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Syriac Letters and James Dagram (A)

  • November 2017
Authors:
Ammar Seddiq Mahmood at University of Mosul
Ammar Seddiq Mahmood
Hadil Sami at AL-hamdaniya University
Hadil Sami
  • AL-hamdaniya University
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Abstract

We be dealt the letters of Syriac language as it is natural numbers, to enter the diagram of James ( A) to the theory of partition, this process will have uses in our daily lives and in confidential correspondence.
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International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
Page | 54
Syriac Letters and James Diagram (A)
Hadil H. Sami1, Prof. Dr. Ammar S. Mahmood2
1Department of Mathematics, College of Education, University of Al-Hamdaniya, Mosul, Iraq.
2 Department of Mathematics, College of Education for Pure Science, University of Mosul, Mosul, Iraq.
ABSTRACT
Will be dealt with the letters of Syriac language as it is natural numbers, to enter the diagram of James )A( to
the theory of partition, this process will have uses in our daily lives and in confidential correspondence.
Keywords: Partition theory, Beta numbers, Syriac Letters.
1. INTRODUCTION
The aim of the study is how to use the Syriac language as a secret message between two people or more.Syriac language
is a Semitic language derived from the Aramaic language which appeared in the first millennium BC, and in the sixth
century BC Syriac language has become the only language of communication in the (fertile crescent) region, till after the
birth of Christ this language gained its new name (Syriac) in the fourth century [5,7].
This language like other Semitic languages has multiple letters which is 22 letters, three of this letters are vowels, but
the rest of the letters are silent, this letters are as follows:
.
The letters do not appear but replace it with meaningless numbers if this message read by a stranger person, from here
the idea started where we saw that James' diagram (A) could help us. First of all, we will explain what James’s diagram
is and then begin the process of linking with Syriac characters. Let be a non-negative integer, a composition μ of r is
a sequence μ=1 ,2, nof non-negative integers suchthat =j
n
j=1 = r, [4]. For example, if = 4, the
following sequences are compositions:
4,3,1,2,2,1,3,2,1,1,1,2,1,1,1,2,1,1,1,1.
The composition μ is said to be a partition of r if j  j+1 , j 1. By using the previous example in the case of
r = 4, the following sequences satisfy the condition of partition:
4,3,1,2,2,2,1,1,1,1,1,1.
Let be a number of redundant part of the partition of r, then we have =1,2,,n= 1
1,2
2,,f
fsuch
that: =j
n
j=1 = l
lf
l=1 , [2].
β - numbers was defined by; see James in [1]: "Fix μ is a partition of r, choose an integer b greater than or equal to
the number of parts of and definei=i+ b i, 1ib. The set 1,2,,bis said to be the set of β
- numbers for µ. For example if we have the partition μ= (6,5,2,2,1) and b = 5 b=5 then β - numbers for partition μ
will be:
* ، ، ، ، ،* ، ، ، ،* ، ـ، ـ ، ـ ، ــ ،
، ـ ، ـ ، ، ، ، ،
International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
Page | 55
Where every β – numbers will be represented by a bead (●) which takes its location in diagram (A) and in case of
nonexistence of β - numbers, then the value in diagram (A) will be represented by a blank )-(. Returning to the previous
example in the case of =6,5,2,2,1and b = 5, then the set of β – numbers are 10,8,4,3,1 and diagram )A) where
e = 2 will be:
and if e = 3
It is possible from diagram (A) we can know the partition that belong to it , by numbering the blanks which precedes
the beads In ascending order from left to right, where the number of blanks preceding any bead is represented by one of
the elements μ, for example, the number of blanks preceding the first bead will represent the value of n, and the
number of blanks preceding the second bead represents n1, thus, until the last bead in diagram (A), all the blanks in
the diagram preceding this bead will be represented by 1. For example, we have the following diagram (A) we will
find its own partition as shown below:
μ=12,8,7,5, 42, 1. Many papers that talk about specific types of movements, see [3,6].
2. THE RELATION BETWEEN SYRIAC WORDS AND JAMES DIAGRAM (A)
In this part we will try to find a suitable way to write each letter of the Syriac language according to diagram (A). The
focus was on choosing a fixed (e) and an equal number of rows for each letter, after the study it was found that e = 7 and
7 of the rows is the best choice as follows:
1
0
3
2
5
4
7
6
9
8
11
10
•
-
•
-
-
•
-
-
-
•
-
•
2
1
0
5
4
3
8
7
6
11
10
9
-
•
-
-
•
•
•
-
-
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•
-
2
-
•
1
-
•
•
4
-
-7
-6
•
-9
•
-8
•
-12
-11
International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
Page | 56
The following diagrams are for the letters that come at the end of the word, as well as we have made clips for the letters
() and () with the rest of the letters for easy connectivity when writing the word.
International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
Page | 57
International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
Page | 58
International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
Page | 59
Here we will have the following question: If we want to write a word, it is likely to consist of a number of letters, thus
what is the partition that denotes that word?
