On Harmonic Curvatures of Null Curves of the AW(k)-Type in Lorentzian Space

2008 ◽  
Vol 63 (5-6) ◽  
pp. 248-252 ◽  
Author(s):  
Mihriban Külahcı ◽  
Mehmet Bektaş ◽  
Mahmut Ergüt
Keyword(s):  
Lorentzian Space ◽  
3 Dimensional ◽  
Null Curves

We investigate null curves of the AW(k)-type (1 ≤ k ≤ 3) in the 3-dimensional Lorentzian space, L3, and give curvature conditions of these curves by using the Cartan frame. Moreover, we study harmonic curvatures of curves of AW(k)-type and show that if the α Frenet curve is of type AW(1), then α is a null helix.

Heterogeneity and neurovascular integration of intraportally transplanted islets revealed by 3-D mouse liver histology

2021 ◽  
Author(s):  
Chien-Chia Chen ◽  
Shih-Jung Peng ◽  
Pei-Yu Wu ◽  
Hung-Jen Chien ◽  
Chih-Yuan Lee ◽  
...  
Keyword(s):  
Islet Transplantation ◽  
Mouse Liver ◽  
Image Data ◽  
Liver Histology ◽  
Systematic Assessment ◽  
3 Dimensional ◽  
Neural Integration ◽  
Quantitative Analyses ◽  
Graft Tissue

Background: Intraportal islet transplantation has been clinically applied for treatment of unstable type 1 diabetes. However, in the liver, systematic assessment of the dispersed islet grafts and the graft-hepatic integration remains difficult, even in animal models. This is due to the lack of global and in-depth analyses of the transplanted islets and their microenvironment. Here, we apply 3-dimensional (3-D) mouse liver histology to investigate the islet graft microstructure, vasculature, and innervation. Methods: Streptozotocin-induced diabetic mice were used in syngeneic intraportal islet transplantation to achieve euglycemia. Optically cleared livers were prepared to enable 3-D morphological and quantitative analyses of the engrafted islets. Results: 3-D image data reveal the clot- and plaque-like islet grafts in the liver: the former are derived from islet emboli and associated with ischemia, whereas the latter (minority) resemble the plaques on the walls of portal vessels (e.g., at the bifurcation) with mild, if any, peri-graft tissue damage. Three weeks after transplantation, both types of grafts are revascularized, yet significantly more lymphatics are associated with the plaque- than clot-like grafts. Regarding the islet reinnervation, both types of grafts connect to the peri-portal nerve plexus and develop peri- and intra-graft innervation. Specifically, the sympathetic axons and varicosities contact the α-cells, highlighting the graft-host neural integration. Conclusion/interpretation: We present the heterogeneity of the intraportally transplanted islets and the graft-host neurovascular integration in mice. Our work provides the technical and morphological foundation for future high-definitional 3-D tissue and cellular analyses of human islet grafts in the liver.

RELATIVISTIC PARTICLES ALONG NULL CURVES IN 3D LORENTZIAN SPACE FORMS

2010 ◽  
Vol 20 (09) ◽  
pp. 2851-2859 ◽  
Author(s):  
ÁNGEL GIMÉNEZ
Keyword(s):  
Vector Fields ◽  
Lagrange Equation ◽  
Killing Vector ◽  
Space Forms ◽  
Lorentzian Space ◽  
Motion Equations ◽  
Critical Curves ◽  
Null Curves ◽  
Cartan Curvature ◽  
Relativistic Particles

We study relativistic particles modeled by actions whose Lagrangians are arbitrary functions on the curvature of null paths in (2 + 1)-dimensions backgrounds with constant curvature. We obtain first integrals of the Euler–Lagrange equation by using geometrical methods involving the search for Killing vector fields along critical curves of the action. In the case in which Lagrangian density depends quadratically on Cartan curvature, it is shown that the mechanical system is governed by a stationary Korteweg–De Vries system. Motion equations are completely integrated by quadratures in terms of elliptic and hyperelliptic functions.

