The paper presents a minimal proof theory which is adequate for proving the main important temporal properties of reactive programs. The properties we consider consist of the classes of invariance and response properties. For each of these classes we present a small set of rules that is complete for verifying properties belonging to this class. We illustrate the application of these rules on se...

This note considers the application of electronic cash to transactions in which many small amounts must be paid to the same payee and in which it is not possible to just pay the total amount afterwards. The most notable example of such a transaction is payment for phone calls. If currently published electronic cash systems are used and a full payment protocol is executed for each of the small a...

Let En ⊂ L 1 be the n-dimensional subspace which appeared in Kašin’s theorem such that L 1 = En ⊕E⊥ n and the L 1 and L 2 norms are universally equivalent on both En and E⊥ n . In this paper, we introduce and study some properties concerning extension and weak Grothendieck’s theorem (WGT). We show that the Schatten space Sp for all 0 < p ≤ ∞ does not verify the theorem of extension. We prove al...

This paper focuses on the design and implementation of a multivariate matrix to evaluate courses verifying compatibility with Tyler's principles within Bloom's criteria. By combining these two constructs, a matrix can be constructed which will provide both a means of evaluating the completeness of a course curriculum unit and a basis for comparing distance-learning curriculum units with their t...

This paper summarizes the first results on interferometric ENVISAT/ ASAR image mode products [1]. We analyzed timing and geometric accuracy as well as the phase of a first interferogram from an IS2 image mode data set (VV polarized). According to the schedule the image mode products of this beam products are the first to be validated [2]. This interferogram is one of the first ENVISAT/ ASAR int...

We describe theorems and computational methods for verifying the Birch and Swinnerton-Dyer conjectural formula for specific elliptic curves over Q of analytic ranks 0 and 1. We apply our techniques to show that if E is a non-CM elliptic curve over Q of conductor ≤ 1000 and rank 0 or 1, then the Birch and Swinnerton-Dyer conjectural formula for the leading coefficient of the L-series is true for...

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