Flat Complexes Research Articles

Homological and homotopical aspects of Gorenstein flat modules and complexes relative to duality pairs

Homological and homotopical aspects of Gorenstein flat modules and complexes relative to duality pairs

Local, colocal, and antilocal properties of modules and complexes over commutative rings

This paper is a commutative algebra introduction to the homological theory of quasi-coherent sheaves and contraherent cosheaves over quasi-compact semi-separated schemes. Antilocality is an alternative way in which global properties are locally controlled in a finite affine open covering. For example, injectivity of modules over non-Noetherian commutative rings is not preserved by localizations, while homotopy injectivity of complexes of modules is not preserved by localizations even for Noetherian rings. The latter also applies to the contraadjustedness and cotorsion properties. All the mentioned properties of modules or complexes over commutative rings are actually antilocal. They are also colocal, if one presumes contraadjustedness. Generally, if the left class in a (hereditary complete) cotorsion theory for modules or complexes of modules over commutative rings is local and preserved by direct images with respect to affine open immersions, then the right class is antilocal. If the right class in a cotorsion theory for contraadjusted modules or complexes of contraadjusted modules is colocal and preserved by such direct images, then the left class is antilocal. As further examples, the class of flat contraadjusted modules is antilocal, and so are the classes of acyclic, Becker-coacyclic, or Becker-contraacyclic complexes of contraadjusted modules. The same applies to the classes of homotopy flat complexes of flat contraadjusted modules and acyclic complexes of flat contraadjusted modules with flat modules of cocycles.

Gorenstein complexes over formal triangular matrix rings

Abstract Let 𝐴 and 𝐵 be rings and 𝑈 a ( B , A ) (B,A) -bimodule. The Gorenstein projective, injective and flat complexes over the formal triangular matrix ring T = ( A 0 U B ) T=\bigl{(}\!\begin{smallmatrix}A&0\\ U&B\end{smallmatrix}\!\bigr{)} are explicitly described. These statements extend some earlier results of Enochs, Cortés-Izurdiaga, Torrecillas, Zhang and Mao in this direction.

Community priorities for obesity prevention among low-income adults in Kuala Lumpur: a discrete choice experiment.

Non-communicable diseases and associated risk factors, such as obesity, are prevalent and increasing in Malaysia. To address this burden and the heightened vulnerability of low-income communities to these risk factors, the Better Health Programme Malaysia conducted a partial-profile discrete choice experiment (DCE) to inform the design of a community-based obesity-prevention programme. The DCE survey was conducted with community members (n = 1453) from three publicly supported low-cost, high-rise flat complexes in urban Kuala Lumpur. In the survey, community members were asked to choose between different sets of potential evidence-based interventions for obesity prevention. Their responses to these choice tasks were analysed to quantify preferences for these different health interventions using a random utility maximization model. Based on these results, we determined participants' relative prioritization of the different options. The most preferred interventions were those that reduced the price of fruit and vegetables; altered cooking practices at restaurants and food vendors to reduce salt, sugar and oil; and offered reward incentives for completing online educational activities. Community members did not prioritize several evidence-based interventions, including changes to product placement or product labelling, suggesting that these effective approaches may be less familiar or simply not preferred by respondents. The DCE enabled the clear articulation of these community priorities for evidence-based interventions that focus on the supply and promotion of affordable healthy foods within the local food environment, as well as community demand for healthier food options.

Synthesis and Spectroscopic Investigations of Schiff Base Ligand and Its Bimetallic Ag(I) Complex as DNA and BSA Binders.

