Schnyder decompositions for regular plane graphs and application to drawing

Schnyder woods are decompositions of simple triangulations into three edge-disjoint spanning trees crossing each other in a specific way. In this article, we define a generalization of Schnyder woods to $d$-angulations (plane graphs with faces of degree $d$) for all $d\geq 3$. A \emph{Schnyder decomposition} is a set of $d$ spanning forests crossing each other in a specific way, and such that each internal edge is part of exactly $d-2$ of the spanning forests. We show that a Schnyder decomposition exists if and only if the girth of the $d$-angulation is $d$. As in the case of Schnyder woods ($d=3$), there are alternative formulations in terms of orientations ("fractional" orientations when $d\geq 5$) and in terms of corner-labellings. Moreover, the set of Schnyder decompositions on a fixed $d$-angulation of girth $d$ is a distributive lattice. We also show that the structures dual to Schnyder decompositions (on $d$-regular plane graphs of mincut $d$ rooted at a vertex $v^*$) are decompositions into $d$ spanning trees rooted at $v^*$ such that each edge not incident to $v^*$ is used in opposite directions by two trees. Additionally, for even values of $d$, we show that a subclass of Schnyder decompositions, which are called even, enjoy additional properties that yield a reduced formulation; in the case d=4, these correspond to well-studied structures on simple quadrangulations (2-orientations and partitions into 2 spanning trees). In the case d=4, the dual of even Schnyder decompositions yields (planar) orthogonal and straight-line drawing algorithms. For a 4-regular plane graph $G$ of mincut 4 with $n$ vertices plus a marked vertex $v$, the vertices of $G\backslash v$ are placed on a $(n-1) \times (n-1)$ grid according to a permutation pattern, and in the orthogonal drawing each of the $2n-2$ edges of $G\backslash v$ has exactly one bend. Embedding also the marked vertex $v$ is doable at the cost of two additional rows and columns and 8 additional bends for the 4 edges incident to $v$. We propose a further compaction step for the drawing algorithm and show that the obtained grid-size is strongly concentrated around $25n/32\times 25n/32$ for a uniformly random instance with $n$ vertices

First principles analysis of lattice dynamics for Fe-based superconductors and entropically-stabilized phases

Modern ab initio calculations are becoming an essential, complementary tool to inelastic x-ray scattering studies, where x-rays are scattered inelastically to resolve meV phonons. Calculations of the inelastic structure factor for any value of Q assist in both planning the experiment and analyzing the results. Moreover, differences between the measured data and theoretical calculations help identify important new physics driving the properties of novel correlated systems. We have used such calculations to better and more efficiently measure the phonon dispersion and elastic constants of several iron pnictide superconductors. This dissertation describes calculations and measurements at room temperature in the tetragonal phase of CaFe2As2 and LaFeAsO. In both cases, spin-polarized calculations imposing the antiferromagnetic order present in the low-temperature orthorhombic phase dramatically improves the agreement between theory and experiment. This is discussed in terms of the strong antiferromagnetic correlations that are known to persist in the tetragonal phase. In addition, we discuss a relatively new approach called self-consistent ab initio lattice dynamics (SCAILD), which goes beyond the harmonic approximation to include phonon-phonon interactions and produce a temperature-dependent phonon dispersion. We used this technique to study the HCP to BCC transition in beryllium

Investigations of hexagonal boron nitride as a semiconductor for neutron detection

Master of ScienceDepartment of Mechanical and Nuclear EngineeringJeffrey GeutherWilliam L. DunnThe properties of hexagonal boron nitride (h-BN) as a semiconductor neutron detection medium were investigated. Single h-BN crystal domains were synthesized by the Chemical Engineering department at Kansas State University (KSU) using crystallization from molten metal solutions. At Texas Tech University (TTU), a detector was fabricated using epitaxial h-BN growth on a sapphire substrate where metallic micro-strip contacts 5 [mu]m apart and 5 nm thick where deposited onto the un-doped h-BN. In this research both the crystal domains synthesized at KSU and the detector fabricated at TTU were tested for neutron response. Neutron irradiation damage/effects were studied in pyrolytic h-BN by placing samples in the central thimble of the TRIGA MARK II reactor at KSU and irradiating at increasing neutron fluences. The domains synthesized at KSU as well as the detector fabricated at TTU showed no response to neutron activity on a MCA pulse height spectrum. Conductivity analysis showed abrupt increases in the conductivity of the pyrolytic h-BN at around a fluence of 10[superscript]1[superscript]4 neutrons per cm[superscript]2. Bandgap analysis by photoluminescence on the irradiated pyrolytic h-BN samples showed shifts in energy due to towards plane stacking disorders upon neutron irradiation. Future efforts may include the introduction of dopants in h-BN growth techniques for charge carrier transport improvement, and mitigation of plane stacking disorders

Effect of Some Medicinal Plants in U.A.E. on Glucose Homeostasis in Rats

Diabetes mellitus is one of the most common endocrine diseases in the world that affects almost 6% of the world population. The treatment of diabetes mellitus takes three main forms. First, diet and exercise. Secondly, insulin therapy, and thirdly, using hypoglycaemic agents (suiphonylureas and biguanides). Many of these agents are not very effective in lowering glucose level in diabetic patients and are either too expensive or have undesirable side effects and contraindications. As a result of this, the search for effective drugs for the treatment of diabetes mellitus continues. Before the introduction of insulin in 1922, the treatment of diabetes mellitus relied heavily on initiatives derived from folk medicine. These initiatives include the use of traditional plants therapies. Many traditional plants treatment for diabetes exist but few have received scientific or medical scrutiny. The use of traditional plants for the treatment of diabetes mellitus is widely practiced in the Middle East. In UAE many traditional plants are used as anti-diabetic remedies, such as the leaves of Rhaza stricta (Al Harmal), Tephrosia apollinea (Dhafra), Zygophyllum simplex (Al hirm), Moringa pere grEna (Shoo), Ziziphus spina-cristi (Al seder), Citrullus colocynthis (Handal) and Teucrium mascatense (Jaadah). In spite of the wide use of these herbs to treat diabetes, no laboratory investigations have been conducted to determine the accuracy of the claims about their anti-diabetic effects. The aim of this study was to examine the efficacy of these plants in the treatment of diabetes mellitus. The aqueous extracts of these plants were incubated with pancreatic fragments to determine whether they have the ability to stimulate insulin secretion. Aqueous extracts of Citrullus colocynthis, Zygophyllum simplex and Tephrosia Apollonia stimulated insulin secretion significantly in vitro. However, only Curullus culocynthis was able to stimulate insulin release in a consistent manner. The oral administration of aqueous extract of Citrullus colocynthis seeds was investigated for its effects on biochemical and metabolic parameters of normal and streptozotocin (STZ)-induced diabetes rats. The results of this study revealed that oral administration of the aqueous extract of the seed significantly reduced blood glucose levels in normal and diabetic rats in a dose-correlate manner. Moreover, aqueous extract of Chrullus colocynthis seeds increased plasma insulin level. In addition, C. colocynthis appeared to induce a significant increase in the number of insulin-secreting cells after induction of diabetes islets. There is strong indication that aqueous Citrullus colocynthis significantly decreased the percentage distribution of glucagon secreting cells. However, the treatments of aqueous extract of C. colocynthis did not completely normalize these parameters as the values were still significantly different from those of controls

Electrical properties of thin metal films

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