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Bravo, Jhon J.,Herrera, Jose L. Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.4
The Padovan sequence is the third-order linear recurrence (𝓟<sub>n</sub>)<sub>n≥0</sub> defined by 𝓟<sub>n</sub> = 𝓟<sub>n-2</sub> + 𝓟<sub>n-3</sub> for all n ≥ 3 with initial conditions 𝓟<sub>0</sub> = 0 and 𝓟<sub>1</sub> = 𝓟<sub>2</sub> = 1. In this paper, we investigate a generalization of the Padovan sequence called the k-generalized Padovan sequence which is generated by a linear recurrence sequence of order k ≥ 3. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences.
ON THE INTERSECTION OF k-FIBONACCI AND PELL NUMBERS
Bravo, Jhon J.,Gomez, Carlos A.,Herrera, Jose L. Korean Mathematical Society 2019 대한수학회보 Vol.56 No.2
In this paper, by using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and $Peth{\ddot{o}}$, we find all generalized Fibonacci numbers which are Pell numbers. This paper continues a previous work that searched for Pell numbers in the Fibonacci sequence.
Bravo, Eduardo,Contardo, Jorge,Cea, Jerson Asian Pacific Journal of Cancer Prevention 2016 Asian Pacific journal of cancer prevention Vol.17 No.3
Background: Chile is one of the countries with the highest prevalence of cholelithiasis worldwide, considering the Mapuche ethnicity as a risk factor for developing this pathology. Moreover, cholelithiasis is the main risk factor for developing gallbladder cancer, being the fifth cause of cancer death in Chile. The purpose of this study was to compare the frequency of cholelithiasis and biliary pathology among the population belonging to Rapanui ethnicity and non-Rapanui population living on Easter Island. Materials and Methods: In this retrospective case-control study, a total of 609 abdominal ultrasonographs performed consecutively in Hanga Roa Hospital during the period August 2012 to January 2015 were analyzed. Multiple logistic regression was used to obtain odds ratio (OR) and 95% confidence intervals (95% CI) of cholelithiasis and biliary pathology, adjusting for age, gender and referral diagnostic hypothesis. Results: In the Rapanui population the frequency for cholelithiasis and biliary pathology was 6.4% and 13%, meanwhile for the non-Rapanui population it was 13% and 22% respectively. Compared to the non-Rapanui Chilean population, the Rapanui ethnicity presented an OR of 0.53 (95% CI: 0.29-0.95) for cholelithiasis and OR of 0.52 (95% CI: 0.33-0.82) for biliary pathology. Conclusions: We found statistically significant ethnic differences in the frequency of cholelithiasis and biliary disease among the population of Rapanui and non-Rapanui ethnicity, so that this could be a protective factor for the development of biliary pathology, given the Chilean population context. Other studies including community population to determine the real prevalence of cholelithiasis and analyze the protective role of Rapanui ethnicity on this disease are necessary.
ON PILLAI'S PROBLEM WITH TRIBONACCI NUMBERS AND POWERS OF 2
Bravo, Jhon J.,Luca, Florian,Yazan, Karina Korean Mathematical Society 2017 대한수학회보 Vol.54 No.3
The Tribonacci sequence ${\{T_n}\}_{n{\geq}0}$ resembles the Fibonacci sequence in that it starts with the values 0, 1, 1, and each term afterwards is the sum of the preceding three terms. In this paper, we find all integers c having at least two representations as a difference between a Tribonacci number and a power of 2. This paper continues the previous work [5].
