A transformation that preserves principal minors of skew-symmetric matrices

Our motivation comes from the work of Engel and Schneider (1980). Their main theorem implies that two symmetric matrices have equal corresponding principal minors of all orders if and only if they are diagonally similar. This study was continued by Hartfiel and Loewy (1984). They found sufficient conditions under which two $n\times n$ matrices\ $A$ and $B$ have equal corresponding principal minors of all orders if and only if $B$ or its transpose $B^{t}$ is diagonally similar to $A$. In this paper, we give a new way to construct a pair of skew-symmetric having equal corresponding principal minors of all orders

An exact method for a discrete multiobjective linear fractional optimization

Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated

Skew-symmetric matrices and their principal minors

Let $V$ be a nonempty finite set and $A=(a_{ij})_{i,j\in V}$ be a matrix with entries in a field $\mathbb{K}$. For a subset $X$ of $V$, we denote by $A[X]$ the submatrix of $A$ having row and column indices in $X$. We study the following problem. Given a positive integer $k$, what is the relationship between two matrices $A=(a_{ij})_{i,j\in V}$, $B=(b_{ij})_{i,j\in V}$ with entries in $\mathbb{K}$ and such that $\det(A\left[ X\right])=\det(B\left[ X\right])$ for any subset $X$ of $V$ of size at most $k$ ? The Theorem that we get in this Note is an improvement of a result of R. Loewy [5] for skew-symmetric matrices whose all off-diagonal entries are nonzero

An exact method for a discrete multiobjective linear fractional optimization

Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.multiobjective programming, integer programming, linear fractional programming, branch and cut

3-uniform hypergraphs: modular decomposition and realization by tournaments

Let $H$ be a 3-uniform hypergraph. A tournament $T$ defined on $V(T)=V(H)$ is a realization of $H$ if the edges of $H$ are exactly the 3-element subsets of $V(T)$ that induce 3-cycles. We characterize the 3-uniform hypergraphs that admit realizations by using a suitable modular decomposition

Modelling thermal effects in agitated vessel and reactor design consideration

The knowledge of the heat transfer coefficient on the inner side of a heated vessel wall is of utmost importance for the design of agitated vessels. The present contribution deals with heat transfer in an agitated vessel containing non-Newtonian liquid. The impellers used are six-blade Turbine (TPD) and a Propeller (TPI). The following aspects are discussed: description of the heat transfer process with the aid of dimensional analysis, heat transfer correlations for agitated liquid and influence of impeller speed on heat transfer

Performance Analysis of Project-and-Forward Relaying in Mixed MIMO-Pinhole and Rayleigh Dual-Hop Channel

In this letter, we present an end-to-end performance analysis of dual-hop project-and-forward relaying in a realistic scenario, where the source-relay and the relay-destination links are experiencing MIMO-pinhole and Rayleigh channel conditions, respectively. We derive the probability density function of both the relay post-processing and the end-to-end signal-to-noise ratios, and the obtained expressions are used to derive the outage probability of the analyzed system as well as its end-to-end ergodic capacity in terms of generalized functions. Applying then the residue theory to Mellin-Barnes integrals, we infer the system asymptotic behavior for different channel parameters. As the bivariate Meijer-G function is involved in the analysis, we propose a new and fast MATLAB implementation enabling an automated definition of the complex integration contour. Extensive Monte-Carlo simulations are invoked to corroborate the analytical results.Comment: 4 pages, IEEE Communications Letters, 201