Self-similar solutions of quasilinear parabolic equations with nonlinear gradient terms

This paper is devoted to study the classification of self-similar solutions to the m ≥ 1,p,q ＞ 0 and p + q ＞ m. For m = 1, it is shown that the very singular self-similar solution exists if and only if nq + (n + 1)p ＜ n + 2, and in case of existence, such solution is unique. For m ＞ 1, it is shown that very singular self-similar solutions exist if and only if 1 ＜ m ＜ 2 and nq + (n + 1)p ＜ 2 + mn, and such solutions have compact support if they exist. Moreover, the interface relation is obtained.     

Three-Page Embeddings of Singular Knots

A semigroup with 15 generators and 84 relations is constructed. The center of the semigroup is in a one-to-one correspondence with the set of all isotopy classes of nonoriented singular knots (links with finitely many double intersections in general position) in ³.     

Weyl’s theorem for totally hereditarily normaloid operators

A Banach space operatorT ∈B(χ) is said to behereditarily normaloid, denotedT ∈ ℋN, if every part ofT is normaloid;T ∈ ℋN istotally hereditarily normaloid, denotedT ∈ ℑHN, if every invertible part ofT is also normaloid. Class ℑHN is large; it contains a number of the commonly considered classes of operators. The operatorT isalgebraically totally hereditarily normaloid, denotedT ∈a — ℑHN, both non-constant polynomialp such thatp(T) ∈ ℑHN. For operatorsT ∈a − ℑHN, bothT andT* satisfy Weyl’s theorem; if also either ind(T−μ)≥0 or ind(T−μ)≤0 for all complexμ such thatT−μ is Fredholm, thenf(T) andf(T*) satisfy Weyl’s theorem for all analytic functionsf ∈ ℋ(σ(T)). For operatorsT ∈a — ℑHN such thatT has SVEP,T* satisfiesa-Weyl’s theorem.     

Fuzzy folding of fuzzy horocycle

In this paper, we will give a new definition for folding of fuzzy horocycle. It introduces the concept of fuzzy horocycle. Also we will deduce the relation between the folding of fuzzy circles and fuzzy horocycles. Theorems governing this type of folding are deduced.     

Boundary Measures for Symmetric Domains and Integral Formulas for the Discrete Wallach Points

Let B be an irreducible hermitian symmetric domain of rank r in Cd and let G := Aut(B) the group of all biholomorphic automorphisms of B. We construct explicit integral formulas for the G-invariant inner products on spaces of holomorphic functions on B associated with the discrete Wallach points and the so-called embedded Wallach points, by means of integration on G-orbits on the boundary B of B and of invariant differential operators acting on symmetric domains of lower rank.     

A New Algorithm for the Petrov Classification of the Weyl Tensor

A new algorithm for the Petrov classification of the Weyl tensor is introduced. It is similar to the Letniowski-McLenaghan algorithm [1] when some of the 's are zero, but offers a completely new approach when all of the 's are nonzero. In all cases, new code in Maple has been implemented.     

Continuous Size Classification of Nanoparticles Utilizing Brownian Motion in Microchannel Size Exclusion Chromatography

This study presents a new method for classifying the sizes of colloidal nanoparticles of below 100 nm in diameter in liquid dispersion using a microchannel size exclusion chromatography (SEC) chip. This chip can classify polydisperse colloidal nanoparticles containing a mix of two monodisperse nanoparticles into several monodisperse particle populations. The particles classified by the SEC chip are then sequentially analyzed by a photon correlation spectroscopy (PCS) method in combination with a flow cell. Two different pillar patterns of such SEC chips were used in experiments to investigate the effects of these patterns on the nanoparticle classification performance. The results obtained were compared with those from a numerical simulation. Standard polystyrene latex particles with diameters of 20 nm and 100 nm were used in this study. The usefulness of this methodology was verified since the simulation and measurement results were in good agreement with each other.     

Sentiment Analysis of Persian Movie Reviews Using Deep Learning

Sentiment analysis aims to automatically classify the subject’s sentiment (e.g., positive, negative, or neutral) towards a particular aspect such as a topic, product, movie, news, etc. Deep learning has recently emerged as a powerful machine learning technique to tackle the growing demand for accurate sentiment analysis. However, the majority of research efforts are devoted to English-language only, while information of great importance is also available in other languages. This paper presents a novel, context-aware, deep-learning-driven, Persian sentiment analysis approach. Specifically, the proposed deep-learning-driven automated feature-engineering approach classifies Persian movie reviews as having positive or negative sentiments. Two deep learning algorithms, convolutional neural networks (CNN) and long-short-term memory (LSTM), are applied and compared with our previously proposed manual-feature-engineering-driven, SVM-based approach. Simulation results demonstrate that LSTM obtained a better performance as compared to multilayer perceptron (MLP), autoencoder, support vector machine (SVM), logistic regression and CNN algorithms.