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[PDF] Top 20 On some power series with algebraic coefficients and Liouville numbers

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On some power series with algebraic coefficients and Liouville numbers

On some power series with algebraic coefficients and Liouville numbers

... transcendental numbers into three disjoint classes, termed S, T and U and this classification has proved to be of consider- able value in the general development of the ... See full document

9

Sums of Involving the Harmonic Numbers and the Binomial Coefficients

Sums of Involving the Harmonic Numbers and the Binomial Coefficients

... obtain some for P r n k ( , , ) and binomial coefficients by means of the Riordan ...establish some identities involving the numbers P r n k ( , , ) and inverse of binomial ...of some ... See full document

10

Some Applications of De Bruijn's Inequality for Power Series

Some Applications of De Bruijn's Inequality for Power Series

... the coefficients are restricted to be real numbers, a case which is of large interest due to the fact that many usual complex functions can be represented as power series with real ... See full document

9

On the transcendence of some power series

On the transcendence of some power series

... is algebraic if it is a zero of a polynomial with integer ...real numbers which are not algebraic are known as ...scendental numbers has a long history and was originated back to ... See full document

8

Formulas for Coefficients of Hundred Cyclotomics and Numbers Battle

Formulas for Coefficients of Hundred Cyclotomics and Numbers Battle

... raised some riddles of cyclotomic polynomials and their coefficients, and the enigma that has pained many mathematicians and researchers, this by the formula F12 and by means of prime numbers as in ... See full document

19

Compounding of distributions: a survey and new generalized classes

Compounding of distributions: a survey and new generalized classes

... The modern era on distribution theory stresses on problem-solving faced by the prac- titioners and applied researchers and proposes a variety of models so that lifetime data set can be better assessed and investigated in ... See full document

35

Nonlinear Algebraic Systems with Three Unknown Variables

Nonlinear Algebraic Systems with Three Unknown Variables

... with coefficients a i to equally leading degree of unknown x of a polynomial g ( x ) , that is m , the number of lines of a matrices with numbers b i coincides with the leading degree of unknown x of a ... See full document

6

Conductances, transference numbers, and activity coefficients of chlorides of some high atomic rare earths in aqueous solution

Conductances, transference numbers, and activity coefficients of chlorides of some high atomic rare earths in aqueous solution

... transference numbers, and activity coefficients of lanthanum chloride, samaric chloride, europic chloride, and ytterbic chloride were determined in order to test the present theories of electrolytic ... See full document

95

BOUNDS OF THE NUMBER OF LEVEL CROSSINGS OF THE RANDOM ALGEBRAIC POLYNOMIALS

BOUNDS OF THE NUMBER OF LEVEL CROSSINGS OF THE RANDOM ALGEBRAIC POLYNOMIALS

... an algebraic or trigonometric polynomial is expected to have when their coefficients are real random ...the coefficients are complex. The coefficients are assumed to be independent normally ... See full document

13

The genetic code, algebraic codes and double numbers

The genetic code, algebraic codes and double numbers

... to algebraic rules, despite the colossal heterogeneity of the molecular structure of ...These algebraic rules of polyhybrid crossbreeding are presented in textbooks since 1906 in the form of Punnett ... See full document

28

Some congruences on q Franel numbers and q Catalan numbers

Some congruences on q Franel numbers and q Catalan numbers

... 8. G. Olive, Generalized powers, Amer. Math. Monthly, 72 (1965), 619-627. 9. H. Pan, A q-analogue of Lehmer’s congruence, Acta Arith., 128 (2007), 303-318. 10. Z.-W. Sun, Congruences for Franel numbers, Adv. in ... See full document

9

Lower and upper bounds of number of zeros of random algebraic polynomials

Lower and upper bounds of number of zeros of random algebraic polynomials

... an algebraic or trigonometric polynomial are expected to have when their coefficients are real random ...the coefficients are complex. The coefficients are assumed to be independent normally ... See full document

10

Inequalities for finite trigonometric sums  An interplay: with some series related to harmonic numbers

Inequalities for finite trigonometric sums An interplay: with some series related to harmonic numbers

... certain series related to harmonic numbers and certain finite trigonometric sums is ...these series in terms of the considered trigonometric sums, and permits us to find sharp inequalities bounding ... See full document

15

Zeros of an algebraic polynomial with nonequal means random
coefficients

Zeros of an algebraic polynomial with nonequal means random coefficients

... This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial a 0 + a 1 x + a 2 x 2 + ··· + a n− 1 x n− 1 . The coefficients a j (j = 0, 1, 2,... ,n−1) are assumed ... See full document

7

Conductances, transference numbers, and activity coefficients of some low atomic number rare earths in aqueous solution

Conductances, transference numbers, and activity coefficients of some low atomic number rare earths in aqueous solution

... transference numbers, and activity coefficients of aqueous solutions of the chlorides of lanthanum, cerium, praseodymium, and neodymium have been determined for concentrations up to ...transference ... See full document

120

Estimating Nielsen Numbers on Wedge Product Spaces

Estimating Nielsen Numbers on Wedge Product Spaces

... It is well known that the fundamental group of the wedge product of spaces is the free product of the fundamental groups of the spaces. In Section 2, we present several proper- ties of free product of groups which we use ... See full document

16

On some properties of the Lüroth type alternating series representations for real numbers

On some properties of the Lüroth type alternating series representations for real numbers

... alternating series algorithm introduced by Knopfmacher and Knopfmacher [6, 7], analogous to a positive one of Oppenheim [8], we may prove that x has a unique finite or infinite representation in the ... See full document

7

Some Algebraic Concepts on Discrete Fuzzy Numbers

Some Algebraic Concepts on Discrete Fuzzy Numbers

... [7]S.S.L.Chang , and L.A.Zadeh,” On fuzzy mapping and control ”, IEEE Trans Man Cybernet., 2(1972),30-34. [8] Diamond.D and Kloeden, “Metric space of fuzzy sets”, Fuzzy Sets and Systems,100(1999), 63-71. [9] ... See full document

9

NOT require the Axiom of Choice; for each xA we have constructed an EXPLICIT left inverse to f. — On the other hand, if we had simply said that one should pick some

NOT require the Axiom of Choice; for each xA we have constructed an EXPLICIT left inverse to f. — On the other hand, if we had simply said that one should pick some

... real numbers, then among other things one can prove that that there is a subset of the reals which is not Lebesgue measurable without using the Axiom of Choice (see any graduate level book on Lebesgue integration; ... See full document

13

Inequality for power series with nonnegative coefficients and applications

Inequality for power series with nonnegative coefficients and applications

... Motivated by the above results we establish in this paper some Jensen’s type inequalities for functions defined by power series with nonnegative coefficients... The following result hold[r] ... See full document

8

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