This article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords. Therefore, by replacing the new codewords, the binary data becomes another binary data regarding the intended goals. One of these goals is to reduce data size. It means that instead of the original codewords of each binary data, it replaced the Huffman codewords to reduce the data size. One of the features of this method is the result of positive compression for any type of binary data, that is, regardless of the size of the code table, the difference between the original data size and the data size after compression will be greater than or equal to zero. Another important and practical feature of this method is the use of symmetric codewords instead of the suggested codewords in order to create symmetry, reversibility and error resistance properties with two-way decoding.

Saffron is grown in arid and semi-arid regions in Iran in late autumn, winter and late spring with rainy season. It should be irrigated by supplemental basin irrigation. Since rainfall is usually delayed in autumn, therefore, a pre-flowering irrigation of about 100 mm is needed. In areas with a seasonal rainfall of 600 mm a post- flowering irrigation of about 50 mm is adequate for economical yield. In areas with seasonal rainfall of 400 and 200 mm continuous supplemental irrigation is needed with intervals of 24 and 15 days or irrigation regimes of 50% ETp and 75% ETp, respectively. In these areas, irrigation regimes can be planned based on crop water stress index (CWSI) of 0.60 and 0.27, respectively. Monthly values of crop coefficient (Kc) and pan coefficient (Kp) for saffron arepresented with the highest values of 1.10 and 0.84, respectively, that occurred in January. For the three-, four-and five-year old fields with higher amount of corm intensity the optimum irrigation water is zero for about 300 mm of rainfall. While for the six-and seven-year old fields the optimum irrigation water is zero for about 500 mm of rainfall. Flower production decreased 49% by using irrigation water with salinity level of 1.7 dS m-1 and no flower produced at salinity level of 4.0 dS m-1, while leaf growth occurred in this salinity. Furthermore, 50% flower yield is produced at soil water salinity of 3.6 dS m-1.

In this article, first we define a Kripke semantics for normal modal Logic with a binary operator and we introduce a system K^2 which is sound and complete for this semantics. Then, we will introduce two translations and show that binary normal modal logic K^2, and unary normal modal logic K, i.e. modal logic with one binary operator, are very closely related by these two translations. We call a translation a faithful interpretation if provability is preserved in both directions. So, with this terminology we will show that these two translations are faithful interpretation of K into K^2 and vice versa. A logic extending K will be a set of formulas containing K closed under its rules and uniform substitution. A logic extending K^2 is similarly defined. Finally, we will prove that the classes of logics extending K and K^2 are closely related as well and there is a 1-1-correspondence between the logics extending K and extending K^2.

Elimination of redundancies in the memory representation is necessary for fast and efficient analysis of large sets of fuzzy data. In this work, we use MTBDDs as the underlying data-structure to represent fuzzy sets and binary fuzzy relations. This leads to elimination of redundancies in the representation, less computations, and faster analyses. We also extended a BDD package (BuDDy) to support MTBDDs in general and fuzzy sets and relations in particular. Representation and manipulation of MTBDD based fuzzy sets and binary fuzzy relations are described in this paper. These include design and implementation of different fuzzy operations such as max, min and max-min composition. In particular, an efficient algorithm for computing max-min composition is presented. Effectiveness of our MTBDD based implementation is shown by applying it on fuzzy connectedness and image segmentation problem. Compared to a base implementation, the running time of the MTBDD based implementation was faster (in our test cases) by a factor ranging from 2 to 27. Also, when the MTBDD based data-structure was employed, the memory needed to represent the final results was improved by a factor ranging from 37.9 to 265.5. We also describe our base implementation which is based on matrices.

In this study, we prepared the binary-binary TCO compounds of SnO2-ZnO by the spray pyrolysis technique. We also investigated the role of MgF2/SiO2 antireflection coatings in reducing optical reflectance in the visible region of TCO. Before preparation, we simulated the optical transmition of the films for optimizing the layer thicknesses. The results of this study showed increasing of optical transmittance in the visible region of TCO by adding antireflection coating layers.

In computer science, a binary decision diagram is a data structure that is used to represent a Boolean function and to consider a compressed representation of relations. This paper considers the notation of T.B.T (total binary truth table), and introduces a novel concept of binary decision (hyper)tree and binary decision (hyper)diagram, directly and in as little time as possible, unlike previous methods. This study proves that every T.B.T corresponds to a binary decision (hyper)tree via minimum Boolean expression and presents some conditions on any given T.B.T for isomorphic binary decision (hyper)trees. Finally, for faster calculations and more complex functions, we offer an algorithm and so Python programming codes such that for any given T.B.T, it introduces a binary decision (hyper)tree.

The dominance graph of the binary words, which is denoted by (Γ _n ) ⃗ , is a directed graph whose vertex set is the set of all binary words of length n. Setting B_1 (w)={1≤ i≤ n┤ | w_i=1}, for every vertex 〖 w_1 w_2… w〗 _n, we join two vertices v and w by an arc if B_1 (w) is contained in B_1 (v). In this paper, we study some graphical parameters of this graph. For example, after computing the distance of every two vertices and the eccentricity of any vertex, it is proved that the diameter and the radius of the underlying graph of (Γ _n ) ⃗ equals 3 and 2, respectively. Also, it is proved that this graph has 〖 3〗 ^n-3(2^n-1) edges. Then we prove that both of the clique nmber and the chromatic number of the dominance graph of binary words of length n are n-1. Among other results, it is shown that the edge chromatic number and the maximum degree of vertices are equal to 2^(n-1)-2. Finally, by a combinatorial method, the independence number of this graph is determined, too.