Basarab loop and the generators of its total multiplication group

A loop (Q; ·) is called a Basarab loop if the identities: (x · yxρ)(xz) = x · yz and (yx) · (xλz · x) = yz · x hold. It was shown that the left, right and middle nuclei of the Basarab loop coincide, and the nucleus of a Basarab loop is the set of elements x whose middle inner mapping Tx are automorphisms. The generators of the inner mapping group of a Basarab loop were refined in terms of one of the generators of the total inner mapping group of a Basarab loop. Necessary and su_cient condition(s) in terms of the inner mapping group (associators) for a loop to be a Basarab loop were established. It was discovered that in a Basarab loop: the mapping x ↦ Tx is an endomorphism if and only if the left (right) inner mapping is a left (right) regular mapping. It was established that a Basarab loop is a left and right automorphic loop and that the left and right inner mappings belong to its middle inner mapping group. A Basarab loop was shown to be an automorphic loop (A-loop) if and only if it is a middle automorphic loop (middle A-loop). Some interesting relations involving the generators of the total multiplication group and total inner mapping group of a Basarab loop were derived, and based on these, the generators of the total inner mapping group of a Basarab loop were finetuned. A Basarab loop was shown to be a totally automorphic loop (TA-loop) if and only if it is a commutative and exible loop. These aforementioned results were used to give a partial answer to a 2013 question and an ostensible solution to a 2015 problem in the case of Basarab loop.

Basarab loop and the generators of its total multiplication group

A loop (Q; ·) is called a Basarab loop if the identities: (x · yxρ)(xz) = x · yz and (yx) · (xλz · x) = yz · x hold. It was shown that the left, right and middle nuclei of the Basarab loop coincide, and the nucleus of a Basarab loop is the set of elements x whose middle inner mapping Tx are automorphisms. The generators of the inner mapping group of a Basarab loop were refined in terms of one of the generators of the total inner mapping group of a Basarab loop. Necessary and su_cient condition(s) in terms of the inner mapping group (associators) for a loop to be a Basarab loop were established. It was discovered that in a Basarab loop: the mapping x ↦ Tx is an endomorphism if and only if the left (right) inner mapping is a left (right) regular mapping. It was established that a Basarab loop is a left and right automorphic loop and that the left and right inner mappings belong to its middle inner mapping group. A Basarab loop was shown to be an automorphic loop (A-loop) if and only if it is a middle automorphic loop (middle A-loop). Some interesting relations involving the generators of the total multiplication group and total inner mapping group of a Basarab loop were derived, and based on these, the generators of the total inner mapping group of a Basarab loop were finetuned. A Basarab loop was shown to be a totally automorphic loop (TA-loop) if and only if it is a commutative and exible loop. These aforementioned results were used to give a partial answer to a 2013 question and an ostensible solution to a 2015 problem in the case of Basarab loop

HOW TO CLASSIFY THE URBAN AREA? A PERSPECTIVE OF MULTI-CRITERIA APPROACH IN THE CONTEXT OF HYPER-DIVERSITY IN SETTLEMENTS IN GHANA

Ghana is experiencing high population growth, rapid urbanization and a constantly accelerating growth of urban areas. Yet, the accurate delineation of urban settlements remains a major challenge faced by urbanists. While emergent urban settlements are being characterized by highly-diverse, heterogeneous, and multiplicity of features, the need to rethink how best to classify new urban growth areas, beyond the commonly used population threshold of ≥ 5000 inhabitants, is becoming increasingly inadequate. Thus, this paper proposes a multi-criteria approach, drawing on the concept of ‘hyper-diversity’. Eight key dimensions – urban form, built-up extent, socio-economic functions, land-use dynamics, occupational structure, governance structure and population size – were identified as a guide to the delineation of new urban settlements. Inferring these dimensions requires accurate spatial and statistical data on prevailing the land-use dynamics. Thus, the paper argues that analyzing satellite-based remote sensing and groundtruth-gathered data may provide standardized and timely information on the aforementioned dimensions. Applying this multi-dimensional approach may be useful for Ghana and similar countries where there is a lack of regular mapping of urban areas.

Decision Support on Monitoring and Disaster Management in Agriculture with Copernicus Sentinel Applications

The successful implementation of the European Commission’s Common Agricultural Policy (CAP) and the insurance coverage in case of a natural disaster requires precise and regular mapping of crop types and detailed delineation of the disasters’ effects by frequent and accurate controls. Free and open access policy to Copernicus Sentinel data offers a big volume of data to the users on a consistent and complete basis. Today, the Sentinels are involved in an increasing number of agriculture applications, but their effective exploitation is still being investigated and the development of efficient tools, aligned to the user’s needs, is yet to be realised. To this end, the DiAS (Disaster and Agriculture Sentinel Applications) project proposes methods for decision support in agriculture using Sentinel data for crop type mapping, as well as mapping of the extend of fire and flood effects in agricultural areas. The DiAS Decision Support System (DSS) is designed in consultation with potential users in participatory approach and aims to provide a prototype tool, which provides assistance to the responsible paying agencies and insurance organizations to make decisions on farmers’ subsidies and compensations. The DiAS DSS prototype and its functionalities are presented in this paper and its use is demonstrated through example applications for two test sites in Greece. The DiAS DSS demonstrates the necessity for the development of similar tools, as this emerges from the user’s requirements, and wishes to stimulate and inspire further research and development.

Cropland Mapping Using Fusion of Multi-Sensor Data in a Complex Urban/Peri-Urban Area

Urban and Peri-urban Agriculture (UPA) has recently come into sharp focus as a valuable source of food for urban populations. High population density and competing land use demands lend a spatiotemporally dynamic and heterogeneous nature to urban and peri-urban croplands. For the provision of information to stakeholders in agriculture and urban planning and management, it is necessary to characterize UPA by means of regular mapping. In this study, partially cloudy, intermittent moderate resolution Landsat images were acquired for an area adjacent to the Tokyo Metropolis, and their Normalized Difference Vegetation Index (NDVI) was computed. Daily MODIS 250 m NDVI and intermittent Landsat NDVI images were then fused, to generate a high temporal frequency synthetic NDVI data set. The identification and distinction of upland croplands from other classes (including paddy rice fields), within the year, was evaluated on the temporally dense synthetic NDVI image time-series, using Random Forest classification. An overall classification accuracy of 91.7% was achieved, with user’s and producer’s accuracies of 86.4% and 79.8%, respectively, for the cropland class. Cropping patterns were also estimated, and classification of peanut cultivation based on post-harvest practices was assessed. Image spatiotemporal fusion provides a means for frequent mapping and continuous monitoring of complex UPA in a dynamic landscape.

Attention and Structural Choice in Sentence Production

This chapter offers a review of experimental evidence about the role of the speaker’s attention in the choice of syntactic structure and the corresponding word order during sentence production. Here, we describe how the speaker’s syntactic choices reflect the regular mapping mechanism that reflects the features of the described event in the produced sentence. One of the most important event parameters that the speaker considers is the changing salience status of the event’s referents. This chapter summarizes current theoretical debate about the interplay between attention and sentence production mechanisms. Finally, it reviews the corresponding experimental evidence from languages with both restricted and flexible word orders.

Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Fixed Point Theorems and Asymptotically Regular Mappings in Partial Metric Spaces

The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed point result for the mappings of this class is proved. Examples show that there are cases when new results can be applied, while old ones (in metric space) cannot. Some common fixed point theorems for sequence of mappings in partial metric spaces are also proved which generalize and improve some known results in partial metric spaces.