We prove duality results for adjoint operators and product norms in the framework of Euclidean spaces. We show how these results can be used to derive condition numbers especially when perturbations on data are measured componentwise relatively to the original data. We apply this technique to obtain formulas for componentwise and mixed condition numbers for a linear function of a linear least s...

Among the invariant factors g of a positive semidefinite analytic function f on R, those g whose zero set Y is a curve are called special. We show that if each special g is a sum of squares of global meromorphic functions on a neighbourhood of Y , then f is a sum of squares of global meromorphic functions. Here sums can be (convergent) infinite, but we also find some sufficient conditions to ge...

Cost function estimation often involves data on a function and a family of its derivatives. It is known that by using such data the convergence rates of nonparametric estimators can be substantially improved. In this paper we propose series-type estimators which incorporate various derivative data into a single, weighted, nonparametric, least-squares procedure. Convergence rates are obtained, w...

Today, mobile and its effective presence in all aspects of human life has become undeniable. The presence compared to the internet and its effect is broader and more progressive. The mobile phones and especially applications such as the SMS services are no longer a technical tool but it has a various media function, cultural, social, economic, political and shaping its own culture. This paper a...

Two groups of pattern-recognition algorithms for hybrid optical-digital computer processing are theoretically and experimentally compared. The first group is based on linear mapping, while the second group is based on feature extraction and eigenvector analysis. We study the relations among various linear-mapping-based algorithms by formulating a more general unified pseudoinverse algorithm. We...

the nature and the existence of political fiqh, in addition to its type and necessity of existence, its origin, function, and effects, and its relevance to politics, have received the attention of moslem philosphers, who categorized fiqh under politics and political sciences. this is an attempt to clarify the philosophy of political fiqh in the framework of political philosophy.

Let φ denote Euler’s totient function. The frequency with which φ(n) is a perfect square has been investigated by Banks, Friedlander, Pomerance, and Shparlinski, while the frequency with which φ(n) is a sum of two squares has been studied by Banks, Luca, Saidak, and Shparlinski. Here we look at the corresponding threesquares question. We show that φ(n) is a sum of three squares precisely sevene...