For example, we have the words () and (), the partition and James diagram are as follows:

= (995,98,928,872,803,77,724,66,62,572,56,45,404,285,6)
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International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
Page | 60
Through what has been explained, the process of writing a partition by the numbering of the blank in each row of the
word from left to right will be arranged in ascending order, thus the first row of the first letter from the left it will be
according to the known rule for finding a partition. As for the first row of the second letter, the value (e) will have a
large role and then the number of beads located in the first row of the first letter to the left, if we move to the third letter
in the first row, the value of (2e) will have the largest role deleted from it number of beads located in the first row of the
first and second letters to the left. Thus, we get to the first row of the last letter it will be as much as (e (the number of
letters - 1)) subtracted from it the number of beads in the first row of letters which preceded the last letter. Now, if we
move to the second row of the first letter to the left, it will be (e (number of letters - 1)) subtracted from it the number of
the beads that preceded it in the first row of all letters except the same letter considering that the partition was basically
calculated previously. This process will be repeated with the rest of the rows and cases, where we will always subtract
the number of beads located before the same site except for the same letter, so through the above, the rule of this will be:
International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
Page | 61
Here, must be attention before everything on the form of the letters such as ، ، ... when used it with the rest of the
letters for the purpose of forming the word here we must shift the letters to the top and in this case we will delete (14)
blanks of each 1 ,,2, , n of each letter. For example, when connecting the two letters and to form the section
 ,here we need to make the letterin parallel with the letter , in this case we will re-write the partition of the
letter which is (308,244) so that after deleting (14) blanks of each μ are (168,104) and thus this will be the new
partition of the letter, and in the same way with the rest of the letters. In the same way we will try to find the general
rule to write a sentence, and for that the rule is:
International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 6 Issue 12, December-2017, Impact Factor: 4.059
Page | 62
REFERENCES
[1]. G. James. (1978); “Some combinatorial results involving Young diagrams” , Math. Proc. Cambridge Phil. Soc., Vol. 83, 1-
10.
[2]. A. S. Mahmood. (2011); “On the intersection of Young's diagrams core”, J. Educ. And Science (Mosul Univ. ), Vol. 24,
no.3, 143 -159.
[3]. A. S. Mahmood and S. S. Ali, (2014);” (Upside-down o direct rotation)β - numbers” , American J. of Math. and Stat. Vol. (4),
no.2, 58-64.
[4]. A. Mathas. (1999); “Iwahori - Hecke Algebras and Schur Algebras of the Symmetric Groups ", Amer. Math. Soc., University
Lecture Series, Vol. 15.
[5]. J.Messo. (2005); “Syriac / Aramaic Language and Culture” , www.midyatcity.com.
[6]. E. F. Mohommed, H. Ibahim, N. Ahmad and A. S. Mahmood. (2016);” Nested chain movement of length 1 of beta-number, in
James abacus diagram” Indoe Global J. of Pure and Applied Mathematics, Vol. 12,no. 4, 2953-2969
[7]. R.Rollinger. (2006); “The Terms Assyria and Syria Again ”, JNES Vol. 65, no. 4.
.
... Sami and Mahmoud introduced [1], [2] different types of encoding Syriac letters. Syriac language is an ancient that derived from the Aramaic language, so in this work, we try to employ the method that used by Ahmed and Mahmoud in [3] due to the increasing of the difficulty of cracking the code as we previously found in [1]. ...
... Sami and Mahmoud introduced [1], [2] different types of encoding Syriac letters. Syriac language is an ancient that derived from the Aramaic language, so in this work, we try to employ the method that used by Ahmed and Mahmoud in [3] due to the increasing of the difficulty of cracking the code as we previously found in [1]. In the beginning, we will introduce the important concepts for the work. ...
... The sum of the elements of each row represents the degree of the vertex in that row, and the sum of the elements of each column represents the degree of the vertex in that column. To apply this method to an Abacus diagram of Syriac letters, it is clear that the Abacus diagram for each letter is an array 7*7 which means it is a square matrix [1]. To encoding of each letter by applying the directed graph will generate a special code for each letter, and this code consists of 14 values, which represent the degree of the outside edges, that starts from the vertex g 1 up to g 7 and then the degree of the inside edges to g 1 up to g 7 that is: Code any letter ( + (g 1 ), . . . ...
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... The set {β 1 , β 2 , ⋯ β b } is said to be the set of β -number for δ, see [1]. Let e be a positive integer number greater than or equal to 2, we can represent numbers by a diagram called e-abacus diagram, see [2], as shown in Table 1: Where every β-numbers will be represented by a (•) which takes its location in e-abacus diagram and in case of non-existence of β-numbers then the value in e-abacus diagram will be represented by a (7,7,6,5,5,5,4,2,1) and e = 4, b = 9 then the set of βnumber is {1, 3,6,8,9,10,12,14,15} then e-abacus diagram for this partition is: Fayers is one of the creators who added a lot to this topic so much so we might refer here to [3][4][5]. Sami and Mahmood [6] developed a design for the shape of the 22 Syriac letters; (to learn more about this language see [7,8], through the e-abacus diagram technology and e = 7 in order to ensure that the shape becomes more accurate and clear if we choose e less than 7. ...
