Multiple fixed-sign solutions for a system of generalized right focal problems with deviating arguments

AbstractWe consider the following system of generalized right focal boundary value problemsui‴(t)=fi(t,u1(ϕ1(t)),u2(ϕ2(t)),…,un(ϕn(t))),t∈[a,b],ui(a)=ui′(t∗)=0,ξui(b)+δui″(b)=0,1⩽i⩽n, where 12(a+b)<t∗<b, ξ⩾0, δ>0 and ϕi, 1⩽i⩽n are deviating arguments. By using different fixed point theorems, we develop several criteria for the existence of three solutions of the system which are of fixed sign on the interval [a,b], i.e., for each 1⩽i⩽n, θiui(t)⩾0 for all t∈[a,b] and fixed θi∈{1,−1}. Examples are also included to illustrate the results obtained

Positive Solutions of Two-point right focal boundary value problems on time scales

AbstractWe consider the following boundary value problem,(−1)n−1yΔn(t)=(−1)p+1F(t,y(σn−1(t))),t∈[a,b]∩T,yΔi(a)=0,0≤i≤p−1,yΔi(σ(b))=0,p≤i≤n−1,where n ≥ 2, 1 ⩽ p ⩽ n - 1 is fixed and T is a time scale. Criteria for the existence of single, double, and multiple positive solutions of the boundary value problem are developed. Upper and lower bounds for these positive solutions are established for two special cases that arise from some physical phenomena. We also include several examples to illustrate the usefulness of the results obtained

General Lidstone Problems: Multiplicity and Symmetry of Solutions

AbstractFor the 2mth order Lidstone boundary value problem,y(2m)t=fyt,y″t,…,y(2i)t,…,y(2(m−1))t,t∈0,1, y(2i)0=y(2i)1=0,0≤i≤m−1, where (−1)mf: Rm→[0,$thinsp;∞) is continuous, growth conditions are imposed on f which yield the existence of at least three symmetric positive solutions. This generalizes earlier papers which have applied Avery's generalization of the Leggett–Williams theorem to Lidstone problems. We then prove the analogous result for difference equations

Global incidence and mortality for prostate cancer: analysis of temporal patterns and trends in 36 countries

Background: Prostate cancer (PCa) is a leading cause of mortality and morbidity globally, but its specific geographic patterns and temporal trends are under-researched. Objective: To test the hypotheses that PCa incidence is higher and PCa mortality is lower in countries with higher socioeconomic development, and that temporal trends for PCa incidence have increased while mortality has decreased over time. Design, setting, and participants: Data on age-standardized incidence and mortality rates in 2012 were retrieved from the GLOBOCAN database. Temporal patterns were assessed for 36 countries using data obtained from Cancer incidence in five continents volumes I–X and the World Health Organization mortality database. Correlations between incidence or mortality rates and socioeconomic indicators (human development index [HDI] and gross domestic product [GDP]) were evaluated. Outcome measurements and statistical analysis: The average annual percent change in PCa incidence and mortality in the most recent 10 yr according to join-point regression. Results and limitations: Reported PCa incidence rates varied more than 25-fold worldwide in 2012, with the highest incidence rates observed in Micronesia/Polynesia, the USA, and European countries. Mortality rates paralleled the incidence rates except for Africa, where PCa mortality rates were the highest. Countries with higher HDI (r = 0.58) and per capita GDP (r = 0.62) reported greater incidence rates. According to the most recent 10-yr temporal data available, most countries experienced increases in incidence, with sharp rises in incidence rates in Asia and Northern and Western Europe. A substantial reduction in mortality rates was reported in most countries, except in some Asian countries and Eastern Europe, where mortality increased. Data in regional registries could be underestimated. Conclusions: PCa incidence has increased while PCa mortality has decreased in most countries. The reported incidence was higher in countries with higher socioeconomic development. Patient summary: The incidence of prostate cancer has shown high variations geographically and over time, with smaller variations in mortality

Global Incidence and mortality of oesophageal cancer and their correlation with socioeconomic indicators temporal patterns and trends in 41 countries

