Weak Extension Research Articles

Algebraically closed algebras in certain small congruence distributive varieties

In a finitely generated congruence distributive variety satisfying a weak congruence extension property, the algebraically closed algebras are precisely updirected unions of maximal subdirectly irreducibles. The class of algebraically closed algebras of such a variety is elementary and definable by Horn sentences.

Weak extension theorem for measure-preserving homeomorphisms of noncompact manifolds

In this paper we deduce weak type extension theorems for the groups of measure-preserving homeomorphisms of noncompact manifolds. As an application, we show that the group of measure- preserving homeomorphisms with compact support of a noncompact connected manifold, endowed with the Whitney topology, is locally contractible.

Crossed Products for Weak Hopf Algebras

Weak crossed products by a weak bialgebra are defined. The resulting structure is not that of a unital algebra but an associative algebra with preunit. A general formula of such a product is given in terms of a weak 2-cocycle and a weak measuring. The relation with weak cleft extensions is studied. Equivalences of weak crossed products are defined and are related to gauge transformations. A relation between cleaving maps is described in terms of gauge transformations.

INFINITE WORDS AND CONFLUENT REWRITING SYSTEMS: ENDOMORPHISM EXTENSIONS

Infinite words over a finite special confluent rewriting system R are considered and endowed with natural algebraic and topological structures. Their geometric significance is explored in the context of Gromov hyperbolic spaces. Given an endomorphism φ of the monoid generated by R, existence and uniqueness of several types of extensions of φ to infinite words (endomorphism extensions, weak endomorphism extensions, continuous extensions) are discussed. Characterization theorems and positive decidability results are proved for most cases.

Influence of property rights on farmers' willingness to plant indigenous fruit trees in Malawi and Zambia

Despite the important role that indigenous fruit trees play in the food security and livelihood of households in southern Africa, investments in the cultivation and conservation of indigenous fruit trees (IFTs) by farm communities is very low. Through the use of reconnaissance surveys, household surveys and focus group discussions, this study assessed the effects of land and tree tenures and household characteristics on farmers’ willingness to plant and domesticate IFTs in Malawi and Zambia. Results revealed that 98% of land cultivated by smallholder farmers in Malawi and Zambia were under customary land tenure system, and were conducive for tree cultivation as opposed to leasehold land tenure systems. The existing land user-rights of customary land were of private property regime, and provided smallholder farmers much freedom in land utilization. Household tree tenure was observed to account for 96% of tree tenure types, and is favourable to IFTs’ cultivation. Farmers’ resource endowment, cultural practices and socio-economic characteristics had overriding effects on fruit tree planting. The weak extension capacity, lack of knowledge in IFT cultivation, seedling scarcity, cultural norms such as matrilineal inheritance system were identified as major disincentives to fruit tree planting. Household size and formal education increased the probability of farmers to plant fruit trees in the study area. Contrary to popular notion, the existing land and tree tenure systems do not impose constrains on the cultivation of IFT by households.

Dependence of volcanic systems on tectonic stress conditions as revealed by features of volcanoes near Izu peninsula, Japan

Five volcanoes, Asama, Fuji, Izu-Tobu, Izu-Oshima and Miyakejima, which are aligned along the same volcanic chain in central Japan, are subjected to different degrees to the stress conditions associated with the continental collision and subduction along wedge shaped trenches near Izu peninsula. At a great distance from the collision boundary, Asama is characterized by an axially symmetric edifice with a unique summit crater for magma effusion and Miyakejima has a similar symmetric structure accompanied by radial eruptive fissures. At the opposite extreme Izu-Tobu, which is the closest to the collision boundary, consists of many small monogenetic volcanoes that lack a central vent. In intermediate locations, Fuji and Izu-Oshima exhibit elongated volcanic edifices with both summit vents and parallel fissures on their flanks for magma effusion. To understand this systematic trend of volcanic features, growth of volcanic systems is analyzed based on magma transport in cylindrical conduits and planar fissures available in individual stress conditions. It is assumed in this analysis that fissures are produced with extensional stresses or high magma pressures enough to overcome compressive stresses and that cylindrical conduits that have arisen from localization of fissures can be persistently used for repeated magma supply. The analysis predicts that volcanoes are classified into the following three types that represent their growth processes in different stress conditions. (1) A polygenetic volcano having an axially symmetric edifice grows with unique magma supply through the central conduit under compressive or neutral stresses, (2) a polygenetic volcano having an elongated edifice grows with a summit crater and eruptive fissures parallel to the elongation under weak extensions, and (3) a group of small monogenetic volcanoes is constructed along many parallel fissures under strong extensions. This classification is examined for the five volcanoes and some other volcanoes in the world. The alternate occurrences of summit and flank eruptions observed at some polygenetic volcanoes are interpreted to be controlled by the summit height, magma densities and stress conditions that influence the pressure of a common magma source.