... Let e be a positive integer number greater than or equal to 2, we can represent numbers by a diagram called e-abacus diagram, see [2], as shown in Table 1: Where every β-numbers will be represented by a (•) which takes its location in e-abacus diagram and in case of non-existence of β-numbers then the value in e-abacus diagram will be represented by a (7,7,6,5,5,5,4,2,1) and e = 4, b = 9 then the set of βnumber is {1, 3,6,8,9,10,12,14,15} then e-abacus diagram for this partition is: Fayers is one of the creators who added a lot to this topic so much so we might refer here to [3][4][5]. Sami and Mahmood [6] developed a design for the shape of the 22 Syriac letters; (to learn more about this language see [7,8], through the e-abacus diagram technology and e = 7 in order to ensure that the shape becomes more accurate and clear if we choose e less than 7. We mention, the following example: The problem that, we want to solve is how we change the parameters of the Syraic letters (to become unreadable as if I were sending a secret message), so we had the concept of "Orbits" presented in 2015 by Mohommed et al the best assistant to solve this dilemma. ...
... It is quite natural to study the basics of the subject matter of coding, for examples we mention each of them [20][21][22], let's understand how we deal with developing ideas here. Perhaps it is important to note that, this coding note that, this coding used for Syriac letters is completely different from how the coding of these letters was handled by Sami and Mahmood [6] which was by extended Vigenere Cipher; (more on this technology can see [22,23], in the sense of using another medium and not died through the scheme itself, also [24,25]. ...
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... (2) (1,1,2) (2,2,2,2) = ((2,2,2,2),((1+(6-4)),(1+(6-4)),(2+(6-4))),(2+(11-7))) = (2,2,2,2,3,3,4,6). (3,7,8,9,9,11,11,12,12,12,14,14,17 ...
... ‫األولى‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬ ‫أخذنا‬(1,1,2,4,4,5,5,5,6,6,6,7,8,8,9,10,10,11,11,11,11,12,12,12,14,16,18) ‫الثانية‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬ ‫ثـ‬ (4,5,5,6,6) ‫ع‬ ‫منو‬ ً ‫مطروحا‬ ‫األولى‬ ‫الكممة‬ ‫(طوؿ‬ ‫الييا‬ ً ‫مضافا‬ ‫العقد‬ ‫دد‬ ‫قيمتو‬ ‫الذي‬ ‫و‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫الى‬ ‫باإلضافة‬ ‫الكممة‬ ‫ىذه‬ ‫في‬ 0 ‫ثـ‬ ) ‫الثالثة‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬(3,7,8,8,8,8,9,9,10,11,12,12,12) ‫الكممة‬ ‫طوؿ‬ ‫مجموع‬ ‫الييا‬ ً ‫مضافا‬ ‫ا‬ ‫باإلضافة‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممتيف‬ ‫في‬ ‫العقد‬ ‫عدد‬ ‫منو‬ ً ‫مطروحا‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫قـ‬ ‫الر‬ ‫لى‬ 4 ‫الذي‬ ‫و‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫و‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫قيمة‬ ‫مجموع‬ ‫يمثؿ‬ ‫الثالثة‬ ‫و‬ ‫الثانية‬ ، ‫كاآلتي:‬ ‫كممات‬ ‫ثالث‬ ‫مف‬ ‫متكونة‬ ‫جممة‬ ‫ئة‬ ‫لتجز‬ ‫العامة‬ ‫القاعدة‬ ‫الى‬ ‫وتوصمنا‬ ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫الهجينة‬ ‫مورس‬ ‫شفرة‬ The hybrid Morse code ‫ىي‬ ‫الناتجة‬ ‫ئة‬ ‫فالتجز‬ : (1,1,2,4,4,5,5,6,6,7,8,8,9,10,10,11,11,11,11,12,12,12,14,16,18,23,24, 24,25,25,29,33,34,34,34,34,35,35,36,37,38,38,38). ‫في‬ ‫الكممات‬ ‫مف‬ ‫عدد‬ ‫ألي‬ ‫العامة‬ ‫القاعدة‬ ‫إلى‬ ‫نتوصؿ‬ ‫يقة‬ ‫الطر‬ ‫بنفس‬ ‫ار‬ ‫باإلستمر‬ ‫وىكذا‬ ‫اآلتي‬ ‫تمثؿ‬ ‫التي‬ ‫و‬ ‫ما‬ ‫جممة‬ : ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫الهجينة‬ ‫مورس‬ ‫شفرة‬ The hybrid Morse code ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫مالحظة‬ ‫المعدلة‬ ‫مورس‬ ‫ة‬ ‫بشفر‬ ‫البحث‬ ‫ىذا‬ ‫تسمية‬ ‫تكوف‬ ‫اف‬ ً ‫ايضا‬ ‫المحتمؿ‬ ‫مف‬ : (The modified Morse code) ‫اليجيف‬ ‫اف‬ ‫اعتبار‬ ‫عمى‬ ‫الباحثيف‬ ‫بعض‬ ‫عند‬ ‫مالئمة‬ ‫اكثر‬ ‫نفسيا‬ ‫ة‬ ‫الشفر‬ ‫مابيف‬ ‫يج‬ ‫مز‬ ‫بانو‬ ‫البداية‬ ‫مف‬ ‫فيو‬ ‫نا‬ ‫مافكر‬ ‫وىذا‬ ‫مختمفتيف‬ ‫مادتيف‬ ‫دمج‬ ‫عمى‬ ‫يطمؽ‬ ‫االعداد‬ ‫ية‬ ‫ونظر‬ ، ‫الجنس‬ ‫نفس‬ ‫مف‬ ‫فيي‬ ‫المعدلة‬ ‫كممة‬ ‫أما‬ ، ‫اضافة‬ ‫أف‬ ‫ير‬ ‫قد‬ ‫الباحثيف‬ ‫بعض‬ ‫الف‬ dash ‫و‬ dot ‫االسـ‬ ‫بيذا‬ ‫تسميتيا‬ ‫ممكف‬ ‫وبالتالي‬ ‫الجنس‬ ‫نفس‬ ‫مف‬ ‫ىي‬ . ...
