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On Strong and Absolute Summability [PDF]
Proceedings of the Glasgow Mathematical Association, 1960 Suppose throughout that λ > 0, κ > - l. γ is real and thatThe series is said to be(i) summable (C, k) to s if (ii) strongly summable (C, k + 1) with index λ, or summable |C, k + 1|λ, to s if(iii) absolutely summable (C, k) with indices γ, λ, or summable |C, k + 1|λ ...
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The Method of almost convergence with operator of the form fractional order and applications
, 2016 The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character.
Kadak, Ugur, Kirisci, Murat
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Molecular Oncology, EarlyView.Pancreatic sensory neurons innervating healthy and PDAC tissue were retrogradely labeled and profiled by single‐cell RNA sequencing. Tumor‐associated innervation showed a dominant neurofilament‐positive subtype, altered mitochondrial gene signatures, and reduced non‐peptidergic neurons.
Elena Genova +14 more
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Absolute Q-Summability Factors
Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1968 In thîs paper we prove the following theorem: k THEOREM; Let (> J be a convex sequence sucb tb^t is eonvengent nIf there exist a [A > 0 such tbat sequence (nj^**^* is JB, logn,«p, Ijp-bounded ...
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Tauberian theorems for absolute summability [PDF]
Proceedings of the American Mathematical Society, 1967 [8, Theorem 21. It is easily seen that for m =1, summability I A, V m and summability f R, X, k | m are the same as summability I A, X J [9] and summability fR, X, kf [21 respectively. Borwein [1] has shown that for An-n summability I R, X, k I m of EaZ is equivalent to its absolute Cesaro summability with index m. 1.2.
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Molecular Oncology, EarlyView.Radiotherapy (RT) response depends on the DNA repair capacity of tumor and host cells. We show that circulating tumor cell (CTC) counts and apoptosis rates before and after RT predict treatment response and outcome, which can be accessed via easily accessible liquid biopsy approaches. Created in BioRender. Wikman, H.
Yvonne Goy +10 more
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Noninclusion theorems: some remarks on a paper by J. A. Fridy
International Journal of Mathematics and Mathematical Sciences, 2000 In 1997, J. A. Fridy gave conditions for noninclusion of ordinary and of absolute summability domains. In the present note, these conditions are interpreted in a natural topological context thus giving new proofs and also explaining why one of these ...
W. Beekmann
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Absolute Abel Summability and Capacity [PDF]
Proceedings of the American Mathematical Society, 1979 Precise limits on the size of exceptional sets for which functions in the Lebesgue class, L α p \mathcal {L}_\alpha ^p , can fail to be absolutely Abel summable are given in terms of Bessel capacity.
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FEBS Open Bio, EarlyView.KLK7, a tissue kallikrein‐related peptidase, is elevated in advanced colorectal cancer and associated with shorter survival. High KLK7 levels in ascites correlate with peritoneal metastasis. In mice, KLK7 overexpression increases metastasis. In vitro, KLK7 enhances cancer cell proliferation, migration, adhesion, and spheroid formation, driving ...
Yosr Z. Haffani +6 more
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On Absolute Weighted Mean Summability
Rocky Mountain Journal of Mathematics, 1993 Using functional analytic techniques, the authors obtain the necessary and sufficient conditions in order that the series \(\sum a_ n\) should be summable \(| R, q_ n |_ k\), \(k \geq 1\), whenever it is summable \(| R, p_ n |\). The results contained in this paper extend the known results of \textit{L. S. Bosanquet} [published in the review in M.
Orhan, C., Sarigöl, M.A.
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