Related papers: Power series expansions for the planar monomer-dim…
In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second order in space, with numerical solutions satisfying all three…
An implicit purification scheme is proposed for calculation of the temperature-dependent, grand canonical single-particle density matrix, given as a Fermi operator expansion in terms of the Hamiltonian. The computational complexity is shown…
This paper concerns the exponentiation of monomial ideals. While it is customary for the exponentiation operation on ideals to consider natural powers, we extend this notion to powers where the exponent is a positive real number. Real…
We propose a method to compute, for a given potential model, an arbitrary coefficient of the effective-range function expanded as a power series in energy. The method is based on a set of recurrence relations at low energy, that allows a…
In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool…
Independent random monomer activities are considered on a mean-feld monomer-dimer model. Under very general conditions on the randomness the model is shown to have a self-averaging pressure density that obeys a solvable variational…
The theory of formal power series and derivation is developed from the point of view of the power matrix. A Loewner equation for formal power series is introduced. We then show that the matrix exponential is surjective onto the group of…
A systematic procedure to study one-dimensional Schr\"odinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting…
Generalized power asymptotic expansions of solutions to differential equations that depend on parameters are investigated. The changing nature of these expansions as the parameters of the model cross critical values is discussed. An…
The fourth-order ordinary differential equation, defining new transcendents, is studied. The self-similar solutions of the Kaup-Kupershmidt and Savada-Kotera equations are shown to be found taking its solutions into account. Equation…
We consider two-loop planar contributions to a three-body form factor at the next-to-leading power in the high-energy limit, where the masses of external particles are much smaller than their energies. The calculation is performed by…
We perform a cosmological analysis in which we allow the primordial power spectrum of scalar perturbations to assume a shape that is different with respect to the usual power-law, arising from the simplest models of cosmological inflation.…
Accurate calculations of solvation free energies remain a central challenge in molecular simulations, often requiring extensive sampling and numerous alchemical intermediates to ensure sufficient overlap between phase-space distributions of…
The maximum particle kinetic energy that can be extracted from an initial six-dimensional phase space distribution motivates the concept of free or available energy. The free energy depends on the allowed operations that can be performed. A…
One reason that free energy difference calculations are notoriously difficult in molecular systems is due to insufficient conformational overlap, or similarity, between the two states or systems of interest. The degree of overlap is…
Fan et al. (2015) recently introduced a remarkable method for increasing asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the…
We find exact power-law solutions for scalar-tensor theories and clarify the conditions under which they can account for an accelerated expansion of the Universe. These solutions have the property that the signs of both the Hubble rate and…
We consider the number of linear extensions of an N-free order P. We give upper and lower bounds on this number in terms of parameters of the corresponding arc diagram. We propose a dynamic programming algorithm to calculate the number. The…
The flexibility of active ($p$) and reactive power ($q$) consumption in distributed energy resources (DERs) can be represented as a (potentially non-convex) set of points in the $p$-$q$ plane. Modeling of the aggregated flexibility in a…
A set of cosmological models that takes into account the variation of the particle number is presented. In this context both dark matter and dark energy can be explained using a single component, without assuming any exotic equation of…