Zeros of irreducible characters in factorised groups

[EN] An element g of a finite group G is said to be vanishing inG if there exists an irreducible character of G such that (g)=0; in this case, g is also called a zero of G. The aim of this paper is to obtain structural properties of a factorised group G=AB when we impose some conditions on prime power order elements gAB which are (non-)vanishing in G.The first author is supported by Proyecto PrometeoII/2015/011, Generalitat Valenciana (Spain). The second author is supported by Proyecto MTM2014-54707-C3-1-P, Ministerio de Economia, Industria y Competitividad (Spain), and by Proyecto Prometeo/2017/057, Generalitat Valenciana (Spain). The third author acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana Spain).Ortiz-Sotomayor, VM.; Felipe Román, MJ.; Martínez-Pastor, A. (2019). Zeros of irreducible characters in factorised groups. Annali di Matematica Pura ed Applicata (1923 -). 198:129-142. https://doi.org/10.1007/s10231-018-0765-5S129142198Arroyo-Jordá, M., Arroyo-Jordá, P., Martínez-Pastor, A., Pérez-Ramos, M.D.: On conditional permutability and factorized groups. Ann. Mat. Pura Appl. 193, 1123–1138 (2014)Arroyo-Jordá, M., Arroyo-Jordá, P., Pérez-Ramos, M.D.: On conditional permutability and saturated formations. Proc. Edinb. Math. Soc. 54, 309–319 (2011)Ballester-Bolinches, A., Cossey, J., Li, Y.: Mutually permutable products and conjugacy classes. Monatsh. Math. 170, 305–310 (2012)Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups. Vol. 53 of de Gruyter Expositions in Mathematics, Berlin (2010)Bianchi, M., Brough, J., Camina, R.D., Pacifici, E.: On vanishing class sizes in finite groups. J. Algebra 489, 446–459 (2017)Brough, J.: Non-vanishing elements in finite groups. J. Algebra 460, 387–391 (2016)Brough, J.: On vanishing criteria that control finite group structure. J. Algebra 458, 207–215 (2016)Brough, J., Kong, Q.: On vanishing criteria that control finite group structure II. ArXiv (2017). arXiv:1702.03179Camina, A.R., Camina, R.D.: Implications of conjugacy class size. J. Group Theory 1(3), 257–269 (1998)Cossey, J., Li, Y.: On the structure of a mutually permutable product of finite groups. Acta Math. Hungar. 154(2), 525–529 (2018)Cossey, J., Wang, Y.: Remarks on the length of conjugacy classes of finite groups. Commun. Algebra 27, 4347–4353 (1999)Doerk, K., Hawkes, T.: Finite Soluble Groups. Vol. 4 of de Gruyter Expositions in Mathematics, Berlin (1992)Dolfi, S., Pacifici, E., Sanus, L.: Groups whose vanishing class sizes are not divisible by a given prime. Arch. Math. (Basel) 94, 311–317 (2010)Dolfi, S., Pacifici, E., Sanus, L., Spiga, P.: On the orders of zeros of irreducible characters. J. Algebra 321, 345–352 (2009)Felipe, M.J., Martínez-Pastor, A., Ortiz-Sotomayor, V.M.: Square-free class sizes in products of groups. J. Algebra 491, 190–206 (2017)Felipe, M.J., Martínez-Pastor, A., Ortiz-Sotomayor, V.M.: Prime power indices in factorised groups. Mediterr. J. Math. 14(6), article: 225 (2017)Isaacs, I.M.: Character Theory of Finite Groups. Academic Press Inc., London (1976)Isaacs, I.M., Navarro, G., Wolf, T.R.: Finite group elements where no irreducible character vanishes. J. Algebra 222, 413–423 (1999)Malle, G., Navarro, G., Olsson, J.B.: Zeros of characters of finite groups. J. Group Theory 3, 353–368 (2000