... ‫األولى‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬ ‫أخذنا‬(1,1,2,4,4,5,5,5,6,6,6,7,8,8,9,10,10,11,11,11,11,12,12,12,14,16,18) ‫الثانية‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬ ‫ثـ‬ (4,5,5,6,6) ‫ع‬ ‫منو‬ ً ‫مطروحا‬ ‫األولى‬ ‫الكممة‬ ‫(طوؿ‬ ‫الييا‬ ً ‫مضافا‬ ‫العقد‬ ‫دد‬ ‫قيمتو‬ ‫الذي‬ ‫و‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫الى‬ ‫باإلضافة‬ ‫الكممة‬ ‫ىذه‬ ‫في‬ 0 ‫ثـ‬ ) ‫الثالثة‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬(3,7,8,8,8,8,9,9,10,11,12,12,12) ‫الكممة‬ ‫طوؿ‬ ‫مجموع‬ ‫الييا‬ ً ‫مضافا‬ ‫ا‬ ‫باإلضافة‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممتيف‬ ‫في‬ ‫العقد‬ ‫عدد‬ ‫منو‬ ً ‫مطروحا‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫قـ‬ ‫الر‬ ‫لى‬ 4 ‫الذي‬ ‫و‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫و‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫قيمة‬ ‫مجموع‬ ‫يمثؿ‬ ‫الثالثة‬ ‫و‬ ‫الثانية‬ ، ‫كاآلتي:‬ ‫كممات‬ ‫ثالث‬ ‫مف‬ ‫متكونة‬ ‫جممة‬ ‫ئة‬ ‫لتجز‬ ‫العامة‬ ‫القاعدة‬ ‫الى‬ ‫وتوصمنا‬ ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫الهجينة‬ ‫مورس‬ ‫شفرة‬ The hybrid Morse code ‫ىي‬ ‫الناتجة‬ ‫ئة‬ ‫فالتجز‬ : (1,1,2,4,4,5,5,6,6,7,8,8,9,10,10,11,11,11,11,12,12,12,14,16,18,23,24, 24,25,25,29,33,34,34,34,34,35,35,36,37,38,38,38). ‫في‬ ‫الكممات‬ ‫مف‬ ‫عدد‬ ‫ألي‬ ‫العامة‬ ‫القاعدة‬ ‫إلى‬ ‫نتوصؿ‬ ‫يقة‬ ‫الطر‬ ‫بنفس‬ ‫ار‬ ‫باإلستمر‬ ‫وىكذا‬ ‫اآلتي‬ ‫تمثؿ‬ ‫التي‬ ‫و‬ ‫ما‬ ‫جممة‬ : ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫الهجينة‬ ‫مورس‬ ‫شفرة‬ The hybrid Morse code ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫مالحظة‬ ‫المعدلة‬ ‫مورس‬ ‫ة‬ ‫بشفر‬ ‫البحث‬ ‫ىذا‬ ‫تسمية‬ ‫تكوف‬ ‫اف‬ ً ‫ايضا‬ ‫المحتمؿ‬ ‫مف‬ : (The modified Morse code) ‫اليجيف‬ ‫اف‬ ‫اعتبار‬ ‫عمى‬ ‫الباحثيف‬ ‫بعض‬ ‫عند‬ ‫مالئمة‬ ‫اكثر‬ ‫نفسيا‬ ‫ة‬ ‫الشفر‬ ‫مابيف‬ ‫يج‬ ‫مز‬ ‫بانو‬ ‫البداية‬ ‫مف‬ ‫فيو‬ ‫نا‬ ‫مافكر‬ ‫وىذا‬ ‫مختمفتيف‬ ‫مادتيف‬ ‫دمج‬ ‫عمى‬ ‫يطمؽ‬ ‫االعداد‬ ‫ية‬ ‫ونظر‬ ، ‫الجنس‬ ‫نفس‬ ‫مف‬ ‫فيي‬ ‫المعدلة‬ ‫كممة‬ ‫أما‬ ، ‫اضافة‬ ‫أف‬ ‫ير‬ ‫قد‬ ‫الباحثيف‬ ‫بعض‬ ‫الف‬ dash ‫و‬ dot ‫االسـ‬ ‫بيذا‬ ‫تسميتيا‬ ‫ممكف‬ ‫وبالتالي‬ ‫الجنس‬ ‫نفس‬ ‫مف‬ ‫ىي‬ . ...
