The isomorphism conjecture for 3-manifold groups and K-theory of virtually poly-surface groups

This article has two purposes. In \cite{R3} (math.KT/0405211) we showed that the FIC (Fibered Isomorphism Conjecture for pseudoisotopy functor) for a particular class of 3-manifolds (we denoted this class by \cal C) is the key to prove the FIC for 3-manifold groups in general. And we proved the FIC for the fundamental groups of members of a subclass of \cal C. This result was obtained by showing that the double of any member of this subclass is either Seifert fibered or supports a nonpositively curved metric. In this article we prove that for any M in {\cal C} there is a closed 3-manifold P such that either P is Seifert fibered or is a nonpositively curved 3-manifold and \pi_1(M) is a subgroup of \pi_1(P). As a consequence this proves that the FIC is true for any B-group (see definition 3.2 in \cite{R3}). Therefore, the FIC is true for any Haken 3-manifold group and hence for any 3-manifold group (using the reduction theorem of \cite{R3}) provided we assume the Geometrization conjecture. The above result also proves the FIC for a class of 4-manifold groups (see \cite{R2}(math.GT/0209119)). The second aspect of this article is to relax a condition in the definition of strongly poly-surface group (\cite{R1} (math.GT/0209118)) and define a new class of groups (we call them {\it weak strongly poly-surface} groups). Then using the above result we prove the FIC for any virtually weak strongly poly-surface group. We also give a corrected proof of the main lemma of \cite{R1}.Comment: 12 pages, AMS Latex file, 1 figure, final version. accepted for publication in K-theor

A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some reference

Analysis of Droplet Train/Moving Substrate Interactions in Ink-Jetting Processes

Ink-jetting technology has been applied to several processes in solid free-form fabrication (SFF) wherein droplets impinge onto a substrate to deposit the build material. Droplet impact behaviour on a surface has been the interest of many researchers; however, few studies have been undertaken to investigate the interaction of droplets with the moving substrate. This paper reports the impact behaviour of the droplets jetted at different frequencies onto a substrate moving over a range of velocities. The phenomena associated with the interaction were classified into three main regimes.Mechanical Engineerin

Robust Facial Emotion Recognition using Marine Predators Algorithm with Deep Convolutional Neural Network

Facial emotion recognition (FER) is a technology that includes the automatic identification and categorization of human sentiments depending on facial emotions. It leverages deep learning (DL), computer vision (CV), and machine learning (ML) methods to analyze the features of an individual's face, like the place of the mouth, eyes, eyebrows, and complete facial movements for determining their emotional conditions. Popular emotions that FER can recognize comprise surprise, sadness, happiness, fear, disgust, and anger. FER employing DL has an advanced application of artificial intelligence (AI) and deep neural networks (DNNs) that contain training methods to automatically recognize and categorize human expressions based on facial expressions. This approach normally comprises convolutional neural networks (CNNs) or highly complex models namely recurrent neural networks (RNNs) and convolutional RNNs (CRNNs) for analyzing and interpreting complex facial features and dynamics. This study introduces a new Robust Facial Emotion Recognition employing the Marine Predators Algorithm with Deep Learning (RFER-MPADL) approach. The main aim of the RFER-MPADL technique is to detect and categorize different kinds of emotions expressed in facial images. To accomplish this, the RFER-MPADL technique initially applies a bilateral filtering (BF) approach for the preprocessing step. Additionally, the RFER-MPADL technique uses the EfficientNet-B0 method for feature extraction. Moreover, the tuning process of the EfficientNet-B0 method was implemented using the MPA. Finally, the classification of facial emotions can be performed by the use of a deep autoencoder (DAE), in turn augments the overall performance of the RFER-MPADL method. The experimental analysis of the RFER-MPADL methodology is assessed on a standard facial expression dataset. The extensive outcomes exhibited the effectual performance of the RFER-MPADL methodology over other methods

Expansive homeomorphisms of the plane

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques involve topological and metric aspects of the plane. The use of a Lyapunov metric function which defines the same topology as the one induced by the usual metric but that, in general, is not equivalent to it is an example of such techniques. The discovery of a hypothesis about the behavior of Lyapunov functions at infinity allows us to generalize some results that are valid in the compact context. Additional local properties allow us to obtain another classification theorem.Comment: 29 pages, 22 figure

Relation entre fracturation et morphologie et leurs implications hydrogéologiques : Exemple des calcaires fissurés de la région de Chéria, (NE Algérien)

La région de Chéria est située au NE Algérien, à 45 kilomètres au Sud- Ouest de la ville de Tébessa. Le bassin versant à étudier s’étend sur une surface de 720 km2, abrite plus de 74300 habitants et caractérisé par un climat semi-aride. La région est formée essentiellement par des calcaires Maestrichtiens et Eocènes qui sont fissurés karstiques et qui constituent le potentiel aquifère de la région. Cette étude tente de conformer les relations entre la morphologie et la fracturation dans les calcaires et les confronter aux écoulements des nappes de ces derniers.Mots-clés: Cheria, Tébessa, calcaire, morphologie, fracturation. Relation fracturing-morpholo- structural and them implications hydrogeologiques. Example of limestones cracks of the area of Chéria (NE Algeria)The area of Chéria is located at Algerian, with 45 kilometers in the South-west of the town of Tébessa.The area catchment to study extends on a surface from 720 km2, shelters more than 74300 inhabitants and characterized by a semi-arid climate.The area is formed primarily by limestones of Maestrichtien and Eocene which are fissured karstic and which constitute the aquiferous potential of the area.This study tries to conform the relations between morphology and the fracturing in limestones and to confront them with the flows of the tablecloths of the latter.Keywords: Chéria, Tébessa, limestone, morphology, fracturing

Neutral gas in Lyman-alpha emitting galaxies Haro 11 and ESO 338-IG04 measured through sodium absorption

Context. The Lyman alpha emission line of galaxies is an important tool for finding galaxies at high redshift, and thus probe the structure of the early universe. However, the resonance nature of the line and its sensitivity to dust and neutral gas is still not fully understood. Aims. We present measurements of the velocity, covering fraction and optical depth of neutral gas in front of two well known local blue compact galaxies that show Lyman alpha in emission: ESO 338-IG 04 and Haro 11. We thus test observationally the hypothesis that Lyman alpha can escape through neutral gas by being Doppler shifted out of resonance. Methods. We present integral field spectroscopy from the GIRAFFE/Argus spectrograph at VLT/FLAMES in Paranal, Chile. The excellent wavelength resolution allows us to accurately measure the velocity of the ionized and neutral gas through the H-alpha emission and Na D absorption, which traces the ionized medium and cold interstellar gas, respectively. We also present independent measurements with the VLT/X-shooter spectrograph which confirm our results. Results. For ESO 338-IG04, we measure no significant shift of neutral gas. The best fit velocity is -15 (16) km/s. For Haro 11, we see an outflow from knot B at 44 (13) km/s and infalling gas towards knot C with 32 (12) km/s. Based on the relative strength of the Na D absorption lines, we estimate low covering fractions of neutral gas (down to 10%) in all three cases. Conclusions. The Na D absorption likely occurs in dense clumps with higher column densities than where the bulk of the Ly-alpha scattering takes place. Still, we find no strong correlation between outflowing neutral gas and a high Lyman alpha escape fraction. The Lyman alpha photons from these two galaxies are therefore likely escaping due to a low column density and/or covering fraction.Comment: 9 pages, 3 figure