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Acta Mathematicae Applicatae
Sinica, Chinese Series
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Current Issue
2018 Vol.34 Issue.2,
Published 20180515
ARTICLES
ARTICLES
209
Semianalytical Formula for Pricing Bilateral Counterparty Risk of CDS with Correlated Credit Risks
Feng LIN, Siyuan XIE, Jingping YANG
Based on the framework of[7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump (JCIR++), and the correlation between the default times is modeled by a copula function. We present a semianalytical formula for pricing bilateral counterparty risk of CDS, which is more convenient to compute through calculating multiple numerical integration or using MonteCarlo simulation without simulating default times. Moreover, we obtain simpler formulae under FGM copulas, Bernstein copulas and
C
^{A,B}
copulas, which can be applied for speeding up the computation and reducing the pricing error. Numerical results under FGM copulas and
C
^{A,B}
copulas show that our method performs better both in computation speed and accuracy.
2018 Vol. 34 (2): 209236 [
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237
Homology Cycles and Dependent Cycles of Hypergraphs
Jianfang WANG, Xin XU
In this paper, some new concepts for hypergraphs are introduced. Based on the previous results, we do further research on cycle structures of hypergraphs and construct a more strictly complete cycle structure system of hypergraphs.
2018 Vol. 34 (2): 237248 [
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249
On Local Constancy of Topological Entropy for Certain Partially Hyperbolic Diffeomorphisms
Lin WANG, Xinsheng WANG, Yujun ZHU
Let
f
:
M
→
M
be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of
f
is of dimension one then the topological entropy is constant on a small
C
^{1}
neighborhood of
f
.
2018 Vol. 34 (2): 249253 [
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254
A Feasible Point Method with Bundle Modification for Nonsmooth Convex Constrained Optimization
Jinbao JIAN, Chunming TANG, Lu SHI
In this paper, a bundle modification strategy is proposed for nonsmooth convex constrained minimization problems. As a result, a new feasible point bundle method is presented by applying this strategy. Whenever the stability center is updated, some points in the bundle will be substituted by new ones which have lower objective values and/or constraint values, aiming at getting a better bundle. The method generates feasible serious iterates on which the objective function is monotonically decreasing. Global convergence of the algorithm is established, and some preliminary numerical results show that our method performs better than the standard feasible point bundle method.
2018 Vol. 34 (2): 254273 [
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274
Remarks on Equality of Two Distributions under Some Partial Orders
Chuancun YIN
In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result are also considered.
2018 Vol. 34 (2): 274280 [
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281
The Folded (2
D
+ 1)cube and Its Uniform Posets
Lihang HOU, BO HOU, Suogang GAO
Let Γ denote the folded (2
D
+ 1)cube with vertex set
X
and diameter
D
≥ 3. Fix
x
∈
X
. We first define a partial order ≤ on
X
as follows. For
y, z
∈
X
let
y
≤
z
whenever ∂(
x, y
) + ∂(
y, z
)=∂(
x, z
). Let
R
(resp.
L
) denote the raising matrix (resp. lowering matrix) of Γ. Next we show that there exists a certain linear dependency among
RL
^{2}
,
LRL, L
^{2}
R
and
L
for each given
Q
polynomial structure of Γ. Finally, we determine whether the above linear dependency structure gives this poset a uniform structure or strongly uniform structure.
2018 Vol. 34 (2): 281292 [
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293
A GohbergSemencul Type Formula for the Inverse of ConjugateToeplitz Matrix and Applications
Yanpeng ZHENG, Sugoog SHON, Zunwei FU
Constructing a kind of cyclic displacement, we obtain the inverse of conjugateToeplitz matrix by the aid of GohbergSemencul type formula. The stability of the inverse formula is discussed. Numerical examples are given to verify the feasibility of the inverse formula. We show how the analogue of our GohbergSemencul type formula leads to an efficient way to solve the conjugateToeplitz linear system of equations. It will be shown the number of real arithmetic operations is not more than known results. The corresponding conjugateHankel matrix is also considered.
