Two cosmological models with non-phantom matter having the same expansion of the universe as phantom cosmologies are constructed. The first model is characterized by the evolving gravitational “constant” G and a dark energy component with a non-conserved energy-momentum tensor. The second model includes two interacting components, the dark energy component and the matter component. Closed form ...

An edge coloring of a simple graph G is said to be proper rainbow-cycle-forbidding (PRCF, for short) if no two incident edges receive the same color and any cycle in G, at least that color. A defined PRCF-good it admits PRCF coloring, deemed PRCF-bad otherwise. In recent work, Hoffman, et al. study colorings find many examples graphs having girth less than or equal 4. They then ask whether such...

An analysis with a transferred hyperfine field has been performed on the spectra of $^{115}\mathrm{In}$ nuclear quadrupole resonance experiments heavy fermion superconductor ${\mathrm{Ce}}_{3}{\mathrm{PtIn}}_{11}$ exhibiting co-occurrence two successive antiferromagnetic orderings (${T}_{\mathrm{N}1}$ = 2.2 K and ${T}_{\mathrm{N}2}$ 2.0 K) followed by superconducting transition (${T}_{\mathrm{c...

The Gale-Hoffman lemma characterizes feasible external flow (supply, demand) in a directed, capacitated network in terms of a number of linear inequalities. These inequalities are generated by considering all node subsets and requiring that the external flow associated with each subset be less or equal to the total capacity of the arcs exiting :from it. For a particularly appealing statement of...

The n-th tensor power of a graph with vertex set V is the on n , where two vertices are connected by an edge if they in each coordinate. One powerful method for upper-bounding largest independent Hoffman bound, which gives upper bound terms its eigenvalues. In this paper we introduce problem sets powers hypergraphs. We show that many prominent open problems extremal combinatorics, such as Turán...

Abstract Katherine Hoffman is a biostatistician in the pulmonary and critical care team of New York City hospital, who found herself part Covid-19 response when outbreak first hit March 2020. This her story

Defect engineering plays an important role in tailoring the electronic transport properties of van der Waals materials. Methods reported so far mainly rely on $e\phantom{\rule{0}{0ex}}x\phantom{\rule{0.333em}{0ex}}s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u$ defect type and concentration, hindering realization new types device functionalities associated with engine...

background: the aim of this work was to establish how well gel dosimeters performed, as substitutes for brain tissue compared with standard phantom materials such as water, polymethyl-methacrylate (or pmma), a150 plastic and te- liquid phantom material for dosimetry of neutron beams in boron neutron capture therapy. materials and methods: thermal neutron fluence, photon dose and epithermal neut...

The $R(1)$, $R(3)$, and $P(3)$ rovibrational transitions in the (2-0) overtone band of HD molecule are measured Doppler-free saturation using technique NICE-OHMS spectroscopy. For line, hitherto not observed saturation, we report a frequency $203\phantom{\rule{0.16em}{0ex}}821\phantom{\rule{0.16em}{0ex}}936\phantom{\rule{0.16em}{0ex}}805\phantom{\rule{0.16em}{0ex}}(60)$ kHz. dispersive line sha...