Related papers: Smiles in delta

We consider the Dirichlet problem for the nonhomogeneous equation $-\Delta_p u -\Delta_q u = \alpha |u|^{p-2}u + \beta |u|^{q-2}u + f(x)$ in a bounded domain, where $p \neq q$, and $\alpha, \beta \in \mathbb{R}$ are parameters. We explore…

In this paper, we consider the asymptotic behavior of positive solutions of the biharmonic equation $$ \Delta^2 u = u^p~~~~~~~in ~ B_1 \backslash \{0\}$$ with an isolated singularity, where the punctured ball $B_1 \backslash \{0\} \subset…

In this paper we study a Dirichlet-type differential inclusion involving the Finsler-Laplace operator on a complete Finsler manifold. Depending on the positive $\lambda$ parameter of the inclusion, we establish non-existence, as well as…

This paper considers a sequence of discrete-time random walk markets with a safe and a single risky investment opportunity, and gives conditions for the existence of arbitrages or free lunches with vanishing risk, of the form of waiting to…

Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should it be given by a limiting value on one…

We extend our framework for the automated calculation of dijet soft functions to observables that do not obey the non-Abelian exponentiation theorem, like jet-veto or grooming soft functions that are sensitive to clustering effects of the…

We study the butterfly effect of the AdS planar black holes in the framework of Einstein's general relativity. We find that the butterfly velocities can be expressed by a universal formula $v_{\rm B}^2 = TS/(2V_{\rm th} P)$. In doing so, we…

We are concerned with the small ball behavior of the smallest singular value of random matrices. Often, establishing such results involves, in some capacity, a discretization of the unit sphere. This requires bounds on the norm of the…

For any strictly positive martingale $S = \exp(X)$ for which $X$ has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials…

We demonstrate that the notions of bi-free independence and combinatorial-bi-free independence of two-faced families are equivalent using a diagrammatic view of bi-non-crossing partitions. These diagrams produce an operator model on a Fock…

Let $\mathcal B$ be an infinite subset of $\{1,2,\dots\}$. We characterize arithmetic and dynamical properties of the $\mathcal B$-free set $\mathcal F_{\mathcal B}$ through group theoretical, topological and measure theoretic properties of…

Numerical experiments of the statistical evolution of an ensemble of non-interacting particles in a time-dependent billiard with inelastic collisions, reveals the existence of three statistical regimes for the evolution of the speeds…

We process snapshots of trajectories of evolution equations with intrinsic symmetries, and demonstrate the use of recently developed eigenvector-based techniques to successfully quotient out the degrees of freedom associated with the…

We use partial zeta functions to analyse the asymptotic behaviour of certain smooth arithmetical sums over smooth k-free integers.

We study face numbers of simplicial complexes that triangulate manifolds (or even normal pseudomanifolds) with boundary. Specifically, we establish a sharp lower bound on the number of interior edges of a simplicial normal pseudomanifold…

There has been much recent interest, initiated by work of the physicists Hatano and Nelson, in the eigenvalues of certain random non-Hermitian periodic tridiagonal matrices and their bidiagonal limits. These eigenvalues cluster along a…

Let $\Omega\subset\mathbb{C}$ be a bounded domain such that there exists an algebraic harmonic function of degree two vanishing on the boundary of $\Omega.$ Then we show that the Khavinson-Shapiro conjecture holds for $\Omega:$ if the…

The discrete dipole approximation (DDA) is a popular numerical method for calculating the scattering properties of atmospheric ice crystals. The standard DDA formulation involves the uniform discretization of the underlying volume integral…

Tensor factorization models are widely used in many applied fields such as chemometrics, psychometrics, computer vision or communication networks. Real life data collection is often subject to errors, resulting in missing data. Here we…

We prove essentially sharp incidence estimates for a collection of $\delta$-tubes and $\delta$-balls in the plane, where the $\delta$-tubes satisfy an $\alpha$-dimensional spacing condition and the $\delta$-balls satisfy a…