Computation of atomic fibers of Z-linear maps
نویسندگان
چکیده
For given matrix A ∈ Zd×n, the set Pb = { z : Az = b, z ∈ Z+ } describes the preimage or fiber of b ∈ Z under the Z-linear map fA : Z+ → Z, x 7→ Ax. The fiber Pb is called atomic if it has no nontrivial Minkowski decomposition, that is, Pb = Pb1 +Pb2 implies b = b1 or b = b2. In this paper we present a novel algorithm to compute such atomic fibers. An algorithmic solution to subproblems, computational examples and applications in optimization and algebra are included as well.
منابع مشابه
Theoretical computation of the quantum transport of zigzag mono-layer Graphenes with various z-direction widths
The quantum transport computations have been carried on four different width of zigzag graphene using a nonequilibrium Green’s function method combined with density functional theory. The computed properties are included transmittance spectrum, electrical current and quantum conductance at the 0.3V as bias voltage. The considered systems were composed from one-layer graphene sheets differing w...
متن کاملTheoretical computation of the quantum transport of zigzag mono-layer Graphenes with various z-direction widths
The quantum transport computations have been carried on four different width of zigzag graphene using a nonequilibrium Green’s function method combined with density functional theory. The computed properties are included transmittance spectrum, electrical current and quantum conductance at the 0.3V as bias voltage. The considered systems were composed from one-layer graphene sheets differing w...
متن کاملA New Approach for Approximating Solution of Continuous Semi-Infinite Linear Programming
This paper describes a new optimization method for solving continuous semi-infinite linear problems. With regard to the dual properties, the problem is presented as a measure theoretical optimization problem, in which the existence of the solution is guaranteed. Then, on the basis of the atomic measure properties, a computation method was presented for obtaining the near optimal so...
متن کاملRegularity of Bounded Tri-Linear Maps and the Fourth Adjoint of a Tri-Derivation
In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Contributions to Discrete Mathematics
دوره 6 شماره
صفحات -
تاریخ انتشار 2011