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...The history of the global vaccination program in 1000+ peer reviewed reports and studies chronologically ordered and chaptered providing the reader with an understanding of disease outbreak, vaccine efficacy, the historic development of vaccines, unwanted contaminants, vacc...

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...onsists of more than 3 million primary source materials spanning the past 1,000 years of world history. As you know, much has happened in the last 1000 years. Events such as: The Evolution of English linguistics in Geoffrey Chaucer’s Canterbury Tales. The discovery, by Europeans, of the American continents. The European Renaissance. Johannes Gutenberg inventing ...

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...nsists of more than 3 million primary source materials spanning the past 1,000 years of world history. As you know, much has happened in the last 1000 years. Events such as: The Evolution of English linguistics in Geoffrey Chaucer’s Canterbury Tales. The discovery, by Europeans, of the American continents. The European Renaissance. Johannes Gutenberg inventin...

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...ng injury to your credit report and credit score. They have to pay a fine of $1000 if you prove them wrong. My creditor presented my credit histor... ... can charge them for violating the FCRA Section 611Part (A) (5) (B) (ii) for $1000. Back to Index We follow the Creative Commons Att... ... your collection agency can be sued for this. They will be charged a fine of $1000. What are the other situations when I can file a case against t...

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...s. “Every taim Jessie cams to see me I’ll tich her a trik to get faster to her 1000 entry stamps and to crieit the conecshen.” And then she sed she ... ...nish this leter, evey word wil get an entry stamp. Theoreticly, you nid abaoot 1000 leters to corect the words you are using in your leters.” It wa... ....” I traid fainding taim to doo ol this. “We want your eyes to see the words 1000 taims. It dazent mater how. Theoreticly if you rid samthing 1000... ...be eibel to rait ol the words properly. I hop you anderstand it is not exactly 1000. It can be much mor, but in two to three weeks you’ll see a difr...

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...e in the energy released by the tremor. An earthquake of magnitude 9 is, therefore, 1000 stronger than a tremor of magnitude 6. The Kobe earthquake ... ...namis affected locales as far as Crescent City, California. The fault extended for 1000 kilometers and there were tens of thousands of aftershocks.... .... Rose - discovered that the haleness of Native-Americans declined markedly in the 1000 years before Columbus "discovered" them. The vast majority... ...ace and damaged another 1.6 million. To recover them would cost $700 million. About 1000 tons of limestone in 3700 separate pieces were quarried in ... ... 3700 separate pieces were quarried in Indiana to overhaul the facade. More than a 1000 laborers worked in three shifts for almost nine months unti... ...mbs. In a cave is southern Utah, fluffy, fresh looking, white popcorn was dated to 1000 years ago. Popcorn was used by the Aztecs and Indians as... ...uthern Russia for Catherine the Great. The tour took 4 years to prepare and covered 1000 miles along the river Dnepr. Throngs of peasants welcomed ... ...ant squid. Giant squids (Architeuthis dux) - up to 20 meters long and one ton (1000 kilograms) heavy - are not fabulous sea monsters. They exis... .... The eyes of this beast - which stalks the darkness of the deepest seas, up to 1000 meters below the surface - are as big as human heads. The s...

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...eoul (1991). He also has two journals describing his emigration, with over 1000 pages and four plays, some of them written for children. One of these,...

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...h pleasant manners and good upbringing who would never steal up to the sum of $1000. However, if $10,000 were laid before him, his education might n...

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... Accordingly, we have protection against stealing a larger sum of money, say $1000. In such a case, we pass from the world of Assiya to the world of...

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... Lupton USA 2000 Wrongness of n vs n 0 100 200 300 400 500 600 700 800 900 1000 0 200 400 600 800 1000 n W(n) 2 To two stars: my doughters Gilda... ...iour is highly erratic. Fig. 1.1 Pseudo-Smarandache-Totient-Function 0 500 1000 1500 2000 2500 3000 3500 4000 1 88 175 262 349 436 523 610 697 784 871... ...ndache-Totient-Function 0 10 20 30 40 50 60 70 80 90 100 0 200 400 600 800 1000 n Zt(n) 7 A table of the Zt(n) values for 60 n 1 £ £ follows: n Zt(... ...Zt(n+k) are all increasing (decreasing respectively) values. For the first 1000 values of Zt(n) the largest found sequences have k=5 and k=4 respect... ...hat upper limit. Problem 2. Find the solution of Zt(n)=n For the first 1000 terms only for n=1, 2 and 5 the equation is satisfied. Are the solutio... ...n m Zt n Zt n L ˛ - - = , ) ( ) ( Hint: the experimental data on the first 1000 values of Zt(n) show a linear grows for the average value of n d . S... ...(n)|Zt(n+1) 2) Zt(n+1)|Zt(n) 12 Examining the first 1000 values of Zt(n), the following solutions to 1) have been found: Zt(1)... ...ber of those solutions limited or unlimited? Solutions to 2) for the first 1000 values of Zt(n): Zt(34)|Zt(33), Zt(46)|Zt(45), Zt(75)|Zt(74), Zt(86)|Z... ... n=11, 21, 22, 23, 28, 29, 32, 35, 42, 43, 46, 49, 51....... For 10000 1 £ £ n the equation ) ( ) ( n n Zt j = admits the following 9 solut...

