On Local Solutions of Second Order Quasi-linear Elliptic Systems with Arbitrary 1-Jet at a Point

We prove a general result on the existence of local solutions of any second order quasi-linear elliptic system with arbitrary 1-jet at a point

Construction of Twice Differentiable Functions with Continuous Laplacian and Bounded Hessian

We construct examples of twice differentiable functions in $\mathbb{R}^n$ with continuous Laplacian and bounded Hessian. The same construction is also applicable to higher order differentiability, the Monge-Amp\`ere equation, and mean curvature equation for hypersurfaces

monitoring of li ion cells with distributed fibre optic sensors

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Irbesartan protects against type 2 diabetic nephropathy by regulating miR-93/VEGF and its downstream effectors

Purpose: To investigate the protective effect of irbesartan against type 2 diabetic nephropathy (T2DN), and the mechanism involved.Methods: Wistar rats (n = 48) were used in this study. Diabetes mellitus (DM) was established in the rats via injection of streptozotocin (STZ). Thereafter, the DM rats were randomly divided into diabetic nephropathy (DN) group and irbesartan group, with 16 rats in each group. Rats in the control group (n = 16) received normal saline in place of irbesartan.Results: Total cholesterol (TC), triglycerides (TGs), high-density lipoprotein cholesterol (HDL-C) and low-density lipoprotein cholesterol (LDL-C), as well as protein expression levels of VEGF, FN, collagen IV in DN group were significantly higher in irbesartan group than the corresponding levels in normal control group, while miR-93 protein expression level was significantly lower than that in normal control group (p < 0.05). However, the expression level of mir-93 was significantly higher in irbesartan group than in DN group, while levels of TC, TGs, HDL-C, LDL-C and VEGF, as well as protein levels of FN and collagen IV protein were significantly lower than those in DN group (p < 0.05). There was no obvious change in the renal tissues of the normal control group. In contrast, in the DN group, glomerularcapillary loop hypertrophy, narrow glomerular cavity, thick basement membrane, mesangial matrix, and vacuolar degeneration in renal tubular epithelial cells, were evident. Compared with DN group, the pathological changes in the irbesartan group were significantly mitigated (p < 0.05).Conclusion: Irbesartan protects DM rats against type 2 diabetic nephropathy by regulating mir-93/VEGF and its downstream effector molecules. This provides some ideas for the development of new drugs for the prevention of type 2 diabetic nephropathy

On the Local Regularity of the Hilbert Transform

In this paper the local regularity of the Hilbert transform is considered, and local smoothness and real analyticity results are obtained