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This is a survey on some known properties of the possible Moore graph (or graphs) ϒ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition of ϒ induced by a vertex subset C, the following graphs are distance-regular: The induced graph of the vertices at distance 1 from C when C is a set of 400 independent vertices; the induced graphs of the vertices at distance 2 from C when C is a vertex or an edge, and the line graph of ϒ. Besides, ϒ is an edge-distance-regular graph. ; This research is partially supported by the project 2017SGR1087 of the Agency for the Management of University and Research Grants (AGAUR) of the Government of Catalonia. This research has also received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922.

The domination game is played on a graph by two players, Dominator and Staller, who alternately choose a vertex of G. Dominator aims to finish the game in as few turns as possible while Staller aims to finish the game in as many turns as possible. The game ends when all vertices are dominated. The game domination number, denoted by &gamma ; g ( G ) (respectively &gamma ; g &prime ; ( G ) ), is the total number of turns when both players play optimally and when Dominator (respectively Staller) starts the game. In this paper, we study a version of this game where the set of chosen vertices is always independent. This version turns out to be another game known as the competition-independence game. The competition-independence game is played on a graph by two players, Diminisher and Sweller. They take turns in constructing maximal independent set M, where Diminisher tries to minimize | M | and Sweller tries to maximize | M | . Note that, actually, it is the domination game in which the set of played vertices is independent. The competition-independence number, denoted by I d ( G ) (respectively I s ( G ) ) is the optimal size of the final independent set in the competition-independence game if Diminisher (respectively Sweller) starts the game. In this paper, we check whether some well-known results in the domination game hold for the competition-independence game. We compare the competition-independence numbers to the game domination numbers. Moreover, we provide a family of graphs such that many parameters are equal. Finally, we present a realization result on the competition-independence numbers.

For generalised SOS model with spin values from countable set on a Cayley tree we consider gradient Gibbs measures(GGMs). Such a measure corresponds to a boundary law (i.e. an infinite dimensional vector-valued function defined on vertices of the Cayley tree) satisfying an infinite system of functional equations. We give several concrete GGMs of boundary laws which are independent from vertices of the Cayley tree and have periodic and mirror-symmetric coordinates. Namely, in this paper the particular classes of height-periodic boundary laws of period $q\leq 3$ are studied and solutions are classified by their period and mirror-symmetry.

Summary In a recent paper Snee and Marquardt [8] considered designs for linear mixture models, where the components are subject to individual lower and/or upper bounds. When the number of components is large their algorithm XVERT yields designs far too extensive for practical purposes.The purpose of this paper is to describe a numerical procedure resulting in a design of fixed size N, which is approximately D‐optimal, and where the components may be subject to linear constraints (f.e. upper or lower bounds). The proposed method is more generally applicable for models linear in the independent variables and the parameters and the convex hull of the experimental region is a polyhedron whose vertices are known.

AbstractBackgroundThe flexible boundaries of special districts allow for overlaps with each other that generate various specialized service bundles on a territorial basis. The combined overlapping boundaries may reveal willingness to have more services at additional costs as the special districts generally provide services selectively to those who reside within their boundaries.ObjectiveThis study aims to investigate whether overlapping special districts sort citizens by income level as reflected by the Tiebout model.MethodsThis study utilizes a cross‐sectional block group data of Ventura County in California, taking numbers of vertices of special districts as independent variable and household income as dependent variable.ResultsEstimation result demonstrates that a greater number of specialized services is associated with higher income levels and varies by service type.ConclusionFindings of this study imply that income segregation could be predetermined by jurisdictional boundary, and that other subjects of urban segregation may have similar pattern.

A simple equilibrium model of network flow, based on the topological properties of a given system, is derived with the aid of matrix algebra. This model is then used to characterise the vertices and edges of a network and to analyse real deviations. It is shown that the equilibrium characteristics are independent of the nature of the flow parameters, and are determined solely by the overall structure of the network. Three examples relating to West German railway systems are given as an illustration of the ease with which the networks can be topologically characterised. An extension of the analysis to take account of transport flow beyond boundaries of a region is suggested, which, however, involves appreciable computation work. The model provides a means of carrying out dynamic transport flow analyses relevant to planning, and is an extension of conventional analyses based on Markov chains.

