Mesh-free simulation of complex LCD geometries

We use a novel mesh-free simulation approach to study the post aligned bistable nematic (PABN) cell. By employing the Qian-Sheng formalism for liquid crystals along with a smooth representation of the surface posts, we have been able to identify two distinct stable configurations. The three-dimensional order field configurations of these states and their elastic free energies are consistent with both experimental results and previous simulation attempts. However, alternative states suggested in previous studies do not appear to remain stable when finite post curvature is considered.</p

Nucleosynthesis in O-Ne-Mg Supernovae

We have studied detailed nucleosynthesis in the shocked surface layers of an Oxygen-Neon-Magnesium core collapse supernova with an eye to determining if the conditions are suitable for r process nucleosynthesis. We find no such conditions in an unmodified model, but do find overproduction of N=50 nuclei (previously seen in early neutron-rich neutrino winds) in amounts that, if ejected, would pose serious problems for galactic chemical evolution.Comment: 12 pages, 1 figure, to be published in Astrophysical Journal Letter

Solution to a problem of Katona on counting cliques of weighted graphs

A subset $I$ of the vertex set $V(G)$ of a graph $G$ is called a $k$-clique independent set of $G$ if no $k$ vertices in $I$ form a $k$-clique of $G$. An independent set is a $2$-clique independent set. Let $\pi_k(G)$ denote the number of $k$-cliques of $G$. For a function $w: V(G) \rightarrow \{0, 1, 2, \dots\}$, let $G(w)$ be the graph obtained from $G$ by replacing each vertex $v$ by a $w(v)$-clique $K^v$ and making each vertex of $K^u$ adjacent to each vertex of $K^v$ for each edge $\{u,v\}$ of $G$. For an integer $m \geq 1$, consider any $w$ with $\sum_{v \in V(G)} w(v) = m$. For $U \subseteq V(G)$, we say that $w$ is uniform on $U$ if $w(v) = 0$ for each $v \in V(G) \setminus U$ and, for each $u \in U$, $w(u) = \left\lfloor m/|U| \right\rfloor$ or $w(u) = \left\lceil m/|U| \right\rceil$. Katona asked if $\pi_k(G(w))$ is smallest when $w$ is uniform on a largest $k$-clique independent set of $G$. He placed particular emphasis on the Sperner graph $B_n$, given by $V(B_n) = \{X \colon X \subseteq \{1, \dots, n\}\}$ and $E(B_n) = \{\{X,Y\} \colon X \subsetneq Y \in V(B_n)\}$. He provided an affirmative answer for $k = 2$ (and any $G$). We determine graphs for which the answer is negative for every $k \geq 3$. These include $B_n$ for $n \geq 2$. Generalizing Sperner's Theorem and a recent result of Qian, Engel and Xu, we show that $\pi_k(B_n(w))$ is smallest when $w$ is uniform on a largest independent set of $B_n$. We also show that the same holds for complete multipartite graphs and chordal graphs. We show that this is not true of every graph, using a deep result of Bohman on triangle-free graphs.Comment: 14 page

Corporate Philanthropy and Its Importance for the Competitiveness of Enterprises − a Review of Research

W literaturze pojawia się coraz więcej danych wskazujących, że filantropia korporacyjna przynosi takie korzyści, jak: wzrost sprzedaży i udziału w rynku, wzmacnianie pozycji marki, poprawa wizerunku, wzrost zdolności przyciągania, motywowania i zatrzymywania pracowników, spadek kosztów operacyjnych i wzrost przychodów, wzrost atrakcyjności dla inwestorów i analityków finansowych. W konsekwencji firmy zaangażowane w działania filantropijne dłużej utrzymują się na rynku i zwiększają swoją konkurencyjność. Artykuł prezentuje przegląd wybranych badań naukowych dotyczących tej problematyki.Monika Kwiecińsk

Retracted “Effect of Shensong Yangxin on heart failure in preserved ejection fraction rat model”

This article previously published in Volume 17 Issue 12 of this journal in December 2018 has been retracted in line with the guidelines&nbsp; from the Committee on Publication Ethics (COPE, http://publicationethics.org/resources/guidelines). Retraction: Zhang W, Sun Q, Chen H, Zhang Q. Effect of Shensong Yangxin on heart failure in preserved ejection fraction rat model. Trop J Pharm Res 2018;&nbsp; 17(12):2427-2432 doi: http://dx.doi.org/10.4314/tjpr.v17i12.17 To the editor:Many readers have written to me with questions about my article. We have found out that there was anomission in the experimental design hence some of the results could not be repeated. Therefore, wedecided that the paper should be retracted to avoid misleading the readers. Sincerely, Qian Sun. Keywords: Heart failure, Ejection fraction, Shensong Yangxi

Pulsar Velocity with Three-Neutrino Oscillations in Non-adiabatic Processes

We have studied the position dependence of neutrino energy on the Kusenko-Segr\`{e} mechanism as an explanation of the proper motion of pulsars. The mechanism is also examined in three-generation mixing of neutrinos and in a non-adiabatic case. The position dependence of neutrino energy requires the higher value of magnetic field such as $B\sim 3\times 10^{15}$ Gauss in order to explain the observed proper motion of pulsars. It is shown that possible non-adiabatic processes decrease the neutrino momentum asymmetry, whereas an excess of electron neutrino flux over other flavor neutrino fluxes increases the neutrino momentum asymmetry. It is also shown that a general treatment with all three neutrinos does not modify the result of the two generation treatment if the standard neutrino mass hierarchy is assumed.Comment: 8 pages, REVTEX, no figure