Abstract: In this article, we used the residual correction method
to deal with transient thermoelastic problems with a hollow spherical
region when the continuum medium possesses spherically isotropic
thermoelastic properties. Based on linear thermoelastic theory, the
equations of hyperbolic heat conduction and thermoelastic motion
were combined to establish the thermoelastic dynamic model with
consideration of the deformation acceleration effect and non-Fourier
effect under the condition of transient thermal shock. The approximate
solutions of temperature and displacement distributions are obtained
using the residual correction method based on the maximum principle
in combination with the finite difference method, making it easier and
faster to obtain upper and lower approximations of exact solutions.
The proposed method is found to be an effective numerical method
with satisfactory accuracy. Moreover, the result shows that the effect
of transient thermal shock induced by deformation acceleration is
enhanced by non-Fourier heat conduction with increased peak stress.
The influence on the stress increases with the thermal relaxation time.
Abstract: Using maximal consistent blocks of tolerance relation
on the universe in incomplete decision table, the concepts of join block
and meet block are introduced and studied. Including tolerance class,
other blocks such as tolerant kernel and compatible kernel of an object
are also discussed at the same time. Upper and lower approximations
based on those blocks are also defined. Default definite decision rules
acquired from incomplete decision table are proposed in the paper. An
incremental algorithm to update default definite decision rules is
suggested for effective mining tasks from incomplete decision table
into which data is appended. Through an example, we demonstrate
how default definite decision rules based on maximal consistent
blocks, join blocks and meet blocks are acquired and how optimization
is done in support of discernibility matrix and discernibility function
in the incomplete decision table.
Abstract: In this paper, we generalize some propositions in [C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. Math. Appl. 59(2010)431-436.] and we give some equivalent conditions for rough subgroups. The notion of minimal upper rough subgroups is introduced and a equivalent characterization is given, which implies the rough version of Lagranges Theorem.