Some issues in blockchain for accounting and the supply chain,with an application of distributed databases to virtual organizations

This paper reviews some recent blockchain‐based applications for information capture, distribution and preservation. As part of that review, this paper examines two key concerns with current blockchain designs for accounting and supply chain transactions: data independence and multiple semantic models for the same information distribution problem. Blockchain applications typically integrate database, application and presentation tiers all in the same ledger. This results in a general inability to query information in the ledger and other concerns. Further, since most applications appear to be private blockchain applications, there is a concern of agents needing to accommodate multiple blockchains depending on who their trading partners are and what they request. Finally, this paper uses a distributed database to design a ‘blockchain‐like’ system for virtual organizations.     

A NOTE ON ARBITRAGE AND CLOSED CONVEX CONES

We give an example of a subspace K of     such that     , where     denotes the closure with respect to convergence in probablity. On the other hand, the cone   C ≔ K − L ^∞₊  is dense in   L ^∞  with respect to the weak-star topology  σ( L ^∞, L ¹)  . This example answers a question raised by I. Evstigneev. The topic is motivated by the relation of the notion of no arbitrage and the existence of martingale measures in Mathematical Finance.     

Sanov meets Cramér again

We introduce a new method for proving large-deviation principles (LDPs). This method amounts to "mixing" a collection of LDPs with a sequence of probability measures that obeys itself an LDP. As an illustration, we construct from empirical measures a sequence of capacity-valued maps that can be considered as an indexed collection of LDPs. The index 1 coincides with Sanov's theorem. By taking a Poisson mixture we establish a new connection with Cramér's theorem.     

The mean-variance investment problem in a constrained financial market

This paper extends the mean-variance analysis and the two-fund separation theorem to a market with some constraints, such as, the incompleteness, prohibition of short-selling, and partial information, with stochastic interest rate, and with stochastic volatility for risky assets. By maximizing a quadratic utility of terminal wealth, we show that the efficient frontier for the problem is a straight line in the mean-standard-deviation diagram. The quadratic utility function exhibits mean-variance efficiency. Our results apply to portfolios of claims in a single period, multiperiod, and continuous time.     

密绕载流无限长螺线管管外的磁场

对于密绕载流无限长螺线管,管外的磁场是否严格为零与管外磁场和管内磁场相比是否可以忽略不计,这是两个完全不同的问题。     

Conditioning as disintegration

Conditional probability distributions seem to have a bad reputation when it comes to rigorous treatment of conditioning. Technical arguments are published as manipulations of Radon–Nikodym derivatives, although we all secretly perform heuristic calculations using elementary definitions of conditional probabilities. In print, measurability and averaging properties substitute for intuitive ideas about random variables behaving like constants given particular conditioning information.
One way to engage in rigorous, guilt-free manipulation of conditional distributions is to treat them as disintegrating measures—families of probability measures concentrating on the level sets of a conditioning statistic. In this paper we present a little theory and a range of examples—from EM algorithms and the Neyman factorization, through Bayes theory and marginalization paradoxes—to suggest that disintegrations have both intuitive appeal and the rigor needed for many problems in mathematical statistics.     

Probability theory in fuzzy sample spaces

This paper tries to develop a neat and comprehensive probability theory for sample spaces where the events are fuzzy subsets of The investigations are focussed on the discussion how to equip those sample spaces with suitable -algebras and metrics. In the end we can point out a unified concept of random elements in the sample spaces under consideration which is linked with compatible metrics to express random errors. The result is supported by presenting a strong law of large numbers, a central limit theorem and a Glivenko-Cantelli theorem for these kinds of random elements, formulated simultaneously w.r.t. the selected metrics. As a by-product the line of reasoning, which is followed within the paper, enables us to generalize as well as to bring together already known results and concepts from literature.Acknowledgement. The author would like to thank the participants of the 23rd Linz Seminar on Fuzzy Set Theory for the intensive discussion of the paper. Especially he is indebted to Professors Diamond and Höhle whose remarks have helped to get deeper insights into the subject. Additionally, the author is grateful to one anonymous referee for careful reading and valuable proposals which have led to an improvement of the first draft.This paper was presented at the 23rd Linz Seminar on Fuzzy Set Theory, Linz, Austria, February 5–9, 2002.     

重心定理在进度控制中的运用

该文主要讲述重心定理的含义以及在进度控制中如何运用它来解决两个平行工序顺序化的问题，并用一个例子说明其步骤，最后给出三条结论。     

The equilibrium set of two-player games with complementarities is a sublattice

Summary. I prove that the equilibrium set in a two-player game with complementarities, and totally ordered strategy spaces, is a sublattice of the joint strategy space. Received: May 31, 2001; revised version: October 4, 2002