This manuscript summarizes the failure mechanisms found in inorganic fullerene-type tungsten disulfide (IF-WS2) nanoparticles treated with diverse pressure loading methods. The approaches utilized to induce failure included: the use of an ultrasonic horn, the buildup of high pressures inside a shock tube which created a shock wave that propagated and impinged in the sample, and impact with military rounds. After treatment, samples were characterized using electron microscopy, powder X-ray diffraction, energy dispersive X-ray spectroscopy, and surface area analysis. The microstructural changes observed in the IF-WS2 particulates as a consequence of the treatments could be categorized in two distinct fracture modes. The most commonly observed was the formation of a crack at the particles surface followed by a phase transformation from the 3D cage-like structures into the 2D layered polymorphs, with subsequent agglomeration of the plate-like sheets to produce larger particle sizes. The secondary mechanism identified was the incipient delamination of IF-WS2. We encountered evidence that the IF-WS2 structure collapse initiated in all cases at the edges and vertices of the polyhedral particles, which acted as stress concentrators, independent of the load application mode or its duration.

International audience ; Recent years have seen social networks gain lot of popularity to share information, connecting millions of people from all over the world. Studying the spread of information, or Information Diffusion in these networks has shaped into a well known field of study with numerous applications in areas such as marketing, politics, and personality evaluation. Researchers have studied information diffusion under various models and opted centrality-based algorithms that offer better results over many other approaches. These algorithms try to select initial seed nodes effectively so as to maximize influence in a network in minimum time. However, since different networks follow different structural properties, motivating the need to study different diffusion strategies for networks with different structural properties. In this paper, we aim to empirically analyze four different measures of centrality to select seed vertices for influence mining on four classes of networks: small-World networks, scale-free networks, small world-scale free networks and random networks. These networks are generated equivalent in size to four semantically different real world social networks. We use two most frequently used diffusion models: Independent Cascade model and Linear Threshold model for analysis. Our results show interesting behavior of various centrality measures for the above said classes of networks.

The article of record as published may be found at http://dx.doi.org/10.3390/inorganics2030377 ; This manuscript summarizes the failure mechanisms found in inorganic fullerene-type tungsten disulfide (IF-WS2) nanoparticles treated with diverse pressure loading methods. The approaches utilized to induce failure included: the use of an ultrasonic horn, the buildup of high pressures inside a shock tube which created a shock wave that propagated and impinged in the sample, and impact with military rounds. After treatment, samples were characterized using electron microscopy, powder X-ray diffraction, energy dispersive X-ray spectroscopy, and surface area analysis. The microstructural changes observed in the IF-WS2 particulates as a consequence of the treatments could be categorized in two distinct fracture modes. The most commonly observed was the formation of a crack at the particles surface followed by a phase transformation from the 3D cage-like structures into the 2D layered polymorphs, with subsequent agglomeration of the plate-like sheets to produce larger particle sizes. The secondary mechanism identified was the incipient delamination of IF-WS2. We encountered evidence that the IF-WS2 structure collapse initiated in all cases at the edges and vertices of the polyhedral particles, which acted as stress concentrators, independent of the load application mode or its duration.

This is a post-peer-review, pre-copyedit version of an article published in Discrete and computational geometry. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00454-020-00189-w ; We give superexponential lower and upper bounds on the number of coloured d-dimensional triangulations whose underlying space is an oriented manifold, when the number of simplices goes to infinity and d=3 is fixed. In the special case of dimension 3, the lower and upper bounds match up to exponential factors, and we show that there are 2O(n)nn6 coloured triangulations of 3-manifolds with n tetrahedra. Our results also imply that random coloured triangulations of 3-manifolds have a sublinear number of vertices. The upper bounds apply in particular to coloured d-spheres for which they seem to be the best known bounds in any dimension d=3, even though it is often conjectured that exponential bounds hold in this case. We also ask a related question on regular edge-coloured graphs having the property that each 3-coloured component is planar, which is of independent interest. ; This project has received funding from the European Research Council under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. ERC-2016-STG 716083 "CombiTop"). G. Perarnau acknowledges an invitation in Paris funded by the ERC Grant CombiTop, during which this project was advanced. ; Postprint (author's final draft)

