Results 81 to 90 of about 3,258,064 (367)

On the Cauchy Problem for a Nonlinear Kolmogorov Equation [PDF]

SIAM Journal on Mathematical Analysis, 2003
We consider the Cauchy problem related to the partial differential equation Lu ≡ ∆xu + h(u)∂yu − ∂tu = f (· ,u ), where (x, y, t) ∈ R N × R × )0 ,T (, which arises in mathematical finance and in the theory of diffusion processes. We study the regularity of solutions regarding L as a perturbation of an operator of Kolmogorov type. We prove the existence
PASCUCCI, ANDREA, Polidoro, Sergio
openaire   +4 more sources

Review of Coherent Anti‐Stokes Raman Scattering Nonresonant Background Removal and Phase Retrieval Approaches: From Experimental Methods to Deep Learning Algorithms

Advanced Photonics Research, EarlyView.
Coherent anti‐stokes Raman spectroscopy (CARS) enables high‐resolution vibrational imaging, yet non‐resonant background (NRB) distorts spectral fidelity. This review highlights NRB removal methods—from experimental strategies and numerical algorithms to emerging deep learning techniques.
Rajendhar Junjuri, Thomas Bocklitz
wiley   +1 more source

Uniqueness and stability result for Cauchy’s equation of motion for a certain class of hyperelastic materials [PDF]

, 2014
We consider Cauchy’s equation of motion for hyperelastic materials. The solution of this nonlinear initial-boundary value problem is the vector field which discribes the displacement which a particle of this material perceives when exposed to stress and ...
A. Wöstehoff, Tal Schuster
semanticscholar   +1 more source

On a generalization of the Cauchy functional equation

Aequationes Mathematicae, 1992
While looking for solutions of some functional equations and systems of functional equations introduced by S. Midura and their generalizations, we came across the problem of solving the equationg(ax + by) = Ag(x) + Bg(y) + L(x, y) (1) in the class of functions mapping a non-empty subsetP of a linear spaceX over a commutative fieldK, satisfying the ...
openaire   +2 more sources

Non‐Invasive Diagnosis of Chronic Myocardial Infarction via Composite In‐Silico‐Human Data Learning

Advanced Science, EarlyView.
This study presents a non‐invasive machine learning model to identify infarct regions in the left ventricle using cardiac strain data. By combining rodent‐based simulated data with limited human data, the model achieves high accuracy in predicting infarct size and location without the need for gadolinium contrast agents, offering a promising ...
Rana Raza Mehdi, Nikhil Kadivar, Tanmay Mukherjee, Emilio A. Mendiola, Akila Bersali, Dipan J. Shah, George Karniadakis, Reza Avazmohammadi   +7 more
wiley   +1 more source

Asymptotic estimates of solution to damped fractional wave equation

Journal of Inequalities and Applications
It is known that the damped fractional wave equation has the diffusive structure as t → ∞ $t\rightarrow \infty $ . Let u ( t , x ) = e − t cosh ( t L ) f ( x ) + e − t sinh ( t L ) L ( f ( x ) + g ( x ) ) $u(t,x)=e^{-t}\cosh (t\sqrt{L})f(x)+e^{-t} \frac{\
Meizhong Wang, Dashan Fan
doaj   +1 more source

Some class of nonlinear partial differential equations in the ring of copolynomials over a commutative ring

Frontiers in Applied Mathematics and Statistics
We study the copolynomials, i.e., K-linear mappings from the ring of polynomials K[x] into the commutative ring K. With the help of the Cauchy–Stieltjes transform of a copolynomial, we introduce and examine a multiplication of copolynomials.
Sergiy L. Gefter, Aleksey L. Piven'
doaj   +1 more source

A Nonlocal Cauchy Problem for Fractional Integrodifferential Equations

Journal of Applied Mathematics, 2012
This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach space X. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness
Fang Li, Jin Liang, Tzon-Tzer Lu, Huan Zhu   +3 more
doaj   +1 more source

Generalized Cauchy equations on groups

Aequationes Mathematicae, 1970
It is well known ([1], [3]) that any measurable solution of the Cauchy functional equationf(x+y)=f(x)+f(y) must actually be continuous. The same is true of some other functional equations likef(x+y)=f(x)f(y),f(x+y)f(x−y)=f(x) 2 −f(y) 2, etc. (cf. [1]). In this note we prove a general result of this type for functional equations on groups.
openaire   +2 more sources

Structure, Mechanics, and Mechanobiology of Fibrocartilage Pericellular Matrix Mediated by Type V Collagen

Advanced Science, EarlyView.
This study defines the structure, mechanics, and mechanobiology of the fibrocartilage pericellular matrix (PCM) using the murine meniscus, showing how collagen V deficiency alters PCM properties and disrupts cell mechanosensitive signaling. Findings emphasize the critical role of PCM in fibrocartilage mechanobiology and suggest targeting it can enhance
Chao Wang, Mingyue Fan, Su Chin Heo, Sheila M. Adams, Thomas Li, Yuchen Liu, Qing Li, Claudia Loebel, Jason A. Burdick, X. Lucas Lu, David E. Birk, Farid Alisafaei, Robert L. Mauck, Lin Han   +13 more
wiley   +1 more source