Articles de revues sur le sujet « Structures en boucle R »

LaNiO3−δ single crystals have been obtained via high pressure floating zone growth under 149 bar of oxygen pressure. We find a radial gradient in the magnetic properties of specimens extracted from the as-grown boule, which we correlate with the appearance of ordered oxygen vacancy structures. This radial oxygen inhomogeneity has been characterized systematically using a combination of magnetization and X-ray scattering measurements. We establish the presence of rhombohedral ( R 3 ¯ c ), oxygen stoichiometric specimens at the periphery of the boule and the presence of a dilute concentration of ordered oxygen-deficient orthorhombic La2Ni2O5 in the center. Furthermore, we demonstrate that the as-grown, oxygen-deficient central regions of the crystal can be annealed under high oxygen pressure, without loss of crystallinity, into fully oxygenated LaNiO3, recovering magnetic properties that are characteristic of stoichiometric specimens from the exterior region of the crystal. Thus, single crystals of LaNiO3−δ possess oxygen content that can be reversibly modified under oxidizing and reducing conditions.

Point defects and their clusters in bismuth germanate single crystals free from grain boundaries and having low density of dislocations were studied by high-resolution diffuse X-ray scattering measurements. Differences in defects in the colourless crystals (type A) and the crystals having yellow tinge (type B), which were grown with different raw materials, were investigated. In addition, interesting differences in defect structures in specimens from different regions of the same boule were investigated. Specimens with diffracting surfaces along (111), (112) and (100) planes were studied. A multicrystal X-ray diffractometer employing a well collimated and highly monochromated Mo Kα1 beam and set in (+,−,−,+) configuration was employed. The diffraction curves of all the samples were quite narrow with half-widths in the range 7–11 arcsec, which are close to the theoretically expected values, if instrumental broadenings are taken into account. The observed distribution of diffuse X-ray scattering (DXS) intensity showed that not all the point defects are isolated but a significant fraction are agglomerated into clusters. Experimental data of DXS intensity were analysed by using a phenomenological model for a small concentration of dislocation loops wherein the point defects are loosely clustered with weak interactions among them. From this analysis, the cluster radius R cl, cluster volume A cl, the number of point defects within a cluster N cl and the relative concentration of the point-defect clusters among the samples were estimated. It was observed that cluster sizes do not vary from sample to sample. However, it was found that the concentration of clusters is approximately twice in the coloured sample compared with that of the colourless sample from the same boule. Annealing of the crystals at 1273 K produced an increase in point-defect clusters by a factor of ∼200. It was accompanied by a reduction in volume of clusters by a factor of ∼0.14.

This presentation proposes an approach to designing technology-enhanced learning (TEL) through the strategic integration of diverse multimodal media forms within a framework informed by the 4E+ view of cognition. The 4E+ cognition framework emphasises the embodied, embedded, enactive, and extended nature of cognition, suggesting that cognition is not solely confined to the brain but extends into the environment while involving the body's interactions with that environment (Carney, 2020; Jianhui , 2019; Menary, 2010; Newen, et al., 2018). In this theoretical context, our study explores how the combination of various modes of media, such as immersive technologies, digital interactive elements, real-world analogue creations, audio, sound, images, videos, animations, text, and the surrounding environment can be orchestrated to create sensorially rich, and more meaningful learning experiences (Gilakjani, et al., 2011; Philippe, et al., 2020; Sankey, et al., 2010). For example, mixed reality (XR) learning design combines immersive media forms to support multi-sensory and expanded cognitive learning (Philippe et al., 2020; Rakkolainen et al., 2021; Villalobos & Videla, 2023). Other relevant approaches include gamification and transmedia storytelling methods (Doumanis et al., 2019; Perry, 2020). By leveraging different modalities, educators can design learning materials that engage learners with different sensory activations and presentation methods (Bouchey et al., 2021). This approach can cater to the 4E+ view of cognition, and subsequently enhancing knowledge acquisition and retention. Examples from our own practice and research (such as the Explora: Chile es Mar, Pipi’s World and O-Tū-Kapua XR learning experiences), as well as current educational examples (Bouchey et al., 2021; Philippe, et al., 2020), demonstrate how multimodal media integration facilitates deeper engagement, critical thinking, and a more holistic understanding of complex concepts. Furthermore, we discuss practical strategies for educators to implement these principles in their TEL design, highlighting the potential of aligning multimodal design choices with the 4E+ cognitive framework. Ultimately, we advocate for a shift towards a more inclusive and effective approach to technology-enhanced learning - one that embraces the diversity of human cognitive processes and leverages multimodal media to communicate meaningful knowledge in ways that resonate with learners' cognitive structures and experiences. Multimodal methods, when aligned with the distributed 4E+ view of cognition, can make TEL appeal and resonate on deeper levels to engage across various sensory, environmental and communication modes. This type of approach acknowledges the diversity of ways that humans process and understand phenomena, and how more effective learning can occur when multiple ways of knowing are engaged and communicated to. Furthermore, through this method, inclusivity can be heightened for students with diverse cultural, neurological or other backgrounds (Anis & Khan, 2023; Boivin & CohenMiller, 2022). Emerging research shows the potential of the 4E+ approach to meet the needs of learning in 21st century technological environments (Videla & Veloz, 2023; Villalobos & Videla, 2023). This presentation contributes to the literature by examining TEL design through a multimodal media lens. It highlights how the holistic 4E+ framework can more effectively and meaningfully engage students than computational, monomodal and bimodal uses of technology in educational settings. References Anis, M., & Khan, R. (2023). Integrating Multimodal Approaches in English Language Teaching for Inclusive Education: A Pedagogical Exploration. Boivin, A. C. N., & CohenMiller, A. (2022). INCLUSION AND EQUITY WITH MULTIMODALITY DURING COVID-19. Keep Calm, Teach On: Education Responding to a Pandemic, 87. Bouchey, B., Castek, J., & Thygeson, J. (2021). Multimodal learning. Innovative Learning Environments in STEM Higher Education: Opportunities, Challenges, and Looking Forward, 35-54. Carney, J. (2020). Thinking avant la lettre: A Review of 4E Cognition. Evolutionary studies in imaginative culture, 4(1), 77-90. Doumanis, I., Economou, D., Sim, G. R., & Porter, S. (2019). The impact of multimodal collaborative virtual environments on learning: A gamified online debate. Computers & Education, 130, 121-138. Gilakjani, A. P., Ismail, H. N., & Ahmadi, S. M. (2011). The effect of multimodal learning models on language teaching and learning. Theory & Practice in Language Studies, 1(10). Jianhui, L. (2019). Transcranial Theory of Mind: A New Revolution of Cognitive Science. International Journal of Philosophy, 7(2), 66-71. Menary, R. (2010). Introduction to the special issue on 4E cognition. Phenomenology and the Cognitive Sciences, 9, 459-463. Newen, A., De Bruin, L., & Gallagher, S. (Eds.). (2018). The Oxford handbook of 4E cognition. Oxford University Press. Perry, M. S. (2020). Multimodal Engagement through a Transmedia Storytelling Project for Undergraduate Students. Gema Online Journal of Language Studies, 20(3). Philippe, S., Souchet, A. D., Lameras, P., Petridis, P., Caporal, J., Coldeboeuf, G., & Duzan, H. (2020). Multimodal teaching, learning and training in virtual reality: a review and case study. Virtual Reality & Intelligent Hardware, 2(5), 421-442. Rakkolainen, I., Farooq, A., Kangas, J., Hakulinen, J., Rantala, J., Turunen, M., & Raisamo, R. (2021). Technologies for multimodal interaction in extended reality—a scoping review. Multimodal Technologies and Interaction, 5(12), 81. Sankey, M., Birch, D., & Gardiner, M. W. (2010). Engaging students through multimodal learning environments: The journey continues. Proceedings of the 27th Australasian Society for Computers in Learning in Tertiary Education, 852-863. Videla, R., & Veloz, T. (2023). The 4E approach applied to education in the 21st century. Constructivist Foundations, 18(2), 153-157. Villalobos, M., & Videla, R. (2023). The roots and blossoms of 4E cognition in Chile: Introduction to the Special Issue on 4E cognition in Chile. Adaptive Behavior, 31(5), 397-404.

