The newly generalized energy storage component namely memristor is a fundamental circuit element so called universal charge-controlled mem-element is proposed for controlling the analysis and coexisting attractors. The governing differential equations of memristor are highly non-linear for mathematical relationships. The mathematical model of memristor is established in terms of newly defined fractal-fractional differential operators so called Atangana-Baleanu, Caputo-Fabrizio and Caputo fractal-fractional differential operator. A novel numerical approach is developed for the governing differential equations of memristor on the basis of Atangana-Baleanu, Caputo-Fabrizio and Caputo fractal-fractional differential operator. We discussed chaotic behavior of memristor under three criteria as (i) varying fractal order, we fixed fractional order, (ii) varying fractional order, we fixed fractal order and (ii) varying fractal and fractional orders simultaneously. Our investigated graphical illustrations and simulated results via MATLAB for the chaotic behaviors of memristor suggest that newly presented Atangana-Baleanu, Caputo-Fabrizio and Caputo fractal-fractional differential operator has generates significant results as compared with classical approach.

Quite recently, Bor \cite{Bor4} has proved a new result on weighted arithmetic mean summability factors of non-decreasing sequences, which includes some known results. In this paper, we extend his result to more general matrix summability method by using an almost increasing sequence and normal matrices in place of a positive non-decreasing sequence and weighted mean matrices, respectively.

An SIS epidemic reaction-diffusion model with saturated incidence rate and spontaneous infection is considered. We establish the existence of endemic equilibrium by using a fixed point theorem. We mainly investigate the effects of diffusion and saturation on asymptotic profiles of the endemic equilibrium. Our analysis shows that the spontaneous infection can enhance persistence of infectious disease.

An algorithm for two-variable rational interpolation is developed. The algorithm is suitable for interpolation cases where neither the number of interpolation points to be used nor the final degrees of the rational interpolant are known a priori. Instead, a maximum degree for the interpolant's numerator and denominator is assumed, and, by testing the condition number of the interpolation system's matrix at each step, the necessary reductions are made so as to cope with non-normality and unattainability occasions. The algorithm can be used for applications of the Evaluation-Interpolation technique in matrix manipulations, such as finding the inverse of a matrix with elements rational functions in two variables. The algorithm avoids completely symbolic calculations, thus keeping the execution time very low even if the system size is large, and achieves accurate function recoveries for greater polynomial degrees than other bivariate rational interpolation methods.

We study the existence and asymptotic behavior of least energy sign-changing solutions for the nonlinear Schr\“{o}dinger equation coupled with the Chern-Simons gauge theory \[ \left\{ \begin{gathered} -\Delta u+ \omega u+\lambda \sum_{j=1}^k\bigg( \frac{h^2(|x|)}{|x|^2}u^{2(j-1)} +\frac{1}{j}\int_{|x|}^\infty \frac{h(s)}{s}u^{2j}(s) ds \bigg)u= f(u) \ \ \text{in}\ \ \mathbb{R}^2 , \hfill \\ {\text{ }}u \in {H^1_r}({\mathbb{R}^2}), \hfill \\ \end{gathered} \right. \] where $\omega, ~\lambda >0$ are constants, $k\in \mathbb{N}^+$ and \[ h(s)=\int_0^s\frac{r}{2}u^2(r)dr. \] Under some suitable assumptions on $f\in C(\R)$, with the help of the Gagliardo-Nirenberg inequality, we apply the constraint minimization argument to obtain a least energy sign-changing solution $u_\lambda$ with precisely two nodal domains. Furthermore, we prove that the energy of $u_\lambda$ is strictly larger than two times of the ground state energy and analyze the asymptotic behavior of $u_\lambda$ as $\lambda\searrow0^+$. Our results cover and improve the existing ones for the gauged nonlinear Schr\”{o}dinger equation when $k\equiv1$.

In this manuscript, some novel exact traveling wave solutions are constructed for $(2+1)$-dimensional Boiti-Leon-Manna-Pempinelli(BLMP) equation. The analytical techniques, namely extended rational sine-cosine method and extended rational sinh-cosh method are utilized for constructing the new solitary wave solutions of BLMP equation. The proposed techniques provides different types of solutions which are expressed in terms of singular periodic wave, solitary waves, bright solitons, dark solitons, periodic wave and kink wave solutions with specific values of parameters.

In this study, we investigate the sum-type singular nonlinear fractional q-integro-differential $m$-point boundary value problem. The existence of positive solutions is obtained by the properties of the Green function, standard Caputo $q$-derivative, Riemann-Liouville fractional $q$-integral and the means of a fixed point theorem on a real Banach space $(\mathcal{X}, \|.\|)$ which has a partially order by using a cone $P \subset \mathcal{X}$. The proofs are based on solving the operator equation $\mathcal{O}_1 x + \mathcal{O}_2 x = x $ such that the operator $\mathcal{O}_1$, $\mathcal{O}_2$ are $r$-convex, sub-homogeneous, respectively and define on cone $P$. As applications, we provide an example illustrating the primary effects.

