On the Collapse of Solutions of the Cauchy Problem for the Cubic Schrödinger Evolution Equation

It is proved that, for some initial data, the solutions of the Cauchy problem for the cubic Schrödinger evolution equation blow up in finite time whose exact value is estimated from above. In addition, lower bounds for the blow-up rate of the solution in certain norms are obtained.

     

On Equitable Colorings of Hypergraphs

Mathematical Notes - A two-coloring is said to be equitable if, on the one hand, there are no monochromatic edges (the coloring is regular) and, on the other hand, the cardinalities of color...     

Two weight commutators in the Dirichlet and Neumann Laplacian settings

In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian ${\mathrm{\Delta }}_{N_{+}}$ on the upper half space ${\mathbb{R}}_{+}^n$ and the reflection Neumann Laplacian ${\mathrm{\Delta }}_N$ on ${\mathbb{R}}^n$ with respect to the weights associated to ${\mathrm{\Delta }}_{N_{+}}$ and ${\mathrm{\Delta }}_N$ respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to ${\mathrm{\Delta }}_N$ is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on ${\mathbb{R}}^n$ and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt $A^p$ weights with $p\in (1,2]$ while the previously known related results cover only $p\in (1,\frac{n+1}{n}]$. We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian ${\mathrm{\Delta }}_{D_{+}}$ on ${\mathbb{R}}_{+}^n$.     

Continuum versus discrete networks,graph Laplacians,and reproducing kernel Hilbert spaces

Motivated by applications to machine learning, we construct a reversible and irreducible Markov chain whose state space is a certain collection of measurable sets of a chosen l.c.h. space $\mathfrak{X}$. We study the resulting network (connected undirected graph), including transience, Royden and Riesz decompositions, and kernel factorization. We describe a construction for Hilbert spaces of signed measures which comes equipped with a new notion of reproducing kernels and there is a unique solution to a regularized optimization problem involving the approximation of $L^2$ functions by functions of finite energy. The latter has applications to machine learning (for Markov random fields, for example).     

Effect of a Thermal-Vacuum Treatment and X-Ray Radiation on the Morphology and Electrical Properties of Titanium Oxide Nanocoatings

Russian Journal of Applied Chemistry - Effect of a simultaneous thermal treatment at 480°C and X-ray radiation (irradiation dose 10?3 C/kg (～4 R) in a vacuum (residual pressure...     

Chiral 7-Oxabicyclo[2.2.1]heptane Building Blocks for Prostanoids

Russian Journal of Organic Chemistry - Methyl (Z)-3-[(2R,3R,4S,5S)-5-(2-methoxy-2-oxoethyl)-3,4-(isopropylidenedioxy)tetrahydrofuran-2-yl]-prop-2-enoate was synthesized, and its intramolecular...     

MHD free convection heat transfer of a water–Fe3O4 nanofluid in a baffled C-shaped enclosure

Journal of Thermal Analysis and Calorimetry - In this paper, the effect of a baffle on free convection heat transfer of a water–Fe3O4 nanofluid in a C-shaped enclosure in the presence of a...     

Development of a New Chromogenic Reagent for the Detection of Organophosphorus Herbicide Glyphosate in Biological Samples

JPC – Journal of Planar Chromatography – Modern TLC - A novel chromogenic reagent was developed for the identification and detection of organophosphorus herbicide. The organophosphorus...     

A new dimeric alkylresorcinol from the stem barks of Swintonia floribunda (Anacardiaceae)

From an EtOAc-soluble fraction of the stem barks of Swintonia floribunda (Anacardiaceae), one new dimeric alkylresorcinol named integracin E (1), together with 4 known compounds (2–5) were isolated. Their chemical structures were elucidated based on the spectroscopic data interpretation. The absolute configuration of 1 was determined by the specific rotation analysis of its acid-catalyzed hydrolysis product. Compound 1 showed potent tyrosinase inhibitory activity with an IC₅₀ value of 48.2?μM.     

SIMS of organic layers with unknown matrix parameters: Locating the interface in dual beam argon gas cluster depth profiles

Four simple methods are evaluated to determine their accuracies for establishing the interface location in secondary ion mass spectrometry intensity depth profiles of organic layers where matrix effects have not been measured. Accurate location requires the separate measurement of each ion's matrix factor. This is often not possible, and so estimates using matrix-less methods are required. Six pure organic material interfaces are measured using many secondary ions to compare their locations from the four methods with those from full evaluation with matrix terms. For different secondary ions, matrix effects cause the apparent interface positions to vary over 20 nm. The shifts in the intensity profiles on going from a layer of P into a layer of Q are in the opposite direction to that for going from Q into P, so doubling layer thickness errors. The four methods are as follows: M1, use of the median interface position in the intensity profiles for the five lightest ions for 15 ≤ m/z ≤ 150; M2, extrapolation of the position for each ion to m/z = 0 for ions with m/z ≤ 150; M3, as M2 but for m/z ≤ 300; and M4, the extreme positions for all m/z ≤ 100. Comparison with the location using matrix terms shows their ranking, from best to worst, to be M4, M3, M1, and M2 with average errors of 10%, 12%, 14%, and 17%, respectively, of the profile interface full widths at half maximum. Use of pseudo-molecular ions is very much poorer, exceeding 50%, and should be avoided.