We study the topology of foliations of close cohomologous Morse forms (smooth closed 1-forms with non-degenerate singularities) on a smooth closed oriented manifold. We show that if a closed form has a compact leave $\gamma $, then any close cohomologous form has a compact leave close to $\gamma $. Then we prove that the set of Morse forms with compactifiable foliations (foliations with no locally dense leaves) is open in a cohomology class, and the number of homologically independent compact leaves does not decrease under small perturbation of the form; moreover, for generic forms (Morse forms with each singular leaf containing a unique singularity; the set of generic forms is dense in the space of closed 1-forms) this number is locally constant.
In this paper, we propose a novel algorithm for a decomposition of 3D binary shapes to rectangular blocks. The aim is to minimize the number of blocks. Theoretically optimal brute-force algorithm is known to be NP-hard and practically infeasible. We introduce its sub-optimal polynomial heuristic approximation, which transforms the decomposition problem onto a graph-theoretical problem. We compare its performance with the state of the art Octree and Delta methods. We show by extensive experiments that the proposed method outperforms the existing ones in terms of the number of blocks on statistically significant level. We also discuss potential applications of the method in image processing.
Let $A$ be a uniformly closed and locally m-convex $\Phi $-algebra. We obtain internal conditions on $A$ stated in terms of its closed ideals for $A$ to be isomorphic and homeomorphic to $C_k(X)$, the $\Phi $-algebra of all the real continuous functions on a normal topological space $X$ endowed with the compact convergence topology.
We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which $0$ is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of $C_0$-semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions to a singularly perturbed differential equation in a Banach space.
We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana and shifted Narayana polynomials.
Fréchet, strongly Fréchet, productively Fréchet, weakly bisequential and bisequential filters (i.e., neighborhood filters in spaces of the same name) are characterized in a unified manner in terms of their images in the Stone space of ultrafilters. These characterizations involve closure structures on the set of ultrafilters. The case of productively Fréchet filters answers a question of S. Dolecki and turns out to be the only one involving a non topological closure structure.
The cluster analysis and the formal concept analysis are both used to
identify significant groups of sirnilar objects. The Rice & Siff’s algorithm joins these two methods for a two-valued object-attribute (0-A) model and often significantly reduces the amount of concepts and the complexity. We consider an 0-A model with graded degrees of attributes. We define a new type of one-sided fuzzification of a conceptual lattice. We generalize the Rice & Siff’s algorithm for this case wrt a fixed rnetric. We prove the basic properties of this new lattice, metric and algorithm and discuss it on a real example.
Irreversible behavior of the ground or a rock mass encompasses both the transition of the ground over a peak strength and further development of the nonreversible movement and deformation. The irreversible ground movement is traditionally considered as the transition to chaos. However the moving ground passes through itself the energy of ground pressure, thermal energy, and exchanges by substances with surrounding rock mass. According to thermodynamics of irreversible processes, such a non-equilibrium ground behavior may create dissipative structures that are the embodiment of self-organization. The paper describes the results of the structures investigation, which have been unveiled with incremental fields of the irreversible ground movement during a landslide development and underground roadway maintenance. These structures were evolving from close interaction of the separate blocks or fragments of the ground and distant cooperation of the short-lived clusters that were periodically rearranging in time and space as the irreversible ground movement started and progressed. Extant techniques restrain basically one prevalent component of the irreversible ground movement. The other two collateral transversal components were usually ignored. However, blocking of these transverse components can prevent the development of a dangerous irreversible movement of the ground and a rock mass.
The present study devises two techniques for visualizing biological sequence data clusterings. The Sequence Data Density Display (SDDD) and Sequence Likelihood Projection (SLP) visualizations represent the input symbolical sequences in a lower-dimensional space in such a way that the clusters and relations of data elements are preserved as faithfully as possible. The resulting unified framework incorporates directly raw symbolical sequence data (without necessitating any preprocessing stage), and moreover, operates on a pure unsupervised basis under complete absence of prior information and domain knowledge.
Set of events from West Bohemian 2008 seismic swarm with known source mechanisms is processed. The events or their slips respectively are clustered into two groups: (i) principal events with slip laying in the main fault plane and (ii) complementary events deviating from that plane. From those slips we constructed image of slip distribution (a new way of data/slip presentation) and from slip distribution and variations we hypothesized about foci zone properties. Namely, we propose that western block is more rigid and compact; the eastern block appears to be constituted from several sub blocks which can interact with each other during the swarm course. Our hypothesis is supported by similar image constructed from relative rupture velocities, which we consider as independent data. The proposed structural model agrees with the existence of the different observed types of source mechanisms. and Kolář Petr, Boušková Alena.