Products of groups and class sizes of pi-elements

[EN] We provide structural criteria for some finite factorised groups G = AB when the conjugacy class sizes in G of certain pi-elements in A boolean OR B are either pi-numbers or pi'-numbers, for a set of primes pi. In particular, we extend for products of groups some earlier resultsM. J. Felipe is supported by Proyecto Prometeo II/2015/011, Generalitat Valenciana (Spain). A. Martínez-Pastor is supported by Proyecto MTM 2014-54707-C3-1-P, Ministerio de Economía, Industria y Competitividad (Spain), and by Proyecto Prometeo/2017/057, Generalitat Valenciana (Spain). The results in this paper are part of the V. M. Ortiz Sotomayor Ph.D. thesis, and he acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana (Spain). The authors are also supported by Proyecto PGC2018-096872-B-I00, Ministerio de Ciencia, Innovación y UniversidadesFelipe Román, MJ.; Martínez-Pastor, A.; Ortiz-Sotomayor, VM. (2020). Products of groups and class sizes of pi-elements. Mediterranean Journal of Mathematics. 17(1):1-20. https://doi.org/10.1007/s00009-019-1444-5S120171Amberg, B., Franciosi, S., de Giovanni, F.: Products of Groups. Oxford University Press Inc., New York (1992)Ballester-Bolinches, A., Cossey, J., Li, Y.: Mutually permutable products and conjugacy classes. Monatsh. Math. 170, 305–310 (2013)Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups, vol. 53 of de Gruyter Expositions in Mathematics, Berlin (2010)Beltrán, A., Felipe, M.J.: Prime powers as conjugacy class lengths of $$\pi$$-elements. Bull. Austral. Math. Soc. 69, 317–325 (2004)Beltrán, A., Felipe, M.J., Malle, G., Moretó, A., Navarro, G., Sanus, L., Solomon, R., Tiep, P.H.: Nilpotent and abelian Hall subgroups in finite groups. Trans. Am. Math. Soc. 368, 2497–2513 (2016)Berkovich, Y., Kazarin, L.S.: Indices of elements and normal structure of finite groups. J. Algebra 283, 564–583 (2005)Doerk, K., Hawkes, T.: Finite Soluble Groups, vol. 4 of de Gruyter Expositions in Mathematics, Berlin (1992)Dolfi, S.: Arithmetical conditions on the length of the conjugacy classes of a finite group. J. Algebra 174, 753–771 (1995)Dolfi, S., Pacifici, E., Sanus, L., Spiga, P.: On the orders of zeros of irreducible characters. J. Algebra 321, 345–352 (2009)Felipe, M.J., Martínez-Pastor, A., Ortiz-Sotomayor, V.M.: Prime power indices in factorised groups, Mediterr. J. Math. 14 (6) (2017), article: 225Felipe, M.J., Martínez-Pastor, A., Ortiz-Sotomayor, V.M.: Zeros of irreducible characters in factorised groups. Ann. Mat. Pura Appl. 198, 129–142 (2019)Itô, N.: On finite groups with given conjugate types I. Nagoya Math. J. 6, 17–28 (1953)Navarro, G., Tiep, P.H.: Abelian Sylow subgroups in a finite group. J. Algebra 398, 519–526 (2014)Zhao, X.H., Guo, X.Y., Shi, J.Y.: On the conjugacy class sizes of prime power order $$\pi$$-elements. South. Asian Bull. Math. 35, 735–740 (2011

Multiplicity of solutions in model‑based multi objective optimization of wastewater treatment plants

Wastewater treatment process design involves the optimization of multiple conflicting objectives. The detection of different equivalent solutions in terms of objective values is crucial for designers in order to efficiently switch to the new optimal operation policies if changes in the process conditions or new constraints occur. In this work, the dynamic multi-objective optimization of a municipal wastewater treatment plant model is carried out. The aim is to simultaneously optimize an economic cost term and an effluent quality index. The selected process variables for the optimization are (1) an aeration factor in the aerated tank previous to the clarifier, and (2) an internal recycle flow rate. Their time profiles are approximated using the control vector parameterization technique. To solve the multi-objective problem and find the Pareto front, the NSGA-II algorithm has been used. The simulation of different realistic scenarios which impose operational constraints (e.g., maintenance operations) reveals that, indeed, multiple solutions exist at least in some areas of the Pareto front. It is observed that different control profiles can produce nearly identical results in terms of Pareto solutions. The a priori knowledge of these equivalent solutions for different scenarios provides the decision makers with alternative choices to be adapted to their organizations policies when events altering decision variables bounds or adding new constraints to the process model occur.The authors are grateful to Ministry of Science, Innovation and Universities (MICINN) and FEDER for their fnancial support (Projects DPI2016-77538-R and RTI2018-099139-B-C21