The present paper treats with constructing a generalized two-fractional-parameter heat conduction model of thermoelasticity with multi-phase-lags. In this the new model, the Fourier heat conduction is replaced by a formula that is more general. In the limited cases, the proposed model reduces to several models of generalized thermoelasticity in the presence and absence of fractional derivatives. The model is then adopted to investigate the problem of a semi-infinite medium subjected a body force and exposed to decaying varying heat. Using the Laplace transform procedure, we obtain the analytical solution for various physical fields. Numerical calculations are depicted in tables and graphs to clarify the effects of the two fractional parameters, external force, and decaying parameter. Finally, the results obtained are discussed in detail and also confirmed with those in the previous literature.

In this report we prove that the hypothesis on the memory term $g$ in \cite% {WenjunYunSun} can be modified to be $g^{\prime }(t)\leq -\zeta (t)g^{p}(t)$% , $t\geq 0,$ $1\leq p<\frac{3}{2}$ where $\zeta (t)$ provides% \begin{equation*} \zeta \left( 0\right) >0,\text{ }\zeta ^{\prime }(t)\leq 0,\text{ }% \int_{0}^{\infty }\zeta \left( s\right) ds=+\infty . \end{equation*}% So the optimal decay results are extended.

We study properties of a piecewise deterministic Markov process modeling the changes in concentration of specific antibodies.The evolution of densities of the process is described by a stochastic semigroup. The long-time behaviour of this semigroup is studied. In particular we prove theorems on its asymptotic stability.

Leader detection and follow it are the main challenges in designing a leader-follower multi-robot system, in addition to the challenge of achieving the formation between the members while tracking the leader. The biological system is one of the main sources of inspiration for understanding and designing such multi-robot systems, especially, the aggregations that follow an external stimulus such as the population of Artemia. In this paper, a dynamic model of a multi-robot system following a spot of light, as a leader will design based on the collective motion behavior of the aggregations of Artemia. The kinematic model will derive based on observation of Artemia behavior under external stimuli, while the dynamic model will be derived based on the newton equation and its parameters will be evaluated by two methods: first one based on the physical structure of the mobile robot and the other based on Least Square Parameter Estimation method. Several experiments have been implemented in order to check the success of the proposed system, which are divided into four scenarios of simulation according to four trajectories, the straight line, circle, zigzag and compound path pattern. V-Rep software has been used for the simulation and results appeared the success of the proposed system and the high performance when robots are tracking the leader.

We investigate a new class of stochastic integro-differential equations driven by L´evy noise. Particularly, based on Schauder’s fixed point theorem, the existence of square-mean almost automorphic mild solution in distribution is obtained by using some conditions which are weaker than Lipschitz conditions. Our result can be seen as a generalisation of the result of [17] and [28] based on the compactness of solution semigroup operators of our slightly different stochastic model. We provide an example to illustrate ours results.

In this paper, we focus on designing a well-conditioned Glarkin spectral methods for solving a two-sided fractional diffusion equations with drift, in which the fractional operators are defined neither in Riemann-Liouville nor Caputo sense, and its physical meaning is clear. Based on the image spaces of Riemann-Liouville fractional integral operators on Lp([a, b]) space discussed in our previous work, after a step by step deduction, three kinds of Galerkin spectral formulations are proposed, the final obtained corresponding scheme of which shows to be well-conditioned—the condition number of the stiff matrix can be reduced from O(N2α) to O(Nα), where N is the degree of the polynomials used in the approximation. Another point is that the obtained schemes can also be applied successfully to approximate fractional Laplacian with generalized homogeneous boundary conditions, whose fractional order α ∈ (0, 2), not only having to be limited to α ∈ (1, 2). Several numerical experiments demonstrate the effectiveness of the derived schemes. Besides, based on the numerical results, we can observe the behavior of mean first exit time, an interesting quantity that can provide us with a further understanding about the mechanism of abnormal diffusion.

UAVs are defined to be aerial vehicles controlled without humans onboard and are used in a large array of missions where tasks automation and human user protection are necessary. The use of UAVs is growing quickly increasing in many application domains as military surveillance, military fight, and frameworks monitoring…etc. UAVs can carry multiple devices in order to execute these functions like cameras, weapons, and equipment of chemical and biological detection. Nowadays, the development of UAVs became the centre of interest of many research workers who are looking to explore its fields of application. There is currently a large array of projects and research subjects emerging in this field. Our work revolves around an assembly and configuration of Quadrotor Drones in telecommunication inspections operations of transmission networks because of their easiest construction and their rapidly services. The user of the realized UAV can control and schedule the operation so intuitive thanks to its graphic control interface.

In concerned article, we investigate a class of boundary value problem of non-linear fractional differential equations. The aforesaid work is committed to the existence, uniqueness and stability analysis for boundary value problem of fractional differential equation. We used the tools of analysis and fixed point theory to establish the conditions for deserted results. At the end, we provided two examples to illustrate the concerned problem.

Encryption and decryption mostly emerge from mathematical discipline. Molecular graphs are models of molecules in which atoms are represented by vertices and chemical bonds by edges of a graph. Graph invariant numbers reflect certain structural features of a molecule that are derived from its molecular graph, known as topological indices. A topological index is a numerical descriptor of a molecule, based on a certain topological features of the corresponding molecular graph. One of the most widely known topological descriptor is the Wiener index. Wiener number is employed to predict boiling point, molar volumes and large number of physico-chemical properties of alkenes. In this paper a new technique is employed to encrypt and decrypt message through the topological index of molecular graph using the linear congruence equations.

Environmental DNA (eDNA) is used for monitoring the occurrence of freshwater organisms. Various studies show a relation between the amount of eDNA detected and target organism abundance, thus providing a potential proxy for reconstructing population densities. However, environmental factors such as water temperature and microbial activity are known to affect the amount of eDNA present as well In this study, we use controlled aquarium experiments using Gammarus pulex L. (Amphipoda) to investigate the relationship between the amount of detectable eDNA through time, pH, and levels of organic material. We found eDNA to degrade faster when organic material was added to the aquarium water, but that pH had no significant effect. We infer that eDNA contained inside cells and mitochondria is extra resilient against degradation, though this may not reflect actual presence of target species. These results indicate that, although estimation of population density might be possible using eDNA, measured eDNA concentration could, in the future, be corrected for local environmental conditions in order to ensure accurate comparisons.

1. Terrestrial plant populations located at the margins of species’ distributions often display reduced sexual reproduction and an increased reliance on asexual reproduction. One hypothesis to explain this phenomenon is that the decline is associated with environmental effects on the energetic costs to produce reproductive organs. 2. In order to clarify the changing processes of sexual reproduction along an altitudinal gradient, we investigated the sexual reproductive parameters, such as the number of sporophytes and gametangia, in Racomitrium lanuginosum, a dioicous moss found on Mt. Fuji. Matured sporophytes were present only below 3000 m, and the number of sporophytes per shoot tended to be lower at higher altitudes. 3. The numbers of male inflorescences per shoot and antheridia per inflorescence and shoot significantly decreased with increasing altitude. In contrast, the numbers of female inflorescences per shoot and archegonia per inflorescence and shoot varied little across altitudes. 4. Synthesis. Our results suggest that the success of sexual reproduction in R. lanuginosum is restricted at higher altitudes on Mt. Fuji by decreases in male gametangia and the subsequent chance of fertilization. These differences between males and females may be caused by differences in the cost of production and development of gametangia, sensitivity to environmental stresses (low air temperature, shortened growth period, and environmental conditions in winter), and phenological patterns at higher altitudes.

Bubble formation from a downward-pointing capillary nozzle was investigated in this study. The experiments were conducted at gas flow rate of 40-5400 mL/h and inner nozzle radius of 0.030-0.255 mm. Experimental results show that microbubbles were formed continuously at moderate Weber number, which was not reported in pervious investigations with injecting gas through an upward-pointing capillary nozzle. High-speed visualization indicates that the formation of microbubbles arises from the convergence of the capillary waves induced by the partial coalescence of larger bubbles. A bubbling regime map is given to identify the critical conditions for the formation of microbubbles. In the present air-water experiments, the generated microbubbles are 20-170 μm in diameter. From experimental data, a scaling law for microbubble size is proposed as a function of Weber and Bond numbers.

The continuously increasing trend of large-tree growth challenges the assertion of the unimodal pattern in classical growth theories. Here, we considered the effect of phenotypic plasticity on growth and extended classical growth equations (i.e., Gompertz and logistic curves) to reconcile this contradiction. Tree growth is indeterminate and modular, and we speculated that a trajectory of tree growth should be viewed as a combination of a series of different unimodal curves, termed cascading growth. Mathematically, the increasing growth trend may be attributable to the later emergence of larger-scale unimodal curves, which depend on some beneficial change of functional traits relative to tree size. To test this hypothesis, we determined tree growth in four plots across the subalpine Abies fabri forest belt on Gongga Mountain in the eastern Tibetan Plateau of China, and then analyzed the effects of some important functional traits (i.e., leaf and stem economics and morphological traits) on the growth curve. Our results indicate that the ideal growth trajectory that is composed of the maximum growth increment of different trees follow a unimodal curve with a cascade characteristic. At individual levels, the emergence of a larger unimodal curve is caused by an increase in the relative amount of canopy and a decrease in the relative amount of sapwood. This study clarifies the general growth rule of large trees, offers a concise way to link traits and growth performance, and reveals the complexity and sustainability of a old forest acting as a carbon sink to some extend.

