Continuous spin models on annealed generalized random graphs

We study Gibbs distributions of spins taking values in a general compact Polish space, interacting via a pair potential along the edges of a generalized random graph with a given asymptotic weight distribution $P$, obtained by annealing over the random graph distribution.First we prove a variational formula for the corresponding annealed pressure and provide criteria for absence of phase transitions in the general case.We furthermore study classes of models with second order phase transitions which include rotation-invariant models on spheres and models on intervals, and classify their critical exponents. We find critical exponents which are modified relative to the corresponding mean-field values when $P$ becomes too heavy-tailed, in which case they move continuously with the tail-exponent of $P$. For large classes of models they are the same as for the Ising model treated in Dommers et al. (2016). On the other hand, we provide conditions under which the model is in a different universality class, and construct an explicit example of such a model on the interval.     

Summability in of a vector measure

We show a picture of the relations among different types of summability of series in the space  of integrable functions with respect to a vector measure m of relatively norm compact range. In order to do that, we study the class of the so‐called m‐1‐summing operators. We give several applications regarding the existence of copies of c ₀ in , as well as on m‐1‐summing operators which are weakly compact, Asplund or weakly precompact.     

Estimates of densities for Lévy processes with lower intensity of large jumps

We obtain general lower estimates of transition densities of jump Lévy processes. We use them for processes with Lévy measures having bounded support, processes with exponentially decaying Lévy measures for large times and for processes with high intensity of small jumps for small times.     

Strict topologies on measure spaces

Let X be a measurable space, let be a family of measurable subsets of it, and let be a subspace of complex measures on X that is also closed under restrictions of measures. In this paper we introduce the ‐convergence topology and the ‐strict topology on . Among other results, we find necessary and sufficient conditions for Hausdorff‐ness and coincide‐ness of these topologies. Applications to Lebesgue spaces, and also examples in Hausdorff topological spaces and locally compact groups are given.     

A classification of orbits admitting a unique invariant measure

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_{\infty }$-invariant and concentrated on a single isomorphism class must be zero, or one, or continuum. Further, such an isomorphism class admits a unique $S_{\infty }$-invariant probability measure precisely when the structure is highly homogeneous; by a result of Peter J. Cameron, these are the structures that are interdefinable with one of the five reducts of the rational linear order $(\mathbb{Q},<)$.     

A Liouville theorem for weighted p−Laplace operator on smooth metric measure spaces

We prove that on a smooth metric measure space with m ?Bakry–Émery curvature bounded from below by ?(m ? 1)K for some constant K ≥0 (i.e., Ric_{f ,m} ≥?(m ? 1)K ), the following degenerate elliptic equation (0.1) has no nonconstant positive solution when p > 1 and constant λ _{f ,p} satisfies Our approach is based on the local Sobolev inequality and the Moser's iterative technique and is different from Cheng‐Yau's method, which was used by Wang‐Zhu in 2012 to derive a same Liouville theorem when 1 < p ≤2, Ric_{f ,m} ≥?(m ? 1)K and the sectional curvature is bounded from below. Copyright © 2016 John Wiley & Sons, Ltd.     

广义Khasminskii条件下自变量分段连续型带Poisson随机测度随机微分方程Euler方法的依概率收敛性

针对满足广义Khasminskii条件的由维纳过程和泊松随机测度驱动的自变量分段连续型随机微分方程(EPCASDEs),给出了Euler方法,广义Khasminskii条件比经典条件包容了更多的EPC.ASDEs.现有文献对该类方程的研究成果较少.针对EPCASDEs在广义Khasminskii条件下证明了全局解的存在唯一性,并研究了Euler方法的依概率收敛性.给出了数值算例支持主要结论.     

考虑底部隆起的浅埋隧道围岩压力计算分析

针对浅埋隧道开挖后底部隆起变形现象,应用极限分析上限法构造了考虑底部隆起变形的围岩压力计算模型,结合线性Mohr-Coulomb准则等推导出极限围岩压力的理论表达式。通过约束条件将围岩压力的计算转化为数学中的最优化问题,编制程序进行了优化计算。将计算结果与工程实测数据及文献计算结果进行了对比,验证了当前方法的可靠性。同时,指出在运用极限分析法处理浅埋隧道围岩压力问题过程中应将隧道底部一同考虑,对隧道底部支护会对整个围岩压力产生影响,有助于隧道结构的整体稳定。研究可以为浅埋隧道的开挖、支护提供一定的理论指导.     

ORSIS – News and further developments

The paper deals with the simulation program Off Road Systems Interactive Simulation (ORSIS) which is the w,orldwide leading simulation tool for off road driving of wheeled vehicles. Even though the present state of development allows a very realistic simulation of the man–vehicle–terrain system, there is continuous further improvement in the computer program’s detail. Some of the recent innovations integrated into the program are presented in this paper. These examples were chosen in a way that the scope of the further developments can be demonstrated. They represent three main directions of the work carried out: the refining of the tire–soil-model, the integration of new technologies and subsystems into the vehicle model and the improvement of the man–machine–interface especially in driving simulators.The first part of the paper describes a further development of the tire–soil-model. A significant improvement has been achieved to include the influence of slippery surfaces on traction in combination with the tire tread pattern. Results from finite element method (FEM) as well as real measurements were used to build up an approach, which qualitatively allows the influence of the positive–negative portion of the tire tread and the lug height of the tire tread on traction to be considered. The basic idea is very simple and straightforward. Moreover the calculation costs are very low, so the enhancement does not affect real time operation.In the second part a physical model for the central tire inflation system (CTIS) is presented. With this model it is possible to simulate the complete pneumatic system of a CTIS, including the air compressor with an accumulator, the pressure line and the wheel valves. The components are modelled by their physical parameters, so an adaptation to different existing tire-pressure-control-systems (TPC) can be made. The paper presents a short review of the modelling and a first validation using real measurements. Furthermore the influence of each parameter, e.g. the discharge flow of the compressor on the inflation time, is presented.The third part of the paper describes a further development of the visualization system. The ORSIS OpenGL graphic engine was separated from the main ORSIS simulation and can be run on different PCs controlled via a network. It is therefore possible to build up very cheap multi-channel visualization systems using consumer PCs running under LinuX. The fact that ORSIS itself is running on a normal PC allows the assembly of comparatively cheap driving simulators of a high end simulation quality.