Generation of well-defined potential metallotherapeutics for cancer treatment, one of the most population-threatening diseases, is challenging and an active area of modern research in view of their unique properties and thus multiple possible pathways of action in cells. Specifically, Schiff base ligands were recognized as very promising building blocks for the construction of stable and active complexes of numerous geometries and topologies. Incorporation of Ag(I) ions allows for the formation of flat complexes with potential unoccupied coordination sites, thus giving rise to specific interactions between the metallotherapeutic and biomolecule of interest. Herein, we present the design, synthesis and characterization of new Schiff base ligand L and its Ag(I) bimetallic complex [Ag2L2]2+ with two planar moieties formed around the metal ions and connected through cyclohexane rings, confirmed by X-ray measurements. The compounds were described in context of their potential use as anticancer drugs through DNA and BSA binding pathways by several spectroscopic methods (CD, UV-Vis, fluorescence). We revealed that both, L and [Ag2L2]2+, interact with similar affinity with CT-DNA (Kb~106 M−1), while they differ in the type and strength of interactions with the model albumin–BSA. [Ag2L2]2+ binds BSA in both a dynamic and static manner with the Ksv = 8.8 × 104 M−1 in the Trp-134 and Trp-213 sites, whereas L interacts with BSA only dynamically (KSV = 2.4 × 104 M−1). This found further confirmation in the CD studies which revealed a reduction in α-helix content in the albumin of 16% in presence of [Ag2L2]2+.

弱Gorenstein投射、内射和平坦复形

弱Gorenstein投射、内射和平坦复形

Review of research, development and application of photovoltaic/thermal water systems

Abstract Among the many techniques for obtaining heat and electricity, solar thermal collectors, photovoltaic (PV) technology and PV/thermal (PV/T) technology have a very important place. The PV/T collectors enable the simultaneous conversion of solar radiation into thermal and electrical energy in a single device, with better space utilization and cost efficiency during construction. Specially designed PV/T collectors can replace the outer walls or roof covers and can be widely used in private houses, flat complexes, hospitals, schools, tourist and other objects for water heating and electrical energy generation. Due to their great application potential, hybrid collectors have been the subject of very intensive scientific research and technical development for many years. In this review article, the focus is on the research, development and application of the PV/T water systems in the last 10 years. The main task of researchers and manufacturers is to increase the efficiency of PV modules and thermal absorbers, using new materials and design types as well as their proper integration into the PV/T collector. It is also necessary to reduce the cost of these systems and make them more competitive in the market. In addition, the importance of PV/T systems is in providing energy in clean and environmentally friendly ways.

N-Cotorsion pairs

Motivated by some properties satisfied by Gorenstein projective and Gorenstein injective modules over an Iwanaga-Gorenstein ring, we present the concept of left and right $n$-cotorsion pairs in an abelian category $\mathcal{C}$. Two classes $\mathcal{A}$ and $\mathcal{B}$ of objects of $\mathcal{C}$ form a left $n$-cotorsion pair $(\mathcal{A,B})$ in $\mathcal{C}$ if the orthogonality relation $\mathsf{Ext}^i_{\mathcal{C}}(\mathcal{A,B}) = 0$ is satisfied for indexes $1 \leq i \leq n$, and if every object of $\mathcal{C}$ has a resolution by objects in $\mathcal{A}$ whose syzygies have $\mathcal{B}$-resolution dimension at most $n-1$. This concept and its dual generalise the notion of complete cotorsion pairs, and has an appealing relation with left and right approximations, especially with those having the so called unique mapping property. The main purpose of this paper is to describe several properties of $n$-cotorsion pairs and to establish a relation with complete cotorsion pairs. We also give some applications in relative homological algebra, that will cover the study of approximations associated to Gorenstein projective, Gorenstein injective and Gorenstein flat modules and chain complexes, as well as $m$-cluster tilting subcategories.

Restricted Projective, Injective and Flat Complexes

We introduce and study the notions of restricted projective, injective and flat complexes of modules. It is shown in the paper that a complex C of modules is restricted projective if and only if for each $$m\in \mathbb {Z}$$ the module $$C^{m}$$ is restricted projective. A similar result for restricted injective complexes is also given. As an application, we characterize the complex of strongly torsion-free modules introduced by Xu.

