Search results for "bundle"

Geometric properties of involutive distributions on graded manifolds

1997

AbstractA proof of the relative version of Frobenius theorem for a graded submersion, which includes a very short proof of the standard graded Frobenius theorem is given. Involutive distributions are then used to characterize split graded manifolds over an orientable base, and split graded manifolds whose Batchelor bundle has a trivial direct summand. Applications to graded Lie groups are given.

Enumeration of L-convex polyominoes by rows and columns

2005

In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.

Triple planes with $p_g=q=0$

2019

We show that general triple planes with p_g=q=0 belong to at most 12 families, that we call surfaces of type I,..., XII, and we prove that the corresponding Tschirnhausen bundle is direct sum of two line bundles in cases I, II, III, whereas is a rank 2 Steiner bundle in the remaining cases. We also provide existence results and explicit constructions for surfaces of type I,..., VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski.

The cup product of Hilbert schemes for K3 surfaces

2003

To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A [n] so that there is canonical isomorphism of rings (H *(X;ℚ)[2]) [n] ≅H *(X [n] ;ℚ)[2n] for the Hilbert scheme X [n] of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle.

Estimating additional root cohesion by exploiting a root topological model based on Leonardo’s Rule

2020

Root topological models are schematic representations of the root structure based on a defined topology graph theory. In the context of hillslope stabilization modeling against rainfall-induced shallow landslides, the root topological models may be used in combination with root strength models assessment, such as the Root Bundle Model (RBM), to estimate the ultimate root reinforcement. The effect of plant roots on slope stabilization is determined by the interaction between soil and the hydrological processes (within the root zone) and the biotechnical characteristics of the root system, such as root length, root density, root tensile strength, root area, root diameter profile and the total…

Vibrations of a continuous web on elastic supports

2017

We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports. peerReviewed

2020

Objective: The suggested link between major depression disorder (MDD) and blood–brain barrier (BBB) alterations supports an impact on the neurovascular unit in this disease condition. Here we inves...

Automatic Recognition and Analysis of Scanned Non-crimp Fabrics for Calculation of their Fluid Flow Permeability

2007

Automatic recognition of scanned images of distorted bi-axial fiber bundle arrangements is considered in order to obtain the overall permeability of the formed fiber network. Scanned images are pre-processed with color normalization followed by usage of a threshold to find the pixels belonging to the bundles, the threads keeping the bundles together, and the distinct gaps formed between the bundles. Since the scanned images virtually have a perfect grayscale, the intensity can be treated as a corresponding signal of the image. Next the regular character of the fiber network is investigated using Fourier analysis on the fiber bundles as well as on the threads. The direction, position, and s…

Dimensionless analysis of RC rectangular sections under axial load and biaxial bending

2012

This paper proposes a numerical procedure able to provide ultimate curvature and moment domains of rectangular RC sections subjected to combined axial load and biaxial bending. The formulation is carried out in dimensionless terms in order to give results that are valid for classes of sections characterized by the same values of the geometric and mechanical parameters governing the section response. The role of some of these parameters is investigated here. The results show possible correlations linking the actual values of moment and curvature to the values corresponding to two cases of uniaxial bending to be considered separately. © 2012 Elsevier Ltd.

On the sway stability improvement of car–caravan systems by articulated connections

2015

The present analysis is addressed to some promising connection arrangements between the towing vehicles and the towed trailers, where the two units are linked by four-bar isosceles trapeziums in place of the conventional pintle hitch. Two types of instability, of the divergent type or the oscillating type, may be analysed by the Routh–Hurwitz criterion or by the direct analysis of the characteristic equation. The constant term of this equation vanishes at the divergent instability threshold (zero of a real root), whereas the equation splits into two lower degree algebraic ‘sub-equations’ when the oscillating instability arises (pair of pure imaginary roots). A large field of geometrical con…