Description of Deaths on Easter Island, 2000-2012 Period
Bravo, Eduardo Francisco,Saint-Pierre, Gustavo Enrique,Yaikin, Pabla Javiera,Meier, Martina Jose Asian Pacific Journal of Cancer Prevention 2014 Asian Pacific journal of cancer prevention Vol.15 No.23
Easter Island is a small island of $180km^2$, located 3,800 km from the Chilean coast and one of the most isolated inhabited places in the world. Since the mid-twentieth century, it has been undergoing an epidemiological transition in relation to the causes of death, from a predominance of infectious to non-communicable diseases (NCDs) such as cardiovascular ailments and cancer. The aim of this study is to describe the causes of death to Easter Island between 2000 and 2012, so the statistical records of Hanga Roa Hospital and death certificates were reviewed. The period under review of 13 years there was a total of 252 deaths, an average to 19.3 deaths per year. The most frequent causes of death found in the general population of Easter Island were cardiovascular diseases (25.4%), followed by neoplasms (23.4%), accidents (18.6%). Related to Rapa Nui people, cardiovascular and neoplastic diseases (both 26.7%) predominate, while in the population without belonging to the ethnic group the main causes were traumatic (25%) and cardiovascular (22.2%). Comparing the leading causes of death of Easter Island with mainland Chile, it can be seen how they resemble. Taking the island death profile, it is necessary to work on public health strategies aimed to this, considering that some of the causes are completely preventable.
Continuous-wave upconverting nanoparticle microlasers
Fernandez-Bravo, Angel,Yao, Kaiyuan,Barnard, Edward S.,Borys, Nicholas J.,Levy, Elizabeth S.,Tian, Bining,Tajon, Cheryl A.,Moretti, Luca,Altoe, M. Virginia,Aloni, Shaul,Beketayev, Kenes,Scotognella, F Nature Publishing Group UK 2018 Nature nanotechnology Vol.13 No.7
Reducing the size of lasers to microscale dimensions enables new technologies<SUP>1</SUP> that are specifically tailored for operation in confined spaces ranging from ultra-high-speed microprocessors<SUP>2</SUP> to live brain tissue<SUP>3</SUP>. However, reduced cavity sizes increase optical losses and require greater input powers to reach lasing thresholds. Multiphoton-pumped lasers<SUP>4–7</SUP> that have been miniaturized using nanomaterials such as lanthanide-doped upconverting nanoparticles (UCNPs)<SUP>8</SUP> as lasing media require high pump intensities to achieve ultraviolet and visible emission and therefore operate under pulsed excitation schemes. Here, we make use of the recently described energy-looping excitation mechanism in Tm<SUP>3+</SUP>-doped UCNPs<SUP>9</SUP> to achieve continuous-wave upconverted lasing action in stand-alone microcavities at excitation fluences as low as 14 kW cm<SUP>−2</SUP>. Continuous-wave lasing is uninterrupted, maximizing signal and enabling modulation of optical interactions<SUP>10</SUP>. By coupling energy-looping nanoparticles to whispering-gallery modes of polystyrene microspheres, we induce stable lasing for more than 5 h at blue and near-infrared wavelengths simultaneously. These microcavities are excited in the biologically transmissive second near-infrared (NIR-II) window and are small enough to be embedded in organisms, tissues or devices. The ability to produce continuous-wave lasing in microcavities immersed in blood serum highlights practical applications of these microscale lasers for sensing and illumination in complex biological environments.
Cancer Prevalence in Easter Island Population - 2006-2010
Rius, Eduardo Bravo,Armaroli, Pabla Yaikin,Contreras, Gustavo Saint-Pierre Asian Pacific Journal of Cancer Prevention 2013 Asian Pacific journal of cancer prevention Vol.14 No.5
In Easter Island, population is composed by original habitants, the Rapa Nui culture and introduced people, mainly from continental Chile, who have a different ethnic origin. The aim of this research was to describe cancer frequency in resident population in Easter Island, and secondarily compare the findings with other islands of Polynesia and continental Chile. We reviewed the statistics of patients treated in Hanga Roa Hospital during the period 2006-2010, finding a total of 49 patients with cancer during the study. The most frequent cancers in Easter Island's people were breast cancer (8 cases), skin (8 cases), cervical (8 cases), lung (5 cases) and gastric (4 cases). According to gender, in females the most frequent cancer was breast, followed by skin and cervical, while in men, lung, prostate and hematopoietic cancers were the most frequent. Most cases of cervical cancer occurred in women of Rapa Nui ethnicity, while most skin cancers were found in non-Rapa Nui people. In case of the most common cancer in Easter Island, education (e.g. Papanicolaou and mammography screening) and prevention in the community (e.g. use sun block, avoid cigarettes) should be useful tools to reduce incidence.