Characterization of Closed Densely Defined Semi-Browder Linear Operators

In the present paper we characterize the closed densely defined semi-Browder operators through the Kato decomposition. Furthermore, we apply the obtained results to give a new characterization of Browder’s essential defect spectrum and Browder’s essential approximate point spectrum under finite rank operator perturbations.     

Means of Hermitian positive-definite matrices based on the log-determinant α-divergence function

The set of Hermitian positive-definite matrices plays fundamental roles in many disciplines such as mathematics, numerical analysis, probability and statistics, engineering, and biological and social sciences. In the last few years, there has been a renewable interest in developing the theory of means for elements in this set. This is due to theoretical and practical implications. In this work we present a one-parameter family of divergence functions for measuring distances between Hermitian positive-definite matrices. We then study the invariance properties of these divergence functions as well as the matrix means based on them. We also give globally convergent algorithms for computing these means.     

BROWDER AND SEMI-BROWDER OPERATORS＊

In this article,we study characterization,stability,and spectral mapping theorem for Browder's essential spectrum,Browder's essential defect spectrum and Browder's essential approximate point spectrum ...     

ON GRAPH MEASURES IN BANACH SPACES AND DESCRIPTION OF ESSENTIAL SPECTRA OF MULTIDIMENSIONAL TRANSPORT EQUATION

In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.     

Blood flow in microvascular networks: a study in nonlinear biology

Plasma skimming and the Fahraeus-Lindqvist effect are well-known phenomena in blood rheology. By combining these peculiarities of blood flow in the microcirculation with simple topological models of microvascular networks, we have uncovered interesting nonlinear behavior regarding blood flow in networks. Nonlinearity manifests itself in the existence of multiple steady states. This is due to the nonlinear dependence of viscosity on blood cell concentration. Nonlinearity also appears in the form of spontaneous oscillations in limit cycles. These limit cycles arise from the fact that the physics of blood flow can be modeled in terms of state dependent delay equations with multiple interacting delay times. In this paper we extend our previous work on blood flow in a simple two node network and begin to explore how topological complexity influences the dynamics of network blood flow. In addition we present initial evidence that the nonlinear phenomena predicted by our model are observed experimentally.     

Construction of a TiO2–Fe3O4‐decorated molecularly imprinted polymer nanocomposite for tartrazine degradation: Response surface methodology modeling and optimization

We synthesized a novel recoverable and reusable photocatalyst system for tartrazine degradation by one‐step incorporation of Fe₃O₄ and TiO₂ nanoparticles into a molecularly imprinted polymer through a facile precipitation polymerization method. The as‐prepared samples were systematically characterized using X‐ray diffraction, infrared spectroscopy, scanning electron microscopy, transmission electron microscopy, energy‐dispersive spectroscopy, and vibrating sample magnetometry. Benefiting from the positive synergistic effect, tartrazine was almost completely degraded under UV‐C within 180 min by the multicomponent photocatalyst (Fe₃O₄ + TiO₂ + MIP) in comparison with far fewer activities by the corresponding NIP system and the nonmagnetic and bare structures. On the other hand, the central composite design in response surface methodology was applied to optimize the tartrazine photocatalytic degradation process. Twenty experiments were conducted by adjusting three parameters (nanocomposite dosage, initial pH of the reaction solution, and initial dye concentration) in the multiple variable analysis method. A satisfactory correlation between the experimental and predicted values was obtained (R² = 0.956). Additionally, ANOVA analysis with a p value of 1.15 × 10^–5 indicated that the model terms are highly significant. Under the determined optimum conditions, a verification experiment was conducted and shown the adequately approximate value between the predicted (99%) and the experimental (97%) results, which confirmed the validity of the model.     

A coupled-channels born-approximation analysis of rare-earth (d,t) transitions

A CCBA (coupled-channels Born approximation) analysis has been performed on a very large set of rare-earth (d, t) transitions. Calculations were performed for states in ¹⁵⁹Gd, ^{161, 163}Dy and ^{165, 167}Er which have been identified as members of rotational bands built on the Nilsson single- hole states $\text{11}\text{2}$^?[505], $\text{1}\text{2}$^?[521], $\text{3}\text{2}$^?[521], $\text{5}\text{2}$^?[523], $\text{5}\text{2}$⁺[642], $\text{5}\text{2}$⁺[633] and $\text{7}\text{2}$⁺[404]. In the cases where the DWBA works well, the CCBA gives results similar to those of DWBA. For the anomalous transitions the CCBA calculations tend to fit better than do the DWBA calculations — but the overall agreement is still rather poor.     

Diffusion phenomena of a cold gas in a thermal plasma stream

The present study involves both experimental investigation and mathematical modeling of the diffusion process of a cold gas injected into a main plasma stream. The cold gas (nitrogen or helium) was injected axially through a water cooled tube located along the centerline of an induction plasma torch. The 2-D distribution of the temperature, velocity and concentration profiles in the plasma flow were measured using enthalpy probe techniques. The results are compared with the predictions of a 2-D, LTE, turbulent mathematical model. The effects of the nature (composition) of the injected gas and its mass flow rate are investigated. The enthalpy probe measurements and the predictions of the model are in good agreement. The effective (turbulent and molecular) transport properties are estimated from a comparison of the measured and calculated profiles of the temperature, velocity and concentration fields. This study sheds light on the basic diffusion mechanisms involved in a widely used configuration of induction plasma reactors, i.e. in which the material to be treated is injected axially into the plasma, through a central water cooled tube.     

Tracing fourth graders’ learning of fractions: early episodes from a year-long teaching experiment

Considerable and significant research¹ has been conducted focusing on what students know about fraction ideas.² However, much of the research looks at student understanding following some instruction. The research³ reported in this paper differs from other studies in three significant ways: (1) the students were 9- and 10-year-old fourth graders; (2) they had not yet had an introduction to operational rules and definitions about fractions; and (3) the research design emphasized a student-centered approach. The research is based on the view that given particular conditions in which students are invited to work together and conduct thoughtful investigations with appropriate materials, they can build fundamental mathematical ideas.