The hydro­thermal synthesis and structural characterization of four novel 3D pillared-layer metal–organic frameworks are studied, revealing how the malleability of copper coordination geometries drives diverse supramolecular isomerism. The findings provide new insights into designing advanced hybrid materials with tailored properties, emphasizing the significant role of reaction conditions and metal ion flexibility in determining network topologies.

Analytical calculations of absorption corrections for X-ray powder diffraction experiments on non-ideal samples with surface roughness, porosity or absorption contrasts from multiple phases require complex mathematical models to represent their material distribution. In a computational approach to this problem, a practicable ray-tracing algorithm is formulated which is capable of simulating angle-dependent absorption corrections in reflection geometry for any given rasterized sample model. Single or multiphase systems with arbitrary surface roughness, porosity and spatial distribution of the phases in any combination can be modeled on a voxel grid by assigning respective values to each voxel. The absorption corrections are calculated by tracing the attenuation of X-rays along their individual paths via a modified shear-warp algorithm. The algorithm is presented in detail and the results of simulated absorption corrections on samples with various surface modulations are discussed in the context of published experimental results.

The growth quality of AlN single crystals was improved by optimizing the crucible structure for Al vapor transport with the help of finite element simulation.

In the conventional crucible structure for AlN crystal growth by physical vapor transport, owing to the long molecular transport path of Al vapor and the disruption of the gas flow by the presence of a deflector, the Al vapor easily forms polycrystals in the growth domain. The result is increased internal stress in the crystals and increased difficulty in growing large-sized crystals. On this basis, with the help of finite element simulations, a novel crucible structure is designed. This crucible not only optimizes the gas transport but also increases the radial gradient of the AlN crystal surface, making the enhanced growth rate in the central region more obvious. The thermal stresses between the deflector and the crystal are also reduced. High-quality AlN crystals with an FWHM of 79 arcsec were successfully grown with this structure, verifying the accuracy of finite element simulation of the growth of AlN crystals. Our work has important guiding significance for the growth of high-quality AlN crystals.

I have always enjoyed photographing objects, be they man made or natural, that have very distinctive lines, shapes, and patterns.  Recently, while in the Palouse, I had the opportunity to solidify this idea and make some photographs very focused on geometric shapes.  There are several that I took that I like quite a bit.  Perhaps […]

Event Begins: Wednesday, November 13, 2024 4:00pm
Location: East Hall
Organized By: Algebraic Geometry Seminar - Department of Mathematics

Joint work with Ailsa Keating (Cambridge). We prove the homological mirror symmetry conjecture of Kontsevich for K3 surfaces in the following form: The Fukaya category of a projective K3 surface is equivalent to the derived category of coherent sheaves on the mirror, which is a K3 surface of Picard rank 19 over the field of formal Laurent series. This builds on prior work of Seidel (who proved the theorem in the case of the quartic surface), Sheridan, Lekili--Ueda, and Ganatra--Pardon--Shende.

I will try to keep prerequisites to a minimum, in particular, I will not assume prior knowledge of the Fukaya category.

Location: Electronic Resource- 

Gabriel Kenoun: Medicine, Human Anatomy, and Geometry books

Song Dai and Qiongling Li
Trans. Amer. Math. Soc. 377 (), 5445-5481.
Abstract, references and article information

Mohammed Abouzaid and Nathaniel Bottman
Bull. Amer. Math. Soc. 61 (), 525-608.
Abstract, references and article information

At Battle High School in Columbia, Mo., students in geometry class have swapped their compasses and protractors for hammers and hard hats. And they're doing it for a good cause.

The unexpected discovery of a geometric phase shows how math and physics are tightly intertwined

Berlin ; Boston : De Gruyter, [2023]

Mathematician Jordan Ellenberg answers the internet's burning questions about geometry. How are new shapes still being discovered? Where are we using Pythagorean theorem in real life? How many holes are in a...straw? Ellenberg answers all these questions and much, much more!Jordan Ellenberg's book Shape is available on Amazon or Penguin Random Househttps://www.amazon.com/gp/product/1984879073?tag=randohouseinc7986-20https://www.penguinrandomhouse.com/books/612131/shape-by-jordan-ellenberg/Director: Lisandro Perez-ReyDirector of Photography: Constantine EconomidesEditor: Richard TrammellExpert: Jordan EllenbergLine Producer: Joseph BuscemiAssociate Producer: Brandon WhiteProduction Manager: D. Eric MartinezProduction Coordinator: Fernando DavilaCasting Producer: Nick SawyerCamera Operator: Christopher EustacheGaffer: Rebecca Van Der MeulenSound Mixer: Michael GugginoProduction Assistant: Sonia ButtPost Production Supervisor: Alexa DeutschPost Production Coordinator: Ian BryantSupervising Editor: Doug LarsenAdditional Editor: Paul TaelAssistant Editor: Billy Ward

Basel ; Boston : Birkhauser, 2007

New York : Springer, 2005

Boston : Birkhäuser, [2005]

Boston : Birkhauser, 2007

Berlin : Springer, 2005

New York : Springer, [2006]

New York : Springer, 2007

Cham : Springer International Publishing : Imprint: Springer, 2018.