In the recent past, regional, national and supranational Science, Innovation and Technology (STI) policies have emphasized supporting interactions and networks between organisations of the innovation system. The policy instrument of the EU in this context are the European Framework Programmes (FPs) that support pre-competitive R&D projects, creating a pan-European network of actors performing joint R&D. In this study, we focus on the embeddedness of European regions in this network. By embeddedness we refer to the notion of centrality in the sense of the Social Network Analysis (SNA) literature. In network theory, vertices that have a more prominent and central network position will more likely benefit from network advantages than actors that have a more distant, peripheral position in the network. A higher network embeddedness of a region, i.e. of organisations located in that region, may increase information and knowledge access in the network, and, thus, create a competitive advantage when it comes to the formation of new collaborations and alliances. The objective of the study is to explain why some regions are able to obtain a better network embeddedness in the European network of R&D cooperation than other regions. For this reason we aim to identify determinants that influence a region's embededdness, involving region-internal factors, such as regional characteristics on their innovation capability, their economic structure and technological specialisation, as well as region-external factors considering the influence of these variables in the neighbourhood of a specific region, referred to as spatial spillovers. To address this question we employ spatial panel modelling techniques, explicitly taking into account the time dimension in our data and the influence of spillovers by specifying a panel spatial durbin error model (SDEM). The dependent variable is the regions' centrality in the FP network for the years 1998-2006, using a sample of 241 NUTS-regions of the EU-25 member states. We aggregate individual FP cooperations to the regional level leading to a network where the nodes are represented by regions and the edges by cross-region collaboration intensities. Using these matrices we calculate a region's centrality relying on two different centrality concepts, namely betweeness- and eigenvector centrality. The independent variables involve regional characteristics related to a region's knowledge production capacity and a region's general economic structure. The results will significantly enrich our understanding of the relationship between a regions network embededdness and its internal and external characteristics.

The CMS Collaboration: et al. ; The first direct, model-independent measurement is presented of the modulus of the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements |Vtb|, |Vtd|, and |Vts|, in final states enriched in single top quark t-channel events. The analysis uses proton-proton collision data from the LHC, collected during 2016 by the CMS experiment, at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb−1. Processes directly sensitive to these matrix elements are considered at both the production and decay vertices of the top quark. In the standard model hypothesis of CKM unitarity, a lower limit of |Vtb| >0.970 is measured at the 95% confidence level. Several theories beyond the standard model are considered, and by releasing all constraints among the involved parameters, the values |Vtb| =0.988 ±0.024, and |Vtd|2+|Vts|2=0.06 ±0.06, where the uncertainties include both statistical and systematic components, are measured ; Individuals have received support from the Marie-Curie programme and the European Research Council and Horizon 2020 Grant, contract Nos. 675440, 752730, and 765710 (European Union); the Leventis Foundation; the Alfred P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium) under the "Excellence of Science – EOS" – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z191100007219010; The Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Deutsche Forschungsgemeinschaft (DFG) under Germany's Excellence Strategy – EXC 2121 "Quantum Universe" – 390833306; the Lendület ("Momentum") Programme and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, the New National Excellence Program ÚNKP, the NKFIA research grants 123842, 123959, 124845, 124850, 125105, 128713, 128786, and 129058 (Hungary); the Council of Science and Industrial Research, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, European Regional Development Fund, the Mobility Plus programme of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/ B/ST2/02861, Sonata-bis 2012/07/E/ST2/01406; the National Priorities Research Program by Qatar National Research Fund; the Ministry of Science and Education, grant no. 14.W03.31.0026 (Russia); the Tomsk Polytechnic University Competitiveness Enhancement Program and "Nauka" Project FSWW-2020-0008 (Russia); the Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa del Principado de Asturias; the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand); The Kavli Foundation; the Nvidia Corporation; the SuperMicro Corporation; The Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA). ; Peer reviewed

