How Many People Can the Earth Support? By Joel E. Cohen. Norton: 1995. Pp. 532. $30, £22.50. UK publication date, 27 March.

Book of numbers

In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated 2D q-Appell polynomials is also derived. Further, certain twice-iterated 2D q-Appell and mixed type special q-polynomials are considered as members of this polynomial class. The determinant expressions and some other properties of these associated members are also obtained. The graphs and surface plots of some twice-iterated 2D q-Appell and mixed type 2D q-Appell polynomials are presented for different values of indices by using Matlab. Moreover, some areas of potential applications of the subject matter of, and the results derived in, this paper are indicated.

https://www.mdpi.com/2073-8994/11/10/1307/pdf

Certain Results for the Twice-Iterated 2D q-Appell Polynomials

In this paper, we introduce a new operator in order to derive some new symmetric properties of k-Fibonacci and k-Lucas numbers and Fibonacci polynomials. By making use of the new operator defined i...

/pdf/symmetric-functions-of-the-k-fibonacci-and-k-lucas-numbers-8yjo6hbm8q.pdf

Symmetric functions of the k-Fibonacci and k-Lucas numbers

In the article we introduce and investigate several new subclasses of q-starlike and q-convex type analytic and multivalent functions involving a generalized Bernardi integral operator, and establish the Fekete-Szego type functional inequalities for these function classes. Besides, the corresponding bound estimates of the coefficients ap+1 and ap+2 are obtained.

Functional inequalities for several classes of q -starlike and q -convex type analytic and multivalent functions using a generalized Bernardi integral operator

In this paper, the Gaussian third-order Jacobsthal and Gaussian third-order Jacobsthal–Lucas polynomials are defined. Then Binet formula and generating functions of these numbers are given. Also, s...

Gaussian third-order Jacobsthal and Gaussian third-order Jacobsthal–Lucas polynomials and their properties

/pdf/some-results-on-the-q-analogues-of-the-incomplete-fibonacci-573rrtnbu3.pdf

SOME RESULTS ON THE q-ANALOGUES OF THE INCOMPLETE FIBONACCI AND LUCAS POLYNOMIALS

This paper is concerned with the combinatorial identities of the harmonic and the hyperharmonic Fibonacci numbers. By using the symmetric algorithm, we get some identities which improve the usual results and generalize known equations. Moreover, with the help of concept of Riordan array, we obtain the generating functions for these numbers and a variety of identities are derived.

/pdf/some-identities-of-harmonic-and-hyperharmonic-fibonacci-1fhu8u51d7.pdf

Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers

Abstract This paper describes properties of three certain classes of rings determined by conditions on idempotents and units, namely, the condition that any two generators of each principal right ideal are associated (UG rings), the condition that every principal right ideal is generated by a sum of a unit and an idempotent (Pr ), and the condition xy = 0 implies xsy = 0 for a sum of idempotent and unit s and any elements x, y of a ring (idun-semicommutative rings). It is proved that the class of all UG rings contains every local as well as every von Neumann regular ring, and the condition Pr is satisfied by both semiperfect and regular rings. Both local and abelian regular rings are proved to be necessarily idun-semicommutative. For all three classes are presented some closure properties and illustrating examples.

Mirac Cetin

Papers

SOME RESULTS ON THE q-ANALOGUES OF THE INCOMPLETE FIBONACCI AND LUCAS POLYNOMIALS

Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers

On rings determined by their idempotents and units