in the case where L and N satisfy monotonicity conditions.
We also discuss an application to control theory.
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4)
AN EXACT SOLUTION OF THE HUBBARD HAMILTONIAN MODEL
FOR HIGH TEMPERATURE SUPERCONDUCTORS
( page 22 – 28 of Vol 1 Namp Journals )
by C.N. Animalu
Department of Physics and Astronomy,
University of Nigeria,
Nsukka, Nigeria
Abstract
Using a 2
x 2 matrix representation of the creation and annihilation operators for an N-fermion
system, we present an exact diagonalization of the Hubbard Hamiltonian for
a strongly correlated many-electron system. The result is applied to the thermodynamic
properties and spin susceptibility of high-temperature superconductors, such
as YBa2Cu307-x (with Tc = 90K) in which superconductivity is believed to occur in Cu02 planes, and whose electronic structure is described by the Hubbard Hamiltonian.
Effects of correlation are observed in the electronic specific heat, which
are not seen in results obtained by the standard mean-field approximation
method, such as the Gutzwiller variational method. The magnetic spin susceptibility
compares favourably with the quantum Monte Carlo simulations of White et al.
Other applications of the method to the many-body problem are discussed.
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5)
A HAMILTONIAN FOR SUPERCONDUCTORS
( page 29 – 31 of Vol 1 Namp Journals )
by E.O. Aiyohuyin*, A. Maduemezia**, G.K. Oyanna*
*Department of Physics,
Edo State University,
Ekpoma, Nigeria
**Vice-Chancellor’s Office,
Edo State University,
Ekpoma, Nigeria
Abstract
From consideration of the physical situation in the normal state of superconductors,
namely that there are electron-electron, electron-ion, and ion-ion interactions,
we show that the Hamiltonian for superconductors is similar to those obtained
by the BCS group, as well as the Hubbard Hamiltonian. In our approximations,
the electron-electron interaction is separated into two parts, namely the
screened Coulombic, and collective interactions. Finally, only those terms
in which electrons are paired, such as 
,
are chosen.
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6)
ON QUANTUM CHAOS
( page 33 – 38 of Vol 1 Namp Journals )
by R. Akin-Ojo
Physics Department,
University of Ibadan,
Ibadan, Nigeria
Abstract
Given a closed Hamiltonian system of n degrees of freedom, with Hamiltonian H(p, q) = T(p) + V(q) = E, where E is a constant
and n 
2, we now know that the system exhibits deterministic (classical) chaos, if H is nonlinear and completely nonintegrable. The question often arises:
How should such a system be quantized, and is there any manifestation of the
(classical) chaoticity in its quantal counterpart? Seeking answers by the
method of reduction of numbers of degrees of freedom, we demonstrate that
some attribute L (related to one of the momenta p) can be quantized,
provided the coordinates q satisfy some relationships. These relationships
are obtained by the method for the “Lax pair” – the potential
V(q) must satisfy some “KdV equation” of “solitary waves”.
Moreover, the relationships reveal that the KdV engenders multiple Schroedinger
operators and this is the manifestation of the chaoticity. Hence, such a quantum-mechanical
system has multiple spectra and therefore it is noisy.
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7)
PERTURBATIVE QUANTUM CHROMODYNAMICS
( page 39 – 46 of Vol 1 Namp Journals )
by O.A. Odundun,
Department of Physics,
Obafemi Awolowo University,
Ile-Ife, Nigeria
Abstract
Introductory covariant perturbation theory for quantum chromodynamics is discussed,
with examples to serve as qualitative illustrative applications.
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8)
EQUILIBRIUM STATISTICAL MECHANICS OF HARD PARTICLE
FLUIDS
( page 47 – 53 of Vol 1 Namp Journals )
by U.F. Edgal
Department of Electrical & Electronic Engineering,
University of Benin,
Benin City, Nigeria
Abstract
The governing equation for the 
-parameter
which features in the density function in classical phase space is solved
in low and high density regimes for the special case of the hard particle
system. The results obtained for the equation of state are shown to compare
favourably with those in the literature. The new solutions also suggest a
re-examination of the nature of critical behaviour in the presence of hard-core
interaction close to “Bernal” density.
