In this work we consider the problem of estimating function-on-scalar regression models when functions are observed over multi-dimensional or manifold domains and with potentially multivariate output. We establish minimax rates convergence present an estimator based on reproducing kernel Hilbert spaces that achieves rate. To better interpret derived rates, extend well-known links between RKHS S...

A viable model for inflation driven by a torsion function in Friedmann background is presented. The scalar spectral index the interval $0.92\lesssim n_{s}\lesssim 0.97$ obtained order to satisfy initial conditions inflation. post inflationary phase also studied, and analytical solutions scale factor energy density generalizes that ones matter dominated universe, indicating just small deviation ...

Direct Volume Rendering (DVR) is commonly used to visualize scalar fields. Quality and significance of rendered images depend on the choice of appropriate transfer functions that assigns optical properties (e.g., color and opacity) to scalar values. We present a method that automatically generates a transfer function based on the topological behavior of a scalar field. Given a scalar field defi...

Summary It is common to want regress a scalar response on random function. This paper presents results that advocate local linear regression based projection as nonparametric approach this problem. Our asymptotic demonstrate functional outperforms its constant counterpart. Beyond the estimation of operator itself, also useful tool for predicting derivative operator, promising mathematical objec...

This paper considers the multidimensional active scalar problem of motion of a function ρ(x, t) by a velocity field obtained by v = −∇N ∗ρ, where N is the Newtonian potential. We prove well-posedness of compactly supported L∞ ∩ L solutions of possibly mixed sign. These solutions include an important class of solutions that are proportional to characteristic functions on a time-evolving domain. ...

This paper considers the multidimensional active scalar problem of motion of a function 25 ρ(x, t) by a velocity field obtained by v = −∇N ∗ρ, where N is the Newtonian potential. 26 We prove well-posedness of compactly supported L∞ ∩ L1 solutions of possibly mixed 27 sign. These solutions include an important class of solutions that are proportional to 28 characteristic functions on a time-evol...

We study the vacuum polarization of a massless minimally coupled scalar field at the horizon of four-charge STU black holes. We compare the results for the standard asymptotically flat black holes and for the black holes obtained in the “subtracted limit”, both in the general static case and at the horizon pole for the general rotating case. The original and the subtracted results are identical...