Let B be a Borel set in E with volume V (B) = ∞. It is shown that almost all lattices L in E contain infinitely many pairwise disjoint d-tuples, that is sets of d linearly independent points in B. A consequence of this result is the following: let S be a star body in E with V (S) = ∞. Then for almost all lattices L in E the successive minima λ1(S,L), . . . , λd(S,L) of S with respect to L are 0...

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space.

We consider isotropic non lower semicontinuous weighted perimeter functionals defined on partitions of domains in R. Besides identifying a condition on the structure of the domain which ensures the existence of minimizing configurations, we describe the structure of such minima, as well as their regularity.

Recently, on-line adaptation of binary classifiers for tracking have been investigated. On-line learning allows for simple classifiers since only the current view of the object from its surrounding background needs to be discriminiated. However, on-line adaption faces one key problem: Each update of the tracker may introduce an error which, finally, can lead to tracking failure (drifting). The ...

It is commonly accepted that tree form has an impact on the productivity of single-grip harvesters. However, it remains unclear, which elements of tree form are significant and to what degree they impact harvesting productivity. This is of particular importance in hardwood dominated stands, where hardwood trees often exhibit complex and variable stem and crown architecture that can complicate a...

This article discusses the relationship between mathematical proof and the digital computer from the viewpoint of the 'sociology of proof': that is, an understanding of what kinds of procedures and arguments count for whom, under what circumstances, as proofs. After describing briefly the first instance of litigation focusing on the nature of mathematical proof, the article describes a variety ...

We propose a practical verification framework for preemptive OS kernels. The framework models the correctness of API implementations in OS kernels as contextual refinement of their abstract specifications. It provides a specification language for defining the high-level abstract model of OS kernels, a program logic for refinement verification of concurrent kernel code with multi-level hardware ...

Fine grain products are harvested in two manual and mechanized forms. Nowadays, common combine harvesters are used, but fine grain products such as Rapeseed, Sesame and Sorghum cannot be harvested with conventional heads of combine harvesters due to the excessive grain loss in the head of the combine. Therefore, the necessity of design and fabricating machines and heads of combine harvesters be...

Using separation logic, this paper presents three Hoare logics (corresponding to different notions of correctness) for the simple While language extended with commands for heap access and modification. Properties of separating conjunction and separating implication are mechanically verified and used to prove soundness and relative completeness of all three Hoare logics. The whole development, i...

(51) We apply 8I to (51) and prove (49). P and t are deened inductively over the structure of sequent trees. In the base case, we have P and t such that (47) is 8x (T(x) T(x)). Consider now the step case. We write (47) in the following form. (52) where P x 1 ; :::; x n ] does not contain occurrences of T. We assume the hypotheses of (52) and derive Tac(x 1) ^ ::: ^ Tac(x m). From (29) we obtain...