Results 71 to 80 of about 11,431,351 (352)
Construction of Planar Harmonic Functions
International Journal of Mathematics and Mathematical Sciences, 2007 Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk can be written in the form f=h+g¯, where h and g are analytic in the open unit disk.
Jay M. Jahangiri +2 more
doaj +1 more source
Classes of Harmonic Functions Defined by Subordination
, 2015 New classes of univalent harmonic functions are introduced. We give sufficient coefficient conditions for these classes. These coefficient conditions are shown to be also necessary if certain restrictions are imposed on the coefficients of these harmonic
J. Dziok
semanticscholar +1 more source
Harmonic functions of general graph Laplacians [PDF]
, 2013 We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an $$L^{p}$$Lp Liouville type theorem which is a quantitative integral $$L^{p}$$Lp estimate of harmonic functions analogous to Karp’s theorem ...
B. Hua, M. Keller
semanticscholar +1 more source
Molecular Oncology, EarlyView.Development of therapies targeting cancer‐associated fibroblasts (CAFs) necessitates preclinical model systems that faithfully represent CAF–tumor biology. We established an in vitro coculture system of patient‐derived pancreatic CAFs and tumor cell lines and demonstrated its recapitulation of primary CAF–tumor biology with single‐cell transcriptomics ...
Elysia Saputra +10 more
wiley +1 more source
Harmonic m-Preinvex Functions and Inequalities
International Journal of Analysis and Applications, 2018 In this paper, we introduce a new class of harmonic functions, which is called harmonic mpreinvex functions for a fixed m. Some Hermite-Hadamard inequality for harmonic m-preinvex functions are derived. Several special cases are discussed as applications
Muhammad Aslam Noor +3 more
doaj +2 more sources
A Probabilistic Characterization of g-Harmonic Functions
AIMS Mathematics, 2017 Associated with a quasi-linear generator function g, we give a definition of g-harmonic functions. The relation between the g-harmonic functions and g-martingales will be delineated.
Liang Cai, Huan-Huan Zhang, Li-Yun Pan
doaj +1 more source
Gradient estimates of harmonic functions and transition densities for Levy processes [PDF]
, 2013 We prove gradient estimates for harmonic functions with respect to a $d$-dimensional unimodal pure-jump Levy process under some mild assumptions on the density of its Levy measure. These assumptions allow for a construction of an unimodal Levy process in
T. Kulczycki, M. Ryznar
semanticscholar +1 more source
Molecular Oncology, EarlyView.Liquid biopsy enables minimally invasive, real‐time molecular profiling through analysis of circulating biomarkers in biological fluids. This Perspective highlights the importance of training pathologists through integrative educational programs, such as the European Masters in Molecular Pathology, to ensure effective and equitable implementation of ...
Marius Ilié +13 more
wiley +1 more source
Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion
, 2011 In this paper, we consider a product of a symmetric stable process in $\mathbb{R}^d$ and a one-dimensional Brownian motion in $\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process.
D Applebaum +10 more
core +1 more source
Molecular Oncology, EarlyView.The LINC01116 long noncoding RNA is induced by hypoxia and associated with poor prognosis and high recurrence rates in two cohorts of lung adenocarcinoma patients. Here, we demonstrate that besides its expression in cancer cells, LINC01116 is markedly expressed in lymphatic endothelial cells of the tumor stroma in which it participates in hypoxia ...
Marine Gautier‐Isola +12 more
wiley +1 more source