Integrodifferential Inequalities Arising in the Theory of Differential Equations

The goal of this paper is to achieve some new results related to integrodifferential inequalities of one independent variable which can be applied as a study of qualitative and quantitative properties of solutions of some nonlinear integral equations

THE ROLE OF INTEGRINS IN THE ACTIVATION OF FIBROBLASTS FROM SKIN, LUNG AND BREAST TISSUE

PhDFibroblasts are abundant mesenchymal cells present in all tissues in a quiescent state, which contribute to wound healing when activated. Cytokine transforming growth factor-β1 (TGF-β1) stimulates fibroblast-myofibroblast differentiation, which induces extracellular matrix secretion, tissue contraction and promotes cancer cell migration. Hence, chronic activity of stromal myofibroblasts correlates with a poor prognosis for cancer and organ fibrosis patients. Therefore, modulating myofibroblast activity may reduce the severity of these diseases. Previous research suggests blockade of transmembrane integrin receptors expressed by fibroblasts prevents TGF-β1- induced differentiation, indicating integrins are attractive therapeutic targets. However, fibroblasts derived from different organs exhibit heterogeneity, although their integrin expression and integrin-regulated differentiation has not been directly compared. The aim of my research was 1) to understand and compare how integrins regulate TGF-β1-induced activation of fibroblasts derived from normal skin, lung and breast tissue; 2) to examine the global gene expression of TGF-β1-treated lung fibroblasts; 3) to identify novel therapeutic targets that modulate TGF-β1-induced activation of lung fibroblasts using a drug library. qPCR showed skin, lung and breast fibroblasts differentially expressed TGF-β1- induced activation markers, including ACTA2, FN1, TIMP3, CTGF and SERPINE1, in addition to integrin genes for α1, α4, α11 and β3. Small-molecule inhibitors of αv integrins only reduced the invasion of TGF-β1-exposed skin fibroblasts, but not lung or breast fibroblasts. siRNA against α11, β3 and β5 decreased TGF-β1-induced collagen contraction and activation marker expression in skin and lung fibroblasts, while α1 siRNA prevented collagen contraction by breast fibroblasts only. RNA sequencing of TGF-β1-treated lung fibroblasts revealed pro-inflammatory and profibrotic pathways were significantly enriched, while screening TGF-β1-treated lung fibroblasts with a FDA-approved drug library identified 46 hits that significantly reduced α-smooth muscle actin and fibronectin expression. Overall, genes are differentially expressed in TGF-β1-treated skin, lung and breast fibroblasts, while different integrins in each fibroblast appear to regulate invasion, TGF-β1-induced collagen contraction and gene expression. RNA sequencing revealed TGF-β1 promotes the expression of a pro-tumour signature in lung fibroblasts and several novel therapeutic targets that modulate the activation of lung fibroblasts have been identified. Understanding these integrin-dependent and independent mechanisms will facilitate the generation of myofibroblast-targeted treatments for cancer and organ fibrosis.Biotechnology and Biological Sciences Research Council (BBSRC) and GlaxoSmithKline

Mathematical analysis of neurological disorder under fractional order derivative

Multiple sclerosis (MS) is a common neurological disorder that affects the central nervous system (CNS) and can cause lesions that spread over space and time. Our study proposes a mathematical model that illustrates the progression of the disease and its likelihood of recurrence. We use Caputo fractional-order (FO) derivative operators to represent non-negative solutions and to establish a steady-state point and basic reproductive number. We also employ functional analysis to prove the existence of unique solutions and use the Ulam-Hyres (UH) notion to demonstrate the stability of the solution for the proposed model. Furthermore, we conduct numerical simulations using an Euler-type numerical technique to validate our theoretical results. Our findings are presented through graphs that depict various behaviors of the model for different parameter values

Meshfree numerical approach for some time-space dependent order partial differential equations in porous media

In this article, the meshfree radial basis function method based on the Gaussian function is proposed for some time-space dependent fractional order partial differential equation (PDE) models. These PDE models have significant applications in chemical engineering and physical science. Some main advantages of the proposed method are that it is easy to implement, and the output response is quick and highly accurate, especially in the higher dimension. In this method, the time-dependent derivative terms are treated by Caputo fractional derivative while space-dependent derivative terms are treated by Riesz, Riemann-Liouville, and Grünwald-Letnikov derivatives. The proposed method is tested on some numerical examples and the accuracy is analyzed by $\|L\|_\infty$

Study of nonlinear generalized Fisher equation under fractional fuzzy concept

Fractional calculus can provide an accurate model of many dynamical systems, which leads to a set of partial differential equations (PDE). Fisher's equation is one of these PDEs. This article focuses on a new method that is used for the analytical solution of Fuzzy nonlinear time fractional generalized Fisher's equation (FNLTFGFE) with a source term. While the uncertainty is considered in the initial condition, the proposed technique supports the process of the solution commencing from the parametric form (double parametric form) of a fuzzy number. Next, a joint mechanism of natural transform (NT) coupled with Adomian decomposition method (ADM) is utilized, and the nonlinear term is calculated through ADM. The obtained solution of the unknown function is written in infinite series form. It has been observed that the solution obtained is rapid and accurate. The result proved that this method is more efficient and less time-consuming in comparison with all other methods. Three examples are presented to show the efficiency of the proposed techniques. The result shows that uncertainty plays an important role in analytical sense. i.e., as the uncertainty decreases, the solution approaches a classical solution. Hence, this method makes a very useful contribution towards the solution of the fuzzy nonlinear time fractional generalized Fisher's equation. Moreover, the matlab (2015) software has been used to draw the graphs

Threshold dynamics of stochastic cholera epidemic model with direct transmission

This paper extends the cholera human-to-human direct transmission model from a deterministic to a stochastic framework. This is expressed as mixed system of stochastic and deterministic differential equations. A Lyapunov function is created to investigate the global stability of the stochastic cholera epidemic, which shows the existence of global positivity of the solution using the theory of stopping time. We then find the threshold quantity of the extended stochastic cholera epidemic model. We derive a parametric condition $\widetilde{R}_0$, and for additive white noise, we establish sufficient conditions for the extinction and the persistence of the cholera infection. Finally, for a suitable choice of the parameter of the system for $\widetilde{R}_0$, we perform numerical simulations for both scenarios of extinction and persistence of the dynamic of the cholera infection

Some well known inequalities for (h1, h2)-convex stochastic process via interval set inclusion relation

This note introduces the concept of (h1, h2)-convex stochastic processes using intervalvalued functions. First we develop Hermite-Hadmard (H.H) type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski and Jensen type inequalities for (h1, h2)-convex stochastic process. Also, we have shown that this is a more generalized and larger class of convex stochastic processes with some remark. Furthermore, we validate our main findings by providing some non-trivial examples.http://www.aimspress.com/journal/MathMathematics and Applied Mathematic

6-(4-Nitro­phen­oxy)hexa­nol

The title compound, C12H17NO4, features an almost planar mol­ecule (r.m.s. deviation for all non-H atoms = 0.070 Å). All methyl­ene C—C bonds adopt an anti­periplanar conformation. In the crystal structure the mol­ecules lie in planes parallel to (12) and the packing is stabilized by O—H⋯O hydrogen bonds