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Since the airborne transmission of SARS-CoV-2 is the key in the spread of COVID-19, the interest in the quality of the air in enclosed spaces has become utmost importance. Natural ventilation is the first obvious option to improve epidemiological security, and general rules have been widely disseminated. Nevertheless, the changes in weather conditions greatly limit the validity of such rules. Here we present a system that, upon the introduction of basic parameters of a given space, its volume, location, orientation, architectural environment and average occupancy, yields optimized ventilation times on the basis of wind meteorological forecasts. It has been successfully implemented in the educative system of the Autonomous Community of Galicia (northwest Spain) and it is currently operative.

In recent years, the demand for health care has increased owing to the ongoing introduction of new health problems and the intensification of existing illnesses. As research in this area progresses, knowledge becomes the primary motivation for patients to adopt a better quality of life. Consequently, many health units have struggled to develop solutions to manage excessive demand while maintaining a high quality of service to enhance patient satisfaction and boost revenues. One of these tactics is using simulation models as a method of operational research to analyze the flow of patients and predict potential solutions to enhance resource efficiency while decreasing waiting time. This work aims to develop and demonstrate a simulation model that replicates the functioning of a hospital unit. For this purpose, data derived from the health services of the Imaging Department of a private hospital, located in Lisbon, Portugal, were used. This model will replicate the daily flow that this department is subjected to by its patients and personnel and depict how the system evolves due to the management of the department's number of resources and examination rooms. At the end of the analyses, several solutions are presented and discussed, from level to level, concerning improvements in the performance of services, resources and patients. However, only the increase in one unit of examination rooms translates into a huge positive impact on waiting times in the respective queues.

Artículo publicado en OA por convenio de la Universidad de Sevilla con el editor.

The assessment of the acute impact of Daylight Saving Time (DST) transitions is a question of great interest for an understanding of the benefits and inconveniences of a practice that is now under public scrutiny in Europe and America.Here we report a thorough analysis of a record of twelve well-known research studies that re- ported increased risks associated with DST transitions in health issues —acute myocardial infarction, ischemic strokes— and in societal issues —accidents, traffic accidents and fatal motor vehicle accidents—.We found that a 5% increase of the risks suffices to understand the reported increased risks associated with the spring transition. Reported values above this threshold are impacted by the sample size of the study.In the case of the autumn transition, no increase of the risks is found.

Social dynamics are shaped by each person's actions, as well as by collective trends that emerge when individuals are brought together. These latter kind of influences escape anyone's control. They are, instead, dominated by aggregate societal properties such as size, polarization, cohesion, or hierarchy. Such features add nuance and complexity to social structure, and might be present, or not, for societies of different sizes. How do societies become more complex? Are there specific scales at which they are reorganized into emergent entities? In this paper we introduce the {\em social complexity spectrum}, a methodological tool, inspired by theoretical considerations about dynamics on complex networks, that addresses these questions empirically. We use as a probe a sociolinguistic process that has unfolded over decades within the north-western Spanish region of Galicia, across populations of varied sizes. We estimate how societal complexity increases monotonously with population size; and how specific scales stand out, at which complexity would build up faster. These scales are noted as dips in our spectra, similarly to missing wavelengths in light spectroscopy. Also, `red-' and `blue-shifts' take place as the general population shifted from more rural to more urban settings. These shifts help us sharpen our observations. Besides specific results around social complexity build-up, our work introduces a powerful tool to be applied in further study cases., 13 pages, 4 figures

We study the stability of the cohabitation of French and Dutch in the Brussels-capital region (Belgium). To this aim, we use available time series of fractions of speakers of monolinguals of both tongues as well as the fractions of bilinguals. The time series span a period from the mid-XIX century until 1947, year of the last accepted linguistic census. During this period, French penetrated the Dutch-vernacular region of Brussels and started a language shift that lasts to this day. The available time series are analyzed with a mathematical model of sociolinguistic dynamics that accounts for cohabitation of languages along bilingualism. Our equations are compatible with long-term coexistence of both languages, or with one tongue taking over and extinguishing the other. A series of model parameters (which we constrain by fitting our equations to the data) determine which long-term trajectory (cohabitation or extinction) would be followed. This allows us to estimate whether the empirical data are compatible with a coexistence of Dutch and French -- in physics terms, whether both tongues are {\em miscible}. Our results tilt towards non-coexistence, or coexistence with a starkly-dominated, minority language. The costs of attempting to sustain such sociolinguistic system are discussed., Comment: 10 pages, 5 figures

