Results 101 to 110 of about 235,552 (326)

Difference Sets and Polynomials

, 2015
We provide upper bounds on the largest subsets of $\{1,2,\dots,N\}$ with no differences of the form $h_1(n_1)+\cdots+h_{\ell}(n_{\ell})$ with $n_i\in \mathbb{N}$ or $h_1(p_1)+\cdots+h_{\ell}(p_{\ell})$ with $p_i$ prime, where $h_i\in \mathbb{Z}[x]$ lie in in the classes of so-called intersective and $\mathcal{P}$-intersective polynomials, respectively.
Lyall, Neil, Rice, Alex
openaire   +2 more sources

Micro and Nanostructural Diversity of Lizard Osteoderm Capping Tissue in Relation to Mechanical Performance

Advanced Functional Materials, EarlyView.
This study shows that lizard osteoderm capping tissue is a hyper‐mineralized hydroxyapatite layer consistently covering the superficial osteoderm surface in those species studied here, yet it varies greatly in morphology, nanostructure, and mechanical performance across species.
Adrian Rodriguez‐Palomo, Marius Didziokas, Malene Siri Berg Jacobsen, Thorbjørn Erik Køppen Christensen, Innokenty Kantor, Mads Ry Vogel Jørgensen, Klaus Pagh Almtoft, Jesper Skovhus Thomsen, Anthony Herrel, Catherine J.A. Williams, Henrik Birkedal   +10 more
wiley   +1 more source

On the boundedness of poles of generalized Padé approximants

Advances in Difference Equations, 2019
Given a function F holomorphic on a neighborhood of some compact subset of the complex plane, we prove that if the zeros of the denominators of generalized Padé approximants (orthogonal Padé approximants and Padé–Faber approximants) for some row sequence
Nattapong Bosuwan
doaj   +1 more source

Bone‐Derived dECM Hydrogels Support Tunable Microenvironments for In Vitro Osteogenic Differentiation

Advanced Healthcare Materials, EarlyView.
A tunable methacrylated decellularized bone matrix hydrogel (dECM‐MA) is developed to support 3D culture of human osteoblasts. The hydrogel preserves bone‐specific ECM cues and allows precise control over mechanical properties. This system provides a customizable platform for studying osteogenic differentiation and modeling bone tissue environments for
Minne Dekker, Luke Hipwood, Akhilandeshwari Ravichandran, Dietmar W. Hutmacher, Christoph Meinert, Jacqui McGovern   +5 more
wiley   +1 more source

Polynomial solutions of differential–difference equations

Journal of Approximation Theory, 2011
We investigate the zeros of polynomial solutions to the differential-difference equation \[ P_{n+1}(x)=A_{n}(x)P_{n}^{\prime}(x)+B_{n}(x)P_{n}(x), n=0,1,... \] where $A_{n}$ and $B_{n}$ are polynomials of degree at most 2 and 1 respectively. We address the question of when the zeros are real and simple and whether the zeros of polynomials of adjacent ...
Dominici, Diego, Driver, Kathy (Cathryn Helena Stanford), Jordaan, Kerstin Heidrun   +2 more
openaire   +4 more sources

Ultrasound‐Triggered Gelation for Restoring Biomechanical Properties of Degenerated Functional Spinal Units

Advanced Healthcare Materials, EarlyView.
This study introduces an innovative approach to treating intervertebral disc degeneration using ultrasound‐triggered in situ hydrogel formation. Proof‐of‐concept experiments using optimized biomaterial and ultrasound parameters demonstrate partial restoration of biomechanical function and successful integration into degenerated disc tissue, offering a ...
Veerle A. Brans, Anna P. Constantinou, Matthew J. Kibble, Valeria Nele, Daniel Reumann, Luca Bau, Sebastien J. P. Callens, James P. K. Armstrong, Nicolas Newell, Constantin C. Coussios, Molly M. Stevens, Michael D. Gray   +11 more
wiley   +1 more source

Use of bessel polynomials for solving differential difference equations

Arab Journal of Basic and Applied Sciences, 2019
In this paper, the linear differential difference equation subject to the mixed conditions has been solved numerically using Bessel polynomials. The solution is obtained in terms of Bessel polynomials.
Zaffer Elahi, Ghazala Akram, Shahid S. Siddiqi   +2 more
doaj   +1 more source

Dimension Polynomials and the Einstein’s Strength of Some Systems of Quasi-linear Algebraic Difference Equations [PDF]

, 2020
Alexander N. Evgrafov, Alexander Levin
openalex   +1 more source

On the Finite Differences of a Polynomial

The Annals of Mathematical Statistics, 1935
In this paper an apparently new and convenient method of finding the successive finite differences of a polynomial is considered. If operationally 4(u + rjr2) = Er7r2 4(u) = (1 + Ari)r2 4o(u) then for any polynomial f(x) of degree "n" f(x) = po xn + P, Xn-1 +--+ Pn = po(x + a)n + qll(x + a)n-I + + qln Eaf(x) = po(x + a)n + pl(x + a)n-' + + Pn Aaf(X) = (
openaire   +2 more sources

AI‐Assisted Design and Evaluation of SLM‐Ti64 Implants for Enhanced Bone Regeneration

Advanced Healthcare Materials, EarlyView.
AI‐driven simulations of biological healing, combining biomechanical modeling and machine learning, enable personalized orthopedic treatments. By decoding healing patterns influenced by implants and patient‐specific factors, this approach advances fracture repair understanding, optimizes implant design, and supports precision medicine and sustainable ...
Muhammad Usama Zaheer, Muhammad Hassan Razzaq, Mehmet Fatih Aycan, Yogendra Kumar Mishra   +3 more
wiley   +1 more source