方程x~3-8=py~2有本原正整数解的判别条件

设p是适合p≡1(mod6)的奇素数.根据二次Diophantine方程的性质,运用初等方法给出了方程x3-8=py2有适合gcd(x,y)=1的正整数解(x,y)的新的判别条件.当p≡1或7(mod24)时,该方程无解;当p≡13(mod24)时,该方程有解(x,y)=(3r2+2,3rs),其中s是适合ps2=3r4+6r2+1的正整数;当p≡19(mod24)时,该方程有解(x,y)=(r2+2,rs),其中s是适合ps2=r4+6r2+12的正整数.     

关于指数Diophanfine方程α^x＋db^y=c^z

设a,b,c,d,l,m,n是给定的适合al+dbm=cn,gcd (a,db)=1,l＞1,m＞1,n＞1的正整数.本文中证明了如果a≡3(mod 8),2‖b,c是素数方幂,(b/a)=-1,(d/a)=1,l=m=2,则方程ax+dby=cz仅有正整数解(x,y,z)=(2,2,n)适合min(x,y,z)＞1.     

关于指数Diophantine方程ax+dby=cz

设a,b,c,d,l,m,n是给定的适合d+ab~m=c~n,gcd(a,ab)=1,l>1,m>1,n>1,的正整数。本文中证明了:如果a=3(mod 8),2||b,c是素数方幂,(b/a)=-1,(d/a)=1,l=m=2,则方程a~x+ab~y=c~z仅有正整数解(x,y,z)=(2,2,n)适合min(x,y,z)>1。     

关于商高数的Jesmanowicz猜想

设u,v是适合u＞v,gcd(u,v)=1以及2 |uv的正整数.运用初等数论方法讨论了方程(2uv)x+(u2-v2)y=(u2+v2)z的正整数解(x,y,z),证明了当(u,v)≡(1,6),(2,5),(5,2),(6,1) (mod 8)时,该方程仅有正整数解(x,y,z)=(2,2,2).     

关于数论函数方程σ(x~3)=y~2的一点注记

对于正整数a,设σ(a)是a的所有约数之和.设p是奇素数,r和s是正整数.文中证明了当x=2rps时,若方程σ(x~3)=y~2满足下列条件之一:(ⅰ)2■r,p≡1(mod 6);(ⅱ)2■r,p≡5(mod 6),2|s;(ⅲ)2■rs,p是Fermat数,则σ(x~3)=y~2没有正整数解(x,y).     

关于Diophantine方程组x+1=3pqa~2,x~2-x+1=3b~2

设p,q是适合3pq的奇素数.根据二次和四次Diophantine方程的结果,运用初等数论方法证明当且仅当(p,q)=(7,13)时方程组x+1=3pqa~2,x~2-x+1=3b~2有正整数解(x,a,b)=(4 367,4,2 521).     

不定方程x(x+1)(x+2)(x+3)=42y(y+1)(y+2)(y+3)的正整数解

当M,N为给定正整数时,为解决不定方程Mx(x+1)(x+2)(x+3)=Ny(y+1)(y+2)(y+3)的求解问题,利用Pell方程基本解性质,同余思想以及递归数列等初等方法得到并证明了在(M,N)=(1,42)时该不定方程仅有正整数解(x,y)=(7,2)。进一步完善了当M=1时,N在50以内有正整数解的情形。     

方程x~3-1=py~2有正整数解的判别条件

设p是适合p≡1(mod6)的奇素数.根据二次Diophantine方程的性质,给出了方程x3-1=py2有正整数解(x,y)的新的判别条件.     

关于四次Thue方程ax~4-(2a+1)x~2y~2+ay~4=-1

设a是一个固定的正整数.为寻求方程ax~4-(2a+1)x~2 y~2+ay~4=-1的解,利用二次和四次Diophantine方程的性质证明了方程ax~4-(2a+1)x~2 y~2+ay~4=-1仅有正整数解(x,y)=(1,1),从而将此类问题彻底解决.     

