ÐWe study implementation issues for spatial convolution filters and their Fourier alternative, with the aim to optimize the accuracy of filter output. We focus on Gaussian scale-space filters and show that there exists a trade-off scale that subdivides the available scale range into two subintervals of equal length. Below this trade-off scale Fourier filtering yields more accurate results than ...

A pooling space is a ranked poset P such that the subposet w+ induced by the elements above w is atomic for each element w of P . Pooling spaces were introduced in [Discrete Mathematics 282:163-169, 2004] for the purpose of giving a uniform way to construct pooling designs, which have applications to the screening of DNA sequences. Many examples of pooling spaces were given in that paper. In th...

In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...

Casteels and Richter have shown that if X and Y are distinct compactifications of a locally finite graph G and f : X → Y is a continuous surjection such that f restricts to a homeomorphism on G, then the cycle space ZX of X is contained in the cycle space ZY of Y . In this work, we show how to extend a basis for ZX to a basis of ZY .

Shier, D.R., E.J. Valvo and R.E. Jamison, Generating the states of a binary stochastic system, Discrete Applied Mathematics 37/38 (1992) 489-500. An important aspect of planning a communication or distribution system is assessing its performance when the components are subject to random failure. Since exact calculation of stochastic performance measures is usually difficult, the behavior of the...

Different methods are available for simultaneous optimization of cross-section, topology and geometry of truss structures. Since the search space for this problem is very large, the probability of falling in local optimum is considerably high. On the other hand, different types of design variables (continuous and discrete) lead to some difficulties in the process of optimization. In this articl...

Nonlinear Knapsack Problems (NKP) are the alternative formulation for the multiple-choice knapsack problems. A powerful approach for solving NKP is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. Despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...

In this paper we study the relationship between the Euclidean and the discrete space. We study discrete operations based on Euclidean functions: the discrete smooth scaling and the discrete-continuous rotation. Conversely, we study Euclidean operations based on discrete functions: the discrete based simplification, the Euclideandiscrete union and the Euclidean-discrete co-refinement. These oper...

Discrete Element Method (DEM) is extensively used for mathematical modeling and simulating the behavior of discrete discs and discrete spheres in two and three dimensional space, respectively. Prediction of particles flow regime, power draw and kinetic energy for a laboratory or an industrial mill is possible by DEM simulation. In this article, a new approach was used to assess the main paramet...