First, the complex Fourier series are used along both circumferential and meridian directions, to expand the integral kernel function and unknown source strength density distributed function.
Following the above computation, it remains to expand this integral, begin{aligned} I =& int_{S^{n}} K delta_{i}^{frac{n+4}{n-4}} lambda_{i}frac{partialdelta_{i}}{partiallambda_{i}} =& int_{B(a_{i},rho)subset B y_{j_{i}},2rho)} K delta_{i}^{frac{n+4}{n-4}} lambda_{i}frac{partialdelta_{i}}{partiallambda _{i}}+O biggl( frac{1}{lambda_{i}^{n}} biggr).
Minkowski's inequality appeared in 1896 [6] (see Minkowski's posthumous [7]) and was expanded to the integral form in the context of (L^{p}) space in 1910 [8], while Hardy's inequality appeared, and was verified and extended in 1920 [9], 2025 [10], and 1928 [1], respectively.
1. (2) Minkowski's inequality appeared in 1896 [6] (see Minkowski's posthumous [7]) and was expanded to the integral form in the context of (L^{p}) space in 1910 [8], while Hardy's inequality appeared, and was verified and extended in 1920 [9], 2025 [10], and 1928 [1], respectively. .
To reach the millions of women who suffer from this disease, lymphedema management must be expanded, as an integral part of the Global Program to Eliminate Lymphatic Filariasis, to all major filariasis-endemic areas worldwide.
In Africa, acacias (Acacia Miller s.l., Mimosoideae) diversified during the Pliocene, colonized, expanded and became integral to open, arid-adapted vegetation the savanna woodlands (Bouchenak-Khelladi et al. 2010; Odee et al. 2012).
Large datasets and machine learning are no longer just tied to computational science, but have expanded to be an integral part of every industry from financial services to healthcare to retail informing business decisions at every level.
Expanding liberation is integral to the national fabric.
They are expanded in terms of an integral transform associated to the sub-Laplacian.
Released on June 25 , 1999for the PlayStation in Japan, Metal Gear Solid: Integral is an expanded edition that features the additional content from the American and European versions of the original game.
In this study, the previously developed concept of integral water storage and energy was expanded to dual-porosity substrates and an analog integral oxygen diffusivity parameter was introduced to simultaneously characterize aeration properties of four common soilless greenhouse growth media.