Nous présentons un modèle de compréhension de la clinique de l’agir sexuel de l’enfant par l’activation d’un mécanisme de la destructivité par emboîtement. À travers la présentation et l’analyse d’une étude de cas, nous constaterons que les agirs sexuels sont aussi révélateurs du fonctionnement familial et institutionnel. Nous aborderons les effets de cette révélation sur les groupes concernés, notamment la capacité disruptive, voire destructive, qu’elle revêt. Prenant racine au sein d’un environnement fragilisé par une histoire traumatique, voire transgénérationnelle, nous découvrirons que les agirs sexuels peuvent entraîner une « boucle groupale interactive d’agirs » face au décontenancement dans l’attente d’une régulation.

Résumé Cet article apporte une contribution théorique au débat sur le sous-investissement en capitaux publics. Il utilise pour cela un jeu différentiel d’accumulation de capitaux entre deux collectivités. Dans ce jeu l’équilibre de Nash en boucle ouverte et la solution centralisée du jeu convergent à long terme vers un régime stationnaire. Dans le long terme nous étudions la nature de l’inefficacité de l’équilibre de Nash en prenant comme référence la solution centralisée utilitariste. Lorsque les stocks d’infrastructures sont des compléments stratégiques, les collectivités surinvestissent (sous-investissent) en présence d’externalités négatives (positives). Lorsque les stocks d’infrastructures sont des substituts stratégiques, les mêmes résultats restent vrais si les collectivités sont similaires. En revanche, nous montrons dans un exemple que lorsque les collectivités ont des structures de coûts assez différentes, la collectivité qui a le coût le plus faible sous-investit tandis que la collectivité qui a le coût le plus fort surinvestit. Nous discutons ensuite brièvement les implications de ces résultats en termes de politiques économiques.

An analysis of plausible crystal structures of R-phase and precursory structures in Ti-Ni based on solely kinematical data on presence and equivalence of extra-reflections of diffraction patterns, as well as further data on symmetry of structure was carried out. A character of possible ordering and displacements, required to form these phases from parent BCC lattice, was determined. A classification of possible structures was given.

Much of recursion theory centers on the structures of different kinds of degrees. Classically there are the Turing degrees and r. e. Turing degrees. More recently, people have studied α-degrees for α an ordinal, and degrees over E-closed sets and admissible sets. In most contexts, deg(0) is the bottom degree and there is a jump operator' such that d' is the largest degree r. e. in d and d' > d. Both the degrees and the r. e. degrees usually have a rich structure, including a relativization to the cone above a given degree.A natural exception to this pattern was discovered by S. Friedman [F], who showed that for certain admissible ordinals β the β-degrees ≥ 0′ are well-ordered, with successor provided by the jump.For r. e. degrees, natural counterexamples are harder to come by. This is because the constructions are priority arguments, which require only mild restrictions on the ground model. For instance, if an admissible set has a well-behaved pair of recursive well-orderings then the priority construction of an intermediate r. e. degree (i.e., 0 < d < 0′) goes through [S]. It is of interest to see just what priority proofs need by building (necessarily pathological) admissible sets with few r. e. degrees.Harrington [C] provides an admissible set with two r. e. degrees, via forcing. A limitation of his example is that it needs ω1 (more accurately, a local version thereof) as a parameter. In this paper, we find locally countable admissible sets, some with three r. e. degrees and some with four.