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...ble 3. Table 2. The distribution of cycles for a few intervals of length 1000. Interval Cycle #1 Cycle #2 Cycle #3 Cycle #4 3 ≤ n ≤ 1002 572 3... ... Interval Cycle #1 Cycle #2 Cycle #3 Cycle #4 3 ≤ n ≤ 1002 572 358 70 - 10001 ≤ n ≤ 11000 651 159 190 - 100001 ≤ n ≤ 101000 759 100 141 0 10000... ...0 - 100001 ≤ n ≤ 101000 759 100 141 0 1000001 ≤ n ≤ 1001000 822 75 86 17 10000001 ≤ n ≤ 100001000 831 42 64 63 100000001 ≤ n ≤1000001000 812 52 4... ...esults. Interval I 2 I 3 Loop I 4 3-50000 18824 236 29757 1181 50001-100000 18255 57 30219 1469 100001-150000 17985 49 30307 1659 150001-200... ...850001-900000 18326 15 29338 2321 900001-950000 18271 24 29444 2261 950001-1000000 18517 31 29257 2195 Average 18335 38 29640 1987 Question nu... ...,2,…,18. 64 1 3 5 7 9 11 13 15 17 19 20 17 14 11 8 5 2 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000 z x y Dist... ...wing that a⋅10 α is divisible by 2 α . 10≡0 (mod 2) 100 ≡0 (mod 4) 1000= 2 3 ⋅5 3 ≡0 (mod 2 3 ) … 10 α ≡0 (mod 2 α ) and then a ⋅10 α... ...≤n≤999. It would have been very interesting to include part of the interval 1000≤n≤9999 but as we can see from (1) already S(1000) has 5784 digits. ... ...l 100≤n≤999. This indicates that the divisibility patterns for the interval 1000≤n≤9999 and further intervals is a completely open question. There ...

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... base 8. To further pursue the matter, the program was rerun for the first 1000 elements of the base 4 sequence and no primes were found. Problem: Are... ...o examine this question for all elements of the sequences up through index 1000. No instances of equality were found. We can also ask if two sequences... ...nce is 25 From this list, note that for elements numbered between 100 and 1000, the sequence of differences between elements divisible by 17 2 follo... ...y 17 2 follow the 1, 97 cycle, and for the elements numbered greater than 1000, the difference cycle is 16, 25, 106. This certainly raises the questi... ... through 2000 For divisibility by 11 2 , note that in the interval 100 to 1000, the difference cycle is 197, 45 and for greater than 1000, the differ... ...e Prime Sequence for primes was modified to search for primes in the first 1000 terms of the above sequence. With the exception of the first element, ... ...modulo 3? To further test this, the program was rerun to examine the first 1000 elements in the sequence 3, 35, 357, . . . and the number of elements... ...lo 3. The program was run for the first 400 odd primes, then for the first 1000 and finally for the first 500. While it was true that in all cases, л(... .... Table 3 Number of odd primes л(n;1,3) л(n;2,3) % л(n;2,3) 400 196 204 51 1000 491 508 50.8 5000 2484 2515 50.3 Table 4 Number of odd primes л(n;1,4)...

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...gits is a square. Proof: The infinite family of numbers (101)2 = 10201 (1000 1)2 = 10002000 I (IOOOOOlf = 1000002000001 etc. are all palindromic... ... element of the infinite family of palindromic numbers (101)3 = 1030301 (1000 1)3 = 100030003000 I (1000001)3 = 1000003000003000001 etc. 14 can... ...Gsing the same family as that for squares and cubes. (101)4 = 104060401 (1000 1)4 = 1000400060004000 I (100000 1)4 = 100000400000600000400000 I et... .... Proof: Consider the infinite family 102 2 = 10404 1002 2 = 1004004 10002 2 = 100040004 etc. which remain in the set after removal of the fi... ...h remain in the set after removal of the first infinite family. Note that 100040004 can be split into squares several different ways 12 , (0002)2 an... ... As can be seen from the initial elements of the set { 0,1,8, I 000,8000, 1000000,8000000, SCDS is infinite Again the question can be asked If all... ...o n < 1 x 10 18 and no solution not an element of the infinite families 1000 00000 8000 000 3k O's 3k O's was found 46 Conjecture 4: There is ... ...ps that are themselves perfect cubes. The first few numbers of SCPD are 1000, 8000, 10648, 27000, Clearly, all numbers of the form 47 mOOO. 000... ...is sequence are 60 SPC(l)1101 = 1011101 = 1 SPC(2)1101 = 10101011101 = 10001 = 73 * 137 SPC(3)/101 = 101010101011101 = 3 * 7 * 13 * 37 * 9901 SP...

