The Dirichlet Problem on the Heisenberg Group III: Harmonic Measure of a certain Half-Space

1986 ◽  
Vol 38 (3) ◽  
pp. 666-671 ◽  
Author(s):  
Bernard Gaveau ◽  
Jacques Vauthier
Keyword(s):  
Heisenberg Group ◽  
Half Space ◽  
Harmonic Measure ◽  
Short Note ◽  
Type Equation ◽  
Probabilistic Argument ◽  
Group Iii ◽  
3 Dimensional ◽  
Degenerate Hypergeometric Function ◽  
Made In

0. Introduction. In this short note we give an explicit computation of the harmonic measure of a half space x > 0 in the 3-dimensional Heisenberg group in terms of a degenerate hypergeometric function. A probabilistic argument reduces the whole problem to a Hermite-type equation on a half line, that we can solve in terms of the function G(l/4, 1/2; x2).A preliminary attempt to compute this kernel was done in [1] p. 107 and, cited by Huber [4]. Unfortunately a small mistake was made in [1] and the problem was still open until now. The first author is very grateful to Prof. Huber for having pointed out the weak argument of [1]. Since that time, other harmonic measures and even Green functions have been explicitly computed (see [2]).

scholarly journals Optical Imaging of the Small Intestine Immune Compartments Across Scales

2021 ◽  
Author(s):  
Arielle Planchette ◽  
Cédric Schmidt ◽  
Olivier Burri ◽  
Mercedes Gomez de Agüero ◽  
Aleksandra Radenovic ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Small Intestine ◽  
High Resolution ◽  
Imaging Modality ◽  
Regions Of Interest ◽  
Label Free ◽  
3 Dimensional ◽  
Wide Range ◽  
Mouse Small Intestine ◽  
Made In

Abstract The limitations of 2D microscopy constrain our ability to observe and understand tissue-wide networks that are, by nature, 3-dimensional. Optical projection tomography enables the acquisition of large volumes (ranging from micrometres to centimetres) in various tissues, with label-free capacities for the observation of auto-fluorescent signals as well fluorescent-labelled targets of interest in multiple channels. We present a multi-modal workflow for the characterization of both structural and quantitative parameters of the mouse small intestine. As proof of principle, we evidence its applicability for imaging the mouse intestinal immune compartment and surrounding mucosal structures. We quantify the volumetric size and spatial distribution of Isolated Lymphoid Follicles (ILFs) and quantify density of villi throughout centimetre long segments of intestine. Furthermore, we exhibit the age- and microbiota-dependence for ILF development, and leverage a technique that we call reverse-OPT for identifying and homing in on regions of interest. Several quantification capabilities are displayed, including villous density in the autofluorescent channel and the size and spatial distribution of the signal of interest at millimetre-scale volumes. The concatenation of 3D image acquisition with the reverse-OPT sample preparation and a 2D high-resolution imaging modality adds value to interpretations made in 3D. This cross-modality referencing technique is found to provide accurate localisation of ROIs and to add value to interpretations made in 3D. Importantly, OPT may be used to identify sparsely-distributed regions of interest in large volumes whilst retaining compatibility with high-resolution microscopy modalities, including confocal microscopy. We believe this pipeline to be approachable for a wide-range of specialties, and to provide a new method for characterisation of the mouse intestinal immune compartment.

scholarly journals Aplikasi Mesin Cetak 3 Dimensi Untuk Pembuatan Saklar Tempat Duduk Pada Mobil KIA Carnival

Infotekmesin ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 44-49
Author(s):  
Onery Andy Saputra ◽  
Sudiro Sudiro ◽  
Utomo Ramelan
Keyword(s):  
Product Design ◽  
3 Dimensional ◽  
Automotive Components ◽  
Original Product ◽  
Product Design Process ◽  
Feasibility Test ◽  
Dimensional Printing ◽  
Printing Machine ◽  
Original Component ◽  
Made In

The types of automotive components today vary greatly. The presence of more components types make it difficult to find suitable automotive components. 3D Printing Machine is a new breakthrough to overcome these problems. This is based on the working concept of a 3-dimensional printing machine that make components done by the product design process and then print it through a 3-dimensional printing machine. This concept is further developed in the form of feasibility test of several aspects which are able to assess the results of the component products in order to be marketed. The purpose of this research is to see the feasibility of 3-dimensional printing machine products in terms of component shapes, component functions, terms of component dimensions and in the terms of similarity to the original product. The research methodology used in this research is descriptive quantitative comparative qualitative. The results of this study are, 1) The 3-dimensional product design has a similarity of 50%, but it is still lacking for the amount of fillet (upper angular curvature of the design). Meanwhile, for the size and shape in general have been made in accordance with the original product. 2) Forms that can be made from 3-dimensional printing still look less ergonomic. 4) The performance or function of the 3-dimensional printing component is able to match its function. 5) The weight of the 3-dimensional priting component is 47.19% heavier than the original component. 6) The dimensions of the components of 3-dimensional printing results on average for flat areas have a deviation of about 5.39% and for the profile field it reaches 35.29%.

