On the Study of Global Solutions for a Nonlinear Equation

The well-posedness of global strong solutions for a nonlinear partial differential equation including the Novikov equation is established provided that its initial value V 0 ( ) satisfies a sign condition and V 0 ( ) ∈ ( ) with > 3/2. If the initial value V 0 ( ) ∈ ( ) (1 ≤ ≤ 3/2) and the mean function of (1 − 2 )V 0 ( ) satisfies the sign condition, it is proved that there exists at least one global weak solution to the equation in the space V( , ) ∈ 2 ([0, +∞), ( )) in the sense of distribution and V ∈ ∞ ([0, +∞) × )

The Local Stability of Solutions for a Nonlinear Equation

The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R) by assuming that the initial value only lies in the space L1(R)∩L∞(R)

On the Study of Global Solutions for a Nonlinear Equation

The well-posedness of global strong solutions for a nonlinear partial differential equation including the Novikov equation is established provided that its initial value v0(x) satisfies a sign condition and v0(x)∈Hs(R) with s>3/2. If the initial value v0(x)∈Hs(R)  (1≤s≤3/2) and the mean function of (1-∂x2)v0(x) satisfies the sign condition, it is proved that there exists at least one global weak solution to the equation in the space v(t,x)∈L2([0,+∞),Hs(R)) in the sense of distribution and vx∈L∞([0,+∞)×R)

Quantitative image analysis of intra-tumoral bFGF level as a molecular marker of paclitaxel resistance

<p>Abstract</p> <p>Background</p> <p>The role of basic fibroblast growth factor (bFGF) in chemoresistance is controversial; some studies showed a relationship between higher bFGF level and chemoresistance while other studies showed the opposite finding. The goal of the present study was to quantify bFGF levels in archived tumor tissues, and to determine its relationship with chemosensitivity.</p> <p>Methods</p> <p>We established an image analysis-based method to quantify and convert the immunostaining intensity of intra-tumor bFGF to concentrations; this was accomplished by generating standard curves using human xenograft tumors as the renewable tissue source for simultaneous image analysis and ELISA. The relationships between bFGF concentrations and tumor chemosensitivity of patient tumors (n = 87) to paclitaxel were evaluated using linear regression analysis.</p> <p>Results</p> <p>The image analysis results were compared to our previous results obtained using a conventional, semi-quantitative visual scoring method. While both analyses indicated an inverse relationship between bFGF level and tumor sensitivity to paclitaxel, the image analysis method, by providing bFGF levels in individual tumors and therefore more data points (87 numerical values as opposed to four groups of staining intensities), further enabled the quantitative analysis of the relationship in subgroups of tumors with different pathobiological properties. The results show significant correlation between bFGF level and tumor sensitivity to the antiproliferation effect, but not the apoptotic effect, of paclitaxel. We further found stronger correlations of bFGF level and paclitaxel sensitivity in four tumor subgroups (high stage, positive p53 staining, negative aFGF staining, containing higher-than-median bFGF level), compared to all other groups. These findings suggest that the relationship between intra-tumoral bFGF level and paclitaxel sensitivity was context-dependent, which may explain the previous contradictory findings on the merit of using plasma or urine bFGF level as a prognostic indicator.</p> <p>Conclusion</p> <p>The present study established a quantitative image analysis method that enabled the measurement of intratumoral bFGF level in archived tissues. The ability to quantify a potential biomarker provided the opportunity to study the relationship between the biomarker and chemosensitivity in tumor subgroups and thereby enabled hypothesis generation for additional translational research.</p

On the L

A nonlinear generalized Degasperis-Procesi equation is investigated. Assuming that the strong solution of the equation is bounded in the sense of L∞R-norm and the initial data belong to the space L1(R)∩L2(R), we prove that the solutions are stable in the space L1(R)

On the Existence of Global Weak Solutions for a Weakly Dissipative Hyperelastic Rod Wave Equation

Assuming that the initial value v0(x) belongs to the space H1(R), we prove the existence of global weak solutions for a weakly dissipative hyperelastic rod wave equation in the space C([0,∞)×R)⋂‍L∞([0,∞);H1(R)). The limit of the viscous approximation for the equation is used to establish the existence

The Optimal Analysis of Default Probability for a Credit Risk Model

A credit risk mathematical model is investigated. Under regular conditions, a different recovery scheme is proposed, which is an extension of the recovery of treasury value scheme (RTV) with time-continuous liquidation. Assuming that a function depends on the optimal time for the liquidation and the recovery rate, we obtain the functional expression of the risky bond price. When the firm value follows a jump-diffusion process with a Log-exponentially distributed jump, we develop a method to obtain the optimal default probability with time-continuous liquidation

