On some functions involving the lcm and gcd of integer tuples

In this paper an explicit formula for the number of tuples of positive integers having the same lowest common multiple n is derived, and some of the properties of the resulting arithmetic function are analyzed. The tuples having also the same greatest common divisor are investigated, while some novel or existing integer sequences are recovered as particular cases. A formula linking the gcd and lcm for tuples of integers is also presented

Complementary iInequalities involving the Stolarsky Mean

an are equal to a and n−k are equal to b, where k is either bq − Dq p,q(a, b) bq − aq · n or bq − Dq p,q(a, b) bq − aq · n + 1, and Dp,q(a, b) denotes the Stolarsky mean of a and b. Moreover, if n, p and q are fixed, then lim b&a k n = 1 2.The author wishs to express his thanks to T. Trif, who provided significant moral and technical support to finish this paper. The author also thanks the reviewers, whose suggestions and "free gifts'' were of great help. Last but not least, his thanks go to the Marie Curie foundation, which gave him the chance to understand Mathematics and its applications from a researcher's perspective

A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation

The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National Research Council of Thailand and Khon Kaen University, Thailand (6200069)

A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation

The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National Research Council of Thailand and Khon Kaen University, Thailand (6200069)

A Horadam-based pseudo-random number generator

Uniformly distributed pseudo-random number generators are commonly used in certain numerical algorithms and simulations. In this article a random number generation algorithm based on the geometric properties of complex Horadam sequences was investigated. For certain parameters, the sequence exhibited uniformity in the distribution of arguments. This feature was exploited to design a pseudo-random number generator which was evaluated using Monte Carlo π estimations, and found to perform comparatively with commonly used generators like Multiplicative Lagged Fibonacci and the 'twister' Mersenne

New results and conjectures on 2-partitions of multisets.

The interplay between integer sequences and partitions has led to numerous interesting results, with implications in generating functions, integral formulae, or combinatorics. An illustrative example is the number of solutions at level n to the signum equation. Denoted by S(n), this represents the number of ways of choosing + and - such that ±1±2±3±···±n = 0 (see A063865 in OEIS). The Andrica-Tomescu conjecture regarding the asymptotic behaviour of S(n) was solved affirmatively in 2013, and new conjectures were formulated since then. In this paper we present recurrence formulae, generating functions and integral formulae for the number of ordered 2-partitions of the multiset M having equal sums. Certain related integer sequences not currently indexed in the OEIS are then presented. Finally, we formulate conjectures regarding the unimodality, distribution and asymptotic behaviour of these sequences.N/

On some results concerning the polygonal polynomials.

In this paper we define the $n$th polygonal polynomial $P_n(z) = (z-1)(z^2-1)\cdots(z^n-1)$ and we investigate recurrence relations and exact integral formulae for the coefficients of $P_n(z)$ and for those of the Mahonian polynomials $Q_n(z)=(z+1)(z^2+z+1)\cdots(z^{n-1}+\cdots+z+1)$. We also explore numerical properties of these coefficients, unraveling new meanings for old sequences and generating novel entries to the Online Encyclopedia of Integer Sequences (OEIS). Some open questions are also formulated.O. Bagdasar's research was supported by a grant of the Romanian National Authority for Research and Innovation, CNCS/CCCDI UEFISCDI, project number PN-III-P2-2.1-BG-2016-0333, within PNCDI III

Influence discovery in semantic networks: An initial approach

Assessing the influence between concepts, which include people, physical objects, as well as theoretical ideas, plays a crucial role in understanding and discovering knowledge. Despite the huge amount of literature on knowledge discovery in semantic networks, there has been little attempt to fully classify and investigate the influence, which also includes causality, of a semantic entity on another one as dynamical entities. In this paper we will introduce an approach to discover and assess influence among nodes in a semantic network, with the aim to provide a tool to identify its type and direction. Even though this is still being developed, the preliminary evaluation shows promising and interesting results

Concise computer mathematics: tutorials on theory and problems

Adapted from a modular undergraduate course on computational mathematics, Concise Computer Mathematics delivers an easily accessible, self-contained introduction to the basic notions of mathematics necessary for a computer science degree. The text reflects the need to quickly introduce students from a variety of educational backgrounds to a number of essential mathematical concepts. The material is divided into four units: discrete mathematics (sets, relations, functions), logic (Boolean types, truth tables, proofs), linear algebra (vectors, matrices and graphics), and special topics (graph theory, number theory, basic elements of calculus). The chapters contain a brief theoretical presentation of the topic, followed by a selection of problems (which are direct applications of the theory) and additional supplementary problems (which may require a bit more work). Each chapter ends with answers or worked solutions for all of the problems