FEYNMAN FORMULAS FOR AN INFINITE-DIMENSIONAL 𝔭-ADIC HEAT TYPE EQUATION

2011 ◽  
Vol 14 (01) ◽  
pp. 137-148 ◽  
Author(s):  
OLGA BELOSHAPKA
Keyword(s):  
Cauchy Problem ◽  
Configuration Space ◽  
Short Note ◽  
Type Equation ◽  
Spatial Variable ◽  
Feynman Formula ◽  
Cartesian Products ◽  
Infinite Dimensional

Smolyanov has introduced1 the term "Feynman formula" (in the configuration space) for the representation of a solution of a Cauchy problem by limit of integrals over finite Cartesian products of the domain of the solution when the number of multipliers tends to infinity. In this paper, such formulas (first written by Smolyanov, Shamarov and Kpekpassi in a short note2) are proved for a family of heat type equations where the spatial variable runs over 𝔭-adic space of countable sequences. Equations with 𝔭-adic variables describe, for example, the dynamics of proteins.

scholarly journals Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups

2020 ◽  
Vol 10 (03) ◽  
pp. 2050016
Author(s):  
Michael Ruzhansky ◽  
Bolys Sabitbek ◽  
Durvudkhan Suragan
Keyword(s):  
Heisenberg Group ◽  
Half Space ◽  
Hardy Inequality ◽  
Euclidean Distance ◽  
Sobolev Inequalities ◽  
Sharp Constant ◽  
Heisenberg Groups ◽  
Hardy Inequalities ◽  
Angle Function ◽  
Distance To The Boundary

In this paper, we present geometric Hardy inequalities for the sub-Laplacian in half-spaces of stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant: [Formula: see text] which solves a conjecture in the paper [S. Larson, Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domain in the Heisenberg group, Bull. Math. Sci. 6 (2016) 335–352]. Here, [Formula: see text] is the angle function. Also, we obtain a version of the Hardy–Sobolev inequality in a half-space of the Heisenberg group: [Formula: see text] where [Formula: see text] is the Euclidean distance to the boundary, [Formula: see text], and [Formula: see text]. For [Formula: see text], this gives the Hardy–Sobolev–Maz’ya inequality on the Heisenberg group.

ELECTROMAGNETIC FIELDS IN AN N‐LAYER ANISOTROPIC HALF‐SPACE

Geophysics ◽  
1967 ◽  
Vol 32 (4) ◽  
pp. 668-677 ◽  
Author(s):  
Douglas P. O’Brien ◽  
H. F. Morrison
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
Plane Wave ◽  
Half Space ◽  
Electric Fields ◽  
Field Measurements ◽  
Large Scatter ◽  
Tensor Impedance ◽  
The Magnetic Field ◽  
Made In

From Maxwell’s equations and Ohm’s law for a horizontally anisotropic medium, it may be shown that two independent plane wave modes propagate perpendicular to the plane of the anisotropy. Boundary conditions at the interfaces in an n‐layered model permit the calculation, through successive matrix multiplications, of the fields at the surface in terms of the fields propagated into the basal infinite half space. Specifying the magnetic field at the surface allows the calculation of the resultant electric fields, and the calculation of the entries of a tensor impedance relationship. These calculations have been programmed for the digital computer and an interpretation of impedances obtained from field measurements may thus be made in terms of the anisotropic layering. In addition, apparent resistivities in orthogonal directions have been calculated for specific models and compared to experimental data. It is apparent that the large scatter of observed resistivities can be caused by small changes in the polarization of the magnetic field.

scholarly journals Studies on transmission of Staphylococcus aureus in an isolation ward for burned patients

1973 ◽  
Vol 71 (1) ◽  
pp. 171-183 ◽  
Author(s):  
Anna Hambraeus
Keyword(s):  
Staphylococcus Aureus ◽  
Phage Group ◽  
Burned Patient ◽  
Staph Aureus ◽  
Group Iii ◽  
Service Areas ◽  
One Year ◽  
Isolation Ward ◽  
Very High ◽  
Made In

SUMMARYA one-year epidemiological investigation was made in an isolation ward for burned patients. The transmission of Staphylococcus aureus was mainly studied. In spite of the design of the ward the cross-infection rate was high. In all, 49 of 69 patients were infected 114 times. Twenty-six of the strains causing infection were found in a patient only, 10 in a member of the staff only and 23 in both patients and staff the week before they caused a new infection. There were three epidemic outbreaks caused by three strains of Staph. aureus all belonging to phage group III; one was resistant to methicillin. Environmental studies with settle plates showed that the number of staphylococci dispersed by a burned patient was often very high. In 8% of the observations in occupied bedrooms the air count of Staph. aureus was more than 1800 col./m.2 hr. However, the counts of Staph. aureus in the corridor and service areas were low. This seems to indicate a rather good protection against airborne transfer of bacteria. Other routes of infection were probably of greater importance.

scholarly journals A symplectic restriction problem

2021 ◽  
Author(s):  
Valentin Blomer ◽  
Andrew Corbett
Keyword(s):  
Asymptotic Formula ◽  
Modular Form ◽  
Half Space ◽  
Imaginary Part ◽  
Dimensional Subspace ◽  
Siegel Modular Form ◽  
3 Dimensional ◽  
Relative Trace Formula ◽  
Lindelöf Hypothesis ◽  
Restriction Problem

AbstractWe investigate the norm of a degree 2 Siegel modular form of asymptotically large weight whose argument is restricted to the 3-dimensional subspace of its imaginary part. On average over Saito–Kurokawa lifts an asymptotic formula is established that is consistent with the mass equidistribution conjecture on the Siegel upper half space as well as the Lindelöf hypothesis for the corresponding Koecher–Maaß series. The ingredients include a new relative trace formula for pairs of Heegner periods.

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