Fourier Integrals in Classical Analysis

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

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OBSERVATION OF THE TRANSVERSE STERN–GERLACH EFFECT IN NEUTRAL POTASSIUM

Canadian Journal of Physics ◽

10.1139/p67-112 ◽

1967 ◽

Vol 45 (4) ◽

pp. 1481-1495 ◽

Cited By ~ 25

Author(s):

Myer Bloom ◽

Eric Enga ◽

Hin Lew

Keyword(s):

Magnetic Field ◽

Angular Velocity ◽

Reference Frame ◽

Inhomogeneous Magnetic Field ◽

Time Dependent ◽

Effective Magnetic Field ◽

Classical Analysis ◽

At Resonance ◽

Rotating Reference Frame

A successful transverse Stern–Gerlach experiment has been performed, using a beam of neutral potassium atoms and an inhomogeneous time-dependent magnetic field of the form[Formula: see text]A classical analysis of the Stern–Gerlach experiment is given for a rotating inhomogeneous magnetic field. In general, when space quantization is achieved, the spins are quantized along the effective magnetic field in the reference frame rotating with angular velocity ω about the z axis. For ω = 0, the direction of quantization is the z axis (conventional Stern–Gerlach experiment), while at resonance (ω = −γH0) the direction of quantization is the x axis in the rotating reference frame (transverse Stern–Gerlach experiment). The experiment, which was performed at 7.2 Mc, is described in detail.

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On the Gibbs phenomenon for Riesz spherical means of multiple Fourier series and Fourier integrals

Analysis Mathematica ◽

10.1007/bf01905111 ◽

1975 ◽

Vol 1 (1) ◽

pp. 31-53 ◽

Cited By ~ 5

Author(s):

B. I. Golubov

Keyword(s):

Fourier Series ◽

Gibbs Phenomenon ◽

Multiple Fourier Series ◽

Spherical Means ◽

Fourier Integrals

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CALINCA—A Novel Pipeline for the Identification of lncRNAs in Podocyte Disease

Cells ◽

10.3390/cells10030692 ◽

2021 ◽

Vol 10 (3) ◽

pp. 692

Author(s):

Sweta Talyan ◽

Samantha Filipów ◽

Michael Ignarski ◽

Magdalena Smieszek ◽

He Chen ◽

...

Keyword(s):

Cell Biology ◽

Mammalian Cells ◽

De Novo ◽

Depth Information ◽

Gene Products ◽

Classical Analysis ◽

Protein Coding ◽

Bioinformatic Pipeline ◽

Non Coding Rnas ◽

Filtration Unit

Diseases of the renal filtration unit—the glomerulus—are the most common cause of chronic kidney disease. Podocytes are the pivotal cell type for the function of this filter and focal-segmental glomerulosclerosis (FSGS) is a classic example of a podocytopathy leading to proteinuria and glomerular scarring. Currently, no targeted treatment of FSGS is available. This lack of therapeutic strategies is explained by a limited understanding of the defects in podocyte cell biology leading to FSGS. To date, most studies in the field have focused on protein-coding genes and their gene products. However, more than 80% of all transcripts produced by mammalian cells are actually non-coding. Here, long non-coding RNAs (lncRNAs) are a relatively novel class of transcripts and have not been systematically studied in FSGS to date. The appropriate tools to facilitate lncRNA research for the renal scientific community are urgently required due to a row of challenges compared to classical analysis pipelines optimized for coding RNA expression analysis. Here, we present the bioinformatic pipeline CALINCA as a solution for this problem. CALINCA automatically analyzes datasets from murine FSGS models and quantifies both annotated and de novo assembled lncRNAs. In addition, the tool provides in-depth information on podocyte specificity of these lncRNAs, as well as evolutionary conservation and expression in human datasets making this pipeline a crucial basis to lncRNA studies in FSGS.

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