A numerical study of Penrose-like inequalities in a family of axially symmetric initial data

Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a stationarity state. In this setting, it follows that the minimal area containing an apparent horizon is bound by the square of the total ADM mass (Penrose inequality conjecture). Following Dain et al. 2002, we construct numerically a family of axisymmetric initial data with one or several marginally trapped surfaces. Penrose and related geometric inequalities are discused for these data. As a by-product, it is shown how Penrose inequality can be used as a diagnosis for an apparent horizon finder numerical routine.Comment: Contribution to the "Encuentros Relativistas Espanoles - Spanish Relativity Meeting ERE07" Proceedings, Tenerife, Spain (September 2007

A new quasi-exactly solvable problem and its connection with an anharmonic oscillator

The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator had been investigated by methods of KS transformation

Global Solution to the Three-Dimensional Incompressible Flow of Liquid Crystals

The equations for the three-dimensional incompressible flow of liquid crystals are considered in a smooth bounded domain. The existence and uniqueness of the global strong solution with small initial data are established. It is also proved that when the strong solution exists, all the global weak solutions constructed in [16] must be equal to the unique strong solution

Ensileability of alfalfa: cutting, maturity and treatment effects

Analysis of ensiling characteristics from late-bud, 10% bloom, and 50% bloom alfalfa, taken within each of four cuttings identified higher pre-ensiled dry matter (DM) content during the first two cuttings, whereas crop buffer capacity was weakest during the third cutting and subsequently strongest throughout the fourth cutting. Initial pH was lowest at the first cutting and increased with each cutting thereafter. Dry matter increased linearly within maturity, whereas late-bud maturity had the highest buffer capacity and initial pH. From hr 24 until d 90, the pH values were consistently highest for late-bud and lowest for 50% bloom silage. 1featments receiving 2% dextrose showed a slightly higher DM. At each of seven laboratory silo opening times, a combination of added dextrose and a lactic acid bacteria inoculant yielded the lowest pH; inoculant alone gave the next lowest pH values through hr 48. From d 3 to 90, pH\u27s were consistently highest for control silages, followed by inoculant. dextrose, and dextrose + inoculant combined

Kinetic Parameters Evaluation for Isoprene Mixed with Aluminum Oxide

AbstractWe analyzed the basic hazard characteristics for isoprene in the manufacturing process by evaluating the runaway reaction, kinetic parameters and safety parameters in this study. Experiments were carried out by calculating the thermal decomposition reactions for isoprene and mixed with aluminum oxide in non-isothermal conditions by differential scanning calorimetry (DSC). Afterwards results indicated that isoprene had a conjugated double bond of unstable structure, and therefore it was prone to produce exothermic reaction during the process of polymerization. Aluminum oxide was applied to mix with isoprene, which could increase the heat release rate. Based on the results, safety information should be provided to government and relevant industries for prevention the accident occur in relevant plants

Quadratic alpha' corrections to T-duality

The quadratic alpha' corrections to the two-dimensional black hole and to its T-dual are calculated. These backgrounds are used to write the covariant form of the quadratic alpha' corrections to the T-duality for general time-dependent backgrounds of dilaton and diagonal metric in the bosonic string theory.Comment: 15 pages, JHEP; typos corrected, references adde

Blow up criterion for compressible nematic liquid crystal flows in dimension three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of gradient of liquid crystal director field.Comment: 22 page

Epitope recognition of peptide-imprinted polymers for Regenerating protein 1 (REG1)

Molecularly imprinted polymers (MIPs) were developed to replace natural antibodies with a cost-effective and durable synthetic material. Molecular imprinting of proteins conventionally utilizes the whole protein as the template, which is complex (as many different epitopes may be imprinted) and expensive. In this work, seven peptides (13–18 amino acids) were synthesized and used as templates for the imprinting and recognition of Regenerating Protein 1 (REG1). REG1 is involved in the proliferation and differentiation of diverse cell types, and was recently described as a urinary biomarker for pancreatic ductal adenocarcinoma (PDAC). Peptide-imprinted poly(ethylene-co-vinyl alcohol)s (PIPs), containing four different mole fractions of ethylene were cast on screen-printed electrodes to find the optimum composition for both the sensing and the extraction of REG1 in an E. coli culture medium. Peptides with fewer than 16 amino acids and two or three aromatic and hydrophobic groups have a higher affinity for MIPs of poly(ethylene-co-vinyl alcohol) (EVAL) with 27 mol% of ethylene, while those with four aromatic and hydrophobic groups have a higher affinity for MIPs with EVALs that contain 32 mol% of ethylene. The peptide / EVAL combination that maximized both imprinting effectiveness and response to REG1B was the sequence NEDRETWVDADLY imprinted into 32 mol% EVAL. This EVAL composition and template peptide were then modified by incorporation of magnetic nanoparticles, thus extending applications for PIPs to include extraction of REG1 protein from E. coli culture medium

Mapping QTL for sex and growth traits in Salt-Tolerant Tilapia (Oreochromis spp. X O. mossambicus)

In aquaculture, growth and sex are economically important traits. To accelerate genetic improvement in increasing growth in salt-tolerant tilapia, we conducted QTL mapping for growth traits and sex with an F2 family, including 522 offspring and two parents. We used 144 polymorphic microsatellites evenly covering the genome of tilapia to genotype the family. QTL analyses were carried out using interval mapping for all individuals, males and females in the family, respectively. Using all individuals, three suggestive QTL for body weight, body length and body thickness respectively were detected in LG20, LG22 and LG12 and explained 2.4% to 3.1% of phenotypic variance (PV). When considering only males, five QTL for body weight were detected on five LGs, and explained 4.1 to 6.3% of PV. Using only females from the F2 family, three QTL for body weight were detected on LG1, LG6 and LG8, and explained 7.9–14.3% of PV. The QTL for body weight in males and females were located in different LGs, suggesting that in salt-tolerant tilapia, different set of genes ‘switches’ control the growth in males and females. QTL for sex were mapped on LG1 and LG22, indicating multigene sex determination in the salt-tolerant tilapia. This study provides new insights on the locations and effects of QTL for growth traits and sex, and sets the foundation for fine mapping for future marker-assisted selection for growth and sex in salt-tolerant tilapia aquaculture

Landau-De Gennes theory of nematic liquid\ud crystals: the Oseen-Frank limit and beyond

We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W 1,2 , to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer.\ud \ud \ud We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions