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Optimal strategies for managing Hepatitis B Virus (HBV) infection: a comprehensive approach through education, vaccination, and therapy. [PDF]
Sci RepAlsinai A, Niazi AUK, Uroej S, Ahmed B.
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Lebesgue functions and multiple function series. II
Acta Mathematica Academiae Scientiarum Hungaricae, 1981[For parts I and II see Acta Math. Acad. Sci. Hung. 37, 481-496 (1981; Zbl 0469.42009), and ibid. 39, 95-105 (1982; Zbl 0491.42030).] - The author continues his considerations on Lebesgue functions for d-multiple function series (*) \(\sum_{k\in Z^+_ d}a_ k\Phi(x)\) which he introduced in part I.
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Optimal Lebesgue Function Type Sums
Acta Mathematica Hungarica, 1997Let \(X_n\) be the set of all grids \(\xi=(\xi_1,\xi_2,\dots,\xi_n)\) with \(1\leq ...
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On the Lebesgue function on infinite interval. I.
Publicationes Mathematicae Debrecen, 2022In Theorem 1 there are considered polynomials, that are orthonormal on [0,\(\infty)\) with respect to some weight function and the corresponding Lebesgue functions \(\lambda_ n\). There are given upper estimates for \(\lambda_ n(x)\), \(0\leq x\leq A- 1\), \(x\geq 0\), \(\phi (x)\in Lip_ M\gamma,\quad (\frac{1}{2}
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1982
If f ∈ L1([-π, π],λ) and for n in ℤ, \( {c_{n}} = {\left( {2\pi } \right)^{{ - 1}}}\int_{{ - \pi }}^{\pi } {f\left( x \right)} {e^{{inx}}}dx \), then \( {\sigma _{N}}\left( f \right):x \mapsto {\left( {N + 1} \right)^{1}}\sum\nolimits_{{k - 0}}^{N} {\left( {\sum\nolimits_{{n = - k}}^{k} {{C_{n}}{e^{{inx}}}} } \right)} \) is the average of the first N +
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If f ∈ L1([-π, π],λ) and for n in ℤ, \( {c_{n}} = {\left( {2\pi } \right)^{{ - 1}}}\int_{{ - \pi }}^{\pi } {f\left( x \right)} {e^{{inx}}}dx \), then \( {\sigma _{N}}\left( f \right):x \mapsto {\left( {N + 1} \right)^{1}}\sum\nolimits_{{k - 0}}^{N} {\left( {\sum\nolimits_{{n = - k}}^{k} {{C_{n}}{e^{{inx}}}} } \right)} \) is the average of the first N +
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On the Lebesgue Function for Polynomial Interpolation
SIAM Journal on Numerical Analysis, 1978Properties of the Lebesgue function associated with interpolation at the Chebyshev nodes ${{\{ \cos [(2k - 1)\pi } {(2n)}}],\, k = 1,2, \cdots ,n\} $ are studied. It is proved that the relative maxima of the Lebesgue function are strictly decreasing from the outside towards the middle of the interval.
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On barycentric interpolation. I. (On the T-Lebesgue function and T-Lebesgue constant)
Acta Mathematica Hungarica, 2015The author proves theorems on the Lebesgue function and Lebesgue constant of barycentric Lagrange interpolation based on an arbitrary node-sytem in \([-1, 1]\). It turns out that the results are very similar to the ones known for the classical Lagrange interpolation. For Part II see [\textit{Á. P. Horváth} and \textit{P. Vértesi}, ibid. 148, No. 1, 147-
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Lebesgue Points of Higher Dimensional Functions
2021In this chapter, we generalize Lebesgue’s theorem proved in Theorem 1.5.4 to higher dimensions and to all summability methods considered in Chaps. 2 and 3.
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Lebesgue Integrable Functions and Sets
1998The general Lebesgue integral is defined, and basic properties are derived. Here, a function is called Lebesgue integrable if approximation from above by lower semicontinuous functions leads to the same result as approximation from below by upper semicontinuous functions. Sets are called integrable when their characteristic functions are.
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