square grid

A many-to-many k-disjoint path cover of a graph joining two disjoint vertex sets S and T of equal size k is a set of k vertex-disjoint paths between S and T that altogether cover every vertex of the graph. The many-to-many k-disjoint path cover is classified as paired if each source in S is further required to be paired with a specific sink in T , or unpaired otherwise. In this paper, we first establish a necessary and sufficient condition for a bipartite cylindrical grid to have a paired many-to-many 2-disjoint path cover joining S and T. Based on this characterization, we then prove that, provided the set S ∪ T contains the equal numbers of vertices from different parts of the bipartition, the bipartite cylindrical grid always has an unpaired many-to-many 2-disjoint path cover. Additionally, we show that such balanced vertex sets also guarantee the existence of a paired many-to-many 2-disjoint path cover for any bipartite toroidal grid even if an arbitrary edge is removed.

Nowadays, with the rapid development of technology, color laser printers, scanner, and imaging devices have become ubiquitous devices in our daily use. Distributed system architectures and logic are becoming increasingly popular. The products that we buy through printers, scanners, and similar devices in our common use area are marked by physical steganography method to follow the illegal activities. These markings are not known by most of society. This data hiding method, which was processed as yellow dots, was discussed in our study, and information about the subject was shared.

Lattice networks are widely used in regular settings like grid computing, distributed control, satellite constellations, and sensor networks. Thus, limits on capacity, optimal routing policies, and performance with finite buffers are key issues and are addressed in this paper. In particular, we study the routing algorithms that achieve the maximum rate per node for infinite and finite buffers in the nodes and different communication models, namely uniform communications, central data gathering and border data gathering. In the case of nodes with infinite buffers, we determine the capacity of the network and we characterize the set of optimal routing algorithms that achieve capacity. In the case of nodes with finite buffers, we approximate the queue network problem and obtain the distribution on the queue size at the nodes. This distribution allows us to study the effect of routing on the queue distribution and derive the algorithms that achieve the maximum rate.

The capacitance between two adjacent nodes on an infinite square grid of identical capacitors can easily be found by superposition, and the solution is found by exploiting the symmetry of the grid. The mathematical problem presented in this work involves the solution of an infinite set of linear, inhomogeneous difference equations which are solved by the method of separation of variables.

Given an orthogonal polygon P , let |Π(P)| be the number of rectangles that result when we partition P by extending the edges incident to reflex vertices towards INT(P). In [4] we showed that |Π(P)| ≤ 1 + r + r 2 , where r is the number of reflex vertices of P. We shall now give sharper bounds both for maxP |Π(P)| and minP |Π(P)|. Moreover, we characterize the structure of orthogonal polygons in general position for which these new bounds are exact.

In this paper we investigate the advantages of using hexagonal grids in raster and volume graphics. In 2D, we present a hexagonal graphical model based on a hexagonal grid. In 3D, we introduce two honeycomb graphical models in which the voxels are hexagonal prisms, and we show that these are the only possible models under certain reasonable conditions. In the framework of the proposed models, we design two-and three-dimensional analytical honeycomb geometry of linear objects, as well as of circles and spheres. We demonstrate certain advantages of the honeycomb models and address algorithmic and complexity issues.

Geometrik desenler Emevi, Abbasi, Karahanli, Gazneli ve Buyuk Selcuklu donemlerinde, cografi bolge ve kullanilan malzemenin turune bagli olmaksizin cokca uygulanmistir. Suslemenin her alaninda cesitli malzemelerle uygulanmis olan geometrik kompozisyonlar bitkisel, yazi ve figurlu kompozisyonlar ile birlikte, Selcuklu, beylikler ve Osmanli devirlerinde de surekli olarak kullanilmistir. Islam eserlerinde kullanilan geometrik desenler kare, besgen, altigen, yedigen, sekizgen, dokuzgen, ongen, on altigen, yirmi dortgen, daire gibi birbirinden farkli geometrik sekillerden olusmaktadir. Bu calismamizda Fas, Hindistan, Iran, Ispanya, Misir, Ozbekistan, Suriye, Turkiye ile Almanya, Amerika, Fransa ve Ingiltere’deki bazi muze ve kutuphanelerde tespit edilen toplam 141 eserdeki 33 farkli kare tabanli geometrik desen, 9 grup halinde incelenmistir. Bu desenler IV.-XX. yuzyillar arasinda uretilmis olan eserlerde yer almaktadir. Bu desenleri daha dogru ve kolay cizebilmek icin tarafimizdan kare t...

Lattice networks are widely used in regular settings like grid computing, distributed control, satellite constellations, and sensor networks. Thus, limits on capacity, optimal routing policies, and performance with finite buffers are key issues and are addressed in this paper. In particular, we study the routing algorithms that achieve the maximum rate per node for infinite and finite buffers in the nodes and different communication models, namely uniform communications, central data gathering and border data gathering. In the case of nodes with infinite buffers, we determine the capacity of the network and we characterize the set of optimal routing algorithms that achieve capacity. In the case of nodes with finite buffers, we approximate the queue network problem and obtain the distribution on the queue size at the nodes. This distribution allows us to study the effect of routing on the queue distribution and derive the algorithms that achieve the maximum rate.