The impact of seasonal time arrangements and the call for its cancellation made by the Juncker Commission in 2018 is analyzed. From the results of the public consultation on time arrangements launched by the European Commission and the Harmonized European Time Use Survey we show that an earlier the onset of human activity predicts less appetence for practicing seasonal regulations of time. The result is in line with the primordial goal of the regulation. The complexity of deciding which clock should survive is reviewed in relation with the span in longitude of Member States. This issue may have helped the decision to stall. We conclude that, in face of the myriad of societal and geographical issues that impact this regulation and the large variability across Member States the European Commission should have not taken a political action on this issue. Instead it should have allowed opt-outs and play the technocratic role of regulating transition dates for those Member State that preferred to continue the practice.

A plethora of temperature induced phase transitions have been observed in $[CH_3NH_3][M(HCOO)_3]$ compounds, where M is Co(II) or Ni(II). Among them, the nickel compound exhibits a combination of magnetic and nuclear incommensurabil-ity below N\'eel temperature. Despite the fact that the zero-field behavior has been previously addressed, here we study in depth the macroscopic magnetic behavior of this compound to unveil the origin of the atypical magnetic response found in it and in its parent family of formate perovskites. In particular, they show a puzzling magnetization reversal in the curves measured starting from low temperatures, after cooling under zero field. The first atypical phenomena is the im-possibility of reaching zero magnetization, even by nullifying the applied external field and even compensating it for the influence earth's magnetic field. Relatively large magnetic fields are needed to switch the magnetization from negative to positive values or vice versa, which is compatible with a soft-ferromagnetic system. The atypical path found in its first magnetization curve and hysteresis loop at low temperatures is the most noticeable feature. The magnetization curve switches from more than 1200 Oe from the first magnetization loop to the subsequent magnetization loops. A feature that cannot be explained using a model based on unbalanced pair of domains. As a result, we decipher this behavior in light of the incommensurate structure of this material. We propose, in particular, that the applied magnetic field induces a mag-netic phase transition from a magnetically incommensurate structure to a magnetically commensurate structure., Comment: 9 pages, 7 figures, 1 table

By March 14th 2022, Spain is suffering the sixth wave of the COVID-19 pandemic. All the previous waves have been intimately related to the degree of imposed mobility restrictions and its consequent release. Certain factors explain the incidence of the virus across regions revealing the weak locations that probably require some medical reinforcements. The most relevant ones relate with mobility restrictions by age and administrative competence, i.e., spatial constrains. In this work, we aim to find a mathematical descriptor that could identify the critical communities that are more likely to suffer pandemic outbreaks and, at the same time, to estimate the impact of different mobility restrictions. We analyze the incidence of the virus in combination with mobility flows during the so-called second wave (roughly from August 1st to November 30th, 2020) using a SEIR compartmental model. After that, we derive a mathematical descriptor based on linear stability theory that quantifies the potential impact of becoming a hotspot. Once the model is validated, we consider different confinement scenarios and containment protocols aimed to control the virus spreading. The main findings from our simulations suggest that the confinement of the economically non-active individuals may result in a significant reduction of risk, whose effects are equivalent to the confinement of the total population. This study is conducted across the totality of municipalities in Spain SI

