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].

GENERALIZED PADOVAN SEQUENCES

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_n)_n≥0 defined by 𝓟_n = 𝓟_n-2 + 𝓟_n-3 for all n ≥ 3 with initial conditions 𝓟₀ = 0 and 𝓟₁ = 𝓟₂ = 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.

Frequency of Cholelithiasis and Biliary Pathology in the Easter Island Rapanui and Non-Rapanui Populations

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.

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.

The structure of the Ni 2p photoemission spectra

Mariela BRAVO-SANCHEZ,Gustavo GOMEZ-SOSA,Dagoberto CABRERA-GERMAN,Alberto HERRERA-GOMEZ 한국진공학회 2016 한국진공학회 학술발표회초록집 Vol.2016 No.8

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.

INVERSE SOURCE STRENGTH RECONSTRUCTION TECHNIQUES FOR DUCTED ACOUSTIC SOURCES

Teresa Bravo,Cedric Maury 한국소음진동공학회 2008 한국소음진동공학회 국제학술대회논문집 Vol.2008 No.7

Sentinel Lymph Node Navigation Surgery for Early Gastric Cancer: Is It a Safe Procedure in Countries with Non- Endemic Gastric Cancer Levels? A Preliminary Experience

Guilherme Pinto Bravo Neto,Elizabeth Gomes Dos Santos,Felipe Carvalho Victer,Marcelo Soares Neves,Carlos Eduardo De Souza Carvalho,Marcia Ferreira Pinto 대한위암학회 2016 Journal of gastric cancer Vol.16 No.1

Purpose: Early diagnosis of gastric cancer is still the exception in Western countries. In the East, as in Japan and Korea, this disease is an endemic disorder. More conservative surgical procedures are frequently performed in early gastric cancer cases in these countries where sentinel lymph node navigation surgery is becoming a safe option for some patients. This study aims to evaluate preliminary outcomes of patients with early gastric cancer who underwent sentinel node navigation surgeries in Brazil, a country with non-endemic gastric cancer levels. Materials and Methods: From September 2008 to March 2014, 14 out of 205 gastric cancer patients underwent sentinel lymph node navigation surgeries, which were performed using intraoperative, endoscopic, and peritumoral injection of patent blue dye. Results: Antrectomies with Billroth I gastroduodenostomies were performed in seven patients with distal tumors. The other seven patients underwent wedge resections. Sentinel basin resections were performed in four patients, and lymphadenectomies were extended to stations 7, 8, and 9 in the other 10. Two patients received false-negative results from sentinel node biopsies, and one of those patients had micrometastasis. There was one postoperative death from liver failure in a cirrhotic patient. Another cirrhotic patient died after two years without recurrence of gastric cancer, also from liver failure. All other patients were followed-up for 13 to 79 months with no evidence of recurrence. Conclusions: Sentinel lymph node navigation surgery appears to be a safe procedure in a country with non-endemic levels of gastric cancer.

Prenatal diagnosis of transposition of the great arteries: an updated review

Nathalie Jeanne Bravo-Valenzuela,Alberto Borges Peixoto,Edward Araujo Júnior 대한초음파의학회 2020 ULTRASONOGRAPHY Vol.39 No.4

Simple transposition of the great arteries (TGA) is a cyanotic heart disease that accounts for 5% to 7% of all congenital heart diseases. It is commonly underdiagnosed in utero, with prenatal detection rates of less than 50%. Simple TGA is characterized by ventriculoarterial discordance, atrioventricular concordance, and a parallel relationship of TGA. The prenatal diagnosis of TGA influences postnatal outcomes and therefore requires planned delivery and perinatal management. For these reasons, it is important to identify the key ultrasound markers of TGA to improve the prenatal diagnosis and consequently provide perinatal assistance. The presence of two vessels instead of three in the three-vessel tracheal view, a parallel course of TGA, and identification of the origin of each of TGA are the key markers for diagnosing TGA. In addition to the classical ultrasound signs, other two-dimensional ultrasound markers such as an abnormal right convexity of the aorta, an I-shaped aorta, and the "boomerang sign" may also be used to diagnose TGA in the prenatal period. When accessible, an automatic approach using fourdimensional technologies such as spatio-temporal image correlation and sonographically-based volume computer-aided analysis may improve the prenatal diagnosis of TGA. This study aimed to review the ultrasound markers that can be used in the antenatal diagnosis of TGA, with a focus on the tools used by ultrasonographers, the obstetric and fetal medicine team, and perinatal cardiologists to improve the diagnosis of this condition.