DFT study on the relative stability of isomeric macrocyclic metal chelates of divalent 4D-element ions with tetradentate (NSSN)- and (NNNN)- “template” ligands

Using the density functional method (DFT) in the OPBE/TZVP//QZP approximation and the Gaussian09 program, geometric parameters and total energies of molecular structures of the Mo(II), Tc(II), Ru(II), Rh(II), Pd(II), Ag(II) and Cd(II) macrotricyclic complexes with (NSSN)- and (NNNN)-coordinations of the ligand donor centers to the complex, arising as a result of complexing between M(II) indicated above, dithiooxamide H 2 N–C(= S)–C(= S)–NH 2 and glyoxal HC(=O)–CH (=O), were calculated. Based on the data of this calculation, it is shown that in the case of Mo(II), Tc(II), Ru(II), Rh(II) and Pd (II) complexes with (NSSN)-coordination of ligand are more stable, whereas in the case of Ag(II) and Cd(II), with (NNNN)-coordination; in addition, for the Mo(II) and Ru(II) complexes, a pseudo-tetrahedral environment of the central metal ion takes place by donor atoms, while for the complexes Tc(II), Rh(II), Pd(II), Ag(II), and Cd(II) are planar ones. The bond lengths and bond angles in the indicated coordination compounds are given and it is noted that the Ag(II) and Cd(II) complexes are almost flat, the Tc(II), Rh(II), and Pd(II) complexes are small, while the Ru(II), a fairly significant deviation from coplanarity. The five-membered metal chelate cycles formed as a result of complexing, in most of these complexes are either practically flat, or exhibit a slight (within 5°) deviation from coplanarity; the only exceptions are the Mo(II) and Ru(II) complexes.

Sedimentary Architecture of Storm-Influenced Tidal Flat Deposits of the Upper Mulichinco Formation, Neuquén Basin, Argentina

This study reports on the Lower Cretaceous upper Mulichinco Formation in the Neuquén Basin, west-central Argentina. The studied succession comprises shallow marine strata, deposited in a mixed wave and tidal flat environment where ebb-tidal currents dominated. We describe mixed storm- and tide-influenced deposits within progradationally stacked high-frequency sequences, and discuss process interaction, sediment dispersal and preservation potential. These storm and tidal deposits mix spatially on bed-, bedset- and sequence scales, suggesting multiscale process interaction. The study investigates a 12 km long continuous outcrop, oriented sub-parallel to the paleocoastline. The succession comprises subtidal flat and meandering tidal channel complexes, with interbedding and interfingering of storm and tidal deposits. The tidal deposits are widespread and comprise moderately sorted sandstones with bimodal paleocurrent directions, single and double mud drapes, reactivation surfaces, and inclined heterolithic stratification. Varying bimodal paleocurrent directions suggest that the paleocoastline was irregular, consisting of both protrusions and bays. Storm deposits are mainly found erosively interbedded with subtidal flat sandstones, and exhibit dm-thick well sorted hummocky and swaley cross-stratified sandstones. These storm deposits show systematic lateral variations in abundance, from dominant to absent, which is linked to subtle variations in water depth along the irregular paleocoastline. As the tidal deposits are widespread across the study area, and with no significant facies change, the varying dispersal of storm-influenced deposits is considered a product of wave refraction, with converging and diverging wave energy at interpreted positions of coastal protrusions and embayments, respectively. Consequently, the irregular paleocoastline morphology caused spatial variability in wave impact and controlled preservation of interbedded storm and tidal deposits at the coastal protrusions, while facilitating complete tidal remobilization of sediments in the embayments. With no evidence for fluvial influence, ebb-tidal currents are considered as the main drivers for sediment dispersal onto the subtidal flat, through the meandering tidal channels.

