自反Banach空间中C0-半群族的稳定性

主要讨论了自反Banach空间中一类C0-半群族{Th(t)}稳定性问题,证明了此类半群族{Th(t)}指数稳定与弱Lp-稳定是等价的.     

一类随机保费率下的风险模型

引入随机变量保费率,对古典风险模型进行推广,主要研究随机保费率下的风险模型,用随机过程和鞅论的方法得出破产概率、末离前最大盈余分布、破产前瞬时盈余与破产赤字的联合分布等精算量分布的具体表达式.     

负权最短路问题的新算法

Bellman-Ford算法自1958年以来一直是负权最短路问题的公认的最好算法之一．1970年,Yen对其进行了改进,理论上可以节省一半的计算量．本文得到了一种比Bellman-Ford算法更加优越的算法．尽管在理论上新算法无法保证完全超越于Yen的改进算法,但在许多情况下需要更少的计算量．     

两指标随机积分方程解的唯一性

在正交增量的随机积分基础上，利用Ｌｉｐｓｃｈｉｔｚ条件，讨论了下面一类两参数随机积分方程解的唯一性。Ｘ（ｓ，ｔ）＝Ｚ（ｓ，０）＋Ｚ（０，ｔ）－Ｚ（０，０）＋∫Ｒｓｔα（ｕ，ｖ，Ｘ）ｄＭｕｖ＋∫Ｒｓｔβ（ｕ，ｖ，Ｘ）ｄｍｕｖ＋∫Ｒ＾ｓｔγ１（ｕ，ｖ，ｕ＇，ｖ＇，Ｘ）ｄＭｕｖｄＭｕ＇ｖ＇＋∫Ｒ＾２ｓｔγ２（ｕ，ｖ，ｕ＇，ｖ＇，Ｘ）ｄＭｕｖｄｍｕ＇ｖ＇＋∫Ｒ＾２ｓｔγ３（ｕ，ｖ，ｕ＇，ｖ＇，Ｘ）ｄｍｕｖ     

On free semigroups of automaton transformations

It is established that the subset of freek-generated subsemigroups of the semigroup of all automaton transformations over a finite alphabet is a second category set (in the sense of the Baire category approach) in the set of allk-generated subsemigroups. A continuum series of pairs of automaton transformations each of which generates a free semigroup of rank two is indicated. A criterion is established for this semigroup to be a finite-automaton group. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 248–259, February, 1998. The author wishes to express his deep gratitude to Professor V. I. Sushchans'kii for permanent help and attention to the research. This research was partially supported by the ISSEP under grant No. GSU 051341.     

Colorimetric Calibration of Video Cameras Using Two Color Constancy Models

Colorimetric calibration of color imaging devices is important to realize device independent color reproductions. However the calibration for digital or video cameras is difficult because a color image is acquired for unknown objects under various unknown illuminants. An experiment was carried out based on two computational color constancy models, the finite-dimensional linear model and the spectral sharpening model, to estimate colorimetric values using image data of a color chart captured by video camera. We estimated the colorimetric values by using a single reference reflectance with known spectral reflectance in a color chart under an unknown illuminant. The accuracy was evaluated by color differences in CIELAB color space and was compared on three different color charts under three different illuminants including a fluorescent lamp. It was confirmed that the two computational models do not require prior knowledge of illuminants and surfaces. The finite-dimensional linear model gave more accurate results than the spectral sharpening model in the simulations and experiments.     

On the Ulam stability of Jensen and Jensen type mappings on restricted domains

In 1941 Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 Bourgin was the second author to treat this problem for additive mappings. In 1982-1998 Rassias established the Hyers-Ulam stability of linear and nonlinear mappings. In 1983 Skof was the first author to solve the same problem on a restricted domain. In 1998 Jung investigated the Hyers-Ulam stability of more general mappings on restricted domains. In this paper we introduce additive mappings of two forms: of “Jensen” and “Jensen type,” and achieve the Ulam stability of these mappings on restricted domains. Finally, we apply our results to the asymptotic behavior of the functional equations of these types.     

Solutions of the Vlasov equation in Lagrange coordinates

We show that the method of “finite-size” particles is a discrete model of the Vlasov equation but in a different (effective) interaction potential. We calculate the effective potential explicitly in the most interesting case of the Coulomb interaction. We find the equations of motion of particles of “finite size” for the Gaussian form factor. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 138–148, April, 2007.     

Heptaphyrins: Expanded porphyrins with seven heterocyclic rings

Expanded porphyrins containing seven pyrrole/heterocyclic rings linked in a cyclic fashion are termed heptaphyrins. The number ofπ-electrons in heptaphyrins depends on the number ofmeso carbon bridges used to link the heterocyclic rings, accordingly heptaphyrins with 28π-electrons and 30π-electrons are reported to date. Both condensation reactions of the appropriate precursors and acid-catalysed oxidative coupling reactions have been utilized to synthesise the heptaphyrins. The 30π heptaphyrins exhibit rich structural diversity where some of the heterocyclic rings in the macrocycle undergo a 180° ring flipping. An overview of the synthetic methods employed for the synthesis of heptaphyrins, their spectroscopic properties, structural behaviour and aromatic properties are highlighted in this paper. Dedicated to Professor C N R Rao on his 70th birthday     

FURTHER INVESTIGATION OF THE J_2-INTEGRAL IN BIMATERIAL SOLIDS

The J_2-integral induced from the interface of bimaterial solids(J_2~(interface))is stud-ied by numerical method.First,the effect on the J_2-integral induced from the interface is verysignificant in bimaterial solids,which is inherently related to that induced from the subinterfacecracks.Moreover,it can be concluded that either the first or the second component of the J_k-vector is always equal to zero when the contour encloses both the cracks and the whole interfacein bimaterial solids.Secondly,it can also be concluded that the interface does produce significanteffect on the J_2-integral induced from the subinterface cracks(J_2~(sub))in bimaterial solids.Thiseffect depends on the geometry of the crack arrangement,which is corresponding to the differentinteraction effect among the cracks and the interface.Moreover,the interface effect on the J_2~(sub)can be neglected when the distance from the crack center to the interface is large enough,whichreveals that the bimaterial solids can be regarded as homogenous solids in fracture analysis whenthe subinterface crack is far enough from the interface.Three examples are given in this paper.