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We show that the number of lines in an $m$--homogeneous supersolvable line arrangement is upper bounded by $3m-3$ and we classify the $m$--homogeneous supersolvable line arrangements with two modular points up-to lattice-isotopy. A lower…
In multi-resolution simulations, different system components are simultaneously modelled at different levels of resolution, these being smoothly coupled together. In the case of enzyme systems, computationally expensive atomistic detail is…
In this note we improve our upper bound given earlier by showing that every 9-fold covering of a point set in the space by finitely many translates of an octant decomposes into two coverings, and our lower bound by a construction for a…
The confluent binomial posets with the atomic function A(n) = max (1,2^(n-2)) are classified. In particular, it is shown that in general there are non-isomorphic intervals of the same length.
Simultaneous two-dimensional trapping of neutral dipolar molecules in low- and high-field seeking states is analyzed. A trapping potential of the order of 20 mK can be produced for molecules like ND3 with time-dependent electric fields. The…
The exploration of cold polar molecules in different geometries is a rapidly developing experimental and theoretical pursuit. Recently, the implementation of optical lattices has enabled confinement in stacks of planes, the number of which…
The utilization of multiple phosphorylation sites in regulating a biological response is ubiquitous in cell signaling. If each site contributes an additional, equivalent binding site, then one consequence of an increase in the number of…
We present a computational scheme for predicting the ligands that bind to a pocket of known structure. It is based on the generation of a general abstract representation of the molecules, which is invariant to rotations, translations and…
This article investigates entanglement of the motional states of massive coupled oscillators. The specific realization of an idealized diatomic molecule in one-dimension is considered, but the techniques developed apply to any massive…
We prove decoupling inequalities for mixed-homogeneous bivariate polynomials, which partially answers a conjecture of Bourgain, Demeter and Kemp.
Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index $2$ that are LCD are characterized algebraically and some good codes are found in this family. Exact…
An ensemble of directed macromolecules on a lattice is considered, where the constituting molecules are chosen as a random sequence of N different types. The same type of molecules experiences a hard-core (exclusion) interaction. We study…
We prove that octants are cover-decomposable, i.e., any 12-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into two coverings. As a corollary, we obtain that any 12-fold…
We show that the semigroup associated to a second-order elliptic system is positive if and only if the differential equations are essentially decoupled and the coefficients are real-valued. This means the system can be replaced by an…
We discuss structural correlations in mixtures of free polymer and colloidal particles based on a microscopic, 2-component liquid state integral equation theory. Whereas in the case of polymers much smaller than the spherical particles the…
In this paper, we introduce poly-Bernoulli numbers with level $2$, related to the Stirling numbers of the second kind with level $2$, and study several properties of poly-Bernoulli numbers with level $2$ from their expressions, relations,…
We present periodic Density Functional Theory calculations of the electronic properties of molecular junctions formed by amine-, and thiol-terminated alkane chains attached to two metal (Au, Ag) electrodes. Based on extensive analysis that…
A polynomial over a ring is called decomposable if it is a composition of two nonlinear polynomials. In this paper, we obtain sharp lower and upper bounds for the number of decomposable polynomials with integer coefficients of fixed degree…
Two-photon absorption (TPA) and other nonlinear interactions of molecules with time-frequency-entangled photon pairs (EPP) has been predicted to display a variety of fascinating effects. Therefore, their potential use in practical…
Scaffold proteins organize cellular processes by bringing signaling molecules into interaction, sometimes by forming large signalosomes. Several of these scaffolds are known to polymerize. Their assemblies should therefore not be understood…