We study preheating in the Palatini formalism with a quadratic inflaton potential and an added $\alpha R^2$ term. In such models, oscillating field repeatedly returns to plateau of Einstein frame potential, on which tachyonic instability fragments condensate within less than e-fold. find that takes place when \gtrsim 10^{13}$ energy density fragmented grows rate $\Gamma/H \approx 0.011 \times \...

In this paper, we study the number of $\mathbb F_{q^n}$-rational points on affine curve $\mathcal{X}_{d,a,b}$ given by equation $$ y^d=ax\text{Tr}(x)+b,$$ where $\text{Tr}$ denote trace function from F_{q^n}$ to F_{q}$ and $d$ is a positive integer. particular, present bounds for F_{q}$-rational and, cases satisfies natural condition, explicit formulas rational are obtained. Particularly, compl...

We consider the Monge-Amp\`ere equation $\det(D^2u)=f$ in $\mathbb{R}^n$, where $f$ is a positive bounded periodic function. prove that $u$ must be sum of quadratic polynomial and For $f\equiv 1$, this classic result by J\"orgens, Calabi Pogorelov. $f\in C^\alpha$, was proved Caffarelli first named author.

Various gedanken experiments of quantum gravity phenomenology in search a complete theory near the Planck scale indicate modification Heisenberg uncertainty principle to generalized (GUP). This leads nontrivial contributions on Hamiltonian nonrelativistic particle moving an arbitrary potential. In this paper we study path integral representation potential using most general form GUP containing ...

Error commission evokes changes in event-related potentials, autonomic nervous system activity, and behavior, presumably reflecting the operation of a cognitive control network. Here we test the hypothesis that errors lead to increased cortical arousal, measurable as changes in electroencephalogram (EEG) alpha band power. Participants performed a Stroop task while EEG was recorded. Following co...

In this paper we apply the $L$-function Ratios Conjecture to compute one-level density for a symplectic family of $L$-functions attached Hecke characters infinite order. When support Fourier transform corresponding test function $f$ reaches $1$, observe transition in main term, as well lower order term. The term is line with behavior recently observed by D. Fiorilli, J. Parks, and A. S\"odergre...

It is demonstrated that the surviving fraction of a population of cells with heterogeneous radio sensitivity, like that composing most malignant tumors, conforms to a different linear quadratic survival relation for dose less than about 3-5 Gy and dose greater than about 7-9 Gy. In the intermediate range of dose the survival relation for the population, as a whole, is not linear quadratic. Cons...

Let M be a connected compact Riemannian manifold possibly with boundary ∂M, let V ∈ C2(M) such that μ(dx) := eV (x)dx is probability measure, where dx the volume and L =Δ +∇V. As continuation to Wang Zhu (2019) convergence in quadratic Wasserstein distance \(\mathbb {W}_{2}\) studied for empirical measures of L-diffusion process (with reflecting if ∂M≠∅), this paper presents exact rate subordin...

In this article we study weighted sums of $n$ i.i.d. Gamma( notation="LaTeX">$\alpha $ ) random variables with nonnegative weights. We show that for notation="LaTeX">$n \geq 1/\alpha the sum equal coefficients maximizes differential e...