LOCV calculations for polarized liquid 3He^3{He} with the spin-dependent correlation

We have used the lowest order constrained variational (LOCV) method to calculate some ground state properties of polarized liquid $^{3}He$ at zero temperature with the spin-dependent correlation function employing the Lennard-Jones and Aziz pair potentials. We have seen that the total energy of polarized liquid $^{3}He$ increases by increasing polarization. For all polarizations, it is shown that the total energy in the spin-dependent case is lower than the spin-independent case. We have seen that the difference between the energies of spin-dependent and spin-independent cases decreases by increasing polarization. We have shown that the main contribution of the potential energy comes from the spin-triplet state.Comment: 14 pages, 5 figures. Int. J. Mod. Phys. B (2008) in pres

Multi-normed spaces

We modify the very well known theory of normed spaces (E, \norm) within functional analysis by considering a sequence (\norm_n : n\in\N) of norms, where \norm_n is defined on the product space $E^n$ for each $n\in\N$. Our theory is analogous to, but distinct from, an existing theory of `operator spaces'; it is designed to relate to general spaces $L^p$ for $p\in [1,\infty]$, and in particular to $L^1$-spaces, rather than to $L^2$-spaces. After recalling in Chapter 1 some results in functional analysis, especially in Banach space, Hilbert space, Banach algebra, and Banach lattice theory that we shall use, we shall present in Chapter 2 our axiomatic definition of a `multi-normed space' ((E^n, \norm_n) : n\in \N), where (E, \norm) is a normed space. Several different, equivalent, characterizations of multi-normed spaces are given, some involving the theory of tensor products; key examples of multi-norms are the minimum and maximum multi-norm based on a given space. Multi-norms measure `geometrical features' of normed spaces, in particular by considering their `rate of growth'. There is a strong connection between multi-normed spaces and the theory of absolutely summing operators. A substantial number of examples of multi-norms will be presented. Following the pattern of standard presentations of the foundations of functional analysis, we consider generalizations to `multi-topological linear spaces' through `multi-null sequences', and to `multi-bounded' linear operators, which are exactly the `multi-continuous' operators. We define a new Banach space ${\mathcal M}(E,F)$ of multi-bounded operators, and show that it generalizes well-known spaces, especially in the theory of Banach lattices. We conclude with a theory of `orthogonal decompositions' of a normed space with respect to a multi-norm, and apply this to construct a `multi-dual' space.Comment: Many update

Hopf algebras: motivations and examples

This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the use of Sweedler's dual

Self-starting circuit for switching regulators

Schematic is provided on a self-starting circuit for a switching regulator which uses a logic circuit to sense a change in output voltage and provides a correction signal for dc power sources. With this device, the total power consumed by the logic circuitry is held to a minimum, and the circuit receives the optimum regulated supply power

Exclusive electroproduction of J/psi mesons

A nonperturbative calculation of elastic electroproduction of the J/psi meson is presented and compared to the experimental data. Our model describes well the observed dependences of the cross sections on the photon virtuality Q2 and on the energy, and the measured ratio R of longitudinal to transverse cross sections.Comment: Five *.eps figure