Cham, Switzerland : Springer, 2018

Thangam Mathai looks at the sari as a canvas on which she can display her art and creativity

An interface of interlocking triangles, snake hoods and more… a look at the sprawling Sri Yantra Maha Meru Temple, Amarkantak, by Chitra Ramaswamy

Across all branches of science, medicine and engineering, high-resolution microscopy is required to understand functionality. Although optical methods have been developed to `defeat' the diffraction limit and produce 3D images, and electrons have proven ever more useful in creating pictures of small objects or thin sections, so far there is no substitute for X-ray microscopy in providing multiscale 3D images of objects with a single instrument and minimal labeling and preparation. A powerful technique proven to continuously access length scales from 10 nm to 10 µm is ptychographic X-ray computed tomography, which, on account of the orthogonality of the tomographic rotation axis to the illuminating beam, still has the limitation of necessitating pillar-shaped samples of small (ca 10 µm) diameter. Large-area planar samples are common in science and engineering, and it is therefore highly desirable to create an X-ray microscope that can examine such samples without the extraction of pillars. Computed laminography, where the axis of rotation is not perpendicular to the illumination direction, solves this problem. This entailed the development of a new instrument, LamNI, dedicated to high-resolution 3D scanning X-ray microscopy via hard X-ray ptychographic laminography. Scanning precision is achieved by a dedicated interferometry scheme and the instrument covers a scan range of 12 mm × 12 mm with a position stability of 2 nm and positioning errors below 5 nm. A new feature of LamNI is a pair of counter-rotating stages carrying the sample and interferometric mirrors, respectively.

GIDVis is a software package based on MATLAB specialized for, but not limited to, the visualization and analysis of grazing-incidence thin-film X-ray diffraction data obtained during sample rotation around the surface normal. GIDVis allows the user to perform detector calibration, data stitching, intensity corrections, standard data evaluation (e.g. cuts and integrations along specific reciprocal-space directions), crystal phase analysis etc. To take full advantage of the measured data in the case of sample rotation, pole figures can easily be calculated from the experimental data for any value of the scattering angle covered. As an example, GIDVis is applied to phase analysis and the evaluation of the epitaxial alignment of pentacene­quinone crystallites on a single-crystalline Au(111) surface.

We introduce the conormal fan of a matroid M, which is a Lagrangian analog of the Bergman fan of M. We use the conormal fan to give a Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle of M. This allows us to express the h-vector of the broken circuit complex of M in terms of the intersection theory of the conormal fan of M. We also develop general tools for tropical Hodge theory to prove that the conormal fan satisfies Poincar'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. The Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle of M, when combined with the Hodge-Riemann relations for the conormal fan of M, implies Brylawski's and Dawson's conjectures that the h-vectors of the broken circuit complex and the independence complex of M are log-concave sequences.

We observe that the DeTurck Laplacian flow of G2-structures introduced by Bryant and Xu as a gauge fixing of the Laplacian flow can be regarded as a flow of G2-structures (not necessarily closed) which fits in the general framework introduced by Hamilton in [4].

We introduce natural deformation classes of generalized K"ahler structures using the Courant symmetry group. We show that these yield natural extensions of the notions of K"ahler class and K"ahler cone to generalized K"ahler geometry. Lastly we show that the generalized K"ahler-Ricci flow preserves this generalized K"ahler cone, and the underlying real Poisson tensor.

Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly logical foundations while ITPs are meant for formalizing existing proofs rather than problem solving. We aim to create a simple human-friendly logical system for mathematical problem solving. We picked the case study of Euclidean geometry as it can be easily visualized, has simple logic, and yet potentially offers many high-school problems of various difficulty levels. To make the environment user friendly, we abandoned strict logic required by ITPs, allowing to infer topological facts from pictures. We present our system for Euclidean geometry, together with a graphical application GeoLogic, similar to GeoGebra, which allows users to interactively study and prove properties about the geometrical setup.

