We investigate the phase structure of lattice QCD for general number of flavors NF . Based on numerical results combined with the result of the perturbation theory we propose the following picture: When NF ≥ 17, there is only a trivial fixed point and therefore the theory in the continuum limit is trivial. On the other hand, when 16 ≥ NF ≥ 7, there is a non-trivial fixed point and therefore the...

The changes in human population often correspond with change in land use, including expansion of urban areas, agriculture and increasing industrialization, which necessitate increasing the available amount of drinking water. As the surface water sources are under the pressure of pollution, it has become necessary to use groundwater at an increasing rate. Groundwater recharge can be abundant in ...

For systems with a finite number of degrees of freedom, it is shown in [1] that first class constraints are Abelianizable if the FaddeevPopov determinant is not vanishing for some choice of subsidiary constraints. Here, for irreducible first class constraint systems with SO(3) or SO(4) gauge symmetries, including a subset of coordinates in the fundamental representation of the gauge group, we e...

Theories of the meaning of life are divided into two categories: nihilistic and anti-nihilistic. The latter is divided, in turn, into the view that life is meaningful and the view that life can be made meaningful. In this paper, we deploy a descriptive-analytic method to discuss Jean-Paul Sartre’s view of nihilism. In his view, God does not exist, the human being is born and dies without a reas...

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Abstract In recent years there has been vigorous debate whether asymptotic transverse macrodispersion exists in steady three‐dimensional (3D) groundwater flows the purely advective limit. This question is tied to topology of 3D flow paths (termed Lagrangian kinematics ), specifically streamlines can undergo braiding motions or wander freely direction. this study we determine which Darcy do admi...