Chemical analysis of archaeological sediments is a research area that has long interested archaeologists but has seen recent developments. It locates concentrations of chemical elements in soils that can be linked to ancient activities responsible for their deposition. The use of X-ray fluorescence spectrometry, a more accessible analytical technique than others, makes it possible to analyze large batches of samples. At Ulpiana, two trenches were studied. In the first area, the presence of a lime pit and a mortar preparation area was identified. The signature of the lime seems to correspond to that produced in a kiln discovered further north. In the second area, a bronze recycling workshop was identified, along with a suspected dye molecule. About the authors Arthur Laenger Arthur Laenger studied history, archaeology, and chemistry at Le Mans University (France) and obtained his PhD in archaeology and the history of the Middle Ages in 2006, under the supervision of A. Durand and A. Martel. His work focuses on the characterization of structures and archaeological sites using an interdisciplinary approach that combines history, archaeology, and chemical soil analysis. Arnaud Martel Arnaud Martel was born in 1974 in Le Mans, France. He undertook studies in chemistry at the Université du Maine, obtaining his PhD in 2001. Subsequently, he conducted postdoctoral research with Prof. G. Guillaumet at ICOA (Orleans, France) and with Prof. H. Ottosson in Uppsala (Sweden). He was appointed assistant professor in 2004 and attained the rank of full professor at the Université du Maine in 2013. His research interests encompass organic chemistry, DFT-assisted elucidation of reaction mechanisms, and analytical chemistry. His research is currently focused on the development of new analytical methodologies applied in a multidisciplinary approach ranging from archaeology to environmental sciences. Aline Durand Aline Durand studied history, latin and anthracology in Paris I Panthéon-Sorbonne University and obtained her PhD under the supervision of R. Fossier and J.-L. Vernet (1991). Assistant professor in Aix-Marseille University (1992-2013), she is full professor of Middle Age history and archaeology at Le Mans University from 2013. She is particularly interested on rural economy of the X th -beginning XIII th centuries in the Mediterranean French area (Languedoc, Provence, Southern French Alps). Her research tries to interweave diverse sources: written documents (diplomatic documentation or agronomic treatises), archaeological data, bioarchaeological and palaeoenvironmental results. She works on agrarian landscapes, vegetal resources management, practices and knowledge on plants. To gain a better understanding of craft production techniques and their environmental impact, she developed an ethnoarchaeological research in Morocco, using archaeological methods observe and record them. Fabien Boucher Fabien Boucher was born in 1978 in Le Mans, France. He first studied chemistry at the University of Maine where he obtained a DUT in Chemistry (the French equivalent of a Bachelor's degree) and continued his studies at the Rennes School of Chemistry (Universityof Rennes). There he obtained an engineering degree in analytical chemistry. After spending more than 10 years in laboratories providing environmental analysis services, he returned to the University of Le Mans as a study engineer. He worked there in particular as a research support in analytical chemistry and participated in the development of new analytical methodologies applied to various fields of chemistry, biology and archaeology.

In this paper, we first study infinitesimal deformations of a Lie conformal algebra and a Lie conformal algebra with a module (called an [Formula: see text] pair), which lead to the notions of the Nijenhuis operator on the Lie conformal algebra and the Nijenhuis structure on the [Formula: see text] pair, respectively. Then, by adding compatibility conditions between Nijenhuis structures and [Formula: see text]-operators, we introduce the notion of an [Formula: see text]-structure on an [Formula: see text] pair and show that an [Formula: see text]-structure gives rise to a hierarchy of pairwise compatible [Formula: see text]-operators. In particular, we show that compatible [Formula: see text]-operators on a Lie conformal algebra can be characterized by Nijenhuis operators on Lie conformal algebras. Finally, we introduce the notions of the conformal r-matrix-Nijenhuis structure and symplectic-Nijenhuis structure on Lie conformal algebras and study their relations.

AbstractIn a paper from 2002, Hovey introduced the Gorenstein projective and Gorenstein injective model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring. These two model structures are Quillen equivalent and in fact there is a third equivalent structure we introduce: the Gorenstein flat model structure. The homotopy category with respect to each of these is called the stable module category of R. If such a ring R has finite global dimension, the graded ring R[x]/(x2) is Gorenstein and the three associated Gorenstein model structures on R[x]/(x2)-Mod, the category of graded R[x]/(x2)-modules, are nothing more than the usual projective, injective and flat model structures on Ch(R), the category of chain complexes of R-modules. Although these correspondences only recover these model structures on Ch(R) when R has finite global dimension, we can set R = ℤ and use general techniques from model category theory to lift the projective model structure from Ch(ℤ) to Ch(R) for an arbitrary ring R. This shows that homological algebra is a special case of Gorenstein homological algebra. Moreover, this method of constructing and lifting model structures carries through when ℤ[x]/(x2) is replaced by many other graded Gorenstein rings (or Hopf algebras, which lead to monoidal model structures). This gives us a natural way to generalize both chain complexes over a ring R and the derived category of R and we give some examples of such generalizations.

The structures of six 1-phenylethylammonium tartrates have been determined and in each of them a distinctive hydrogen-bonded anion substructure can be identified. (S)-1-Phenylethylammonium (R,R)-hydrogen tartrate [(I), P21, Z′ = 1] contains anion sheets built from a single type of R_4^4(22) ring with cations pendent, via three N—H...O hydrogen bonds, from just one face of the sheet. (S)-1-Phenylethylammonium rac-hydrogen tartrate [(II), P21, Z′ = 2] and its enantiomorph (R)-1-phenylethylammonium rac-hydrogen tartrate [(III), P21, Z′= 2] contain anion sheets built from four types of ring, R_2^2(10), R_2^2(12), R^4_2(14) and R_4^4(20), and there are cations pendent from both faces of the sheet. The anion substructure in bis[(S)-1-phenylethylammonium] (R,R)-tartrate [(IV), P21, Z′ = 1] consists of simple C(5) chains, which are linked into sheets by the cations, while in bis(rac-1-phenylethylammonium) (R,R)-tartrate [(V), P21, Z′ = 2] there are anion sheets containing two distinct types of R_4^4(22) ring, with equal numbers of (R) and (S) cations pendent from each face of the anion sheet. Bis[(R)-1-phenylethylammonium] rac-tartrate methanol hemisolvate [(VI), P1, Z′ = 4, with 14 independent components in the asymmetric unit] contains anion sheets built from two types of R_2^2(12) ring and two types of R_6^6(32) ring; half of the cations and half of the methanol molecules are pendent from each face of the sheet.

Abstract Three new organotin(IV) structures of general formula RSn(S 2CN R′ R″) 2Cl, where R′ ≠ R″, namely MeSn · [S 2CN(Me)(Cy)] 2Cl ( 1), MeSn[S 2CN( i-Pr)(CH 2Ph)] 2Cl ( 2) and PhSn[S 2CN(Et)( i-Pr)] 2Cl ( 3) are described. Each structure features tin in a distorted octahedral geometry defined by a C ClS 4donor set as a result of two chelating dithiocarbamate ligands. In all cases the tin-bound carbon and chloride atoms are cis. The shorter Sn–S bond lengths in 3are correlated with the presence of the relatively more electronegative Sn-bound phenyl substituent. The new structures conform to the structural motif adopted by all other compounds with the formula RSn(S 2CN R′ R″) 2Cl, where R′ = R″, suggesting the unsymmetrical substitution pattern of the dithiocarbamate ligands in the present study does not influence the adoption of this structural motif. The homogeneity in the structural motif notwithstanding, non-systematic variations in geometric parameters are found in these structures indicating an overall influence of crystal packing upon molecular geometry.