Aim: Threats faced by narrowly distributed endemic plant species in the face of the Earth’s sixth mass extinction and climate change exposure are especially severe for taxa on islands. We investigated the current and projected distribution and range changes of Cochemiea halei, an island endemic cactus. This taxon is of conservation concern, currently listed as vulnerable on the International Union for the Conservation of Nature Red List and as a species of special concern under Mexican federal law. The goals of this study are to 1). identify the correlations between climate variables and current suitable habitat for C. halei; 2). determine if the species is a serpentine endemic or has a facultative relationship with ultramafic soils; 3). predict range changes of the species based on climate change scenarios. Location: The island archipelago in Bahía Magdalena on the Pacific coast, Baja California Sur, Mexico. Methods: We used temperature and precipitation variables at 30 arcsecond resolution and soil type, employing multiple species distribution modeling methods, to identify important climate and soil conditions driving current habitat suitability. The best model of current suitability is used to predict possible effects of four climate change scenarios based on best case to worst case representative concentration pathways, with projected climate data from two general circulation models, over two time periods. Main conclusions: The occurrence of the species is found to be strongly correlated with ultramafic soils. The most important climate predictor for habitat suitability is annual temperature range. The species is predicted to undergo range contractions from 21% to 53%, depending on the severity and duration of exposure to climate change. The broader implications for a wide range of narrowly adapted, threatened and endemic plant species indicate an urgent need for threat assessment based on habitat suitability and climate change modeling.

Demulsification is an important process for dehydration of crude oil and environmental remediation. The intrinsic structure of metal-organic frameworks (MOFs) endows MOFs with amphipathicity and meets the requirement of demulsifier. Herein, we studied the demulsification performance, process and characteristic using MIL-100(Fe). The amphipathicity of MIL-100(Fe) is crucial for demulsification. The demulsification efficiency (DE) for model emulsion excessed 99% within 30 min at optimal condition, and dehydration efficiency for crude oil emulsion was up to 79% within 5 min. The DE can be maintained when the pH ranged from 10.0 to 4.0, and it increased along with an increase of salinity (1~1000 mmol•L-1). Component analysis revealed that the degradation of sodium dodecyl sulfonate occurred by an abstraction of SO32-, which could eliminate the potential risk of emulsifying again. Therefore, this study confirmed that enhancing the interaction with emulsion is an effective strategy for new demulsifier to against the harsh conditions.

Bubble size distribution and bubble ellipticity were measured as a function of axial position in a vertically oriented semi-batch gas-liquid Taylor vortex reactor with varying gas flow rate and inner cylinder rotation speed producing axial Reynolds numbers in the range 23.8-119 and azimuthal Reynolds numbers up to 4.2×104. The mean bubble size increases monotonically with axial distance from the bottom of the reactor at the location of gas injection. The functional form of the growth of the mean bubble size with axial position depends upon the azimuthal Reynolds number. Specifically, when the azimuthal Reynolds number is less than 1.3×104, the mean bubble size increases linearly with axial distance from the bubble injection point. In contrast, for azimuthal Reynolds numbers greater than this critical value, the mean bubble size increases with axial distance in a sigmoidal manner.

Informative/Abstract:Estimating streamflow is time and labour intensive due to the necessity of developing a rating curve. The development of a rating curve involves acquiring at least thirty in-field measurements of streamflow across a wide range of flow levels, which can be costly and impractical in remote regions with limited seasonal access. Here we showcase an automated system which accurately estimates streamflow multiple times each day, greatly facilitating the development of rating curves for remote or seasonally inaccessible sites. The system uses an emerging technique referred to as particle image velocimetry (PIV) to track the movement of objects and flow structure features on the mobile water surface to generate velocity vector grids. Velocity grids were used to calculate streamflow and facilitate the development of a rating curve. This represents the first use of an automated PIV system to estimate streamflow in small streams (< 5 m wide) and the first system to automatically distribute particles for facilitated PIV analysis.Keywords: Particle Image Velocimetry, Streamflow Monitoring, Automated Systems, Particle TracerFunding: This research was funded through the Ministry of Natural Resources and Forestry, the Canada-Ontario Agreement Fund, and the Queen Elizabeth II Graduate Scholarship in Science and Technology.