2018 Vol. 34 (2): 293303 [
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304
PainlevéKuratowski Stability of the Solution Sets to Perturbed Vector Generalized Systems
Zaiyun PENG, Yong ZHAO, Xinmin YANG
In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the PainlevéKuratowski convergence of global efficient solution sets of a family of perturbed problems to the corresponding global efficient solution set of the generalized system is obtained, where the perturbations are performed on both the objective function and the feasible set. Then, the density and PainlevéKuratowski convergence results of efficient solution sets are established by using gamma convergence, which is weaker than the assumption of continuous convergence. These results extend and improve the recent ones in the literature.
2018 Vol. 34 (2): 304317 [
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318
Attractor Bifurcation and Phase Transition for Liquid
^{4}
He
Chen PENG
Experiments show that the liquid helium4 has either superfluid phase or solid phase when temperature decreases or the pressure of the system changes. In this paper, we discuss the equations which govern these phase transitions and derive the criterions for these phase changes. Meanwhile, we give related approximate solutions and draw the phase diagram. In addition, we also prove that the liquid helium4 bifurcates from the trivial solution to an attractor as parameters cross certain critical value. The topological structure of the bifurcated attractor is also illustrated.
2018 Vol. 34 (2): 318329 [
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330
A Note about MultiHilbert Transform on
D
(R
^{n}
)
Mingquan WEI, Feng SHEN, Dunyan YAN
In this paper, we first prove that, for a nonzero function
f
∈
D
(R
^{n}
), its multiHilbert transform
H
_{n}
f
is bounded and does not have compact support. In addition, a new distribution space
D
'
_{H}
(R
^{n}
) is constructed and the definition of the multiHilbert transform is extended to it. It is shown that
D
'
_{H}
(R
^{n}
) is the biggest subspace of
D
'(R
^{n}
) on which the extended multiHilbert transform is a homeomorphism.
2018 Vol. 34 (2): 330343 [
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344
Some Existence Theorems on All Fractional (
g, f
)factors with Prescribed Properties
Sizhong ZHOU, Tao ZHANG
Let
G
be a graph, and
g, f
:
V
(
G
) →
Z
^{+}
with
g
(
x
) ≤
f
(
x
) for each
x
∈
V
(
G
). We say that
G
admits all fractional (
g, f
)factors if
G
contains an fractional
r
factor for every
r
:
V
(
G
) →
Z
^{+}
with
g
(
x
) ≤
r
(
x
) ≤
f
(
x
) for any
x
∈
V
(
G
). Let
H
be a subgraph of
G
. We say that
G
has all fractional (
g, f
)factors excluding
H
if for every
r
:
V
(
G
) →
Z
^{+}
with
g
(
x
) ≤
r
(
x
) ≤
f
(
x
) for all
x
∈
V
(
G
),
G
has a fractional
r
factor
F
_{h}
such that
E
(
H
) ∩
E
(
F
_{h}
)=ø, where
h
:
E
(
G
) →[0, 1] is a function. In this paper, we show a characterization for the existence of all fractional (
g, f
)factors excluding
H
and obtain two sufficient conditions for a graph to have all fractional (
g, f
)factors excluding
H
.
2018 Vol. 34 (2): 344350 [
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351
Conservatory of KaupKupershmidt Equation to the Concept of Fractional Derivative with and without Singular Kernel
Abdon ATANGANA, Emile Franc Doungmo GOUFO
Making use of the traditional Caputo derivative and the newly introduced CaputoFabrizio derivative with fractional order and no singular kernel, we extent the nonlinear KaupKupershmidt to the span of fractional calculus. In the analysis, different methods of fixedpoint theorem together with the concept of piccard
L
stability are used, allowing us to present the existence and uniqueness of the exact solution to models with both versions of derivatives. Finally, we present techniques to perform some numerical simulations for both nonlinear models and graphical simulations are provided for values of the order
α
=1.00; 0.90. Solutions are shown to behave similarly to the standard wellknown traveling wave solution of KaupKupershmidt equation.
2018 Vol. 34 (2): 351361 [
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362
Equitable Coloring of Three Classes of 1planar Graphs
Xin ZHANG, Huijuan WANG, Lan XU
A graph is 1planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. A plane graph with nearindependent crossings or independent crossings, say NICplanar graph or ICplanar graph, is a 1planar graph with the restriction that for any two crossings the four crossed edges are incident with at most one common vertex or no common vertices, respectively. In this paper, we prove that each 1planar graph, NICplanar graph or ICplanar graph with maximum degree △ at least 15, 13 or 12 has an equitable △coloring, respectively. This verifies the wellknown ChenLihWu Conjecture for three classes of 1planar graphs and improves some known results.
