Introduction. - In Mathematical Analysis, integrals are sometimes difficult to solve by integration methods, for this reason it is necessary to think of numerical methods to solve them, if these are definite integrals, even more so when it comes to double integrals. Objective: The ability to solve these integrals depends a lot on the solution knowledge and experience, for this reason the present study presents an alternative solution by numerical methods. Methodology: A double integral conceptually calculates the volume bounded by a surface over a region, the region may be rectangular or non-rectangular. The present study solves the type of indifferently, for which partitions are made along x and y of the region, thus showing a mesh within points (x,y) of the region, which are evaluated in the function f(x,y), which represents the surface, Results: with these values the integral is solved horizontally using the Simpson method and with the result of these it is solved vertically with the same method, obtaining the result of the double integral with excellent precision, Conclusions: a method of calculating double integrals  is then proposed with numerical calculation for rectangular or non-rectangular regions.

Introduction:  When solving non-homogeneous linear differential equations with constant coefficients, it is necessary to find a solution that corresponds to the homogeneous part, denoted as , and a part that corresponds to the non-homogeneous part, denoted as . In the case where the non-homogeneous part has the form , where "a" is one of the roots corresponding to the characteristic equation factors of the differential equation, a peculiarity arises in the solution. Depending on the order in which the factors are found, when setting up the successive integral, it may appear that there are two solutions for . However, upon verifying them in the differential equation, they both satisfy it. This may lead to the belief that it does not comply with the Cauchy's theorem, which states that the differential equation has a unique solution. However, when applying the initial conditions to the general solution: , it does comply with the theorem, confirming that the non-homogeneous linear differential equation with constant coefficients has a unique solution when solved using the method of successive integrals. Thus, the study confirms and verifies that Cauchy's theorem guarantees the existence and uniqueness of a solution that satisfies the initial conditions of an ordinary differential equation. Objective:  Objective: Check that the solution solved by successive integration of a linear ordinary differential equation with constant coefficients, leads to a particular solution of the unique differential equation. Methodology: In the present study, for the resolution of non-homogeneous linear ordinary deferential equations with constant coefficients, the method of successive integrals is used, in addition to using the criterion of verification of the solution of a differential equation, to determine by means of Cauchy's theorem, that the solution is unique in a differential equation when it has specific initial conditions. Results: Starting from a specific case when the non-homogeneous part has the form  where a is a root of the characteristic equation, apparently two solutions are found for the solution, it is verified that the solution is unique by obtaining the solution of the differential equation, with a given initial condition. Conclusion: It is verified that the solution solved by successive integration of a linear ordinary differential equation of constant coefficients, leads to a particular solution of the unique differential equation. General area of ​​study: mathematical analysis. Specific area of ​​study: non-homogeneous linear Ordinary Differential Equations with constant coefficients.

Introduction: In Ecuador in recent years there have been various traffic accidents in which interprovincial buses are involved due to numerous factors that produced these accidents that cause human losses and material damages. Objective: The objective of this work is to analyze the quality and safety of the occupants when they are transferred from one place to another, through the study of the thermal affectation in the microstructure of the material during the welding process. Methodology: The work methodology consists of analyzing the microstructure of welded ASTM A-500 steel specimens through SMAW and GMAW processes and considering standard welding parameters that are used in the country's bodywork industries. For the analysis, the front part of the bus has been considered due to the importance of the loads on this element, the union of the specimens was developed by means of a butt joint and the analysis of thermal stresses in the material was executed in the Ansys software. Results: The microstructural analysis of the specimens before and after the welding processes show the presence of pearlite and ferrite mostly without changes in the morphology of the material, from the thermal analysis it is determined that the GMAW process presents a higher index of thermal conductivity with a value of 0,9255W/ and the maximum deformation that the material presents is 0.17167 mm. Conclusions: Under the parameters analyzed, since there are no changes in the microstructure, it is concluded that a heat treatment is not necessary before or after the welding processes, therefore the mechanical properties of the material are not affected. From thermal analysis it is determined that the zone of influence of heat is approximately 1.5-2mm.

