The Hybrid Numbers of Padovan and Some Identities

In this article, we will define Padovan’s hybrid numbers, based on the new noncommutative numbering system studied by Özdemir ([7]). Such a system that is a set involving complex, hyperbolic and dual numbers. In addition, Padovan’s hybrid numbers are created by combining this set, satisfying the relation ih = −hi = ɛ + i. Given this, some properties and identities are shown for these numbers, such as Binet’s formula, generating matrix, characteristic equation, norm, and generating function. In addition, these numbers are extended to the integer field and some identities are made.

Modeling and optimum design band pass filter for mid IR region

In this study, we design narrow band pass filter for window (3_5) ?m dependent on the needle optimization method , and a comparison with global designs published -Also, the effect of change parameter design on the optical performance of filter was studded and being able to overcome the difficulties of the design.In this study, the adoption of homogeneous optical properties materials as thin film depositing on a substrate of germanium at wavelength design (? = 4 ?m). For design this kind of filters we used advanced computer program (Matlab )to build a model design dependent both matrix characteristic and Needle technique. In this paper we refer to the type of Mert function , which is used for correct optical performance access to the target in very short time.

Osteoconductive Nanocomposite Materials for Bone Regeneration

Bone defect is one of the most important problem in orthopaedic therapy in which application of a biomaterial filling is necessary. Such material should be biocompatible, osteoconductive and porous as well as bioactive and compatible with the bone tissue. Subject of the work was investigations on nanocomposite membrane materials which consisted on synthetic polymer – poly-e-caprolactone (PCL) matrix and ceramic nanoparticles; tricalcium phosphate (TCP) and silica (SiO2) as a nano-filler. The nanocomposite membrane materials were produced by two-step dispersion of the nanoparticles in the biopolymer matrix. Characteristic of nanoparticles were made using transmission electron microscope (TEM), distribution of nanoparticles size (DLS) and specific surface area (BET). The morphology of nanocomposites and homogenous distribution of nanoadditives were made using scanning electron microscope with EDS analysis. Introduction of the nanofillers into the polymer matrix was monitored by thermal analysis method (TG-DCS). It was shown that the TCP nanoparticles affected stronger pore size and distribution but also the polymer structure (crystallity, physicochemical properties of the surface). Treatment of the nanocomposite samples in the simulated body fluid (SBF) induced some changes on the surface of the material containing bioactive ceramic nanoparticles. The results of the tests with SBF showed that the material is able to produce apatite structure on its surface (EDS analysis)

Detecting Backbone of Weighted Complex Network

In order to explore key nodes natures and find out the core of weighted networks, the study advanced backbone network (BN) conception, developed largest eigenvalue algorithm of weight matrix (LEAWM) which utilized matrix characteristic spectrum to detect BN nodes, and done empirical research for two networks: (1) US air lines network, (2) stocks network of coal and power sectors in china stock market. The empirical results indicate that LEAWM is efficient for detecting the BN nodes with some important properties such as bigger degree and betweenness, BN is the core and backbone of its mother network.

Otosclerosis: Pathology of the local focus and perilymph

Data from numerous pathohistological, histochemical, immunohistochemical and biochemical studies of the otosclerotic tissue in the otic capsule are reviewed and correlated systematically in order to get more complete insight of the local cellular and molecular events in otosclerosis and to derive the basic knowledge from them. The following parameters are focused: sites and distribution of the otosclerotic foci, classification of the local events in otosclerosis, active and inactive otosclerotic foci, osteoid cells, enzyme activity of the otosclerotic foci and perilymph, components of the bone inorganic constituents and matrix. Characteristic morphologic changes and microscopic appearance of the otosclerotic foci are defined as well as the metabolic processes and enzyme disbalances of the disorder with respect to the phase of the otosclerotic bone resorption and formation. The authors specially stress the necessity of constant monitoring and critical evaluation of both the research data and the general concepts in the multifactorial field of otosclerosis.

Direct and Inverse Wave Propagation in the Frequency Domain via the Weyl Operator Symbol Calculus

Wave field splitting, invariant imbedding, and phase space methods reformulate the Helmholtz wave propagation problem in terms of an operator scattering matrix characteristic of the modeled environment. The equations for the reflection and transmission operators are first-order in range, nonlinear (Riccati-like), and, in general, nonlocal. The singularity structure of the corresponding Weyl operator symbols plays a crucial role in the development of both direct and inverse wave propagation algorithms.