Bergman subspaces and subkernels: Degenerate LpL^p mapping and zeroes

Regularity and irregularity of the Bergman projection on $L^p$ spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable $\gamma$. A surprising consequence of the analysis is that, whenever $\gamma$ is irrational, the Bergman projection is bounded only for $p=2$.Comment: 21 pages, 2 figure

The Bergman projection on fat Hartogs triangles: L^p boundedness

A class of pseudoconvex domains in $\mathbb{C}^{n}$ generalizing the Hartogs triangle is considered. The $L^p$ boundedness of the Bergman projection associated to these domains is established, for a restricted range of $p$ depending on the "fatness" of domains. This range of $p$ is shown to be sharp

A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs

The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)-S$ are colored white) such that $V(G)$ is turned black after finitely many applications of "the color-change rule": a white vertex is converted black if it is the only white neighbor of a black vertex. The \emph{strong metric dimension}, $sdim(G)$, of a graph $G$ is the minimum among cardinalities of all strong resolving sets: $W \subseteq V(G)$ is a \emph{strong resolving set} of $G$ if for any $u, v \in V(G)$, there exists an $x \in W$ such that either $u$ lies on an $x-v$ geodesic or $v$ lies on an $x-u$ geodesic. In this paper, we prove that $Z(G) \le sdim(G)+3r(G)$ for a connected graph $G$, where $r(G)$ is the cycle rank of $G$. Further, we prove the sharp bound $Z(G) \leq sdim(G)$ when $G$ is a tree or a unicyclic graph, and we characterize trees $T$ attaining $Z(T)=sdim(T)$. It is easy to see that $sdim(T+e)-sdim(T)$ can be arbitrarily large for a tree $T$; we prove that $sdim(T+e) \ge sdim(T)-2$ and show that the bound is sharp.Comment: 8 pages, 5 figure

Evolution of a Simulation Testbed into an Operational Tool

This paper describes the evolution over a 20-year period of the Future ATM (Air Traffic Management) Concepts Evaluation Tool (FACET) from a National Airspace System (NAS) based simulation testbed into an operational tool. FACET was developed as a testbed for assessing futuristic ATM concepts, e.g., automated conflict detection and resolution. NAS Constraint Evaluation and Notification Tool (NASCENT) is an application, within FACET, for alerting airspace users of inefficiencies in flight operations and advising time- and fuel-saving reroutes.It is currently in use at American Airlines Integrated Operations Center in Fort Worth, TX. The concepts assessed,research conducted, and the operational capability developed, along with the NASA support and achievements are presented in this paper

Projections onto LpL^p-Bergman spaces of Reinhardt Domains

For $1<p<\infty$, we emulate the Bergman projection on Reinhardt domains by using a Banach-space basis of $L^p$-Bergman space. The construction gives an integral kernel generalizing the ($L^2$) Bergman kernel. The operator defined by the kernel is shown to be absolutely bounded projection on the $L^p$-Bergman space on a class of domains where the $L^p$-boundedness of the Bergman projection fails for certain $p \neq 2$. As an application, we identify the duals of these $L^p$-Bergman spaces with weighted Bergman spaces.Comment: Final verson with typos fixed. To appear in Advances in Mathematic

Reducing Calorie Intake May Not Help You Lose Body Weight

Background Previously a meta-analysis found that multi-vitamin/mineral supplementation reduced mild psychiatric symptoms. To establish mechanisms, and to pin-point the individuals most likely to benefit, the role of various polymorphisms were examined. Supplementation was found to influence mild-psychiatric symptoms depending on the form of particular genes: genes that are risk factors for psychiatric disease and influence mechanisms by which drugs act. Methods In a double-blind trial young healthy males rated psychiatric symptoms, before and after taking vitamin/mineral supplements for three months, and the response was related to single nucleotide polymorphisms associated with catecholamines and serotonin. Outcomes With rs1800497 (Taq1A; dopamine D2 receptor), those with the CT allele benefitted from a vitamin/mineral supplement. Similarly with rs1800955 (DRD4 – dopamine D4 receptor), the mood of those with the CC allele benefitted selectively. With rs6296 (HTR1B) only those with the GC alleles responded, and with rs6311 (HTR2A) supplementation produced a beneficial response in those with the GG allele. With rs1050565 (5HTT gene - Human Serotonin Transporter gene) supplementation increased the mental health of those with the AA allele. Interpretation In a situation where a substantial proportion of patients do not benefit from drug therapy, and there is an element of trial and error when prescribing, it was proposed that future work should consider distinguishing patients depending on various polymorphisms and micro-nutrient status. In those with particular alleles, we should consider if drug administration and vitamin / mineral status interact synergistically to influence the therapeutic outcom