Existence of positive solutions of a superlinear boundary value problem with indefinite weight

We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change its sign. We assume that the function $g\colon\mathopen{[}0,+\infty\mathclose{[}\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, so as the case $g(s)=s^{p}$, with $p>1$, is covered. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.Comment: 12 pages, 4 PNG figure

PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics

In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x real. We will give a complete characterization of three different classes of operators associated with the differential expression H: The class of all self-adjoint (Hermitian) operators, the class of all PT symmetric operators and the class of all P-self-adjoint operators. Surprisingly, some of the PT symmetric operators associated to this expression have no resolvent set

Density-potential mappings in quantum dynamics

In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed point problem. This idea was used to generalize the existence and uniqueness theorems underlying time-dependent density functional theory. In this work we extend this proof to allow for more general norms and provide a numerical implementation of the fixed-point iteration scheme. We focus on the one-dimensional case as it allows for a more in-depth analysis using singular Sturm-Liouville theory and at the same time provides an easy visualization of the numerical applications in space and time. We give an explicit relation between the boundary conditions on the density and the convergence properties of the fixed-point procedure via the spectral properties of the associated Sturm-Liouville operator. We show precisely under which conditions discrete and continuous spectra arise and give explicit examples. These conditions are then used to show that in the most physically relevant cases the fixed point procedure converges. This is further demonstrated with an example.Comment: 20 pages, 8 figures, 3 table

High Li+ and Na+ Conductivity in New Hybrid Solid Electrolytes based on the Porous MIL-121 Metal Organic Framework

Solid-state electrolytes (SSEs) can leapfrog the development of all-solid-state batteries (ASSBs), enabling them to power electric vehicles and to store renewable energy from intermittent sources. Here, a new hybrid Li+ and Na+ conducting SSE based on the MIL-121 metal-organic framework (MOF) structure is reported. Following synthesis and activation of the MOF, the free carboxylic units along the 1D pores are functionalized with Li+ or Na+ ions by ion exchange. Ion dynamics are investigated by broadband impedance spectroscopy and by Li-7 and Na-23 NMR spin-lattice relaxation. A crossover at 50 degrees C (Li+) and at 10 degrees C (Na+) from correlated to almost uncorrelated motion at higher temperature is observed, which is in line with Ngai\u27s coupling model. Alternatively, in accordance to the jump relaxation model of Funke, at low temperature only a fraction of the jump processes are successful as lattice rearrangement in the direct vicinity of Li+ (Na+) is slow. H-1 NMR unambiguously shows that Li+ is the main charge carrier. Conductivities reach 0.1 mS cm(-1) (298 K, Na+) while the activation energies are 0.28 eV (Li+) and 0.36 eV (Na+). The findings pave the way towards development of easily tunable and rationally adjustable high-performance MOF-based hybrid SSEs for ASSBs

The Cerebrospinal Fluid in Multiple Sclerosis

Investigation of cerebrospinal fluid (CSF) in the diagnostic work-up in suspected multiple sclerosis (MS) patients has regained attention in the latest version of the diagnostic criteria due to its good diagnostic accuracy and increasing issues with misdiagnosis of MS based on over interpretation of neuroimaging results. The hallmark of MS-specific changes in CSF is the detection of oligoclonal bands (OCB) which occur in the vast majority of MS patients. Lack of OCB has a very high negative predictive value indicating a red flag during the diagnostic work-up, and alternative diagnoses should be considered in such patients. Additional molecules of CSF can help to support the diagnosis of MS, improve the differential diagnosis of MS subtypes and predict the course of the disease, thus selecting the optimal therapy for each patient

2-(4-(Biphenyl-4-ylamino)-6-chloropyrimidin-2-ylthio)octanoic acid (HZ52) - a novel type 5-lipoxygenase inhibitor with favorable molecular pharmacology and efficacy in vivo.