The hybrid Morse code
Article
Full-text available
  • Mar 2019
In this research, Morse code was introduced in a new type, which we called the hybrid to be appropriate between the code itself and the theory of fragmentation, which could later be used as a type of encryption in messages between two or more parties.
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... (2) (1,1,2) (2,2,2,2) = ((2,2,2,2),((1+(6-4)),(1+(6-4)),(2+(6-4))),(2+(11-7))) = (2,2,2,2,3,3,4,6). (3,7,8,9,9,11,11,12,12,12,14,14,17 ...
... ‫األولى‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬ ‫أخذنا‬(1,1,2,4,4,5,5,5,6,6,6,7,8,8,9,10,10,11,11,11,11,12,12,12,14,16,18) ‫الثانية‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬ ‫ثـ‬ (4,5,5,6,6) ‫ع‬ ‫منو‬ ً ‫مطروحا‬ ‫األولى‬ ‫الكممة‬ ‫(طوؿ‬ ‫الييا‬ ً ‫مضافا‬ ‫العقد‬ ‫دد‬ ‫قيمتو‬ ‫الذي‬ ‫و‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫الى‬ ‫باإلضافة‬ ‫الكممة‬ ‫ىذه‬ ‫في‬ 0 ‫ثـ‬ ) ‫الثالثة‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬(3,7,8,8,8,8,9,9,10,11,12,12,12) ‫الكممة‬ ‫طوؿ‬ ‫مجموع‬ ‫الييا‬ ً ‫مضافا‬ ‫ا‬ ‫باإلضافة‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممتيف‬ ‫في‬ ‫العقد‬ ‫عدد‬ ‫منو‬ ً ‫مطروحا‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫قـ‬ ‫الر‬ ‫لى‬ 4 ‫الذي‬ ‫و‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫و‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫قيمة‬ ‫مجموع‬ ‫يمثؿ‬ ‫الثالثة‬ ‫و‬ ‫الثانية‬ ، ‫كاآلتي:‬ ‫كممات‬ ‫ثالث‬ ‫مف‬ ‫متكونة‬ ‫جممة‬ ‫ئة‬ ‫لتجز‬ ‫العامة‬ ‫القاعدة‬ ‫الى‬ ‫وتوصمنا‬ ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫الهجينة‬ ‫مورس‬ ‫شفرة‬ The hybrid Morse code ‫ىي‬ ‫الناتجة‬ ‫ئة‬ ‫فالتجز‬ : (1,1,2,4,4,5,5,6,6,7,8,8,9,10,10,11,11,11,11,12,12,12,14,16,18,23,24, 24,25,25,29,33,34,34,34,34,35,35,36,37,38,38,38). ‫في‬ ‫الكممات‬ ‫مف‬ ‫عدد‬ ‫ألي‬ ‫العامة‬ ‫القاعدة‬ ‫إلى‬ ‫نتوصؿ‬ ‫يقة‬ ‫الطر‬ ‫بنفس‬ ‫ار‬ ‫باإلستمر‬ ‫وىكذا‬ ‫اآلتي‬ ‫تمثؿ‬ ‫التي‬ ‫و‬ ‫ما‬ ‫جممة‬ : ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫الهجينة‬ ‫مورس‬ ‫شفرة‬ The hybrid Morse code ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫مالحظة‬ ‫المعدلة‬ ‫مورس‬ ‫ة‬ ‫بشفر‬ ‫البحث‬ ‫ىذا‬ ‫تسمية‬ ‫تكوف‬ ‫اف‬ ً ‫ايضا‬ ‫المحتمؿ‬ ‫مف‬ : (The modified Morse code) ‫اليجيف‬ ‫اف‬ ‫اعتبار‬ ‫عمى‬ ‫الباحثيف‬ ‫بعض‬ ‫عند‬ ‫مالئمة‬ ‫اكثر‬ ‫نفسيا‬ ‫ة‬ ‫الشفر‬ ‫مابيف‬ ‫يج‬ ‫مز‬ ‫بانو‬ ‫البداية‬ ‫مف‬ ‫فيو‬ ‫نا‬ ‫مافكر‬ ‫وىذا‬ ‫مختمفتيف‬ ‫مادتيف‬ ‫دمج‬ ‫عمى‬ ‫يطمؽ‬ ‫االعداد‬ ‫ية‬ ‫ونظر‬ ، ‫الجنس‬ ‫نفس‬ ‫مف‬ ‫فيي‬ ‫المعدلة‬ ‫كممة‬ ‫أما‬ ، ‫اضافة‬ ‫أف‬ ‫ير‬ ‫قد‬ ‫الباحثيف‬ ‫بعض‬ ‫الف‬ dash ‫و‬ dot ‫االسـ‬ ‫بيذا‬ ‫تسميتيا‬ ‫ممكف‬ ‫وبالتالي‬ ‫الجنس‬ ‫نفس‬ ‫مف‬ ‫ىي‬ . ...
