The Goldbach Conjecture Is True

Let 2m>2, m∈ℤ, be the given even number of the Strong Goldbach Conjecture Problem. Then, m can be called the median of the problem. So, all Goldbach partitions (p,q)exist a relationship, p=m−dand q=m+d, where p≤qand d is the distance from m to either p or q. Now we denote the finite feasible solutions of the problem as S(2m)={ (2,2m−2),(3,2m−3),⋅⋅⋅,(m,m) }. If we utilize the Eratosthenes sieve principle to efface those false objects from set S(2m)in pistages, where pi∈P, pi≤2m, then all optimal solutions should be found. The Strong Goldbach Conjecture is true since we proved that at least one optimal solution must exist to the problem. The Weak Goldbach Conjecture is true since it is a special case of the Strong Goldbach Conjecture. Therefore, the Goldbach Conjecture is true.

Optimal Static Partition Configuration in ARINC653 System

ARINC653 systems, which have been widely used in avionics industry, are an important class of safety-critical applications. Partitions are the core concept in the Arinc653 system architecture. Due to the existence of partitions, the system designer must allocate adequate time slots statically to each partition in the design phase. Although some time slot allocation policies could be borrowed from task scheduling policies, no existing literatures give an optimal allocation policy. In this paper, we present a partition configuration policy and prove that this policy is optimal in the sense that if this policy fails to configure adequate time slots to each partition, nor do other policies. Then, by simulation, we show the effects of different partition configuration policies on time slot allocation of partitions and task response time, respectively.

Allometric response of perennial Pennisetum centrasiaticum Tzvel to nutrient and water limitation in the Horqin Sand Land of China

Optimal partitioning theory （OPT） suggests that plants should allocate relatively more biomass to the organs that acquire the most limited resources. The assumption of this theory is that plants trade off the biomass allocation between leaves, stems and roots. However, variations in biomass allocation among plant parts can also occur as a plant grows in size. As an alternative approach, allometric biomass partitioning theory （APT） asserts that plants should trade off their biomass between roots, stems and leaves. This approach can minimize bias when comparing biomass allocation patterns by accounting for plant size in the analysis. We analyzed the biomass allo- cation strategy of perennial Pennisetum centrasiaticum Tzvel in the Horqin Sand Land of northern China by treating samples with different availabilities of soil nutrients and water, adding snow in winter and water in summer. We hypothesized that P. centrasiaticum alters its pattern of biomass allocation strategy in response to different levels of soil water content and soil nitrogen content. We used standardized major axis （SMA） to analyze the allometric rela- tionship （slope） and intercept between biomass traits （root, stem, leaf and total biomass） of nitrogen/water treat- ments. Taking plant size into consideration, no allometric relationships between different organs were significantly affected by differing soil water and soil nitrogen levels, while the biomass allocation strategy of P. centrasiaticum was affected by soil water levels, but not by soil nitrogen levels. The plasticity of roots, leaves and root/shoot ratios was ＇true＇ in response to fluctuations in soil water content, but the plasticity of stems was consistent for trade-offs between the effects of water and plant size. Plants allocated relatively more biomass to roots and less to leaves when snow was added in winter. A similar trend was observed when water was added in summer. The plasticity of roots, stems and leaves was a function of plant size, and remained unchanged in response to different soil nitrogen levels.

Realization of error correction and reconciliation of continuous quantum key distribution in detail

The efficiency of reconciliation in the continuous key distribution is the main factor which limits the ratio of secret key distribution. However, the efficiency depends on the computational complexity of the algorithm. This paper optimizes the two main aspects of the reconciliation process of the continuous key distribution： the partition of interval and the estimation of bit. We use Gaussian approximation to effectively speed up the convergence of algorithm. We design the estimation function as the estimator of the SEC （sliced error correction） algorithm. Therefore, we lower the computational complexity and simplify the core problem of the reconciliation algorithm. Thus we increase the efficiency of the reconciliation process in the continuous key distribution and then the ratio of the secret key distribution is also increased.