Stress calculation on bevel gears with FEM influence vectors

In order to be able to carry out an optimal gear design with the aim of cost reduction and the careful handling of resources, load capacity is an important criterion for the evaluation of a gear. For the calculation of the flank and root load capacity, a precise loaded tooth contact analysis (LTCA) is necessary. With LTCA software like BECAL, influence numbers are used to calculate the deformation of the gear. These influence numbers are calculated with a BEM-module and considered for calculating the local root stress. This method simplifies the coupling stiffness in tooth width direction with a decay function and neglects the influence of local differences in tooth stiffness. In this publication, this simplification shall be questioned and evaluated.Therefore, a new method for calculating stress with FEM influence vectors is presented. This method enables the calculation of full stress tensors at any desired location in the gear with the efficiency of the influence number method. Additionally, the influence of local stiffness variations in the gear is taken into account. Various gear examples show the influence of material connections at the pinion root and the influence of the rim thickness of a wheel on the root stress. To validate the accuracy and the time efficiency of the new calculation method and to compare the results to current state-of-the-art simulations, a well-documented series of tests from the literature is recalculated and evaluated.

Distribution of root numbers of Hecke characters attached to some elliptic curves

In this paper, we show that an action on the set of elliptic curves with j = 1728 j=1728 preserves a certain kind of symmetry on the local root number of Hecke characters attached to such elliptic curves. As a consequence, we give results on the distribution of the root numbers and their average of the aforementioned Hecke characters.

Transcriptome Signatures in Pseudomonas simiae WCS417 Shed Light on Role of Root-Secreted Coumarins in Arabidopsis-Mutualist Communication

Pseudomonas simiae WCS417 is a root-colonizing bacterium with well-established plant-beneficial effects. Upon colonization of Arabidopsis roots, WCS417 evades local root immune responses while triggering an induced systemic resistance (ISR) in the leaves. The early onset of ISR in roots shows similarities with the iron deficiency response, as both responses are associated with the production and secretion of coumarins. Coumarins can mobilize iron from the soil environment and have a selective antimicrobial activity that impacts microbiome assembly in the rhizosphere. Being highly coumarin-tolerant, WCS417 induces the secretion of these phenolic compounds, likely to improve its own niche establishment, while providing growth and immunity benefits for the host in return. To investigate the possible signaling function of coumarins in the mutualistic Arabidopsis-WCS417 interaction, we analyzed the transcriptome of WCS417 growing in root exudates of coumarin-producing Arabidopsis Col-0 and the coumarin-biosynthesis mutant f6′h1. We found that coumarins in F6′H1-dependent root exudates significantly affected the expression of 439 bacterial genes (8% of the bacterial genome). Of those, genes with functions related to transport and metabolism of carbohydrates, amino acids, and nucleotides were induced, whereas genes with functions related to cell motility, the bacterial mobilome, and energy production and conversion were repressed. Strikingly, most genes related to flagellar biosynthesis were down-regulated by F6′H1-dependent root exudates and we found that application of selected coumarins reduces bacterial motility. These findings suggest that coumarins’ function in the rhizosphere as semiochemicals in the communication between the roots and WCS417. Collectively, our results provide important novel leads for future functional analysis of molecular processes in the establishment of plant-mutualist interactions.

Local Root Numbers for Heisenberg-Representations — Some Explicit Results

Heisenberg representations [Formula: see text] of (pro-)finite groups [Formula: see text] are by definition irreducible representations of the two-step nilpotent factor group [Formula: see text] Better known are Heisenberg groups which can be understood as allowing faithful Heisenberg representations. A special feature is that [Formula: see text] will be induced by characters [Formula: see text] of subgroups in multiple ways, where the pairs [Formula: see text] can be interpreted as maximal isotropic pairs. If [Formula: see text] is a [Formula: see text]-adic number field and [Formula: see text] the absolute Galois group then maximal isotropic pairs rewrite as [Formula: see text] where [Formula: see text] is an abelian extension and [Formula: see text] a character. We will consider the extended local Artin-root-number [Formula: see text] for those [Formula: see text] which are essentially tame and express it by a formula not depending on the various maximal isotropic pairs [Formula: see text] for [Formula: see text]

