Related papers: Revisiting type-2 triangular norms on normal conve…

Let $d\ge 2$ and $T$ be the convolution operator $Tf(x)=\int_{\reals^{d-1}} f(x'-t,x_d-|t|^2)\,dt$, which is is bounded from $L^{(d+1)/d}(\reals^d)$ to $L^{d+1}(\reals^d)$. We show that any critical point $f\in L^{(d+1)/d}$ of the…

In 2016 and 2017, Haihui Fan, Don Hadwin and Wenjing Liu proved a commutative and noncommutative version of Beurling's theorems for a continuous unitarily invariant norm $\alpha $ on $L^{\infty}(\mathbb{T},\mu)$ and tracial finite von…

We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to…

We characterize two-weight inequalities for certain maximal truncations of the Hilbert transform in terms of testing conditions on simpler functions. For 1<p<2 and two positive Borel measures u, v on R, we assume that u is doubling, and we…

Hadwiger's theorem is a Helly-type theorem involving common transversals to families of convex sets instead of common intersections. Subsequently, Pollack and Wenger identified a necessary and sufficient condition, called a consistent…

We consider a class of two-dimensional functions f(x,y) with the property that the smallness of its rectangular norm implies the smallness of rectangular norm for f(x,x+y). Also we study a family of functions f(x,y) having a similar…

The Dimensional Regularization of Bollini and Giambiags (Phys. Lett. {\bf B 40}, 566 (1972), Il Nuovo Cim. {\bf B 12}, 20 (1972). Phys. Rev. {\bf D 53}, 5761 (1996)) can not be defined for all Schwartz Tempered Distributions Explicitly…

We classify regularity for Lagrangian mean curvature type equations, which include the potential equation for prescribed Lagrangian mean curvature and those for Lagrangian mean curvature flow self-shrinkers and expanders, translating…

We define new natural variants of the notions of weighted covering and separation numbers and discuss them in detail. We prove a strong duality relation between weighted covering and separation numbers and prove a few relations between the…

The present study is motivated by the study of reference [1], where the generalized second law of thermodynamics has been investigated for a flat FRW universe for two viable models of $f(T)$ gravity. In the present work, we have considered…

We investigate T-duality of a closed string moving in a weakly curved background of the second order. A previously discussed weakly curved background consisted of a flat metric and a linearly coordinate dependent Kalb-Ramond field with an…

This thesis investigates the quantum properties of T-duality invariant formalisms of String Theory. We introduce and review duality invariant formalisms of String Theory including the Doubled Formalism. We calculate the background field…

In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the theory of normal forms for non-commuting operators, and obtain as an application a commutativity criterion for…

For any integer $m\ge0$, we recall that triangular numbers are those $\mathbf{T}(m)=\frac{m(m+1)}{2}$. A conjecture of Sun Zhi-Wei states that an integer $2^n\pm n$ with any $n>2$ can not be a triangular number. The motivation of this work…

We prove a converse theorem for a family of L functions of degree 2 with gamma factor coming from a holomorphic cuspform. We show these L functions coincide with either those coming from a newform or a product of L functions arising from…

Let $T$ be a complete, model complete o-minimal theory extending the theory of real closed ordered fields and assume that $T$ is power bounded. Let $K$ be a model of $T$ equipped with a $T$-convex valuation ring $\mathcal{O}$ and a…

We prove that any translating soliton for the mean curvature flow which is noncollapsed and uniformly 2-convex must be the rotationally symmetric bowl soliton. In particular, this proves a conjecture of White and Wang, in the 2-convex case…

We make some observations about Rosenberg's Levi-Civita connections on noncommutative tori, noting the non-uniqueness of torsion-free metric-compatible connections without prescribed connection operator for the inner *-derivations, the…

As a corollary to our main theorem we give a new proof of the result that the norm of the Hilbert transform on L^2(w) has norm bounded by a the A_2 characteristic of a weight to the first power, a theorem of one of us. This new proof begins…

We construct non-commutative theories with the Moyal-Weyl product in the Double Field Theory (DFT) framework. We deform the infinitesimal generalized diffeomorphisms and the Leibniz rule in a consistent way. The prescription requires a…