A Non-terrestrial Network (NTN) comprising Low Earth Orbit (LEO) satellites can enable connectivity to underserved areas, thus complementing existing telecom networks. The high-speed satellite motion poses several challenges at the physical layer such as large Doppler frequency shifts. In this paper, an analytical framework is developed for statistical characterization of Doppler shift in an NTN where LEO satellites provide communication services to terrestrial users. Using tools from stochastic geometry, the users within a cell are grouped into disjoint clusters to limit the differential Doppler across users. Under some simplifying assumptions, the cumulative distribution function (CDF) and the probability density function are derived for the Doppler shift magnitude at a random user within a cluster. The CDFs are also provided for the minimum and the maximum Doppler shift magnitude within a cluster. Leveraging the analytical results, the interplay between key system parameters such as the cluster size and satellite altitude is examined. Numerical results validate the insights obtained from the analysis.

A vertical geometry light emitting diode is disclosed that is capable of emitting light in the red, green, blue, violet and ultraviolet portions of the electromagnetic spectrum. The light emitting diode includes a conductive silicon carbide substrate, an InGaN quantum well, a conductive buffer layer between the substrate and the quantum well, a respective undoped gallium nitride layer on each surface of the quantum well, and ohmic contacts in a vertical geometry orientation.

A turbomachine blade or vane is made of composite material including fiber reinforcement obtained by three-dimensional weaving of yarns and densified by a matrix. The blade or vane includes a first portion constituting at least an airfoil exhibiting two faces each connecting a leading edge to a trailing edge, the first portion forming a single part with at least one second portion present only on one of the faces of the airfoil, the second portion constituting a portion of at least one of the following elements: a flowpath delimiting outer portion of an inner platform, an inner portion of an inner platform, a flowpath delimiting inner portion of an outer platform, and an outer portion of an outer platform, the portions of the fiber reinforcement corresponding to the first and the second portions of the blade being at least partially mutually imbricated, with yarns of the first portion of the fiber reinforcement penetrating into the second portion of the fiber reinforcement.

An X-ray arrangement is suitable to record absorption, phase contrast, and dark field images of an object. The visibility of low absorbing specimens is improved and required radiation dose is reduced. The assembly includes an X-ray source; two or more gratings; a position-sensitive detector with spatially modulated detection sensitivity; a recorder for recording the images; an evaluator for evaluating the intensities for each pixel to identify the characteristic of the object for each individual pixel as an absorption and/or a differential phase contrast and/or an x-ray scattering dominated pixel. Images are collected by rotating from 0 to n or 2n either the sample or the assembly. The gratings are produced with planar geometry. The X-rays pass through the gratings parallel to the substrate. The grating structures extend along the X-ray path which determines the phase shift. The attenuation of the X-rays caused by the grating structures is no longer given by the thickness, but by the length of the grating structures.

A hypodermic needle featuring a multi-beveled point geometry is disclosed. In one embodiment, the multi-beveled point features a primary bevel, a pair of tip bevels, and a pair of middle bevels each intermediate the primary bevel and a respective one of the tip bevels. The primary and middle bevels are provided at angles of inclination, measured between the central axis and a reference plane that are substantially identical. The tip bevels are formed at an angle of inclination respective to the central axis which is not equal to the angle of inclination at which the primary and middle bevels are formed. The resulting five-beveled point geometry contributes to a more continuous bevel face free of abrupt intercepts or transitions between the respective bevel faces, lessening the penetration force required to urge the needle point through skin, flesh, or other material.

A linear actuator for a variable-geometry member of a turbocharger includes a piston/rod assembly that can axially translate and also pivot to a limited extent. A permanent magnet is mounted in a fixed position within the actuator. A non-magnetized flux carrier is mounted in the piston/rod assembly, and its movement alters the magnetic field of the magnet. A Halls effects sensor detects the magnetic field and the signals produced by the sensor are used for determining axial position of the piston/rod assembly.

Considerable damage to rails, wheels, and trucks can result from geometric anomalies in the wheelsets, rails, and truck hardware. A solution for identifying and quantifying geometric anomalies known to influence the service life of the rolling stock or the ride comfort for the case of passenger service is described. The solution comprises an optical system, which can be configured to accurately perform measurements at mainline speeds (e.g., greater than 100 mph). The optical system includes laser line projectors and imaging cameras and can utilize structured light triangulation.

“Starry Night” Ceilings For Home Theaters, Studios And Businesses Provide Uniquely Aesthetic Acoustic Treatment

The US-made carbon fiber fork lets you choose between 44mm or 52mm of rake.
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