On the growth of solutions of some higher order linear differential equations with entire coefficients

In this paper, we investigate the order and the hyper-order of entire solutions of the linear differential equation \begin{equation*} f^{\left( k\right) }+\left( D_{k-1}+B_{k-1}e^{b_{k-1}z}\right) f^{\left(k-1\right) }+ ... +\left( D_{1}+B_{1}e^{b_{1}z}\right) f^{\prime }+\left( D_{0}+A_{1}e^{a_{1}z}+A_{2}e^{a_{2}z}\right) f=0 \end{equation*} where $A_{j}\left( z\right)$ $\left( \not\equiv 0\right)$ $(j=1,2)$, $B_{l}\left( z\right)$ $\left( \not\equiv 0\right)$ $(l=1,...,k-1)$, $D_{m}$ $(m=0,...,k-1)$ are entire functions with $\max \{\sigma \left( A_{j}\right), \sigma \left( B_{l}\right), \sigma \left( D_{m}\right) \}<1$, $a_{1}$, $a_{2}$, $b_{l}$ $(l=1,...,k-1)$ are complex numbers. Under some conditions, we prove that every solution $f\left( z\right) \not\equiv 0$ of the above equation is of infinite order and with hyper-order 1

Energy usage and temperature distribution in old mega factories

Global environmental problems and the rising cost of energy puts industries under pressure to reduce energy consumption and lower their carbon footprint. Old “mega factories” use a lot of energy to maintain the production and working environment in an optimal condition when compared to newer factories. Heating cost can amount to more than 26% of the annual utility bill despite the mild climate of the United Kingdom. Intelligent cost reduction solutions, suitable management strategies and contemporary low carbon policies can significantly reduce this energy consumption without incorporating the latest and expensive technical solutions. Extensive research was carried out at a manufacturing plant with large old buildings to investigate multifarious solutions of low cost energy saving methods. Environmental plant data was obtained and analysed to understand thermal characteristics of the factory space. Non-uniform temperature distribution, consistently high average temperatures and an unstable machine environment all contributed to unnecessary expenses. Cost effective implementations, such as secure high speed doors, management strategies and employee awareness, consistent temperature monitoring and communication can create more uniform temperature distribution for a more stable working and manufacturing environment. The average temperature within this plant could be reduced by adequate measures and the comfort for employees and the machinery environment could be simultaneously improved to guarantee smoother operations and lower carbon footprint

Scanned Potential Microscopy of Edge and Bulk Currents in the Quantum Hall Regime

Using an atomic force microscope as a local voltmeter, we measure the Hall voltage profile in a 2D electron gas in the quantum Hall (QH) regime. We observe a linear profile in the bulk of the sample in the transition regions between QH plateaus and a distinctly nonlinear profile on the plateaus. In addition, localized voltage drops are observed at the sample edges in the transition regions. We interpret these results in terms of theories of edge and bulk currents in the QH regime.Comment: 4 pages, 5 figure

Nanostructured Al-ZnO/CdSe/Cu2O ETA solar cells on Al-ZnO film/quartz glass templates

The quartz/Al-ZnO film/nanostructured Al-ZnO/CdSe/Cu2O extremely thin absorber solar cell has been successfully realized. The Al-doped ZnO one-dimensional nanostructures on quartz templates covered by a sputtering Al-doped ZnO film was used as the n-type electrode. A 19- to 35-nm-thin layer of CdSe absorber was deposited by radio frequency magnetron sputtering, coating the ZnO nanostructures. The voids between the Al-ZnO/CdSe nanostructures were filled with p-type Cu2O, and therefore, the entire assembly formed a p-i-n junction. The cell shows the energy conversion efficiency as high as 3.16%, which is an interesting option for developing new solar cell devices

The importance of parameter choice in modelling dynamics of the eye lens

The lens provides refractive power to the eye and is capable of altering ocular focus in response to visual demand. This capacity diminishes with age. Current biomedical technologies, which seek to design an implant lens capable of replicating the function of the biological lens, are unable as yet to provide such an implant with the requisite optical quality or ability to change the focussing power of the eye. This is because the mechanism of altering focus, termed accommodation, is not fully understood and seemingly conflicting theories require experimental support which is difficult to obtain from the living eye. This investigation presents finite element models of the eye lens based on data from human lenses aged 16 and 35 years that consider the influence of various modelling parameters, including material properties, a wide range of angles of force application and capsular thickness. Results from axisymmetric models show that the anterior and posterior zonules may have a greater impact on shape change than the equatorial zonule and that choice of capsular thickness values can influence the results from modelled simulations

Molecular Biomarkers of Vascular Dysfunction in Obstructive Sleep Apnea

Untreated and long-lasting obstructive sleep apnea (OSA) may lead to important vascular abnormalities, including endothelial cell (EC) dysfunction, hypertension, and atherosclerosis. We observed a correlation between microcirculatory reactivity and endothelium-dependent release of nitric oxide in OSA patients. Therefore, we hypothesized that OSA affects (micro)vasculature and we aimed to identify vascular gene targets of OSA that could possibly serve as reliable biomarkers of severity of the disease and possibly of vascular risk. Using quantitative RT-PCR, we evaluated gene expression in skin biopsies of OSA patients, mouse aortas from animals exposed to 4-week intermittent hypoxia (IH; rapid oscillations in oxygen desaturation and reoxygenation), and human dermal microvascular (HMVEC) and coronary artery endothelial cells (HCAEC) cultured under IH. We demonstrate a significant upregulation of endothelial nitric oxide synthase (eNOS), tumor necrosis factor-alpha-induced protein 3 (TNFAIP3; A20), hypoxia-inducible factor 1 alpha (HIF-1α?? and vascular endothelial growth factor (VEGF) expression in skin biopsies obtained from OSA patients with severe nocturnal hypoxemia (nadir saturated oxygen levels [SaO2]<75%) compared to mildly hypoxemic OSA patients (SaO2 75%–90%) and a significant upregulation of vascular cell adhesion molecule 1 (VCAM-1) expression compared to control subjects. Gene expression profile in aortas of mice exposed to IH demonstrated a significant upregulation of eNOS and VEGF. In an in vitro model of OSA, IH increased expression of A20 and decreased eNOS and HIF-1α expression in HMVEC, while increased A20, VCAM-1 and HIF-1αexpression in HCAEC, indicating that EC in culture originating from distinct vascular beds respond differently to IH stress. We conclude that gene expression profiles in skin of OSA patients may correlate with disease severity and, if validated by further studies, could possibly predict vascular risk in OSA patients

Post translational changes to α-synuclein control iron and dopamine trafficking : a concept for neuron vulnerability in Parkinson's disease

Parkinson's disease is a multifactorial neurodegenerative disorder, the aetiology of which remains elusive. The primary clinical feature of progressively impaired motor control is caused by a loss of midbrain substantia nigra dopamine neurons that have a high α-synuclein (α-syn) and iron content. α-Syn is a neuronal protein that is highly modified post-translationally and central to the Lewy body neuropathology of the disease. This review provides an overview of findings on the role post translational modifications to α-syn have in membrane binding and intracellular vesicle trafficking. Furthermore, we propose a concept in which acetylation and phosphorylation of α-syn modulate endocytic import of iron and vesicle transport of dopamine during normal physiology. Disregulated phosphorylation and oxidation of α-syn mediate iron and dopamine dependent oxidative stress through impaired cellular location and increase propensity for α-syn aggregation. The proposition highlights a connection between α-syn, iron and dopamine, three pathological components associated with disease progression in sporadic Parkinson's disease