Post-Newtonian estimation in relativistic optics

A post-Newtonian analysis of the theory of gravity based on the metricg _ij(x,y)= _ij(x)+/c ²(1–1n ²)y _iy_j with the index of refractionn(x, y) is given. A generalized Lagrange space endowed with this metric is used for the study of gravitational phenomena. The index of refractionn(x, y) is expanded in integer powers of the gravitational potentialU=GM/rc ² andv ²/c ². It is shown that solar system tests impose a constraint on a combination of the constant, the post-Newtonian parameters defining the index of refractionn(x, y), and the post-Newtonian parameter associated to the Riemannian metric _ij(x).     

Relativistic optics of nondispersive media

The relativistic optics of the nondispersive media endowed with the metric g_ij(x) [Eq. (1.6)] and with a nonlinear connection [Eq. (1.2)] is studied. The d-connection [Eqs. (3.3)– (3.4)] relates the conformal and projective properties of the space- time. A post-Newtonian estimation for the metric g_ij(x) is also given. It is shown that the solar system tests impose a constraint [Eq. (4.20)] on a combination of the post- Newtonian parameters describing the model.     

Self-duality equations for spherically symmetric SU(2) gauge fields

A model of spherically symmetric SU(2) gauge theory is considered. The self-duality equations are written and it is shown that they are compatible with the Einstein-Yang-Mills equations. It is proven that the SU(2) gauge model is self-dual on a Schwarzschild space-time but not on a Reissner-Nordstr?m one. Received: 24 May 2002 / Accepted: 1 July 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: gzet@phys.tuiasi.ro Communicated by A. Sch?fer     

On the tensor operators in parallelizable spaces

The tensor-operators over parallelizable spaces are defined. Their Hermitian conjugation is defined by introducing an inner product based on the tensor-integral Some properties of the ordinary operators are generalized for the tensor-operators     

Gauge theory onR×S 3 topology

A model for gauge theories over a compact Lie group is described using R × S³ as background space. The U(1) and SU(2) gauge theories are considered as particular examples, and a comparison with other results is given. Our results differ from those of Carmeli and MalinFound. Phys. 16, 791 (1986);17, 193 (1987)] by a supplementary term in the curvature tensor due to the noncommutativity of derivatives used on R × S³ space. Some observations about supersymmetry and gravity on R × S³ space are also given.     

Gravitation theory in the spacetimeR×S 3

A geometric formulation of the gravitation theory in the spacetime R × S ³ is given. A linear connection is introduced on the tangent bundle T(R × S ³ ) and then the connection coefficients and the Riemann curvature tensor are calculated. It is shown that their expressions differ from those of Carmeli and Malin [Found. Phys.17, 407 (1987)] by supplementary terms due to the noncommutativity of derivatives used on the spacetime R × S ³ . The Einstein field equations are written as usually and a comparison with other results is given. Finally, some observations about a possible gauge theory of gravitation in the spacetime R × S ³ are made.     

Bioguided Fractionation of Local Plants against Matrix Metalloproteinase9 and Its Cytotoxicity against Breast Cancer Cell Models: In Silico and In Vitro Study (Part II)

In our previous work, the partitions (1 mg/mL) of Ageratum conyzoides (AC) aerial parts and Ixora coccinea (IC) leaves showed inhibitions of 94% and 96%, respectively, whereas their fractions showed IC₅₀ 43 and 116 µg/mL, respectively, toward Matrix Metalloproteinase9 (MMP9), an enzyme that catalyzes a proteolysis of extracellular matrix. In this present study, we performed IC₅₀ determinations for AC n-hexane, IC n-hexane, and IC ethylacetate partitions, followed by the cytotoxicity study of individual partitions against MDA-MB-231, 4T1, T47D, MCF7, and Vero cell lines. Successive fractionations from AC n-hexane and IC ethylacetate partitions led to the isolation of two compounds, oxytetracycline (OTC) and dioctyl phthalate (DOP). The result showed that AC n-hexane, IC n-hexane, and IC ethylacetate partitions inhibit MMP9 with their respective IC₅₀ as follows: 246.1 µg/mL, 5.66 µg/mL, and 2.75 × 10⁻² µg/mL. Toward MDA-MB-231, 4T1, T47D, and MCF7, AC n-hexane demonstrated IC₅₀ 2.05, 265, 109.70, and 2.11 µg/mL, respectively, whereas IC ethylacetate showed IC₅₀ 1.92, 57.5, 371.5, and 2.01 µg/mL, respectively. The inhibitions toward MMP9 by OTC were indicated by its IC₅₀ 18.69 µM, whereas DOP was inactive. A molecular docking study suggested that OTC prefers to bind to PEX9 rather than its catalytic domain. Against 4T1, OTC showed inhibition with IC₅₀ 414.20 µM. In conclusion, this study furtherly supports the previous finding that AC and IC are two herbals with potential to be developed as triple-negative anti-breast cancer agents.     

Towards a quantization of gauge fields on de Sitter group by functional integral method

A formulation of the de Sitter symmetry as a purely inner symmetry defined on a fixed Minkowski space-time is presented. We define the generators of the de Sitter group and write the structure equations using a constant deformation parameter λ. The conserved gauge currents are calculated, and their physical meaning is given. Local gauge transformations and the corresponding covariant derivative depending on the gauge fields are also obtained. We study the behavior of gauge fields, the torsion and curvature tensors and give a regularization technique in terms of the ζ function.     

Corrections to Schwarzschild solution in noncommutative gauge theory of gravity

A deformed Schwarzschild solution in noncommutative gauge theory of gravitation is obtained. The gauge potentials (tetrad fields) are determined up to the second order in the noncommutativity parameters Θμν${\Theta }^{\mu \nu }$. A deformed real metric is defined and its components are obtained. The noncommutativity correction to the red shift test of general relativity is calculated and it is concluded that the correction is too small to have observable effects. Implications of such a deformed Schwarzschild metric are also mentioned.     

Schwarzschild-de-Sitter Solution in Quantum Gauge Theory of Gravity

We use the theory based on the gravitational gauge group G to obtain a spherical symmetric solution of the field equations for the gravitational potentials on a Minkowski space-time. The gauge group G is defined and then we introduce the gauge-covariant derivative Dμ. The strength tensor of the gravitational gauge field is also obtained and a gauge-invariant Lagrangian including the cosmological constant is constructed. A model whose gravitational gauge potentials A^α μ （x） have spherical symmetry, depending only on the radial coordinate τ is considered and an analytical solution of these equations, which induces the Schwarzschild-de-Sitter metric on the gauge group space, is then determined. All the calculations have been performed by GR Tensor II computer algebra package, running on the Maple V platform, along with several routines that we have written for our model.