Search results for "Linear form"
showing 10 items of 47 documents
The Bishop–Phelps–Bollobás point property
2016
Abstract In this article, we study a version of the Bishop–Phelps–Bollobas property. We investigate a pair of Banach spaces ( X , Y ) such that every operator from X into Y is approximated by operators which attain their norm at the same point where the original operator almost attains its norm. In this case, we say that such a pair has the Bishop–Phelps–Bollobas point property (BPBpp). We characterize uniform smoothness in terms of BPBpp and we give some examples of pairs ( X , Y ) which have and fail this property. Some stability results are obtained about l 1 and l ∞ sums of Banach spaces and we also study this property for bilinear mappings.
The effect of wind on jumping distance in ski jumping – fairness assessed
2012
The special wind compensation system recently adopted by Federation Internationale de Ski (FIS; International Ski Federation) to consider the effects of changing wind conditions has caused some controversy. Here, the effect of wind on jumping distance in ski jumping was studied by means of computer simulation and compared with the wind compensation factors used by FIS during the World Cup season 2009/2010. The results showed clearly that the effect of increasing head/tail wind on jumping distance is not linear: +17.4 m/ − 29.1 m, respectively, for a wind speed of 3 m/s. The linear formula used in the trial period of the wind compensation system was found to be appropriate only for a limited…
Novel 3D bio-macromolecular bilinear descriptors for protein science: Predicting protein structural classes
2015
In the present study, we introduce novel 3D protein descriptors based on the bilinear algebraic form in the ℝn space on the coulombic matrix. For the calculation of these descriptors, macromolecular vectors belonging to ℝn space, whose components represent certain amino acid side-chain properties, were used as weighting schemes. Generalization approaches for the calculation of inter-amino acidic residue spatial distances based on Minkowski metrics are proposed. The simple- and double-stochastic schemes were defined as approaches to normalize the coulombic matrix. The local-fragment indices for both amino acid-types and amino acid-groups are presented in order to permit characterizing fragme…
A survey on solvable sesquilinear forms
2018
The aim of this paper is to present a unified theory of many Kato type representation theorems in terms of solvable forms on a Hilbert space \((H,\langle\cdot,\cdot\rangle)\) In particular, for some sesquilinear forms Ω on a dense domain \(D\subseteq\mathcal {H}\) one looks for a representation \(\Omega(\xi,\eta)= \langle T\xi,\eta\rangle\) \((\xi\epsilon\mathcal{D}\mathcal(T),\eta\epsilon D)\) where T is a densely defined closed operator with domain \(D(\mathcal{T})\subseteq \mathcal{D}\). There are two characteristic aspects of a solvable form on H. One is that the domain of the form can be turned into a reexive Banach space that need not be a Hilbert space. The second one is that represe…
Laguerre Matrix-Collocation Method to Solve Systems of Pantograph Type Delay Differential Equations
2020
In this study, an improved matrix method based on collocation points is developed to obtain the approximate solutions of systems of high-order pantograph type delay differential equations with variable coefficients. These kinds of systems described by the existence of linear functional argument play a critical role in defining many different phenomena and particularly, arise in industrial applications and in studies based on biology, economy, electrodynamics, physics and chemistry. The technique we have used reduces the mentioned delay system solution with the initial conditions to the solution of a matrix equation with the unknown Laguerre coefficients. Thereby, the approximate solution is…
General formulae for polarization observables in two-body break-up of deuteron photodisintegration
1988
The formal expressions of all possible polarization observables ind(γ,N)N with polarized photons and oriented deuterons are derived in terms of thet-matrix elements. Furthermore, using the multipole expansion of thet-matrix, all observables are expanded in terms of Legendre polynomials or associated functions, the coefficients of which are given as bilinear forms of the multipole moments and allow a model independent analysis of experimental data.
Representation Theorems for Solvable Sesquilinear Forms
2017
New results are added to the paper [4] about q-closed and solvable sesquilinear forms. The structure of the Banach space $\mathcal{D}[||\cdot||_\Omega]$ defined on the domain $\mathcal{D}$ of a q-closed sesquilinear form $\Omega$ is unique up to isomorphism, and the adjoint of a sesquilinear form has the same property of q-closure or of solvability. The operator associated to a solvable sesquilinear form is the greatest which represents the form and it is self-adjoint if, and only if, the form is symmetric. We give more criteria of solvability for q-closed sesquilinear forms. Some of these criteria are related to the numerical range, and we analyse in particular the forms which are solvable…
Iterative construction of Dupin cyclides characteristic circles using non-stationary Iterated Function Systems (IFS)
2012
International audience; A Dupin cyclide can be defined, in two different ways, as the envelope of an one-parameter family of oriented spheres. Each family of spheres can be seen as a conic in the space of spheres. In this paper, we propose an algorithm to compute a characteristic circle of a Dupin cyclide from a point and the tangent at this point in the space of spheres. Then, we propose iterative algorithms (in the space of spheres) to compute (in 3D space) some characteristic circles of a Dupin cyclide which blends two particular canal surfaces. As a singular point of a Dupin cyclide is a point at infinity in the space of spheres, we use the massic points defined by J.C. Fiorot. As we su…
A Kato's second type representation theorem for solvable sesquilinear forms
2017
Kato's second representation theorem is generalized to solvable sesquilinear forms. These forms need not be non-negative nor symmetric. The representation considered holds for a subclass of solvable forms (called hyper-solvable), precisely for those whose domain is exactly the domain of the square root of the modulus of the associated operator. This condition always holds for closed semibounded forms, and it is also considered by several authors for symmetric sign-indefinite forms. As a consequence, a one-to-one correspondence between hyper-solvable forms and operators, which generalizes those already known, is established.
THE BISHOP-PHELPS-BOLLOBAS THEOREM FOR BILINEAR FORMS
2013
In this paper we provide versions of the Bishop-Phelps-Bollobás Theorem for bilinear forms. Indeed we prove the first positive result of this kind by assuming uniform convexity on the Banach spaces. A characterization of the Banach space Y Y satisfying a version of the Bishop-Phelps-Bollobás Theorem for bilinear forms on ℓ 1 × Y \ell _1 \times Y is also obtained. As a consequence of this characterization, we obtain positive results for finite-dimensional normed spaces, uniformly smooth spaces, the space C ( K ) \mathcal {C}(K) of continuous functions on a compact Hausdorff topological space K K and the space K ( H ) K(H) of compact operators on a Hilbert space H H . On the other hand, the B…