The Mapping Order (spin 17)
This section is referring to wiki page-19 of gist section-15 that is inherited from the gist section-103 by prime spin-28 and span- with the partitions as below.
/lexer
Rational Objects
In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n. Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).
The central problem is to determine when a Diophantine equation has solutions, and if it does, how many. Two examples of an elliptic curve, that is, a curve of genus 1 having at least one rational point. Either graph can be seen as a slice of a torus in four-dimensional space (Wikipedia).
One of the main reason is that one does not yet have a mathematically complete example of a quantum gauge theory in four-dimensional space-time. It is even a sign that Einstein's equations on the energy of empty space are somehow incomplete.
Throughout his life, Einstein published hundreds of books and articles. He published more than 300 scientific papers and 150 non-scientific ones. On 5 December 2014, universities and archives announced the release of Einstein’s papers, comprising more than 30,000 unique documents (Wikipedia).
Speculation is that the unfinished book of Ramanujan's partition, series of Dyson's solutions and hugh of Einstein's papers tend to solve it.
Dyson introduced the concept in the context of a study of certain congruence properties of the partition function discovered by the mathematician Srinivasa Ramanujan who the one that found the interesting behaviour of the taxicab number 1729.
The concept was introduced by Freeman Dysonin a paper published in the journal Eureka. It was presented in the context of a study of certain congruence properties of the partition function discovered by the Indian mathematical genius Srinivasa Ramanujan. (Wikipedia)
Young tableaux were introduced by Alfred Young, a mathematician at Cambridge University, in 1900. They were then applied to the study of the symmetric group. Their theory was further developed by many mathematicians, including W. V. D. Hodge
In number theory and combinatorics, rank of a partition of a positive integer is a certain integer associated with the partition meanwhile the crank of a partition of an integer is a certain integer associated with that partition (Wikipedia).
Supersymmetry
In mathematics, the rank of a partition is the number obtained by subtracting the number of parts in the partition from the largest part in the partition.
On the other hand, one does not yet have a mathematically complete example of a quantum gauge theory in 4D Space vs Time, nor even a precise definition of quantum gauge theory in four dimensions. Will this change in the 21st century? We hope so! (Clay Institute’s - Official problem description).
25 + 19 + 13 + 7 = 64 = 8 × 8 = 8²
The True Prime Pairs:
(5,7), (11,13), (17,19)
|--------------- 7¤ ---------------|
|-------------- {89} --------------|👈
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
| 5 | 7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 |{18}| 18 | 12 |{13}|
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
∆ ∆ |---- {48} ----|---- {48} ----|---- {43} ----|👈
7 13 |----- 3¤ -----|----- 3¤ -----|----- 3¤ -----|
|-------------------- 9¤ --------------------|
∆ |-- 25 ---|
19 ∆
5 x 5
SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet’s 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition
Family Number Group +3, +6, +9 being activated by the Aetheron Flux Monopole Emanations, creating Negative Draft Counterspace, Motion and Nested Vortices.) (RodinAerodynamics)
This idea was taken as the earliest in 1960s Swinnerton-Dyer by using the University of Cambridge Computer Laboratory to get the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known.
From these numerical results the conjecture predicts that the data should form a line of slope equal to the rank of the curve, which is 1 in this case drawn in red in red on the graph (Wikipedia).
Dyson discovered that the eigenvalue of these matrices are spaced apart in exactly the same manner as _[Mo Unfortunately the rotation of this eigenvalues deals with four-dimensional space-time which was already a big issue.
In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture.
Perelman’s proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries (ClayMath Institute).
More generally, the central problem is to determine when an equation in n-dimensional space has solutions. However at this point, we finaly found that the prime distribution has something to do with the subclasses of rank and crank partitions.
