Non-fillable Augmentations of Twist Knots

We establish new examples of augmentations of Legendrian twist knots that cannot be induced by orientable Lagrangian fillings. To do so, we use a version of the Seidel –Ekholm–Dimitroglou Rizell isomorphism with local coefficients to show that any Lagrangian filling point in the augmentation variety of a Legendrian knot must lie in the injective image of an algebraic torus with dimension equal to the 1st Betti number of the filling. This is a Floer-theoretic version of a result from microlocal sheaf theory. For the augmentations in question, we show that no such algebraic torus can exist.

Correcting Thornthwaite potential evapotranspiration using a global grid of local coefficients to support temperature-based estimations of reference evapotranspiration and aridity indices

Thornthwaite’s formula is globally an optimum candidate for large scale applications of potential evapotranspiration and aridity assessment at different climates and landscapes since it has the lower data requirements compared to other methods and especially from the ASCE-standardized reference evapotranspiration (former FAO-56), which is the most data demanding method and is commonly used as benchmark method. The aim of the study is to develop a global database of local coefficients for correcting the formula of monthly Thornthwaite potential evapotranspiration (Ep) using as benchmark the ASCE-standardized reference evapotranspiration method (Er). The validity of the database will be verified by testing the hypothesis that a local correction coefficient, which integrates the local mean effect of wind speed, humidity and solar radiation, can improve the performance of the original Thornthwaite formula. The database of local correction coefficients was developed using global gridded temperature and Er data of the period 1950–2000 at 30 arc-sec resolution (~1 km at equator) from freely available climate geodatabases. The correction coefficients were produced as partial weighted averages of monthly Er / Ep ratios by setting the ratios’ weight according to the monthly Er magnitude and by excluding colder months with monthly values of Er or Ep < 45 mm month−1 because their ratio becomes highly unstable for low temperatures. The validation of the correction coefficients was made using raw data from 525 stations of Europe, California-USA and Australia including data up to 2020. The validation procedure showed that the corrected Thornthwaite formula Eps using local coefficients led to a reduction of RMSE from 37.2 to 30.0 mm m−1 for monthly and from 388.8 to 174.8 mm y−1 for annual step estimations compared to Ep using as benchmark the values of Er method. The corrected Eps and the original Ep Thornthwaite formulas were also evaluated by their use in Thornthwaite and UNEP (United Nations Environment Program) aridity indices using as benchmark the respective indices estimated by Er. The analysis was made using the validation data of the stations and the results showed that the correction of Thornthwaite formula using local coefficients increased the accuracy of detecting identical aridity classes with Er from 63 % to 76 % for the case of Thornthwaite classification, and from 76 % to 93 % for the case of UNEP classification. The performance of both aridity indices using the corrected formula was extremely improved in the case of non-humid classes. The global database of local correction factors can support applications of reference evapotranspiration and aridity indices assessment with the minimum data requirements (i.e. temperature) for locations where climatic data are limited. The global grids of local correction coefficients for Thornthwaite formula produced in this study are archived in PANGAEA database andcan be assessed using the following link: https://doi.pangaea.de/10.1594/PANGAEA.932638 (Aschonitis et al., 2021).

Exploring the Equity of Traditional and Ride-Hailing Taxi Services during Peak Hours

Many people criticize the inequity of traditional taxi (TT) services and believe the entry of ride-hailing taxis (RT) can address the issue. However, this has been understudied in the literature. This paper aims to estimate the equity of TT and RT services during peak hours and to study how the entry of RT affects equity by analyzing trip data of TT and RT in New York City in 2010 and 2017 (before and after the entry of RT). First, we used the Lorenz curve and the Gini coefficient to estimate the equity of taxi services against population and employment. The results show that the equity of RT in 2017 is higher than that of TT and the equity of TT + RT in 2017 is higher than that of 2010. Mixed geographically weighted regression (MGWR) was applied to determine whether the relationships between taxi trips and population/employment would vary across different taxi zones. The coefficient of variation (CV) of local coefficients of population/employment is used as an indicator of equity. Results show that RT services were more equitable than TT services in 2017 and that the overall taxi service in 2017 was more equitable than that of 2010.

Cohomology of Homotopy Colimits of Simplicial Sets and Small Categories

This paper deals with well-known weak homotopy equivalences that relate homotopy colimits of small categories and simplicial sets. We show that these weak homotopy equivalences have stronger cohomology-preserving properties than for local coefficients.

Methodology for quantitative assessment of ecological efficiency of geotechnologies

The article presents the results of work aimed at solving the problem of mining waste generation by creating a methodology of wastefree technology. According to the authors, the problem of solid mining waste can be solved by building a technology with a completely closed cycle of circulation of matter. An integral non-waste coefficient for the field development technology has been proposed, which is defined as the sum of local coefficients obtained for each technological level. By the value of the general coefficient, it is possible to estimate the relative amount of solid waste for an operating mining and processing enterprise, as well as to carry out a comparative analysis of the options considered at the design stage.