Dynamic uniqueness for stochastic chains with unbounded memory

We say that a probability kernel exhibits dynamic uniqueness (DU) if all the stochastic chains starting from a fixed past coincide on the future tail $\sigma$-algebra. Our first theorem is a set of properties that are pairwise equivalent to DU which allow us to understand how it compares to other more classical concepts. In particular, we prove that DU is equivalent to a weak-${?}^2$ summability condition on the kernel. As a corollary to this theorem, we prove that the Bramson–Kalikow and the long-range Ising models both exhibit DU if and only if their kernels are ${?}^2$ summable. Finally, if we weaken the condition for DU, asking for coincidence on the future $\sigma$-algebra for almost every pair of pasts, we obtain a condition that is equivalent to $\beta$-mixing (weak-Bernoullicity) of the compatible stationary chain. As a consequence, we show that a modification of the weak-${?}^2$ summability condition on the kernel is equivalent to the $\beta$-mixing of the compatible stationary chain.     

On the regularity of American options with regime-switching uncertainty

We study the regularity of the stochastic representation of the solution of a class of initial–boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal stopping problem such as the price of an American-style option in finance. We show continuity and smoothness of the value function using coupling and time-change techniques. As an application, we find the minimal payoff scenario for the holder of an American-style option in the presence of regime-switching uncertainty under the assumption that the transition rates are known to lie within level-dependent compact sets.     

On the martingale problem and Feller and strong Feller properties for weakly coupled Lévy type operators

This paper considers the martingale problem for a class of weakly coupled Lévy type operators. It is shown that under some mild conditions, the martingale problem is well-posed and uniquely determines a strong Markov process $(X,\Lambda )$. The process $(X,\Lambda )$, called a regime-switching jump diffusion with Lévy type jumps, is further shown to possess Feller and strong Feller properties under non-Lipschitz conditions via the coupling method.     

Partial stochastic dominance via optimal transport

In recent years, a range of measures of “partial” stochastic dominance have been introduced. These measures attempt to determine the extent to which one distribution is dominated by another. We assess these measures from intuitive, axiomatic, computational and statistical perspectives. Our investigation leads us to recommend a measure related to optimal transport as a natural default.     

Global Lipschitz regularizing effects for linear and nonlinear parabolic equations

In this paper we prove global bounds on the spatial gradient of viscosity solutions to second order linear and nonlinear parabolic equations in (0,T)×R^N$(0,T)\times {\mathbb{R}}^N$. Our assumptions include the case that the coefficients be both unbounded and with very mild local regularity (possibly weaker than the Dini continuity), the estimates only depending on the parabolicity constant and on the modulus of continuity of coefficients (but not on their L^∞$L^{\infty }$-norm). Our proof provides the analytic counterpart to the probabilistic proof used in Priola and Wang (2006) [35] (J. Funct. Anal. 2006) to get this type of gradient estimates in the linear case. We actually extend such estimates to the case of possibly unbounded data and solutions as well as to the case of nonlinear operators including Bellman–Isaacs equations. We investigate both the classical regularizing effect (at time t>0$t>0$) and the possible conservation of Lipschitz regularity from t=0$t=0$, and similarly we prove global Hölder estimates under weaker assumptions on the coefficients. The estimates we prove for unbounded data and solutions seem to be new even in the classical case of linear equations with bounded and Hölder continuous coefficients. Applications to Liouville type theorems are also given in the paper. Finally, we compare in an appendix the analytic and the probabilistic approach discussing the analogy between the doubling variables method of viscosity solutions and the probabilistic coupling method.     

Reactions in Water – A Greener Approach Using Ruthenium Catalysts

Reactions using transition metals as catalysts have emerged as an efficient method in the recent times. However, the selection of solvent plays a crucial role in this regard. Several solvents used traditionally suffer majorly with problems of toxicity; high boiling point etc. leading to drastic reaction conditions. Water being a non‐toxic, non‐inflammable and environmentally benign can replace the hazardous organic solvents in laboratory as well as industry. Maintaining a minimum catalyst loading percentage we can advantageously avail high levels of selectivity. Water was found to be a good solvent medium for several metal catalysed reactions. An intramolecular deprotonation mechanism is followed by the ruthenium (II) catalysts in water; thereby, facilitating the catalytic action of the metal. These studies can help the industrial chemists to utilize water as a solvent for their reactions towards improvement of their waste management procedure. This review mainly focuses on the several recent developments in the above direction.     

Coupling resonance of floating slab and supporting concrete box structure

This paper mainly investigates the effect of coupling resonance of floating slab and supporting short concrete box. The similarities and differences in vibration behaviors between long (30 m) and short (1.5 m) lengths of concrete box structures with the same cross-section were analyzed with finite element model (FEM). The results suggest that the major local modes for vibration and structure-borne sound radiation for long and short box structures are the same. A short concrete hollow box was constructed to verify the theoretical vibration results, and six combinations of floating slabs were installed on the box to identify the vibration and structure-borne sound control by experimental method. The resonance modes due to either concrete box or floating slab should degrade the vibration isolation performance of the floating system. There may be strong coupling between roll mode (rigid body rotation mode in the y-z plane) of the floating slab and local distortion mode of the short box structure and this can change the vibration resonance frequencies and amplify the vibration.     

S波段相对论速调管放大器输入腔的3维分析与模拟

 利用3维软件设计了适用于S波段相对论速调管放大器的单重入输入腔,该腔体采用了偏心设计,以便减小耦合孔处的不均匀场对腔间隙场的影响,分析了腔体耦合孔尺寸对腔间隙场均匀性的影响;建立了带输入波导结构的3维输入腔开放腔模型,并应用此模型,采用3维PIC程序模拟了注入微波功率、束直流对输入腔间隙后束流调制的影响。研究结果表明：耦合孔尺寸对腔间隙电场均匀性影响较大,当耦合孔离轴越近时,腔间隙场越不均匀;在结构参数和束参数固定的条件下,基波电流调制深度随着间隙电压的增加而增加,但达到最大基波调制电流的漂移距离几乎不变;在结构参数和注入微波参数固定的条件下,束直流越大,达到最大基波调制电流所需的漂移距离越短。研究结果为腔体的设计和输入腔束流调制实验提供了参考依据。     

TM模场入射到金属光栅的表面增强喇曼散射计算分析

以纳米量级金属履带矩形光栅为模型,研究了表面增强喇曼散射的特性.针对TM模的入射光,采用严格的耦合波原理对金属表面的衍射场进行了分析,并用数值计算方法讨论了光栅深度、光栅占空比等参量对金属表面增强的影响以及增强因子随光栅深度的变化关系.结果显示：当入射光波长为700 nm、入射角度为10°、光栅周期p=600 nm、 光栅深度d=37.5 nm、占空比为1/3时,获得最大增强,增强因子G达104倍.