Zero divisors and prime elements of bounded semirings

A semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. A bounded semiring is a semiring equipped with a compatible bounded partial order. In this paper, properties of zero divisors and prime elements of a bounded semiring are studied. In particular, it is proved that under some mild assumption, the set Z（A） of nonzero zero divisors of A is A ／ {0, 1}, and each prime element of A is a maximal element. For a bounded semiring A with Z（A） = A ／ {0, 1}, it is proved that A has finitely many maximal elements if ACC holds either for elements of A or for principal annihilating ideals of A. As an application of prime elements, we show that the structure of a bounded semiring A is completely determined by the structure of integral bounded semirings if either ｜Z（A）｜ = 1 or ｜Z（A）｜ -- 2 and Z（A）2 ≠ 0. Applications to the ideal structure of commutative rings are also considered. In particular, when R has a finite number of ideals, it is shown that the chain complex of the poset I（R） is pure and shellable, where I（R） consists of all ideals of R.     

再论Mobius变换中的n阶循环群判据

用二阶方阵的幂运算取代Mobius变换的迭代运算,导出了Mobius变换为n阶循环群的判据,并对判据进行了简化,最后给出了它们的应用.     

幂指数小于2的无标度网络的性质

很多现实的复杂网络都具有无标度特性,其节点度具有幂律分布的规律。主要讨论幂指数γ<2的无标度网络的性质,指出当γ<2时,网络中最小度的节点数以及网络的平均度都与网络大小N有某种数量关系。通过与γ≥2的无标度网络对比,该类特殊网络呈现出不同的性质和行为,网络的边与节点相比呈现快速增长,具有更大的平均度,网络中有更多的边,网络不再稀疏。     

Influence of quantum degeneracy on the performance of a gas Stirling engine cycle

Based on the state equation of an ideal quantum gas, the regenerative loss of a Stirling engine cycle working with an ideal quantum gas is calculated. Thermal efficiency of the cycle is derived. Furthermore, under the condition of quantum degeneracy, several special thermal efficiencies are discussed. Ratios of thermal efficiencies versus the temperature ratio and volume ratio of the cycle are made. It is found that the thermal efficiency of the cycle not only depends on high and low temperatures but also on maximum and minimum volumes. In a classical gas state the thermal efficiency of the cycle is equal to that of the Carnot cycle. In an ideal quantum gas state the thermal efficiency of the cycle is smaller than that of the Carnot cycle. This will be significant for deeper understanding of the gas Stirling engine cycle.     

Nonstationary ideal incompressible fluid flows: Conditions of existence and uniqueness of solutions

The problem of formulating minimal conditions on input data that can guarantee the existence and uniqueness of solutions of the boundary value problems describing non-one-dimensional ideal incompressible fluid flow is considered using as an example the initial boundary value problem in a space-time cylinder constructed on a bounded flow domain with the nonpenetration condition on its boundary (which corresponds to fluid flow in a closed vessel). The existence problems are considered only for plane flows, and the uniqueness issues for three-dimensional flows as well. The required conditions are obtained in the form of conditions specifying that the vorticity belongs to definite functional Orlicz spaces. The results are compared with well-known results. Examples are given of admissible types of singularities for which the obtained results are valid, which is a physical interpretation of these results. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 130–145, July–August, 2008.     

A study on the distribution of adsorbed nanoparticles

We use Monte Carlo simulation to calculate the distributions of particles under adsorption force near planar and cylindrical surfaces,respectively.Both hard sphere interaction and repulsive Yukawa (screened coulomb) interaction are employed in our simulations.We study the influence of the inter-particle potentials.The difference between the MC simulation results and the analytical results of ideal gas model shows that the interaction between particles plays an important role in the density distribution under external fields.Moreover,the 2-dimensional constructions of particles close to the surface are studied and show relations of the interaction between particles.These results may indicate us how to improve the methods of building nanoparticle coatings and nano-scale patterns.     

Sorting of bending magnets for the SSRF booster

The Shanghai Synchrotron Radiation Facility(SSRF)booster ring,a full energy injector for the storage ring,is deigned to accelerate the electron beam energy from 150MeV to 3.5GeV that demands high extraction efficiency at the extraction energy with low beam loss rate when electrons are ramping.Closed orbit distortion(COD)caused by bending magnet field uniformity errors which affects the machine performance harmfully could be effectively reduced by bending magnet location sorting.Considering the affections of random errors in measurement,both ideal sorting and realistic sorting are studied based on measured bending magnet field uniformity errors and one reasonable combination of bending magnets which can reduce the horizontal COD by a factor of 5is given as the final installation sequence of the booster bending magnets in this paper.     

First synthesis of cyclic organogermanium peroxides, 1,2,4,5,7,8-hexaoxa-3-germonanes

First, previously unknown, cyclic organogermanium peroxides, 1,2,4,5,7,8-hexaoxa-3-germonanes, were synthesized by the reaction of 1,1′-dihydroperoxydi(cyclododecyl)peroxide with (di)alkyl(aryl)dihalogengermanes. The new compounds have a higher tendency to undergo hydrolysis compared to silicon-containing analogs.     

Geodesic ideal triangulations exist virtually

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.

     

Multilinear Components of the Prime Subvarieties of the Variety Var(M2(F))

We describe the multilinear components of the prime subvarieties of the variety Var(M ₂(F)) generated by the matrix algebra of order 2 over a field of characteristic p>0.