Ricci Flow
0 (1, 1) blue_0 ◄--- 0
1 (1, 1) blue_1
2 (1, 1) blue_2
3 (1, 1) blue_3
4 (1, 1) blue_4
5 (2, 1) purple_5
6 (2, 1) purple_0
7 (3, 1) red_1
8 (3, 1) red_2
9 (3, 1) red_3
10 (3, 1) red_4
11 (4, 1) yellow_5
12 (4, 1) yellow_0
13 (5, 1) green_1
14 (5, 1) green_2
15 (5, 1) green_3
16 (5, 1) green_4
17 (0, 1) cyan_5
18 (0, 1) cyan_0 ◄--- 18
19 (1, 1) blue_1
20 (1, 1) blue_2
21 (1, 1) blue_3
22 (1, 1) blue_4
23 (2, 1) purple_5
24 (2, 1) purple_0
25 (2, 1) purple_1
26 (2, 1) purple_2
27 (2, 1) purple_3
28 (2, 1) purple_4
29 (2, -1) blue_5
30 (2, -1) blue_0 ◄--- 30
31 (1, -1) cyan_1
32 (1, -1) cyan_2
33 (1, -1) cyan_3
34 (1, -1) cyan_4
35 (1, -1) cyan_5
36 (1, -1) cyan_0 ◄--- 36
37 (1, 1) blue_1
38 (1, 1) blue_2
39 (1, 1) blue_3
40 (1, 1) blue_4
41 (2, 1) purple_5
42 (2, 1) purple_0
43 (3, 1) red_1
44 (3, 1) red_2
45 (3, 1) red_3
46 (3, 1) red_4
47 (4, 1) yellow_5
48 (4, 1) yellow_0
49 (4, 1) yellow_1
50 (4, 1) yellow_2
51 (4, 1) yellow_3
52 (4, 1) yellow_4
53 (4, -1) red_5
54 (4, -1) red_0
55 (4, -1) red_1
56 (4, -1) red_2
57 (4, -1) red_3
58 (4, -1) red_4
59 (4, 1) yellow_5
60 (4, 1) yellow_0
61 (5, 1) green_1
62 (5, 1) green_2
63 (5, 1) green_3
64 (5, 1) green_4
65 (5, 1) green_5
66 (5, 1) green_0
67 (5, -1) yellow_1
68 (5, -1) yellow_2
69 (5, -1) yellow_3
70 (5, -1) yellow_4
71 (4, -1) red_5
72 (4, -1) red_0
73 (3, -1) purple_1
74 (3, -1) purple_2
75 (3, -1) purple_3
76 (3, -1) purple_4
77 (3, -1) purple_5
78 (3, -1) purple_0
79 (3, 1) red_1
80 (3, 1) red_2
81 (3, 1) red_3
82 (3, 1) red_4
83 (4, 1) yellow_5
84 (4, 1) yellow_0
85 (4, 1) yellow_1
86 (4, 1) yellow_2
87 (4, 1) yellow_3
88 (4, 1) yellow_4
89 (4, -1) red_5
90 (4, -1) red_0
91 (4, -1) red_1
92 (4, -1) red_2
93 (4, -1) red_3
94 (4, -1) red_4
95 (4, -1) red_5
96 (4, -1) red_0
97 (3, -1) purple_1
98 (3, -1) purple_2
99 (3, -1) purple_3
100 (3, -1) purple_4
101 (2, -1) blue_5
102 (2, -1) blue_0 ◄--- 102
-----
103 (1, -1) cyan_1
104 (1, -1) cyan_2
105 (1, -1) cyan_3
106 (1, -1) cyan_4
107 (0, -1) green_5
108 (0, -1) green_0
109 (5, -1) yellow_1
110 (5, -1) yellow_2
111 (5, -1) yellow_3
112 (5, -1) yellow_4
113 (4, -1) red_5
114 (4, -1) red_0
115 (4, -1) red_1
116 (4, -1) red_2
117 (4, -1) red_3
118 (4, -1) red_4
119 (4, -1) red_5
120 (4, -1) red_0
121 (4, -1) red_1
122 (4, -1) red_2
123 (4, -1) red_3
124 (4, -1) red_4