An analytical algorithm is proposed to represent eigensolutions [λm2, ψm(r)]m=1∞ of an imperfect structure C containing cracks in terms of crack configuration σc and eigensolutions [ωn2, φn(r)]n=1∞ of a perfect structured without P the cracks. To illustrate this algorithm on mechanical systems governed by the two-dimensional Helmholtz operator, the Green’s identity and Green’sfunction of P are used to represent ψm(r) in terms of an infinite series of φn(r). Substitution of the ψn(r) representation into the Kamke quotient of C and stationarity of the quotient result in a matrix Fredholm integral equation. The eigensolutions of the Fredholm integral equation then predict λm2 and ψm(r) of C. Finally, eigensolutions of two rectangular elastic solids under antiplane strain vibration, one with a boundary crack and the other with an oblique internal crack, are calculated numerically.

Observational evidence indicates that the frequency of internal structures (such as rings, bars, spirals, etc.) is preferentially enhanced for spirals in binary systems (e.g. Elmegreen et al. 1990). In this context we study the tidal effects produced due to two spiral galaxies in a near grazing relative orbit with a near parabolic relative velocity, as such barely bound encounters are the most frequent ones. Both the spirals are endowed with an inner and an outer ring.The spiral galaxies (of radius R) are modeled by an exponential disk of scale length α = 4/R, with a (static) thickness (Chatterjee 1990), and a spherical polytropic bulge (n=0, 3, 4 equally weighted combination) containing 1/3 of the mass; about 10% of the mass of the disk contains gas particles. Two polytropic rings (n=1; Ostriker 1964), are projected on the disk at 1/4 (inner) and 3/4 (outer) of its radius. Though the rings are gaseous, they are here treated as density enhancements. The gravitational potential is softened with softening constants of ∊ = r∘/5, r∘/3, and 0.8r∘, for the bulge, stellar and gaseous components of the disk, respectively. Here r∘ is the radius containing 75% of the total mass of the spiral. The softening constant for the polytropic rings is 0.35, while the mutual gravitational interaction is softened with a softening constant of r∘/4.

In the paper mentioned in the title (this Journal, vol. 52 (1987), pp. 208–213), it is shown that if ⊨ “V = HC is recursively inaccessible” is ω-standard -nonstandard, then = s.p.() has at most four r. e. degrees. They are 0 = deg(∅), = deg{e ∣ We is a recursive well-ordering of ω}, = deg{R ∣ ⊨ “R codes a well-ordering”}, and ∨ . Furthermore, 0 < < ∨ and 0 < . Then it is claimed that < < ∨ and = ∨ if are each possible. In fact, < < ∨ always.The mistake in the argument is that the model ≤T is really a structure on a set, which we may as well take as ω: there is an R ⊆ ω × ω, R ≤T, and ‹ω, R› ≃ . So a copy of coded as a relation on ω is ≤ over . But there is no reason to think that the restriction of the isomorphism of and ‹ω, R› to is Σ1().

We introduce a graph structure \(\Gamma^{\ast}_2(R)\) for commutative rings with unity. We study some of the properties of the graph \(\Gamma^{\ast}_2(R)\). Also we study some parameters of \(\Gamma^{\ast}_2(R)\) and find rings for which \(\Gamma^{\ast}_2(R)\) is split.

Let $R$ be a ring and $M$ be a monoid with a twisting map $f : M \times M \rightarrow U(R)$ and an action map $\omega : M \rightarrow Aut(R)$. The objective of our work is to extend the reflexive properties of rings by focusing on the crossed product $R \ast M$ over $R$. In order to achieve this, we introduce and examine the concept of strongly $CM$-reflexive rings. Although a monoid $M$ and any ring $R$ with an idempotent are not strongly $CM$-reflexive in general, we prove that $R$ is strongly $CM$-reflexive under some additional conditions. Moreover, we prove that if $R$ is a left $p.q.$-Baer (semiprime, left $APP$-ring, respectively), then $R$ is strongly $CM$-reflexive. Additionally, for a right Ore ring $R$ with a classical right quotient ring $Q$, we prove $R$ is strongly $CM$-reflexive if and only if $Q$ is strongly $CM$-reflexive. Finally, we discuss some relevant results on crossed products.

Let R be a commutative ring with identity and let I be an ideal of R. In this paper we study the amalgamated duplication ring R ⋈ I introduced by D'Anna and Fontana. By assuming that (1, i) is a unit in R ⋈ I for every i ∈ I, it is shown that R ⋈ I is uniquely clean (respectively, n-clean, weakly clean, n-good) if and only if R is uniquely clean (respectively, n-clean, weakly clean, n-good). Conditions for R ⋈ I to be almost clean are also discussed.

