In this article, we have modeled mortality rates of Peruvian female and male populations during the period of 1950-2017 using the two-factor Lee-Carter (LC) model. The stochastic mortality model was introduced by Lee and Carter (1992) and has been used by many authors for fitting and forecasting the human mortality rates. The Singular Value Decomposition (SVD) approach is used for estimation of the parameters of the LC model. Utilizing the best fitted auto regressive integrated moving average (ARIMA) model we forecast the values of the time dependent parameter of the LC model for the next thirty years. The forecasted values of life expectancy at different age group with 95% confidence intervals are also reported for the next thirty  years. In this research we use the data, obtained from the Peruvian National Institute of Statistics (INEI).  

Currently the coronavirus (COVID-19) infection has become a public health problem worldwide. In December 2019, in the city of Wuhan, province of Hubei, China, the first cases of pneumonia of unknown etiology were reported, which incremented rapidly in other provinces of the country. Subsequently, SARS-CoV2 was identified as the causal agent and in mid-January 2020, the World Health Organization (WHO) reported over 280 confirmed cases of COVID-19 in China, Thailand, Japan and Korea. In South America, the first case of COVID-19 is made known on February 26, 2020 in the city of Sao Paulo, Brazil, identified as a male patient of 61 years of age from the region of Lombardy in Italy. Soon after there were other confirmed cases imported from the Asian and European continents in other south American countries.

Currently the coronavirus (COVID-19) infection has become a public health problem worldwide. In December 2019, in the city of Wuhan, province of Hubei, China, the first cases of pneumonia of unknown etiology were reported, which incremented rapidly in other provinces of the country. Subsequently, SARS-CoV2 was identified as the causal agent and in mid-January 2020, the World Health Organization (WHO) reported over 280 confirmed cases of COVID-19 in China, Thailand, Japan and Korea. In South America, the first case of COVID-19 is made known on February 26, 2020 in the city of Sao Paulo, Brazil, identified as a male patient of 61 years of age from the region of Lombardy in Italy. Soon after there were other confirmed cases imported from the Asian and European continents in other south American countries.

The success of the Peruvian peasant patrols in the fight against subversion or as a result of a more autonomous local process of rural populations in combating rustling and other forms of external aggression has been widely documented in contemporary literature (see, among others, , Churats et al., 2001, Degregori et al., 1996, Guerrero Bravo 2001, Hernández 2000, Yrigoyen 2001). This success, together with the social breadth of the movement and its way of operating in areas supposedly reserved for urban political instances, has even led some authors to propose the Peruvian peasant patrols as "some of the most vital new ways of doing politics in the planet" (Starn 1992).

D. Lavayen would like to recognize the financial support provided by CONCYTEC (Peru) and The World Bank, through the Pontifical Catholic University of Peru and FONDECYT (Peru): ?Funding Contract N?10-2018-FONDECYT/WB PhD programs in strategic and general areas?. Part of this work has also been supported by Comunidad de Madrid - multiannual agreement with UC3M (?Excelencia para el Profesorado Universitario? - EPUC3M21) - Fifth regional research plan 2016-2020, The authors would also like to thank Dr. M. A. Martinez-Casanova from the Materials Science and Engineering and Chemical Engineering Department at UC3M for his help during testing. All authors approved the version of the manuscript to be published.

The predictive philosophy contributes to improving productivity, reducing system failures and reducing unplanned downtime in a non-invasive way to the machine, for which the test bench is based on the German standard VDI2221, using mathematical models to select the materials and the design of the final prototype. The development of the project consists of applying vibration analysis, thermographic analysis and the quality of energy in which each measurement and the correlation that exist between them is shown; in addition, the inverse Fourier transform was used to demonstrate the amplitude and frequency ranges according to the theoretical equation proposed in the Matlab program, it can also be seen the higher order vibrations of 22.1 is located at the same critical point of the SP7 measurement with a temperature of 34.6 ° C and an emissivity of 0.95, likewise the Power quality measureme...

This research was possible thanks to the support of CONCYTEC- Peru, agreement No. 167 FONDECYT-UNI and the Faculty of Sciences of the National University of Engineering, Peru. The spectra of absorption, fluorescence and electron microscopy were obtained thanks to the collaboration with the IFUNAM of Mexico. The high resolution electronic microscopy images were obtained thanks to the collaboration with University of Sonora, Mexico.