En este artículo se analizan las dificultades de aprendizaje de la Teoría de la Relatividad Restringida deEinstein. La información se ha obtenido y seleccionado de las bases de datos Web of Science, Scopus,Educational Resources Information Center y Google Scholar, teniendo en cuenta los índices de valoraciónJournal Citation Reports (JCR), Scimago Journal Rank (SJR) e Índice Compuesto de Difusión Secundaria (ICDS).Para el análisis y las conclusiones se establecieron las dificultades de aprendizaje del alumnado relacionadas con laRelatividad Restringida de Einstein, respecto a los siguientes conceptos: Espacio y tiempo. Causalidad ysimultaneidad. Sistemas de referencia. Energía. Masa. Luz. El presente estudio ha constituido el fundamento del diseño de una propuesta de enseñanza basada en laformulación geométrica de Minkowski, dirigida a estudiantes de bachillerato In this article we analyze the learning difficulties of Einstein's Theory of Restricted Relativity. The information has been obtained and selected from the Web of Science, Scopus, Educational Resources Information Center and Google Scholar databases, taking into account the Journal Citation Reports (JCR),Scimago Journal Rank (SJR) and Composite Index of Secondary Dissemination (ICDS).For the analysis and the conclusions the learning difficulties of the students related to the Restricted Relativity of Einstein were established, with respect to the following concepts: Space and time. Causality and simultaneity. Reference frames. Energy. Mass. Light. This study has been the basis for the design of a teaching proposal based on the geometric formulation of Minkowski, aimed at high school students X. P. y J. M. D. C. hacen constar que el presente trabajo se enmarca en los proyectos ESPIGA (PGC2018-096581-B-C22) y EAMARE-STEAM (EDU2017-84979-R) y agradecen la financiación al fondo Europeo de Desarrollo Regional (FEDER)/Agencia Estatal de Investigación del Ministerio de Ciencia, Innovación y Universidades. I. A. agradece la ayuda de los proyectos ED431B 2018/57, de la Consellería de Educación,Universidad y Formación Profesional (Xunta de Galicia) y FIS2017-83762-P, del Ministerio de Economía, Industria y Competitividad. Á. P. agradece la ayuda de los proyectos MTM2016–75140–P, de la Agencia Estatal de Investigación, co-financiado por fondos FEDER, y R 2016/022, de la Xunta de Galicia SI

With the goal of developing didactic tools, we consider the geometrization of the addition of velocities in special relativity by using Minkowski diagrams in momentum space. For the case of collinear velocities, we describe three ruler-and-compass constructions that provide simple graphical solutions working with the mass-shell hyperbola in a 1 + 1-dimensional energy–momentum plane. In the spirit of dimensional scaffolding, we use those results to build a generalization in 1 + 2 dimensions for the case of non-collinear velocities, providing in particular a graphical illustration of how the velocity transverse to a boost changes while the momentum remains fixed. We supplement the discussion with a number of interactive applets that implement the diagrammatic constructions and constitute a visual tool that should be useful for students to improve their understanding of the subtleties of special relativity.

The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. After identification of the population readiness to follow social restrictions, by analyzing the social media, we incorporate this effect in a version of the model that allow us to check different scenarios. This is realized by considering a Monte Carlo discrete version of the previous model coupled via a complex network. Then, we apply optimal control theory to maximize the number of people returning to "normal life" and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool., Comment: Paper whose final and definite form is published Open Access by 'Scientific Reports', ISSN 2045-2322, Springer Nature. Submitted 01/Sept/2020; Revised 16/Dec/2020; Accepted 27/Jan/2021; Published by [www.nature.com/scientificreports], see [https://doi.org/10.1038/s41598-021-83075-6]

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The aim of this work was to show the evolution over time of the dynamic moduli in components made of Polybutylene Terephthalate reinforced with glass fiber when they are held to temperatures close to the glass transition temperature over time. For this purpose, PBT samples reinforced with short, glass fibers of Ultradur&reg, material with 0%, 20%, and 50% in weight content were tested. Dynamic moduli showed an increment with glass fiber content showing a nonlinear behavior with the temperature. The evolution of storage modulus was depicted by means of a modified law of mixtures with an effectiveness factor depending on temperature and fiber content, whereas the evolution over time was obtained with a time&ndash, temperature transformation generated with the TTS Data Analysis software of TA-instruments for a given temperature. Storage modulus showed a linear relationship with glass fiber content when components were held to temperatures near to their respective glass transition temperature, obtained from the maximum of loss modulus curve with temperature. In summary, the value and evolution of dynamic moduli of PBT samples improved with glass fiber content, allowing us to increase the durability of components when they are submitted to high-temperature environments.