RESUMENEl culto a los muertos es una práctica documentada en el ser humano desde tiempos prehistóricos. Uno de los fenómenos funerarios que revisten mayor popularidad dentro de la Prehistoria Reciente es el megalitismo, desarrollado en amplios territorios de Europa desde mediados del v milenio cal BC, y caracterizado por la construcción de grandes tumbas colectivas cuyo imaginario permanece en el folclore popular hasta nuestros días. En este trabajo se ofrece una interpretación de las prácticas funerarias que engloban dicho fenómeno a partir del estudio regional del conjunto megalítico de la Lora burgalesa, en el noreste de la Submeseta Norte española. Tras décadas de estudio, que en los últimos años se ha focalizado en el análisis de las colecciones esqueléticas, ha sido posible profundizar en el conocimiento de las sociedades que enterraban a sus muertos en estas tumbas. Palabras clave: megalitismo, prácticas funerarias, enterramientos colectivosTopónimos: Lora burgalesa, Submeseta Norte españolaPeriodo: Neolítico Final, Calcolítico ABSTRACTThe cult of the death has been a well-documented human activity since prehistoric times. A popular funerary phenomenon of Neolithic period is megalithism, developed in large areas of Europe from the mid-5th millennium BC. It is characterised by the construction of large collective tombs that have remained in popular folklore to the present day. This paper offers an interpretative approach to the funerary practices involved in this phenomenon from the regional study of the megalithic complex of la Lora burgalesa, in the northeast of the Spanish North Plateau. Decades of study, which in recent years focus on the analysis of skeletal collections, have provided us with a better knowledge of the societies that buried their ancestors in these tombs. Keywords: megalithism, funerary practices, collective tombsPlace names: Lora burgalesa, Spanish North PlateauPeriod: Late Neolithic, Chalcolithic REFERENCIASAcsádi, G. y Nemeskéri, J. (1970): History of Human Life, Span and Mortality. Budapest, Akadémiai Kiadó.Alesan, A., Malgosa, A. y Simó, C. (1999): “Looking into the demography of an Iron Age population in the Western Mediterranean. I. Mortality”. American Journal of Physical Anthropology, 110(3): 285-301.AlQahtani, S. J., Hector, M. P. y Liversidge, H. M. (2010): “Brief communication: The London atlas of human tooth development and eruption”. American Journal of Physical Anthropology, 142(3): 481-490. —(2014): “Accuracy of dental age estimation charts: Schour and Massler, Ubelaker and the London Atlas”. American Journal of Physical Anthropology, 154(1): 70-78.Alt, K. W., Zesch, S., Garrido-Pena, R., Knipper, C., Szécsényi-Nagy, A., Roth, C., … y Rojo-Guerra, M. A. (2016): “A community in life and death: The late neolithic megalithic tomb at Alto de Reinoso (Burgos, Spain)”. PLoS ONE, 11(1). Álvarez-Vidaurre, E. (2006): “Percepción y reutilización de monumentos durante la prehistoria reciente: El caso de Navarra”. Cuadernos de Arqueología de la Universidad de Navarra, 14: 117-150.Andrés-Rupérez, M. T. (2000): “El espacio funerario dolménico: abandono y clausura”. Saldvie, 1: 59-76.Aranda, G., Díaz-Zorita, M., Hamilton, D., Milesi, L. y Sánchez, M. (2020): “The radiocarbon chronology and temporality of the megalithic cemetery of Los Millares (Almería, Spain)”. Archaeological and Anthropological Sciences, 12(5): 1-17.Balzeau, A., Turq, A., Talamo, S. et al. (2020): “Pluridisciplinary evidence for burial for the La Ferrassie 8 Neandertal child”. Scientific Reports, 10, 21230. Barrett, J. C. (1988): “The living, the dead and the ancestors: Neolithic and Early Bronze Age mortuary practices”. En J. C. Barrett y A. Kinnes (eds.): The Archaeology of Context in the Neolithic and Bronze Age. Sheffield: Department of Prehistory Beckett, J. y Robb, J., (2006): “Neolithic Burial Taphonomy, Ritual and Interpretation in Britain and Ireland: A Review”. En R. Gowland y C. Knüsel, C. (Eds.): The Social Archaeology of Funerary Remains. Oxbow, Oxford. Bellido, A. y Gómez, J. L. (1996): “Megalitismo y rituales funerarios”. Complutum extra, 6(1): 141-152.Bello, S. y Andrews, P. (2006): “The intrinsic pattern of preservation of human skeletons and its influence on the interpretation of funerary behaviours”. En R. Gowland y C. Knüsel (Eds.): Social archaeology of funerary remains. Oxford, Oxbow: 1-13.Benet, N., Pérez, R. y Santonja M. (1997): “Evidencias campaniformes en el valle medio del Tormes.” En II Congreso de Arqueología Peninsular: Zamora 24-27 de septiembre de 1996. Fundación Afonso Henriques: 449-470.Binford, L. R. (1971): “Mortuary Practices: Their Study and Their Potential”. Memoirs of the Society for American Archaeology, 25: 6-29.Bocquet-Appel, J.P. y Masset, C. (1977) : “Estimateurs en paléodémographie”. L´Homme, 4: 65-90. Boz, B. y Hager, L. (2014): “Making sense of social behavior from disturbed and commingled skeletons: A case study from Çatalhöyük, Turkey”. En A. Osterholtz, K. Baustian y D. Martin (Eds.): Commingled and Disarticulated Human Remains. New York, Springer: 17-33.Bronk Ramsey, C. (2009): “Bayesian analysis of radiocarbon dates”. Radiocarbon, 51(1), 337-360.Brown, D. (1991): Human universals. New York, McGraw-Hill.Bueno, P., Barroso, R., y de Balbín, R. (2010): “Entre lo visible y lo invisible: registros funerarios de la Prehistoria reciente de la Meseta Sur”. En P. Bueno et al. (Eds.): Arqueología, Sociedad, Territorio y Paisaje. Estudios sobre Prehistoria Reciente, Protohistoria y transición al mundo romano en Homenaje a Mª. Dolores Fernández Posse. Madrid, CSIC: 53-74.—(2016): “Between east and west: megaliths in the centre of the Iberian Peninsula”. En Laporte L. y Scarre Ch. Eds.: The megalithic architectures of Europe. Oxford Oxbow books: 157-166. https://doi.org/10.2307/j.ctvh1dpw8.19Carbonell, E. y Mosquera, M. (2006): “The emergence of a symbolic behaviour: the sepulchral pit of Sima de los Huesos, Sierra de Atapuerca, Burgos, Spain”. Comptes Rendus Palevol, 5: 155-160.Carmona, E., Arnaiz, M. Á. y Alameda, M. C. (2014): “El dolmen de Arroyal I: usos y modificaciones durante el iii milenio cal A.C.”. En J. Honrado et al. (Eds.): II Jornadas de Jóvenes Investigadores del Valle del Duero. Del Neolítico a la Antigüedad Tardía (León 2012), 2. Valladolid, Glyphos: 41-54.Cauwe, N. (1997): “Les morts en mouvement. Essai sur l´origine des rites funeraires mégalithiques”. En A. Rodrígez Casal, (ed.): O Neolítico atlántico e as orixes do megalitismo. Santiago de Campostela, Universidad de Santiago: 719-737.Chamberlain, A. (2006): Demography in Archaeology. New York, Cambridge University Press.—(2009): “Archaeological Demography”. Human Biology, 81 (3): 275-286. Childe, V. G. (1958): Los orígenes de la sociedad europea. Madrid, Ciencia Nueva.Cintas-Peña, M. y Herrero-Corral, A. M. (2020). “Missing prehistoric women? Sex ratio as an indicator for analyzing the population of Iberia from the 8th to the 3rd millennia BC”. Archaeological and Anthropological Sciences, 12(11): 1-13.Clarke, D. L. (1978): Analytical archaeology (Second edition-original 1968). London, Methuen.Delibes, G. (1995): “Ritos funerarios, demografía y estructura social entre las comunidades neolíticas de la submeseta norte”. En R. Fábregas, F. Pérez y C. Fernández (coords.): Arqueoloxia da Morte na Peninsula Iberica desde as orixes ata o Medievo, Xinzo de Limia, Biblioteca Limiá: 61-94. —(2000): “Itinerario arqueológico de los dólmenes de Sedano (Burgos)”. Trabajos de Prehistoria, 57 (2): 89-103.—(2010): “La investigación de las sepulturas colectivas monumentales del iv milenio A.C. en la Submeseta Norte española. Horizonte 2007”. En J. Fernández-Eraso, J. y J. Mujika (Eds.): Actas del Congreso Internacional sobre Megalitismo y otras manifestaciones funerarias contemporáneas en su contexto social, económico y cultural. Munibe. Suplemento 32. Donostia, Sociedad de Ciencias Aranzadi: 12-56.Delibes, G. y Rojo, M. (1997): “C14 y secuencia megalítica en la Lora burgalesa: acotaciones a la problemática de las dataciones absolutas referentes a yacimientos dolménicos”. En A. Rodríguez Casal (ed.): O Neolítico atlántico e as orixes do megalitismo. Santiago de Campostela, Universidad de Santiago: 391–414.—(2002): “Reflexiones sobre el trasfondo cultural del polimorfismo megalítico en la Lora burgalesa”. Archivo Español de Arqueología, 75 (185-186): 21-35. Delibes, G., Rodríguez-Marcos, J. A., Sanz, C. y del Val, J. M. (1982): “Dólmenes de Sedano I. El sepulcro de corredor de Ciella”. Noticiario Arqueológico Hispanico, 14: 149–196.Delibes, G., Rojo, M. A. y Sanz, C. (1986): “Dólmenes de Sedano II. El sepulcro de corredor de Las Arnillas (Moradillo de Sedano, Burgos)”. Noticiario Arqueológico Hispanico, 27: 7–41.Delibes, G., Moreno, M. y Valle, A. del (2011): “Dólmenes de Sedano (Burgos) y criadero cuprífero de Huidobro: Una relación todavía posible”. En P. Bueno et al. (eds.): Arqueología, sociedad, territorio y paisaje. Estudios sobre Prehistoria Reciente, Protohistoria y transición al mundo romano en homenaje a M.ª Dolores Fernández Posse. Madrid, CSIC: 35-52. Delibes, G., Rojo, M. y Represa, I. (1993): Dólmenes de la Lora. Valladolid, Junta de Castilla y León.Delibes, G. y Santonja, M. (1987): “Anotaciones en torno al megalitismo del occidente de la Meseta (Salamanca y Zamora)”. En Megalitismo en la Península Ibérica, Madrid, Asociación de Amigos de la Arqueología: 200-210.Díaz-Zorita, M. (2013): The Copper Age in south-west Spain: A bioarchaeological approach to prehistoric social organisation. Doctoral dissertation, Durham University.Díaz-Zorita, M., Aranda, G., Escudero, J., Robles, S., Lozano, Á., Sánchez, M. y Alarcón, E. (2016): “Estudio bioarqueológico de la necrópolis megalítica de El Barranquete (Níjar, Almería)”. Menga, 7: 71-98.Díaz-Zorita, M., Aranda, G., Robles, S., Escudero, J., Sánchez, M. y Lozano, Á. (2017): “Estudio bioarqueológico de la necrópolis megalítica de Panoría (Darro, Granada)”. Menga, 8: 91-114.Dietrich, O., Köksal-Schmidt, Ç, Notroff, J. y Schmidt, K. (2013): “Establishing a Radiocarbon Sequence for Göbekli Tepe. State of Research and New Data”. Neo-Lithics, 1/13: 36-41.Duday, H. (1987): “Organisation et fonctionnement d’une sépulture collective néolithique. L’aven de la Boucle à Corconne (Gard)”. En Anthropologie physique et archéologie: méthodes d’étude des sépultures. Paris, CNRS: 89-104.