Changes in pancreatic levodopa uptake in patients with obesity and new-onset type 2 diabetes: an 18F-FDOPA PET-CT study. [PDF]
Kwon Y+7 more
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Association between the serum uric acid-to-creatinine ratio and cardiovascular mortality in maintenance hemodialysis patients. [PDF]
Huang W+10 more
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Regulating islet stress responses through CD47 activation. [PDF]
Kale A+9 more
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No sex differences in the association between regional brain structure abnormalities and cognitive functioning in a geriatric memory clinic population. [PDF]
Lamé A+8 more
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Some results on the beta function and the incomplete beta function
Asian-European Journal of Mathematics, 2015The incomplete Beta function B(a,b; x) is defined for a,b > 0 and 0 < x < 1. This definition was extended to negative integer values of a and b by Ozcaḡ et al. using neutrix limits.
Mongkolsery Lin+2 more
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The First Eulerian Integral, called the Beta Function, is defined by B(x, y) =folt-1(1 -t)Y-ldt, which converges for x > 0 and y > 0. The well-known equation connecting the Beta and Gamma functions, B(x, y) = r(x)r(y)/r(x+y), is therefore valid only for positive real x and y. However, this relation is commonly used as a definition, to extend B(x, y) so
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New integral inequalities for preinvex functions via generalized beta function
Journal of Interdisciplinary Mathematics, 2019In this study, we establish some new integral inequalities for the logarithmically p-preinvex functions by using generalizes beta function. This work extends and generalized the results appeared in the literature.
P. Mohammed
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Normalized Incomplete Beta Function: Log-Concavity in Parameters and Other Properties
, 2015The logarithmic concavity/convexity in parameters of the normalized incomplete beta function has been established by Finner and Roters in 1997 as a corollary of a rather difficult result, based on generalized reproductive property of certain ...
D. Karp
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Inequalities for the beta function
Analysis Mathematica, 2014We prove the following inequalities involving Euler’s beta function. (i) Let α and β be real numbers. The inequalities $\left( {\frac{{y^{z - x} }} {{x^{z - y} z^{y - x} }}} \right)^\alpha \leqslant \frac{{B(x,x)^{z - y} B(z,z)^{y - x} }} {{B(y,y)^{z - x} }} \leqslant \left ...
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