Introduction: according to the  norms decreed in the Constitution of the Republic of Ecuador it is essential to state that in the Organic Integral Criminal Code, currently in force in Ecuadorian legislation, it was determined in this work that prior to the investigation this does not have to be reserved for those persons who participate in the intervention in the criminal process because it would violate the guarantees of the process as well as leave defenseless of the persons involved, it is important to state in the framework of any analysis that a prior investigation is a possible administrative activity of the Prosecutor's Office in which the elements of conviction must be obtained to begin a trial against the accused. Objective: to determine whether the confidentiality of the inquiry in the processes of the person under investigation. Methodology: this research has a documentary-bibliographic character, consisting of the compilation of sources of doctrinal, legal and jurisprudence information compiled through books, libraries, digital repositories, and computer databases in order to give a logical support and order to the ideas presented in relation to the effective exercise of the right to technical defense. Conclusion: by the organic law that has the provision and because it is established in the appropriate constitution there can be no denial to the requests of the victim, suspects or investigated of the physical or electronic certified copies and of the simple copies of the files of the pre-criminal procedure both in the Units of Criminal Guarantees and in the prosecutor's offices.

Introduction: The legality of assisted death is a controversial topic worldwide due to various bioethical aspects. While countries like Luxembourg and Canada have legalized euthanasia, improving the patient's quality of life, negative concerns have also emerged, such as the abandonment of palliative options. Objective: The main purpose of this study is to describe the various bioethical approaches both in favor and against assisted death in Ecuador. Methodology: This article is a descriptive bibliographic review, in which information was compiled from the last 5 years using databases such as PubMed, Scopus, Web of Science, EMBASE, and MedRxiv. Bioethical approaches in favor of assisted death were addressed to alleviate patient symptoms and improve their quality of life. Results: The results indicate that in Ecuador, the constitution contemplates the right to life, so the decriminalization of death is a delicate issue. However, in other countries like the United States and Canada, the decision in favor of assisted death depends on the patient. Furthermore, Ecuador's Comprehensive Penal Code presents ambiguous laws on assisted death, with legal gaps that prevent its application in the health system. Conclusion: Even though the arguments for and against euthanasia are solid, the decision must be adapted to the patient's context and the health system. The need for clearer regulations is evident to avoid misinterpretations and potential abuses.

Introduction. Childhood cancer is one of the main causes of death in the world, this disease generates changes in the lifestyle of the child and the family, several spheres are affected after a diagnosis, for this reason the Pediatric Palliative Care (PPC) arises with the purpose of attending the physical, psychological, social and spiritual needs of the oncologic child and his family. Objective. The aim of this study is to describe the implementation of palliative care in terminally ill pediatric oncology patients. Methodology. A descriptive systematic bibliographic review was carried out in the Scopus, Taylor & Francis, Web Of Science, ProQuest and PubMed databases, the selected articles were subjected to inclusion and exclusion criteria and were reflected by the Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) method, obtaining 19 articles as a result of the purification. Results. The studies reflect the clinical, emotional, spiritual, and social alterations presented by pediatric oncology patients after their diagnosis, and the different medical, psychological, social, and spiritual interventions conducted by the professionals, as well as the benefits at the emotional, behavioral, spiritual, social, biological, and family levels. Conclusion. The research analyzed focuses on the physiological level and, to a lesser extent, on psychological, social, or spiritual intervention. Multidisciplinary care is the scarcity of specialized personnel, observing that psychological care is often addressed by professionals from other health areas such as doctors, nurses, etc., a comparable situation is observed in the social and spiritual area.

Introduction. Diseases transmitted by pathogenic bacteria constitute a worldwide public health issue; these affect low and middle-income countries, e.g., South American countries. Objective. To describe the primary diseases transmitted by pathogenic bacteria present in food in South America. Methodology. This article is a literature review; electronic databases from 2016 were used to select scientific articles due to the lack of recent scientific articles. In addition, the PRISMA method was used to classify the information, where 43 studies were included. Results. The most predominant bacterial-transmitted disease was salmonellosis (17/38; 44.7%). The most frequent etiologic agents were Salmonella spp. at 46.5% and E. coli at 25.6%. In Ecuador, Colombia, Peru, and Chile, salmonellosis was the most prevalent bacteria-borne disease, with 41.7%, 24.5%, 30%, and 50%, respectively, in Paraguay and Brazil, diarrheal syndrome, and Argentina, hemorrhagic colitis, hemolytic uremic syndrome, and thrombotic thrombocytopenic purpura. Conclusion. The most predominant bacterial transmitted disease in South America is salmonellosis; the most frequent etiological agents associated with outbreaks were Salmonella spp. and E. coli. Salmonellosis predominates in Ecuador, Colombia, Peru, and Chile, while in Paraguay and Brazil, it was a diarrheal syndrome, and in Argentina, hemorrhagic colitis, hemolytic uremic syndrome, and thrombotic thrombocytopenic purpura.