SIGNIFICANCE: The options that can help patients with congenital color vision defect, to a better professional and leisure adaptation, are very limited. Different haploscopic lenses can be considered, and their effects need to be investigated in patients with different defects. PURPOSE: The purpose of this study was to present and discuss the effect of a pair of asymmetric long-pass filters fitted for deuteranopia, with the result of a 60% improvement in distinguishing red-green plates when compared with baseline. CASE REPORT: We report the case of a 51-year-old man with congenital deuteranopia fitted with haploscopic ChromaGen filters. During the 2-month follow-up, we observed a decrease in left-eye logMAR visual acuity and contrast sensitivity with an increased ability to discriminate the plates of different color vision tests (Ishihara, Farnsworth, and Hardy-Rand-Rittler). The visual outcomes are discussed considering the spectral sensitivity curves of each filter, measured with a spectrophotometric device. CONCLUSIONS: This report describes an improvement in the ability to resolve color vision plates after using asymmetric haploscopic filters showing a left-eye decrease in logMAR visual acuity and contrast sensitivity function. Subjects with a history of color vision deficiency might benefit from using haploscopic filters that selectively minimize the transmittance within a specific bandwidth to improve the color discrimination in deutan color vision deficiency. The simultaneous analysis of the color vision outcomes and transmittance spectrum of the haploscopic filters might contribute to a better understanding of the mechanisms behind the claimed efficacy of these devices.

The morphogeometric analysis of the corneal structure has become a clinically relevant diagnostic procedure in keratoconus (KC) as well as the in vivo evaluation of the corneal biomechanical properties. However, the relationship between these two types of metrics is still not well understood. The current study investigated the relationship of corneal morphogeometry and volume with two biomechanical parameters: corneal hysteresis (CH) and corneal resistance factor (CRF), both provided by an Ocular Response Analyzer (Reichert). It included 109 eyes from 109 patients (aged between 18 and 69 years) with a diagnosis of keratoconus (KC) who underwent a complete eye examination including a comprehensive corneal topographic analysis with the Sirius system (CSO). With the topographic information obtained, a morphogeometric and volumetric analysis was performed, defining different variables of clinical use. CH and CRF were found to be correlated with these variables, but this correlation was highly influenced by corneal thickness. This suggests that the mechanical properties of KC cornea contribute only in a partial and limited manner to these biomechanical parameters, being mostly influenced by morphogeometry under normal intraocular pressure levels. This would explain the limitation of CH and CRF as diagnostic tools for the detection of incipient cases of KC. This publication was carried out in the framework of the Thematic Network for Co-Operative Research in Health (RETICS) reference number RD12/0034/0007 and RD16/0008/0012, financed by the Carlos III Health Institute—General Subdirection of Networks and Cooperative Investigation Centers (R&D&I National Plan 2008–2011) and the European Regional Development Fund (FEDER). The author David P. Piñero has been supported by the Ministry of Economy, Industry, and Competitiveness of Spain within the program Ramón y Cajal, RYC-2016-20471.

Given the rapidly evolving landscape of linguistic prevalence, whereby a majority of the world's existing languages are dying out in favor of the adoption of a comparatively fewer set of languages, the factors behind this phenomenon has been the subject of vigorous research. The majority of approaches investigate the temporal evolution of two competing languages in the form of differential equations describing their behavior at large scale. In contrast, relatively few consider the spatial dimension of the problem. Furthermore while much attention has focused on the phenomena of language shift---the adoption of majority languages in lieu of minority ones---relatively less light has been shed on linguistic coexistence, where two or more languages persist in a geographically contiguous region. Here, we study the geographical component of language spread on a discrete medium to monitor the dispersal of language species at a microscopic level. Language dynamics is modeled through a reaction-diffusion system that occurs on a heterogeneous network of contacts based on population flows between urban centers. We show that our framework accurately reproduces empirical linguistic trends driven by a combination of the Turing instability, a mechanism for spontaneous pattern-formation applicable to many natural systems, the heterogeneity of the contact network, and the asymmetries in how people perceive the status of a language. We demonstrate the robustness of our formulation on two datasets corresponding to linguistic coexistence in northern Spain and southern Austria., 21 pages, 10 figures

