3,392 research outputs found
A subalgebra of the Hardy algebra relevant in control theory and its algebraic-analytic properties
We denote by A_0+AP_+ the Banach algebra of all complex-valued functions f
defined in the closed right half plane, such that f is the sum of a holomorphic
function vanishing at infinity and a ``causal'' almost periodic function. We
give a complete description of the maximum ideal space M(A_0+AP_+) of A_0+AP_+.
Using this description, we also establish the following results:
(1) The corona theorem for A_0+AP_+.
(2) M(A_0+AP_+) is contractible (which implies that A_0+AP_+ is a projective
free ring).
(3) A_0+AP_+ is not a GCD domain.
(4) A_0+AP_+ is not a pre-Bezout domain.
(5) A_0+AP_+ is not a coherent ring.
The study of the above algebraic-anlaytic properties is motivated by
applications in the frequency domain approach to linear control theory, where
they play an important role in the stabilization problem.Comment: 17 page
Properties of the superconducting state in compressed Sulphur
The thermodynamic properties of the superconducting state in Sulphur under
the pressure at 160 GPa were determined. It has been shown that: (i) the
critical value of the Coulomb pseudopotential is equal to 0.127; (ii) the
critical temperature (T_{C} =17 K) should be calculated by using the modified
Allen-Dynes formula; (iii) the effective electron-electron interaction is
attractive in the range of frequencies from zero to the frequency slightly
lesser than the maximum phonon frequency (~ 0.85\Omega_{max}); (iv) the
dimensionless ratios 2\Delta (0)/k_{B}T_{C}, $\Delta C(T_{C})/C^{N}(T_{C}) and
T_{C}C^{N}(T_{C})/H^{2}_{C}(0) are equal to 3.7, 1.65 and 0.16 respectively;
(v) the ratio of the effective to bare electron mass reaches maximum of 1.77
for T=T_{C}.Comment: 3 pages, 5 figure
On the use of non-canonical quantum statistics
We develop a method using a coarse graining of the energy fluctuations of an
equilibrium quantum system which produces simple parameterizations for the
behaviour of the system. As an application, we use these methods to gain more
understanding on the standard Boltzmann-Gibbs statistics and on the recently
developed Tsallis statistics. We conclude on a discussion of the role of
entropy and the maximum entropy principle in thermodynamics.Comment: 29 pages, uses iopart.cls, major revisions of text for better
readability, added a discussion about essentially microcanonical ensemble
On the tensor convolution and the quantum separability problem
We consider the problem of separability: decide whether a Hermitian operator
on a finite dimensional Hilbert tensor product is separable or entangled. We
show that the tensor convolution defined for certain mappings on an almost
arbitrary locally compact abelian group, give rise to formulation of an
equivalent problem to the separability one.Comment: 13 pages, two sections adde
Crystalline ground states for classical particles
Pair interactions whose Fourier transform is nonnegative and vanishes above a
wave number K_0 are shown to give rise to periodic and aperiodic infinite
volume ground state configurations (GSCs) in any dimension d. A typical three
dimensional example is an interaction of asymptotic form cos(K_0 r)/r^4. The
result is obtained for densities rho >= rho_d where rho_1=K_0/2pi,
rho_2=(sqrt{3}/8)(K_0/pi)^2 and rho_3=(1/8sqrt{2})(K_0/pi)^3. At rho_d there is
a unique periodic GSC which is the uniform chain, the triangular lattice and
the bcc lattice for d=1,2,3, respectively. For rho>rho_d the GSC is nonunique
and the degeneracy is continuous: Any periodic configuration of density rho
with all reciprocal lattice vectors not smaller than K_0, and any union of such
configurations, is a GSC. The fcc lattice is a GSC only for rho>=(1/6
sqrt{3})(K_0/pi)^3.Comment: final versio
Generalized Induced Norms
Let ||.|| be a norm on the algebra M_n of all n-by-n matrices over the
complex field C. An interesting problem in matrix theory is that "are there two
norms ||.||_1 and ||.||_2 on C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for
all A in M_n. We will investigate this problem and its various aspects and will
discuss under which conditions ||.||_1=||.||_2.Comment: 8 page
Ionisation by quantised electromagnetic fields: The photoelectric effect
In this paper we explain the photoelectric effect in a variant of the
standard model of non relativistic quantum electrodynamics, which is in some
aspects more closely related to the physical picture, than the one studied in
[BKZ]: Now we can apply our results to an electron with more than one bound
state and to a larger class of electron-photon interactions. We will specify a
situation, where ionisation probability in second order is a weighted sum of
single photon terms. Furthermore we will see, that Einstein's equality
for the maximal kinetic energy of
the electron, energy of the photon and ionisation gap
is the crucial condition for these single photon terms to be nonzero.Comment: 59 pages, LATEX2
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