162,537 research outputs found
A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations
A bi-Hamiltonian formulation is proposed for triangular systems resulted by
perturbations around solutions, from which infinitely many symmetries and
conserved functionals of triangular systems can be explicitly constructed,
provided that one operator of the Hamiltonian pair is invertible. Through our
formulation, four examples of triangular systems are exhibited, which also show
that bi-Hamiltonian systems in both lower dimensions and higher dimensions are
many and varied. Two of four examples give local 2+1 dimensional bi-Hamiltonian
systems and illustrate that multi-scale perturbations can lead to
higher-dimensional bi-Hamiltonian systems.Comment: 16 pages, to appear in J. Math. Phy
A refined invariant subspace method and applications to evolution equations
The invariant subspace method is refined to present more unity and more
diversity of exact solutions to evolution equations. The key idea is to take
subspaces of solutions to linear ordinary differential equations as invariant
subspaces that evolution equations admit. A two-component nonlinear system of
dissipative equations was analyzed to shed light on the resulting theory, and
two concrete examples are given to find invariant subspaces associated with
2nd-order and 3rd-order linear ordinary differential equations and their
corresponding exact solutions with generalized separated variables.Comment: 16 page
Singlet fermion dark matter and electroweak baryogenesis with radiative neutrino mass
The model of radiative neutrino mass with dark matter proposed by one of us
is extended to include a real singlet scalar field. There are then two
important new consequences. One is the realistic possibility of having the
lightest neutral singlet fermion (instead of the lightest neutral component of
the dark scalar doublet) as the dark matter of the Universe. The other is a
modification of the effective Higgs potential of the Standard Model, consistent
with electroweak baryogenesis.Comment: 9 pages, no figure
Extension of Hereditary Symmetry Operators
Two models of candidates for hereditary symmetry operators are proposed and
thus many nonlinear systems of evolution equations possessing infinitely many
commutative symmetries may be generated. Some concrete structures of hereditary
symmetry operators are carefully analyzed on the base of the resulting general
conditions and several corresponding nonlinear systems are explicitly given out
as illustrative examples.Comment: 13 pages, LaTe
Gravitational Thermodynamics of Space-time Foam in One-loop Approximation
We show from one-loop quantum gravity and statistical thermodynamics that the
thermodynamics of quantum foam in flat space-time and Schwarzschild space-time
is exactly the same as that of Hawking-Unruh radiation in thermal equilibrium.
This means we show unambiguously that Hawking-Unruh thermal radiation should
contain thermal gravitons or the contribution of quantum space-time foam. As a
by-product, we give also the quantum gravity correction in one-loop
approximation to the classical black hole thermodynamics.Comment: 7 pages, revte
Triplicity of Quarks and Leptons
Quarks come in three colors and have electric charges in multiples of
one-third. There are also three families of quarks and leptons. Whereas the
first two properties can be understood in terms of unification symmetries such
as SU(5), SO(10), or E_6, why there should only be three families remains a
mystery. I propose how all three properties involving the number three are
connected in a fivefold application of the gauge symmetry SU(3).Comment: 10 pages, including 2 figure
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Examining the Relationships Among Categorization, Stereotype Activation, and Stereotype Application.
Increased category salience is associated with increased stereotyping. Prior research has not examined the processes that may account for this relationship. That is, it is unclear whether category salience leads to increased stereotyping by increasing stereotype activation (i.e., increased accessibility of stereotypic information), application (i.e., increasing the tendency to apply activated stereotypes), or both processes simultaneously. We examined this question across three studies by manipulating category salience in an implicit stereotyping measure and by applying a process model that provides independent estimates of stereotype activation and application. Our results replicated past findings that category salience increases stereotyping. Modeling results showed that category salience consistently increased the extent of stereotype application but increased stereotype activation in more limited contexts. Implications for models of social categorization and stereotyping are discussed
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