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9)
HEAT TRANSFER TO A LIQUID FILM ON AN UNSTEADY STRETCHING
SURFACE
( page 55 – 59 of Vol 1 Namp Journals )
by R.O. Ayeni & J.O. Oladele
Department of Pure and Applied Mathematics,
Oyo State University of Technology,
Ogbomoso, Nigeria
Abstract
An investigation into heat transfer into a liquid film on an unsteady stretching
surface is carried out. Using similarity transformations, both momentum and
energy equations are reduced to ordinary differential equations. To obtain
heat transfer, we use both asymptotic and numerical techniques.
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10)
SOLAR RADIATION MODELS IN NIGERIA: A CASE FOR VALIDATION
OF RESULTS
( page 61 – 69 of Vol 1 Namp Journals )
by A.A.L. Maduekwe
Department of Physics,
University of Lagos,
Lagos, Nigeria
Abstract
Solar radiation regression models developed for the Nigerian environment are
rarely validated. Authors of such models appear to ignore the dangers of publishing
models which are not validated. A case study is made with monthly mean data
for a period of ten years in Sokoto, Nigeria. Regression models were created
for predicting solar radiation which is horizontal when it reaches the earth’s
surface. Two methods of validation were used: (a) the collection of fresh
data, and (b) data splitting or cross-validation. The results depend on whether
prediction data sets are different from estimation data sets. The method of
data splitting introduces difficulties when the estimation data set and the
prediction data set differ in predictive performance and coefficient estimates.
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11)
A BASIC CODE FOR PLOTTING DISPERSION CURVES IN A COLD
PLASMA
( page 71 – 75 of Vol 1 Namp Journals )
by S.D. Salihu, B. Chike-Obi
Department of Physics,
University of Ilorin,
Ilorin, Nigeria
Abstract
We have developed a BASIC code for plotting the dispersion curves for waves
in a cold plasma. The programme algorithm is based on the evaluation of a
many-valued polynomial function of wave frequency and angle of propagation.
Typical dispersion curves are discussed. Design efforts to minimize the effects
of singularities on the curves are analyzed.
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12)
ENTROPY RATE IN SOLAR WIND FLOW
( page 77 – 80 of Vol 1 Namp Journals )
by O.D. Makinde & S. Idowu
Department of Mathematics ,
Rivers State University of Sci. & Tech.,
Port Harcourt, Nigeria
Abstract
In this paper, the entropy rate in solar wind flow is analyzed by considering
fluid dynamical models of a spherically symmetric, expanding, and heat conducting
gas under gravity. Based on certain simplifying postulates, the fluid equations
of continuity, momentum, energy, and a thermodynamic relation that involves
entropy, are obtained and solved analytically. The entropy rate is shown to
give two critical solutions, one increasing and the other decreasing.
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13)
THE ONSET AND SATURATION OF THE IONOSPHERIC
LOWER HYBRID MODE
( page 81 – 85 of Vol 1 Namp Journals )
by B. Chike-Obi
Department of Physics ,
University of Ilorin,
Ilorin, Nigeria
Abstract
Ionospheric noise shows strong peaks at lower hybrid frequencies. It is proposed
that wave-particle energy exchange processes lead to the growth of a beam
instability which has mode frequencies centred on the lower hybrid frequency.
The onset of the beam instability and its saturation through energy transfer
to part of the ion population are analyzed. The theory has implications for
ionospheric radio communications.
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14)
A MAGNETOTELLURIC METHOD FOR DETERMINING AQUIFER DEPTHS
( page 87 – 94 of Vol 1 Namp Journals )
by M.B. Asokhia
Department of Physics,
Edo State University,
Ekpoma, Nigeria
Abstract
A magnetotelluric method for determining aquifer depths is described, which
was tested along the “Blue Road Traverse” in central Sweden. It
was necessary to choose a sampling interval as low as 0.04s, to ensure that
thin aquifers were not missed in interpretation. The depth of the “Blue
Road” aquifer was estimated to be about 38m, for a depth of about 1km
investigated. The merits of the magnetotelluric method over other methods
of investigating aquifer depths are discussed.
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