Satins, lattices, and extended Euclid's algorithm

Motivated by the design of satins with draft of period m and step a, we draw our attention to the lattices $$L(m,a)=\langle (1,a),(0,m)\rangle$$ L ( m , a ) = ⟨ ( 1 , a ) , ( 0 , m ) ⟩ where $$1\le a<m$$ 1 ≤ a < m are integers with $$\gcd (m,a)=1$$ gcd ( m , a ) = 1 . We show that the extended Euclid's algorithm applied to m and a produces a shortest no null vector of L(m, a) and that the algorithm can be used to find an optimal basis of L(m, a). We also analyze square and symmetric satins. For square satins, the extended Euclid's algorithm produces directly the two vectors of an optimal basis. It is known that symmetric satins have either a rectangular or a rombal basis; rectangular basis are optimal, but rombal basis are not always optimal. In both cases, we give the optimal basis directly in terms of m and a.

Kerr–Schild metrics in teleparallel gravity

We show that the Kerr–Schild ansatz can be extended from the metric to the tetrad, and then to teleparallel gravity where curvature vanishes but torsion does not. We derive the equations of motion for the Kerr–Schild null vector, and describe the solution for a rotating black hole in this framework. It is shown that the solution depends on the chosen tetrad in a non-trivial way if the spin connection is fixed to be the one of the flat background spacetime. We show furthermore that any Kerr–Schild solution with a flat background is also a solution of $$f({\mathcal {T}})$$ f ( T ) gravity.

CCNV Space-Times as Potential Supergravity Solutions

It is of interest to study supergravity solutions preserving a nonminimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the space-time admits a Killing spinor and hence a null or time-like Killing vector field. Any space-time admitting a covariantly constant null vector (CCNV) field belongs to the Kundt class of metrics and more importantly admits a null Killing vector field. We investigate the existence of additional non-space-like isometries in the class of higher-dimensional CCNV Kundt metrics in order to produce potential solutions that preserve some supersymmetries.

Injection of hTERT-Transduced Endothelial Progenitor Cells Promotes Beneficial Aortic Changes in a High-Fat Dietary Model of Early Atherosclerosis

Objectives: Cultured endothelial progenitor cells (EPCs) display troubling issues that adversely affect their applicability to endothelial regeneration. We hypothesized that transduction of the human telomerase catalytic subunit (hTERT) gene would enhance EPC function in treating dietary-induced early atherosclerosis (AS). Methods: A dietary-induced early AS model was successfully constructed in 90 healthy male rats, while 30 healthy control (HC) rats were normally fed. Four experimental groups were constructed: an untreated HC group; an untreated AS group injected with PBS; a null EPC AS group injected with null vector-transduced EPCs, and an hTERT EPC AS group injected with hTERT-transduced EPCs. Two months postinjection, abdominal aortas were extracted to validate EPC integration and comparatively assess mRNA and protein expression of the early atherosclerotic markers VCAM-1, ICAM-1, LFA-1, Mac-1, CD44, MCP-1, endothelial nitric oxide synthase (eNOS), and apolipoprotein E. Results: In vitro, hTERT transduction of EPCs resulted in a significantly superior proliferative capacity as well as significantly higher NO, iNOS, and LDH secretory capacity. In vivo injection of hTERT-transduced EPCs produced significant reductions in CD44 and MCP-1 expression as well as a significant increase in eNOS expression relative to injection with null vector-transduced EPCs (all p < 0.05). Conclusion: hTERT-transduced human EPCs may be useful in treating dietary-induced early AS.

Generalized Mattig’s relation in Brans–Dicke–Rastall gravity

The geodesic deviation equation (GDE) is being studied in Brans–Dicke–Rastall (BDR) gravity. We briefly discuss the BDR gravity and then construct GDE for FLRW metric. In this way, the obtained geodesic deviation equation will correspond to the BDR gravity. Eventually, we solve numerically the null vector GDE to obtain from Mattig relation, the deviation vector [Formula: see text] and observer area distance [Formula: see text] and compare the results with [Formula: see text]CDM model.

Dirac equation and optical scalars in the Einstein-Cartan theory

The article deals with the Dirac equation in the Newman-Penrose formalism within the framework of Einstein-Cartan theory and behavior of isotropic congruence of autoparallels, i. e. a congruence of the curves along which tangent null vector transferred in parallel.