4,113 research outputs found
A modification of the Dewilde–van der Veen method for inversion of finite structured matrices
AbstractWe study a class of block structured matrices R={Rij}i,j=1N with a property that the solution of the corresponding system Rx=y of linear algebraic equations may be performed for O(N) arithmetic operations. In this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms. These algorithms are related to those suggested by P.M. Dewilde and A.J. van der Veen (Time-varying Systems and Computations, Kluwer Academic Publishers, New York, 1998) for a class of finite and infinite matrices with a small Hankel rank. The algorithms presented here are more transparent and are a modification of the algorithms from the above reference. The approach and the proofs are essentially different from those in the above-mentioned reference. The paper contains also analysis of complexity and results of numerical experiments
Dynamical breakdown of Abelian gauge chiral symmetry by strong Yukawa interactions
We consider a model with anomaly-free Abelian gauge axial-vector symmetry,
which is intended to mimic the standard electroweak gauge chiral SU(2)_L x
U(1)_Y theory. Within this model we demonstrate: (1) Strong Yukawa interactions
between massless fermion fields and a massive scalar field carrying the axial
charge generate dynamically the fermion and boson proper self-energies, which
are ultraviolet-finite and chirally noninvariant. (2) Solutions of the
underlying Schwinger-Dyson equations found numerically exhibit a huge
amplification of the fermion mass ratios as a response to mild changes of the
ratios of the Yukawa couplings. (3) The `would-be' Nambu-Goldstone boson is a
composite of both the fermion and scalar fields, and it gives rise to the mass
of the axial-vector gauge boson. (4) Spontaneous breakdown of the gauge
symmetry further manifests by mass splitting of the complex scalar and by new
symmetry-breaking vertices, generated at one loop. In particular, we work out
in detail the cubic vertex of the Abelian gauge boson.Comment: 11 pages, REVTeX4, 10 eps figures; additional remarks and references
added; version published in Phys. Rev.
Eigenstructure of order-one-quasiseparable matrices. Three-term and two-term recurrence relations
AbstractThis paper presents explicit formulas and algorithms to compute the eigenvalues and eigenvectors of order-one-quasiseparable matrices. Various recursive relations for characteristic polynomials of their principal submatrices are derived. The cost of evaluating the characteristic polynomial of an N×N matrix and its derivative is only O(N). This leads immediately to several versions of a fast quasiseparable Newton iteration algorithm. In the Hermitian case we extend the Sturm property to the characteristic polynomials of order-one-quasiseparable matrices which yields to several versions of a fast quasiseparable bisection algorithm.Conditions guaranteeing that an eigenvalue of a order-one-quasiseparable matrix is simple are obtained, and an explicit formula for the corresponding eigenvector is derived. The method is further extended to the case when these conditions are not fulfilled. Several particular examples with tridiagonal, (almost) unitary Hessenberg, and Toeplitz matrices are considered.The algorithms are based on new three-term and two-term recurrence relations for the characteristic polynomials of principal submatrices of order-one-quasiseparable matrices R. It turns out that the latter new class of polynomials generalizes and includes two classical families: (i) polynomials orthogonal on the real line (that play a crucial role in a number of classical algorithms in numerical linear algebra), and (ii) the Szegö polynomials (that play a significant role in signal processing). Moreover, new formulas can be seen as generalizations of the classical three-term recurrence relations for the real orthogonal polynomials and of the two-term recurrence relations for the Szegö polynomials
Implicit QR for Companion-like Pencils
A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized eigenvalues of certain NxN rank structured matrix pencils using O(N^2) ops and O(N) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method
Exclusive Decays and CP Violation in the General two-Higgs-doublet Model
We calculate all the branching ratios and direct CP violations of
decays in a most general two-Higgs-doublet model with spontaneous CP violation.
As the model has rich CP-violating sources, it is shown that the new physics
effects to direct CP violations and branching ratios in some channels can be
significant when adopting the generalized factorization approach to evaluate
the hadronic matrix elements, which provides good signals for probing new
physics beyond the SM in the future B experiments.Comment: 21 page
Seesaw Mass Matrix Model of Quarks and Leptons with Flavor-Triplet Higgs Scalars
In a seesaw mass matrix model M_f = m_L M_F^{-1} m_R^\dagger with a universal
structure of m_L \propto m_R, as the origin of m_L (m_R) for quarks and eptons,
flavor-triplet Higgs scalars whose vacuum expectation values v_i are
proportional to the square roots of the charged lepton masses m_{ei}, i.e. v_i
\propto \sqrt{m_{ei}}, are assumed. Then, it is investigated whether such a
model can explain the observed neutrino masses and mixings (and also quark
masses and mixings) or not.Comment: version accepted by EPJ
Correlation between Leptonic CP Violation and mu-tau Symmetry Breaking
Considering the - symmetry, we discuss a direct linkage between
phases of flavor neutrino masses and leptonic CP violation by determining three
eigenvectors associated with for a complex
flavor neutrino mass matrix in the flavor basis. Since the Dirac CP
violation is absent in the - symmetric limit, leptonic CP violation
is sensitive to the - symmetry breaking, whose effect can be
evaluated by perturbation. It is found that the Dirac phase () arises
from the - symmetry breaking part of and
an additional phase () is associated with the - symmetric part
of , where stands for an matrix
element (=). The phase is redundant and can be removed
but leaves its effect in the Dirac CP violation characterized by . The perturbative results suggest the exact formula of mixing
parameters including that of and , which turns out to be free
from the effects of the redundant phases. As a result, it is generally shown
that the maximal atmospheric neutrino mixing necessarily accompanies either
or , the latter of which indicates
maximal CP violation, where is the - mixing
angle.Comment: 16 pages, ReVTeX, references updated, typos corredcted, published
version in Physical Reviews
Distributed Order Derivatives and Relaxation Patterns
We consider equations of the form , ,
where , is a distributed order derivative, that is the
Caputo-Dzhrbashyan fractional derivative of order , integrated in
with respect to a positive measure . Such equations are
used for modeling anomalous, non-exponential relaxation processes. In this work
we study asymptotic behavior of solutions of the above equation, depending on
properties of the measure
The rare decays B --> K(*) anti-K(*) and R-parity violating supersymmetry
We study the branching ratios, the direct CP asymmetries in decays and the polarization fractions of decays by employing the QCD factorization in the minimal
supersymmetric standard model with R-parity violation. We derive the new upper
bounds on the relevant R-parity violating couplings from the latest
experimental data of , and some of these constraints
are stronger than the existing bounds. Using the constrained parameter spaces,
we predict the R-parity violating effects on the other quantities in decays which have not been measured yet. We find that the
R-parity violating effects on the branching ratios and the direct
asymmetries could be large, nevertheless their effects on the longitudinal
polarizations of decays are small. Near future
experiments can test these predictions and shrink the parameter spaces.Comment: 31 pages with 10 figure
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