125 (4, -1) red_5
126 (4, -1) red_0
127 (3, -1) purple_1
128 (3, -1) purple_2
129 (3, -1) purple_3
130 (3, -1) purple_4
131 (2, -1) blue_5
132 (2, -1) blue_0
133 (2, -1) blue_1
134 (2, -1) blue_2
135 (2, -1) blue_3
136 (2, -1) blue_4
137 (2, 1) purple_5
138 (2, 1) purple_0
139 (3, 1) red_1
140 (3, 1) red_2
141 (3, 1) red_3
142 (3, 1) red_4
143 (3, 1) red_5
144 (3, 1) red_0
145 (3, 1) red_1
146 (3, 1) red_2
147 (3, 1) red_3
148 (3, 1) red_4
149 (4, 1) yellow_5
150 (4, 1) yellow_0
151 (5, 1) green_1
152 (5, 1) green_2
153 (5, 1) green_3
154 (5, 1) green_4
155 (5, 1) green_5
156 (5, 1) green_0
157 (5, -1) yellow_1
158 (5, -1) yellow_2
159 (5, -1) yellow_3
160 (5, -1) yellow_4
161 (5, -1) yellow_5
162 (5, -1) yellow_0
163 (5, 1) green_1
164 (5, 1) green_2
165 (5, 1) green_3
166 (5, 1) green_4
167 (0, 1) cyan_5
168 (0, 1) cyan_0 ◄--- 168=π(1000)
p r i m e s
1 0 0 0 0 0
2 1 0 0 0 1
3 2 0 1 0 2
4 3 1 1 0 3
5 5 2 1 0 5
6 7 3 1 0 7
7 11 4 1 0 11
8 13 5 1 0 13
9 17 0 1 1 17 ◄--- has a total of 18-7 = 11 composite √
10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
-----
11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19
12 29 2 -1 1 ∆3 ◄--- 2nd ∆prime ◄--- Fibonacci Index #20
13 31 1 -1 1 ∆4
14 37 1 1 1 ∆5 ◄--- 3th ∆prime ◄--- Fibonacci Index #21
15 41 2 1 1 ∆6
16 43 3 1 1 ∆7 ◄--- 4th ∆prime ◄--- Fibonacci Index #22
17 47 4 1 1 ∆8
18 53 4 -1 1 ∆9
19 59 4 1 1 ∆10
20 61 5 1 1 ∆11 ◄--- 5th ∆prime ◄--- Fibonacci Index #23
21 67 5 -1 1 ∆12
22 71 4 -1 1 ∆13 ◄--- 6th ∆prime ◄--- Fibonacci Index #24
23 73 3 -1 1 ∆14
24 79 3 1 1 ∆15
25 83 4 1 1 ∆16
26 89 4 -1 1 ∆17 ◄--- 7th ∆prime ◄--- Fibonacci Index #25
27 97 3 -1 1 ∆18
28 101 2 -1 1 ∆19 ◄--- 8th ∆prime ◄--- Fibonacci Index #26
29 103 1 -1 1 ∆20
30 107 0 -1 1 ∆21
31 109 5 -1 0 ∆22
32 113 4 -1 0 ∆23 ◄--- 9th ∆prime ◄--- Fibonacci Index #27
33 127 3 -1 0 ∆24
34 131 2 -1 0 ∆25
35 137 2 1 0 ∆26
36 139 3 1 0 ∆27
37 149 4 1 0 ∆28
38 151 5 1 0 ∆29 ◄--- 10th ∆prime ◄--- Fibonacci Index #28
39 157 5 -1 0 ∆30
40 163 5 1 0 ∆31 ◄--- 11th ∆prime ◄--- Fibonacci Index #29
-----
41 167 0 1 1 ∆0
42 173 0 -1 1 ∆1
43 179 0 1 1 ∆2 ◄--- ∆∆1
44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
45 191 2 1 1 ∆4
46 193 3 1 1 ∆5 ◄--- ∆∆3 ◄--- 2nd ∆∆prime ◄--- Fibonacci Index #31
47 197 4 1 1 ∆6
48 199 5 1 1 ∆7 ◄--- ∆∆4
49 211 5 -1 1 ∆8
50 223 5 1 1 ∆9
