Search results for "Real-valued function"
showing 10 items of 12 documents
Some Problems on Homomorphisms and Real Function Algebras
2001
In this paper we solve a problem about the representation of all homomorphisms on a real function algebra as point evaluations and another two about function algebras in which homomorphisms are point evaluations on sequences in the algebra.
A remark on differentiable functions with partial derivatives in Lp
2004
AbstractWe consider a definition of p,δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p,δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.
On the inductive inference of recursive real-valued functions
1999
AbstractWe combine traditional studies of inductive inference and classical continuous mathematics to produce a study of learning real-valued functions. We consider two possible ways to model the learning by example of functions with domain and range the real numbers. The first approach considers functions as represented by computable analytic functions. The second considers arbitrary computable functions of recursive real numbers. In each case we find natural examples of learnable classes of functions and unlearnable classes of functions.
Real symplectic formulation of local special geometry
2006
We consider a formulation of local special geometry in terms of Darboux special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the metric is obtained which is manifestly $\mathbf{Sp}(2n,\mathbb{R})$ covariant. Unlike the rigid case the metric is not given by the Hessian of the real function $S(P)$ which is the Legendre transform of the imaginary part of the holomorphic prepotential. Rather it is given by an expression that contains $S$, its Hessian and the conjugate momenta $S_I=\frac{\partial S}{\partial P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional) metric proportional to the Hessian with an appropriate conformal factor.
Observations on the Darboux coordinates for rigid special geometry
2006
We exploit some relations which exist when (rigid) special geometry is formulated in real symplectic special coordinates $P^I=(p^\Lambda,q_\Lambda), I=1,...,2n$. The central role of the real $2n\times 2n$ matrix $M(\Re \mathcal{F},\Im \mathcal{F})$, where $\mathcal{F} = \partial_\Lambda\partial_\Sigma F$ and $F$ is the holomorphic prepotential, is elucidated in the real formalism. The property $M\Omega M=\Omega$ with $\Omega$ being the invariant symplectic form is used to prove several identities in the Darboux formulation. In this setting the matrix $M$ coincides with the (negative of the) Hessian matrix $H(S)=\frac{\partial^2 S}{\partial P^I\partial P^J}$ of a certain hamiltonian real fun…
Best Proximity Points for Some Classes of Proximal Contractions
2013
Given a self-mapping g: A → A and a non-self-mapping T: A → B, the aim of this work is to provide sufficient conditions for the existence of a unique point x ∈ A, called g-best proximity point, which satisfies d g x, T x = d A, B. In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x → d g x, T x, thereby getting an optimal approximate solution to the equation T x = g x. An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-s…
Invariant pattern recognition based on 1-D Wavelet functions and the polynomial decomposition
1997
Abstract A new filter, consisting of 1-D Wavelet functions is suggested for achieving optical invariant pattern recognition. The formed filter is actually a real function, hence, it is theoretically possible to be implemented under both spatially coherent and spatially incoherent illuminations. The filter is based on the polynomial expansion, and is constructed out of a scaled bank of filters multiplied by 1-D Wavelet weight functions. The obtained output is shown to be invariant to 2-D scaling even when different scaling factors are applied on the different axes. The computer simulations and the experimental results demonstrate the potential hidden in this technique.
Sulla K-variazione Essenziale di Una Funzione reale
2005
In this paper we consider a definition of essentialK-variation for real functions which gives information on the absolute integrability of its approximate derivate on a measurable set.
Suggestions to the Reader
1998
Each section of the book consists of two parts that have different goals. The first part, namely the text itself, is systematically developed. It consists of definitions and proven assertions assembled in an organized fashion and with no significant gaps for the reader to fill. All propositions and theorems, unless ready consequences of definitions and previously proven assertions, are proved in detail.
Non-linear systems under impulsive parametric input
1999
In this paper the problem of the response of non-linear systems excited by an impulsive parametric input is treated. For such systems the response exhibits a jump depending on the amplitude of the impulse as well as on the value of the state variables immediately before the impulse occurrence. Recently, the jump prediction has been obtained in a series form. Here the incremental rule for any scalar real valued function is obtained in an analytical form involving the jump of the state variables. It is also shown that the formulation for the jump evaluation is also able to give a new step-by-step integration technique.