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...all option on the real economy and, especially, on real estate and emerging technologies. R amounts, therefore, to the premium on this option. Income inequality is growing because of the decline in the role and importance of labor, which is being gradually supplanted by capital assets, such as robots and computers as well as being offshored, outsourced, and downsized. Agai...

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...This research will determine why leftism is on the rise and whether US national security is being threatened. The causes are a combination of extreme inequality with regards to income per capita, an increased awareness among the populace as to its unequal situation, a poor display of US foreign policy, and an increase in education levels throughout the region. Based on the...

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...Alone, or Aid as Currently Practiced, Significantly Reduces Poverty MYTH #6: Microcredit & Income Generation are Miracle Cures for Poverty MYTH #7: Inequality is Inevitable and is Less of a Problem than Poverty MYTH #8: Mainstream Economists Want Governments to Play Only a Minimal Role in the Economy MYTH #9: Whatever Governments Do, the Private Sector Can Do Better M...

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...arandache, Sukanto Bhattacharya, in in , Vol. 3, No. JJ05, 81-88, 2005................41 CALCULUS....................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using Super...

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...arandache, Sukanto Bhattacharya, in in , Vol. 3, No. JJ05, 81-88, 2005................41 CALCULUS....................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using Super...

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...This book is about how to improve global living standards. Topics include economic growth, income inequality, poverty, corruption, causes of the decline of the middle class, sustainable development, emerging technologies, and more. Below is a list of questions answered throughout: * Which nations have the best livin...

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...hapter 18: Free Trade Chapter 19: Cooperative Socialism Failed Chapter 20: Employment Chapter 21: Why Developed Economies Are Slowing Chapter 22: Inequality and Standard of Living Chapter 23: Why Inequality Exists Chapter 24: Taxation Chapter 25: Welfare Chapter 26: Wages Chapter 27: Inequality-Based Tax System Chapter 28: Charity Chapter 29: Sustainable Develop...

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...ust, eth- nic and racial conflicts, oppression, economic inequity, and gender inequality will all give way to mutual trust and respect. People and c...

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...y positive integern, letm be the largest positive integer that satisfy the inequality m(2m−1)≤n< (m+1)(2m+1). Nowwedefinea(n) =m(2m−1),andcalla(n)asthe...

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...round." "I don't really," he said. " If Bin Laden is so rich it isn't inequality that he hates. Tyrants like building up empires but he doesn't s...

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...nds (We don’t include CSWs in this list). This is in keeping with the gender inequality that is prevalent in India; for urban men in Tamil Nadu are...

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...h! Quite far away above all others!!!' This tightly constructed and passionate study of enforced marriage in the world of Radical politics and social inequality, records the lifelong attempt of Countess Lovel to justify her claim to her title, and her daughter Anna's legitimacy, after her husband announces that he already has a wife. However, mother and daughter are driven...

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...om soon displays considerable wisdom in his decisions). In many ways, the book is a social satire, particularly compelling in its condemnation of the inequality that existed between the classes in Tudor England. In that sense, Twain abandoned the wry Midwestern style for which he was best known and adopts a style reminiscent of Charles Dickens. (Summary from Wikipedia.org)...

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...elements of a triangle . . . . . . . . . . . . . . . . 13 4 On a geometric inequality for the medians, bisectors and simedians of an angle of a triang... .... . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5 On Emmerich’s inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 6 On a ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 6 On a geometric inequality of Arslanagi c and Milo sevi c . . . . . . . . . . . . 23 7 A... ...d Milo sevi c . . . . . . . . . . . . 23 7 A note on the Erd os-Mordell inequality for tetrahedrons . . . . . . . . . . 25 8 On certain inequalitie... ...eralizations of the Smarandache function . . . . . . . . . . . 141 9 On an inequality for the Smarandache function . . . . . . . . . . . . . . . 150 1... ... r (r = radius of the incircle) we obtain p 0 = r R p: (4) 9 Now, Euler’s inequality 2r R gives relation (3). For the proof of (2) we shall apply th... ... 0; i.e. 2(A +B +C) X (b +c) A a : Adding A +B +C to both sides of this inequality, and by taking into account of A +B +C = , anda +b +c = 2s (whe... ... triangle) we get (ii) X A a 3 2s . This may be compared with Nedelcu’s inequality (see [3], p.212) (ii)’ X A a < 3 4R . 13 Another inequality of... ...ively circumscribed circle of the triangle. 3. By the arithmetic-geometric inequality we have X A a 3 ABC abc 1 3 : (2) Then, from (ii) and (2) ...