HYDROLOGICAL REGIME AND FREEZING OF HUMMOCKY BOGS ON THE EUROPEAN NORTH OF RUSSIA

The development of the European North of Russia, where flat and high-hummocky bog complexes are spread, requires information on the processes of formation of their hydrological regime and freezing of this territory. For the first time, based on observational data, for the period from 1993 to 2013, characteristics of the hydrological regime and freezing of hummocky bogs in Northern European Russia are presented, the case study of the Lovozerskoye bog. The observations were carried out in accordance with the unified methods, approved for the specialized network of Roshydromet bog stations. The regularities of the formation of the hydrological regime of hummocky bogs have been revealed: bog water level drops dramatically from the beginning of freezing to the end of March, rises during snow melt period, slightly drops in summer and rises in autumn. The main feature of hummocky bogs is permafrost, which determines their specific structure. It has been discovered that gravitation snowmelt and liquid precipitation waters relatively quickly run down the hummocks over the frozen layer into hollows between them. Levels of bog waters on the hummocks are absent for a longer period of time. In spring, the amplitude of water level rise in swamplands is on average 60–80 cm. Air temperature and insulation properties of snow are the main factors that influence the bog freezing. Hummocks freeze out as deep as 63–65 cm, which corresponds to the depth of their seasonal thawing in the warm period of the year, and adjoin the permafrost. The greatest depth of freezing of the swamplands is 82 – 87 cm, with an average of 68 cm. The frozen layer at swamplands thaws out from both its upper and bottom sides. The melting of the frozen layer at hummocks occurs only from the bog surface with an average intensity of 0,51 cm/day.

Blue-emitting bolaamphiphilic zwitterionic iridium(iii) complex.

Aggregation induced emission is a very interesting phenomenon that recently has attracted a lot of interest. Most of the examples deal with organic molecules or flat metal complexes. Here we demonstrate that, by design, even iridium compounds can display this process without shifting the emission energy. In order to enhance the aggregation properties we have focussed on amphiphilic complexes. We report the synthesis and photophysical characterisation of a blue-emitting bolaamphiphilic zwitterionic Ir(iii) complex and an analogous cationic amphiphilic compound, used as a reference. The bolaamphiphile exhibited blue (λmax = 450 nm) emission in dilute, deaerated solution with a photoluminescence quantum yield (PLQY) of 22%, similar to the related cationic amphiphilic complex. The bolaamphiphile displayed significant emission enhancement in the solid state, with an emission quantum yield that reach 52%. Interestingly, the emission of the cationic analogue suffers from aggregation quenching in the solid state, (PLQY = 3%) as is common for these type of complexes. A correlation between the photophysical data and the arrangement in the solid state is discussed.

Temporal and spatial changes in grain size on a macro-tidal channel-flat complex: results from Kingsport, Nova Scotia, Bay of Fundy

Understanding the processes that lead to seasonal changes in grain size on muddy macro-tidal flat and channel complexes will assist efforts to predict future changes caused by climate change and construction of infrastructure like tidal power generators, wind farms, and causeways. Surficial sediment samples were collected for disaggregated inorganic grain size (DIGS) analysis every month for 1 year from a tidal flat and from a tidal channel and its banks in Kingsport, NS, Canada, which is located in the Minas Basin of the Bay of Fundy. A process-based parameterization of the DIGS distribution was used to determine floc fraction, representative of the percentage of fine-grained material deposited to the seabed in flocs. Small changes in floc fraction occurred seasonally in the channel. Values were higher in late winter and lower in late summer. A more pronounced seasonal variation in floc fraction was observed on the tidal flats. Observed changes in floc fraction correlated with elevation. Results from this study are discussed in terms of the controls on floc fraction which include suspended particulate matter concentration (SPM), turbulence, and stickiness in the water column, all of which can be used to understand the formative processes responsible for shaping the bottom sediment texture.

On Ding injective, Ding projective and Ding flat modules and complexes

We characterize Ding modules and complexes over Ding-Chen rings. We show that, over a Ding-Chen ring $R$, the Ding projective (respectively, Ding injective, respectively, Ding flat) $R$-modules coincide with the Gorenstein projective (respectively, Gorenstein injective, respectively, Gorenstein flat) modules, which, in turn, are noth\-ing more than modules appearing as a cycle of an exact complex of projective (respectively, injective, respectively, flat) modules. We prove a similar characterization for chain complexes of $R$-modules: a complex~$X$ is Ding projective (respectively, Ding injective, respectively, Ding flat) if and only if each component $X_n$ is Ding projective (respectively, Ding injective, respectively, Ding flat). Along the way, we generalize some results of Stovicek and Bravo, Gillespie and Hovey to obtain other interesting corollaries. For example, we show that, over any Noetherian ring, any exact chain complex with Gorenstein injective components must have all cotorsion cycle modules, that is, $Ext ^1_R(F,Z_nI) = 0$ for any such complex $I$ and flat module $F$. On the other hand, over any coherent ring, the cycles of any exact complex $P$ with projective components must satisfy $Ext ^1_R(Z_nP,A) = 0$ for any absolutely pure module~$A$.