Electronic Health Literacy Across the Lifespan: Measurement Invariance Study

Background: Electronic health (eHealth) information is ingrained in the healthcare experience to engage patients across the lifespan. Both eHealth accessibility and optimization are influenced by lifespan development, as older adults experience greater challenges accessing and using eHealth tools as compared to their younger counterparts. The eHealth Literacy Scale (eHEALS) is the most popular measure used to assess patient confidence locating, understanding, evaluating, and acting upon online health information. Currently, however, the factor structure of the eHEALS across discrete age groups is not well understood, which limits its usefulness as a measure of eHealth literacy across the lifespan. Objective: The purpose of this study was to examine the structure of eHEALS scores and the degree of measurement invariance among US adults representing the following generations: Millennials (18-35-year-olds), Generation X (36-51-year-olds), Baby Boomers (52-70-year-olds), and the Silent Generation (71-84-year-olds). Methods: Millennials (N=281, mean 26.64 years, SD 5.14), Generation X (N=164, mean 42.97 years, SD 5.01), and Baby Boomers/Silent Generation (N=384, mean 62.80 years, SD 6.66) members completed the eHEALS. The 3-factor (root mean square error of approximation, RMSEA=.06, comparative fit index, CFI=.99, Tucker-Lewis index, TLI=.98) and 4-factor (RMSEA=.06, CFI=.99, TLI=.98) models showed the best global fit, as compared to the 1- and 2-factor models. However, the 4-factor model did not have statistically significant factor loadings on the 4th factor, which led to the acceptance of the 3-factor eHEALS model. The 3-factor model included eHealth Information Awareness, Search, and Engagement. Pattern invariance for this 3-factor structure was supported with acceptable model fit (RMSEA=.07, Δχ2=P>.05, ΔCFI=0). Compared to Millennials and members of Generation X, those in the Baby Boomer and Silent Generations reported less confidence in their awareness of eHealth resources (P<.001), information seeking skills (P=.003), and ability to evaluate and act on health information found on the Internet (P<.001). Results: Young (18-48-year olds, N=411) and old (49-84-year olds, N=419) adults completed the survey. A 3-factor model had the best fit (RMSEA=.06, CFI=.99, TLI=.98), as compared to the 1-factor, 2-factor, and 4-factor models. These 3-factors included eHealth Information Awareness (2 items), Information Seeking (2 items), and Information and Evaluation (4 items). Pattern invariance was supported with the acceptable model fit (RMSEA=.06, Δχ2=P>.05, ΔCFI=0). Compared with younger adults, older adults had less confidence in eHealth resource awareness (P<.001), information seeking skills (P<.01), and ability to evaluate and act upon online health information (P<.001). Conclusions: The eHEALS can be used to assess, monitor uniquely, and evaluate Internet users’ awareness of eHealth resources, information seeking skills, and engagement abilities. Configural and pattern invariance was observed across all generation groups in the 3-factor eHEALS model. To meet gold the standards for factor interpretation (ie, 3 items or indicators per factor), future research is needed to create and assess additional eHEALS items. Future research is also necessary to identify and test items for a fourth factor, one that captures the social nature of eHealth

Biomanufacture of nano-Pd(0) by Escherichia coli and electrochemical activity of bio-Pd(0) made at the expense of H2 and formate as electron donors

Objective: Palladised cells of Desulfovibrio desulfuricans and Shewanella oneidensis have been reported as fuel cell electrocatalysts but growth at scale may be unattractive/costly; we have evaluated the potential of using E. coli, using H2/formate for Pd-nanoparticle manufacture. Results: Using ‘bio-Pd’ made under H2 (20 wt%) cyclic voltammograms suggested electrochemical activity of bio-NPs in a native state, attributed to proton adsorption/desorption. Bio-Pd prepared using formate as the electron donor gave smaller, well separated NPs; this material showed no electrochemical properties, and hence little potential for fuel cell use using a simple preparation technique. Bio-Pd on S. oneidensis gave similar results to those obtained using E. coli. Conclusion: Bio-Pd is sufficiently conductive to make an E. coli-derived electrochemically active material on intact, unprocessed bacterial cells if prepared at the expense of H2, showing potential for fuel cell applications using a simple one-step preparation method

Self-rated health in middle-aged and elderly Chinese : distribution, determinants and associations with cardio-metabolic risk factors

Background: Self-rated health (SRH) has been demonstrated to be an accurate reflection of a person's health and a valid predictor of incident mortality and chronic morbidity. We aimed to evaluate the distribution and factors associated with SRH and its association with biomarkers of cardio-metabolic diseases among middle-aged and elderly Chinese. Methods: Survey of 1,458 men and 1,831 women aged 50 to 70 years, conducted in one urban and two rural areas of Beijing and Shanghai in 2005. SRH status was measured and categorized as good (very good and good) vs. not good (fair, poor and very poor). Determinants of SRH and associations with biomarkers of cardio-metabolic diseases were evaluated using logistic regression. Results: Thirty two percent of participants reported good SRH. Males and rural residents tended to report good SRH. After adjusting for potential confounders, residence, physical activity, employment status, sleep quality and presence of diabetes, cardiovascular disease, and depression were the main determinants of SRH. Those free from cardiovascular disease (OR 3.68; 95%CI 2.39; 5.66), rural residents (OR 1.89; 95% CI 1.47; 2.43), non-depressed participants (OR 2.50; 95% CI 1.67; 3.73) and those with good sleep quality (OR 2.95; 95% CI 2.22; 3.91) had almost twice or over the chance of reporting good SRH compared to their counterparts. There were significant associations -and trend- between SRH and levels of inflammatory markers, insulin levels and insulin resistance. Conclusion: Only one third of middle-aged and elderly Chinese assessed their health status as good or very good. Although further longitudinal studies are required to confirm our findings, interventions targeting social inequalities, lifestyle patterns might not only contribute to prevent chronic morbidity but as well to improve populations' perceived health