51 227 0 1 2 ∆10
52 229 1 1 2 ∆11 ◄--- ∆∆5 ◄--- 3rd ∆∆prime ◄--- Fibonacci Index #32
53 233 2 1 2 ∆12
54 239 2 -1 2 ∆13 ◄--- ∆∆6
55 241 1 -1 2 ∆14
56 251 0 -1 2 ∆15
57 257 0 1 2 ∆16
58 263 0 -1 2 ∆17 ◄--- ∆∆7 ◄--- 4th ∆∆prime ◄--- Fibonacci Index #33
59 269 0 1 2 ∆18
60 271 1 1 2 ∆19 ◄--- ∆∆8
61 277 1 -1 2 ∆20
62 281 0 -1 2 ∆21
63 283 5 -1 1 ∆22
64 293 4 -1 1 ∆23 ◄--- ∆∆9
65 307 3 -1 1 ∆24
66 311 2 -1 1 ∆25
67 313 1 -1 1 ∆26
68 317 0 -1 1 ∆27
69 331 5 -1 0 ∆28
70 337 5 1 0 ∆29 ◄--- ∆∆10
71 347 0 1 1 ∆30
72 349 1 1 1 ∆31 ◄--- ∆∆11 ◄--- 5th ∆∆prime ◄--- Fibonacci Index #34
73 353 2 1 1 ∆32
74 359 2 -1 1 ∆33
75 367 1 -1 1 ∆34
76 373 1 1 1 ∆35
77 379 1 -1 1 ∆36
78 383 0 -1 1 ∆37 ◄--- ∆∆12
79 389 0 1 1 ∆38
80 397 1 1 1 ∆39
81 401 2 1 1 ∆40
82 409 3 1 1 ∆41 ◄--- ∆∆13 ◄--- 6th ∆∆prime ◄--- Fibonacci Index #35
83 419 4 1 1 ∆42
84 421 5 1 1 ∆43 ◄--- ∆∆14
85 431 0 1 2 ∆44
86 433 1 1 2 ∆45
87 439 1 -1 2 ∆46
88 443 0 -1 2 ∆47 ◄--- ∆∆15
89 449 0 1 2 ∆48
90 457 1 1 2 ∆49
91 461 2 1 2 ∆50
92 463 3 1 2 ∆51
93 467 4 1 2 ∆52
94 479 4 -1 2 ∆53 ◄--- ∆∆16
95 487 3 -1 2 ∆54
96 491 2 -1 2 ∆55
97 499 1 -1 2 ∆56
98 503 0 -1 2 ∆57
99 509 0 1 2 ∆58
100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36
-----
101 523 5 -1 1 ∆2 ◄--- ∆∆18 ◄--- 1st ∆∆∆prime ◄--- Fibonacci Index #37 √
102 541 5 1 1 ∆3 ◄--- ∆∆∆1 ◄--- 1st ÷÷÷composite ◄--- Index #(37+2)=#39 √
103 547 5 -1 1 ∆4
104 557 4 -1 1 ∆5 ◄--- ∆∆∆2 ◄---2nd ∆∆∆prime √
105 563 4 1 1 ∆6
106 569 4 -1 1 ∆7 ◄--- ∆∆∆3 ◄--- 3rd ∆∆∆prime √
107 571 3 -1 1 ∆8
108 577 3 1 1 ∆9
109 587 4 1 1 ∆10
110 593 4 -1 1 ∆11 ◄--- ∆∆∆4 ◄--- 2nd ÷÷÷composite ◄--- Index #(37+3)=#40 √
111 599 4 1 1 ∆12
112 601 5 1 1 ∆13 ◄--- ∆∆∆5 ◄--- 4th ∆∆∆prime √
113 607 5 -1 1 ∆14
114 613 5 1 1 ∆15
115 617 0 1 2 ∆16
116 619 1 1 2 ∆17 ◄--- ∆∆∆6 ◄--- 3rd ÷÷÷composite ◄--- Index #(37+5)=#42 √
117 631 1 -1 2 ∆18
118 641 0 -1 2 ∆19 ◄--- ∆∆∆7 ◄--- 5th ∆∆∆prime √
119 643 5 -1 1 ∆20
120 647 4 -1 1 ∆21
121 653 4 1 1 ∆22
122 659 4 -1 1 ∆23 ◄--- ∆∆∆8 ◄--- 4th ÷÷÷composite ◄--- Index #(37+7)=#44 √
123 661 3 -1 1 ∆24
124 673 3 1 1 ∆25
125 677 4 1 1 ∆26
126 683 4 -1 1 ∆27
127 691 3 -1 1 ∆28
128 701 2 -1 1 ∆29 ◄--- ∆∆∆9 ◄--- 5th ÷÷÷composite ◄--- Index #(37+11)=#48 √
129 709 1 -1 1 ∆30
130 719 0 -1 1 ∆31 ◄--- ∆∆∆10 ◄--- 6th ÷÷÷composite ◄--- Index #(37+13)=#50 √
131 727 5 -1 0 ∆32
132 733 5 1 0 ∆33
