Action of μq(g) on Its Positive Part μq+(g)

In this paper,two kinds of skew derivations of a type of Nichols algebras are introduced,and then the relationship between them is investigated.In particular they satisfy the quantum Serre-relations.Therefore,the algebra generated by these derivations and corresponding automorphisms is a homomorphic image of the Drinfeld-Jimbo quantum enveloping algebra μq(g),which proves the Nichols algebra becomes aμq(g)-module algebra.But the Nichols algebra considered here is exactly μq+(g),namely,the positive part of the Drinfeld-Jimbo quantum enveloping algebra μq(g),it turns out that μq+(g)is a μq(g)-module algebra.     

单模辐射场作用下两二能级原子的Wigner－Yanase偏态信息

研究了与单模辐射场作用过程中两二能级原子的Wigner －Yanase信息。结果表明：两原子总Wigner－Yanase偏态信息依赖于处于基态｜gg>，第一激发态（｜eg>＋｜ge>）／2和第二激发态｜ee>的概率。由于光场的作用， Wigner－Yanase偏态信息呈现出周期性的丢失与恢复现象，但原子间的偶极－偶极相互作用对Wigner－Yanase信息的丢失有阻抗作用。     

Partial Groupoid Actions: Globalization,Morita Theory,and Galois Theory

In this article, we introduce the notion of a partial action of a groupoid on a ring as well as we give a criteria for the existence of a globalization of it. We construct a Morita context associated to a globalizable partial groupoid action, and we introduce the notion of a partial Galois extension, which is related to the strictness of this context.     

An elementary approach to dynamics and bifurcations of skew tent maps

In this paper, the dynamics of skew tent maps are classified in terms of two bifurcation parameters. In time series analysis such maps are usually referred to as continuous threshold autoregressive models (TAR(1)-models) after Tong (Non-Linear Time Series, Clarendon Press, Oxford, UK, 1990). This study contains results simplifying the use of TAR(1)-models considerably, e.g. if a periodic attractor exists it is unique. On the other hand, we also claim that care must be exercised when TAR models are used. In fact, they possess a very special type of dynamical pattern with respect to the bifurcation parameters and their transition to chaos is far from standard.     

Pricing Options on Defaultable Stocks*

? ?. This work was inspired by the SAMSI workshops on Financial Mathematics, Statistics and Econometrics (Fall 2005, Spring 2006 North Carolina). The author wishes to thank the organizers for the travel grant to participate in this stimulating event. I also would like to thank Bo Yang for his research assistance and the two anonymous referees and an anonymous associate editor for their valuable suggestions. Stock option price approximations are developed for a model which takes both the risk of default and the stochastic volatility into account. The intensity of defaults is assumed to be influenced by the volatility. It is shown that it might be possible to infer the risk neutral default intensity from the stock option prices. The proposed option price approximation has a rich implied volatility surface structure and fits the data implied volatility well. A calibration exercise shows that an effective hazard rate from bonds issued by a company can be used to explain the impliedvolatility skew of the option prices issued by the same company. It is also observed that the implied yield spread obtained from calibrating all the model parameters to the option prices matches the observed yield spread.     

Closed Form Approximations for Spread Options

Abstract

Market mechanisms are increasingly being used as a tool for allocating somewhat scarce but unpriced rights and resources, and the European Emission Trading Scheme is an example. By means of dynamic optimization in the contest of firms covered by such environmental regulations, this article generates endogenously the price dynamics of emission permits under asymmetric information, allowing inter-temporal banking and borrowing. In the market, there are a finite number of firms and each firm's pollution emission follows an exogenously given stochastic process. We prove the discounted permit price is a martingale with respect to the relevant filtration. The model is solved numerically. Finally, a closed-form pricing formula for European-style options is derived.     

Action of U_q(g) on Its Positive Part U_q~+(g)

In this paper,two kinds of skew derivations of a type of Nichols algebras are intro- duced,and then the relationship between them is investigated.In particular they satisfy the quantum Serre relations.Therefore,the algebra generated by these derivations and correspond- ing automorphisms is a homomorphic image of the Drinfeld-Jimbo quantum enveloping algebra U q (g),which proves the Nichols algebra becomes a U q (g)-module algebra.But the Nichols alge- bra considered here is exactly U + q (g),namely,the posi...     

关于斜McCoy环

For a ring endomorphism α,we introduce α-skew McCoy rings which are generalizations of α-rigid rings and McCoy rings,and investigate their properties.We show that if α t = I R for some positive integer t and R is an α-skew McCoy ring,then the skew polynomial ring R[x;α] is α-skew McCoy.We also prove that if α（1） = 1 and R is α-rigid,then R[x;α]/ x 2 is αˉ-skew McCoy.     

Koszulity for graded skew PBW extensions

Pre-Koszul and Koszul algebras were defined by Priddy [15 Priddy, S. (1970). Koszul resolutions. Trans. Am. Math. Soc. 152:39–60.[Crossref] , [Google Scholar]]. There exist some relations between these algebras and the skew PBW extensions defined in [8 Gallego, C., Lezama, O. (2011). Gröbner bases for ideals of σ-PBW extensions. Comm. Algebra 39(1):50–75.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]. In [24 Suárez, H., Reyes, A. (submitted for publications). Koszulity for skew PBW extensions over fields. [Google Scholar]] we gave conditions to guarantee that skew PBW extensions over fields it turns out homogeneous pre-Koszul or Koszul algebra. In this paper we complement these results defining graded skew PBW extensions and showing that if R is a finite presented Koszul 𝕂-algebra then every graded skew PBW extension of R is Koszul.