Blue energy for sustainable water reclamation in WWTPs

The benefits of wastewater (WW) reclamation to alleviate the stress of freshwater resources are counterbalanced by the required energy demand to drive the treatments. This handicap can be considerably minimized when renewable energy sources are integrated to perform this process, increasing the environmental and energy sustainability of the reclamation process. This work reports the assessment of a new strategy for WW reclamation in shoreline wastewater treatment plants (WWTPs) through the conversion of the salinity gradient energy (SGE) generated in the contact between reclaimed water (RW) and seawater (SW) to electricity by the use of reverse electrodialysis (RED). Secondary effluents from the selected WWTP were further treated by a simple remediation process consisting of coagulation-flocculation and solids removal, ending with a filtration stage; the obtained RW contained 0.008 M NaCl and was used as low concentrated solution in the RED stack; besides, filtered SW with 0.5 M NaCl, was employed as high concentrated solution. The plant run for 480 h, reaching gross power up to 1.43 W/m2 without decay along the operation time indicating that no fouling issues appeared in this time period. This represents a great improvement in comparison to the results published in the literature so far; the slight increase in the salinity of RW still allowed for its further reuse. Thus, a novel and energy sustainable strategy to promote WW reclamation with simultaneous SGE recovery is presented.The authors want to acknowledge financial support from the Community of Cantabria - Regional Plan for the project: Gradisal “RM16-XX-046-SODERCAN/FEDER”, as well as the projects funded by the Spanish Ministry of Economy and Competitiveness CTQ2015-66078-R, and CTM2017-87850-R. This research is also being supported by the Project “HYLANTIC”-EAPA_204/2016, which is co-financed by the European Regional Development Fund in the framework of the Interreg Atlantic program

Aplicación de nanotubos de Ti/TiO2 en pilas de combustible microbianas

[ESP] En este trabajo se han elaborado y caracterizado electrodos formados por nanotubos de Ti/TiO2 (TiNT) para su posterior uso como material catódico en pilas de combustible microbianas (MFCs). Su evaluación se llevó a cabo en sistemas de doble cámara separados por una membrana intercambiadora de protones basada en el líquido iónico cloruro de metiltrioctil amonio. El proceso se llevó a cabo en discontinuo, a 25ºC y como sustrato se usó agua residual de base oleica con una carga orgánica de 400mg.L-1. La eficiencia de los materiales desarrollados se midió en términos de eliminación de demanda química de oxígeno (CODR 70%) y potencia generada (12.13mW.m-3). [ENG] In this work, Ti/TiO2 nanotubes (TiNT) electrodes were prepared, characterized and applied as cathode electrodes in double chamber microbial fuel cells (MFCs). The anode used was carbon rod/graphite granules and the separator was a homogeneous proton exchange membrane based on methyltrioctylammonium chloride. Industrial wastewater from a production factory of paraffin oil with a chemical oxygen demand initial value of 400mg.L-1(COD) was used as substrate. The analysis was performed in batch mode at 25°C and the efficiency of the microbial fuel cells was assessed in terms of soluble organic matter removal (70%) and capability of power generation (12.13mW.m-3).Centro Universitario de la Defensa. Escuela de Turismo de Cartagena. Escuela Técnica Superior de Ingeniería Industrial UPCT. Escuela Técnica Superior de Ingeniería de Telecomunicación (ETSIT). Escuela de Ingeniería de Caminos y Minas (EICM). Escuela de Arquitectura e Ingeniería de Edificación (ARQ&IDE). Parque Tecnológico de Fuente Álamo. Navantia. Campus Mare Nostrum. Estación Experimental Agroalimentaria Tomás Ferr

Evaluation of Ionic Liquids as In Situ Extraction Agents during the Alcoholic Fermentation of Carob Pod Extracts

