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941.
We present branching-on-hyperplane methods for solving mixed integer linear and mixed integer convex programs. In particular,
we formulate the problem of finding a good branching hyperplane using a novel concept of adjoint lattice. We also reformulate
the problem of rounding a continuous solution to a mixed integer solution. A worst case complexity of a Lenstra-type algorithm
is established using an approximate log-barrier center to obtain an ellipsoidal rounding of the feasible set. The results
for the mixed integer convex programming also establish a complexity result for the mixed integer second order cone programming
and mixed integer semidefinite programming feasibility problems as a special case. Our results motivate an alternative reformulation
technique and a branching heuristic using a generalized (e.g., ellipsoidal) norm reduced basis available at the root node. 相似文献
942.
Khakim D. Ikramov 《Computational Mathematics and Mathematical Physics》2011,51(4):505-512
Suppose that one should verify whether a given complex n × n matrix can be converted into a real matrix by a unitary similarity transformation. Sufficient conditions for this property
to hold were found in an earlier publication of this author. These conditions are relaxed in the following way: as before,
the spectrum is required to be simple, but pairs of complex conjugate eigenvalues $
\lambda ,\bar \lambda
$
\lambda ,\bar \lambda
are now allowed. However, the eigenvectors corresponding to such eigenvalues must not be orthogonal. 相似文献
943.
For the generalized saddle-point problems with non-Hermitian (1,1) blocks, we present an HSS-based constraint preconditioner,
in which the (1,1) block of the preconditioner is constructed by the HSS method for solving the non-Hermitian positive definite
linear systems. We analyze the invertibility of the HSS-based constraint preconditioner and prove the convergence of the preconditioned
iteration method. Numerical experiments are used to demonstrate the efficiency of the preconditioner as well as the corresponding
preconditioned iteration method, especially when the (1,1) block of the saddle-point matrix is essentially non-Hermitian. 相似文献
944.
945.
For an integer N greater than 5 and a triple \({\mathfrak{a}}=[a_{1},a_{2},a_{3}]\) of integers with the properties 0<a i ≤N/2 and a i ≠a j for i≠j, we consider a modular function \(W_{\mathfrak{a}}(\tau)=\frac{\wp (a_{1}/N;L_{\tau})-\wp (a_{3}/N;L_{\tau})}{\wp (a_{2}/N;L_{\tau})-\wp(a_{3}/N;L_{\tau})}\) for the modular group Γ 1(N), where ?(z;L τ ) is the Weierstrass ?-function relative to the lattice L τ generated by 1 and a complex number τ with positive imaginary part. For a pair of such triples \({\mathfrak{A}}=[{\mathfrak{a}},{\mathfrak{b}}]\) and a pair of non-negative integers F=[m,n], we define a modular function \(T_{{\mathfrak{A}},F}\) for the group Γ 0(N) as the trace of the product \(W_{\mathfrak{a}}^{m}W_{\mathfrak{b}}^{n}\) to the modular function field of Γ 0(N). In this article, we study the integrality of singular values of the functions \(W_{\mathfrak{a}}\) and \(T_{{\mathfrak{A}},F}\) by using their modular equations. We prove that the functions \(T_{{\mathfrak{A}},F}\) for suitably chosen \({\mathfrak{A}}\) and F generate the modular function field of Γ 0(N), and from Shimura reciprocity and Gee–Stevenhagen method we obtain that singular values \(T_{{\mathfrak{A}},F}(\tau)\) for suitably chosen \({\mathfrak{A}}\) and F generate ring class fields. Further, we study the class polynomial of \(T_{{\mathfrak{A}},F}\) for Schertz N-system. 相似文献
946.
Brice Franke 《Extremes》2011,14(1):127-152
We investigate the recursive sequence Z
n
: = max {Z
n − 1,λ(Z
n − 1)X
n
} where X
n
is a sequence of iid random variables with exponential distributions and λ is a periodic positive bounded measurable function. We prove that the Césaro mean of the sequence λ(Z
n
) converges toward the essential minimum of λ. Subsequently we apply this result and obtain a limit theorem for the distributions of the sequence Z
n
. The resulting limit is a Gumbel distribution. 相似文献
947.
Two cellular embeddings i: G → S and j: G → S of a connected graph G into a closed orientable surface S are equivalent if there is an orientation-preserving surface homeomorphism h: S → S such that hi = j. The genus polynomial of a graph G is defined by
$
g\left[ G \right](x) = \sum\limits_{g = 0}^\infty {a_g x^g ,}
$
g\left[ G \right](x) = \sum\limits_{g = 0}^\infty {a_g x^g ,}
相似文献
948.
In this paper we formulate a continuous-time behavioral (à la cumulative prospect theory) portfolio selection model where the losses are constrained by a pre-specified upper bound. Economically
the model is motivated by the previously proved fact that the losses occurring in a bad state of the world can be catastrophic
for an unconstrained model. Mathematically solving the model boils down to solving a concave Choquet minimization problem with an additional upper bound. We derive the optimal solution explicitly for such a loss control model. The optimal
terminal wealth profile is in general characterized by three pieces: the agent has gains in the good states of the world,
gets a moderate, endogenously constant loss in the intermediate states, and suffers the maximal loss (which is the given bound
for losses) in the bad states. Examples are given to illustrate the general results. 相似文献
949.
In this paper, we consider a non-local PDE model with delay for population dynamics in ℝ
n
. First, we prove the existence and uniqueness of weak solutions under some suitable decayed assumptions on non-local term
at infinity. Then, we obtain the global attractor by proving ω-limit compactness property of the solution operator semigroup. 相似文献
950.
As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric
orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with
a category of polyhedrally-constructible sheaves on ℝ
n
. In this paper we investigate and reprove some of Kawamata’s results from this perspective. 相似文献
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