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The category of metric spaces is a subcategory of quasi-metric spaces. It is shown that the entropy of a map when symmetric properties is included is greater or equal to the entropy in the case that the symmetric property of the space is not considered. The topological entropy and Shannon entropy have similar properties such as nonnegativity, subadditivity and conditioning reduces entropy. In other words, topological entropy is supposed as the extension of classical entropy in dynamical systems. In the recent decade, different extensions of Shannon entropy have been introduced. One of them which generalizes many classical entropies is unified $(r,s)$-entropy. In this paper, we extend the notion of unified $(r, s)$-entropy for the continuous maps of a quasi-metric space via spanning and separated sets. Moreover, we survey unified $(r, s)$-entropy of a map for two metric spaces that are associated with a given quasi-metric space and compare unified $(r, s)$-entropy of a map of a given quasi-metric space and the maps of its associated metric spaces. Finally we define Tsallis topological entropy for the continuous map on a quasi-metric space via Bowen's definition and analyze some properties such as chain rule.

Genetic diversity in perennial Salvia judaica Boiss (Judean sage) and Salvia palaestina Benth (Palestinian sage) species using touch-up directed amplification of minisatellite region DNA (TU-DAMD) has been performed in two separated sets; in the first set (set A) the initial annealing temperature was increased from 50 °C to 55 °C, whereas, in the second one (set B), it increased from 55 °C to 60 °C by 0.5 °C/cycle during the first 10 PCR amplification cycles. Fifteen DAMD primers have been tested for each set. Set (A) produced 89.39% polymorphism level (P%) with polymorphic information content (PIC) average of 0.33 and marker index (MI) average of 3.96. Whereas, in set (B) these values were recorded to be 94.02%, 0.34 and 3.98 for P%, PIC and MI, respectively. Data showed that the two mentioned sets successfully highlighted high polymorphism level between the two studied Salvia sp. This work studies genetic diversity of S. judaica and S. palaestina species using TU-DAMD test as a novel molecular marker.

In the present paper, we introduce the notions of (1, 2)∗-fuzzy soft b-separated sets, (1, 2)∗-fuzzy soft b-connectedness and (1, 2)∗-fuzzy soft b-compactness in fuzzy soft bitopological spaces. Then, some basic topological properties of these notions are investigated. Also, some illustrative examples are given to show the importance of the obtained theorems.

Animals have always played an important role in our everyday life. They are given more attention than inanimate objects, which have been adaptive during the evolution of mankind, with some animal species still presenting a real threat to us. In this study, we focused on the species usually evaluated as the scariest and most disgusting in the animal kingdom. We analyzed which characteristics (e.g., weight, potential threat for humans) influence their evaluation in a nonclinical Central European WEIRD population (Western, educated, industrialized, rich, and democratic). The tested animals were divided into two separated sets containing 34 standardized photos evoking predominantly one negative emotion, fear or disgust. The pictures were ranked according to their emotional intensity by 160 adult respondents with high inter-rater agreement. The most fear-eliciting species are mostly large vertebrates (e.g., carnivorans, ungulates, sharks, crocodiles), whereas smaller fear-evoking vertebrates are represented by snakes and invertebrates are represented by arachnids. The most disgust-evoking animals are human endo- and ectoparasites or animals visually resembling them. Humans emotionally react to fear-evoking animals that represent a real threat; however, identifying truly dangerous disgust-evoking animals might be harder. The results also support a somewhat special position of snakes and spiders.

In this paper we introduce the notion of pair of weakly chain separated sets in a topological space. If two sets are chain separated in the topological space, then they are weakly chain separated in the same space. We give an example of weakly chain separated sets in a topological space that are not chain separated in the space. Then we study the properties of these sets. Also we mention the criteria for two kind of topological spaces by using the notion of chain. The topological space is totally separated if and only if any two different singletons (unit subsets) are weakly chain separated in the space, and it is the discrete if and only if any pair of different nonempty subsets are chain separated. Moreover we give a criterion for chain connected set in a topological space by using the notion of weakly chain separateness. This criterion seems to be better than the criterion of chain connectedness by using the notion of pair of chain separated sets. Then we prove the properties of chain connected, and as a consequence of connected sets in a topological space by using the notion of weakly chain separateness.

Two separated sets of laboratory experiments were studied for barley seeds treating using a microwave and ultraviolet irradiation. In the microwave set, seeds have been exposed to the microwave radiations (2450 MHz) for 0 sec (control, MW0), 5 sec (MW1), 10 sec (MW2), and 20 sec (MW3), while in the ultraviolet set, seeds have exposed to UV-C radiation (254 nm) for 0 min (control, UV0), 30 min (UV1), 60 min (UV2), and 120 min (UV3). The aim is to study the influences of different exposure time from MW and UV-C radiation on some barley seed germination parameters and to choose the fitting model Logistic (Log) or Gompertz (Gom) suited to cumulative germination curves under the influence of these factors.  The results of this study showed higher seed germination percentage (93.33%) at the exposure time MW2 and UV3 (88.33%), whereas the lowest value (66.67%) recorded in MW3 treatment. The results also appeared the best values at MW2 in SG, 6.24 seed day-1; in GRI, 31.19% day-1, and in GI, 87.67, as well as at UV2 in MGT, 3.32 day. The higher value of asymptotic germination barley seeds was found with Gom function (97.24%, and 88.71%) at MW2 and UV3, respectively. Besides, Gom functions at MW1 and UV2 give the highest maximum germination rates at 2,08 and 2.51% h-1, respectively. The results of the Log equation illustrated the highest value of germination percentage of the inflection point has recorded in 43.85 and 47.37 % on UV3 and MW2 treatments, respectively. For the fitting growth curve, the results have proven that the Gom function was shown the lowest values in MSE in all MW and UV exposure times, as compared with the Log function. So, the results of the Gom function were more fit for the growth curve for MW and UV treatments, as compared with the Log function.

International audience Following the proof of the purity conjecture for weakly separated sets, recent years have revealed a variety of wider classes of pure domains in different settings. In this paper we show the purity for domains consisting of sets that are weakly separated from a pair of “generic” sets I and J. Our proof also gives a simple formula for the rank of these domains in terms of I and J. This is a new instance of the purity phenomenon which essentially differs from all previously known pure domains. We apply our result to calculate the cluster distance and to give lower bounds on the mutation distance between cluster variables in the cluster algebra structure on the coordinate ring of the Grassmannian. Using a linear projection that relates weak separation to the octahedron recurrence, we also find the exact mutation distances and cluster distances for a family of cluster variables.