This thesis is focused on combining the atomically resolved microscopic picture with the ultrafast sub picosecond picture of laser induced phase transitions in 1T-TaS2. The combination of scanning tunneling microscopy (STM) and pump-probe measurements, gives insight not only into the microscopic ordering and topological nature of different laser induced states in 1T-TaS2, but also into the conditions at which they are formed and the timescales at which they appear. The layered transition metal dichalcogenide 1T-TaS2 has undergone a recent resurgence of interest with the discovery of a stable hidden state, which can be induced by an ultrashort laser or electrical pulse. Since the transition is fast, the material became a very promising candidate for future cryogenic memory elements. I performed multiple excitation intensity dependent switching experiments at different temperatures in order to construct a phase diagram of photoinduced states in 1T-TaS2. It turns out that optical switching to the hidden state is very robust, while on the other hand switching to the other observed states cannot be controllably reproduced using an 800 nm laser. The threshold fluence for switching to the hidden state appears to be temperature independent, suggesting that only the density of the photoinduced carriers is important for the transition. Other photoinduced states such as the amorphous state and states with different chiralities seem to appear more randomly. At high laser powers, I discovered a novel kind of laser induced transformation that is a single layer polytype transformation from 1T to 1H polytype, where local heating and fast quench play a crucial role in formation of the new state. The polytype transformed layer shows a phase transition between the stripe phase and a network of hexagonal vertices, as seen with STM, which show interesting topological nature. I also examined the domain walls between the domains of different chiralities in 1T-TaS2, which appear to have a non-trivial structure. In order to combine the ultrafast measurements with atomically resolved STM scans, I built a prototype THz gated STM. I built and characterized several THz single cycle pulse sources and used them to excite the STM tip. I observed up to 20 pA of rectified THz current, which is expected enough to observe changes in time resolved measurements. The device was not finalized during my research work, but I am nevertheless showing the interesting and helpful experimental observations in order to make the future optimization of the THz resolved STM easier. ; Doktorsko delo je posvečeno povezavi med atomsko ločljivimi mikrokopskimi slikami in ultrahitrimi pod pikosekundnimi meritvami lasersko vzbujenih faznih prehodov v 1T-TaS2. Kombinacija vrstične tunelske mikroskopije (STM) in vzbuditveno testne tehnike nam da vpogled ne le v mikroskopsko sliko urejanja in topološko naravo različnih lasersko vzbujenih stanj, temveč tudi v pogoje pod katerimi se ta stanja pojavijo in v časovno skalo na kateri se oblikujejo. 1T-TaS2 je plastoviti dihalkogenid prehodnih kovin, ki je vzbudil veliko zanimanje z odkritjem stabilnega skritega stanja, ki ga lahko vzbudimo z ultrahitrim laserskim ali električnim sunkom. Ker je prehod hiter, je 1T-TaS2 postal zelo dober kandidat za ultrahitre nizkotemperaturne spominske elemente prihodnosti. Izvedel sem več meritev, kjer sem spreminjal moč in fluenco laserskega snopa pri različnih temperaturah z namenom sestaviti fazni diagram fotoinduciranih stanj v 1T-TaS2. Izkaže se, da je optični preklop v skrito stanje zelo robusten in da je mejna fluenca za preklop enaka pri vseh temperaturah. Po drugi strani pa je preklop med ostalimi stanji težko ponovljiv pri uporabi laserja z valovno dolžino 800 nm. Tako se amorfno stanje in stanja z domenami različnih kiralnosti pri preklapljanju pojavljajo naključno. Pri uporabi visokih moči laserja sem opazil novo vrsto laserske transformacije v kristalu, in sicer gre za politipno transformacijo vrhnje plasti materiala iz 1T v 1H politip, kjer ključno vlogo igra lokalno segrevanje in hitro ohlajanje. Na transformirani površini lahko opazujemo fazni prehod med fazama s črtami in trikotno mrežo, ki kažeta zanimive topološke lastnosti. Podrobneje sem preučil tudi domenske stene med domenami različne kiralnosti, ki nimajo trivialne strukture. Z namenom združiti ultrahitre meritve z atomsko ločljivimi STM slikami sem sestavil teraherčno (THz) prožen STM. Sestavil in karakteriziral sem nekaj virov ultrahitrih teraherčnih sunkov in jih uporabil za vzbujanje konice tunelskega mikroskopa. Opazil sem do 20 pA usmerjenega THz toka, kar je dovolj za opazovanje sprememb v časovno ločljivih meritvah. Naprava v času mojega dela ni bila popolnoma dokončana. Izsledki so kljub temu predstavljeni kot pomoč pri nadaljnji izgradnji in optimizaciji naprave.