Anhydrous ethanol is a promising alternative to gasoline in fuel engines. However, since ethanol forms an azeotrope with water, high-energy-consumption separation techniques such as azeotropic distillation, extractive distillation, and molecular sieves are needed to produce anhydrous ethanol. This work discusses the potential development of an integrated process for bioethanol production using ionic liquids and Ceratonia siliqua as a carbohydrate source for further fermentation of the aqueous extracts. A four-stage counter-current system was designed to improve the sugar extraction yield to values close to 99%. The alcoholic fermentation of the extracts showed ethanol concentrations of 95 g/L using the microorganism Saccharomyces cerevisae. The production of anhydrous ethanol through extractive distillation with ethylene glycol was simulated using CHEMCAD software, with an energy consumption of 13.23 MJ/Kg of anhydrous ethanol. Finally, several ionic liquids were analyzed and are proposed as potential solvents for the recovery of bioethanol for the design of an integrated extraction-fermentation-separation process, according to their ability to extract ethanol from aqueous solutions and their biocompatibility with the microorganism used in this study.This research was funded by the Fundación Séneca, grant number 20957/PI/18 and The Ministry of Economy and Competitiveness (MINECO) grant number RTI2018-099011-B-I00

Efecto de ciclos hidratación-deshidratación durante la germinación en semillas del género ferocactus

El proceso de germinación para la planta es una etapa arriesgada durante su ciclo de vida, en especial para aquellas pertenecientes a zonas áridas como ocurre con las cactáceas, que pasan por períodos discontinuos de hidratación, por lo que, la memoria de hidratación es un proceso vital y una adaptación natural para estas plantas. En el presente trabajo se utilizaron las semillas de E. grusonii, F. clausen, F. peninsulae, F. pilosus, F. recurvus; de las cuales únicamente la última de estas evidenció dicho fenómeno al expresar curvas de germinación similares a F. peninsulae, planta que en el 2014 fue confirmada la presencia de este proceso; la temperatura, además del agua, fue un factor de restricción en los ensayos, al someter a las especies a distintas temperaturas que afectaron en mayor medida la germinación conforme esta disminuyó.The germination process for the plant is a risky stage during its life cycle, especially for those belonging to arid areas such as cacti, which go through discontinuous periods of hydration, so hydration memory is a process vital and a natural adaptation for these plants. In the present work the seeds of E. grusonii, F. clausen, F. peninsulae, F. pilosus, F. recurvus were used; of which only the last of these evidenced this phenomenon by expressing germination curves similar to F. peninsulae, a plant that in 2014 was confirmed the presence of this process; temperature, in addition to water, was a restriction factor in the tests, by subjecting the species to different temperatures that affected germination to a greater extent as it decreased

Deep eutectic solvents for the extraction of fatty acids from microalgae biomass: Recovery of omega-3 eicosapentaenoic acid

Microalgae are a vast group of autotrophic microorganisms whose metabolic diversity makes them a natural source of valuable organic compounds such as lipids, carbohydrates, proteins, vitamins, and bioactive molecules. Several microalgae species contain notable amounts of polyunsaturated fatty acids, particularly eicosapentaenoic acid (EPA), which is an important alpha-linolenic acid derivative for human health. Conventional methods are considered effective at recovering total lipids from microalgae, however, they imply the use of large volumes of organic solvents such as methanol and chloroform, which are toxic and pose environmental risks. Thus, it is necessary to find new methods involving sustainable and green extracting phases. Deep eutectic solvents (DES) are renewable compounds often formed, but not exclusively, by quaternary ammonium salts and non-hydrated metal halides. Due to their availability, low cost, biodegradability, and environmental friendliness, DES are a promising alternative to organic solvents in extraction processes. This work assesses the efficiency of several DES phases for the extraction of fatty acids from the microalgae Nannochloropsis gaditana with a special interest in the recovery of EPA. The tested phases include mixtures containing choline chloride, lactic acid, ethylene glycol, and sodium acetate. Their performances were compared to those provided by conventional methods based on the use of organic solvents. Specifically, an in-situ transesterification process based on methanol with 10 %v/v of HCl was optimized in terms of temperature, time, and catalyst amount to be used as a reference. The results show that several of the tested eutectics such as choline chloride-ethylene glycol were capable of matching and even outperforming the best results obtained for EPA, with 104 % of extracted EPA methyl ester as the percentage of the mass obtained with HCl-methanol. The extraction capacity of DES was also improved by microalgae biomass pretreatment using ultrasonic and NaCl-based methods in a further stage. In the case of EPA extraction, and under optimal conditions, DES were capable of recovering over 18 % more quantity than the obtained with HCl-methanol. These results demonstrate that DES are effective at both recovering total fatty acids from pretreated biomass and at selectively recovering EPA using both unpretreated and pretreated biomass.The authors wish to acknowledge the financial support of the Ministry of Science, Innovation, and Universities (MICINN) ref. RTI2018-099011-B-I00 and the Seneca Foundation Science and Technology Agency of the Region of Murcia ref. 20957/PI/18. Dr. Sergio Sánchez Segado wishes to acknowledge The Ministry of Science, Innovation, and Universities of Spain its support through the “Beatriz Galindo” Fellowship BEAGAL18/00079

