A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the maximum of the entropy is found.

Let G be a graph of order n. Let lpt(G) be the minimum cardinality of a set X of vertices of G such that X intersects every longest path of G and define lct(G) analogously for cycles instead of paths. We prove that • lpt(G) 6 ⌈

An aerobic Lactobacillus plantarum culture displayed growth stagnation during early growth. Transcriptome analysis revealed that resumption of growth after stagnation correlated with activation of CO(2)-producing pathways, suggesting that a limiting CO(2) concentration induced the stagnation. Analogously, increasing the CO(2) gas partial pressure during aerobic fermentation prevented the tempor...

The -calculus [1] adds explicit substitutions to the -calculus so as to provide a theoretical framework within which the implementation of functional programming languages can be studied. This paper generalises the -calculus to provide a linear calculus of explicit substitutions which analogously describes the implementation of linear functional programming languages.

For polynomial functors G, we show how to generalize the classical notion of regular expression to G-coalgebras. We introduce a language of expressions for describing elements of the final G-coalgebra and, analogously to Kleene’s theorem, we show the correspondence between expressions and finite G-coalgebras.

A vertex v of a graph G is domination null in G if g(v) = 0 for every minimum fractional dominating function g on G. Packing nullity is defined analogously, with reference to fractional closed neighborhood packings. We give classes of examples and examine graph operations that produce or preserve such vertices; several open problems are posed.

This work intends to be a generalization and a simplification oI me tecm~,~=~o employed in [2], by the proposal of a general strategy to prove satisfiability theorems for NLGM-s ( normal logics with graded modalities), analogously to the well known technique of the canonical models by Lemmon and Scott for classical modal logics.

We describe a class of monoids where c-rational languages can be deened analogously to trace theory and where these languages are precisely the recognizable ones. The proofs rely on Ramsey's theorem, distributive lattice theory and on Hashigushi's rank function generalized to our left divisibility monoids. We obtain Ochma nski's theorem on recognizable languages in free partially commutative mo...

In [11] and [12] (textbooks for teachers’ training colleges written by B. Pelle) isometry and similarity are defined not in the classical way but as a product. We continue this way of definition refer to the affine transformation and collineation, and study the fundamental theorems of these mappings analogously to those of isometry and similarity. AMS Classification Number: 00A35 (ZDM: G55, G59)

Patankar-type schemes are linearly implicit time integration methods designed to be unconditionally positivity-preserving. However, there only little results on their stability or robustness. We suggest two approaches analyze the performance and robustness of these methods. In particular, we demonstrate problematic behaviors that, even very simple linear problems, can lead undesired oscillation...