相关论文: Computation of Atomic Fibers of Z-Linear Maps

For given matrix $A\in\Z^{d\times n}$, the set $P^I_{A,b}=\{z:Az=b,z\in\Z^n_+\}$ describes the preimage or fiber of $b\in\Z^d$ under the $\Z$-linear map $f_A:\Z^n_+\to\Z^d$, $x\mapsto Ax$. The fiber $P^I_{A,b}$ is called atomic, if…

In this paper, a new class of optical fibers is studied, i.e. microstructured fibers or photonic crystal fibers (PCF). The main objective is to characterize these fibers using different dispersion diagrams and present an interface that…

A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…

Connected components of real algebraic sets are semi-algebraic, i.e. they are described by a boolean formula whose atoms are polynomial constraints with real coefficients. Computing such descriptions finds topical applications in optical…

Let $X$ be a smooth projective surface such that linear and numerical equivalence of divisors on $X$ coincide and let $\sigma\subseteq |D|$ be a linear pencil on $X$ with integral general fibers. A fiber of $\sigma$ will be called special…

A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1,1) x…

We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite…

Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to…

We describe theoretically a setup in which a tapered optical nanofibre is introduced into an optical lattice potential for cold atoms. Firstly, we consider the disturbance to the geometry of the lattice potential due to scattering of the…

The paper describes a new algorithm of construction of the nonlinear arithmetic triangle on the basis of numerical simulation and the binary system. It demonstrates that the numbers that fill the nonlinear arithmetic triangle may be…

In this paper we consider $m$ ($m \geq 1$)conjunctions of Max-atoms that is atoms of the form $\max(z,y) + r \geq x$, where the offset $r$ is a real constant and $x,y,z$ are variables. We show that the Max-atom problem (MAP) belongs to…

We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…

With its three independent parameters, the $ABCD$ matrix serves as the beam transfer matrix in optics. If it is transformed to an equi-diagonal form, the matrix has only two independent parameters determined by optical devices. It is shown…

We show how it is possible to realize quantum computations on a system in which most of the parameters are practically unknown. We illustrate our results with a novel implementation of a quantum computer by means of bosonic atoms in an…

Parameterized algebraic curves and surfaces are widely used in geometric modeling and their manipulation is an important task in the processing of geometric models. In particular, the determination of the intersection loci between points,…

Let $p$ be a prime, $m$ be a positive integer ( $m \geq 1$, and $m \geq 2$ if $p=2$), and $\chi_n$ be a multiplicative complex character on $\mathbb F^*_{p^m}$ with order $n| (p^m-1)$. We show that a partition $\mathcal A_1 \cup \mathcal…

Fiber-reinforced ceramic-matrix composites are advanced materials resistant to high temperatures, with application to aerospace engineering. Their analysis depends on the detection of embedded fibers, with semi-supervised techniques usually…

Most proteins perform their biological function by interacting with one or more molecular partners. In this respect, characterizing the features of the molecular surface, especially in the portions where the interaction takes place, turned…

Let $M$ be a Puiseux monoid, that is, a monoid consisting of nonnegative rationals (under addition). A nonzero element of $M$ is called an atom if its only decomposition as a sum of two elements in $M$ is the trivial decomposition (i.e.,…

We prove results on fibers of polynomial mappings Rn ! Rn and deduce when such mappings are surjective under certain conditions.