We further the study of the duality theory of linear space-time codes over finite fields by showing that the only finite linear temporal correlated codes with a duality theory are the column distance codes and the rank codes. We introduce weight enumerators for both these codes and show that they have MacWilliams-type functional equations relating them to the weight enumerators of their duals. ...

Low-rank matrix recovery (LMR) is a rank minimization problem subject to linear equality constraints, and it arises in many fields such as signal and image processing, statistics, computer vision, system identification and control. This class of optimization problems is generally NP-hard. A popular approach replaces the rank function with the nuclear norm of the matrix variable. In this paper, ...

We define several notions of rank-width for countable graphs. We compare, for each of them the width of a countable graph with the least upper-bound of the widths of its finite induced subgraphs. A width has the compactness property if these two values are equal. Our notion of rank-width that uses quasi-trees (trees where paths may have the order type of rational numbers) has this property. So ...

We prove that the maximal order type of the wqo of linear orders of finite Hausdorff rank under embeddability is φ2(0), the first fixed point of the ε-function. We then show that Fräıssé’s conjecture restricted to linear orders of finite Hausdorff rank is provable in ACA0 + “φ2(0) is well-ordered” and, over RCA0, implies ACA ′ 0 + “φ2(0) is well-ordered”.

A tree-automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. The finite condensation rank (FC-rank) of a linear ordering measures how far it is away from being dense. We prove that the FC-rank of every tree-automatic linear ordering is below ω. This general...

Linear stability analysis of the three dimensional plane wake flow is performed using a mapped finite di?erence scheme in a domain which is doubly infinite in the cross–stream direction of wake flow. The physical domain in cross–stream direction is mapped to the computational domain using a cotangent mapping of the form y = ?cot(??). The Squire transformation [2], proposed by Squire, is also us...

We consider linear codes over some fixed finite field extension Fqm/Fq, where Fq is an arbitrary finite field. In [1], Gabidulin introduced rank metric codes, by endowing linear codes over Fqm with a rank weight over Fq and studied their basic properties in analogy with linear codes and the classical Hamming distance. Inspired by the characterization of the security in wiretap II codes in terms...

In this study, the general partial differential equation of unsteady groundwater flow through non-homogeneous and anisotropic aquifer was solved by the fully implicit finite difference method with control volume approach. The calibration of permeability and storage coefficients as model parameters was performed by a transformation technique and application of Powell's non-linear optimization me...

In this article, we formalize a matrix of Z-module and its properties. Specially, we formalize a matrix of a linear transformation of Z-module, a bilinear form and a matrix of the bilinear form (Gramian matrix). We formally prove that for a finite-rank free Z-module V , determinant of its Gramian matrix is constant regardless of selection of its basis. Z-module is necessary for lattice problems...