—(2006): « L’Archéothanatologie ou l’archéologie de la mort. Translated by Knüsel”. En Gowland R.L. and Knüsel, C.J. (Eds.) Social Archaeology of Funerary Remains. Oxford, Oxbow Books: 30-56.Duday, H., Courtaud, P., Crubezy, É., Sellier, P. y Tillier, A. M. (1990): «L’Anthropologie «de terrain»: reconnaissance et interprétation des gestes funéraires”. Bulletins et Mémoires de La Société d’Anthropologie de Paris, 2(3): 29–49. Fabián, J. F. (1995): El aspecto funerario durante el Calcolítico y los inicios de la Edad del Bronce en la Meseta Norte. Salamanca, Universidad de Salamanca.Ferembach, D., Schwidetzky, I. y Stloukal, M. (1980). “Recommendations for Age and Sex Diagnoses of Skeletons”. Journal of Human Evolution, 9: 517–549.Fernández-Crespo, T. (2015): “Aportación de la Arqueoantropología a la interpretación de la dinámica sepulcral de las tumbas megalíticas de Cameros (La Rioja, España)”. Trabajos de Prehistoria, 72(2): 218–237. Fernández-Crespo, T. y de la Rúa, C. (2015): “Demographic evidence of selective burial in megalithic graves of northern Spain”. Journal of Archaeological Science, 53: 604-617. —(2016): “Demographic differences between funerary caves and megalithic graves of northern Spanish Late Neolithic/Early Chalcolithic”. American Journal of Physical Anthropology, 160(2): 284-297. Fernández-Eraso, J. y Mujica, J. A. (2013): “The megalithic station of the Rioja Alavesa: chronology, origins and utilisation cycles”. Zephyrus, 71: 89-106.Furholt, M. y Müller, J. (2011): “The earliest monuments in Europe: architecture and social structures (5000-3000 cal BC)”. En M. Furholt, F. Lüth y J. Müller (eds.): Megaliths and Identities. Early Monuments and Neolithic Societies from the Atlantic to the Baltic. Bonn: R. Habelt: 15-32.Gallay, A. (2006): Les sociétés megalithiques. Pouvoir des hommes, memoires des morts. Lausanne, Le savoir suisse.Garrido-Pena, R. (2000): El Campaniforme en la Meseta Central de la Península Ibérica (c. 2500-2000 AC.) (Vol. 892). BAR International Series, Oxford.Gil-Merino, R., Moreno, M., Delibes, G., Villalobos, R. (2018): “Luz para ver y ser vista: los efectos de la iluminación solar durante el solsticio de invierno en los dólmenes de corredor de la provincia de Burgos”. Munibe, 69: 157-175.Guerra, E., Delibes, G., Zapatero, P. y Villalobos, R. (2009): “Primus Inter Pares: Estrategias de diferenciación social en los sepulcros megalíticos de la Submeseta Norte española”. BSAA Arqueología, 75: 41-65.Hertz, R. (1990): La muerte y la mano derecha. Alianza Universidad n.º 637, Madrid.Huidobro, L. (1957): “Descubrimiento megalítico en Nocedo (Sedano)”. En Actas del IV Congreso Nacional de Arqueología. Zaragoza, Institución Fernando El Católico: 125-126.Larsen, C. (1995): “Biological Changes in Human Populations with Agriculture”. Annual Review of Anthropology, 24(1): 185-213. Leclerc, J. (1990) : « La notion de sépulture”. Bulletins et Mémoires de la Société d’Anthropologie de Paris, 2(3): 13-18.Ledermann, S. (1969): Nouvelles tables-types de mortalité. Paris, PUF (Travaux et Documents, 53).Livi-Bacci, M. (1990): Historia mínima de la población mundial. Ariel, Barcelona.Lyman, R. L. (1994): “Quantitative units and terminology”. Zooarchaeology, 59(1): 36-71.Maluquer de Motes, J. (1960): “Nuevos hallazgos de la cultura del vaso campaniforme en la Meseta”. Zephyrus, 11: 119-130.Martín-Vela, R., Delibes, G. y Municio, L. (2021): “Megalitos al norte de la Sierra de Guadarrama: primicias de la excavación del dolmen de Santa Inés en Bernardos (Segovia)”. CuPAUAM, 47(2): 11-38. Martinón-Torres, M., d’Errico, F., Santos, E. et al. (2021): “Earliest known human burial in Africa”. Nature, 593: 95–100. Masset, C. (1971): «Erreurs systématiques dans la détermination de l’âge par les sutures crâniennes”. Bulletins et Mémoires de la Société d›anthropologie de Paris, 7(1): 85-105.—(1972): “The megalithic tomb of la Chaussée-Tirancourt.” Antiquity, 46(184): 297-300.Masset, C. (1987): «Le recrutement d’un ensemble funéraire”. En H. Duday, H. y C. Masset (eds.): Anthropologie physique et archéologie: méthodes d’études des sépultures. Bordeaux, CNRS: 111-134.Moreno, M. (2004): Megalitismo y Geografía. Análisis de los factores de localización espacial de los dólmenes de la provincia de Burgos. Studia Archaeologica, n.º 93. Valladolid, Universidad de Valladolid. Moreno, M., Delibes, G., López-Sáez, J. A., Manzano, S., Villalobos, R., Fraile, A. y Basconcillos, J. (2010-2012): “Nuevos datos sobre una alineación de menhires en el norte de Burgos: el yacimiento de Las Atalayas, en Avellanosa del Páramo (Burgos)”. Sautuola, 16-17: 71-93.Moreno, M., Delibes, G. Villalobos, R. y Basconcillos, J. (2020): Tumbas de Gigantes. Dólmenes y túmulos en la provincia de Burgos. Diputación Provincial de Burgos.—(2021): Territorio Megalítico. Burgos, Agrupación de Municipios Territorio Megalítico. Reimer, P. J., Austin, W. E., Bard, E. y Talamo, S. (2020): “The IntCal20 Northern Hemisphere radiocarbon age calibration curve (0–55 cal kBP)”. Radiocarbon, 62(4): 725-757.Renfrew, C. (1972): The Emergence of Civilisation. The Cyclades and the Aegean in the Third Millennium B.C. London, Methuen.—(1976): “Megaliths, territories and populations”. En S. J. Laet (Ed.): Acculturation and continuity in Atlantic Europe Mainly during the Neolithic period and the Bronze Age. Papers presented at the IV Atlantic Colloquium. Brugge, De Tempel: 198-220.—(1983): “The social archaeology of megalithic monuments”. Scientific American, 249(5): 152-163.Robb, J. (2016): “What can we really say about skeletal part representation, MNI and funerary ritual? A simulation approach”. Journal of Archaeological Science: Reports, 10: 684-692. Rojo Guerra, M. Á. (1990): “Monumentos megalíticos de la Lora Burgalesa: Exégesis del emplazamiento”. Boletín Del Seminario de Estudios de Arte y arqueología: BSAA, 52: 53-63.—(1993): El fenómeno megalítico en la Lora burgalesa. Tesis doctoral mecanografiada. Universidad de Valladolid.Rojo, M.A., Delibes, G., Edo, M. y Fernández, J.L. (1995): “Adornos de calaíta en los ajuares dolménicos de la Provincia de Burgos: Apuntes sobre su composición y procedencia”. Rubricatum, 1: 239-250.Rojo, M., Kunst, M., Garrido, R., García, I. y Morán, G. (2005): Un desafío a la eternidad: tumbas monumentales en el valle de Ambrona. Arqueología en Castilla y León (Vol. 14). Valladolid, Junta de Castilla y León.Roksandic, M. (2002): “Position of skeletal remains as a key to understanding mortuary behavior”. En Haglund, W. D. y Sorg, M. H. (Eds.): Advances in forensic taphonomy: method, theory, and archaeological perspectives: 99-117.Sánchez-Quinto, F., Malmstrom, H., Fraser, M. y Jakobsson, M. (2019): “Megalithic tombs in western and northern Neolithic Europe were linked to a kindred society”, PNAS, 116 (19): 9469-9474. Santa Cruz, A. (2022): Caracterización antropológica y temporalidad de los sepulcros megalíticos de la Lora (Burgos). Tesis doctoral (inédita). Universidad de Valladolid. Santa Cruz, A., Delibes, G. y Villalobos, R. (2020a): “Sobre la impronta campaniforme en los dólmenes de la Lora (Burgos): dataciones de C-14 y naturaleza funeraria”. En Estudios In memoriam Prof. Emilio Illarregui. Segovia, IE Universidad: 23-39.—(2020b): “Nueva serie de dataciones radiocarbónicas sobre hueso humano para el dolmen de Los Zumacales (Simancas, Valladolid)”. Trabajos de Prehistoria, 77(1): 130-147.Schulting, R. J. (2015): “Mesolithic skull cults?”. En K. von Hackwitz y R. Peyroteo-Stjerna (eds.): Ancient Death Ways. Institutionen för arkeologi och antik historia, Uppsala: 19-46.Schulz Paulsson, B. (2019): “Radiocarbon dates and Bayesian modeling supportmaritime diffusion model for megaliths in Europe”. PNAS, 116, 9: 3460-3465.Séguy, I. y Buchet, L. (2013): Handbook of Palaeodemography. London: Springer.Sellier, P. (1996): “La mise en évidence d’anomalies demographiques et leur interprétatión: population, recrutement et práctiques funéraires de tumulus de Courtesoult”. En J. F. Piningre (ed.): Nécrópoles et société au première Âge du Fer: le tumulus de Courtesoult (Haute-Saône). Paris: Maison des Sciences d l’Homme, 54: 188-202.Sherratt, A. (1990): “The genesis of megaliths: Monumentality, ethnicity and social complexity in Neolithic north-west Europe”. World Archaeology, 22(2), 147-166.Silva, A. M. (2003): “Portuguese populations of late Neolithic and Chalcolithic periods exhumed from collective burials: an overview”. Anthropologie, 41(1-2): 55-64.Smith, M. y Brickley, M. (2009): People of the long barrows: life, death and burial in the earlier Neolithic. Stroud, History Press.Stloukal, M. (1974): “Recherches paléodémographiques en Tchécoslovaquie”. Historická demografie, 7: 5-28.Tejedor Rodríguez, C. (2014): “Reconstruyendo ‘biografías megalíticas’: algunos ejemplos de alteraciones estructurales en monumentos megalíticos del valle del Duero”. En Actas de Las II Jornadas de Jóvenes Investigadores del Valle del Duero. Glyphos: 67-86.Thomas, J. (1991): Rethinking the Neolithic. London, Cambridge University Press.Tilley, C. (1984): “Ideology and the legitimation of power in the middle neolithic of southern Sweden”. En D. Miller y C. Tilley (Eds.): Ideology, power and prehistory. New directions in archaeology. Cambridge university press, Nueva York: 111-146.Ucko, P. J. (1969): “Ethnography and archaeological interpretation of funerary remains”. World archaeology, 1(2): 262-280.Villalobos García, R. (2014): “The megalithic tombs of the Spanish Northern Meseta. Material, political and ideological ties between the Neolithic people and their territory”. Préhistoires Méditerranéennes, (Colloque), 1-17. http:// pm.revues.org/1047—(2015): Análisis de las transformaciones sociales en la Prehistoria Reciente de la Meseta Norte Española (milenios vi-iii cal a. C.) a través del empleo de la variscita y otros minerales verdes como artefactos sociotécnicos. [Universidad de Valladolid]. http://uvadoc.uva.es/handle/10324/16693—(2016): Análisis de las transformaciones sociales en la Prehistoria Reciente de la Meseta Norte Española (milenios vi-iii cal a.C.). Studia Archaeologica, 101. Universidad de Valladolid.—(2016): Una aproximación cuantitativa al trabajo destinado a la arquitectura monumental en la Prehistoria Reciente de la Meseta Norte Española. SPAL-Revista de Prehistoria y Arqueología, (25), 43-66.Zapatero, P. (2012): “El sepulcro de La Velilla, en Osorno (Palencia), dentro del marco del fenómeno megalítico de la Meseta Norte”. Patrimonio Histórico de Castilla y León, 46: 51-58.—(2015): El Neolítico en el Noroeste de la Cuenca del Duero: el yacimiento de La Velilla en el Valle del Valdivida (Palencia). Tesis doctoral mecanografiada: Universidad de Valladolid.

