735 research outputs found
A generalization of Sturm's comparison theorem
The Riccati equation method is used to establish a new comparison theorem for
systems of two linear first order ordinary differential equation. This result
is based on a, so called, concept of "null-classes", and is a generalization of
Sturm's comparison theorem.Comment: 8 page
Oscillatory and non oscillatory criteria for linear four dimensional hamiltonian systems
The Riccati equation method is used for study the oscillatory and non
oscillatory behavior of solutions of linear four dimensional hamiltonian
systems. An oscillatory and two non oscillatory criteria are proved. On an
example the obtained oscillatory criterion is compared with some well known
results.Comment: 12 page
Stability criteria for second order linear ordinary differential equations
We use some properties of solutions of Riccati equation for establishing
boundedness and stability criteria for solutions of second order linear
ordinary differential equations. We show that the conditions on coefficients of
the equations, appearing in the proven criteria, do not follow from the
conditions, which ensure the application of the WKB approximation to the second
order linear equations. On these examples we compare the obtained results wit
the results obtained by the Liapunov and Bogdanov methods, by a method
involving estimates of solutions in the Lozinski's logarithmic norms, and by
the freezing method. We compare these results with the Wazevski's theorem as
well.Comment: 15 page
Oscillatory criteria for the second order linear ordinary differential equations in the marginal sub extremal and extremal cases
The Riccati equation method is used to establish three new oscillatory
criteria for the second order linear ordinary differential equations in the
marginal, sub extremal and extremal cases.We show that the first of these
criteria implies the J. Deng's oscillatory criterion. An extremal oscillatory
condition for the Mathieu's equation is obtained. The obtained results are
compared with some known oscillatory criteria.Comment: 18 page
New oscillation criteria for linear matrix Hamiltonian systems
By the use of Riccati equation technique new approaches (in particular a
unitary transformation approach) are used to obtain new oscillation criteria
for linear matrix Hamiltonian systems in a new direction. That direction is to
break the positive definiteness restriction, imposed on one of coeffcients of
the Hamiltonian system.Comment: 9 page
Phase Diagram for Spinning and Accreting Neutron Stars
Neutron star configurations are considered as thermodynamical systems for
which a phase diagram in the angular velocity (Omega) - baryon number (N) plane
is obtained with a dividing line N_{crit}(Omega) for quark core configurations.
Trajectories of neutron star evolution in this diagram are studied for
different scenarios defined by the external torque acting on the star due to
radiation and/or mass accretion. They show a characteristic change in the
rotational kinematics when the star enters the quark core regime. For isolated
pulsars the braking index signal for deconfinement has been studied in its
dependence on the mass of the star. Model calculations of the spin evolution of
accreting low-mass X-ray binaries in the phase diagram have been performed for
different values of the initial magnetic field, its decay time as well as
initial mass and mass accretion rate. Population clustering of these objects at
the line N_{crit}(Omega) in the phase diagram is suggested as an observable
signal for the deconfinement phase transition if it exists for spinnning and
accreting neutron stars.Comment: 20 pages, 10 figure
Deconfinement transition in rotating compact stars
Using the formalism of general relativity for axially symmetric gravitational
fields and their sources - rotating compact stars - a perturbation theory with
respect to angular velocity is developed and physical quantities such as mass,
shape, momentum of inertia and total energy of the star are defined. The change
of the internal structure of the star due to rotation has been investigated and
the different contributions to the moment of inertia have been evaluated
separately. Numerical solutions have been performed using a two-flavor model
equation of state describing the deconfinement phase transition as constrained
by the conservation of total baryon number and electric charge. During the spin
down evolution of the rotating neutron star, below critical values of angular
velocity a quark matter core can appear which might be detected as a
characteristic signal in the pulsar timing. Within the spin-down scenario due
to magnetic dipole radiation it is shown that the deviation of the braking
index from could signal not only the occurrence but also the size of a
quark core in the pulsar. A new scenario is proposed where, due to mass
accretion onto the rapidly rotating compact star, a spin-down to spin-up
transition might signal a deconfinement transition in its interior.Comment: 10 pages, 9 figures; A&A accepte
The behavior of solutions of the systems of two first order linear ordinary differential equations
The Riccati equation method is used for study the behavior of solutions of
the systems of two linear first order ordinary differential equations. All
types of oscillation and regularity of these system are revealed. A
generalization of Leighton's theorem is obtained. Three new principles for the
second order linear differential equations are derived. Stability and non
conjugation criteria are proved for the mentioned systems, as well as estimates
are obtained for the solutions of the last ones.Comment: 61 pages, 18 figures, 3 paragraph
On the stability of systems of two linear first-order ordinary differential equations
The Riccati equation method is used to establish some new stability criteria
for systems of two linear first-order ordinary differential equations. It is
shown that two of these criteria in the two dimensional case imply the Routh -
Hurwitz's criterion.Comment: 14 page
Global solvability criteria for some classes of nonlinear second order ordinary differential equations
The Riccati equation method is used to establish some global solvability
criteria for some classes of second order nonlinear ordinary differential
equations. Two oscillation theorems are proved. The results are applied to the
Emden - Fowler equation and to the Van der Pol type equation.Comment: 26 page
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