and Applied Analysis 3 2. Preliminaries LetM : R → R be anN-function, that is,M is continuous, convex, withM t > 0 for t > 0, M t /t → 0 as t → 0 and M t /t → ∞ as t → ∞. The N-function M conjugate to M is defined byM t sup{st −M s : s > 0}. Let P and Q be two N-functions. P Q means that P grows essentially less rapidly than Q; that is, for each ε > 0, P t Q εt −→ 0 as t −→ ∞. 2.1 The N-functio...

T he purpose of this paper is the evaluation of suitability ofspatial error STAR model for modeling convergence of social welfare of Iran's provinces between 2000 and 2013. In this paper the LM tests show that the non-linear method is appropriate for convergence evaluation. In addition, the results indicate that 2 groups of provinces are separable: group 1 in which the social welfare...

We describe a technique for solving for the orbital elements of multiple planets from radial velocity (RV) and/or astrometric data taken with 1 m/s and μas precision, appropriate for efforts to detect Earth-massed planets in their stars’ habitable zones, such as NASA’s proposed Space Interferometry Mission. We include details of calculating analytic derivatives for use in the Levenberg-Marquard...

the aim of this paper is to introduce and study a new concept of strong double δ ( a ) σ -convergence sequences with respect to an orlicz function, and some properties of the resulting sequencespaces were also examined. in addition, we define the δ ( a ) σ -statistical convergence and establish someconnections between the spaces of strong double δ ( a ) σ -convergence sequences and the space of...

the concept of ${mathscr{f}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{f}}$. its equivalence to the concept of ${mathscr{f}}$-convergence in uniform spaces is proved. this convergence generalizes many kinds of convergence, including the well-known statistical convergence.

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

We provide a framework for preconditioning nonlinear three-dimensional electromagnetic inverse scattering problems using nonlinear conjugate gradient (NLCG) and limited memory (LM) quasi-Newton methods. Key to our approach is the use of an approximate adjoint method that allows for an economical approximation of the Hessian that is updated at each inversion iteration. Using this approximate Hes...

in this paper, we discuss the equivalent conditions of pretopological and topological $l$-fuzzy q-convergence structures and define $t_{0},~t_{1},~t_{2}$-separation axioms in $l$-fuzzy q-convergence space. {furthermore, $l$-ordered q-convergence structure is introduced and its relation with $l$-fuzzy q-convergence structure is studied in a categorical sense}.

Efficient second order algorithm for training feedforward neural networks is presented. The algorithm has a similar convergence rate as the Lavenberg-Marquardt (LM) method and it is less computationally intensive and requires less memory. This is especially important for large neural networks where the LM algorithm becomes impractical. Algorithm was verified with several examples.

Artificial Neural Networks (ANN) techniques, mostly Back-Propagation Neural Network (BPNN) algorithm has been used as a tool for recognizing a mapping function among a known set of input and output examples. These networks can be trained with gradient descent back propagation. The algorithm is not definite in finding the global minimum of the error function since gradient descent may get stuck ...