Constructing equivariant maps for representations

We show that if Γ is a discrete subgroup of the group of the isometries of ℍ k , and if ρ is a representation of Γ into the group of the isometries of ℍ n , then any ρ-equivariant map F:ℍ k →ℍ n extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Then, we show that the weak extension we obtain is actually a measurable ρ-equivariant map in the classical sense. We use this fact to obtain measurable versions of Cannon-Thurston-type results for equivariant Peano curves. For example, we prove that if Γ is of divergence type and ρ is non-elementary, then there exists a measurable map D:∂ℍ k →∂ℍ n conjugating the actions of Γ and ρ(Γ). Related applications are discussed.

Pairwise Comparisons Based Non-Numerical Ranking

A systematic procedure for deriving weakly ordered non-numerical rankings from given sets of data is proposed and analysed. The data are assumed to be collected using the Pairwise Comparisons paradigm. The concept of a partially ordered approximation of an arbitrary binary relation is formally defined and some solutions are proposed. The problem of testing and the importance of indifference and the power of weak order extensions are also discussed.

The weak extension property and finite axiomatizability for quasivarieties

We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, ${\rm RSD}(\wedge)$, and the weak extension property, ${\rm WEP}$. We prove that if ${{{\cal K}}}\subseteq {{{\ca

Managing soils in Sub-Saharan Africa: Challenges and opportunities for soil and water conservation

I n this 21st century, agriculture continues to be an important sector for sustainable development and poverty reduction in Sub-Saharan Africa. Research indicates that 1% growth in this sector translates into 2.5% growth in income for the poor people in the region. However, such growth is still low and per capita food production has been insufficient and decreasing over time because it is based on smallholder agriculture that often provides insufficient incentives to use land resources sustainably. Compounding problems include volatility in input prices, markets, and climate, declining farm sizes as a result of rising population pressures, weak extension services, low adoption of improved technologies, and limited government investments. In addition, Sub-Saharan Africa continues to experience destructive extraction, over-exploitation, and inadequate conservation of soil and water. More work needs to be done to demonstrate to policy makers, development partners, and society at large the full contribution that will be made to poverty alleviation by increasing and sustaining agricultural productivity through investments in soil rehabilitation, water harvesting and utilization, and reduction of land degradation. Several success stories of local soil and water conservation activities practiced by farmers in Sub-Saharan Africa exist, but the challenge is to scale these successes to wider implementation.

Seasonal and intraseasonal surface chlorophyll‐a variability along the northwest African coast

Five years of SeaWiFS ocean color data are used to characterize the variability of surface chlorophyll (SCHL) over seasonal and intraseasonal timescales along the northwest African coast (between 10°N and 33°N). This variability is interpreted in regards of remotely sensed wind stress and sea surface temperature and of climatological surface nitrate concentration. Three regions with fairly different behaviors are identified: the region of the subtropical gyre (24°N–33°N) is characterized by a weak seasonality and chlorophyll confined at the coast. The inter‐gyre region off Cape Blanc (19°N–24°N) is characterized by a weak seasonality and a persistent large offshore extension of chlorophyll. The region of the recirculation gyre (10°N–19°N) is characterized by a strong seasonality and a large offshore extension of chlorophyll from February to May followed by an abrupt chlorophyll drop that propagates northward from May to June. The seasonal variability is well explained by the seasonal variability in wind‐forcing. Nutrient limitation is the key factor that explains the weak offshore extension of chlorophyll in the North. The chlorophyll drop in the South is attributed to the weakening of the wind‐forcing and the simultaneous advection of warm water from the South by a coastal and seasonal branch of the North Equatorial Counter Current (NECC). Intraseasonal variability is present in all regions. The cases of good correlation between the intraseasonal variability of the chlorophyll and of the wind‐forcing are found to be associated with weak chlorophyll offshore extension and large nutrient limitation.