Geometrik desenler Emevi, Abbasi, Karahanli, Gazneli ve Buyuk Selcuklu donemlerinde, cografi bolge ve kullanilan malzemenin turune bagli olmaksizin cokca uygulanmistir. Suslemenin her alaninda cesitli malzemelerle uygulanmis olan geometrik kompozisyonlar bitkisel, yazi ve figurlu kompozisyonlar ile birlikte, Selcuklu, beylikler ve Osmanli devirlerinde de surekli olarak kullanilmistir. Islam eserlerinde kullanilan geometrik desenler kare, besgen, altigen, yedigen, sekizgen, dokuzgen, ongen, on altigen, yirmi dortgen, daire gibi birbirinden farkli geometrik sekillerden olusmaktadir. Bu calismamizda Fas, Hindistan, Iran, Ispanya, Misir, Ozbekistan, Suriye, Turkiye ile Almanya, Amerika, Fransa ve Ingiltere’deki bazi muze ve kutuphanelerde tespit edilen toplam 141 eserdeki 33 farkli kare tabanli geometrik desen, 9 grup halinde incelenmistir. Bu desenler IV.-XX. yuzyillar arasinda uretilmis olan eserlerde yer almaktadir. Bu desenleri daha dogru ve kolay cizebilmek icin tarafimizdan kare t...

Self-assembly of CuI and 1,12-diphenyl-5,8-dioxa-2,11-dithiadodecane (L), a podal ligand with S 2 O 2 donor set, afforded a unique square-grid type coordination polymer [Cu 4 I 4 L 2 ] n (1). X-ray analysis of 1 shows that cubane-like Cu 4 I 4 clusters are located at the nodes of the square-grid and connected to four ligands by Cu-S bonds forming a layer structure. The layers are stacked with an ABAB sequence. Photoluminescence behavior of 1 was also investigated.

Reaction of potassium ferricyanide with a mixture of nickel(II) chloride hexahydrate and trans-1,2-diaminocyclohexane (L) produces both a ferrocyanide ([ Clearly, the formation of 1 is accompanied by the reduction of ferricyanide to ferrocyanide. Interestingly, the relative amounts of the formation of 1 and 2 depends on the nickel(II):diamine ratio and the volume of the reaction mixture. It has been established from spectrophotometric titration that trans-1,2-diaminocyclohexane is responsible for the reduction of [Fe(CN) 6 ] 3À to [Fe(CN) 6 ] 4À . The ferrocyanide analogue, 1, can also be prepared by mixing potassium ferrocyanide with the nickel(II)-diamine solution. Among the six cyanides of each hexacyanoferrate(II), four coordinate to four different nickel(II) centers to form cyano-bridged two-dimensional square grids. The remaining two cyanides form strong hydrogen bonds with two hydrogens of one water of crystallization to result in squares, which can be considered as appended to the two-dimensional grids. The hydrogen bonds involving the hydrogens of amine groups of one 2D grid and the oxygens forming the appended squares of another 2D grid generate the third dimension of the structure. Variable-temperature (2-300 K) magnetic susceptibility measurements reveal that the nickel(II) centers in 1 are practically non-correlated.

Self-assembly of CuI and 1,12-diphenyl-5,8-dioxa-2,11-dithiadodecane (L), a podal ligand with S2O2 donor set, afforded a unique square-grid type coordination polymer [Cu4I4L2]n (1). X-ray analysis of 1 shows that cubane-like Cu4I4 clusters are located at the nodes of the square-grid and connected to four ligands by Cu–S bonds forming a layer structure. The layers are stacked with an ABAB sequence. Photoluminescence

Geometric ornaments were widely applied in the periods of Umayyad, Abbasi,
Karakhanid, Gazneli and Great Seljuk periods, regardless of the geographical
region and the type of material used. In addition to the geometric
compositions, herbal, writing and figured compositions applied with almost
every material in every aspect of decoration, it continued its existence
uninterruptedly throughout the Seljuk, Principalities and Ottoman periods.
The geometric patterns used in Islamic works consist of different geometric
shapes such as square, hexagon, pentagon, decagon, octagon, twenty
quadrilateral, circular. In this study we have obtained from some source
Morocco, India, Iran, Spain, Egypt, Uzbekistan, Syria, 33 different geometric
ornaments with square base, in a total of 141 works identified in some
museums and libraries in the UK and Turkey, were investigated in 9 groups.
These ornaments takes place in the works produced between IV.-XX. centuries
A new grid system with square base has been created to draw these patterns
more practically by us. This is the new approach we're talking about. In
addition, the detailed drawings of the patterns are shown through the new grid
created by grouping the patterns that are similar to each other or can be
considered as variation of each other. Detailed pattern analysis could not be
made due limitations of the article, only shown that patterns are placed on the
grid.