Mathematics

In this study, we develop a stochastic framework for computing Delta sensitivities in energy markets, where both prices and traded volumes are modeled as correlated stochastic processes. Within this framework, we analyze two complementary…

In this article, we investigate the local well-posedness of the nonlinear Schr\"odinger equation on the two-dimensional sphere $\mathbb{S}^2$: \begin{align*} i\partial_tu+\Delta_{g}u=F(u). \end{align*} The nonlinearity $F(u)$ is assumed to…

We show that there is no infinite spin at total collisions for $-\kappa$-homogeneous N-body problem in higher dimensional Euclidean space $\mathbb{R}^d$, in which $0 < \kappa < 2$ ($\kappa = 1$ the Newtonian case), provided the limiting…

In this paper, we construct several explicit examples of singular sets of Hausdorff dimension $(n-2)$ in $\mathbb{R}^n$ on free boundaries for an elliptic system modeling long range segregation. The system has been previously studied by…

Motivated by the recent work of Lipton on the M\"obius energy of helix curves, we extend the study to the $L^p$ asymptotics of the meromorphic family \[ M_\rho(t) = \frac{\rho^2+1}{\rho^2 t^2 + 4 \sin^2(t/2)} - \frac{1}{t^2}. \] The helix…

Let $X$ be a Gorenstein minimal $3$-fold of general type whose canonical map is generically finite. We prove that if $p_g(X)> 243$, then the degree of the canonical map is at most $72$. Moreover, equality holds only if the general fibre $F$…

In this paper, we propose a new view, which leads to almost sure well-posedness in $H^{s}(\mathbb{R}), s\geq 0$, for studying stochastic KdV equations. Different from \cite{de1999white} or \cite{kdvmuti}, by introducing a solution space…

In large scale X ray Computed Tomography (CT) inverse problems, the forward and back projectors are often generated using different discretizations. This discrepancy leads to unmatched pairs of projections, resulting in inconsistent normal…

We propose and analyze a second-order consistent-splitting scheme, based on the generalized scalar auxiliary variable (GSAV) approach, for the two-dimensional perturbed Boussinesq system. The system is obtained by subtracting a stable,…

A partial Latin square of order $n$ is called $\epsilon$-dense if each row and each column contains at most $\epsilon n$ filled cells, and each symbol occurs at most $\epsilon n$ times. A partial Latin square is said to be completable if…

Each year, disruptions in the air transportation network strand millions of passengers and cost airlines billions in revenue. Airline networks prioritize operational and cost efficiency through hub-and-spoke structures that maximize…

Analysing costs is crucial for optimising the operational efficiency and resource allocation in systems evolving under uncertainty. In this paper, we study the distribution of costs associated with the evolution of level-dependent…

We derive explicit formulas for the HOMFLY polynomials of the torus links $T(3,n)$ using braid groups and the skein relation. We first treat the case of $T(2,n)$ and then derive a five-term linear recurrence for an auxiliary sequence…

We propose a variational approach to principal spectral values of non-selfadjoint operator pencils $\mathcal L u=\lambda\mathcal G u$, where the weight operator $\mathcal G$ may be singular. The aim is to obtain Rayleigh-type minimax…

The moduli space of meromorphic Higgs bundles admits a Poisson structure due to the independent work of Bottacin and Markman. In this paper, we revisit the symplectic leaves of this Poisson structure for the tame case. We study the partial…

This paper addresses the inverse problem of simultaneously recovering the fractional order $\alpha \in (0,1)\cup (1,2)$ and the time-dependent source factor $p(t)$ in the Cauchy problem for an evolution equation with a general self-adjoint…

We construct infinitely many embedded minimal hypersurfaces of pairwise distinct irreducible topological types in the unit $4$-sphere $\mathbb{S}^4$, which provides a new answer to a problem of Hsiang. These examples are topologically…

We study Witt-vector affine Springer fibers for tame equi-valued conjugacy classes in tamely ramified groups. Similar to the approach of Goresky-Kottwitz-MacPherson in the equal characteristic setting, we show that they admit pavings by…

This is an update of an expository article on the geometrization of orbital integrals of spherical Hecke functions on reductive groups over non-archimedean local fields, appeared in Proceedings of ICCM 2019. Compared to the published…

Let $r\ge 3$ and let $1>p_1\ge p_2\ge\cdots\ge p_n>0$. Let $\mu_{\mathbf p}$ denote the product measure on $2^{[n]}$ where each coordinate $i$ is included independently with probability $p_i$. A family $\mathcal A\subseteq 2^{[n]}$ is…