蕴涵环交换性的某些多项恒等式

设ｍ＞１，ｎ，ｐ，ｑ，ｒ，ｓ均为正整数，Ｒ是一个具有单位元１的环．证明了：如果Ｒ中的任意ｘ，ｙ满足且Ｒ具有Ｑ（ｍ）性质，则Ｒ是一个交换环．此外，在适当的条件下确立了Ｒ的交换性．     

Arboreality predicts Batrachochytrium dendrobatidis infection level in tropical direct-developing frogs

Pathogen-mediated changes in host behaviour can result from hosts altering their habitat preferences. Although infection risk with pathogenic fungus Batrachochytrium dendrobatidis in amphibians is associated with environments favouring its growth, the relationship with microhabitat use has not been examined. Here, we aim to determine if microhabitats used by frogs during their nocturnal activity predict B. dendrobatidis prevalence and infection intensity. Our focal host, Eleutherodactylus coqui, is a habitat generalist that uses multiple habitats from the forest floor to the canopy. We analysed data on B. dendrobatidis occurrence in 157 adults and 122 juveniles at El Yunque National forest in Puerto Rico. We categorized each individual’s nocturnal microhabitat as forest floor, curled palm fronds in the floor, arboreal bromeliads and foliage or tree trunks 50 cm to 2.5 m above ground. We found that frogs on the forest floor had the greatest B. dendrobatidis prevalence (73%), compared with those active in vegetation above ground (55%). Overall, the probability of B. dendrobatidis infection in frogs using microhabitats on the forest floor was twice as great as for those on arboreal substrates. Differences in B. dendrobatidis prevalence and intensity in E. coqui may be explained by specific abiotic conditions of microenvironments (temperature and humidity) affecting both pathogen and host, and by the age-specific ecological requirements of hosts. Adults were found to be most active in microhabitats where individuals had lower infection burdens, suggesting pathogen-modulated habitat choice. This work has important implications for the evolutionary dynamics of enzootic diseases and provides data that may inform potential mitigation strategies against a generalist amphibian pathogen.     

Spawning behaviour of Engystomops pustulatus (Anura: Leptodactylidae)

Foam nests have evolved independently in several amphibian groups as an adaptive response to prevent predation and desiccation in dry environments. Nests are normally laid on ponds, or in underground galleries, humid forest leaf litter or terrestrial bromeliads. They are built when males or females beat a foam precursor associated with the egg masses extruded by the female. The spawning process requires the synchronic actions of the mating pair to obtain a hemispheric nest that protects the offspring. Herein, we describe the spawning behaviour of Engystomops pustulatus based on videos from 13 nesting couples from the lowlands of western Ecuador. Three variables were measured as indicators of male effort: duration of mixing events, duration of resting periods, and number of kicks per mixing event. We consider that not only male physical effort but also female behaviour influences nest structure. We suggest that nest building requires prolonged and intense physical activity by the male as well as the female’s steady position during spawning and female’s oviposition site selection. Nest building has two phases. In the first phase, the duration of resting periods, the duration of mixing events, and the number of kicks increase and are highly variable. During the second phase the three variables stabilise until the end. The volume of the nest increased mainly during the second phase. In four nesting events we observed kicking movements by the female. To our knowledge, this is the first time that female kicking has been observed in leptodactylid frogs. The function of this behaviour is unknown but our observations suggest that it may be triggered by insufficient male effort. Traditionally, female mate choice in Engystomops has been explained under models of indirect benefits exclusively. We argue that the prolonged male activity during nesting could influence female fitness directly. This will allow the operation of sexual selection via direct benefits.     

Melatonin transport into mitochondria

Melatonin is a well-known, nighttime-produced indole found in bacteria, eukaryotic unicellulars, animals or vascular plants. In vertebrates, melatonin is the major product of the pineal gland, which accounts for its increase in serum during the dark phase, but it is also produced by many other organs and cell types. Such a wide distribution is consistent with its multiple and well-described functions which include from the circadian regulation and adaptation to seasonal variations to immunomodulatory and oncostatic actions in different types of tumors. The discovery of its antioxidant properties in the early 1990s opened a new field of potential protective functions in multiple tissues. A special mention should be made regarding the nervous system, where the indole is considered a major neuroprotector. Furthermore, mitochondria appear as one of the most important targets for the indole’s protective actions. Melatonin’s mechanisms of action vary from the direct molecular interaction with free radicals (free radical scavenger) to the binding to membrane (MLT1A and MLT1B) or nuclear receptors (RZR/RORα). Receptor binding has been associated with some, but not all of the indole functions reported to date. Recently, two new mechanisms of cellular uptake involving the facilitative glucose transporters GLUT/SLC2A and the proton-driven oligopeptide transporter PEPT1/2 have been reported. Here we discuss the potential importance that these newly discovered transport systems could have in determining the actions of melatonin, particularly in the mitochondria. We also argue the relative importance of passive diffusion vs active transport in different parts of the cell.     

Babylonian solar theory on the Antikythera mechanism

This article analyzes the angular spacing of the degree marks on the zodiac scale of the Antikythera mechanism and demonstrates that over the entire preserved 88° of the zodiac, the marks are systematically placed too close together to be consistent with a uniform distribution over 360°. Thus, in some other part of the zodiac scale (not preserved), the degree marks have been spaced farther apart. By contrast, the day marks on the Egyptian calendar scale are spaced uniformly, apart from minor errors. A solar equation of center is apparent which rises by nearly 2.7° over the preserved portion of the zodiac. The placement of the degree marks indicates that, in the preserved portion of the zodiac, the Sun was considered to run at a uniform pace of about 30° per synodic month, which is consistent with the Sun’s speed in the fast zone of the Babylonian solar theory of System A.

     

Morphology of tube-like threads related to Limnochares aquatica (L., 1758) (Acariformes: Hydrachnidia: Limnocharidae) in the laboratory

Water mites Limnochares aquatica (L., 1758) during maintenance in the laboratory for a long period of time in constant conditions periodically produced certain whitish flocculent material consisting of long rigid unbranched tube-like threads 1.3 ± 0.3 µm in diameter crossing freely. These threads were studied using light-optical as well as transmission electron microscopical and scanning electron microscopical methods. Microbiological staining was also applied to the threads to exclude their bacterial or fungal origin. The thread wall is built of fine fibrils arranged at different angles to the long axis of threads that is reflected in a certain stratification of the wall. Threads are mostly hollow or may contain electron-dense homogeneous material. No cell components are present in the thread composition. Numerous dermal glands with their small slit-like orifice scattered throughout the mite body surface are thought to produce these threads. Most probably the thread formation is a reaction of mites to stress under laboratory conditions, and this is expected to be a type of defensive reaction.     

A Proposal for the Automatic Computation of Envelopes of Families of Plane Curves

Journal of Systems Science and Complexity - The idea of envelope of a family of plane curves is an elementary notion in differential geometry. As such, its implementation in dynamic geometry...