Crossed Products in Weak Contexts

We define the general notion of crossed products in a weak context, which generalizes the ones defined by Blattner, Cohen and Montgomery, Doi and Takeuchi in the context of Hopf algebras and the one given by Brzezinski. Also, the crossed products obtained by the authors, for weak Hopf algebras living in a symmetric monoidal category and weak C-cleft extensions associated to weak entwined structures, are particular instances of this theory.

Jurassic Tectonics of North China: A Synthetic View

Abstract: This paper gives a synthetic view on the Jurassic tectonics of North China, with an attempt to propose a framework for the stepwise tectonic evolution history. Jurassic sedimentation, deformation and magmatism in North China have been divided into three stages. The earliest Jurassic is marked by a period of magmatism quiescence (in 205–190 Ma) and regional uplift, which are considered to be the continuation of the “Indosinian movement” characterized by continent‐continent collision between the North and South China blocks. The Early to Middle Jurassic (in 190–170 Ma) was predominated by weak lithospheric extension expressed by mantle‐derived plutonism and volcanism along the Yanshan belt and alongside the Tan‐Lu fault zone, normal faulting and graben formation along the Yinshan‐Yanshan tectonic belt, depression and resuming of coal‐bearing sedimentation in vast regions of the North China block (NCB). The Middle to Late Jurassic stage started at 165±5 Ma and ended up before 136 Ma; it was dominated by intensive intraplate deformation resulting from multi‐directional compressions. Two major deformation events have been identified. One is marked by stratigraphic unconformity beneath the thick Upper Jurassic molasic series in the foreland zones of the western Ordos thrust‐fold belt and along the Yinshan‐Yanshan belt; it was predated 160 Ma. The other one is indicated by stratigraphic unconformity at the base of the Lower Cretaceous and predated 135 Ma. During this last stage, two latitudinal tectonic belts, the Yinshan‐Yanshan belt in the north and the Qinling‐Dabie belt in the south, and the western margin of the Ordos basin were all activated by thrusting; the NCB itself was deformed by the NE to NNE‐trending structural system involving thrusting, associated folding and sinistral strike‐slip faulting, which were spatially partitioned. Foliated S‐type granitic plutons aged 160–150 Ma were massively emplaced in the Jiao‐Liao massif east of the Tan‐Lu fault zone and indicate important crustal thickening in this part of the NCB. The Jurassic deformation patterns, different tectonic systems and multi‐directional contractions in North China recorded far‐field effects of synchronous convergences, toward the East Asian continent, of three different plates, the Siberian plate in the north, the paleo‐Pacific oceanic plate in the east and the Lhasa block in the southwest. This Middle to Late Jurassic intraplate orogenesis and pervasive shortening deformation preceded lithospheric attenuation and thinning in East China, which most possibly started by the Early Cretaceous around 135 Ma.

LAM-ICPMS U–Pb dating of kimberlitic perovskite: Eocene–Oligocene kimberlites from the Kundelungu Plateau, D.R. Congo

Kimberlites are small-volume melts whose eruption is related to weak extension of the lithosphere, and their ages can carry important tectonic information. We have carried out in situ LAM-ICPMS U–Pb dating of groundmass perovskite in two kimberlitic pipes (Kambeli and Msipashi) in Kundelungu Plateau (SE Congo). The method is validated by the analysis of perovskites from four previously dated South African Group I kimberlites. Intercepts of regression lines on inverse-Concordia plots yield precise U–Pb ages (2 σ = 2–6 Ma) and a well-constrained value for the 207Pb/ 206Pb of the common-Pb component. The ages of Group I kimberlites in Kimberley District cluster around 87 Ma, similar to those determined by other techniques demonstrating the robustness of the technique. The perovskites from the Kundelungu kimberlites that are intrusive into the Biano Subgroup (Neoproterozoic Katangan Supergroup) yield an age of 32.3 ± 2.2 Ma. The Eocene–Oligocene age of the Kundelungu kimberlites corresponds to the opening of the northern part of the East African Rift and implies the southward prolongation of this extension. Considering the position of the Kundelungu Plateau and gravity data for the region, the kimberlite intrusion may reflect extension on the Lake Mweru-Luapula graben. The Luizi impact structure in the Kundelungu Plateau, previously described as Pleistocene, pre-dates the kimberlitic event.