133 739 5 -1 0 ∆34
134 743 4 -1 0 ∆35
135 751 3 -1 0 ∆36
136 757 3 1 0 ∆37 ◄--- ∆∆∆11 ◄--- 6th ∆∆∆prime √
137 761 4 1 0 ∆38
138 769 5 1 0 ∆39
139 773 0 1 1 ∆40
140 787 1 1 1 ∆41 ◄--- ∆∆∆12 ◄--- 7th ÷÷÷composite ◄--- Index #(37+17)=#54 √
141 797 2 1 1 ∆42
142 809 2 -1 1 ∆43 ◄--- ∆∆∆13 ◄--- 7th ∆∆∆prime √
143 811 1 -1 1 ∆44
144 821 0 -1 1 ∆45
145 823 5 -1 0 ∆46
146 827 4 -1 0 ∆47 ◄--- ∆∆∆14 ◄--- 8th ÷÷÷composite ◄--- Index #(37+19)=#56 √
147 829 3 -1 0 ∆48
148 839 2 -1 0 ∆49
149 853 1 -1 0 ∆50
150 857 0 -1 0 ∆51
151 859 5 -1 -1 ∆52
152 863 4 -1 -1 ∆53 ◄--- ∆∆∆15 ◄--- 9th ÷÷÷composite ◄--- Index #(37+23)=#60 √
153 877 3 -1 -1 ∆54
154 881 2 -1 -1 ∆55
155 883 1 -1 -1 ∆56
156 887 0 -1 -1 ∆57
157 907 5 -1 -2 ∆58
158 911 4 -1 -2 ∆59 ◄--- ∆∆∆16 ◄--- 10th ÷÷÷composite ◄--- Index #(37+29)=#66 √
159 919 3 -1 -2 ∆60
169 929 2 -1 -2 ∆61 ◄--- ∆∆∆17 ◄--- 8th ∆∆∆prime √
161 937 1 -1 -2 ∆62
162 941 0 -1 -2 ∆63
163 947 0 1 -2 ∆64
164 953 0 -1 -2 ∆65
165 967 5 -1 -3 ∆66
166 971 4 -1 -3 ∆67 ◄--- ∆∆∆18 ◄--- 11th ÷÷÷composite ◄--- Index #(37+31)=#68 √
167 977 4 1 -3 ∆68
168 983 4 -1 -3 ∆69
169 991 3 -1 -3 ∆70
170 997 3 1 -32 ∆71 ◄--- ∆∆∆19 ◄--- 9th ∆∆∆prime √
The Ricci flow is a pde for evolving the metric tensor in a Riemannian manifold to make it rounder, in the hope that one may draw topological conclusions from the existence of such "round" metrics.
Poincaré hypothesized that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere (Wikipedia)
The Ricci Flow method has now been developed not only in to geometric but also to the conversion of facial shapes in three (3) dimensions to computer data. A big leap in the field of AI (Artificial intelligence). No wonder now all the science leads to it.
So what we've discussed on this wiki is entirely nothing but an embodiment of this solved Poincare Conjecture. This is the one placed with id: 10 (ten) which stands as the basic algorithm of π(10)=(2,3,5,7).
Many relevant topics, such as trustworthiness, explainability, and ethics are characterized by implicit anthropocentric and anthropomorphistic conceptions and, for instance, the pursuit of human-like intelligence. AI is one of the most debated subjects of today and there seems little common understanding concerning the differences and similarities of human intelligence and artificial intelligence (Human vs AI).