En la arena educativa, uno de los focos de tensión irresuelto en la actualidad es el propio de las relaciones entre la escuela pública y la escuela privada. Los partidarios de cada opción participan en un debate apasionado con posiciones sustentadas básicamente en argumentos religiosos, políticos y sociales y ello, ante la carencia de estudios que posibiliten el conocimiento de la génesis y desarrollo de la escuela privada y permitan su tratamiento propiamente educativo. En consecuencia se ha determinado seguir el devenir histórico de la conformación de un sistema de instrucción nacional público y privado junto con el concepto de libertad de enseñanza, garante entre otros de la libertad de creación de centros, al menos desde el liberalismo doceañista hasta los albores de la Guerra Civil en un triángulo matriz cuyos vértices quedan determinados en cada momento histórico por ia ideología gubernamental, la todopoderosa actuación de la Iglesia católica y las siempre escasas partidas económicas dedicadas a la instrucción. El trabajo sigue la metodología de la investigación histórica tradicional procurando interpretar los hechos acaecidos basándose en documentos históricos. El punto de partida no puede ser otro que el R.D. de 1 de julio de 1902 documento que conforma un instrumento de inspección estatal de escuelas privadas que tradicionalmente habían quedado fuera de su control y la documentación consiguiente de más de un centenar de centros educativos que solicitan los trámites de apertura y funcionamiento dirigidos a la Universidad Literaria de Sevilla. Ellos son una fuente de información primigenia acerca de los cuadros de enseñanza (asignaturas, gabinetes y material científico) y documentos de filiación (certificados de buena conducta y residencia )entre otros, además de las condiciones de moralidad e higiene en que se desenvolvían .imprescindibles en la autorización del establecimiento. En esos momentos históricos , la necesaria reforma educativa en cuanto a leyes educativas, planes de estudios, contenidos.etc, cede paso al pulso, estatista de una parte; confesional de otra, por el control político e ideológico de la escuela. A comienzos del s. XX la ciudad de Huelva alcanza elevados índices demográficos y económicos debidos en buena parte a la actividad minera. Así, las necesidades de la población se traducen, bajo la premisa de la mejora de los servicios públicos, a veces en manos privadas, en una mayor demanda de agua, mercados de abastos y escuelas, entre otros. En 1901 el Gobernador civil propondrá al Consistorio una profunda reforma en el abastecimiento de aguas . Urge trazar una red apropiada que provea de agua potable a la población. A este problema se le une poco después, en el verano, las obras de la nueva plaza de abastos que quedarán paralizadas debido a problemas en el ensamblaje metálico de la cubierta .En lo referente a las escuelas, no pocas veces los planteamientos educativos quedarán en un segundo plano, advirtiéndose principalmente el coste que suponen las subvenciones, gratificaciones, construcciones, pago de haberes. en un mapa escolar variopinto donde toman acomodo la escuela pública - nacional, la católica, 1a escuela laica y un colegio. Otro de los problemas que preocupa ai consistorio es el de la mendicidad de oficio, que será estudiado en la Comisión de Beneficencia y el abaratamiento de los artículos de primera necesidad, aspectos de una sociedad en rápido crecimiento. El estudio de la escuela primaria privada requiere el establecimiento de cortes cronológicos. En el primero, que abarca desde principios de siglo hasta 1923 se hace patente el desarrollo "autónomo" de los colegios religiosos aprovechando los pactos con la Iglesia, las confrontaciones políticas, los beneficiosos procedimientos administrativos , al menos en lo relativo a la titulación^ la desidia que acompañaba estos temas. Con Primo de Rivera, el restablecimiento del R.D. de i de julio de 1902 y la proliferación de escuelas y colegios de congregaciones e institutos religiosos. El planteamiento novedoso de la escuela unificada de manos de la República y su programa laico y secular izad or culminará con disposiciones que dictarán la supresión de subvenciones a colegios religiosos, la incautación de sus edificios y la desaparición de algunos colegios. La escuela no oficial de Huelva forma un mosaico complejo y variado. Junto a la escuela de la mina surgida a partir de 1873 con la llegada de capitales extranjeros para la explotación de los criaderos de minerales y a escuela evangélica, tan ligada a ella y algunas pocas escuelas privadas no confesionales .laicas y racionalistas toleradas y vigiladas de cerca , ya en la capital, ya en la provincia, por los servidores de la Iglesia católica. Junto a unos pocos colegios para hijos