacent vertices u and v in H such that |V(C)| ≥3(d(u) d(u)) -2.     

《新标准英语》第三册 Module 4 Unit 1

教学片段一：热身,激趣 1. Greeting： songs and chants 2. Warming-up ： Number game： （ 1 ）Count 1-12,then 12- 1;（2）看卡片说数字（First say the numbers,the nadd the numbers）     

《牛津小学英语》5B Unit 4 An English friend Part A

教学过程Step 1.Free talk(略)Step 2.Presentation and drill 1.Before listening Activity 1 T:Now,boys and girls,do you know my hobbies? Look at this picture,and then guess.S 1:You like playing games.     

Complex oscillation of certain high non-homogeneous linear differential equations

1 Introduction and main results a Im this paper, we use the standard notations of the Nevanlinna theory (see Refs. [1-3]); and denote the order of growth of f ( z ) by σ ( f), the exponent of convergence of the zero-sequence and the sequence of distinct zeroes of f ( z ) by λ ( f) and λ ( f), respectively. It recalls the following definitions. Definition 1 [5]. Let f ( z )be a meromorphic function, then the hyper-order σ 2( f)of f ( z ) is defined by _____ 2 σ ( f ) = lr i→m∞ loglologg…     

Separation of acearylenes from high-temperature coal tar

High-temperature coal tar was extracted with petroleum ether(PE) under ultrasonic irradiation and the extracts were analyzed with gas chromatograph/mass spectrometer.The acearylene fractions including acenaphthylene,aceanthrylene and cyclopentapyrene were enriched together and named E,which was then transferred to a cartridge in Isolera-One flash chromatography.Three groups of compounds were eluted out with ethyl acetate/PE mixed solvent(volume ratio 1:9) and named E 1,E 2 and E 3 according to their main components.Acenaphthylene accounted for 78.2% in E 1,aceanthrylene 71.6% in E 2 and cyclopentapyrene 75.9% in E 3,respectively.The three groups of acearylenes were purified by Sephadex LH-20 column chromatography with ethanol/cyclohexane mixed solvent(volume ratio 1:4),and then confirmed with nuclear magnetic resonance spectrometer.This method indicates that flash chromatography has a good effect on separating the compounds with a similar structure after extraction under ultrasonic irradiation.     

魔力英语题(Ⅺ)

蓄丫州梦曰卜卜召‘‘‘山曰-一一..，.一-一‘口矛。轰砚东”，石.冠叠一、听录音，把诗歌填写完整。(江苏施燕) FiveLittle Turke珍Five Iitt{e turkeyss怕nding One waddledo俨，and then there Were four. Four littleturkeys Onewadd{edoff，and then there We泊three. Three little tu水eys With. One wadd泊d浦，and then there were two一下四。1 ithe turkeys One waddledoff，and then there was one. One little turkey一——’For soon wil，eomeT行anksgiving Da丫嚓l口…k姗曲11 dleo仔(如鸭子般)摇摇晃晃地走开二、…     

Antitumor effects of human interferon-alpha 2b secreted by recombinant bacillus Calmette-Guérin vaccine on bladder cancer cells