... ‫األولى‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬ ‫أخذنا‬(1,1,2,4,4,5,5,5,6,6,6,7,8,8,9,10,10,11,11,11,11,12,12,12,14,16,18) ‫الثانية‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬ ‫ثـ‬ (4,5,5,6,6) ‫ع‬ ‫منو‬ ً ‫مطروحا‬ ‫األولى‬ ‫الكممة‬ ‫(طوؿ‬ ‫الييا‬ ً ‫مضافا‬ ‫العقد‬ ‫دد‬ ‫قيمتو‬ ‫الذي‬ ‫و‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫الى‬ ‫باإلضافة‬ ‫الكممة‬ ‫ىذه‬ ‫في‬ 0 ‫ثـ‬ ) ‫الثالثة‬ ‫الكممة‬ ‫ئة‬ ‫تجز‬(3,7,8,8,8,8,9,9,10,11,12,12,12) ‫الكممة‬ ‫طوؿ‬ ‫مجموع‬ ‫الييا‬ ً ‫مضافا‬ ‫ا‬ ‫باإلضافة‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممتيف‬ ‫في‬ ‫العقد‬ ‫عدد‬ ‫منو‬ ً ‫مطروحا‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫قـ‬ ‫الر‬ ‫لى‬ 4 ‫الذي‬ ‫و‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫و‬ ‫الثانية‬ ‫و‬ ‫األولى‬ ‫الكممة‬ ‫بيف‬ ‫المحصور‬ ‫اغ‬ ‫الفر‬ ‫قيمة‬ ‫مجموع‬ ‫يمثؿ‬ ‫الثالثة‬ ‫و‬ ‫الثانية‬ ، ‫كاآلتي:‬ ‫كممات‬ ‫ثالث‬ ‫مف‬ ‫متكونة‬ ‫جممة‬ ‫ئة‬ ‫لتجز‬ ‫العامة‬ ‫القاعدة‬ ‫الى‬ ‫وتوصمنا‬ ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫الهجينة‬ ‫مورس‬ ‫شفرة‬ The hybrid Morse code ‫ىي‬ ‫الناتجة‬ ‫ئة‬ ‫فالتجز‬ : (1,1,2,4,4,5,5,6,6,7,8,8,9,10,10,11,11,11,11,12,12,12,14,16,18,23,24, 24,25,25,29,33,34,34,34,34,35,35,36,37,38,38,38). ‫في‬ ‫الكممات‬ ‫مف‬ ‫عدد‬ ‫ألي‬ ‫العامة‬ ‫القاعدة‬ ‫إلى‬ ‫نتوصؿ‬ ‫يقة‬ ‫الطر‬ ‫بنفس‬ ‫ار‬ ‫باإلستمر‬ ‫وىكذا‬ ‫اآلتي‬ ‫تمثؿ‬ ‫التي‬ ‫و‬ ‫ما‬ ‫جممة‬ : ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫الهجينة‬ ‫مورس‬ ‫شفرة‬ The hybrid Morse code ‫صديق‬ ‫عوار‬ ‫د.‬ ‫هحوود‬ ‫بكر‬ ‫اهيم‬ ‫إبر‬ ‫اوية‬ ‫ر‬ & ‫مالحظة‬ ‫المعدلة‬ ‫مورس‬ ‫ة‬ ‫بشفر‬ ‫البحث‬ ‫ىذا‬ ‫تسمية‬ ‫تكوف‬ ‫اف‬ ً ‫ايضا‬ ‫المحتمؿ‬ ‫مف‬ : (The modified Morse code) ‫اليجيف‬ ‫اف‬ ‫اعتبار‬ ‫عمى‬ ‫الباحثيف‬ ‫بعض‬ ‫عند‬ ‫مالئمة‬ ‫اكثر‬ ‫نفسيا‬ ‫ة‬ ‫الشفر‬ ‫مابيف‬ ‫يج‬ ‫مز‬ ‫بانو‬ ‫البداية‬ ‫مف‬ ‫فيو‬ ‫نا‬ ‫مافكر‬ ‫وىذا‬ ‫مختمفتيف‬ ‫مادتيف‬ ‫دمج‬ ‫عمى‬ ‫يطمؽ‬ ‫االعداد‬ ‫ية‬ ‫ونظر‬ ، ‫الجنس‬ ‫نفس‬ ‫مف‬ ‫فيي‬ ‫المعدلة‬ ‫كممة‬ ‫أما‬ ، ‫اضافة‬ ‫أف‬ ‫ير‬ ‫قد‬ ‫الباحثيف‬ ‫بعض‬ ‫الف‬ dash ‫و‬ dot ‫االسـ‬ ‫بيذا‬ ‫تسميتيا‬ ‫ممكف‬ ‫وبالتالي‬ ‫الجنس‬ ‫نفس‬ ‫مف‬ ‫ىي‬ . ...
