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The Second-Level General Fractional Derivatives and Applications
International Journal of Analysis and ApplicationsIn the theory of fractional calculus, we focus on the general fractional calculus because it provides a more precise and flexible modeling tool for a wide range of complex dynamical systems. We initially consider the Sonin and Kochubei kernels along with
H. Masiha, M. Ghasemi, M. de la Sen
semanticscholar +2 more sources
, 2013 NOTE: to view these items please visit http://dynkincollection.library.cornell.eduInterview conducted by Eugene Dynkin with Issac Sonin on May 20, 2013 in College Park ...
Sonin, Isaac
core +6 more sources
THE 1ST LEVEL GENERAL FRACTIONAL DERIVATIVES AND SOME OF THEIR PROPERTIES [PDF]
Journal of Mathematical Sciences, 2022 In this paper, we first provide a short summary of the main properties of the so-called general fractional derivatives with the Sonin kernels introduced so far.
Yuri Luchko
semanticscholar +1 more source
The General Fractional Integrals and Derivatives on a Finite Interval
Mathematics, 2023 The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for the functions on the real positive semi-axis.
Mohammed Al-Refai, Yuri Luchko
doaj +1 more source
Theoretical Economics, Volume 16, Issue 2, Page 477-506, May 2021., 2021 We consider a platform that provides probabilistic forecasts to a customer using some algorithm. We introduce a concept of miscalibration, which measures the discrepancy between the forecast and the truth. We characterize the platform's optimal equilibrium when it incurs some cost for miscalibration, and show how this equilibrium depends on the ...
Yingni Guo, Eran Shmaya
wiley +1 more source
Scaling Up Your Kernels to 31×31: Revisiting Large Kernel Design in CNNs [PDF]
Computer Vision and Pattern Recognition, 2022 We revisit large kernel design in modern convolutional neural networks (CNNs). Inspired by recent advances in vision transformers (ViTs), in this paper, we demonstrate that using a few large convolutional kernels instead of a stack of small kernels could
Xiao-Han Ding +5 more
semanticscholar +1 more source
More ConvNets in the 2020s: Scaling up Kernels Beyond 51x51 using Sparsity [PDF]
International Conference on Learning Representations, 2022 Transformers have quickly shined in the computer vision world since the emergence of Vision Transformers (ViTs). The dominant role of convolutional neural networks (CNNs) seems to be challenged by increasingly effective transformer-based models.
Shiwei Liu +9 more
semanticscholar +1 more source
Sonine Transform Associated to the Dunkl Kernel on the Real Line [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We consider the Dunkl intertwining operator $V_α$ and its dual ${}^tV_α$, we define and study the Dunkl Sonine operator and its dual on $\mathbb{R}$. Next, we introduce complex powers of the Dunkl Laplacian $Δ_α$ and establish inversion formulas for the Dunkl Sonine operator $S_{α,β}$ and its dual ${}^tS_{α,β}$.
openaire +5 more sources
Home ranges and space use of muskrats Ondatra zibethicus in restricted linear habitats
Wildlife Biology, Volume 16, Issue 4, Page 400-408, December 2010., 2010 Abstract Modern farming practices in the midwestern United States have drastically altered the landscape. Most wetlands have been drained, and small streams are channelized to transport excess water away from tile‐drained agricultural fields. Loss of critical wetland habitat has shifted the distribution of muskrats Ondatra zibethicus, an economically ...
Adam A. Ahlers +3 more
wiley +1 more source
Fredholm‐Volterra integral equation with potential kernel
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 6, Page 321-330, 2001., 2001 A method is used to solve the Fredholm‐Volterra integral equation of the first kind in the space L2(Ω) × C(0, T), Ω={(x,y):x2+y2≤a}, z = 0, and T < ∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω] × [Ω]), while the kernel of Volterra integral term is a positive and continuous function ...
M. A. Abdou, A. A. El-Bary
wiley +1 more source