• Kyungpook Mathematical Journal
• /
• 제56권2호
• /
• pp.367-370
• /
• 2016

In this paper, we consider the generalized Lucas sequence which is the (p, q) - Lucas sequence. Then we used the Binet's formula to show some properties of the (p, q) - Lucas number. We get some generalized identities of the (p, q) - Lucas number.

• 인터넷정보학회논문지
• /
• 제24권1호
• /
• pp.27-37
• /
• 2023

본 논문에서는 파도반 수열을 이용하여 새로운 루카스-파도반(Lucas-Padovan) 수열을 정의하고, 이를 이용하여 새로운 위상적 상호연결 네트워크(Interconnection Networks)를 구축한다. 루카스-파도반 수열의 부분 수열을 이용하여 음이 아닌 정수를 코딩(Coding)하고, 이를 이용하여 루카스-파도반 큐브(Cubes)를 새롭게 구축하여 위상적 성질을 다룬다.

• 한국응급구조학회지
• /
• 제22권3호
• /
• pp.67-76
• /
• 2018

Purpose: The purpose of this study was to evaluate the quality of chest compressions and ventilation when using an mechanical device(LUCAS) and 2-men manual cardiopulmonary resuscitation(CPR) performed on a minikin, as well as to propose a more effective CPR method during transit. Methods: Data were collected by LUCAS and manual virtual reality based ambulance simulation. Analysis was performed using SPSS software 12.0. The average and standard deviation of chest compression depth and ventilation were analyzed using descriptive statistics and t-test. Results: In the virtual reality based LUCAS and manual CPR results, LUCAS showed better chest compression and lower incomplete chest release than manual CPR. During CPR with a chest compression-ventilation ratio of 30:2 in virtual reality ventilation with bag-valve mask was able to deliver an adequate volume of breathing. Conclusion: It is suggested that rescuers on ambulance may consider using LUCAS as an alternative to high-quality chest compression during transit.

• 호남수학학술지
• /
• 제40권1호
• /
• pp.199-210
• /
• 2018

In this paper we obtain some formulae for several sums of generalized Fibonacci numbers $U_n$ and generalized Lucas numbers $V_n$ and their dual forms $G_n$ and $H_n$ by using extensions of an interesting identity by A. R. Amini for Fibonacci numbers to these four kinds of generalizations and their first and second derivatives.

• Kyungpook Mathematical Journal
• /
• 제61권3호
• /
• pp.473-486
• /
• 2021

We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions. From these polynomial relations, we deduce interesting identities with Fibonacci and Lucas numbers, and Euler numbers. The results must be regarded as companion results to some Fibonacci-Bernoulli identities, which we derived in our previous paper.

• Korean Journal of Mathematics
• /
• 제31권1호
• /
• pp.63-73
• /
• 2023

In this paper, we determine all repdigits, which are difference of two Pell and Pell-Lucas numbers. It is shown that the largest repdigit which is difference of two Pell numbers is 99 = 169 - 70 = P₇ - P₆ and the largest repdigit which is difference of two Pell-Lucas numbers is 444 = 478 - 34 = Q₇ - Q₄.

• Journal of applied mathematics & informatics
• /
• 제40권1_2호
• /
• pp.243-257
• /
• 2022

In this paper, we present and prove an new theorem on symmetric functions. By using this theorem, we derive some new generating functions of the products of (p, q)-Fibonacci numbers, (p, q)-Lucas numbers, (p, q)-Pell numbers, (p, q)-Pell Lucas numbers, (p, q)-Jacobsthal numbers and (p, q)-Jacobsthal Lucas numbers with Chebyshev polynomials of the first kind.

• Kyungpook Mathematical Journal
• /
• 제56권4호
• /
• pp.1125-1133
• /
• 2016

In this paper we introduce h(x)-B-Tribonacci and h(x)-B-Tri Lucas polynomials. We also obtain the identities for these polynomials.

• 호남수학학술지
• /
• 제42권1호
• /
• pp.49-62
• /
• 2020

In this paper, we consider interesting binomial and alternating binomial triple sums evaluated in multiplication forms in terms of the Fibonacci and Lucas numbers.

• 대한수학회논문집
• /
• 제38권1호
• /
• pp.89-96
• /
• 2023

Edgar obtained an identity between Fibonacci and Lucas numbers which generalizes previous identities of Benjamin-Quinn and Marques. Recently, Dafnis provided an identity similar to Edgar's. In the present article we give some generalizations of Edgar's and Dafnis's identities.