Narrow Results

In this paper, the different properties of generalized Vaidya spacetime are considered. We define the location of horizons. We show that the apparent horizon can contain the event horizon. The locations of all types of horizons are compared with the ones in the usual Vaidya spacetime. We investigate the time-like geodesics in this spacetime. New corrections to Schwarzschild and Vaidya cases appear and we give conditions when these corrections are not negligible. Also, we consider the conformal Killing vector and transform the metric to conformally static coordinates. We introduce a new constant of motion along null and time-like geodesics, which is generated by a homothetic Killing vector. The conformally static coordinates allow diagonalizing of the generalized Vaidya spacetime. The surface gravity has been calculated for the dust and stiff fluid cases.

The Hamiltonian of two modes coupled harmonic oscillators in noncommutative phase-space can be expressed in the standard quadric form by introducing a coordinate transformation. As a result, the coupling items are eliminated and the Hamiltonian can be simplified to the two modes independent harmonic oscillators. Then, the corresponding energy spectrums are obtained with an algebraic method.

Eigenfunctions of the Lévy Laplacian with an arbitrary real number as an eigenvalue are constructed by means of a coordinate change of white noise distributions. The Lévy Laplacian is diagonalized on the direct integral Hilbert space of such eigenfunctions and the corresponding equi-continuous semigroup is obtained. Moreover, an infinite dimensional stochastic process related to the Lévy Laplacian is constructed from a one-dimensional stable process.

In this paper, a method for calculating all the Hückel molecular orbitals (MO) of large (16.000 atoms) carbon zigzag nanotubes is presented. These MO have been obtained by combining the singular value decomposition (SVD), the Sylvester–Hadamard transform, and the theory of Hamiltonian–Symplectic matrices. Numerical diagonalization of hermitian matrices is reviewed and improved. A new, more advantageous, (tri-diagonal) algorithm is proposed and analyzed. The reactivity of the atoms is described by calculating their free valence indices.

In this study, we give another formula to all the generalized tribonacci ${(T_n(x,y,z))}_{n\in \mathbb{N}}$ and generalized tribonacci-Lucas ${(L_n(x,y,z))}_{n\in \mathbb{N}}$ polynomials by using the combinatorial calculus and their sum. Then, we give the explicit formula of partial derivative of such polynomials $\partial T_n(x,y,z)$, $\partial L_n(x,y,z)$ with respect to one of those variables and describe some properties.

In this work we start from the idea that intentionality is the chief characteristic of intelligent behavior, both cognitive and deliberative. Investigating the "originality of intelligent life" from this standpoint means investigating "intentional behavior" in living organisms. In this work, we ask epistemological questions involved in making the intentional behavior the object of physical and mathematical inquiry. We show that the subjective component of intentionality can never become object of scientific inquiry, as related to self–consciousness. On the other hand, the inquiry on objective physical and logical components of intentional acts is central to scientific inquiry. Such inquiry concerns logical and semantic questions, like reference and truth of logical symbols constituted as such, as well as their relationship to the "complexity" of brain networking. These suggestions concern cognitive neuroscience and computability theory, so to constitute one of the most intriguing intellectual challenges of our age. Such metalogical inquiry suggests indeed some hypotheses about the amazing "parallelism", "plasticity" and "storing capacity" that mammalian and ever human brains might exhibit. Such properties, despite neurons are over five orders of magnitude slower than microchips, make biological neural nets much more efficient than artificial ones even in execution of simple cognitive and behavioral tasks.