Search results for "implicit function"

Reordering Method and Hierarchies for Quantum and Classical Ordered Binary Decision Diagrams

2017

We consider Quantum OBDD model. It is restricted version of read-once Quantum Branching Programs, with respect to “width” complexity. It is known that maximal complexity gap between deterministic and quantum model is exponential. But there are few examples of such functions. We present method (called “reordering”), which allows to build Boolean function g from Boolean Function f, such that if for f we have gap between quantum and deterministic OBDD complexity for natural order of variables, then we have almost the same gap for function g, but for any order. Using it we construct the total function REQ which deterministic OBDD complexity is \(2^{\varOmega (n/log n)}\) and present quantum OBD…

Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs

2014

In the paper we investigate a model for computing of Boolean functions – Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models. We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k + 1. We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient …

Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis

2000

Our aim is to present sufficient conditions ensuring Hoffman's error bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations (variational inequalities), and sensitivity analysis and on other problems like Lipschitzian properties of polyhedral multivalued mappings as well as weak sharp minima or linear conditioning. We show how the information about our sufficient conditions can be used to provide a computable constant such that Hoffman's error bound holds. We also show that this error bound is nothing but the classical Farkas lemma for linear …

Periodic and quasi-periodic orbits of the dissipative standard map

2011

We present analytical and numerical investigations of the dynamics of the dissipative standard map. We first study the existence of periodic orbits by using a constructive version of the implicit function theorem; then, we introduce a parametric representation, which provides the interval of the drift parameter ensuring the existence of a periodic orbit with a given period. The determination of quasi--periodic attractors is efficiently obtained using the parametric representation combined with a Newton's procedure, aimed to reduce the error of the approximate solution provided by the parametric representation. These methods allow us to relate the drift parameter of the periodic orbits to th…

The impact of procedural and conceptual teaching on students' mathematical performance over time

2019

The goal of the present study is to investigate the impact of procedural and conceptual teaching on students' mathematical performance over time. For this purpose, implicit differentiation and inte...

Supershape Recovery from 3D Data Sets

2006

In this paper, we apply supershapes and R-functions to surface recovery from 3D data sets. Individual supershapes are separately recovered from a segmented mesh. R-functions are used to perform Boolean operations between the reconstructed parts to obtain a single implicit equation of the reconstructed object that is used to define a global error reconstruction function. We present surface recovery results ranging from single synthetic data to real complex objects involving the composition of several supershapes and holes.

On the existence of invariant curves of twist mappings of an annulus

1983

Genetic algorithms for 3d reconstruction with supershapes

2009

Supershape model is a recent primitive that represents numerous 3D shapes with several symmetry axes. The main interest of this model is its capability to reconstruct more complex shape than superquadric model with only one implicit equation. In this paper we propose a genetic algorithms to re-construct a point cloud using those primitives. We used the pseudo-Euclidean distance to introduce a threshold to handle real data imperfection and speed up the process. Simulations using our proposed fitness functions and a fitness function based on inside-outside function show that our fitness function based on the pseudo-Euclidean distance performs better.

Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice

2005

We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity whic…

Inverse response of polypropylene to gamma radiation under vacuum

1997

Abstract The effect of gamma radiation under vacuum on polypropylene is analysed on the basis of a simple kinetic model. The influence of the irradiation parameters, total absorbed dose and dose rate, on the rates of the main reactions occurring during irradiation, i.e. β-scission, addition to double bonds and termination, is studied. Using kinetic equations, and free radical and double bond balance relationships, we show that it is possible to rationalize the response of polypropylene to gamma radiation. In particular, on the basis of the mathematical solutions of these equations, we obtain the equation of an ‘inversion curve’, implicit function of the irradiation parameters, which gives t…