The Effect of Material Properties on the Perceived Shape of Three-Dimensional Objects

Perceiving the shape of three-dimensional objects is essential for interacting with them in daily life. If objects are constructed from different materials, can the human visual system accurately estimate their three-dimensional shape? We varied the thickness, motion, opacity, and specularity of globally convex objects rendered in a photorealistic environment. These objects were presented under either dynamic or static viewing condition. Observers rated the overall convexity of these objects along the depth axis. Our results show that observers perceived solid transparent objects as flatter than the same objects rendered with opaque reflectance properties. Regional variation in local root-mean-square image contrast was shown to provide information that is predictive of perceived surface convexity.

Branching laws for classical groups: the non-tempered case

This paper generalizes the Gan–Gross–Prasad (GGP) conjectures that were earlier formulated for tempered or more generally generic L-packets to Arthur packets, especially for the non-generic L-packets arising from Arthur parameters. The paper introduces the key notion of a relevant pair of Arthur parameters that governs the branching laws for ${{\rm GL}}_n$ and all classical groups over both local fields and global fields. It plays a role for all the branching problems studied in Gan et al. [Symplectic local root numbers, central critical L-values and restriction problems in the representation theory of classical groups. Sur les conjectures de Gross et Prasad. I, Astérisque 346 (2012), 1–109] including Bessel models and Fourier–Jacobi models.

ОЦІНКА ЕФЕКТИВНОСТІ ВИЯВЛЕННЯ НЕОДНОРІДНОСТЕЙ НА ЗОБРАЖЕННІ ЗА ДОПОМОГОЮ МАКСИМУМА БІАМПЛІТУДИ

The subject of the article is to analyze the effectiveness of a new method for detecting heterogeneities in a digital image by estimating the bimagnitude maximum of the pixel intensities. The aim is to evaluate the effectiveness of the new method of detecting heterogeneities in the image using the maximum of the bimagnitude compared to the known method based on the estimation of the local root mean square deviation (LRMSD) of pixel intensity values. The objectives of the paper are the following: to formalize the procedure for computing the bimagnitude maximum of the pixels in the local segment; create a test image with different contrast values on the borders; to develop a mathematical model for calculating in the Matlab system the efficiency of detecting heterogeneities in the image in the presence of additive Gaussian noise with different values of noise RMS; provide for analysis and comparison of the graphs the receiver operating characteristic (ROC) contained the number of correctly classified non-homogeneous areas versus the number of incorrectly classified areas. The used methods are the following: bispectral data analysis method; methods of probability theory and mathematical statistics; methods of digital image processing. The following results were obtained. A boundary map for the test image without distortion and the presence of additive Gaussian noise with a variance equal to 0.2 is constructed for two types of detectors: the first one is based on the maximum amplitude and the second one is based on the estimation of the local RMS. The results of computer simulations show that both detectors fine-tune the boundary for the images in the absence of noise. But in the presence of additive noise, the detector based on the biamplitude maximum provides a significant advantage. Graphs of the dependence of the number of correctly classified inhomogeneous sections on the number of incorrectly classified areas for the proposed and known reference detection methods are represented. The area under the curve (AUC) values that characterize the efficiency of detecting heterogeneities in the image are calculated. The scientific novelty of the obtained results is the following: a new approach of detecting inhomogeneities in the image is proposed with the help of a new informative feature estimated in the form of the local biamplitude maximum. To analyze the effectiveness of the proposed method, a test image was formed with different border contrast values. Using the proposed technique and the known method, boundary maps were constructed for the test image without distortion and in the presence of additive Gaussian noise. To evaluate the effectiveness of two methods, the graphs were plotted against the number of correctly classified inhomogeneous sites by the number of incorrectly classified (ROC) for both proposed and known detection methods. A detector based on the local RMS value is more effective at small Gaussian noise variance values, but as the noise variance increases, detector based on the biamplitude maximum estimation is more effective. The calculated AUC values for studied methods based on local RMS estimation and maximum biamplitude estimation are equal to 0. 678 and 0. 8468, respectively. Even though the proposed method loses efficiency, the bispectrum-based method is more effective at large values of noise variance, in particular, when the noise RMS is 0.6, AUC = 0.8748.