The Hybrid Morse code
Article
Full-text available
  • Feb 2018
In this paper, we introduce a new Morse code, we called hybrid, to be suitable between Morse code and partition theory.
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... Before we start applying Vigenere cipher to Syriac letters, we know that any person, who knows the Syriac language and the sequence of its letters, is able to break the cipher. So in this research, the researchers decided to rearrange the letters according to the partition and beads of each letter that were found by Sami and Mahmood [4]. It is arranged by knowing the number of beads formed for each letter, then we start from the letter that has the lowest number, gradually to the last letter that has the most number of beads. ...
... For example, the letter A, when repeated, becomes a new sequence A '. Syriac letters and symbols will be arranged in the same way we did in (3) depending on the number of beads and partition of each letter. In [4], only Syriac letters partition has been found, since we added new symbols, so we need to find partition for it, as shown below (Fig. 4). ...
Encoding syriac letters in partition theory using extended Vigenere cipher
Article
Full-text available
  • Feb 2020
Since the topic of e-Abacus diagram appeared in 1978 through its application within the partition theory, where this representation was one of the ideas of cryptography, many researchers study this subject from a purely theoretical perspective without practical application to it. Many researchers have shown interest in it by starting to apply purely mathematically, but starting in the past few years they have been searching for ideas that serve the topic. This research deals with the Vigenere Cipher, which is one of the multi­alphabet ciphers and in the past it was one of the most popular ciphers. For its simplicity and resistance to frequency analysis tests for messages encoded with simple ciphers such as Caesar’s Cipher through. Its application to the Syriac letters, which is one of the oldest ancient languages, used exclusively when reading religious hymns, for Christians in some regions of the world and in other regions as a trading language. In 2017 it was carefully studied through the above diagram and made the application more confidential among its users in terms of trying to find a suitable agreement between the English language letters and Syriac. Special signs and symbols were used in the Syriac language to be able to address the problem of the difference in the number of letters between the two languages. As well as the possibility of using the Cipher between the letters of the Syriac language
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... Before we start applying Vigenere cipher to Syriac letters, we know that any person, who knows the Syriac language and the sequence of its letters, is able to break the cipher. So in this research, the researchers decided to rearrange the letters according to the partition and beads of each letter that were found by Sami and Mahmood [4]. It is arranged by knowing the number of beads formed for each letter, then we start from the letter that has the lowest number, gradually to the last letter that has the most number of beads. ...
... For example, the letter A, when repeated, becomes a new sequence A '. Syriac letters and symbols will be arranged in the same way we did in (3) depending on the number of beads and partition of each letter. In [4], only Syriac letters partition has been found, since we added new symbols, so we need to find partition for it, as shown below (Fig. 4). ...
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... The subject of the main diagram that has been expanded by Mahmood and others [8] presented new additions that resulted in more important topics. Also, new additions to the topic of partition theory and β-numbers [9] led to the emergence of the idea of coding the Syriac letters in 2017 [10,11]. In 2018 and 2019, both Mahmood and Mahmood [12,13] presented the idea of coding English letters and, where adding these letters according to the rule was remarkably useful. ...
Splitting the e-Abacus Diagram in the Partition Theory
Research
Full-text available
  • Nov 2021
In the partition theory, there is more then one form of representation of dedication, most notably the Abacus diagram, which gives an accurate and specific description. In the year 2019, Mahmood and Mahmood presented the idea of merging more than two plans, and then the following question was raised: Is the process of separating any somewhat large diagram into smaller schemes possible? The general formula to split e-abacus diagram into two or more equal or unequal parts was achieved in this study now.
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... This will provide later the possibility of adopting it as a type of encoding or encryption in many applications on the topic of partition, thus opening new horizons for scientific research in this direction. See [8][9][10][11][12][13][14][15]. ...
Replacing the Content in e-Abacus Diagram II
Article
Full-text available
  • Jul 2021
In our normal life, we sometimes need a process of replacing something with another to get out of the stereotype. From this point of view, Mahmood’s attempted in the year 2020 to replace the content in the first main e-abacus diagram. He found the general rule for finding the value of the new partition after the replacement from the original partition. Here we raise the question: Can we find the appropriate mechanisms for the remainder of the main e-abacus diagram?