Vehicular networks are based on the wireless exchange of information between vehicles and between vehicles and road side units. To avoid overloading the radio channel, different distributed congestion control mechanisms have been proposed in the literature. A widely adopted mechanism to control congestion is packet rate control. It controls the number of packets that each vehicle transmits to the radio channel through packet dropping. Packet dropping has been shown to effectively improve the radio communications performance thanks to the reduction of the channel load and packet collisions. However, from the application perspective, packets dropped by congestion control mechanisms are not transmitted and are therefore lost. This paper demonstrates for the first time that, while packet dropping can improve the performance at the radio level, it degrades the performance at the application level. This raises the question on whether current congestion control protocols based on packet dropping are actually suitable for vehicular networks.

In this research, a new sequential batch reactor (SBR) coupled to an internal magnetic separator was developed. The separator consists of a set of axially magnetized permanent toroidal magnets, distributed along a non-magnetic steel rod, uniformly spaced with alternate polarity, which provide an external magnetic field of up to 1.2 T. The feasibility of magnetic separation was assessed for the retention of the nanobiocatalyst based on laccase immobilized on silica-coated MNPs. The proof of concept was evaluated for the enzymatic decolorization of the methyl green (MG) dye and the oligomerization of rutin, with virtually complete recovery of the nanobiocatalyst (99%) and high biotransformation efficiency of both compunds. The characterization of the reaction products of MG by laccase was conducted by high performance liquid chromatography (HPLC) with a diode array detector (DAD) coupled to mass spectrometry (MS) using the electrospray ionization source (ESI) (HPLC-DAD-ESI-MS). Moreover, the biotransformation products showed less microtoxicity than the parent compound and increased biodegradability. Beyond laboratory scale experiments, the reactor proposed here was scaled-up to a volume of 100 L and the environmental performance and cost analysis were estimated.

Magnetic resonance imaging (MRI) is considered the gold standard to reliably diagnose inflammation in the temporomandibular joint (TMJ) of patients with juvenile idiopathic arthritis (JIA). However, even MRI imaging is dependent on the familiarity of the radiologist with the normal appearance of the TMJ; therefore, new approaches are needed. Our purpose here is to improve imaging quality of cone beam computed tomography (CBCT) as a tool to help in the diagnosis of JIA in the TMJ. We have designed and applied a filter (the Stacking Enhancement Filter) over a stock of CBCT images from the TMJs of two patients with JIA. We then made a visual comparison of the results with archival images from MRI of the same patients, to show that the filter substantially improves the visual quality of the image. The work on the image contrast and the increase of the difference of appearance between tissues of different densities (all the anatomical structures that are present within the joint) leads to an improvement of the resulting images of the TMJ without the use of a chemical contrast agent. We conclude that CBCT could be used as a filter tool for the analysis of the TMJs affected by arthritis. Our image processing technique yields images that possible improve the range of use of CBCT.

Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the one-dimensional case, charge and current densities, the electric field E and the scalar and vector potentials get a geometric interpretation in spacetime diagrams. The geometric vector derivative applied to these magnitudes yields simple expressions leading to concepts like displacement current, continuity and gauge or retarded time, with a clear geometric meaning. As the geometric vector derivative is invertible, we introduce simple Green's functions and, with this, it is possible to obtain retarded Li\'enard-Wiechert potentials propagating naturally at the speed of light. In two dimensions, these magnitudes become more complex, and a magnetic field B appears as a pseudoscalar which was absent in the one-dimensional world. The laws of induction reflect the relations between E and B, and it is possible to arrive to the concepts of capacitor, electric circuit and Poynting vector, explaining the flow of energy. The solutions to the wave equations in this two-dimensional scenario uncover now the propagation of physical effects at the speed of light. This anticipates the same results in the real three-dimensional world, but endowed in this case with a nature which is totally absent in one or three dimensions. Electromagnetic waves propagating entirely at the speed of light can thus be viewed as a consequence of living in a world with an odd number of spatial dimensions. Finally, in the real three-dimensional world the same set of simple multivector differential expressions encode the fundamental laws and concepts of electromagnetism., Comment: 32 pages, 26 figures

