环F_2+uF_2+u~2F_2上循环码的Gray距离

定义了环R=F2+uF2+u2 F2(u3=0)到F32的一个新的Gray映射.首先介绍环R上奇长度的循环码的挠码,给出了各阶挠码的生成多项式.利用一阶挠码与二阶挠码确立了R上奇长度的循环码的Gray距离.     

On the equation 1k+2k+···+nk=x 2

Periodica Mathematica Hungarica -     

On (q 2 + q + 2, q + 2)-arcs in the Projective Plane PG(2, q)

A (k,n)-arc in PG(2,q) is usually defined to be a set of k points in the plane such that some line meets in n points but such that no line meets in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow to be a multiset, that is, permit to contain multiple points. The case k=q ²+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q ²+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q ²+q+2 and minimum distance q ². Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q ²+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem.     

A ternary Diophantine inequality by primes with one of the form $$p=x^2+y^2+1$$ p = x 2 + y 2 + 1

The Ramanujan Journal - In this paper we solve the ternary Piatetski-Shapiro inequality with prime numbers of a special form. More precisely we show that, for any fixed $$1<\frac{427}{400}$$...     

Über Diskretheitsbedingungen und die diophantische Gleichungax 2 +by 2 +cz 2=dxyz

Ohne ZusammenfassungHerrn Professor Reinhold Baer in Erinnerung gewidmet.     

环F2+uF2+vF2上线性码广义Gray像

本文定义了环F2+uF2+vF2到域F2的广义Gray映射φ像,研究了环F2+uF2+vF2上线性码的广义Gray像.利用广义Gray映射φ的线性性,证明了环F2+uF2+vF2上线性码C的广义Gray像φ(C)满足dH(C)=dH(φ(C))且φ(C⊥)φ(C)⊥.同时,给出了F2+uF2+vF2上循环码C的广义Gray像φ(C)为F2上的4-拟循环码.     

Le equazioni diofanteeax 4-bx 2+1=□, 4x 4+x 2 y 2+4y 4=□.

Summary Si determinano tre classi di quartiche u²=ax⁴+1, a e b interi, b²−4a≠□ per le quali l'appartenenza di un punto razionale (x₀,y₀),x₀≠0 porta l'esistenza nella stessa quartica di infiniti punti razionali. Si dimostra pure che l'equazione 4x²+x²y²+4y⁴=□ non ammette soluzioni intere con |xy| > 1. A BeniaminoSegre nel suo 70^mo compleanno. Entrata in Redazione il 26 febbraio 1973.     

Pairs of square-free values of the type n2 + 1, n2 + 2

Czechoslovak Mathematical Journal - We show that there exist infinitely many consecutive square-free numbers of the form n2 + 1, n2 + 2. We also establish an asymptotic formula for the number of...     

关于1~k+2~k+…+n~k求和的三种方法

就差分方法、伯努利公式以及组合公式三种方法对 ∑ni=1ik求和 .     

关于不定方程x~2-kxy+y~2+px=0

设p为奇素数.讨论了不定方程x~2-kxy+y~2+px=0,给出了这类方程求解的一些必要条件.     

A simple method for solving the diophantine equation Y2 = X4 + aX3 + bX2 + cX + d

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A simple method for solving the diophantine equation Y2 = X4 + aX3 + bX2 + cX + d

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环F_2+uF_2上长为2~e的(1+u)-循环码

最近,环F2+uF2上的线性码引起了编码研究者极大的兴趣.本文证明了R[x]/〈xn+1+u〉是有限链环,其中R=F2+uF2=F2[u]/〈u2〉且n=2e.从而给出了F2+uF2上的所有长为2e的(1+u)-循环码,进而给出了所有(1+u)-循环码的对偶码.证明了F2+uF2上不存在长为2e的非平凡的自对偶的(1+u)-循环码.     

Equilibrium constants of UO 2 2+ , Cu2+ with dicarboxylic acids in dioxane-water mixtures

The interactions of uranyl and copper ions with dicarboxylic acids such as succinic, itaconic, adipic and malonic acids have been investigated in 20, 40, 60 and 80% (v/v) dioxane-water mixtures at 30°C and 0·06 ionic strength by Calvin-Bjerrum titration technique. UO ₂ ²⁺ , Cu²⁺ form only 1:1 complexes with succinic, itaconic and adipic acids and both 1:1 and 1:2 with malonic acid in the pH range 2·5–5. The plots of pK/log K vs mole fraction gave linear while those with 1/D gave non-linear. The complexation equilibria: are proposed. The radius of anionic ligand is calculated from Born equation and attempts are made to understand the medium effect on the pK values.