Related papers: Discretized sum-product type problems: Energy vari…

Those galaxy clusters which do not belong to the superclusters are referred to as the isolated clusters. Their relative abundance at a given epoch may be a powerful constraint of the dark energy equation of state since it depends strongly…

Let $X$ be a finite collection of sets (or "clusters"). We consider the problem of counting the number of ways a cluster $A \in X$ can be partitioned into two disjoint clusters $A_1, A_2 \in X$, thus $A = A_1 \uplus A_2$ is the disjoint…

We prove new exponents for the energy version of the Erd\H{o}s-Szemer\'edi sum-product conjecture, raised by Balog and Wooley. They match the previously established milestone values for the standard formulation of the question, both for…

The direct comparison of two different continuum discretization methods towards the solution of a composite particle scattering off a nucleus is presented. The first approach -- the Continumm-Discretized Coupled Channel method -- is based…

First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite…

Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…

We establish power saving asymptotics for the sum of the divisor function along a binary quartic form, improving on work of Daniel. The proof involves an application of a recent two dimensional delta method due to Li, Rydin-Myerson, and…

P. Flajolet and B. Salvy \cite{FS1998} prove the famous theorem that a nonlinear Euler sum $S_{i_1i_2\cdots i_r,q}$ reduces to a combination of sums of lower orders whenever the weight $i_1+i_2+\cdots+i_r+q$ and the order $r$ are of the…

The calculation of the discrete atomistic energy of a crystal near the continuum limit encounters difficulties caused by the geometric discrepancy between the continuum region occupied by the body, and the discrete collection of lattice…

This is a sequel to the paper arXiv:1312.6438 by the same authors. In this sequel, we quantitatively improve several of the main results of arXiv:1312.6438, and build on the methods therein. The main new results is that, for any finite set…

In this paper, we discuss the role played by additional set-theoretic assumptions in the investigation of the existence of nontrivial twisted sums of $c_0$ and spaces of continuous functions on nonmetrizable compact Hausdorff spaces.

We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…

We are going to review recent advances in the theory of exclusive nonleptonic B decays. The emphasis is going to be on the factorization hypothesis and the role of nonfactorizable contributions for nonleptonic B decays. In particular, we…

B decay sum rules relate exclusive B semileptonic decay matrix elements to forward B-meson matrix elements of operators in HQET. At leading order the operators that occur are the b-quark kinetic energy $\lambda_1$ and chromomagnetic energy…

We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…

We derive the first two moment sum rules of the conduction electron retarded self-energy for both the Falicov-Kimball model and the Hubbard model coupled to an external spatially uniform and time-dependent electric field (this derivation…

We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated regime.…

In this paper, we study the soliton resolution conjecture for Type II singular solutions $\overrightarrow{u}(t)$ to the focusing energy critical wave equation in $R^d\times [0,T_+)$, with $3\leq d\leq 5$. Suppose that $u$ has a singularity…

Using an example of a mixed discrete-continuum representation of charges under the periodic boundary condition, we show that the exact pairwise form of the Ewald sum, which is well-defined even if the system is non-neutral, provides a…

Rare exclusive $B_c^\ast \rightarrow D_{s}~l^+ l^-$ decays are analyzed in the framework of the three--point QCD sum rules approach. The two gluon condensate corrections to the correlation function are included and the form factors of this…