Linear‐Time Algorithms for Scattering Number and Hamilton‐Connectivity of Interval Graphs

We prove that for all an interval graph is ‐Hamilton‐connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only if it contains a Hamilton cycle, as well as a characterization of interval graphs with positive scattering numbers in terms of the minimum size of a path cover. We also give an time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best‐known time bound for solving this problem. As a consequence of our two results, the maximum k for which an interval graph is k‐Hamilton‐connected can be computed in time.     

Photopolymer for Optical Holography and Holographic Interferometry

Summary: In our laboratory, we have continued in experimental study of acrylamide-based photopolymer recording material. Our exposition and detection setup was used for real-time measurements of a diffraction grating formation process. Based on the results of our measurements, the chemical composition of the material was modified to increase sensitivity, value of refractive index modulation and stability of the formed structure. Recently, the material has been successfully applied to holographic interferometry.     

Ring closure and rearrangement reactions of 4-azido-2-oxoquinoline-3-carboxylates and 4-azidocoumarin-3-carboxylates

4-Azido-2-oxoquinoline-3-carboxylates and 4-azidocoumarin-3-carboxylates 6 , which were obtained from the corresponding 4-hydroxy derivatives 1 via 4-tosylates 2 or 4-chloro compounds 4 , cyclized upon thermolysis to 3-alkoxyisoxazolo[4,3-c]quinolin-4(5H)-ones or the corresponding coumarins 8 , whereas at slightly higher temperatures a 3-O, 4-O-rearrangement took place to give the 4-alkoxy-isoxazolo[4,3-c]-quinolin-3-ones and the corresponding coumarins 9. The necessary reaction conditions could be obtained easily with the help of differential scanning calorimetry.     

Über einige Derivate des Methyläthylhydrochinon

Ohne Zusammenfassung     

Shortest single axioms for commutative moufang loops of exponent 3

In this note, we attempt to find all shortest single product axioms for commutative Moufang loops of exponent 3. These investigations were aided by the automated theorem-prover Prover9 and the model-generator Mace4.     

On the computational complexity of partial covers of Theta graphs

By use of elementary geometric arguments we prove the existence of a special integral solution of a certain system of linear equations. The existence of such a solution then yields the NP-hardness of the decision problem on the existence of locally injective homomorphisms to Theta graphs with three distinct odd path lengths.