Model Checking Synchronized Products of Infinite Transition Systems

Formal verification using the model checking paradigm has to deal with two aspects: The system models are structured, often as products of components, and the specification logic has to be expressive enough to allow the formalization of reachability properties. The present paper is a study on what can be achieved for infinite transition systems under these premises. As models we consider products of infinite transition systems with different synchronization constraints. We introduce finitely synchronized transition systems, i.e. product systems which contain only finitely many (parameterized) synchronized transitions, and show that the decidability of FO(R), first-order logic extended by reachability predicates, of the product system can be reduced to the decidability of FO(R) of the components. This result is optimal in the following sense: (1) If we allow semifinite synchronization, i.e. just in one component infinitely many transitions are synchronized, the FO(R)-theory of the product system is in general undecidable. (2) We cannot extend the expressive power of the logic under consideration. Already a weak extension of first-order logic with transitive closure, where we restrict the transitive closure operators to arity one and nesting depth two, is undecidable for an asynchronous (and hence finitely synchronized) product, namely for the infinite grid.

Beyond shape and gravity: children’s ideas about the Earth in space reconsidered

Children’s ideas about the Earth in space have been of interest to science educators and cognitive psychologists for some time. By focusing almost exclusively on shape and gravity alone, however, other important Earth attributes have been largely neglected or overlooked. Findings from a quasi‐experimental study of knowledge acquisition and concept learning in astronomy among 9‐ to 11‐year‐olds attending a single primary school in England are presented which not only begin to address the situation but challenge some of the common assertions in this field. The processes of weak and radical knowledge restructuring and conceptual extension as well as conceptual change are exemplified.

Extension of vector-valued functions

We discuss problems of extension of vector-valued functions defined on subsets of a domain $\Omega\subset\mathbb{R}^N$ which have weak extensions belonging to a space $\mathscr{H}(\Omega)$ of smooth functions. We look for conditions which ensure that there exists an extension in the corresponding space $\mathscr{H}(\Omega,E)$ of vector-valued functions.

Propositional dynamic logic with recursive programs

We extend the propositional dynamic logic PDL of Fischer and Ladner with a restricted kind of recursive programs using the formalism of visibly pushdown automata [R. Alur, P. Madhusudan, Visibly pushdown languages, in: Procceings of the 36th Annual ACM Symposium on Theory of Computing (STOC 2004), 2004, ACM, pp. 202–211]. We show that the satisfiability problem for this extension remains decidable, generalising known decidability results for extensions of PDL by non-regular programs. Our decision procedure establishes a 2-E xpT ime upper complexity bound, and we prove a matching lower bound that applies already to rather weak extensions of PDL with non-regular programs. Thus, we also show that such extensions tend to be more complex than standard PDL.

The cohomology group of weak entwining structure

In this paper, we reveal that a weak entwining structure admits a rich cohomology theory. As an application we compute the cohomology of a weak entwining structure associated to a weak coalgebra-Galois extension.

Jurassic Deformation in and Around the Ordos Basin, North China

The Jurassic era was an important period for tectonic development of the East Asia continent in general, and can be divided into two different deformation stages around the Ordos basin in particular. It was under weak extension during the Early to Middle Jurassic, with the stretching direction in N-S to NNE-SSW, and the stretching deformation mainly occurred in zones surrounding the Ordos basin. This extension was possibly associated with intra-continental stress adjustment following the Late Triassic collision between North and South China Blocks along the Qinling ranges. During the Middle to Late Jurassic, the tectonic regime changed in the Ordos basin to multi-directed compressions, with the maximum stress axes oriented in W-E, NW-SE, and NE-SW; the boundary compressional belts with different trends and structural styles were formed around the Ordos basin. The formation of the N-S trending thrust and nappe belt developed along the western margin of the Ordos basin, resulted from the eastward extrusion of the Alashan and Longxi blocks; and the eastern boundary belt is characterized by W-dipping back-thrust reverse faults and associated folds, which is inferred to occur on the frontal hinging wall ramp (HWR) of a westward propagated decollement system beneath the Shanxi faulted uplift. Large-scale thrust and nappe structures and inversion tectonics of the Early to Middle Jurassic grabens along the Daqingshan in the north of the Ordos basin indicate strong N-S crustal shortening and rejuvenation of the Yinshan Range. The boundary structural belts around the Ordos basin well record multi-directed compressions and continental crust thickening during the Middle to Late Jurassic, which were dynamically associated with far-field effects produced by synchronous convergences toward the East Asia continent of three different plates (Siberia, Paleo-Pacific, and Tethys). This multi-directed compressional deformation accelerated hydrocarbon generation and had profound impact on the accumulation and localization of the multi-energy mineral deposits in the Ordos basin.