de obreros, los colegios de primera y segunda enseñanza, garantes de una educación de calidad para la pujante clase media y los colegios y escuelas de órdenes, institutos y congregaciones religiosas, que se asientan en la capital y en desarrolladas localidades provinciales para ofertar junto a una educación de calidad otra de caridad para los más desfavorecidos. Queda patente la importancia de la escuela católica > parte medular del sistema educativo y ello por un doble motivo; por el número creciente de escuelas y colegios establecidos, y por la colonización creciente de sus enseñanzas en el currículo , sin olvidar el papel inspector que ejercen en el resto de escuelas, Restan las escuelas particulares, las más numerosas, las que se encuentran diseminadas por toda la geografía onubense, de corte mayoritariamente femenino si se atiende a la dirección y clientela y que subsiste a duras penas con exiguos pagos o cicateras subvenciones de los ayuntamientos a cambio de matricular a un determinado número de alumnos pobres, aliviando así las sonrojantes listas de matriculación escolar. El mapa escolar ha de completarse con la labor educativa y social de Manuel Siurot en sus Escuelas del Sagrado Corazón de Jesús, transmisor de las enseñanzas de Manjón y !a Escuela Francesa , verdadero referente educativo capitalino que perdura actualmente, Finaliza este trabajo reparando en los protagonistas inmediatos del hecho educativo: el profesorado y el alumnado. Dividido el periodo acotado en cuatro décadas , se estudian en cada una las titulaciones y obligaciones de maestros y maestras, haciendo referencia a los planes de estudio y, cuando los datos lo permiten, reparar en aspectos tales como el estado civil, procedencia, edad y número de maestros y maestras, así como la oferta educativa y los niveles de asistencia en las escuelas públicas, privadas, de patronato y subvencionadas, aspectos que permiten caracterizar la escuela en el periodo mencionado. Esta es nuestra contribución al conocimiento de la escuela privada, conocimiento modesto tanto por la dimensión local como por el estudio de una documentación que refleja parcialmente la realidad, pues si bien es cierto que hemos seguido fielmente todos los documentos de los archivos mencionados, también es cierto que por el camino se han quedado cientos de escuelas "amigas" que quedan fuera de control aunque aún perduren en la memoria. Queda abierta una vía para futuras investigaciones. ; In the educational arena, one of the tension focal points still unresolved at present Is the one belonging to the relationship between the state school and the private (Independent) school. Supporters of each option take part in a passionate debate with positions essentially sustained by religious, political and social arguments due to the lack of studies that make possible the understanding of the genesis and development of the private (independent) school and enable their proper educational treatment. Consequently, it has been determined to follow the historical development of configuration of a national state and private education system together with the concept of academic freedom, guarantor of, among others, the freedom of establishment of centres, at least from the doceanista liberalism to the dawn of the Civil War in a matrix triangle whose vertices are determined in each historical period by the governmental ideology, the powerful action of the Catholic Church and the always scarce economic funds devoted to instruction. The study follows the methodology of traditional historical research trying to interpret the events based on historical documents. The starting point can not be other than the Royal Decree of 1st July 1902, a document that functions as a state inspection instrument of private (independent) schools that had traditionally been beyond its control and the consequent documentation of more than a hundred education centres applying for the opening and operation procedures directed to the Literary University of Seville. They are a primal source of information with regards to teaching charts (subjects, offices and scientific equipment) and affiliation documents (certificates of good behaviour and residence) among others, including the morality and hygiene conditions where they were working, essential for the approval of the establishment. In those historical moments, the necessary educational reform in terms of education laws, curricula, contents.etc, gives way to the arm wrestle, state-controlled on the one hand, confessional on the other, for the political and ideological control of the school. At the beginning of the twentieth century, the city of Huelva reaches high demographic and economic indices largely due to the mining activity. Thus, the population necessities are