Search results for "vector"
showing 10 items of 2660 documents
Ultrarelativistic bound states in the spherical well
2016
We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator $(-\Delta )^{1/2}$, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral datafor lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled $E_{(k,l)}$ series. For each orbital label $l=0,1,2,...$ the label $k =1,2,...$ enumerates consecutive $l$-th series eigenvalues. Each of them is $2l+1$-degenerate. …
Spectral rigidity and invariant distributions on Anosov surfaces
2014
This article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity results are of independent interest and imply the existence of many geometric invariant distributions on the unit sphere bundle. In particular, we show that on any Anosov surface $(M,g)$, given a smooth function $f$ on $M$ there is a distribution in the Sobolev space $H^{-1}(SM)$ that is invariant under the geodesic flow and whose projection to $M$ i…
Almost square Banach spaces
2014
We single out and study a natural class of Banach spaces -- almost square Banach spaces. In an almost square space we can find, given a finite set $x_1,x_2,\ldots,x_N$ in the unit sphere, a unit vector $y$ such that $\|x_i-y\|$ is almost one. These spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2. We provide several examples and characterizations of almost square spaces. We prove that non-reflexive spaces which are M-ideals in their biduals are almost square. We show that every separable space containing a copy of $c_0$ can be renormed to be almost square. A local and a weak version of almost square spa…
Generalized Metric Spaces and Locally Uniformly Rotund Renormings
2009
A class of generalized metric spaces is a class of spaces defined by a property shared by all metric αspaces which is close to metrizability in some sense [Gru84]. The s-spaces are defined by replacing the base by network in the Bing-Nagata-Smirnov metrization theorem; i.e. a topological space is a αspace if it has a αdiscrete network. Here we shall deal with a further re- finement replacing discrete by isolated or slicely isolated. Indeed we will see that the identity map from a subset A of a normed space is A of a normedslicely continuous if, and only if, the weak topology relative to A has a s-slicely isolated network. If A is also a radial set then we have that the identity map Id : (X,…
An extension of Guo's theorem via k--contractive retractions
2006
Abstract Let X be a infinite-dimensional Banach space. We generalize Guo's Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k- ψ -contractions and condensing mappings, under a condition which depends on the infimum k ψ of all k ⩾ 1 for which there exists a k- ψ -contractive retraction of the closed unit ball of the space X onto its boundary.
Geometric mean and triangles inscribed in a semicircle in Banach spaces
2008
AbstractWe consider the triangles with vertices x, −x and y where x,y are points on the unit sphere of a normed space. Using the geometric means of the variable lengths of the sides of these triangles, we define two geometric constants for Banach spaces. These constants are closely related to the modulus of convexity of the space under consideration, and they seem to represent a useful tool to estimate the exact values of the James and Jordan–von Neumann constants of some Banach spaces.
THE 1-HARMONIC FLOW WITH VALUES IN A HYPEROCTANT OF THE N-SPHERE
2014
We prove the existence of solutions to the 1-harmonic flow — that is, the formal gradient flow of the total variation of a vector field with respect to the [math] -distance — from a domain of [math] into a hyperoctant of the [math] -dimensional unit sphere, [math] , under homogeneous Neumann boundary conditions. In particular, we characterize the lower-order term appearing in the Euler–Lagrange formulation in terms of the “geodesic representative” of a BV-director field on its jump set. Such characterization relies on a lower semicontinuity argument which leads to a nontrivial and nonconvex minimization problem: to find a shortest path between two points on [math] with respect to a metric w…
Bot recognition in a Web store: An approach based on unsupervised learning
2020
Abstract Web traffic on e-business sites is increasingly dominated by artificial agents (Web bots) which pose a threat to the website security, privacy, and performance. To develop efficient bot detection methods and discover reliable e-customer behavioural patterns, the accurate separation of traffic generated by legitimate users and Web bots is necessary. This paper proposes a machine learning solution to the problem of bot and human session classification, with a specific application to e-commerce. The approach studied in this work explores the use of unsupervised learning (k-means and Graded Possibilistic c-Means), followed by supervised labelling of clusters, a generative learning stra…
Extracting Features from Social Media Networks Using Semantics
2016
This paper focuses on the analysis of social media content generated by social networks (e.g. Twitter) in order to extract semantic features. By using text categorization to sort text feeds into categories of similar feeds, it has been proved to reduce the overhead that is required to retrieve these feeds and at the same time, it provides smaller pools in which further investigations can be made easier. The aim of this survey is to draw a user profile, by analysing his or her tweets. In this early stage of research, being a pre-processing phase, a dictionary based approach is considered. Moreover, the paper describes an algorithm used in analysing the text and its preliminary results. This …
Peptide classification using optimal and information theoretic syntactic modeling
2010
Accepted version of an article published in the journal: Pattern Recognition. Published version available on Sciverse: http://dx.doi.org/10.1016/j.patcog.2010.05.022 We consider the problem of classifying peptides using the information residing in their syntactic representations. This problem, which has been studied for more than a decade, has typically been investigated using distance-based metrics that involve the edit operations required in the peptide comparisons. In this paper, we shall demonstrate that the Optimal and Information Theoretic (OIT) model of Oommen and Kashyap [22] applicable for syntactic pattern recognition can be used to tackle peptide classification problem. We advoca…