NULL HELICES IN LORENTZIAN SPACE FORMS

2001 ◽  
Vol 16 (30) ◽  
pp. 4845-4863 ◽  
Author(s):  
ANGEL FERRÁNDEZ ◽  
ANGEL GIMÉNEZ ◽  
PASCUAL LUCAS
Keyword(s):  
Minkowski Space ◽  
Complete Classification ◽  
Space Forms ◽  
Lorentzian Space ◽  
Low Dimensions ◽  
Minkowski Space Time ◽  
Minimum Number ◽  
Null Curves ◽  
Lorentzian Space Forms

In this paper we introduce a reference along a null curve in an n-dimensional Lorentzian space with the minimum number of curvatures. That reference generalizes the reference of Bonnor for null curves in Minkowski space–time and it is called the Cartan frame of the curve. The associated curvature functions are called the Cartan curvatures of the curve. We characterize the null helices (that is, null curves with constant Cartan curvatures) in n-dimensional Lorentzian space forms and we obtain a complete classification of them in low dimensions.

Choroidal Thinning in Diabetes Type 1 Detected by 3-Dimensional 1060 nm Optical Coherence Tomography

2012 ◽  
Vol 53 (11) ◽  
pp. 6803 ◽  
Author(s):  
Marieh Esmaeelpour ◽  
Simon Brunner ◽  
Siamak Ansari-Shahrezaei ◽  
Susanne Nemetz ◽  
Boris Považay ◽  
...  
Keyword(s):  
Optical Coherence Tomography ◽  
Diabetes Type ◽  
Diabetes Type 1 ◽  
Optical Coherence ◽  
3 Dimensional

Rotations and Screw Motion with Timelike Vector in 3-Dimensional Lorentzian Space

2011 ◽  
Vol 22 (4) ◽  
pp. 1081-1091 ◽  
Author(s):  
Osman Keçilioğlu ◽  
Siddika Özkaldi ◽  
Halit Gündoğan
Keyword(s):  
Timelike Vector ◽  
Lorentzian Space ◽  
3 Dimensional ◽  
Screw Motion

On the explicit characterization of spherical curves in 3-dimensional Lorentzian space L3

2003 ◽  
Vol 11 (4) ◽  
pp. 389-397
Author(s):  
K. Ilarslan ◽  
C. Camci ◽  
H. Kocayigit ◽  
H. H. Hacisalihoglu
Keyword(s):  
Lorentzian Space ◽  
3 Dimensional ◽  
Explicit Characterization

On the explicit characterization of spherical curves in 3-dimensional Lorentzian space

2003 ◽  
Vol 11 (4) ◽  
pp. 389-397
Author(s):  
K. Ilarslan ◽  
C. Camci ◽  
H. Kocayigit ◽  
H. H. Hacisalihoglu
Keyword(s):  
Lorentzian Space ◽  
3 Dimensional ◽  
Explicit Characterization

scholarly journals The Narrow-Line Regions of Seyfert and Radio Galaxies

1997 ◽  
Vol 159 ◽  
pp. 264-279
Author(s):  
Andrew S. Wilson
Keyword(s):  
Close Association ◽  
Line Emission ◽  
Seyfert Galaxies ◽  
Narrow Line ◽  
Interstellar Gas ◽  
Ionized Gas ◽  
3 Dimensional ◽  
High Resolution Images ◽  
Seyfert Nucleus

AbstractThis paper reviews the morphology, excitation, and ionization of the gas in the narrow and extended narrow line regions (NLRs and ENLRs) in AGNs. Many high-resolution images of the NLRs of Seyfert galaxies are now available from HST. In some galaxies, these images reveal straight, sharp-edged V-shaped structures (believed to be the projections of 3-dimensional cones), while in others there is a close association between the ionized gas and the radio components. The latter effect arises through radiative shocks driven into the surrounding interstellar gas by the outwardly moving radio components or jets. Photoionization models of ionization-bounded clouds are quite successful in reproducing the line intensity ratios, but a number of problems remain. These problems may be resolved if matter-bounded clouds are also present. Differences between the excitation levels of different NLRs and ENLRs may reflect variations in the fraction of matter-bounded clouds as well as variations in the ionization parameter. I discuss the issue of whether the radiation responsible for photoionizing the gas in Seyfert 2 galaxies originates from a hidden, compact type 1 Seyfert nucleus or from photoionizing shocks within the NLR. These two scenarios are hard to distinguish between. The photoionizing-shock model requires surprisingly high pre-shock densities, raising the question of whether the shocks are sufficiently energetic to power the observed line emission.

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