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In the current work, we build a difference analog of the Caputo fractional derivative with generalized memory kernel (𝜇L2-1𝜎 formula). The fundamental features of this difference operator are studied, and on its ground, some difference schemes generating approximations of the second order in time for the generalized time-fractional diffusion equation with variable coefficients are worked out. We have proved stability and convergence of the given schemes in the grid L 2 L_{2} -norm with the rate equal to the order of the approximation error. The achieved results are supported by the numerical computations performed for some test problems.

In this paper, we introduce a multi-domain Muntz-polynomial spectral collocation method with graded meshes for solving second kind Volterra integral equations with a weakly singular kernel. This method is particularly suitable for problems whose solutions contain non-integer exponent factors. We carry out a rigorous error analysis of hp-version in the L ∞ - and weighted L 2 -norms. Several numerical examples are presented to demonstrate the efficiency and accuracy of the method.

We employed camera traps to collect data on the activity patterns, across a 24 hour period, of three free ranging adult Chinese crocodile lizards (Shinisaurus crocodilurus), a primitive reptile and the only lizard species in the family Shinisauridae. Our study demonstrated that during the non-hibernation season, diurnal Chinese crocodile lizard spent 96.73% of their time immobile (rest+sleep), 2.89% moving and 0.26% basking. Individuals regularly woke up around 5:30 AM and rested between 7:30AM to 8:20 PM. Four substrates used by Chinese crocodile lizards with per branch for 47.07±33.3% the ground for 28.34±15.56%, bodies of water for 1.2±0.7% and stem .for 0.9±0.43%. Additional analyses suggest that several factors including the exploitation of a small home range, a high starvation tolerance, extended periods of immobility (sleep + rest), and inhabiting a stable environment, enable the Chinese crocodile lizard to minimize energy costs associated with travel and thermoregulation, promoting its survival over long evolutionary periods.

Submergence tolerance is crucial when thinking in promising species for restoration of ecosystems prone to suffer extreme flooding events. In this study, two-year-old seedlings of Distylium chinense were subjected to one field study and five controlled experiments: unsubmerged and watered daily as controls (CK) and completely submerged for 30, 60, 90 and 120 days, respectively followed by a 60-day recovery period to test the submergence tolerance. The results showed that the survival decreased with the increasing flooding duration. Different submergence duration treatments affected dry mass accumulation and carbohydrate content of roots, stems and leaves. Flooding stress affected the activities of pyruvate decarboxylase (PDC), ethanol dehydrogenase (ADH) and lactic dehydrogenase (LDH) enzymes, which indicated the roots and leaves adapt to long-term flooding by reinforcing their anaerobic respiration and activities of ADH were higher than those of LDH for roots and leaves with stronger alcoholic fermentation mainly. After de-submergence, the recovery patterns of carbohydrate were coincided with those of dry mass accumulation of the roots, stems and leaves. A significant regression equation analysis showed root starch content and dry mass accumulation were the major factors affecting the seedling survival. And D. chinense accumulated substantial amounts of carbohydrate before submergence and invested more in roots and stems than in leaves, which enhances long-term survival under submergence. Carbohydrate storage is a key functional trait that can explain high survival under submergence. D. chinense may have adopted a suite of growth and respiratory metabolic adaptation strategies to survive long-term submergence.

In this manuscript, we consider an efficient dissipation-preserving finite element method for a class of two-dimensional nonlinear fractional wave equations on irregular convex domains. We show that the fully discrete method preserves the discrete energy structures under the same boundary conditions as the continuous model. Furthermore, the optimal order error estimates of the fully discrete scheme are proved in detail. Finally, the numerical simulations, which are based on spatial unstructured meshes, are presented to confirm the correctness of the theoretical results.

Play behavior is a significant trait of immature nonhuman primates (hereafter primates), which may play important roles in sensory, locomotor, socio-cognitive, and developmental processes in primates. It has been suggested that function of play is to practice and improve motor skills related to foraging, avoiding predation, attracting mates, raising offspring, and also is to strength social skills concerning to cementing friendly relationships and defraying aggression among individuals. From September 2009 to August 2010, we investigated play behaviors of 1-12-month-old white-headed langur (Trachypithecus leucocephalus) which is a critically endangered primate endemic to China. During this study, we recorded 4,421 play bouts and 1,302 minutes of play time of 7 infants in total. We found that infants had different play behavior patterns at different ages. Specifically, non-social play behaviors appeared at 1 month of age, social play behaviors at 2 months, and all types of social and non-social play behaviors at 3 months. The frequency and duration of non-social play peaked at 5 months and then decreased, while social play appeared at 2 months and gradually increased with age. Non-social play did not differ between the sexes, whereas social play showed sex specificity, with higher frequency and duration of social play in male infants than in female infants. In addition, male and female white-headed langur infants appeared to prefer the individuals of same sex as social playmates. In conclusion, we first reported the pattern of play behavior of a critically endangered langur aged 1 to 12 months though the sample size is small, our results suggest they may have the adaptation of play behaviors in ages and sexes, which may help them adapt to their habitat and social system.