Periodic solutions to a kind of neutral functional differential equation in the critical case

In this paper, we consider a kind of neutral functional differential equation as follows:

     

On Crossing Event Formulas in Critical Two-Dimensional Percolation

Several formulas for crossing functions arising in the continuum limit of critical two-dimensional percolation models are studied. These include Watts's formula for the horizontal-vertical crossing probability and Cardy's new formula for the expected number of crossing clusters. It is shown that for lattices where conformal invariance holds, they simplify when the spatial domain is taken to be the interior of an equilateral triangle. The two crossing functions can be expressed in terms of an equianharmonic elliptic function with a triangular rotational symmetry. This suggests that rigorous proofs of Watts's formula and Cardy's new formula will be easiest to construct if the underlying lattice is triangular. The simplification in a triangular domain of Schramm's bulk Cardy's formula is also studied.     

On a class of singular biharmonic problems involving critical exponents

This paper deals with the following class of singular biharmonic problems

     

A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms

Let be a bounded domain such that . We obtain existence of sign-changing solutions for the Dirichlet problem on Ω,u=0 on ∂Ω for suitable positive numbers μ and λ.     

Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem

The following singular elliptic boundary value problem is studied:

     

管内电缆导体稳定性理论与实验研究

管内电缆导体 ,又称 CICC,是目前大型低温超导磁体的首选导体。随着超导技术的发展 ,CICC在大型超导核聚变实验装置及超导储能磁体中的应用具有不可比拟的优越性。为降低导体成本而提出了在 CICC中采用的超导股线配以纯铜股线的设计方案 ,开展含纯铜股线 CICC稳定性机理及实验的研究 ,并开发 CICC优化设计软件 ,对 CICC在高科技中的应用意义重大。     

大电流超导材料临界电流的感应法测量

文中总结了感应法测量大电流超导材料临界电流的方法 ,叙述测量的原理及装置 ,分析对环电流进行定标时可能产生的误差及减少误差的措施 ,给出计算结果 ,并对之进行讨论     

Utilization of the BARC critical facility for ADS related experiments

The paper discusses the basic design of the critical facility, whose main purpose is the physics validation of AHWR. Apart from moderator level control, the facility will have shutdown systems based on shutoff rods and multiple ranges of neutron detection systems. In addition, it will have a flux mapping system based on 25 fission chambers, distributed in the core. We are planning to use this reactor for experiments with a suitable source to simulate an ADS system. Any desired sub-criticality can be achieved by adjusting the moderator level. Apart from perfecting our experimental techniques, in simple configurations, we intend to study the one-way coupled core in this facility. Preliminary calculations, employing a Monte Carlo code TRIPOLI, are presented.      

Randomness and a step-like distribution of pile heights in avalanche models

This paper considers a one-parameter family of sand-piles. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean pile height is used to describe the crossover. The height densities corresponding to the models with relaxation of both types approach one another as the parameter increases. Relaxation is supposed to deal with the local losses of grains by a fixed amount. In that case the densities show a step-like behaviour in contrast to the peaked shape found in the models with the local loss of grains down to a fixed level [S. Lübeck, Phys. Rev. E 62, 6149 (2000)]. A spectral approach based on the long-run properties of the pile height considers the models with deterministic and random relaxation more accurately and distinguishes between the two cases for admissible parameter values.