Related papers: Sagan numbers
Normal numbers were introduced by Borel and later proven to be a weak notion of algorithmic randomness. We introduce here a natural relativization of normality based on generalized number representation systems. We explore the concepts of…
By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…
This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were…
Given a rational elliptic surface X over an algebraically closed field, we investigate whether a given natural number k can be the intersection number of two sections of X. If not, we say that k a gap number. We try to answer when gap…
Curiously overlooked in physics is its dependence on the transmission of numbers. For example the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical…
We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.
The difficulties of detecting association, measuring correlation, and establishing cause and effect have fascinated mankind since time immemorial. Democritus, the Greek philosopher, underscored well the importance and the difficulty of…
The partisans of the hypothesis of the Indian origin of the numerals create confusion between the history of the Indian mathematics and the history of our modern numerals. To argue the thesis of the Indian origin of the numbers they…
Prigogine and Stengers (1988) have pointed to the centrality of the concepts of "time and eternity" for the cosmology contained in Newtonian physics, but they have not addressed this issue beyond the domain of physics. The construction of…
The world runs on communicated sequences of symbols, e.g. numerals. Examining both engineered and natural communications networks reveals an unsuspected order that depends on contact with an unpredictable entity. This order has three roots.…
Rationals are known to form interesting and computationally rich structures, such as Farey sequences and infinite trees. Little attention is being paid to more general, systematic exposition of the basic properties of fractions as a set.…
Gabor analysis which can be traced back to Dennis Gabor's influential 1946 paper \emph{Theory of communication}, is concerned with both the theory and the applications of the approximation properties of sets of time and frequency shifts of…
Indigenous Australian practices, developed and honed over thousands of years, weave science with storytelling. In this Indigenous science series, we'll look at different aspects of First Australians' traditional life and uncover the…
In this book we introduce the notion of interval semigroups using intervals of the form [0, a], a is real. Several types of interval semigroups like fuzzy interval semigroups, interval symmetric semigroups, special symmetric interval…
In the paper, the author derives several "diagonal" recurrence relations, constructs some inequalities, finds monotonicity, and poses a conjecture related to Stirling numbers of the second kind.
We confirm a conjectural supercongruence involving Catalan numbers, which is one of the 100 selected open conjectures on congruences of Sun. The proof makes use of hypergeometric series identities and symbolic summation method.
In this paper we present a new mathematical conception based on a new method for ordering the integers. The method relies on the assumption that negative numbers are beyond infinity, which goes back to Wallis and Euler. We also present a…
Riemannian geometry in four dimensions naturally leads to an SL(3) connection that annihilates a basis for self-dual two-forms. Einstein's equations may be written in terms of an SO(3) connection, with SO(3) chosen as an appropriate…
Optical orthogonal codes (OOCs) are sets of $(0,1)$-sequences with good auto- and cross-correlation properties. They were originally introduced for use in multi-access communication, particularly in the setting of optical CDMA…
The Stern sequence (s(n)) is defined by s(0) = 0, s(1) = 1, s(2n) = s(n), s(2n+1) = s(n) + s(n+1). Stern showed in 1858 that gcd(s(n),s(n+1)) = 1, and that for every pair of relatively prime positive integers (a,b), there exists a unique n…