Many of the new MV-valued fuzzy structures, including intuitionistic, neutrosophic, or fuzzy soft sets, can be transformed into so-called almost MV-valued fuzzy sets, or, equivalently, fuzzy sets with values in dual pair of semirings (in symbols, (R,R*)-fuzzy sets). This transformation allows any construction of almost MV-valued fuzzy sets to be retransformed into an analogous construction for these new fuzzy structures. In that way, approximation theories for (R,R*)-fuzzy sets, rough (R,R*)-fuzzy sets theories, or F-transform theories for (R,R*)-fuzzy sets have already been created and then retransformed for these new fuzzy structures. In this paper, we continue this trend and define, on the one hand, the theory of extensional (R,R*)-fuzzy sets defined on sets with fuzzy similarity relations with values in dual pair of semirings and power sets functors related to this theory and, at the same time, the theory of cuts with relational morphisms of these structures. Illustratively, the reverse transformations of some of these concepts into new fuzzy structures are presented.

Research on the morphological structures of R. apiculata and R. mucronata was carried out in three different regions from July to December 2018. The research aimed at observing and documenting the morphological structure of R. apiculata and R. mucronata. Samples were collected from selected locations in Peninsular Malaysia. Subsequently, samples were processed as herbarium vouchers. The vegetative and reproductive structures of both species were observed and identified. 55 morphological features were recorded and annotated as result of this research. The research revealed that vegetative and reproductive structures could differentiate R. mucronata from R. apiculata. According to this research, there were no significant differences in the morphological structures of R. apiculata and R. mucronata from three different locations. As a consequence, the data acquired in this research would be valuable for future studies on Rhizophora species.