Oesophageal cancers (adenocarcinomas [AC] and squamous cell carcinomas [SCC]) are characterized by high incidence/mortality in many countries. We aimed to delineate its global incidence and mortality, and studied whether socioeconomic development and its incidence rate were correlated. The age-standardized rates (ASRs) of incidence and mortality of this medical condition in 2012 for 184 nations from the GLOBOCAN database; national databases capturing incidence rates, and the WHO mortality database were examined. Their correlations with two indicators of socioeconomic development were evaluated. Joinpoint regression analysis was used to generate trends. The ratio between the ASR of AC and SCC was strongly correlated with HDI (r = 0.535 [men]; r = 0.661 [women]) and GDP (r = 0.594 [men]; r = 0.550 [women], both p &lt; 0.001). Countries that reported the largest reduction in incidence in male included Poland (Average Annual Percent Change [AAPC] = −7.1, 95%C.I. = −12,−1.9) and Singapore (AAPC = −5.8, 95%C.I. = −9.5,−1.9), whereas for women the greatest decline was seen in Singapore (AAPC = −12.3, 95%C.I. = −17.3,−6.9) and China (AAPC = −5.6, 95%C.I. = −7.6,−3.4). The Philippines (AAPC = 4.3, 95%C.I. = 2,6.6) and Bulgaria (AAPC = 2.8, 95%C.I. = 0.5,5.1) had a significant mortality increase in men; whilst Columbia (AAPC = −6.1, 95%C.I. = −7.5,−4.6) and Slovenia (AAPC = −4.6, 95%C.I. = −7.9,−1.3) reported mortality decline in women. These findings inform individuals at increased risk for primary prevention

Acute Encephalopathy Associated with Influenza A Infection in Adults

We report acute encephalopathy associated with influenza A infection in 3 adults. We detected high cerebrospinal fluid (CSF) and plasma concentrations of CXCL8/IL-8 and CCL2/MCP-1 (CSF/plasma ratios >3), and interleukin-6, CXCL10/IP-10, but no evidence of viral neuroinvasion. Patients recovered without sequelae. Hyperactivated cytokine response may play a role in pathogenesis

Genotype Distribution and Sequence Variation of Hepatitis E Virus, Hong Kong

Most acute cases of infection with hepatitis E virus (HEV) in Hong Kong were autochthonous, sporadic, and occurred in older adults. All except 1 isolate belonged to genotype 4; most were phylogenetically related to swine isolates. The epidemiology is similar to that in industrialized countries, where zoonosis is the major source of HEV infection in humans

New exact solution of Dirac-Coulomb equation with exact boundary condition

It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z > 137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.Comment: 12 pages,no figure

Effect of surface pretreatments on the adherence of porcelain enamel to a type 316L stainless steel

Porcelain enameled 316L stainless steel with different surface pretreatments was produced by a slurry-fusion technique for evaluation of the enamel/steel adherence using an electrical conductivity meter. From the measured results, it is found that the adherence of the porcelain enamel to the steel depends on the roughness of the enamel-steel interface, which, in turn, is controlled by surface pretreatments of the steel substrates. The difference in the adherence of the enameled steel can be explained from an examination of the microstructure of enamel-steel interfaces by scanning electron microscopy. Good adherence is associated with those specimens that have a long enamel-steel interface contour, i.e., rough interfaces. In addition, X-ray diffraction analysis of the delaminated enamel fragments upon impact deformation reveals that failure of the enamel coatings in an oxidized steel occurred at the oxide-steel interface which is supposed to have strong chemical bonding, and that the oxide scales present before enameling are partially dissolved in the enamel during firing. The difference in the coefficients of thermal expansion among enamel, oxide, and steel is likely to play an important role in determining the failure mode of the enameled stainless steel. In summary, these results suggest that the adherence of the porcelain enamel to the 316L stainless steel is mainly controlled by a mechanism of mechanical interlocking. (C) 1999 Kluwer Academic Publishers