translated, under the premise of improving public services, sometimes in private hands, in a higher demand for water, food markets and schools among others. In 1901 the Civil Governor will propose to the City Council a major remodelling of the water supply, it urges to design an appropriate network for providing drinking water to the population. This concern is joined shortly after, in summertime, by the building work of the new food market that will be paralysed due to problems with the metallic structure of the roof. With regards to schools, not rarely educational approaches will remain in the background, noticing mainly the costs involving subsidies, school fees, building work, salary payments.in a diverse school map that accomodates the state elementary school - the national, the Catholic, the secular school and a secondary school. Other problems that concern the City Council are the proffesional begging, which will be studied by the Charity Committee, and the price reduction of prime necessity goods, aspects of a society in rapid growth, The study of the private elementary school requires the establishment of chronological frames. In the first one, spanning from the beginning of the century until 1923, is patent the "autonomous" development of religious schools taking advantage of pacts with the Church, political confrontations, beneficial administrative procedures, at least in terms of qualifications, or the apathy that accompanied these issues. With Primo de Rivera, the restoration of the Royal Decree of 1st July 1902 and the proliferation of elementary and secondary schools of religious congregations and religious high schools. The original approach of the unified school thanks to the Republic and its lay and secular plan will culminate in provisions that will dictate the abolition of subsidies to religious schools, the seizure of their buildings and the dissapearance of some schools. The non-official school of Huelva forms a complex and varied mosaic. Together with the school of the mine emerged from 1873 with the arriving of foreign capital for the exploitation of mineral farms and the Evangelical school, so bound to it and a few non-religious private schools, secular and rationalist tolerated and closely monitored, in the capital and the province, by the servants of the Catholic Church. Together with a few schools for the children of labourers, primary and secondary schools, guarantors of a quality education for the burgeoning middle class and elementary and secondary schools of religious orders, high schools and religious congregations, that establish themselves in the capital and in developed provincial localities to offer besides a quality education, a charity one for the most deprived people, it becomes clear the importance of the Catholic school, core of the education system and this is obvious for two reasons: because of the growing number of established primary and secondary schools, and the growing colonisation of their teachings in the curriculum, not forgetting the inspector role they play in the other schools. It remains to mention private home-schools, the most numerous ones, which are scattered throughout the geography of Huelva, mainly for girls if we look into their management and customers, and that hardly survive with meagre payments or stingy subsidies from Town Councils in exchange of enrolling a certain number of poor pupils, relieving in that way the embarrasing school enrolment lists. The school map should be completed with the educational and social work of Manuel Siurot in his schools of the Sagrado Corazón de Jesús, transmitter of the Manjon and French School pedagogies, real capital educational model that currently endures. This paper finishes noticing the immediate leading figures in the educational process: teachers and pupils. Dividing the chosen period in four decades, the qualifications and duties of teachers are estudied in each of them, referencing to the curricuium and, when data allows it, notice aspects such as marital status, origin, age and number of teachers as well as the educational provision and attendance standards of state schools, private (independent) schoois, sponsored schools and subsidised schools, ail aspects that allow to picture the school in the mentioned period of time. This is our contribution to the knowledge of the private (independent) school, modest knowledge for both the local dimension and the study of documentation that reflects the reality only partially, even if we have accurateily followed all the documents of the mentioned archives, it is also true that we had left behind hundred of private "child-friendly" schools (escuelas "amigas3) outside our matter of study even if they still endure in our memory, An avenue for future research remains open.