This is a Unified Field description based on the holographic Time Dilation Cosmology, TDC, model, which is an eternal continuum evolving forward in the forward direction of time, at the speed of light, c, at an invari...This is a Unified Field description based on the holographic Time Dilation Cosmology, TDC, model, which is an eternal continuum evolving forward in the forward direction of time, at the speed of light, c, at an invariant 1 s/s rate of time. This is the Fundamental Direction of Evolution, FDE. There is also an evolution down time dilation gradients, the Gravitational Direction of Evolution, GDE. These evolutions are gravity, which is the evolutionary force in time. Gravitational velocities are compensation for the difference in the rate of time, dRt, in a dilation field, and the dRtis equal to the compensatory velocity’s percentage of c, and is a measure of the force in time inducing the velocity. In applied force induced velocities, the dRt is a measure of the resistance in time to the induced velocity, which might be called “anti-gravity” or “negative gravity”. The two effects keep the continuum uniformly evolving forward at c. It is demonstrated that gravity is already a part of the electromagnetic field equations in way of the dRt element contained in the TDC velocity formula. Einstein’s energy formula is defined as a velocity formula and a modified version is used for charged elementary particle solutions. A time dilation-based derivation of the Lorentz force ties gravity directly to the electromagnetic field proving the unified field of gravity and the EMF. It is noted how we could possibly create gravity drives. This is followed by a discussion of black holes, proving supermassive objects, like massive black hole singularities, are impossible, and that black holes are massless Magnetospheric Eternally Collapsing Objects (MECOs) that are vortices in spacetime. .展开更多
Let Ep^2＋p（resp.E2^2＋p） be a （2＋p）-dimensional pseudo-Euclidean space with the index p （resp.2）. The maximal spacelike or minimal timelike translation surfaces M^2 in Ep^2＋p or E2^2＋p are considered and a c...Let Ep^2＋p（resp.E2^2＋p） be a （2＋p）-dimensional pseudo-Euclidean space with the index p （resp.2）. The maximal spacelike or minimal timelike translation surfaces M^2 in Ep^2＋p or E2^2＋p are considered and a complete classification is given.展开更多
In the light of great importance of curves and their frames in many differentbranches of science, especially differential geometry as well as geometric properties andthe uses in various fields, we are interested here ...In the light of great importance of curves and their frames in many differentbranches of science, especially differential geometry as well as geometric properties andthe uses in various fields, we are interested here to study a special kind of curves calledSmarandache curves in Lorentz 3-space. Then, we present some characterizations for thesecurves and calculate their Darboux invariants. Moreover, we classify TP, TU, PU andTPU-Smarandache curves of a spacelike curve according to the causal character of thevector, curve and surface used in the study. Besides, we give some of differential geometricproperties and important relations between that curves. Finally, to demonstrate ourtheoretical results a computational example is given with graph.展开更多
文摘This is a Unified Field description based on the holographic Time Dilation Cosmology, TDC, model, which is an eternal continuum evolving forward in the forward direction of time, at the speed of light, c, at an invariant 1 s/s rate of time. This is the Fundamental Direction of Evolution, FDE. There is also an evolution down time dilation gradients, the Gravitational Direction of Evolution, GDE. These evolutions are gravity, which is the evolutionary force in time. Gravitational velocities are compensation for the difference in the rate of time, dRt, in a dilation field, and the dRtis equal to the compensatory velocity’s percentage of c, and is a measure of the force in time inducing the velocity. In applied force induced velocities, the dRt is a measure of the resistance in time to the induced velocity, which might be called “anti-gravity” or “negative gravity”. The two effects keep the continuum uniformly evolving forward at c. It is demonstrated that gravity is already a part of the electromagnetic field equations in way of the dRt element contained in the TDC velocity formula. Einstein’s energy formula is defined as a velocity formula and a modified version is used for charged elementary particle solutions. A time dilation-based derivation of the Lorentz force ties gravity directly to the electromagnetic field proving the unified field of gravity and the EMF. It is noted how we could possibly create gravity drives. This is followed by a discussion of black holes, proving supermassive objects, like massive black hole singularities, are impossible, and that black holes are massless Magnetospheric Eternally Collapsing Objects (MECOs) that are vortices in spacetime. .
文摘Let Ep^2＋p（resp.E2^2＋p） be a （2＋p）-dimensional pseudo-Euclidean space with the index p （resp.2）. The maximal spacelike or minimal timelike translation surfaces M^2 in Ep^2＋p or E2^2＋p are considered and a complete classification is given.
文摘In the light of great importance of curves and their frames in many differentbranches of science, especially differential geometry as well as geometric properties andthe uses in various fields, we are interested here to study a special kind of curves calledSmarandache curves in Lorentz 3-space. Then, we present some characterizations for thesecurves and calculate their Darboux invariants. Moreover, we classify TP, TU, PU andTPU-Smarandache curves of a spacelike curve according to the causal character of thevector, curve and surface used in the study. Besides, we give some of differential geometricproperties and important relations between that curves. Finally, to demonstrate ourtheoretical results a computational example is given with graph.
