Many problems in science and engineering require the solving of linear systems of equations. As the problems get larger it becomes increasingly important to exploit the sparsity inherent in many such linear systems. It is well recognized that finding a fill-reducing ordering is crucial to the success of the numerical solution of sparse linear systems. The use of hybrid ordering partitioner is e...

A convenient method for defining a quasi-ordering, such as those used for proving termination of rewriting, is to choose the minimum of a set of quasi-orderings satisfying some desired traits. Unfortunately, a minimum in terms of set inclusion can be non-existent even when an intuitive “minimum” exists. We suggest an alternative to set inclusion, called “leanness”, show that leanness is a parti...

The high-pressure dynamics of a computer-modeled silica melt is studied in the framework of the mode-coupling theory of the glass transition (MCT) using static-structure input from molecular-dynamics (MD) computer simulation. The theory reproduces the experimentally known viscosity minimum (diffusivity maximum) as a function of density or pressure and explains it in terms of a corresponding min...

The size-Ramsey number $R^{(k)}(H)$ of a $k$-uniform hypergraph $H$ is the minimum edges in $G$ with property that each $2$-edge coloring contains monochromatic copy $H$. For $k\ge2$ and $n\in\mathbb{N}$, tight path on $n$ vertices $P^{(k)}_{n,k-1}$ defined as for which there an ordering its such edge set consists all $k$-element intervals consecutive this ordering. We show lower bound paths, i...

Multiple-input-multiple-output (MIMO) system has become one of the major focuses in the research community of wireless communication and information theory. Due to the channel characteristics, severe inter-symbol interference (ISI) may occur to the transmitted signals. Therefore it is necessary to use an equalizer to counter the effect of the channel. The effect of fading and interference effec...

Progressive coding is an important feature of compression schemes. Wavelet coders are well suited for this purpose because the wavelet coefficients can be naturally ordered according to decreasing importance. Progressive fractal coding is feasible, but it was proposed only for hybrid fractal-wavelet schemes. We introduce a progressive fractal image coder in the spatial domain. A Lagrange optimi...

The Lieb–Mattis theorem on the antiferromagnetic ordering of energy levels is generalized to SU(N) extended Hubbard model with Heisenberg exchange and pair-hopping terms. It is proved that the minimum energy levels among the states from equivalent representations are nondegenerate and ordered according to the dominance order of corresponding Young diagrams. In particular, the ground states form...

Five ordering algorithms for the nonserial dynamic programming algorithm for solving sparse discrete optimization problems are compared in this paper. The benchmarking reveals that the ordering of the variables has a significant impact on the run-time of these algorithms. In addition, it is shown that different orderings are most effective for different classes of problems. Finally, it is shown...

The nature of the magnetic ordering in TbNi2B2C has been investigated using neutron diffraction techniques on powdered polycrystalline samples. The results show that the Tb moments order below 15.5 K into an incommensurate magnetic structure. The magnetic order consists of a longitudinal modulation of the Tb moments with a wave vector of (0.556 0 0) at 1.5 K along the a*-direction. On increasin...

Five ordering algorithms for the nonserial dynamic programming algorithm for solving sparse discrete optimization problems are compared in this paper. The benchmarking reveals that the ordering of the variables has a significant impact on the run-time of these algorithms. In addition, it is shown that different orderings are most effective for different classes of problems. Finally, it is shown...