In this study, we investigate the effects of noncommutative Quantum Mechanics in three dimensions on energy levels a charged isotropic harmonic oscillator presence uniform magnetic field z-direction. The extension problem to proves be non-trivial. We obtain first-order corrections energy-levels closed form low limit weak noncommutativity. most important result can note is that all due noncommut...

Perturbative study of many quantum field models has lead to many impressive results: beta functions for QED and for the Φ4 theory are known up to the fifth order whereas that of QCD up to the fourth order [1]-[7]. These studies however are based on the expansion in the small coupling constant such that the behavior at large couplings is completely missed. Although the possibility of a perturbat...

In this paper, I want to deal with the triviality threat to computationalism. On one hand, the controversial and vague claim that cognition involves computation is still denied. On the other, contemporary physicists and philosophers alike claim that all physical processes are indeed computational or algorithmic. This claim would justify the computationalism claim by making it utterly trivial. I...

Let C be an algebraically closed field with trivial derivation and let F denote the differential rational field C〈Yij〉, with Yij , 1 ≤ i ≤ n − 1, 1 ≤ j ≤ n, i ≤ j, differentially independent over C. We show that there is a Picard-Vessiot extension E ⊃ F for a matrix equation X ′ = XA(Yij), with differential Galois group SOn, with the property that if F is any differential field with field of co...

We study the fermionic extension of the E10/K(E10) coset model and its relation to eleven-dimensional supergravity. Finite-dimensional spinor representations of the compact subgroup K(E10) of E10(R) are studied and the supergravity equations are rewritten using the resulting algebraic variables. The canonical bosonic and fermionic constraints are also analysed in this way, and the compatibility...

This paper describes an extension of SVG that supports the drawing of graphs in terms of nodes and edges in between nodes. The graph drawing primitives support a variety of different node shapes, edge connection points, and edges. Both nodes and edges can be labeled. Two or more nodes can be aggregated as a single node, and an entire graph can be embedded into a single node. In addition, a numb...

We say a tame Galois field extension L/K with Galois group G has trivial Galois module structure if the rings of integers have the property that OL is a free OK [G]-module. The work of Greither, Replogle, Rubin, and Srivastav shows that for each algebraic number field other than the rational numbers there will exist infinitely many primes l so that for each there is a tame Galois field extensio...

We say a tame Galois field extension L/K with Galois group G has trivial Galois module structure if the rings of integers have the property that OL is a free OK [G]-module. The work of Greither, Replogle, Rubin, and Srivastav shows that for each algebraic number field other than the rational numbers there will exist infinitely many primes l so that for each there is a tame Galois field extensio...

We prove that given any knot k of genus g, k fails to be strongly n-trivial for all n, n ≥ 3g − 1.