Finite collections of objects are considered 0-dimensional. Objects that are "dragged" versions of zero-dimensional objects are then called one-dimensional. Similarly, objects which are dragged one-dimensional objects are two-dimensional, and so on.
The basic ideas leading up to this result (including the dimension invariance theorem, domain invariance theorem, and Lebesgue covering dimension) were developed by Poincaré, Brouwer, Lebesgue, Urysohn, and Menger (MathWorld).
Spacetime Patterns
329 + 109 + 109 + 71 = 329 + 289 = 618 = 1000/1.618 = 1000/φ
2 + 60 + 40 = 102
1st layer:
It has a total of 1000 numbers
Total primes = π(1000) = 168 primes
2nd layer:
It will start by π(168)+1 as the 40th prime
It has 100x100 numbers or π(π(10000)) = 201 primes
Total cum primes = 168 + (201-40) = 168+161 = 329 primes
3rd layer:
Behave reversal to 2nd layer which has a total of 329 primes
The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
This 1000 primes will become 1000 numbers by 1st layer of the next level
Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1
In vector calculus, the Jacobian matrix of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.
It’s possible to build a Hessian matrix for a Newton’s method step using the Jacobian method. You would first flatten out its axes into a matrix, and flatten out the gradient into a vector. (Tensorflow)
When the subclasses of partitions are flatten out into a matrix, you want to take the Jacobian of each of a stack of targets with respect to a stack of sources, where the Jacobians for each target-source pair are independent.
When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant. Both the matrix and (if applicable) the determinant ad often referred to simply as the Jacobian in literature. (Wikipedia)
Double Strands
$True Prime Pairs:
(5,7), (11,13), (17,19)
| 168 | 618 |
-----+-----+-----+-----+-----+ ---
19¨ | 3¨ | 4¨ | 6¨ | 6¨ | 4¤ -----> assigned to "id:30" 19¨
-----+-----+-----+-----+-----+ ---
17¨ | 5¨ | 3¨ | .. | .. | 4¤ ✔️ ---> assigned to "id:31" |
+-----+-----+-----+-----+ |
{12¨}| .. | .. | 2¤ (M & F) -----> assigned to "id:32" |
+-----+-----+-----+ |
11¨ | .. | .. | .. | 3¤ ----> Np(33) assigned to "id:33" -----> 👉 77¨
-----+-----+-----+-----+-----+ |
19¨ | .. | .. | .. | .. | 4¤ -----> assigned to "id:34" |
+-----+-----+-----+-----+ |
{18¨}| .. | .. | .. | 3¤ -----> assigned to "id:35" |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
43¨ | .. | .. | .. | .. | .. | .. | .. | .. | .. | 9¤ (C1 & C2) 43¨
-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
139¨ | 1 2 3 | 4 5 6 | 7 8 9 |
Δ Δ Δ
Here we adopt an analysis of variance called N/P-Integration that was applied to find the best set of environmental variables that describe the density out of distance matrices.
With collaborators, we regularly work on projects where we want to understand the taxonomic and functional diversity of microbial community in the context of metadata often recorded under specific hypotheses. Integrating (N-/P- integration; see figure below) these datasets require a fair deal of multivariate statistical analysis for which I have shared the code on this website. (Umer.Ijaz)
It can be used to build parsers/compilers/interpreters for various use cases ranging from simple config files to full fledged programming languages.
With theoretical foundations in Information Engineering (Discrete Mathematics, Control Theory, System Theory, Information Theory, and Statistics), my research has delivered a suite of systems and products that has allowed me to carve out a niche within an extensive collaborative network (>200 academics). (Umer.Ijaz)
Since such interactions result in a change in momentum, they can give rise to classical Newtonian forces of rotation and revolution by means of orbital structure.
As you can see on the left sidebar (dekstop mode) a total of 102 items will be reached by the end of Id: 35.
So when they transfered to Id: 36 it will cover 11 x 6 = 66 items thus the total will be 102 + 66 = 168