Estandarización de RT-PCR durante la expresión diferencial de genes en el proceso de hidratacióndeshidratación de Ferocactus peninsulae y Ferocactus recurvus

El objetivo del presente estudio fue estandarizar la técnica de RT-PCR para la expresión diferencial de genes durante la germinación de F. peninsulae y F. recurvus con tiempos de hidratación-deshidratación. Se empleó cDNA obtenido previamente a distintos tiempos de germinación con un tratamiento de hidratación y deshidratación. Previo a la estandarización, se diseñaron los iniciadores a utilizar por medio del programa primer3 para posteriormente evaluar su calidad junto con la del cDNA, la RT-PCR se llevó a cabo con kits comerciales. Se amplificaron regiones de los genes CASP, ULP, SEEP, LEAP, FEER, TRXH, junto con ACTINA para cactáceas como testigo. Los resultados de la RT-PCR determinaron en relación a la expresión de actina y la técnica fue capaz de reconocer diferencias de expresión entre cada tiempo, gen y especie.The objective of this study was to standardize the RT-PCR technique for differential gene expression during germination of F. peninsulae and F. recurvus with hydrationdehydration times. CDNA previously obtained at different germination times was used with a hydration and dehydration treatment. Prior to standardization, the first ones to be used were designed through the primerr program to subsequently evaluate their quality along with that of the cDNA. The RT-PCR was carried out with commercial kits. Regions of the CASP, ULP, SEEP, LEAP, FEER, TRXH genes were amplified, along with ACTINA for cacti as control. The results of the RT-PCR were determined in relation to actin expression and the technique was able to recognize differences in expression among each time, gene and species

A family study on first episode of psychosis patients: exploring neuropsychological performance as an endophenotype

Introduction: Family studies provide a suitable approach to analyzing candidate endophenotypes of schizophrenia, including cognitive features. Objective: To characterize different neurocognitive functions in a group of patients with first episode of psychosis (FEP), their first-degree relatives (parents and siblings), and healthy controls (HC), in order to identify potential endophenotypes for schizophrenia spectrum disorders (SSD). Methods: Participants were assessed in the context of a national project in Spain called PAFIP-FAMILIAS. They completed the same neuropsychological battery, which included tests of verbal memory, visual memory, processing speed, working memory, executive functions, motor dexterity, attention, and theory of mind. Group comparisons were performed using one-way ANOVA, followed by tests of multiple comparisons when appropriate. Results: One hundred thirty-three FEP patients were included, as well as 244 of their first-degree relatives (146 parents and 98 siblings) and 202 HC. In general, relatives showed an intermediate performance between the HC and the FEP patients in all neurocognitive domains. However, the domains of executive functions and attention stood out, as relatives (especially parents) showed similar performance to FEP patients. This was replicated when selecting patients subsequently diagnosed with schizophrenia and their relatives. Conclusion: These findings suggest that executive and attention dysfunctions might have a family aggregation and could be relevant cognitive endophenotypes for psychotic disorders. The study shows the potential of exploring intra-family neuropsychological performance supporting neurobiological and genetic research in SSD.Funding information: Instituto de Salud Carlos III; Fundación Marqués de Valdecilla; Universidad de Cantabria Acknowledgments: The authors wish to thank the PAFIP-FAMILIAS research team, and especially all the patients and their relatives who participated in the study. The PAFIP-FAMILIAS project received funding from the Carlos III Health Institute (FIS PI17/00221). Additionally, this work was supported by a Miguel Servet contract from the Carlos III Health Institute (Dr. Rosa Ayesa-Arriola) (CP18/00003), and a predoctoral contract (Nancy Murillo-Garcia) from the Valdecilla Biomedical Research Institute and the University of Cantabria (BOC49, REF. IDI-13)