Objective:Our objective was to construct a recombinant bacillus Calmette-Guérin vaccine(rBCG) that secretes human interferon-alpha 2b(IFNα-2b) and to study its immunogenicity and in vitro antitumor activity against human bladder cancer cell lines T24 and T5637.Methods:The signal sequence BCG Ag85B and the gene IFNα-2b were amplified from the genome of BCG and human peripheral blood,respectively,by polymerase chain reaction(PCR).The two genes were cloned in Escherichia coli-BCG shuttle-vector pMV261 to obtain a new recombinant plasmid pMV261-Ag85B-IFNα-2b.BCG was transformed with the recombinant plasmid by electroporation and designated rBCG-IFNα-2b.Mononuclear cells were isolated from human peripheral blood(PBMCs) and stimulated with rBCG-IFNα-2b or wild type BCG for 3 d,and then cultured with human bladder cancer cell lines T24 and T5637.Their cytotoxicities were measured by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide(MTT) assay.Results:BCG was successfully transformed with the recombinant plasmid pMV261-Ag85B-IFNα-2b by electroporation and the recombinant BCG(rBCG-IFNα-2b) was capable of synthesizing and secreting cytokine IFNα-2b.PBMC proliferation was enhanced significantly by rBCG-IFNα-2b,and the cytotoxicity of PBMCs stimulated by rBCG-IFNα-2b to T24 and T5627 was significantly stronger in comparison to wild type BCG.Conclusions:A recombinant BCG,secreting human IFNα-2b(rBCG-IFNα-2b),was constructed successfully and was superior to control wild type BCG in inducing immune responses and enhancing cytotoxicity to human bladder cancer cell lines T24 and T5637.This suggests that rBCG-IFNα-2b could be a promising agent for bladder cancer patients in terms of possible reductions in both clinical dosage and side effects of BCG immunotherapy.     

幽灵男孩:逃离困住他的躯体

Lulu Miller (Host):When Martin Pistorius was a little boy growing up in South Africa,he was mostly thinking about 1)electronics. Joan Pistorius (Martin's mother):He was always going to be an electric man,as he told me,when he grew up.And the...and then... Miller:Martin's life took an unexpected turn. Rodney Pistorius (Martin's father):He had just turned 12. Miller:He 2)came down with a strange illness. Rodney:He was sleeping whenever we didn't wake him up.Eh,he was 3)permanently lying down in the 4)fetal position.     

Module 3 Unit 1 I like football

<正>一、揭题示标1.导入Greatings.T:Hello,boys and girls.S:Hello,Miss Feng.T:How are you?S:I’m fine,thank you.And you?T:I’m fine,too.Thank you.T:Now,let’s look at the pictures and then listen to the chant.2.板书课题Unit 1 I like football.3.出示学习目标。二、学习指导1.先根据图片自主感知课文Page 14-15的内容,圈出生词。(2分钟)2.然后听课文录音,借助图片、录单,自主模仿单词发音同时     

Normal families and shared values of meromorphic functions

We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods and Function Theory, 2001, 1 (1): 289-299], and generalized two new normality criterions. Let F be a family of meromorphic functions in a domain D, a a non-zero finite complex number, B a positive real number, and k and m two positive integers satisfying m>2k 4. If every function denoted by f belonging to F has only zeros with multiplicity at least k and satisfies f m(z)f (k)(z)=a??f (k)(z)?≤B or f m(z)f (k)(z)=a??f (z)?≥B, then F is normal in D.     

2003年10—11月国际外语教学研究学术会议信息

October 2003 3-5. (Europe and Eurasia) IATEFL HungaryConference October 3-5, 2003. Contact Person: EszterFalus, 1146 Budapest, Ajtosi Durer sor 19-21, Hungary.FAX: 00-36-1-460-4403. E-mail eszter.falus@iate-fl. hu. Web site http://www.iatefl.hu/. 10-12. (Europe and Eurasia) INGED-Turkey,BETA-Romania, ETAI-Israel, and TESOL-Greece. Joint     