We study the stability of two coexisting languages (Catalan and Spanish) in Catalonia (North-Eastern Spain), a key European region in political and economic terms. Our analysis relies on recent, abundant empirical data that is studied within an analytic model of population dynamics. This model contemplates the possibilities of long-term language coexistence or extinction. We establish that the most likely scenario is a sustained coexistence. The data needs to be interpreted under different circumstances, some of them leading to the asymptotic extinction of one of the languages involved. We delimit the cases in which this can happen. Asymptotic behavior is often unrealistic as a predictor for complex social systems, hence we make an attempt at forecasting trends of speakers towards $2030$. These also suggest sustained coexistence between both tongues, but some counterintuitive dynamics are unveiled for extreme cases in which Catalan would be likely to lose an important fraction of speakers. As an intermediate step, model parameters are obtained that convey relevant information about the prestige and interlinguistic similarity of the tongues as perceived by the population. This is the first time that these parameters are quantified rigorously for this couple of languages. Remarkably, Spanish is found to have a larger prestige specially in areas which historically had larger communities of Catalan monolingual speakers. Limited, spatially-segregated data allows us to examine more fine grained dynamics, thus better addressing the likely coexistence or extinction. Variation of the model parameters across regions are informative about how the two languages are perceived in more urban or rural environments., Comment: 10 pages, 3 figures, preprint

Spin-phonon coupling in rare-earth based manganites with double perovskite structure plays a crucial role in the magnetoelectric properties of these ferromagnetic materials. Particularly, on Y2CoMnO6 (YCMO), it is assumed that spin-phonon coupling is related to the induced ferroelectric polarization. This confers to YCMO a multiferroic characteristic. In this work, we probed the spin-phonon coupling in YCMO by temperature-dependent Raman spectroscopy measurements in ceramic samples obtained by the nitrate decomposition method. Raman scattering revealed some anomalies that could be attributed to a weak spin-phonon coupling, an unconventional behavior for rare-earth based manganites with double perovskite structure, in which the coupling does not fit with the quadratic magnetization.

In this work, the incorporation of dicyanamide building blocks in organic–inorganic hybrid compounds is found to be a promising strategy for the synthesis of multiwalled carbon nanotubes embedded with magnetic nanoparticles (M@CNTs). Following a novel one-step, scalable and fast synthetic route, M@CNTs are obtained by simple calcination of the organic–inorganic hybrid perovskite [TPrA][M(dca)3] (TPrA = tetrapropylammonium, M = Ni2+ and Co2+, dca = dicyanamide). The resulting M@CNTs (M = Ni and Co) display a regular morphology and an essentially mesoporous network of ∼250 m2 g−1, whereas the Co@CNT composite displays a broad pore size distribution (PSD) up to 6 nm, Ni@CNTs show a strictly controlled unimodal PSD, centered at around 5 nm. Monitoring of their thermal decomposition by X-ray diffraction, electron microscopy, thermogravimetric and spectroscopic analyses allows proposing a calcination mechanism and establishing the conditions to obtain optimal materials. Moreover, magnetization studies reveal a ferromagnetic behaviour of the obtained M@CNTs, with small coercive fields due to the size of the magnetic nanoparticles. In addition, preliminary assays of oil adsorption–desorption capacity reveal a promising potential for spilled oil recovery using this easily-synthesized materials. All these physicochemical properties make these composites good candidates for other nitrogen-rich CNT common applications., The authors are grateful for the financial support from Ministerio de Economía y Competitividad MINECO and EU‐FEDER under project ENE2014‐56237‐C4‐4‐R and Xunta de Galicia under project GRC2014/042. J. M. B.‐G. wants to thanks Barrié Foundation for a predoctoral fellowship and S. Y.‐V. to the Xunta de Galicia for a postdoctoral fellowship

We consider a modification of the model proposed by Abrams and Strogatz to describe the death of a language when it competes with a stronger one within the same community of speakers. The modification opened the possibility of coexistence of both languages under some conditions, but so far it has not been possible to write down the expression of the equilibrium points. In this paper, we nontrivially use bifurcation theory to calculate under which conditions such coexistence arises; namely, we calculate the specific ranges of the parameters that describe the modified model to have this situation, paying special attention to the cases that yield a stable cohabitation of two monolingual populations along with a bilingual one.