Method for Orthogonal Edge Routing of Directed Layered Graphs with Edge Crossings Reduction

This paper presents a method for automated orthogonal edge routing of directed layered graphs using the described edge crossings reduction heuristic algorithm. The method assumes the nodes are pre-arranged on a rectangular grid composed of layers across the flow direction and lanes along the flow direction. Both layers and lanes are separated by rectangular areas defined as pipes. Each pipe has associated segment tracks. The edges are represented as orthogonal polylines consisting of line segments and routed along the shortest paths. Each segment is assigned to a pipe and to a segment track in it. The edge crossings reduction uses an iterative algorithm to resolve crossings between segments. Conflicting segments are reassigned to adjacent segment tracks, either by swapping with adjacent segments, or by inserting new tracks and calculating the shortest paths of edges. The algorithm proved to be efficient and was implemented in an interactive graph design tool.

Hexagonal Grid-Based Framework for Mobile Robot Navigation

The paper addresses the problem of mobile robots’ navigation using a hexagonal lattice. We carried out experiments in which we used a vehicle equipped with a set of sensors. Based on the data, a traversable map was created. The experimental results proved that hexagonal maps of an environment can be easily built based on sensor readings. The path planning method has many advantages: the situation in which obstacles surround the position of the robot or the target is easily detected, and we can influence the properties of the path, e.g., the distance from obstacles or the type of surface can be taken into account. A path can be smoothed more easily than with a rectangular grid.

Synthesis and crystal structures of Zn(II) and Cd(II) coordination polymers derived from the flexible N-(4-carboxyphenyl)iminodiacetic acid and auxiliary ligands

Two coordination polymers [Cd3(CPIDA)2(bib)(H2O)2] n 1 and {[Zn6(CPIDA)4(bix)3]·8H2O} n 2 (H3CPIDA = N-(4-carboxyphenyl) iminodiacetic acid, bib = 1,4-bis(N-imidazolyl)butane, bix = 1,4-bis(imidazol-1-ylmethyl)benzene), have been hydrothermally synthesized and characterized by analytical and IR spectroscopic data. Compound 1 displays an interesting 3D framework with trinodal (4,5)-connected topology, consisting of (4,4) rectangular grid double layers linked by trans-bib ligands. In 2, the corrugated nets with couples of central symmetrical chains constructed by CPIDA3− and bridging trans-bix ligands are pillared by infinite tubes made from CPIDA3− and cis-bix ligands to build a new 3D porous framework with parallelogram-shaped channels, exhibiting a pentanodal (3,4)-connected topology. Moreover, compounds 1 and 2 show intense solid state fluorescence at room temperature.

Discrete Vortex Method Of Flow Around A Cylinder In A Channel Using Simple Grid System

Modelling of unidirectional and oscillatory flows around a cylinder in a channel using a simple overlapping grid system are carried out. The importance of this cylinder-wall configuration is the effect of blockage which suppress the development of the vortex shedding The polar grid system of the cylinder is then overlapped with the rectangular grid system of the wall. The length of rectangular grid element is about the same as the length of the polar grid system in the cylinder surface. The use of such overlapping grid system is for reducing the CPU time, i.e. in calculating the vortex velocity since the CPU time in calculating the vortices velocity takes the longest time. This method is not only time efficient, but also gives a better distribution of surface vorticity as the scattered vortices around the body are now concentrated on grid point. In this study there is no vortex-to-vortex interaction, but instead it uses node-to-node interactions. Velocity calculation also uses this overlapping grid in which the new incremental shift position then summed up to get the total new vortices position. In this overlapping system the grid can be either off or on depend on process involved to get rid of the nodes not being used. The engineering applications of this topic is to simulate the loading pipeline placed in the channel such as in the heat exchanger or simulation of U-tube experiment or other system. The in-line and transverse force coefficients are found by integrating the pressure around the cylinder surface. The flow patterns are then can be obtained and presented. The comparison of the results with experimental evidence is presented and also the range of good results is discussed.

Limiting accuracy of two-dimensional parabolic equation solution using split-step Fourier transform method

Numerical solution of the wave parabolic equation on a rectangular grid is analyzed, when the method of discrete split-step Fourier transform (FT) is used to calculate the values of the field in an inhomogeneous medium at the next step in the range. The goal was to identify the limiting possibilities of the FT method itself, so studies were carried out for the case of radio wave propagation in free space. Two related problems were solved: what is the minimum value of the root-mean-square error (RMSE) of the field calculation and what should be the values of the transfer coefficients of the Fourier series harmonics and the values of the coefficients of the artificial absorbing layer (AL) both depending on the parameters of the computational scheme. It is shown that the dependence of the RMSE on the distance to the source always has the maximum. The forms of the optimal AL differ from those traditionally used primarily due to the presence of a significant imaginary component.

Revitalizing Keno: A Call for Pattern-Based Proposition Bets

Keno is a renowned game of chance offered by both lotteries and casinos throughout the world. The premise of the game is simple: a set of numbers is drawn at random and players are paid for selecting all or most of those numbers in advance. The mathematical foundation governing the odds and payouts for these basic wagers is elementary. More sophisticated bets, however, have associated probabilities which cannot be easily calculated by applying a manageable series of formulas. As a result, keno’s wagering menu has remained stagnant since the game’s widespread inception. Namely, proposition bets, now commonplace in virtually every other form of gaming, have never been developed for keno to any large degree. This is both unfortunate and surprising because keno is ideally suited for such an expansion. Unlike most other lottery-style games, keno highlights all drawn numbers on a rectangular grid, creating random visual patterns at the conclusion of each drawing. Creative new wagers based on these patterns are rigorously derived herein. These new additions should greatly enhance the game for both gamblers and enterprising gaming operators alike.