2018 Vol. 34 (2): 362372 [
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19
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373
Detailing Losses in the
M/M
/1/1 Transient Loss System
Pierpaolo FERRANTE
This paper is aimed at investigating the transient losses in the
M/M
/1/1 Erlang loss system. We evaluate the explicit form of the probability distribution of the number of losses in the time interval[0,
t
) and provide two alternative representations:one based on the iterated derivatives of hyperbolic sinus and cosine and the other on the spherical modified Bessel function of the second kind. The mathematical structures of the transient loss rate and of the transient probability of losing all customers are described and several analytical properties are derived.
2018 Vol. 34 (2): 373385 [
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386
Neighbor Connectivity of Two Kinds of Cayley Graphs
Yijie SHANG, Rongxia HAO, Meimei GU
In this paper, we determine the neighbor connectivity
κ
_{NB}
of two kinds of Cayley graphs:alternating group networks
AN
_{n}
and star graphs
S
_{n}
; and give the exact values of edge neighbor connectivity
λ
_{NB}
of
AN
_{n}
and Cayley graphs generated by transposition trees Γ
_{n}
. Those are
κ
_{NB}
(
AN
_{n}
)=
n
1,
λ
_{NB}
(
AN
_{n}
)=
n
2 and
κ
_{NB}
(
S
_{n}
)=
λ
_{NB}
(Γ
_{n}
)=
n
1.
2018 Vol. 34 (2): 386397 [
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17
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398
Global Regularity for a 2D Model of ElectroKinetic Fluid in a Bounded Domain
Miaochao CHEN, Shengqi LU, Qilin LIU
In this paper, we consider an initial boundary value problem for a 2D model of electrokinetic fluid in a smooth and bounded domain. We prove that the model has a unique globalintime smooth solution.
2018 Vol. 34 (2): 398403 [
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404
Fluid Model Modulated by an M/M/1 Working Vacation Queue with Negative Customer
Xiuli XU, Xianying WANG, Xiaofeng SONG, Xiaoqing LI
This paper investigates a fluid model driven by an M/M/1 queue with working vacations and RCE (Removal of customer in the end) policy of negative customer. In the external environment, the negative customer is not served by the server and only removes the positive customer in the end onetoone. We establish a fluid flow model based on this stochastic process, and obtain the mean buffer content and the probability of empty buffer for this fluid queue using the LT (Laplace transform) method. Moreover, several special cases of the model here are obtained. Finally, some numerical examples are presented to demonstrate the effects of parameters on the performance indices of the fluid model.
2018 Vol. 34 (2): 404415 [
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416
On the Irrotational Approximation to Adiabatic Chaplygin Gas Dynamic System
LI WANG
In this paper we mainly study the difference of the weak solutions generated by a wave front tracking algorithm for the steady adiabatic Chaplygin gas dynamic system and the steady irrotational system. Under the hypothesis that the initial data are of sufficiently small total variation, we prove that the difference between the solutions to these two systems can be bounded by the cube of the total variation of the initial perturbation.
2018 Vol. 34 (2): 416429 [
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430
The Prolongation Structure of a Coupled Kdv Equation
Yangjie JIA, Wenshan DUAN
The new coupled KdV equation proposed by Ohta and Hirota, in which the phase shift depends on the mutual positions of solitons at the initial time, is investigated in the framework of prolongation structure theory. Its Lax representation is constructed.
2018 Vol. 34 (2): 430437 [
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438
Weighted and Resonance Quasilinear Elliptic Problems with Jumping Nonlinearities
Gao JIA, Chunyan DAI, Jie CHEN
In this paper, the existence of a nontrivial solution for a class of quasilinear elliptic equations with a disturbance term in a weighted Sobolev space is proved. The proofs rely on Galerkin method, Brouwer's theorem and a new weighted compact Sobolevtype embedding theorem established by V.L. Shapiro.
2018 Vol. 34 (2): 438450 [
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