The cosmological evolution in Nonlinear Born-Infeld(hereafter NLBI) scalar field theory with negative potentials was investigated. The cosmological solutions in some important evolutive epoches were obtained. The different evolutional behaviors between NLBI and linear scalar field theory have been presented. A notable characteristic is that NLBI scalar field behaves as ordinary matter nearly th...

The cosmological evolution in Nonlinear Born-Infeld(hereafter NLBI) scalar field theory with negative potentials was investigated. The cosmological solutions in some important evolutive epoches were obtained. The different evolutional behaviors between NLBI and linear scalar field theory have been presented. A notable characteristic is that NLBI scalar field behaves as ordinary matter nearly th...

The cosmological evolution in Nonlinear Born-Infeld(hereafter NLBI) scalar field theory with negative potentials was investigated. The cosmological solutions in some important evolutive epoches were obtained. The different evolutional behaviors between NLBI and linear(canonical) scalar field theory have been presented. A notable characteristic is that NLBI scalar field behaves as ordinary matte...

Let E be a nonempty finite set, and let V be a real or complex vector space. In these notes we write F(E, V ) for the vector space of V -valued functions on E. Suppose that E1, E2 are nonempty finite sets, and that V is the vector space of real or complex-valued functions on E2. In this case we can identify F(E1, V ) with the vector space of real or complex-valued functions on the Cartesian pro...

We present the simple and direct proof of the determinantal formula for the scalar product of Bethe eigenstate with an arbitrary dual state. We briefly review the direct calculation of the general scalar product with the help of the factorizing operator and the construction of the factorizing operator itself. We also comment on the previous determination of the scalar product of Bethe eigenstat...

Abstract. This paper will introduce noncommutative analogs of monomial symmetric functions and fundamental noncommutative symmetric functions. The expansion of ribbon Schur functions in both of these basis is nonnegative. With these functions at hand, one can derive a noncommutative Cauchy identity as well as study a noncommutative scalar product implied by Cauchy identity. This scalar product ...

6 Vectors 1 6.1 Displacement Vectors . . . . . . . . . . . . . . . . . . . . . . . 2 6.2 The Parallelogram Law of Vector Addition . . . . . . . . . . . 4 6.3 The Length of Vectors . . . . . . . . . . . . . . . . . . . . . . 5 6.4 Scalar Multiples of Vectors . . . . . . . . . . . . . . . . . . . . 6 6.5 Linear Combinations of Vectors . . . . . . . . . . . . . . . . . 6 6.6 Linear Dependence and ...

 Casimir entropy is an important aspect of casimir effect and at the nanoscale is visible. In this paper, we employ the path integral method to ‎obtain a‎ ‎general‎ relation for casimir entropy and ‎i‎nternal energy of arbitrary shaped objects in the presence of two, three and four dimension scalar fields and ‎the‎ electromagnetic field. For this purpose, using Lagrangian and based on a perturb...

We discuss existence, non-uniqueness and regularity of one- two-sided solutions initial value problems for scalar quasi-linear ordinary differential equations where the condition corresponds to an impasse point equation. With a geometric approach, we reduce problem questions in dynamical systems theory. As application, detail second-order form g(x)u?=f(x,u,u?) with imposed at simple zero g. Thi...