Stable foliations near a traveling front for reaction diffusion systems

We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical reactions models and solid fuel combustion. In this way we complement the orbital stability results from earlier papers by A. Ghazaryan, S. Schecter and Y. Latushkin. The essential spectrum of the differential operator obtained by linearization at the front touches the imaginary axis. In spaces with exponential weights, one can shift the spectrum to the left. We study the nonlinear equation on the intersection of the unweighted and weighted spaces. Small translations of the front form a center unstable manifold. For each small translation we prove the existence of a stable manifold containing the translated front and show that the stable manifolds foliate a small ball centered at the front

On Suprememum of a set in A Dedikind Complete Topological Space

The supremum for a set in a multi-dimensional, Dedikind complete topological space is defined. The example is given to illustrate that the condition of Dedilind complete is necessary for the existence of supremum

Stable foliations near a traveling front for reaction diffusion systems

We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical kinetics and solid fuel combustion. In this way we complement the orbital stability results from earlier papers by A. Ghazaryan, S. Schecter and Y. Latushkin. The essential spectrum of the differential operator obtained by linearization at the front touches the imaginary axis. In spaces with exponential weights, one can shift the spectrum to the left. We study the nonlinear equation on the intersection of the unweighted and weighted spaces. Small translations of the front form a center unstable manifold. For each small translation we prove the existence of a stable manifold containing the translated front and show that the stable manifolds foliate a small ball centered at the front

A Missing Value Filling Model Based on Feature Fusion Enhanced Autoencoder

With the advent of the big data era, the data quality problem is becoming more critical. Among many factors, data with missing values is one primary issue, and thus developing effective imputation models is a key topic in the research community. Recently, a major research direction is to employ neural network models such as self-organizing mappings or automatic encoders for filling missing values. However, these classical methods can hardly discover interrelated features and common features simultaneously among data attributes. Especially, it is a very typical problem for classical autoencoders that they often learn invalid constant mappings, which dramatically hurts the filling performance. To solve the above-mentioned problems, we propose a missing-value-filling model based on a feature-fusion-enhanced autoencoder. We first incorporate into an autoencoder a hidden layer that consists of de-tracking neurons and radial basis function neurons, which can enhance the ability of learning interrelated features and common features. Besides, we develop a missing value filling strategy based on dynamic clustering that is incorporated into an iterative optimization process. This design can enhance the multi-dimensional feature fusion ability and thus improves the dynamic collaborative missing-value-filling performance. The effectiveness of the proposed model is validated by extensive experiments compared to a variety of baseline methods on thirteen data sets

Effects of Xinwei granule on expression levels of cyclin D1 and its upstream genes in gastric intraepithelial neoplasia tissues

Purpose: To explore the effects of Xinwei granule (XWG) on low-grade gastric intraepithelial neoplasia (LGIN) and the underlying mechanisms. Methods: To establish LGIN model, Wistar rats were treated with N-methyl-N'-nitrosoguanidine for 3 months. LGIN model rats were randomly grouped into five groups (n = 15), viz, negative control (NC), normal saline (NS) group, Xinwei granule (XWG) group, Weifuchun tablet (WFCT) group, and vatacoenayme tablet (VT) group. Normal rats (n = 17) served as negative control. Histological evaluation of gastric mucosa was undertaken using hematoxylin and eosin staining. Quantitative realtime polymerase chain reaction (qRT-PCR), western blot, and immunohistochemical assays were performed to determine mRNA expressions, protein expression, and the distribution of cyclin D1, kruppel-like factor 4 (KLF4), and p21-WAF1-CIP1, respectively. Results: Compared with LGIN group, the body weight of the rats increased in XWG, WFCT, and VT groups. The pathological characteristics of LGIN group were alleviated by XWG, WFCT and VT treatments. The positive expression of cyclin D1 was enhanced in LGIN group, but reduced in XWG, WFCT and VT groups. The expression levels of KLF4 and p21-WAF1-CIP1, upstream regulators of cyclin D1 reduced in LGIN groups. However, administration of XWG, WFCT and VT strengthened the expressions of KLF4 and p21-WAF1-CIP1. More importantly, the protective effects of XWG against LGIN were superior to those of WFCT and VT. Conclusion: Xinwei granules alleviate LGIN in vivo by inhibiting cyclin D1 expression and enhancing KLF4 and p21-WAF1-CIP1 expression

Heat Dissipation Performance of Micro-channel Heat Sink with Various Protrusion Designs

This research will focus on studying the effect of aperture size and shape of the micro-channel heat sink on heat dissipation performance for chip cooling. The micro-channel heat sink is considered to be a porous medium with fluid subject inter-facial convection. Derivation based on energy equation gives a set of governing partial differential equations describing the heat transfer through the micro-channels. Numerical simulation, including steady-state thermal analysis based on CFD software, is used to create a finite element solver to tackle the derived partial differential equations with properly defined boundary conditions related to temperature. After simulating three types of heat sinks with various protrusion designs including micro-channels fins, curly micro-channels fins, and Micro-pin fins, the result shows that the heat sink with the maximum contact area per unit volume will have the best heat dissipation performance, we will interpret the result by using the volume averaging theorem on the porous medium model of the heat sink

Stability of planar fronts for a class of reaction diffusion systems

Dissertation supervisor: Dr. Yuri Latushkin.Includes vita.The purpose of this thesis is to study stability of one-dimensional traveling waves and multidimensional planar fronts as well as space-independent steady states for a class of reaction diffusion systems that arise in combustion theory and chemical-reaction models. We begin by extending the recent one-dimensional stability results for reaction diffusion equations of this type. Using spaces with exponential weights, we shift the spectrum of the differential operator obtained by linearizing the equation about the front into the stable half-plane, and study the nonlinear equation on the intersection of the unweighted and weighted spaces. In this space, we prove the existence of a stable foliation in vicinity of the traveling front solution, that is, we show that each translation of the front has a stable manifold formed by solutions converging to the translation. The results provide a better understanding of the dynamics near the front, and improve the known stability theorems. In addition, we prove stability of the end states of the front. We then turn to stability of the planar front solutions and their end states for a class of reaction diffusion equations in multidimensional space. We study the case when the spectrum of the linearization in the direction of the front touches the imaginary axis. This setting is a generalization of the relevant multidimensional stability results known in the literature. Passing to the exponential weights, we obtain appropriate estimates for the nonlinear terms of the equation govering the evolution of the perturbations of the front in the intersection of the unweighted and weighted spaces. We then show that the unweighted norm of the solutions of the equation with small initial data remains bounded while the weighted norm algebraically decays for large times. Also, we prove stability of the end states of the front.Includes bibliographical references (pages 192-196)