The distance functions such as G(r), K(r), H(r), g(r) and systematic scanning method connected with variance analysis have been used for quantitative characterization of functionally gradient materials structures. The methods have been tested on computer generated 3D model polycrystalline structures with diverse type of gradient function. Usefulness of the presented methods for quantitative description of FGM structures has been evaluated.

Let $G$ be a group with identity $e$, $R$ a $G$-graded commutative ring with unity $1$ and $M$ a $G$-graded $R$-module. In this article, we unify the concepts of graded prime ideals and graded primary ideals into a new concept, namely, graded $\delta$-primary ideals. Also, we unify the concepts of graded $2$-absorbing ideals and graded $2$-absorbing primary ideals into a new concept, namely, graded $2$-absorbing $\delta$-primary ideals. A number of results about graded prime, graded primary, graded $2$-absorbing and graded $2$-absorbing primary ideals are extended into these new structures. Finally, we extend the concept of graded $\delta$-primary ideals into graded $\delta$-primary submodules. A number of results about graded prime, graded primary submodules are extended into this new structure.

AbstractWe show that if the given cotorsion pair $(\mathcal{A},\mathcal{B})$ in the category of modules is complete and hereditary, then both of the induced cotorsion pairs in the category of complexes are complete. We also give a cofibrantly generated model structure that can be regarded as a generalization of the projective model structure.