In this paper we study the approximation by rectangular partial sums of a double Fourier series with respect to the Walsh–Kaczmarz system in the spaces C and L. From our results we obtain different criteria of the uniform convergence and L-convergence of a double Fourier–Kaczmarz series. 2000 Mathematics Subject Classification: Primary 41A50; Secondary 42C10.

It is well known that the Mathieu series has a wide application in mathematics science. In this paper, we use the elementary method and construct some new inequalities to study the computational problem of the partial reciprocal sums related to the Mathieu series and obtain an interesting inequality and a related identity.

We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series r has a cyclic image if there is a rational number q such that all nonzero coefficients of r are integer powers of q. Mathematics Subject Classification. 11B85, 11U05, 68Q45.

Let p = 1/q ∈ Z \ {0,±1}. The new bound μ(hp(1)) 6 2.46497868 . . . for the irrationality measure of the q-harmonic series hp(1) = ∑∞ n=1 q n/(1 − qn) is proved. The essential ingredient of the proof is a permutation group originated by classical transform of the Heine series. 2000 Mathematics Subject Classification. 11J82, 33D15.

Annoucements • Office = MATH 221 (Directly above the Mathematics Department Office.) • Email = [email protected] • Text = “Baby Rudin” – Principles of Mathematical Analysis 3/e by Walter Rudin • Course Website = “http://www.math.ubc.ca/∼feldman/m321/” • Topics: – Riemann-Stieltjes integral (§6) – Sequences & Series of functions (§7) – Power Series, Special Functions, Fourier Series (§8) – Ano...

This is the second volume of the new series “Mathematics and its Applications” published by the Union of Bulgarian Mathematicians∗ Petar Popivanov, the author of the book, is a well known expert in the theory of partial differential equations (PDE), who has published several books and over 120 research articles. Since 1969 he works at the Institute of Mathematics and Informatics of the Bulgaria...

How many distinctions, in Latin, quantum distinctiones. We suggest approach of anthropic principle based on anthropic reference system which should be applied equally both in theoretical physics and in mathematics. We come to principle that within reference system of life subject of mathematics (that of thinking) should be equated with subject of physics (that of nature). For this reason we ent...

Riemann’s theorems on the rearrangement of absolutely convergent and conditionally convergent series of real numbers are analysed within Bishop-style constructive mathematics. The constructive proof that every rearrangement of an absolutely convergent series has the same sum is relatively straightforward; but the proof that a conditionally convergent series can be rearranged to converge to what...

A century ago, Srinivasa Ramanujan -- the great self-taught Indian genius of mathematics died, shortly after returning from Cambridge, UK, where he had collaborated with Godfrey Hardy. contributed numerous outstanding results to different branches mathematics, like analysis and number theory, a focus on special functions series. Here we refer apparently weird values which assigned two simple di...