Results 41 to 50 of about 5,152 (170)
q-Supercongruences from squares of basic hypergeometric series
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022 We give some new $q$-supercongruences on truncated forms of squares of basic hypergeometric series. Most of them are modulo the cube of a cyclotomic polynomial, and two of them are modulo the fourth power of a cyclotomic polynomial. The main ingredients of our proofs are the creative microscoping method, a lemma of El Bachraoui, and the Chinese ...
Victor J. W. Guo, Long Li
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Advanced Science, EarlyView.Frontal lobe traumatic brain injury is associated with hyperactivity of an insular–orbitofrontal circuit in both patients and mice. By combination of integrating functional imaging, cell‐type–specific circuit manipulation, single‐cell transcriptomics, and whole‐cell recordings, this work identifies the downregulation of the potassium channel KCNC3 in ...
Meng‐Ge Li +10 more
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Mathematical Methods in the Applied Sciences, EarlyView.A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay +2 more
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New Phytologist, EarlyView.Synthetic community complexity reduction designs. Summary Plant growth is influenced by the composition of its associated microbiome. The inherent complexity and functional redundancy of natural plant microbiomes present a formidable barrier to understanding the myriad biological interactions therein.
Dean Pettinga +8 more
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Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture
Symmetry, Integrability and Geometry: Methods and Applications, 2009 We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which ...
Robin Langer +2 more
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FEBS Open Bio, Volume 16, Issue 8, Page 1563-1592, August 2026.Activation of the mitochondrial protein OXR1 increases pSyn129 αSynuclein aggregation by lowering ATP levels and altering mitochondrial membrane potential, particularly in response to MSA‐derived fibrils. In contrast, ablation of the ER protein EMC4 enhances autophagic flux and lysosomal clearance, broadly reducing α‐synuclein aggregates.
Sandesh Neupane +11 more
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Particle seas and basic hypergeometric series
Advances in Applied Mathematics, 2003 A particle sea is a geometrical arrangement in the upper half plane, of two types of symbols, say squares and circles, subject to some conditions. Loosely speaking, particle seas are in some sense an analogue of Ferrers graphs from the theory of partitions.
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Advanced Science, Volume 13, Issue 43, 3 August 2026.In renal calcium oxalate stone formation, G6PC downregulation leads to lactate accumulation. This lactate mediates CBP/p300‐dependent lactylation of SNAIL1 at K206, promoting its nuclear translocation. Nuclear SNAIL1 activates the TGF‐β/SMAD3 pathway, driving epithelial‐mesenchymal transition and fibrosis, which ultimately facilitates crystal ...
Kai Liu +16 more
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Paternal Circadian Disruption Impairs Offspring Cognition via Sperm microRNAs
Advanced Science, Volume 13, Issue 37, 3 July 2026.Paternal circadian disruption remodels the sperm small RNA payload, elevating miR‐92a‐3p/miR‐25‐3p levels and perturbing early embryonic gene regulatory programs. Microinjection experiments and single‐embryo transcriptomics reveal sex‐specific developmental vulnerabilities, ultimately impairing offspring hippocampal synaptic plasticity and cognition ...
Kexin Zou +22 more
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A short proof of an identity of Sylvester
International Journal of Mathematics and Mathematical Sciences, 1999 We present two short proofs of an identity found by Sylvester and rediscovered by Louck. The first proof is an elementary version of Knuth's proof and is analogous to Macdonald's proof of a related identity of Milne.
Gaurav Bhatngar
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