Curvilinear coordinates and the dushenskii relation in the theory of molecular spectra. A general approach

1991 ◽  
Vol 55 (1) ◽  
pp. 674-678
Author(s):  
V. I. Berezin ◽  
M. D. �l'kin
Keyword(s):  
Curvilinear Coordinates ◽  
Molecular Spectra

Curvilinear coordinates and Dushinsky effect in the theory of molecular spectra

1992 ◽  
Author(s):  
Valentin I. Berezin ◽  
Mikhail D. El'kin ◽  
Vladimir V. Nechaev
Keyword(s):  
Curvilinear Coordinates ◽  
Molecular Spectra

Reaction of organolithium compounds with 1-substituted 2,4,6-triphenylpyridinium perchlorates

1989 ◽  
Vol 54 (7) ◽  
pp. 1880-1887 ◽  
Author(s):  
Marián Schwarz ◽  
Josef Kuthan
Keyword(s):  
Visible Range ◽  
Molecular Spectra ◽  
Organolithium Compounds ◽  
Phenylmagnesium Bromide

The reaction of organolithium compounds with 1-substituted 2,4,6-triphenylpyridinium perchlorates Ia-Ic produces mixtures of 1,4-dihydropyridines IIa-IIe and 1,2-dihydropyridines IIIa-IIIe. Analogous reactions of phenylmagnesium bromide with compounds Ia-Ic proceed with very low conversions (less than 1%). Photochromism in visible range is observed only with the compounds II which have two aromatic substituents at 4-position, whereas compounds III and IId show no visible photochromism. The molecular spectra of the compounds newly prepared are discussed.

Certain problems with the application of stochastic diffusion processes for description of chemical engineering phenomena; Diffusion equations in curvilinear coordinates

1991 ◽  
Vol 56 (3) ◽  
pp. 602-618
Author(s):  
Vladimír Kudrna
Keyword(s):  
Heat Transfer ◽  
Mass Transport ◽  
Probability Density ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Curvilinear Coordinates ◽  
Diffusion Equations ◽  
Parabolic Partial Differential Equations ◽  
Spherical Coordinates ◽  
Transformation Procedure

Parabolic partial differential equations used in chemical engineering for the description of mass transport and heat transfer and analogous relationship derived in stochastic processes theory are given. A standard transformation procedure is applied, allowing these relations to be generally written in curvilinear coordinates and particular expressions for cylindrical and spherical coordinates to be derived. The relation between the probability density for the position of a discernible particle and the concentration of a set of such particles is discussed.

scholarly journals Rare Gain-of-Function KCND3 Variant Associated with Cerebellar Ataxia, Parkinsonism, Cognitive Dysfunction, and Brain Iron Accumulation

2021 ◽  
Vol 22 (15) ◽  
pp. 8247
Author(s):  
Cheng-Tsung Hsiao ◽  
Thomas F. Tropea ◽  
Ssu-Ju Fu ◽  
Tanya M. Bardakjian ◽  
Pedro Gonzalez-Alegre ◽  
...  
Keyword(s):  
Cerebellar Ataxia ◽  
Iron Accumulation ◽  
Molecular Spectra ◽  
Loss Of Function ◽  
Brain Iron ◽  
Gain Of Function ◽  
Progressive Cerebellar Ataxia ◽  
Voltage Dependent ◽  
Window Current

Loss-of-function mutations in the KV4.3 channel-encoding KCND3 gene are linked to neurodegenerative cerebellar ataxia. Patients suffering from neurodegeneration associated with iron deposition may also present with cerebellar ataxia. The mechanism underlying brain iron accumulation remains unclear. Here, we aim to ascertain the potential pathogenic role of KCND3 variant in iron accumulation-related cerebellar ataxia. We presented a patient with slowly progressive cerebellar ataxia, parkinsonism, cognitive impairment, and iron accumulation in the basal ganglia and the cerebellum. Whole exome sequencing analyses identified in the patient a heterozygous KCND3 c.1256G>A (p.R419H) variant predicted to be disease-causing by multiple bioinformatic analyses. In vitro biochemical and immunofluorescence examinations revealed that, compared to the human KV4.3 wild-type channel, the p.R419H variant exhibited normal protein abundance and subcellular localization pattern. Electrophysiological investigation, however, demonstrated that the KV4.3 p.R419H variant was associated with a dominant increase in potassium current amplitudes, as well as notable changes in voltage-dependent gating properties leading to enhanced potassium window current. These observations indicate that, in direct contrast with the loss-of-function KCND3 mutations previously reported in cerebellar ataxia patients, we identified a rare gain-of-function KCND3 variant that may expand the clinical and molecular spectra of neurodegenerative cerebellar disorders associated with brain iron accumulation.

XVI.—On Triple Systems of Surfaces and Non-Orthogonal Curvilinear Coordinates

1927 ◽  
Vol 46 ◽  
pp. 194-205 ◽  
Author(s):  
C. E. Weatherburn
Keyword(s):  
Curvilinear Coordinates ◽  
Triple Systems ◽  
Orthogonal Curvilinear Coordinates ◽  
Orthogonal Systems ◽  
Considerable Detail

The properties of “triply orthogonal” systems of surfaces have been examined by various writers and in considerable detail; but those of triple systems generally have not hitherto received the same attention. It is the purpose of this paper to discuss non-orthogonal systems, and to investigate formulæ in terms of the “oblique” curvilinear coordinates u, v, w which such a system determines.

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