4,788 research outputs found
Complete Weight Enumerators of a Family of Three-Weight Linear Codes
Linear codes have been an interesting topic in both theory and practice for
many years. In this paper, for an odd prime , we present the explicit
complete weight enumerator of a family of -ary linear codes constructed with
defining set. The weight enumerator is an mmediate result of the complete
weight enumerator, which shows that the codes proposed in this paper are
three-weight linear codes. Additionally, all nonzero codewords are minimal and
thus they are suitable for secret sharing.Comment: 13 pages. arXiv admin note: text overlap with arXiv:1505.0632
Global solutions to planar magnetohydrodynamic equations with radiation and large initial data
A global existence result is established for a free boundary problem of
planar magnetohydrodynamic fluid flows with radiation and large initial data.
Particularly, it is novelty to embrace the constant transport coefficient. As a
by-product, the free boundary is shown to expand outward at an algebraic rate
from above in time
Complete Weight Enumerators of Some Linear Codes
Linear codes have been an interesting topic in both theory and practice for
many years. In this paper, for an odd prime , we determine the explicit
complete weight enumerators of two classes of linear codes over
and they may have applications in cryptography and secret sharing schemes.
Moreover, some examples are included to illustrate our results.Comment: 11 page
The Complete Weight Enumerator of Several Cyclic Codes
Cyclic codes have attracted a lot of research interest for decades. In this
paper, for an odd prime , we propose a general strategy to compute the
complete weight enumerator of cyclic codes via the value distribution of the
corresponding exponential sums. As applications of this general strategy, we
determine the complete weight enumerator of several -ary cyclic codes and
give some examples to illustrate our results.Comment: 18 page
Global Existence and Optimal Decay Rates of Solutions for Compressible Hall-MHD Equations
In this paper, we are concerned with global existence and optimal decay rates
of solutions for the three-dimensional compressible Hall-MHD equations. First,
we prove the global existence of strong solutions by the standard energy method
under the condition that the initial data are close to the constant equilibrium
state in -framework. Second, optimal decay rates of strong solutions in
-norm are obtained if the initial data belong to additionally.
Finally, we apply Fourier splitting method by Schonbek [Arch.Rational Mech.
Anal. 88 (1985)] to establish optimal decay rates for higher order spatial
derivatives of classical solutions in -framework, which improves the work
of Fan et al.[Nonlinear Anal. Real World Appl. 22 (2015)].Comment: 31 page
The weight distributions of two classes of p ary cyclic codes with few weights
Cyclic codes have attracted a lot of research interest for decades as they
have efficient encoding and decoding algorithms.
In this paper, for an odd prime , the weight distributions of two classes
of -ary cyclic codes are completely determined. We show that both codes have
at most five nonzero weights.Comment: 20 page
A Class of Three-Weight Linear Codes and Their Complete Weight Enumerators
Recently, linear codes constructed from defining sets have been investigated
extensively and they have many applications. In this paper, for an odd prime
, we propose a class of -ary linear codes by choosing a proper defining
set. Their weight enumerators and complete weight enumerators are presented
explicitly. The results show that they are linear codes with three weights and
suitable for the constructions of authentication codes and secret sharing
schemes.Comment: 18 page
Boundary Layer Problems for the Two-dimensional Inhomogeneous Incompressible Magnetohydrodynamics Equations
In this paper, we study the well-posedness of boundary layer problems for the
inhomogeneous incompressible magnetohydrodynamics(MHD) equations, which are
derived from the two dimensional density-dependent incompressible MHD
equations.Under the assumption that initial tangential magnetic field is not
zero and density is a small perturbation of the outer constant flow in
supernorm,the local-in-time existence and uniqueness of inhomogeneous
incompressible MHD boundary layer equation are established in weighted Conormal
Sobolev spaces by energy method. As a byproduct, the local-in-time
well-posedness of homogeneous incompressible MHD boundary layer equations with
any large initial data can be obtained.Comment: 52 page
Strong Solution to the Density-dependent Incompressible Nematic Liquid Crystal Flows
In this paper, we investigate the density-dependent incompressible nematic
liquid crystal flows in or dimensional bounded domain. More
precisely, we obtain the local existence and uniqueness of the solutions when
the viscosity coefficient of fluid depends on density. Moreover, we establish
blowup criterions for the regularity of the strong solutions in dimension two
and three respectively. In particular, we build a blowup criterion just in
terms of the gradient of density if the initial direction field satisfies some
geometric configuration. For these results, the initial density needs not be
strictly positive.Comment: 46 page. arXiv admin note: text overlap with arXiv:1204.4966,
arXiv:1211.0131 by other author
Blow up and global existence for the periodic Phan-Thein-Tanner model
In this paper, we mainly investigate the Cauchy problem for the periodic
Phan-Thein-Tanner (PTT) model. This model is derived from network theory for
the polymeric fluid. We prove that the strong solutions of PTT model will blow
up in finite time if the trace of initial stress tensor \tr \tau_0(x) is
negative. This is a very different with the other viscoelastic model. On the
other hand, we obtain the global existence result with small initial data when
\tr \tau_0(x)\geq c_0>0 for some . Moreover, we study about the large
time behavior
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