Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Imaging and correlation used for guided laser lithotripsy

High-speed imaging of phenomena akin to laser lithotripsy is performed. A new method for guiding laser light for the stone destruction is proposed. This is based on a combination of signals obtained from the correlation of fluorescent and ballistic images.     

Reaction dynamics of synthesis of superheavy elements

Based on the theory of the compound nucleus reaction, a brief review is given on the special aspects of the reaction dynamics in the synthesis of the superheavy elements (SHE), where the fusion probability is the most unknown factor. A new viewpoint of the fusion reaction is proposed that it consists of two processes; the first process up to the contact of two nuclei of the incident channel and the second one of a dynamical evolution to the spherical compound nucleus from the contact configuration. The fusion probability is, thus, given as a product of a contact probability and a formation probability. Analytic studies of the latter probability are discussed in the one-dimensional model, where a simple expression is given to the so-called extra-push energy in terms of the reduced friction, the curvature parameter of the conditional saddle point and the nuclear temperature. Preliminary results of numerical analyses of the contact probability are given, using the surface friction model (SFM). Remarks are given on the present status of our knowledge and for future developments. Received: 1 May 2001 / Accepted: 4 December 2001     

Automorphisms of Green Orders and Their Derived Categories

In an earlier paper, Raphaël Rouquier and the author introduced the group of self-equivalences of a derived category. In the case of a Brauer tree algebra, we determined a nontrivial homomorphism of the Artin braid group to this group of self-equivalences. The class of Brauer tree algebras include blocks of finite group rings over a large enough field with cyclic defect groups. In the present paper we give an integral version of this homomorphism. Moreover, we identify some interesting arithmetic subgroups with natural groups of self-equivalences of the derived category.     

A new formula for the saddle-to-scission time

We propose a new formula for the saddle-to-scission time that is more general that the one based on Kramers' approach. Its validity and applicability is then studied in detail. Such a formula is useful for the evaluation of the fission time of very heavy nuclei.     

Agents facilitating the electric field-induced fusion of intact rabbit erythrocytes

In the recent years, the role of specific membrane active agents in the electrofusion process has started to draw attention, and it has been found that the presence of various substances in the cell medium can affect the fusion process either in a positive or negative way. In this work, the effect of several proteins, bivalent cations and antibiotics was tested with respect to their ability to protect intact erythrocytes from hemolysis and facilitate the fusion process. The effect of different sugars was also studied. Among the different proteins, pronase and proteinase were found to be the most effective. With respect to bivalent cations, Ca2+ and Mn2+ were more effective while Mg2+ was less important. From the antibiotics, penicillin caused a negative effect while streptomycin acted positively. Finally, glucose medium was found to be the most effective compared to all sugars tested. The results indicated that there are strong differentiations of the induced effects caused by each substance, and some possible mechanisms of action of these agents on the erythrocyte membrane were discussed.     

聚醚醚酮酮和含联苯聚醚醚酮酮共聚物的熔融热

根据Ｆｌｏｒｙ热力学统计理论和比容－熔融热作国法，由ＤＳＣ结果得到了不同联苯含量的聚醚醚酮酮－含联苯聚醚醚酮酮（ＰＥＥＫＫ－ＰＥＢＥＫＫ）共聚物的熔融热，两种方法获得的结果吻合。在此基础上给出了ＰＥＥＫＫ－ＰＥＢＥＫＫ共聚物不同联苯含量的熔点计算表达式。结果还表明，随着联苯含量ｎＢ，的变化，明显改变；当ｎＢ＝０．３５时，ＰＥＥＫＫＰＥＢＥＫＫ共聚物的值最小。     

An efficient fault-tolerant decentralized commit protocol for single site failure

To maintain consistency on a distributed database system, a commit protocol is often employed to ensure that either all the sub-transactions of a transaction commit or all abort. Special care needs to be taken to ensure the correct functioning of a commit protocol in the face of node failures during the execution of the protocol. A protocol is said to be fault-tolerant if it properly commits or aborts, even if nodes fail.In this paper, we present a fault tolerant decentralized commit protocol which is message optimal in the absence of failures. Furthermore, the protocol (FTDCP) ensures that all sites can achieve a consistent final decision by at most 4 extra messages in the single site failure situation.     

Monte Carlo simulations of down-scattered neutron and knock-on deuteron spectra in deuterium-tritium capsule implosions

A Monte Carlo particle tracking (MCPT) code has been developed and coupled to hydrodynamic simulations to generate and track primary and scattered neutrons in addition to scattered charged particles by post-processing. This code uses one dimensional (1-D) deuterium-tritium implosion profiles, and the computed down-scattered neutron and knock-on deuteron spectra are analyzed for different areal densities. The mixing effects on the spectra of down-scattered neutron and knock-on deuteron are also investigated. The implementation of the numerical scheme is analyzed, and the particle splitting technique is adopted, which is proven to efficiently reduce computational effort.