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This hybrid model is elaborated by being inspired by the mechanisms of a neuromimetic network whose structure is constrained by the discrete reverse-time state-space equations.
By using the way of weight functions and the Hermite-Hadamard inequality, a half-discrete reverse Mulholland-type inequality with a best constant factor is given.
By means of weight functions and the improved Euler-Maclaurin summation formula, a more accurate half-discrete reverse Hilbert-type inequality with the kernel ( min { 1, ( x − γ ) ( n − η ) } ) β ( max { 1, ( x − γ ) ( n − η ) } ) α and a best constant factor is given.
In this paper, by means of weight functions and the improved Euler-Maclaurin summation formula, a more accurate half-discrete reverse Hilbert-type inequality with the kernel ( min { 1, ( x − γ ) ( n − η ) } ) β ( max { 1, ( x − γ ) ( n − η ) } ) α similar to (5) and a best constant factor is given.
In this paper, by using the way of weight functions and the Hermite-Hadamard inequality, a half-discrete reverse Mulholland-type inequality similar to (6) is given as follows: ∫ 0 ∞ f ( x ) ∑ n = 1 ∞ a n ln e ( n + 1 2 ) x d x > π { ∫ 0 ∞ 1 − θ 1 ( x ) x 1 − p 2 f p ( x ) d x } 1 p { ∑ n = 1 ∞ ( n + 1 2 ) q − 1 a n q ln 1 − q 2 ( n + 1 2 ) } 1 q.
Recently, Yang [18] gave a half-discrete Hilbert inequality with multi-parameters, and [19] gave the following half-discrete reverse Hilbert-type inequality with the best constant factor 4: For 0 < p < 1, 1 p + 1 q = 1, we have θ 1 ( x ) ∈ ( 0, 1 ), and ∫ 0 ∞ f ( x ) ∑ n = 1 ∞ min { x, n } a n d x > 4 { ∫ 0 ∞ 1 − θ 1 ( x ) x 1 − 3 p 2 f p ( x ) d x } 1 p { ∑ n = 1 ∞ a n q n 1 − 3 q 2 } 1 q.
The experimental results presented are the first to show evidence of discrete forward and reverse stress-induced thermoelastic martensitic transformations in nanometer-scaled volumes of material.
* data from 454 Titanium sequencing run The use of oligos containing isomeric nucleotide bases to inhibit the enzymatic activity of MMLV-RT at a discrete point in reverse transcription of a template represents a novel application of the expanded genetic alphabet.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com