Dual subspaces of operators

In this note we introduce some new constructions of dual spaces of operators, which are, of course, at the same time, operator spaces in the sense of Pisier (2003) [12]. We exemplify the utility of these constructs by establishing, in this more general setting, a curious and little known result from the theory of dual algebras, namely from Chevreau and Pearcy (1991) [11].     

Sociometric triads as multi‐variate systems†

Binary choices (choose v. not choose) among three persons may be viewed as variables and the possible choices in a triad as a 64 celled contingency table, amenable to analysis in terms of log linear effects. Fifteen non‐redundant effects occur, of which four appear consistently in a data bank of 384 sociograms. Consequently, it is claimed one may reproduce the triad frequencies in most sociograms by the effects implied by four propositions: (A) P is more likely to choose O when O chooses P, net of all other variables; (B) P is more likely to choose O when X chooses O. This association is particularly strong when imitation produces transitivity; (C) when X chooses O (O chooses X), P tends to choose both or neither; and (D) P tends to choose an X who favors P's choices. P tends to not choose an X who favors P's non‐choices.     

The Rings of Witt Vectors for Noncommutative Rings with Some Rich Structure

In this article, for a noncommutative ring A with some rich structure, we define a ring of Witt vectors with coefficients in A, which is noncommutative unless A is commutative.     

Copula理论在复合期权定价中的应用

本文使用风险中性评价方法分三部分计算了复合期权的价值,针对需要计算联合分布的第二部分,通过选取边缘分布为GARCH模型的二元正态Copula模型进行推理验证,结果求得的联合分布与使用风险中性评价方法的计算结果一致.进一步计算得到了时间相依的复合期权的价值,并且给出了使用Bayes时序诊断法和Z检验来诊断期权定价时其出现价格大的波动时的局部拐点的方法.     

Schmidt modes and entanglement

Motivated by their frequent use in quantum mechanical studies of entanglement, we give a brief overview of Schmidt modes and Schmidt decompositions of two-particle wave functions. We discuss methods of their derivation and include a little-known approach used in the original work by E. Schmidt [Math. Annalen, 63 (1906), 433]. This employs the bipartite wave function itself rather than the more complicated two-party reduced density matrix. As an illustration, Schmidt modes for two-photon polarisation qutrits are derived in a general form. The derivation is accompanied by a series of simple examples with special choices of parameters. Relationships between Schmidt modes, polarisation Stokes vectors and entanglement are also discussed.     

Biodegradable polymers in gene‐silencing technology

Small interfering RNAs (siRNAs) technology has shown great promise as a new class of therapeutics invention for treatment of cancer and other diseases. siRNA has been used extensively in blocking various genes and is presently being evaluated as a therapeutic for cancer and viral disease. Despite the excitement about this remarkable biological process for sequence specific gene regulation, the major limitations against the use of siRNAs‐based therapeutics are their rapid degradation by serum nuclease, poor cellular uptake, and rapid renal clearance following systemic delivery, off‐target effects, and induction of immune responses. Many researchers have tried to overcome these limitations with developing nuclease‐resistant chemically modified siRNAs and variety of synthetic and natural biodegradable lipids and polymers for siRNA delivery to enhance efficacy and safety profiles. An ideal siRNAs‐based delivery system must be clinically suitable, safe, and effective. This review discuss the recent progress of biodegradable polymers in siRNA delivery technology.     

Removal of envelope protein-free retroviral vectors by anion-exchange chromatography to improve product quality

We have investigated the role of the retroviral lipid bilayer and envelope proteins in the adsorption of retroviral vectors (RVs) to a Fractogel DEAE matrix. Intact RVs and their degradation components (envelope protein-free vectors and solubilized vector components) were adsorbed to this matrix and eluted using a linear gradient. Envelope protein-free RVs (Env(-)) and soluble envelope proteins (gp70) eluted in a significantly lower range of conductivities than intact RVs (Env(+)) (13.7-30 mS/cm for Env(-) and gp70 proteins vs. 47-80 mS/cm for Env(+)). The zeta (zeta)-potential of Env(+) and Env(-) vectors was evaluated showing that envelope proteins define the pI of the viral particles (pI (Env(+)) < 2 versus 3 < pI (Env(-)) < 4) and that Env(+) and Env(-) vectors have similar zeta-potentials within pH 5 and 8. The results presented herein indicate that the adsorption of retroviral particles occurs through multi-point interaction of the envelope proteins with the cationic groups on the chromatographic matrix. The strength of this adsorption is thus dependent on the amount of envelope protein present in the viral lipid bilayer. In conclusion, AEXc enables the separation of gp70 proteins as well as envelope protein-free vectors constituting a significant improvement to the quality of retroviral preparations for gene therapy applications.     

Conditional limiting distribution of beta-independent random vectors

The paper deals with random vectors in , possessing the stochastic representation , where R is a positive random radius independent of the random vector and is a non-singular matrix. If is uniformly distributed on the unit sphere of , then for any integer m<d we have the stochastic representations and , with W≥0, such that W² is a beta distributed random variable with parameters m/2,(d−m)/2 and (U₁,…,U_m),(U_m+1,…,U_d) are independent uniformly distributed on the unit spheres of and , respectively. Assuming a more general stochastic representation for in this paper we introduce the class of beta-independent random vectors. For this new class we derive several conditional limiting results assuming that R has a distribution function in the max-domain of attraction of a univariate extreme value distribution function. We provide two applications concerning the Kotz approximation of the conditional distributions and the tail asymptotic behaviour of beta-independent bivariate random vectors.