Food capture and escape behavior of Leposternon microcephalum Wagler, 1824 (Squamata: Amphisbaenia)

Amphisbaenians are fossorial reptiles that have a cylindrical and elongated body covered with scales arranged in rings, and are all apodal, except for the three species of the genus Bipes. The amphisbaenian diet consists of a variety of invertebrates and small vertebrates. As these animals live underground, many aspects of their natural history are difficult to study. Most feeding studies of amphisbaenians have focused on the composition of the diet and feeding ecology, and the data available on feeding behavior are based on precursory observations. The present study describes the food capture behavior of Leposternon microcephalum Wagler, 1824 in captivity. In this experiment we used non-live bait (moist cat food), which was placed near a burrow opening, on the surface of the substrate. Three animals were monitored visually and filmed using cellphone cameras deployed at fixed points, to capture images from the dorsal and lateral perspectives of the study subjects. Two principal types of behavior were observed: the capture of food and defense mechanisms. The strategies used to capture the food were similar to those observed in other fossorial species. Although the backward movement has already been observed and described, we were able to record this movement being used as an escape strategy. These findings enrich our knowledge on different aspects of the natural history of the amphisbaenians.

Existence of Fixed Points in Fuzzy Strong b-Metric Spaces

In the present research, modern fuzzy technique is used to generalize some conventional and latest results. The objective of this paper is to construct and prove some fixed-point results in complete fuzzy strong b-metric space. Fuzzy strong b-metric (sb-metric) spaces have very useful properties such as openness of open balls whereas it is not held in general for b-metric and fuzzy b-metric spaces. Due to its properties, we have worked in these spaces. In this way, we have generalized some well-known fixed-point theorems in fuzzy version. In addition, some interesting examples are constructed to illustrate our results.

On Solution of Boundary Value Problems via Weak Contractions

The aim is to present a new relational variant of fixed point result that generalizes various fixed point results of the existing theme for contractive type mappings. As an application, we solve a periodic boundary value problem and validate all assertions with the help of nontrivial examples. We also highlight the close connections of the fixed point results equipped with a binary relation to that of graph related metrical fixed point results. Radically, these investigations unify the theory of metrical fixed points for contractive type mappings.

Enhanced Beetle Antennae Algorithm for Chemical Dynamic Optimization Problems’ Non-Fixed Points Discrete Solution

Dynamic optimization is an important research topic in chemical process control. A dynamic optimization method with good performance can reduce energy consumption and prompt production efficiency. However, the method of solving the problem is complicated in the establishment of the model, and the process of solving the optimal value has a certain degree of difficulty. Based on this, we proposed a non-fixed points discrete method of an enhanced beetle antennae optimization algorithm (EBSO) to solve this kind of problem. Firstly, we converted individual beetles into groups of beetles to search for the best and increase the diversity of the population. Secondly, we introduced a balanced direction strategy, which explored extreme values in new directions before the beetles updated their positions. Finally, a spiral flight mechanism was introduced to change the situation of the beetles flying straight toward the tentacles to prevent the traditional algorithm from easily falling into a certain local range and not being able to jump out. We applied the enhanced algorithm to four classic chemical problems. Meanwhile, we changed the equal time division method or unequal time division method commonly used to solve chemical dynamic optimization problems, and proposed a new interval distribution method—the non-fixed points discrete method, which can more accurately represent the optimal control trajectory. The comparison and analysis of the simulation test results with other algorithms for solving chemical dynamic optimization problems show that the EBSO algorithm has good performance to a certain extent, which further proves the effectiveness of the EBSO algorithm and has a better optimization ability.

A Modified Krasnosel’skiǐ–Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings

For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel’skiǐ–Mann algorithm for which we prove a strong convergence theorem. We also empirically compare the rate of convergence of the modified Krasnosel’skiǐ–Mann algorithm and of the simple Krasnosel’skiǐ fixed point algorithm. Based on the numerical experiments reported in the paper we conclude that, for the class of enriched nonexpansive mappings, it is more convenient to work with the simple Krasnosel’skiǐ fixed point algorithm than with the modified Krasnosel’skiǐ–Mann algorithm.

Stability of Fixed Points in an Approximate Solution of the Spring-Mass Running Model

We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct analytical approximations of solutions in the considered model. The model itself consists of two sets of differential equations - one set describes the motion of the centre of mass of a runner in contact with the ground (support phase), and the second set describes the phase of no contact with the ground (flight phase). By appropriately concatenating asymptotic solutions for the two phases we are able to reduce the dynamics to a onedimensional apex to apex return map. We find sufficient conditions for this map to have a unique stable fixed point. By numerical continuation of fixed points with respect to energy, we find a transcritical bifurcation in our model system.MSC 2020 Classification: 34C20, 34D05, 37N25, 70K20, 70K42, 70K50, 70K60

$$\alpha $$-Firmly nonexpansive operators on metric spaces

We extend to p-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise averaged mappings. Our main contribution is establishing a calculus for these mappings in p-uniformly convex spaces, showing in particular how the property is preserved under compositions and convex combinations. This is of central importance to splitting algorithms that are built by such convex combinations and compositions, and reduces the convergence analysis to simply verifying that the individual components have the required regularity pointwise at fixed points of the splitting algorithms. Our convergence analysis differs from what can be found in the previous literature in that the regularity assumptions are only with respect to fixed points. Indeed we show that, if the fixed point mapping is pointwise nonexpansive at all cluster points, then these cluster points are in fact fixed points, and convergence of the sequence follows. Additionally, we provide a quantitative convergence analysis built on the notion of gauge metric subregularity, which we show is necessary for quantifiable convergence estimates. This allows one for the first time to prove convergence of a tremendous variety of splitting algorithms in spaces with curvature bounded from above.

Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication

The physical implementation of continuoustime memristor makes it widely used in chaotic circuits, whereas discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize TiO2 memristor model, and the discretized model also meets the three fingerprinter characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling the proposed TiO2 memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete TiO2 memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.