Search results for "Intersection"
showing 10 items of 213 documents
“Ill-Conditioned” Vertices
1970
The round-off errors tend to increase particularly rapidly after pivoting at “ill-conditioned” vertices. Those vertices where two or more hyperplanes, each representing one constraint, intersect at a very slight angle are considered as “ill-conditioned”. An “ill-conditioned” vertex is for instance given by the intersection of the two constraints: $$\eqalign{ & 3\,{{\rm{x}}_{\rm{1}}}\, + \,{{\rm{x}}_{\rm{2}}}\, \le \,6 \cr & {{\rm{x}}_{\rm{1}}}\, + \,.354\,{{\rm{x}}_{\rm{2}}}\, \le \,2.001 \cr} $$
Thin Points of Brownian Motion Intersection Local Times
2005
Let \(\ell \) be the projected intersection local time of two independent Brownian paths in \(\mathbb{R}^d \) for d = 2, 3. We determine the lower tail of the random variable \(\ell \)(B(0, 1)), where B(0, 1) is the unit ball. The answer is given in terms of intersection exponents, which are explicitly known in the case of planar Brownian motion. We use this result to obtain the multifractal spectrum, or spectrum of thin points, for the intersection local times.
Efficient analysis of cubic junction of rectangular waveguides using admittance-matrix representation
2000
In the paper an efficient and accurate method, based on the multimode-admittance-matrix representation and the theory of cavities, is proposed for the analysis of a six-port ‘cubic’ junction composed of the orthogonal intersection of three rectangular waveguides. Very simple closed-form analytical expressions are explicitly detailed for all matrix elements of this basic key building block. More general waveguide multiport junctions, composed of a central cubic junction with arbitrarily shaped waveguide access ports, are also studied using a segmentation procedure. To validate the theory, numerical results are first discussed for a standard rectangular waveguide six-port cross junction. Fina…
Line based motion estimation and reconstruction of piece-wise planar scenes
2011
We present an algorithm for reconstruction of piece-wise planar scenes from only two views and based on minimum line correspondences. We first recover camera rotation by matching vanishing points based on the methods already exist in the literature and then recover the camera translation by searching among a family of hypothesized planes passing through one line. Unlike algorithms based on line segments, the presented algorithm does not require an overlap between two line segments or more that one line correspondence across more than two views to recover the translation and achieves the goal by exploiting photometric constraints of the surface around the line. Experimental results on real i…
IWILDS'20
2020
Web search is one of the most ubiquitous online activities and often used for learning purposes, i.e., to extend one's knowledge or skills about certain topics or procedures. The importance of learning as an outcome of Web search has been recognized in research at the intersection of information retrieval, human-computer interaction, psychology, and educational sciences. Search as Learning (SAL) research examines relationships between querying, navigation, and reading behavior during Web search and the resulting learning outcomes, and how they can be measured, predicted, and supported. IWILDS aims to provide a platform to the interdisciplinary SAL community, with the objective to bring toge…
Ultrafast decay of the excited singlet states of thioxanthone by internal conversion and intersystem crossing.
2010
The experimental ultrafast photophysics of thioxanthone in several aprotic organic solvents at room temperature is presented, measured using femtosecond transient absorption together with high-level ab initio CASPT2 calculations of the singlet- and triplet-state manifolds in the gas phase, including computed state minima and conical intersections, transition energies, oscillator strengths, and spin-orbit coupling terms. The initially populated singlet pi pi* state is shown to decay through internal conversion and intersystem crossing processes via intermediate n pi* singlet and triplet states, respectively. Two easily accessible conical intersections explain the favorable internal conversio…
Mirror symmetry and toric degenerations of partial flag manifolds
1998
In this paper we propose and discuss a mirror construction for complete intersections in partial flag manifolds $F(n_1, ..., n_l, n)$. This construction includes our previous mirror construction for complete intersection in Grassmannians and the mirror construction of Givental for complete flag manifolds. The key idea of our construction is a degeneration of $F(n_1, ..., n_l, n)$ to a certain Gorenstein toric Fano variety $P(n_1, ..., n_l, n)$ which has been investigated by Gonciulea and Lakshmibai. We describe a natural small crepant desingularization of $P(n_1, ..., n_l, n)$ and prove a generalized version of a conjecture of Gonciulea and Lakshmibai on the singular locus of $P(n_1, ..., n…
The Topology of the Milnor Fibration
2020
The fibration theorem for analytic maps near a critical point published by John Milnor in 1968 is a cornerstone in singularity theory. It has opened several research fields and given rise to a vast literature. We review in this work some of the foundational results about this subject, and give proofs of several basic “folklore theorems” which either are not in the literature, or are difficult to find. Examples of these are that if two holomorphic map-germs are isomorphic, then their Milnor fibrations are equivalent, or that the Milnor number of a complex isolated hypersurface or complete intersection singularity \((X, \underline {0})\) does not depend on the choice of functions that define …
Separation properties of continuous maps in codimension 1 and geometrical applications
1992
Abstract Nuno Ballesteros, J.J. and M.C. Romero Fuster, Separation properties of continuous maps in codimension 1 and geometrical applications, Topology and its Applications 46 (1992) 107-111. We show that the image of a proper closed continuous map, f , from an n -manifold X to an ( n + 1)-manifold Y , such that H 1 (Y; Z 2 ) =0 , separates Y into at least two connected components provided the self-intersections set of f is not dense in any connected component of Y . We also obtain some geometrical applications.
Multiobjective optimization and decision making in engineering sciences
2021
AbstractReal-world decision making problems in various fields including engineering sciences are becoming ever more challenging to address. The consideration of various competing criteria related to, for example, business, technical, workforce, safety and environmental aspects increases the complexity of decision making and leads to problems that feature multiple competing criteria. A key challenge in such problems is the identification of the most preferred trade-off solution(s) with respect to the competing criteria. Therefore, the effective combination of data, skills, and advanced engineering and management technologies is becoming a key asset to a company urging the need to rethink how…