BACKGROUND AND PURPOSE: 5-Lipoxygenase (5-LO) is the key enzyme in the biosynthesis of pro-inflammatory leukotrienes (LTs) representing a potential target for pharmacological intervention with inflammation and allergic disorders. Although many LT synthesis inhibitors are effective in simple in vitro test systems, they frequently fail in vivo due to lack of efficacy. Here, we attempted to assess the pharmacological potential of the previously identified 5-LO inhibitor 2-(4-(biphenyl-4-ylamino)-6-chloropyrimidin-2-ylthio)octanoic acid (HZ52). EXPERIMENTAL APPROACH: We evaluated the efficacy of HZ52 in vivo using carrageenan-induced pleurisy in rats and platelet-activating factor (PAF)-induced lethal shock in mice. We also characterized 5-LO inhibition by HZ52 at the cellular and molecular level in comparison with other types of 5-LO inhibitor, that is, BWA4C, ZM230487 and hyperforin. KEY RESULTS: HZ52, 1.5 mg·kg⁻¹ i.p., prevented carrageenan-induced pleurisy accompanied by reduced LTB(4) levels and protected mice (10 mg·kg⁻¹, i.p.) against PAF-induced shock. Detailed analysis in cell-based and cell-free assays revealed that inhibition of 5-LO by HZ52 (i) does not depend on radical scavenging properties and is reversible; (ii) is not impaired by an increased peroxide tone or by elevated substrate concentrations; and (iii) is little affected by the cell stimulus or by phospholipids, glycerides, membranes or Ca²⁺. CONCLUSIONS AND IMPLICATIONS: HZ52 is a promising new type of 5-LO inhibitor with efficacy in vivo and with a favourable pharmacological profile. It possesses a unique 5-LO inhibitory mechanism different from classical 5-LO inhibitors and seemingly lacks the typical disadvantages of former classes of LT synthesis blockers

First-passage and first-exit times of a Bessel-like stochastic process

We study a stochastic process $X_t$ related to the Bessel and the Rayleigh processes, with various applications in physics, chemistry, biology, economics, finance and other fields. The stochastic differential equation is $dX_t = (nD/X_t) dt + \sqrt{2D} dW_t$, where $W_t$ is the Wiener process. Due to the singularity of the drift term for $X_t = 0$, different natures of boundary at the origin arise depending on the real parameter $n$: entrance, exit, and regular. For each of them we calculate analytically and numerically the probability density functions of first-passage times or first-exit times. Nontrivial behaviour is observed in the case of a regular boundary.Comment: 15 pages, 6 figures, submitted to Physical Review

Effects of Repeated Intrathecal Triamcinolone-Acetonide Application on Cerebrospinal Fluid Biomarkers of Axonal Damage and Glial Activity in Multiple Sclerosis Patients

Multiple sclerosis (MS) is the most common inflammatory disease of the central nervous system in young adults. Over time, the disease progresses and, with accumulating disability, symptoms such as spasticity may occur. Although several treatment options are available, some patients may not respond to first-line therapeutics. However, some of these patients may benefit from intrathecally administered triamcinolone-acetonide (TCA), a derivative of glucocorticosteroids (GCS).GCSmay have neurotoxic effects, and cell apoptosis may occur. The aim of this study was to investigate the effects of TCA on biomarkers in the cerebrospinal fluid (CSF) suggestive of neurodegeneration

Controlled Growth of a Line Defect in Graphene and Implications for Gate-Tunable Valley Filtering

Atomically precise tailoring of graphene can enable unusual transport pathways and new nanometer-scale functional devices. Here we describe a recipe for the controlled production of highly regular "5-5-8" line defects in graphene by means of simultaneous electron irradiation and Joule heating by applied electric current. High-resolution transmission electron microscopy reveals individual steps of the growth process. Extending earlier theoretical work suggesting valley-discriminating capabilities of a graphene 5-5-8 line defect, we perform first-principles calculations of transport and find a strong energy dependence of valley polarization of the charge carriers across the defect. These findings inspire us to propose a compact electrostatically gated "valley valve" device, a critical component for valleytronics