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...ates hs 2 +5s+4;0i in C. Let us denote by a k;i an element of A with coordinateshk;ii in C. First, we determine the minimal nonnegative s for which th... ... c n = 1 X k=0 [ 1 1+[ ¼ C (k) n ] ]; (13) c n =¡2 1 X k=0 ³(¡2[ ¼ C (k) n ]); (14) c n = 1 X k=0 1 ¡(1¡[ ¼ C (k) n ]) : (15) In [16] is shown that th... ...g F(n)= n X k=1 f(k) we rewrite (12) as n Y k=1 (P d (k)) f(k) F(n) = n Y k=1 k ( P[ n k ] s=1 f(ks))=(F(n)) : (21) Then we use the well-known Jensen'... ...or arbitrary positive numbers x k , ® k (k=1 ;2;:::;n) such that n X k=1 ® k =1; for the case: x k =P d (k); ® k = f(k) F(n) : Thus we obtain from (21... ...obtain from (21) inequality n X k=1 f(k):P d (k)¸( n X k=1 f(k)): n Y k=1 k ( P[ n k ] s=1 f(ks))=( P n s=1 f(s)) : (22) If f(x)´1 then (22) yields th... ...n X k=1 g(k) k ): n Y k=1 ( k p k) ( P[ n k ] s=1 g(ks) s )=( P n s=1 g(s) s ) ; (24) because of (2). Let g(x)´1: Then (24) yields the very interestin... ...(x=x 1 :x 2 ::::x k )g for each natural number k¸1. Let us consider m as an in¯nite sequence for m=2;3;:::.Then 2 is a subsequence of m. Therefore, th... ... holds for n=1;2;3;:::. Let p 1 =2 ;p 2 =3 ;p 3 =5 ;p 4 =7 ;::: be the sequence of all primes. Itisobviousthatthissequenceisasubsequenceof2. Hence, th... ...)´[ n 2 +3n+4 4 ]( 1 ) (see [16]). Therefore, for any m¸2andn=1;2;3;:::we have a (m) n ·a (2) n ·µ(n): Hence, there exists ¸(n) such that ¸(n)·µ(n) an...

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...) log ( ( 2 + ≤ n n E p n If 0 n it is not too big, we can prove that the inequality is true for smaller or equal values than 0 n . It is nece... ... ( 2 ( =       + n n n E E π If we check the inequality: (2) n n n E 2 )) 1 ) log ( ( ... ... n C n n n n n π π π We can experimentaly check this last inequality saying that it checks for a lot of values and the difference ...

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...mean value 33 Lv Chuan On the primitive numbers of power and its triangle inequality 37 Ding Liping The additive analogue of Smarandache simple funct... ...inger-Verlag, 1976. ON THE PRIMITIVE NUMBERS OF POWER AND ITS TRIANGLE INEQUALITY Ding Liping Department of Mathematics, Northwest University, Xi’... ...ng the elementary method to study the properties of , and give a triangle inequality for it. Keywords: Primitive numbers; Arithmetical property; tria... ...ality for it. Keywords: Primitive numbers; Arithmetical property; triangle inequality. 1. Introduction Let be a prime, be any xed positive integer,... ...ary methods to study the arithmetical properties of , and give a triangle inequality for it. That is, we shall prove the following: Theorem 1. Let b... ...em 1. Let be an odd prime, be positive integer. Then we have the triangle inequality Theorem 2. There are in nite integers satisfying 2. Proof of t... ... From (1), (2) we can immediately get Now the theorem 1 follows from this inequality and the induction. Next we complete the proof of theorem 2. For ... ...of , we have and taking the logistic computation in the two sides of the inequality, we get (1) Then using the Euler’s summation formula we have (... ...s a -full number. That is, if then . Now we can easily get the following inequality: (4) From (3) and (4), we can write So we have (5) 76 RESEAR...

