18,498 research outputs found
Entire solutions of delay differential equations of Malmquist type
In this paper, we investigate the delay differential equations of Malmquist
type of form \begin{equation*} w(z+1)-w(z-1)+a(z)\frac{w'(z)}{w(z)}=R(z,
w(z)),~~~~~~~~~~~~~~(*) \end{equation*} where is an irreducible
rational function in with rational coefficients and is a rational
function. We characterize all reduced forms when the equation admits a
transcendental entire solutions with hyper-order less than one. When we compare
with the results obtained by Halburd and Korhonen[Proc.Amer.Math.Soc.,
forcoming],we obtain the reduced forms without the assumptions that the
denominator of rational function has roots that are nonzero
rational functions in . The growth order and value distribution of
transcendental entire solutions for the reduced forms are also investigated
Improved distance sensitivity oracles via tree partitioning
We introduce an improved structure of distance sensitivity oracle (DSO). The
task is to pre-process a non-negatively weighted graph so that a data structure
can quickly answer replacement path length for every triple of source, terminal
and failed vertex. The previous best algorithm constructs in time
a distance sensitivity oracle of size that
processes queries in time. As an improvement, our oracle takes up
space, while preserving query efficiency and
preprocessing time. One should notice that space complexity and query time of
our novel data structure are asymptotically optimal
Angle-of-Attack Modulation in Trajectory Tracking for a Reusable Launch Vehicle
This paper deals with the problem of angle-of-attack modulation with the aim
of enhancing transient performance of entry guidance during bank reversals,
while compensating adverse effects of fast time-varying transient disturbances.
An extended single-input/single-output system is developed in the velocity
domain by means of a dynamic extension technique, and explicitly captures the
trajectory dynamics of angle-of-attack modulation. A normal form for this
extended system is derived for the sake of employing a feedback linearization
controller. Further, the control characteristics of angle-of-attack modulation
is found to be a non-minimum phase behavior under two common conditions in a
near- equilibrium glide flight. Therefore, the issue of angle-of-attack
modulation is formulated as robust output stabilization of the non-minimum
phase system. A disturbance observer-based feedback linearization technique is
used to design a robustly dynamical output-feedback controller for
angle-of-attack modulation, and an internal-state feedback controller for
bank-angle modulation is used to stabilize the unstable internal dynamics.
Numerical simulations are conducted to demonstrate that the performance of the
proposed method of angle-of-attack modulation is enhanced compared to the
existing shuttle method.Comment: 29 pages, 12 figure
A Weak Galerkin Finite Element Scheme for the Biharmonic Equations by Using Polynomials of Reduced Order
A new weak Galerkin (WG) finite element method for solving the biharmonic
equation in two or three dimensional spaces by using polynomials of reduced
order is introduced and analyzed. The WG method is on the use of weak functions
and their weak derivatives defined as distributions. Weak functions and weak
derivatives can be approximated by polynomials with various degrees. Different
combination of polynomial spaces leads to different WG finite element methods,
which makes WG methods highly flexible and efficient in practical computation.
This paper explores the possibility of optimal combination of polynomial spaces
that minimize the number of unknowns in the numerical scheme, yet without
compromising the accuracy of the numerical approximation. Error estimates of
optimal order are established for the corresponding WG approximations in both a
discrete norm and the standard norm. In addition, the paper also
presents some numerical experiments to demonstrate the power of the WG method.
The numerical results show a great promise of the robustness, reliability,
flexibility and accuracy of the WG method.Comment: 28 pages. arXiv admin note: substantial text overlap with
arXiv:1303.0927, arXiv:1309.5560, arXiv:1510.06001 by other author
Zeno dynamics in quantum open systems
Quantum Zeno effect shows that frequent observations can slow down or even
stop the unitary time evolution of an unstable quantum system. This effect can
also be regarded as a physical consequence of the the statistical
indistinguishability of neighboring quantum states. The accessibility of
quantum Zeno dynamics under unitary time evolution can be quantitatively
estimated by quantum Zeno time in terms of Fisher information. In this work, we
investigate the accessibility of quantum Zeno dynamics in quantum open systems
by calculating noisy Fisher information, in which a trace preserving and
completely positive map is assumed. We firstly study the consequences of
non-Markovian noise on quantum Zeno effect and give the exact forms of the
dissipative Fisher information and the quantum Zeno time. Then, for the
operator-sum representation, an achievable upper bound of the quantum Zeno time
is given with the help of the results in noisy quantum metrology. It is of
significance that the noise affecting the accuracy in the entanglement-enhanced
parameter estimation can conversely be favorable for the accessibility of
quantum Zeno dynamics of entangled states.Comment: 6 pages, 2 figure
Quantum Metrological Bounds for Vector Parameter
Precise measurement is crucial to science and technology. However, the rule
of nature imposes various restrictions on the precision that can be achieved
depending on specific methods of measurement. In particular, quantum mechanics
poses the ultimate limit on precision which can only be approached but never be
violated. Depending on analytic techniques, these bounds may not be unique.
Here, in view of prior information, we investigate systematically the precision
bounds of the total mean-square error of vector parameter estimation which
contains independent parameters. From quantum Ziv-Zakai error bounds, we
derive two kinds of quantum metrological bounds for vector parameter
estimation, both of which should be satisfied. By these bounds, we show that a
constant advantage can be expected via simultaneous estimation strategy over
the optimal individual estimation strategy, which solves a long-standing
problem. A general framework for obtaining the lower bounds in a noisy system
is also proposed.Comment: 8 pages, 4 figure
Acceleration of weak Galerkin methods for the Laplacian eigenvalue problem
Recently, we proposed a weak Galerkin finite element method for the Laplace
eigenvalue problem. In this paper, we present two-grid and two-space skills to
accelerate the weak Galerkin method. By choosing parameters properly, the
two-grid and two-space weak Galerkin method not only doubles the convergence
rate, but also maintains the asymptotic lower bounds property of the weak
Galerkin method. Some numerical examples are provided to validate our
theoretical analysis.Comment: 4 figure2, 20 page
The Shifted-inverse Power Weak Galerkin Method for Eigenvalue Problems
This paper proposes and analyzes a new weak Galerkin method for the
eigenvalue problem by using the shifted-inverse power technique. A high order
lower bound can be obtained at a relatively low cost via the proposed method.
The error estimates for both eigenvalue and eigenfunction are provided and
asymptotic lower bounds are shown as well under some conditions. Numerical
examples are presented to validate the theoretical analysis.Comment: 19 pages, 3 table
Quantization on Generalized Heisenberg-Virasoro Algebra
In a recent paper by the authors, Lie bialgebra structures on generalized
Heisenberg- Virasoro algebra L are considered. In this paper, the explicit
formula of the quantization on generalized Heisenberg-Virasoro algebra is
presented.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1004.3646,
arXiv:1004.3645 by other author
Lanthanum-Cerium Based Bulk Metallic Glasses with Superior Glass-Forming Ability
A quinary (La0.5Ce0.5)65Al10(Co0.6Cu0.4)25 alloy with superior glass-forming
ability (GFA), identified by the formation of fully glassy rod of 32 mm in
diameter by tilt-pour casting, was reported. By comparing with the GFA of
quarternary (La0.5Ce0.5)65Al10TM25 and ternary Ln65Al10TM25 alloys (Ln = La or
Ce; TM = Co or Cu), we suggest that the strong frustration of crystallization
by utilizing the coexistence of La-Ce and Co-Cu to complicate competing
crystalline phases is helpful to construct BMG component with superior GFA.Comment: 15 pages, 4 figures, 1 tabl
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