After the 1916 success of General relativity that explained gravity by adding time as a fourth dimension, physicists have been trying to explain other physical fields by adding extra dimensions. In 1921, Kaluza and Klein has shown that under certain conditions like cylindricity (∂gij/∂x 5 = 0), the addition of the 5th dimension can explain the electromagnetic field. The problem with this approa...

In this paper, we discuss the competition of two species for a single essential growth-limiting nutriment with viral infection that affects only first species. Although classical models without suggest competitive exclusion, model exhibits stable coexistence both We reduce fourth-dimension proposed to three-dimension one. Thus, competing is demonstrated using theory uniform persistence applied ...

The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synth...

OBJECTIVE Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. RESEARCH DESIGN AND METHODS We conducted a cross-sectional study ...

We give a new proof of the almost sharp Moser–Trudinger inequality on smooth compact Riemannian manifolds based Moser Euclidean spaces and generalize it to with continuous metrics higher order Sobolev boundary under several conditions. These generalizations can be applied fourth Q curvature equations in dimension 4.

WE live in a world of three dimensions. We measure objects by their length, breadth and thickness. The position of a point can be described by three coordinates , x, y and z. We can not escape from the inside of a spherical surface except by passing through it, but if we are standing in a circle on a surface we escape from it by stepping over it. It is amusing to try to imagine a fourth dimensi...

Moments are expectation values of products powers position and momentum, taken over quantum states (or averages a set classical particles). For free particles, the evolution in case is closely related to that particles. Here we consider symmetrized moments for particles one dimension, first examining geometric properties up fourth order, as determined by their extrema inflections. These specifi...

Addiction is a mental illness in which psychiatric conditions imply a prominent burden. Psychopathological symptoms in substance use disorder (SUD) patients are usually viewed as being assignable to the sphere of a personality trait or of comorbidity, leaving doubts about the presence of a specific psychopathology that could only be related to the toxicomanic process. Our research group at the ...