The Killing Fields

Heavy metal pollution poses a serious threat to public health Rich in mineral resources, Hunan Province in central China is known as "the land of nonferrous metals.

Review and Analysis: United States Secret Wars in Cambodia: Long-Term Impacts and Consequences

The People’s Army of Vietnam (PAVN) decided to use conventional warfare to unify Vietnam. The United States military operation against the Ho Chi Minh Trail traffic began in 1959. The (PAVN) connected a series of old trails leading from North Vietnam to South Vietnam via Laos and Cambodia. In the 1960s the network of trails was expanded. Trail traffic was interdicted by repeated CIA (Air America) and US Air Force (Operation Ranch Hand) tactical herbicide spraying and bombing missions. During the late 1960s, the Khmer Rouge Army slowly grew in eastern Cambodia during a time when America was spraying and bombing the Ho Chi Minh Trail. On February 22, 1969, the PAVN launched a new offensive against American forces in South Vietnam from their sanctuaries in Cambodia. President Richard Nixon and Dr. Henry Kissinger, decided to spray and bomb Cambodia, a neutral country, to eliminate the PAVN sanctuary base camps. The damage and loss of life as a result of U.S. air campaign resulted in the insurgency (Khmer Rouge) being able to recruit civilian members. This created a dual effect of strengthening the popularity of the Khmer Rouge, led by Pol Pot, enabling him to overthrow the Khmer Republic in 1975. The primary objectives of this study are to determine the political impacts and consequences of: 1) the 1959 United States secret war on the Ho Chi Minh Trail in Cambodia and 2) the 1969 President Nixon’s decision to destroy the PAVN bases hidden in the Cambodian jungles. These United States secret wars in Cambodia had long-lasting effects on Cambodian political, social, and economic stability.

Generalized elastic curves in the Lorentz flat space L^4

In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures.

BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS

Using non-linear connection of Finsler manifold M, the existence of local coordinates which is normalized at a point x is proved, and the Laplace operator A on 1-form of M is defined by non-linear connection and its curvature tensor. After proving the maximum principle theorem of Hopf-Bochner on M, the Bochner type vanishing theorem of Killing vectors and harmonic 1-form are obtained.

Intrinsic Topological Structure of Entropy of Kerr Black Holes

In the light of Ф-mapping method and the relationship between entropy and the Euler characteristic, the intrinsic topological structure of entropy of Kerr black holes is studied. From the Ganss-Bonnet-Chem theorem, it is shown that the entropy of Kerr black hole is determined by singularities of the Killing vector field of spacetime. These singularities naturally carry topological numbers, Hopf indices and Brouwer degrees, which can also be viewed as topological quantization of entropy of Kerr black holes. Specific results S = A/4 for non-extreme Kerr black holes and S = 0 for extreme ones are calculated independently by using the above-mentioned methods.

Conformal Vector Fields on Finsler Warped Product Manifolds

In this paper,we study the conformal vector fields on Finsler warped product manifolds.We obtain a system of equivalent equations that the conformal vector fields on Finsler warped product manifolds satisfy and completely characterize conformal vector fields on such manifolds.Further,by solving the equation,we give the classification.And we also give some examples.

A Kenmotsu Metric as a *-conformal Yamabe Soliton with Torse Forming Potential Vector Field

The purpose of the present paper is to deliberate *-conformal Yamabe soliton,whose potential vector field is torse-forming on Kenmotsu manifold.Here,we have shown the nature of the soliton and find the scalar curvature when the manifold admitting *-conformal Yamabe soliton on Kenmotsu manifold.Next,we have evolved the characterization of the vector field when the manifold satisfies *-conformal Yamabe soliton.Also we have embellished some applications of vector field as torse-forming in terms of *-conformal Yamabe soliton on Kenmotsu manifold.We have developed an example of *-conformal Yamabe soliton on 3-dimensional Kenmotsu manifold to prove our findings.

Homogeneous Finsler spaces with only one orbit of prime closed geodesics

When a closed Finsler manifold admits continuous isometric actions,estimating the number of orbits of prime closed geodesics seems a more reasonable substitution for estimating the number of prime closed geodesics.To extend the results of Duan,Long,Rademacher,Wang and others on the existence of two prime closed geodesics to the equivariant situation,we propose the question if a closed Finsler manifold has only one orbit of prime closed geodesics if and only if it is a compact rank-one Riemannian symmetric space.In this paper,we study this problem in homogeneous Finsler geometry,and get a positive answer when the dimension is even or the metric is reversible.We guess the rank inequality and the algebraic techniques in this paper may continue to play an important role for discussing our question in the non-homogeneous situation.