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We study discrete versions of fractional integral operators along curves and surfaces. $l^p \to l^q$ estimates are obtained from upper bounds of the number of solutions of associated Diophantine systems. In particular, this relates the…
We present a mathematical model to decompose a longitudinal deformation into normal and abnormal components. The goal is to detect and extract subtle quivers from periodic motions in a video sequence. It has important applications in…
We construct and analyze the Standard Model of electroweak and strong interactions in multiscale spacetimes with (i) weighted derivatives and (ii) $q$-derivatives. Both theories can be formulated in two different frames, called fractional…
Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent…
X-band accelerator for multi-bunches has been a new way to produce high luminosity and energy efficiency bunches. As the smaller size and multi-bunches, the wakefield is more severe in X-band accelerator, unless some means of strongly…
We compute the generic one-loop contribution involving scalar leptoquarks (LQ) to the $W$ and $Z$ leptonic decay widths. In our computation we include for the first time the finite terms and the corrections due to the external momenta of…
A low-order method is presented for aerodynamic prediction of wings operating at near-stall and post-stall flight conditions. The method is intended for use in design, modeling, and simulation. In this method, the flow separation due to…
In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…
This article reports on a full replication study in computational fluid dynamics, using an immersed boundary method to obtain the flow around a pitching and rolling elliptical wing. As in the original study, the computational experiments…
Multi-step forecasting is often described through a simple rule of thumb: recursive strategies are said to have high bias and low variance, while direct strategies are said to have low bias and high variance. We revisit this belief by…
Bluff body wakes in stratified fluids are known to exhibit a rich range of dynamic behavior that can be categorized into different regimes based on Reynolds number ($Re$) and Froude number ($Fr$). Topological differences in wake structure…
A theoretical study of the band gap reduction under tensile stress is performed and validated through experimental measurements. First-principles calculations based on density functional theory (DFT) are performed for uniaxial stress…
Deformable mirrors with very high order correction generally have smaller dynamic range of motion than what is required to correct seeing over large aperture telescopes. As a result, systems will need to have an architecture that employs…
A multilayered plate theory which uses transverse shear warping functions issued from three-dimensional elasticity is presented. Two methods to obtain these transverse shear warping functions are detailed. The warping functions are issued…
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…
In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photoacoustic or thermoacoustic tomography. We derive and analyze…
The longitudinal structure function for nucleons and nuclei is considered at fixed $\sqrt{s}$ and $Q^2$ to the minimum value of $x$ given by $Q^2/s$. This is done using the expansion method and color dipole model in the next-to-leading…
Higher-order tensors appear in various areas of mechanics as well as physics, medicine or earth sciences. As these tensors are highly complex, most are not well understood. Thus, the analysis and the visualization process form a highly…
Particle energy chirp is shown to be a useful instrument in the staging laser wake field acceleration directed to generation of high-quality dense electron beams. The chirp is a necessary tool to compensate non-uniformity of acceleration…
We develop a numerical scheme to determine which planar snake motions are optimal for locomotory efficiency, across a wide range of frictional parameter space. For a large coefficient of transverse friction, we find that retrograde…