begin{abstract}using the fixed point method, we prove the generalized hyers--ulam--rassiasstability of the following functional equation in multi-banach spaces:begin{equation} sum_{ j = 1}^{n}fbig(-2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}big) =(n-6) fbig(sum_{ i = 1}^{n} x_{i}big) + 9 sum_{ i = 1}^{n}f(x_{i}).end{equation}end{abstract}

We develop analytical tools for performance analysis of multiple TCP flows (which could be using TCP CUBIC, TCP Compound, TCP New Reno) passing through a multi-hop network. We first compute average window size for a single TCP connection (using CUBIC or Compound TCP) under random losses. We then consider two techniques to compute steady state throughput for different TCP flows in a multi-hop ne...

This paper aims to address the combination of distributed generation placement and dynamic distribution network reconfiguration. Herein, a multi-strategy multi-objective improved black widow algorithm is proposed. A model established, which considers objectives minimizing active power loss, voltage deviation, carbon emission. The proposed significantly enhances traversal capability search speed...

In this paper, we extend a multi-valued contraction mapping to a cyclic multi-valued contraction mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued contraction mapping. Our results extend, generalize and unify Nadler’s multi-valued contraction mapping and many fixed point theorems for multivalued mappings. © 2012 Elsevier Ltd. All rights reserved.

Cubic membranes are soft three-dimensional crystals found within cell organelles in a variety of living systems, despite the aphorism of Fedorov: 'crystallization is death'. They consist of multi-bilayer lipid-protein stacks, folded onto anticlastic surfaces that resemble triply periodic minimal surfaces, forming highly swollen crystalline sponges. Although cubic membranes have been observed in...

We propose a new method called C-SOM for function approximation. C-SOM extends the standard Self-Organizing Map (SOM) with a combination of Local Linear Mapping (LLM) and cubic spline based interpolation techniques to improve standard SOMs' generalization capabilities. CSOM uses the gradient information provided by the LLM technique to compute a cubic spline interpolation in the input space bet...

We demonstrate the direct three-dimensional imaging of densely packed colloidal nanostructures using stimulated emission depletion microscopy. A combination of two de-excitation patterns yields a resolution of 43 nm in the lateral and 125 nm in the axial direction and an effective focal volume that is by 126-fold smaller than that of a corresponding confocal microscope. The mapping of a model s...

This paper investigates some modular powering functions suitable for cryptography. It is well known that the Rabin encryption function is a 4-to-1 mapping and breaking its one-wayness is secure under the factoring assumption. The previously reported encryption schemes using a powering function are variants of either the 4-to-1 mapping or higher n-to-1 mapping, where n > 4. In this paper, we pro...