Results 101 to 110 of about 12,258,354 (255)

The history of Down syndrome–associated Alzheimer's disease; past, present, and future [PDF]

Alzheimers Dement
Abstract The landscape of Down syndrome–associated Alzheimer's disease (DSAD) research reflects decades of scientific endeavor and collaborative effort, charting a remarkable journey from initial observations to the elucidation of complex genetic and molecular mechanisms.
Maure‐Blesa L, Carmona‐Iragui M, Lott I, Head E, Wisniewski T, Rafii M, Espinosa J, Flórez J, Mobley W, Holland A, Strydom A, Zaman S, Fortea J.   +12 more
europepmc   +2 more sources

Where Mathematical Symbols Come From

Topics in Cognitive Science, EarlyView.
Abstract There is a sense in which the symbols used in mathematical expressions and formulas are arbitrary. After all, arithmetic would be no different if we would replace the symbols ‘+$+$’ or ‘8’ by different symbols. Nevertheless, the shape of many mathematical symbols is in fact well motivated in practice.
Dirk Schlimm
wiley   +1 more source

Schrödinger–Hardy system without the Ambrosetti–Rabinowitz condition on Carnot groups

Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we study the following Schrödinger–Hardy system \begin{equation*} \begin{cases} -\Delta_{\mathbb{G}}u-\mu\frac{\psi^2}{r(\xi)^2}u=F_u(\xi,u,v)\ &{\rm in}\ \Omega, \\ -\Delta_{\mathbb{G}}v-\nu\frac{\psi^2 }{r(\xi)^2}v=F_v(\xi,u,v)\
Wenjing Chen, Fang Yu
doaj   +1 more source

Representation formulas and Fatou-Kato theorems for heat operators on stratified groups [PDF]

Rendiconti di Matematica e delle Sue Applicazioni, 2005
In this note, we provide a characterization of non-negative L-caloric functions on strips, where L is a sub-Laplacian on a stratified group. We prove representation results, Fatou-type and uniqueness theorems analogous to the classical Poisson Stieltjes ...
Andrea Bonfiglioli, Francesco Uguzzoni
doaj  

Benzochalcogenodiazoles, Synthesis, and Applications in Medicinal Chemistry and Photomedicine

European Journal of Organic Chemistry, Volume 28, Issue 23, June 23, 2025.
Benzochalcogenodiazoles (BXD) including benzoxadiazoles, benzothiadiazoles, and benzoselenadiazoles are initially mainly designed for optoelectronic materials as electron‐deficient cores. Nevertheless, they are now extending their application to biology.
Jean‐Elie Zheng, Xavier Franck, Thibault Gallavardin   +2 more
wiley   +1 more source

Multiple solutions for possibly degenerate equations in divergence form

Electronic Journal of Differential Equations, 2016
Via variational methods, we establish the existence of at least two distinct weak solutions for the Dirichlet problem associated to a possibly degenerate equation in divergence form.
Andrea Pinamonti
doaj  

Existence of infinitely many solutions for critical sub-elliptic systems via genus theory

Communications in Analysis and Mechanics
We are devoted to the study of the following sub-Laplacian system with Hardy-type potentials and critical nonlinearities $ \begin{equation*} \left\{\begin{aligned} -\Delta_{\mathbb{G}}u-\mu_{1}\frac{\psi^{2}u}{\text{d}(z)^{2}} = \lambda_{1}\frac{\psi^{
Hongying Jiao, Shuhai Zhu , Jinguo Zhang
doaj   +1 more source

High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential

Abstract and Applied Analysis, 2014
Let {X1,X2,…,Xm} be the basis of space of horizontal vector fields in a Carnot group G=(Rn ...
Pengcheng Niu, Kelei Zhang
doaj   +1 more source

A Roadmap for Biomass‐Driven Development of Sustainable Phase Change Materials

ChemSusChem, Volume 18, Issue 11, June 2, 2025.
This comprehensive review advances the scientific understanding of sustainability and circularity in phase change material (PCM) fabrication by providing a strategic framework for developing composites from abundant, renewable resources. By screening biomass‐derived PCMs, carbons, and biopolymers, a roadmap is outlined for the development of ...
Alina Brzęczek‐Szafran, Magdalena Gwóźdź, Nicolas Brun, Marcin Wysokowski, Karolina Matuszek   +4 more
wiley   +1 more source

Local Monotonicity and Isoperimetric Inequality on Hypersurfaces in Carnot groups

Bruno Pini Mathematical Analysis Seminar, 2010
Let G be a k-step Carnot group of homogeneous dimension Q. Later on we shall present some of the results recently obtained in [32] and, in particular, an intrinsic isoperimetric inequality for a C2-smooth compact hypersurface S with boundary @S.
Francesco Paolo Montefalcone
doaj