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...d. Along with other Eastern Indo-Aryan languages, Bengali evolved circa 1000–1200 AD from the Magadhi Prakrit, which developed from the Sanskrit ...

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... of less than 5.000000 digits and it is optimized for numbers of more than 1000 digits.. Using this Program, I have found the following prime nu...

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...(second edition) American Research Press Rehoboth 2002 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 0 . 0 512345678 ∆ PRE / ARB*10... ...000.00 1500.00 2000.00 2500.00 3000.00 0 . 0 512345678 ∆ PRE / ARB*1000 PRE ARB*1000 ARB(MMSE Esti.) PRE Cut-off Point 2 M. Khoshnevisan, S. Sa... ...) in isolation, but also the wider length of the interval of ∆. 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 0 . 0 512345678 ∆ PRE / ARB*10... ...000.00 1500.00 2000.00 2500.00 3000.00 0 . 0 512345678 ∆ PRE / ARB*1000 PRE ARB*1000 ARB(MMSE Esti.) PRE Cut-off Point 19 4. MODIFIED CLASS OF SHRI...

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...rated by the following example. Example 1.2.9: Let A B = 32 0100 10 1000 31 0101 ⎡ ⎤⎡ ⎤ ⎢ ⎥⎢ ⎥ ∪ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎣ ⎦⎣ ⎦ and B B = 011 012... ... A B B B = 32 012 10 10 1 31 ⎡⎤ ⎡ ⎤ ⎢⎥ ⎢ ⎥ ⎢⎥ − − ⎣ ⎦ ⎢⎥ ⎣⎦ ∪ 011 0100 100 1000 011 0101 010 ⎡ ⎤ ⎡⎤ ⎢ ⎥ − ⎢⎥ ⎢ ⎥ ⎢⎥ ⎢ ⎥ ⎢⎥ ⎢ ⎥ ⎣⎦ ⎣ ⎦ = 234 10... ...1101 22 01202 ⎡⎤ ⎢⎥ ⎡ ⎤ − ⎢⎥ ⎢ ⎥ ⎢⎥ ∪ ⎢ ⎥ ⎢⎥ ⎢ ⎥ ⎢⎥ ⎣ ⎦ ⎢⎥ −− ⎣⎦ B B = 10001 21100 01 40101 21 21201 34 11111 −⎡⎤ ⎢⎥ ⎡ ⎤ − ⎢⎥ ⎢ ⎥ ⎢⎥ − ∪ ⎢ ⎥ ⎢⎥ ... ...as block bimatrices. Example 1.4.6: Let A B = 32 10 4000 0101 0210 1000 1010 5100 2110 − ⎡⎤ ⎡⎤ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ∪ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ − ⎣⎦ ⎣⎦ B B = ... ...10) and denoted by |A B |. Example 1.5.2: Let A B = 3012 0510 0100 1000 0215 0104 0012 1111 − ⎡⎤ ⎡⎤ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ∪ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎣⎦ ⎣⎦ be t... ... relative to the standard basis i.e., A = 9001 100 0200 210 0051 302 1000 − ⎡⎤ ⎡ ⎤ ⎢⎥ ⎢ ⎥ ⎢⎥ ∪ ⎢ ⎥ ⎢⎥ ⎢ ⎥ ⎢⎥ ⎣ ⎦ − ⎣⎦ . Find null bispace o... ...the related or associated bimatrix of T with the standard basis be A = 1000 0 300 62000 020 11100 111 00120 11014 − ⎡ ⎤ ⎢ ⎥ ⎡⎤ ⎢ ⎥ ⎢⎥ ⎢ ⎥ ∪ ⎢⎥ ⎢...

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... NOIDA , INDIA. */ FILE* f; unsigned long np = 0; unsigned long try_arr[1000]; unsigned long n = 0; unsigned long num_div = 0; unsigned long div... ...; unsigned long n = 0; unsigned long num_div = 0; unsigned long div_arr[10000]; unsigned long max_length = 0; unsigned long width_arr[1000]; uns... ...ze.. n = 0; np = 0; num_div = 0; unsigned long i; for(i = 0; i < 1000; i++) width_arr[i] = 0; // take input.. printf("Enter number..:\... ...= 3, we get the Smarandache additive cubic sequence. 1, 8, 125, 512, 1000, 1331, … 3) Smarandache (m th ) Power Additive n th power Sequence: ... ...r Additive n th power Sequence: When m=2 and n=3 we get 1, 27, 216, 1000, . . ., 798005999, . . . 10973607685048, . . . A large number of o... ...ache Patterned Perfect Cube Sequences Consider the sequences 10011, 100011, 1000011, 1000011, . . . where t n = 1 followed by... ...e formed by the cubes of the numbers in this sequence is 1003303631331, 1000330036301331, 1000033000363001331, 100000... ...c sequence. The first few numbers in this sequence are 1, 8, 125, 512, 1000, 1331, 8000, 19683, 35937, . . . Theorem: The cube of the number ... ...sequences, where the second is the squares of the first. 11, 101, 1001, 10001, 100001, . . . 121, 10201, 1002001, 100020001, . . . The...