Translation invariance and finite additivity in a probability measure on the natural numbers by Robert Gardner, Robert Price

“…Inspired by the two envelopes exchange paradox, a finitely additive probability measure m on the natural numbers is introduced. The measure is uniform in the sense that m({i})=m({j}) for all i,j∈ℕ. …”
Get full text

An introduction of F-graphs, a graph-theoretic representation of natural numbers by E. J. Farrell

Subjects: Get full text

Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation by Robert Reynolds, Allan Stauffer

“…We consider a Hurwitz-Lerch zeta function Φs,z,a sum over the natural numbers. We provide an analytically continued closed form solution for this sum in terms of the addition of Hurwitz-Lerch zeta functions. …”
Get full text

Lucas numbers of the form PX2, where P is prime by Neville Robbins

“…Let Ln denote the nth Lucas number, where n is a natural number. Using elementary techniques, we find all solutions of the equation: Ln=px2 where p is prime and p<1000.…”
Get full text

Graceful numbers by Kiran R. Bhutani, Alexander B. Levin

“…We construct a labeled graph D(n) that reflects the structure of divisors of a given natural number n. We define the concept of graceful numbers in terms of this associated graph and find the general form of such a number. …”
Get full text

More on lines in Euclidean Ramsey theory by Conlon, David, Wu, Yu-Han

“…Answering a question raised by Fox and the first author and independently by Arman and Tsaturian, we show that there is a natural number $m$ and a red/blue-colouring of $\mathbb{E}^n$ for every $n$ that contains no red copy of $\ell _3$ and no blue copy of $\ell _m$.…”
Get full text

Arithmetic functions associated with infinitary divisors of an integer by Graeme L. Cohen, Peter Hagis

“…The infinitary divisors of a natural number n are the products of its divisors of the form pyα2α, where py is a prime-power component of n and ∑αyα2α (where yα=0 or 1) is the binary representation of y. …”
Get full text

Some special cases on Stolarsky’s means by Cesare Palmisani

“…In the subfamily of SM having a natural number as parameter, we geometrically interpret one of them in particular as a real elliptic cone. …”
Get full text

Commutator Length of Finitely Generated Linear Groups by Mahboubeh Alizadeh Sanati

“…The commutator length “cl(𝐺)” of a group 𝐺 is the least natural number 𝑐 such that every element of the derived subgroup of 𝐺 is a product of 𝑐 commutators. …”
Get full text

The trajectory-coherent approximation and the system of moments for the Hartree type equation by V. V. Belov, A. Yu. Trifonov, A. V. Shapovalov

“…The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter ℏ (ℏ→0), are constructed with a power accuracy of O(ℏ N/2), where N is any natural number. In constructing the semiclassically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for centered moments) is essentially used. …”
Get full text

Unique gating strategy identifier based on the Prime Population System and Gödel Numbers by Antonio Cosma

“…The unique identifiers hold since according to the fundamental theorem of arithmetic, every natural number other than one either is a prime or is a product of prime numbers, and every nonprime number can be factored into a product of prime in only one way. …”
Get full text

Some results concerning exponential divisors by Peter Hagis

“…If the natural number n has the canonical form p1a1p2a2…prar then d=p1b1p2b2…prbr is said to be an exponential divisor of n if bi|ai for i=1,2,…,r. …”
Get full text

Consecutive Power Occurrences in Sturmian Words by Bell, Jason, Schulz, Chris, Shallit, Jeffrey

“…We then give a general result showing that for every $e \in [1,(5+\sqrt{5})/2)$ there is a natural number $N$, depending only on $e$, such that every Sturmian word has the property that the distance between consecutive ending positions of $e$-powers occurring in the word is uniformly bounded by $N$.…”
Get full text

Influence of Number of Pole Pairs on Torque Ripple of Magnetic Gear by Huang Zhangxian, Jing Libing

“…The research results show that the torque ripple can be effectively reduced by selecting the magnetic gear with <italic>P</italic>₁=4， <italic>P</italic>₁:<italic>P</italic>₂=1:<italic>n</italic>+0.25 or 1:<italic>n</italic>+0.75 （<italic>n</italic> is a natural number）.…”
Get full text

Radio and Radial Radio Numbers of Certain Sunflower Extended Graphs by Mohammed K. A. Kaabar, Kins Yenoke

“…For any integer k, 1≤k≤d, radio k−coloring of G is an assignment φ of color (positive integer) to the vertices of G such that da,b+φa−φb≥1+k, ∀a,b∈VG, where da,b is the distance between a and b in G. The biggest natural number in the range of φ is called the radio k−chromatic number of G, and it is symbolized by rckφ. …”
Get full text

Complex Diophantine interval-valued Pythagorean normal set for decision-making processes by Murugan Palanikumar, Nasreen Kausar, Ponnaiah Tharaniya, Željko Stević, Fikadu Tesgera Tolasa

“…Consequently, it is evident that the models are significantly influenced by the natural number $$\nabla$$ . To further demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and applied to a numerical example. …”
Get full text

Links between Main Frequencies of Established Rotating Stall and Rotational Frequencies and/or Blade Passing Frequencies by Yeshayahou Levy, Asaf Modelevsky, Joseph Pismenny, Jens Friedrichs, Detlev Wulff

“…The ratios between the main frequency of rotating stall and rotational frequency may be considered in the form of exact ratios of small natural numbers if the pressure signals in compressors during rotating stall include the rotor rotation frequency component. …”
Get full text

A topological property of β(N) by Anastase Nakassis

“…In this paper we prove that the Stone-Cech-compactification of the natural numbers does not admit a countable infinite decomposition into subsets homeomorphic to each other and to the said compactification.…”
Get full text

On the Probabilistic Proof of the Convergence of the Collatz Conjecture by Kamal Barghout

“…A new approach towards probabilistic proof of the convergence of the Collatz conjecture is described via identifying a sequential correlation of even natural numbers by divisions by 2 that follows a recurrent pattern of the form x,1,x,1…, where x represents divisions by 2 more than once. …”
Get full text

On the K-th extension of the Sieve of eratosthenes by Antonio R. Quesada

“…For a given k we let the initial set Sk consists of natural numbers relatively prime to the first k primes, and find the rules governing the positions of the multiples of the remaining elements.…”
Get full text