On two Diophantine inequalities over primes

Let $1<c<37∕18,c\ne 2$ and $N$ be a sufficiently large real number. In this paper, we prove that, for almost all $R\in (N,2N]$, the Diophantine inequality $|p_1^c+p_2^c+p_3^c?R|<{log}^{?1}N$ is solvable in primes $p_1,p_2,p_3$. Moreover, we also investigate the problem of six primes and prove that the Diophantine inequality $|p_1^c+p_2^c+p_3^c+p_4^c+p_5^c+p_6^c?N|<{log}^{?1}N$ is solvable in primes $p_1,p_2,p_3,p_4,p_5,p_6$ for sufficiently large real number $N$.     

混合幂的素变数丢番图逼近

证明了:如果λ_1,λ_2,λ_3,λ_4是正实数,λ_1/λ_2是无理数和代数数,V是well-spaced序列,δ0,那么对于v∈V,v≤X,ε0,使得|λ_(1p_1~2)+λ_(2p_2~2)+λ_(3p_3~3)+λ_(4p_4~3)-v|v~(-δ)没有素数解p1,p2,p3,p4的v的个数不超过O(X~(20/21+21δ+ε)).     

New maximal prime gaps and first occurrences

The search for first occurrences of prime gaps and maximal prime gaps is extended to . New maximal prime gaps of 806 and 906 are found, and sixty-two previously unpublished first occurrences are found for gaps varying from 676 to 906.

     

The Proof of Inseparable Prime AW^＊—Algebras Being Primitive C^＊—Algebras

The relation between the inseparable prime C^*-algebras and primitive C^*-algebras is studied,and we prove that prime AW^*-algebras are all primitive C^*-algebras.     

Synthesis of 4′4″(5″)-dibenzo-18-crown-6-disulfonic acid disalsolidinide,disalsolinide, and dianabasinide

New disulfamides of dibenzo-18-crown-6 with salsolidine, salsoline, and anabasine were prepared by condensation of the corresponding alkaloids with 4,4(5)-dibenzo-18-crown-6-disulfonyl chlorides.Presented at the 5th International Symposium on the Chemistry of Natural Compounds (Tashkent, Uzbekistan, May 20–23, 2003).Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 413–415, September–October, 2004.     

Reactions of 9,10-phenanthrenequinone and its nitro derivatives with acetone in the presence of Al2O3

The addition of acetone to 9,10-phenanthrenequinone and 2-nitro-, 2,7-dinitro-, and 2,4,7-trinitro-9,10-phenanthrenequinones in the presence of Al₂O₃ affords mono- and bisadducts. The crystal structures of 10-hydroxy-10-(2-oxopropyl)-2-nitro-9,10-dihydrophenanthren-9-one and 9,10:10,9-bishemiketal of 9,10-dihydroxy-2-nitro-9,10-bis(2-oxopropyl)-9,10-dihydrophenanthrene were determined.     

环的素谱的若干注记

对于可换环Ｒ,本通过考察ＳｐｅｃＲ和Ｈ０Ｒ,得到了关于广义素环和广义半素环的一些结果,另一方面,本还得到了有关连通性与道路连通性的几个结果。     

一种基于扩展素数码和单重合序列的二维光正交码EPC/OCS

以扩展素数码(EPC)作为时间扩频伪随机序列,单重合序列(OCS)作为波长跳频伪随机序列,构造了一种新的二维光正交码EPC/OCS,并分析了码字的互相关性能.与修正素数跳频码MPHC相比,EPC/OCS的波长数并不局限于素数,可以是任意整数,不仅构造灵活,而且可充分利用MW OCDMA系统的有效波长数.当系统的有效波长数大于某个素数时,EPC/OCS不仅码字容量大于MPHC,而且互相关性能也有所改善.理论分析表明,EPC/OCS可降低MW OCDMA系统误码率.     

例外型Chevalley群G_2(q)的h函数值

设G是有限群,πe(G)表示G中元素的阶的集合,h(πe(G))表示满足πe(H)=πe(G)条件的有限群H的同构类类数,本文证明了例外型Chevalley群G2(q)的h函数值为1或∞.     

Acid association quotients of bis-tris in aqueous sodium chloride media to 125°C

The ionic strength and temperature dependencies of the molal acid association quotients of 2,2-Bis(hydroxymethyl)-2,2,2-nitrilotriethanol (also abbreviated as bis-tris) were determined potentiometrically in a concentration cell fitted with hydrogen electrodes. The emf was recorded for equimolal bis-tris/bis- trisHCl buffer solutions from 5 to 125°C at approximately 25°C intervals, and at nine ionic strengths from 0.05 to 5.0m (NaCl). The molal association quotients, combined with infinite dilution values from the literature, are described precisely by a seven parameter equation which yielded the following thermodynamic quantities at infinite dilution and 25°C: logK=6.481±0.003, H ^o =–28.5±0.2 kJ-mol ^–1 , S ^o =28.5±0.8 J-K ^–1 -mol ^–1 , and C _P ^o =–22±5 J-K ^–1 -mol ^–1 . The equation incorporates a simple three term expression for logK, but requires four terms to describe the rather complex ionic strength dependence despite the reaction being isocoulombic. The molal association quotients from this study and the literature were also subjected to the Pitzer ion interaction treatment.