Introduction: In recent years, eosinophilic esophagitis has emerged as one of the main causes of chronic gastrointestinal morbidity. Despite its low prevalence, there has been a steady increase in incidence, secondary to new lifestyle changes. Currently, there are established treatment protocols, hence it's crucial to be aware of the latest updates for the well-being of patients. Methodology: This is a narrative bibliographic review study, a broad literature review, about the update in the therapeutic management of eosinophilic esophagitis in adults, such as Pub Med, Scielo, Cochrane Library, and Science Direct, as part of the PRISMA strategy. Results: 57 studies were reviewed, which compiled the main recommendations on the update in the therapeutic management of eosinophilic esophagitis in adults. Conclusions: Eosinophilic esophagitis is a chronic disease secondary to an immune dysregulation process, whose incidence is increasing and its management should be comprehensive and be made up of pathologists, allergists, and nutrition specialists. This should be suspected in any patient with symptoms of refractory GERD or with dysphagia to solids or liquids, especially in young atopic males, besides clinical suspicion alone is an indication for a prompt endoscopic study and biopsy, even in a patient with a normal-looking esophagus.

Introduction: The Covid-19 pandemic, globally, had repercussions on various aspects of the health of affected patients. Beyond respiratory compromise, it was evident that a large part had nutritional compromise such as sarcopenia, which is defined as the presence of loss of muscle mass and muscle function. Objective: To substantiate sarcopenia in adult patients post covid-19. Methodology: A narrative bibliographic review was conducted, for which articles selected from official pages of the Catholic University of Cuenca, in scientific databases such as: Pubmed, Scopus, and the Virtual Health Library were chosen. Results: The lack of resolutive capacity of medical centers in the face of the COVID-19 pandemic overlooked the nutritional evaluation of hospitalized patients, increasing the risk of sarcopenia, a pathology that increases morbidity and mortality and hospital stay.

Introduction: The circadian rhythm regulates metabolic changes in 24-hour cycles. In healthcare workers with night shifts, lower quality of life, emotional fatigue, and obesity are observed. Studies indicate sleep and dietary disturbances, with possible traits of anxiety or depression. Metabolic and cardiovascular diseases worsen with disruptions in the sleep-wake cycle. Objective: To establish the metabolic effects of circadian rhythm disruption in hospital healthcare workers. Methodology: This study is a narrative literature review on the metabolic effects of circadian rhythm disruption in hospital healthcare workers. Articles from the last 5 years in English and Spanish, from various sources and countries, were included. Relevant keywords were used, and studies without open access were excluded. Results were synthesized in a database with information on author, year, study type, population, and observed metabolic effects. Results: Circadian rhythm disruption in healthcare workers is associated with changes in the ability to process stimuli and alterations in clock genes affecting metabolic health. Increased fasting glucose levels and alterations in phospholipid metabolism, with elevated triglycerides and HDL, were observed. Night shift workers experience sleep disorders, chronic fatigue, work-related stress, and reduced performance compared to conventional schedules, increasing the risk of occupational accidents. Conclusion: Circadian rhythm disruption in healthcare workers is linked to diabetes, hypertension, and metabolic syndrome. Rotating night shift workers every 2 months normalizes the circadian rhythm and reduces long-term metabolic effects. Prolonged night shifts without adequate rest cause physical problems and increase the risk of depression and Burnout syndrome. Night work affects attention and critical judgment, posing risks to patients. Lack of staff, insufficient rest periods, and poor diet are major contributors to circadian disruption.