Investigation on apoptosis of neuronal cells induced by Amyloid beta-Protein

Objective: To construct a PC12 cell strain with neuronal differentiation, and observe the apoptosis and pro-liferation activity effects induced these cells by Amyloid beta-Protein (Aβ-43). Methods: 1) PC12 cells in logarithmicgrowth phase were subcultured for 24 h. After the culture fluid was changed, the cells were treated with Rat-β-NGF andcultured for 9 days. 2) Neuronal differentiation of PC12 cells in logarithmic growth phase were divided into four groups:control group (0), experimental group (1), experimental group (2) and experimental group (3). The concentrations of Aβ inthe four groups were 0 μmol/L, 1.25 μ mol/L, 2.5 μ mol/L and 5 μmol/L, respectively. The cells were harvested at 24, 48 and72 h later and stained with AnnexinV-FITC/PI after centrifugation and washing. Then flow cytometry was conducted toexamine the apoptosis percentage. 3) NGF-induced PC12 cells were selected and Aβ with different concentrations wasadded. The final concentrations of Aβ were 0 μmol/L, 1.25 μmol/L, 2.5 μmol/L and 5 μ mol/L, respectively. After the cellswere incubated in an atmosphere of 5% CO2 at 37 ℃ in an incubator for 72 h, the OD values were examined. Results: 1)Neuronal differentiated PC 12 cell lines were successfully established. 2) Flow cytometric examination indicated that Aβ(1.25, 2.5, and 5.0 μmol/L) could effectively induce apoptosis of neuronal-differented cells at the 24 h, 48 h and 72 h timepoints. 3) Aβ (0-5.00 μ mol/L) had no obvious effect on proliferation or restraining of the neuronal differentiation of thePC 12 cells after a 72 h interacting process. Conclusion: This investigation revealed successful neuronal differentiation of thePC12 cell strain. The induction of apoptosis of the neurocytes by various concentrations of Aβ was observed and the in-fluence of Aβ on induced proliferation of PC 12 cells by Rat-β-NGF was revealed. This study -05 provide basis for futureresearch on the molecular cure of AD and interdiction of AD evolution.     

巧证一类绝对值不等式

不等式的证明,技巧性强,难度大,又是高考的重点.很多学生望而生畏,无从下笔,本文通过几例来说明一类绝对值不等式的证明.思想方法:归一法———消去几个参变量,只留下其中一个变量.【例1】已知二次函数f(x)=ax2 bx c,｜f(0)｜≤2,｜f(1)｜≤1,｜f(-1)｜≤1.求证:当x∈[-1,1]时,恒有｜f(x)｜≤178.证明:由已知,f(1)=a b c,f(-1)=a-b c,f(0)=c∴a=f(-1) f(1)-2f(0)2b=f(1)-f(-1)2,c=f(0)∴｜f(x)｜=｜f(-1) f(1)-2f(0)2x2 f(1)-f(-1)2x f(0)｜=｜f(-1)(12x2-12x) f(1)(12x2 12x) f(0)(-x2 1)｜≤｜12x2-12x｜ ｜12x2 12x｜ 2｜-x2 1｜=-2x2-x …     

Abnormal cortical functional connections in Alzheimer＇s disease： analysis of inter- and intra-hemispheric EEG coherence

To investigate inter- and intra-hemispheric electroencephalography (EEG) coherence at rest and during photic stimulation of patients with Alzheimer‘s disease (AD). Thirty-five patients (12 males, 23 females; 52-64 y) and 33 sex- and age-matched controls (12 males, 21 females; 56-65 y) were recruited in the present study. EEG signals from C3-C4, P3-P4, TS-T6 and O1-O2 electrode pairs resulted from the inter-hemispheric action, and EEG signals from C3-P3, C4-P4, P3-O1, P4-O2, C3-O1, C4-O2, TS-O1 and T6-O2 electrode pairs resulted from the intra-hemispheric action. The influence of inter- and intra-hemispheric coherence on EEG activity with eyes closed was examined, using fast Fourier transformation from the 16 sampled channels. The frequencies of photic stimulation were fixed at 5, l0 and 15 Hz, respectively. The general decrease of AD patients in inter- and intra-hemispheric EEG coherence was more significant than that of the normal controls at the resting EEG, with most striking decrease observed in the alpha-1 (8.0-9.0 Hz) and alpha-2 (9.5-12.5 Hz) bands. During photic stimulation, inter- and intra-hemispheric EEG coherences of the AD patients having lower values in the alpha (9.5-10.5 Hz) band than those of the control group. It suggests that under stimulated and non-stimulated conditions, AD patients had impaired inter- and intra-hemispheric functional connections, indicating failure of brain activation in alpha-related frequency.     

Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative

~~4[0,1]Csatisfyingand()hr ?*umu'k(mh r)and*uisanonnegativeconcavefunction.Moreover,ifoneofthefollowingconditionsissatisfied:(1)A B>0;(2)C D<0;(3)f(t,0,0)0,0t1,then*u(t)>0,00suchthatmax{():01,0,80}64,rrr?#ft,u,vtuvthentheproblem(P)hasatleastonesolutionu*C4[0,1]satisfying*urand()*"u8randu*isanonnegativeconcavefunction.Moreover,iff(t,0,0)0,0t1,thenu*(t)>0,0相似文献   

Meromorphic functions sharing one value by weight

The uniqueness of meromorphic fuctions sharing one value was studied. Using the concept of weighted sharing, we proved the following theorem. For two meromorphic functions f and g which are not polynominals of degree less than a positive integer k, if f nf (k) and g ng (k) share (1,2), where n is another positive integer not less than k 10, then f nf (k) identically equals g ng (k) or f nf (k)g ng (k) identically equals 1. Particularly for k =1, we improved the results of Yang [Yang CC, Hua XH, Uniqueness and value-sharing of meromorphic functions, Annales Academi? Scientiarum Fennic? Mathematica, 1997, 22: 395-406], and Fang [Fang ML, Hua XH, Entire function that share one value, Journal of Nanjing University, 1996, 13(1): 44-48. (In Chinese)].     

Two-parameters quasi-filled function algorithm for nonlinear integer programming

INTRODUCTION Considering the following nonlinear integer programming problem: (PI) min f(x), s.t. x∈XI, (1) where XI?In is a bounded and closed box set con- taining more than one point, In is the set of integer points in n . If we suppose that f(x) satisfies the following conditions: if x∈XI, then f(x)=f(x), otherwise f(x)= ∞, then Problem PI is equal to the following nonlinear integer programming problem (UPI) min f(x), s.t. x∈In. (2) The formulation in PI allows the set XI t…     

一类代数式求值问题的巧妙解法

前不久在教学中碰到这样一道习题:已知x1、x2是方程x2 x-1=0的两个根,求代数式(x12 2x1-1)·(x22 2x2-1)的值.班上大多数学生都是采用以下方法进行的: 原式:(x1x2)2 2x12x2-x12 2x1x22 4x1x2-2x1-x22-2x2 1=(x1x2)2 2x1x2(x1 x2)-(x1 x2)2 6x1x2-2(x1 x2) 1.     

And连接的英语习语

在英语中,有许多介词、名词或时间/地点副词等由"and"连接而形成英语习语,你知道它们的意思吗?请看: 1.now and then: 不时 2.first and last: 总的说来     

2002年全国高中数学联赛试题另解选讲

与往年相比 ,2 0 0 2年全国高中数学联赛试题总体难度有所降低 .一试更加接近高考 ,加试题也容易入手 .下面是笔者提供的异于命题组标准答案的部分题目的解答 ,仅供参考 .第一试一、选择题第 2题　若实数 x、y满足 (x + 5 ) 2 + (y-12 ) 2 =14 2 ,则 x2 + y2的最小值为 (B)(A) 2 .　 (B) 1.　 (C) 3 .　 (D) 2 .另解 1:记 x2 + y2 =M 1(x + 5 ) 2 + (y -12 ) 2 =14 2 22 -1得 :2 (5 x -12 y) + 13 2 =14 2 -M即 5 x -12 y + M -2 72 =0 3圆心 (-5 ,12 )到公共弦方程 3的距离为d =| -5 2 -12 2 + M -2 72 |5 2 + (-12 ) 2 ≤ 14解得 1≤ …