Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields

We study the arithmetic of Eisenstein cohomology classes (in the sense of G. Harder) for symmetric spaces associated to GL_2 over imaginary quadratic fields. We prove in many cases a lower bound on their denominator in terms of a special L-value of a Hecke character providing evidence for a conjecture of Harder that the denominator is given by this L-value. We also prove under some additional assumptions that the restriction of the classes to the boundary of the Borel-Serre compactification of the spaces is integral. Such classes are interesting for their use in congruences with cuspidal classes to prove connections between the special L-value and the size of the Selmer group of the Hecke character.Comment: 37 pages; strengthened integrality result (Proposition 16), corrected statement of Theorem 3, and revised introductio

Combination of pulsed laser ablation and inert gas condensation for the synthesis of nanostructured nanocrystalline, amorphous and composite materials

A new instrument combining pulsed laser ablation and inert gas condensation for the production of nanopowders is presented. It is shown that various nanostructured materials, such as regular metallic, semiconducting, insulating materials, complex high entropy alloys, amorphous alloys, composites and oxides can be synthesized. The unique variability of the experimental set-up is possible due to the reproducible control of laser power (pulse energy and repetition rate), laser ablation pattern on the target, and experimental conditions during the inert gas condensation, all of which can be controlled and optimized independently. Microstructure analysis of the as-prepared composite and amorphous Ni(60)Nb(40) nanopowders establishes the instrument's ability for the synthesis of materials with unique compositions and atomic structure. It is further shown that small variations of the synthesis parameters can influence materials properties of the final product, in terms of particle size, composition and properties. As an example, the laser power has been used to control the magnetic properties of amorphous Ni(60)Nb(40) nanopowders. A few selected examples of the manifold possibilities of the new synthesis apparatus are presented in this report together with detailed structural characterization of the produced nanopowders

Total Roman {2}-domination in graphs

[EN] Given a graph G = (V, E), a function f: V -> {0, 1, 2} is a total Roman {2}-dominating function if every vertex v is an element of V for which f (v) = 0 satisfies that n-ary sumation (u)(is an element of N (v)) f (v) >= 2, where N (v) represents the open neighborhood of v, and every vertex x is an element of V for which f (x) >= 1 is adjacent to at least one vertex y is an element of V such that f (y) >= 1. The weight of the function f is defined as omega(f ) = n-ary sumation (v)(is an element of V) f (v). The total Roman {2}-domination number, denoted by gamma(t)({R2})(G), is the minimum weight among all total Roman {2}-dominating functions on G. In this article we introduce the concepts above and begin the study of its combinatorial and computational properties. For instance, we give several closed relationships between this parameter and other domination related parameters in graphs. In addition, we prove that the complexity of computing the value gamma(t)({R2})(G) is NP-hard, even when restricted to bipartite or chordal graphsCabrera García, S.; Cabrera Martinez, A.; Hernandez Mira, FA.; Yero, IG. (2021). Total Roman {2}-domination in graphs. Quaestiones Mathematicae. 44(3):411-444. https://doi.org/10.2989/16073606.2019.1695230S41144444

Cobalt and zinc halide complexes of 4-chloro and 4-methylaniline : syntheses, structures and magnetic behavior

Please read abstract in the article.The Carlson School of Chemistry and Biochemistry, Clark University and the Department of Chemistry, Brandeis University. F. X. would like to acknowledge the funding from the European Union's Horizon 2020 research and innovation program under the Marie Skodowska-Curie grant agreement No 701647.http://www.elsevier.com/locate/poly2020-08-01hj2019Chemistr