Diophantine方程p~x+q~y=z~2（英文）

设p和q是两个奇素数,且p相似文献   

Yeast 14-3-3 proteins

14-3-3 proteins form a family of highly conserved proteins which are present in all eukaryotic organisms investigated, often in multiple isoforms, up to 13 in some plants. They interact with more than 200 different, mostly phosphorylated proteins. The molecular consequences of 14-3-3 binding are diverse: this binding may result in stabilization of the active or inactive phosphorylated form of the protein, to a conformational alteration leading to activation or inhibition, to a different subcellular localization, to the interaction with other proteins or to shielding of binding sites. The binding partners, and hence the 14-3-3 proteins, are involved in almost every cellular process and 14-3-3 proteins have been linked to several diseases, such as cancer, Alzheimer's disease, the neurological Miller-Dieker and spinocerebellar ataxia type 1 diseases and bovine spongiform encephalopathy (BSE). The yeasts Saccharomyces cerevisiae and Schizosaccharomyces pombe both have two genes encoding 14-3-3 proteins, BMH1 and BMH2 and rad24 and rad25, respectively. In these yeasts, 14-3-3 proteins are essential in most laboratory strains. As in higher eukaryotes, yeast 14-3-3 proteins bind to numerous proteins involved in a variety of cellular processes. Recent genome-wide studies on yeast strains with impaired 14-3-3 function support the participation of 14-3-3 proteins in numerous yeast cellular processes. Given the high evolutionary conservation of the 14-3-3 proteins, the experimental accessibility and relative simplicity of yeasts make them excellent model organisms for elucidating the function of the 14-3-3 protein family.     

Investigation of selected toxicological parameters of γ-pentachlorocyclohexene (γ-PCCH)

The toxic effects of the γ-hexachlorocyclohexane metabolite γ-pentachlorocyclohexene (γ-PCCH) were studied by acute and subacute (6 weeks) experiments. The investigations included cerebral convulsibility with chemoshock (Tetrazolium), reactivity with hot plate method, the learning ability with learning tests, and peripheral nervous activity (EMG). Nociceptive reaction time was not influenced, the learning process (6 weeks) was inhibited by γ-PCCH. The conduction velocity of the peripheral nerve was decreased. At the end of the 6th week liver enlargement was found.     

3-苄硫基噻吩、3-糠硫基噻吩和3-十二烷硫基噻吩的合成及其香气特征

-40℃下,3-溴噻吩先与n-丁基锂反应,再依次加入碘、活性镁粉和二硫醚,在室温下分别反应4、4.5、4.5h,分别合成3-苄硫基噻吩、3-糠硫基噻吩和3-十二烷硫基噻吩,收率分别为51.1%、29.0%和27.4%.这些化合物结构都通过IR、MS和~1HNMR测试技术进行了表征,并对其进行了初步香味评价.结果表明,它们都具有基本肉香味特征,阈值为19.78～30.11mg·kg~(-1),留香时间可达2.5～3.5h.     

Part 3

正论坛、公益、科普,微信、微博、抖音……横向观察社会各界在爱眼日期间的主题活动,我们能看出围绕着"普遍的眼健康"这一主题,医院、学校、眼镜企业、行业及协(商)会等是如何开展与自身职能相关、自己最为擅长的活动的。而纵览历年爱眼日的主题,回顾企业和单位每年活动的变化,我们也能动态且辩证地感受到,随着社会生活、行业企业的发展,爱眼日的主题有了显著的变化。     

问答3则

1 何为直接/间接网版的优缺点? 优点: 直接/间接网版能分辨并印出精细图纹而且墨层厚。有各种厚度的膜片,因此可用于不同目数的丝网。只要操作得当就能获得良好的耐用性。 这种制版方法已流行多年,因为它通过提供优秀的印刷质量、良好的耐用性和多方面的适应