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... The partition theory has a big role as there is no past research in this domain being the regulator to code (or Secret -Word) a word. We would like to mention that [1] was to study the code subject by using an (unknown) language to many, which is the Syriac language (that resemble the Arabic language by having merged letters and each letter three ways to written depending on its position in the word, in the beginning, middle and the end of the words) and this idea with different vision than what is found in this paper. Let be a positive integer. ...
Secret-word by e-abacus diagram I
Article
Full-text available
  • Nov 2018
This experiment may be applied before with certain and special roles, but never applied under partition theory (Abacus James Diagram) conditions. Therefore, we would have to find an appropriate design for each character to enable us sending a word represented as increasing number with meaning only for beneficiaries. © 2019, University of Baghdad-College of Science. All rights reserved.
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On The Intersection of Young's Diagrams Core
Article
Full-text available
  • Jan 2010
In this paper, we will introduce the method of intersection of -numbers for any partition of a non-negative integer . The results of this intersection are represented and specificated the exactly position according to a "guide value" and a "main diagram". By using the same method we will create a new way for this intersection after finding the core of each "guide".
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Remarks of the intersection of Youngs diagrams core
Article
Full-text available
  • Sep 2012
In this research, many simple new techniques will be used supported by numerical and theoretical proofs of the methods of the intersection of beta- number for any partition mu of r; which represented by Mahmood in 2010, in which he could appoint the location and the number of beads using "Guide Value" and " The Main Diagram" methods.
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(Upside-down Direct rotation) beta-numbers
Article
Full-text available
  • Feb 2014
For any /mu of a non- negative integer number r, there exist a diagram (A) of /beta - numbers for each e, where e is a positive integer number greater than or equal to 2; which introduced by James in 1978. These diagrams (A) play an enormous role in Iwahori-Hecke algebras and q-Schur algebras; as presented by Fayers in 2007. Mahmood gave new diagrams by applying the upside down application on the main diagram (A) in 2013. Another new diagrams were presented by the authors by applying the direct rotation application on the main diagram (A) in 2013. In the present paper, we introduced some other new diagrams (A1), ( A2) and (A3) by employing the composition of upside down application with direct rotation application of 3 different degrees namely 90, 180 and 270 degrees respectively on the main diagram (A). We concluded that we can find the successive main diagrams (A1), (A2) and (A3) for the guides b2, b3...and be depending on the main diagrams (A1), ( A2) and ( A3) for b1 and set these facts as results named Rule (3.1.2), (3.2.2) and (3.3.2) respectively.
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Nested chain movement of length 1 of beta number in James Abacus diagram
Article
Full-text available
  • Jan 2016
James abacus diagram is a graphical representation for any partition μ of a positive integer t. One way of producing the diagram is by using beta number with the special number of even columns e, where e ≥ 2. This paper constructs a new method for partition μ with a single motion of nested chain movement of length 1 in James abacus diagram. First, the establishment of an arithmetic sequence among the nested chains of the diagram position is considered. Then, for the movement, we select several beta numbers as the initial points in every chain. The location of the rest of the beta numbers in the James abacus diagram would be changed anticlockwise by length 1 accordingly when the positions of initial beta numbers are changed. Using these new nested chains, a new diagram Atc1 that displays a new partition, is constructed. Furthermore, guides, which are finite number of partitions that are obtained from the original partition after adding zeros, are developed. The number of common beta numbers among these developed guides are then determined. We have established rules to obtain new diagram using a single motion of nested chain movement of length 1. The new diagram can be used in areas of number theory and design. Finally, the proposed method is employed as a special type of James abacus diagram where the number of columns is an even integer smaller than the number of rows in the diagram.
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Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group
Article
Full-text available
  • Jul 1998
These notes give a fully self--contained introduction to the (modular) representation theory of the Iwahori--Hecke algebras and the q--Schur algebras of the symmetric groups. The central aim of this work is to give a concise, but complete, and an elegant, yet quick, treatment of the classification of the simple modules and of the blocks of these two important classes of algebras. I don't know where RG got this PDF file from. It is a preliminary version and differs substantially from the published version.
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Some combinatorial results involving Young diagrams
Article
In the first half of this paper we introduce a new method of examining the q-hook structure of a Young diagram, and use it to prove most of the standard results about q-cores and q-quotients. In particular, we give a quick new proof of Chung's Conjecture (2), which determines the number of diagrams with a given q-weight and says how many of them are q-regular. In the case where q is prime, this tells us how many ordinary and q-modular irreducible representations of the symmetric group there are in a given q-block. None of the results of section 2 is original. In the next section we give a new definition, the p-power diagram, which is closely connected with the p-quotient. This concept is interesting because when p is prime a condition involving the p-power diagram appears to be a necessary and sufficient criterion for the diagram to be p-regular and the corresponding ordinary irreducible representation of to remain irreducible modulo p. In this paper we derive combinatorial results involving the p-power diagram, and in a later article we investigate the relevant representation theory.(Received March 29 1977)
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  • Jan 2006
  • R Rollinger
R.Rollinger. (2006); "The Terms Assyria and Syria Again ", JNES Vol. 65, no. 4. .