Gorenstein flat and projective (pre)covers

We consider a right coherent ring R. We prove that the class of Gorenstein flat complexes is covering in the category of complexes of left R-modules Ch(R). When R is also left n-perfect, we prove that the class of Gorenstein projective complexes is special precovering in Ch(R).

FP $$_n$$ n -Injective and FP $$_n$$ n -Flat Complexes

Let R be an arbitrary ring and $$n\ge 0$$ be an integer or $$n = \infty $$ . We introduce and study FP $$_n$$ -injective and FP $$_n$$ -flat complexes of modules, which unify the following notions: (FP-)injective and flat complexes (Yang and Liu in Commun Algebra 38:131–142, 2010; Enochs and Garcia Rozas in J Algebra 210:86–102, 1998), absolutely clean and level complexes (Bravo and Gillespie in Commun Algebra 44:2213–2233, 2016) and weak injective and weak flat complexes (Gao and Huang in Glasgow Math J 58:539–557, 2016). Suppose that $$n>1$$ is an integer. It is shown that a complex C is FP $$_n$$ -injective (resp. FP $$_n$$ -flat) if and only if C is exact and all cycles of C are FP $$_n$$ -injective (resp. FP $$_n$$ -flat) as R-modules. Then we investigate duality pairs relative to the FP $$_n$$ -injective and FP $$_n$$ -flat complexes. It is shown that the pairs (fp $$_n\mathcal {I}$$ , fp $$_n\mathcal {F}$$ ) and (fp $$_n\mathcal {F}$$ , fp $$_n\mathcal {I}$$ )) are duality pairs, where fp $$_n\mathcal {I}$$ and fp $$_n\mathcal {F}$$ denote the subcategories of FP $$_n$$ -injective and FP $$_n$$ -flat complexes, respectively. As applications, we get that any complex admits an FP $$_n$$ -injective (resp. FP $$_n$$ -flat) cover and preenvelope. In addition, cotorsion pairs associated with the FP $$_n$$ -injective and FP $$_n$$ -flat complexes are considered.

Flat complexes, pure periodicity and pure acyclic complexes

The paper can be viewed as an addition and extension of the recent paper of Emmanouil (2016) [5]. Among others, an alternative functor category approach to Emmanouil's results is presented. By applying an idea of Neeman (2008) [16] and the main results obtained there, we prove that a chain complex F in a locally finitely presented Grothendieck category A is pure acyclic if and only if any chain map f:P→F from a complex P of pure-projective objects in A to F is null-homotopic. As a consequence we prove that any pure periodic object in A is pure-projective. Moreover, we show that A is pure semisimple if and only if A has the pure QF-property, that is, every pure-injective object in A is pure-projective.

CARTAN–EILENBERG FP-INJECTIVE COMPLEXES

In this article, we extend the notion of FP-injective modules to that of Cartan–Eilenberg complexes. We show that a complex $C$ is Cartan–Eilenberg FP-injective if and only if $C$ and $\text{Z}(C)$ are complexes consisting of FP-injective modules over right coherent rings. As an application, coherent rings are characterized in various ways, using Cartan–Eilenberg FP-injective and Cartan–Eilenberg flat complexes.

Gorenstein n-FP-injective and Gorenstein n-flat complexes

In this paper, we introduce and study the notions of Gorenstein n-FP-injective and Gorenstein n-flat complexes, which are special cases of Gorenstein FP-injective and Gorenstein flat complexes respectively. We prove that over a left n-coherent ring R the class of all Gorenstein n-FP-injective (resp., Gorenstein n-flat) complexes is injectively (resp., projectively) resolving and we discuss the relationship between Gorenstein n-FP-injective and Gorenstein n-flat complexes.