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...2 2 1 3 ) ( p j n k n k » = , and then the theorem is a consequence of inequality 2 n n £ . Theorem 1.1.7 n k n Zt k ‡ = ) ( 1 ) ( j Proof... ...? Examining the results of a computer search looks like that the following inequality hold: ) 2 ( ) 1 ( ) ( + + < n Zt n Zt n Zt . Is this true for... .... 15 Unsolved question: Is this true for all values of n? Checking the inequality ) 2 ( ) 1 ( ) ( + > + n Zt n Zt n Zt only one solution among t... ...t integers k such that Zw(k)=p is given by the exponent a of the following inequality: 30 ) ln( ) ln( , p h a is that h a p £ £ Since a must be the l... ... 1 1 1 ) ( 1 lim Is this limit related to g? Problem 5. Is the following inequality satisfied 43 = < - - < + n k n a g n a k a n a 1 ) ( 2 1 ... ...roblem 25. Is there any Smarandache sequence a(n) such that the following inequality is satisfied? ))) ( ln(ln( )) ( ln( ) 4 ln( ) 2 1 ( 2 ))) ( ln(l... ...>0. Problem 18. For the first values of the Sdf(n) function the following inequality is true: 1000 1 2 8 1 ) ( £ £ + £ n for n n Sdf n Is this stil... ...87 Problem 19. For the first values of the Sdf(n) function the following inequality is true: 1000 1 1 ) ( 73 . 0 £ £... ...0 ? Problem 20. For the first values of the Sdf(n) function the following inequality hold: 1000 2 ) ( 1 1 4 1 £ < < + - n for n n Sdf n Is this stil...

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...s …………………. 174 3.10 Smarandache Reciprocal Function and An Elementary Inequality 176 3.11 Smarandache Maximum Reciprocal Representation Fu... ... DP (k) + (n 2 – 5n +8)/2, n > 3. k=3 Proof: The inequality will be established in two steps. Proposition A For every n,... ...#n)] + 2 n – 1. Regarding the general case, O [D r (1#n)], we derive an inequality. Let (d 1, d 2 , d 3 , . . . d r ) be an element of O [D r (1... ...nctions give us another way of generalizing the Arithmetic-Geometric Mean Inequality. One can easily prove that: (x 1 x 2 x 3 x 4 ) 1/4 ≤ [{ (x ... .../ 3 ≤ {x 1 + x 2 + x 3 + x 4 }/ 4. The generalization of the above inequality can also be easily established. Section 14 110 On the In... ... p 3 k3 . . . p s ks . Also, by the choice of the numbers we have the inequality p i ki ≤ n 1/3 < p i ki +1 . Multiplying all the inequ... ...s sequence is defined as the number of perfect squares m that satisfy the inequality nk + 1 ≤ m ≤ nk + n. For n = 12, the first few terms ... ...ng at zero) of SPPCPS(n,k) is the number of kth powers m that satisfy the inequality nr + 1 ≤ m ≤ nr + n. For example, the first term of SPPC... ...e of C. Section 10 Smarandache Reciprocal Function and An Elementary Inequality Definition: The Smarandache Reciprocal Function S c (n) is de...

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... insurance provider. The insurance is cost-effective only if the following inequality holds: log e (X – k) ≥ p (X) lo... ...ctured product information transmission By the well-known Kraft’s inequality we have K = Σ n 2 –li ≤ 1, where l i stands for some defini... ... K = 0 as it corresponds to the maximal entropy condition. Therefore the inequality occurs if and only if p i ≠ 2 –li . Though the Shannon- Fano c... ...≥ ½ … (4.17) 83 Inequality (4.17) gets us back to the Kraft’s inequality. This shows that t... ...ously decodable code having the Shannon-Fano lengths l i . By multiplying inequality (4.16) by p i and summing we get: Σ n (p i log 2 p i -1 )... ...ementary risky assets within a financial structured product). Using Gibbs inequality, it can be show that the following limit can be imposed for bou...