In this paper, we prove the hypercontra,ctivity of a non-differentiable Gaussian generalized Mehler semigroup using direct probabilistic argumcents, This result implics the exponential convergence of the scmigroup at ...In this paper, we prove the hypercontra,ctivity of a non-differentiable Gaussian generalized Mehler semigroup using direct probabilistic argumcents, This result implics the exponential convergence of the scmigroup at infinity. Under some additional hypotheses, we also） establish the absolute continuity of the semigroup with respect to its invariant mcasure.展开更多
We show that Mehler's formula can be used to handle several formulas involving the quantization of singular Hamiltonians. In particular, we diagonalize in the Hermite basis the Weyl quantization of the characteris...We show that Mehler's formula can be used to handle several formulas involving the quantization of singular Hamiltonians. In particular, we diagonalize in the Hermite basis the Weyl quantization of the characteristic function of several domains of the phase space.展开更多
Different aspects of mathematical finance benefit from the use Hermite polynomials, and this is particularly the case where risk drivers have a Gaussian distribution. They support quick analytical methods which are co...Different aspects of mathematical finance benefit from the use Hermite polynomials, and this is particularly the case where risk drivers have a Gaussian distribution. They support quick analytical methods which are computationally less cumbersome than a full-fledged Monte Carlo framework, both for pricing and risk management purposes. In this paper, we review key properties of Hermite polynomials before moving on to a multinomial expansion formula for Hermite polynomials, which is proved using basic methods and corrects a formulation that appeared before in the financial literature. We then use it to give a trivial proof of the Mehler formula. Finally, we apply it to no arbitrage pricing in a multi-factor model and determine the empirical futures price law of any linear combination of the underlying factors.展开更多
The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polyn...The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions.展开更多
光是光合作用不可或缺的底物。然而过量的光照会对光合生物造成氧化胁迫和严重的损害。为了应对持续变化的光环境,蓝藻演化形成了灵活的电子传递网络。围绕光系统I(photosystem I,PSI)的循环电子传递(cyclic electron transport,CET)将...光是光合作用不可或缺的底物。然而过量的光照会对光合生物造成氧化胁迫和严重的损害。为了应对持续变化的光环境,蓝藻演化形成了灵活的电子传递网络。围绕光系统I(photosystem I,PSI)的循环电子传递(cyclic electron transport,CET)将电子从铁氧还蛋白Fd回流到质体醌(plastoquinone,PQ)库,产生ATP且不积累NADPH。在蓝藻和高等植物中发现了2种不同的CET途径,即NDH依赖途径和PGR5依赖途径。蓝藻中黄素二铁蛋白Flv1/Flv3参与了类梅勒(Mehler-like)反应,从PSI接受电子直接将氧气还原为水,且没有活性氧的形成。以集胞藻为试验材料,通过分析不同的CET和Flv突变株在不同光照条件下的生理特征以及其P700氧化/还原动力学,进而研究CET途径和类梅勒反应在集胞藻中的功能。结果表明NDH-1复合体对CET的贡献率超过90%,维持细胞能在持续高光环境下生长,而迅速应激的类梅勒反应在缓解瞬时高光胁迫时发挥了重要作用。因此我们认为在集胞藻中NDH-1介导的循环电子途径是稳固支持其适应高光逆境的主要机制,而类梅勒反应则是在现有主要途径严重不足时的1个备用途径。响应迅速的FLV路径是野生型和NDH-1突变株的补足。展开更多
A new (non-unitary) representation of the general linear group of white noise space on Hida’s test and distribution spaces is presented. The relevant representative operators are natural generalization of Fourier-Meh...A new (non-unitary) representation of the general linear group of white noise space on Hida’s test and distribution spaces is presented. The relevant representative operators are natural generalization of Fourier-Mehler transforms.展开更多
文摘In this paper, we prove the hypercontra,ctivity of a non-differentiable Gaussian generalized Mehler semigroup using direct probabilistic argumcents, This result implics the exponential convergence of the scmigroup at infinity. Under some additional hypotheses, we also） establish the absolute continuity of the semigroup with respect to its invariant mcasure.
文摘We show that Mehler's formula can be used to handle several formulas involving the quantization of singular Hamiltonians. In particular, we diagonalize in the Hermite basis the Weyl quantization of the characteristic function of several domains of the phase space.
文摘Different aspects of mathematical finance benefit from the use Hermite polynomials, and this is particularly the case where risk drivers have a Gaussian distribution. They support quick analytical methods which are computationally less cumbersome than a full-fledged Monte Carlo framework, both for pricing and risk management purposes. In this paper, we review key properties of Hermite polynomials before moving on to a multinomial expansion formula for Hermite polynomials, which is proved using basic methods and corrects a formulation that appeared before in the financial literature. We then use it to give a trivial proof of the Mehler formula. Finally, we apply it to no arbitrage pricing in a multi-factor model and determine the empirical futures price law of any linear combination of the underlying factors.
文摘The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions.
基金Elite Youth Program of Chinese Academy of Agricultural Sciences and the Agricultural Science and Technology Innovation Program。
文摘光是光合作用不可或缺的底物。然而过量的光照会对光合生物造成氧化胁迫和严重的损害。为了应对持续变化的光环境,蓝藻演化形成了灵活的电子传递网络。围绕光系统I(photosystem I,PSI)的循环电子传递(cyclic electron transport,CET)将电子从铁氧还蛋白Fd回流到质体醌(plastoquinone,PQ)库,产生ATP且不积累NADPH。在蓝藻和高等植物中发现了2种不同的CET途径,即NDH依赖途径和PGR5依赖途径。蓝藻中黄素二铁蛋白Flv1/Flv3参与了类梅勒(Mehler-like)反应,从PSI接受电子直接将氧气还原为水,且没有活性氧的形成。以集胞藻为试验材料,通过分析不同的CET和Flv突变株在不同光照条件下的生理特征以及其P700氧化/还原动力学,进而研究CET途径和类梅勒反应在集胞藻中的功能。结果表明NDH-1复合体对CET的贡献率超过90%,维持细胞能在持续高光环境下生长,而迅速应激的类梅勒反应在缓解瞬时高光胁迫时发挥了重要作用。因此我们认为在集胞藻中NDH-1介导的循环电子途径是稳固支持其适应高光逆境的主要机制,而类梅勒反应则是在现有主要途径严重不足时的1个备用途径。响应迅速的FLV路径是野生型和NDH-1突变株的补足。
文摘A new (non-unitary) representation of the general linear group of white noise space on Hida’s test and distribution spaces is presented. The relevant representative operators are natural generalization of Fourier-Mehler transforms.
