Phenotypic diversity, or disparity, can be explained by simple genetic drift or, if functional constraints are strong, by selection for ecologically relevant phenotypes. We here studied phenotypic disparity in head shape in aquatic snakes. We investigated whether conflicting selective pressures related to different functions have driven shape diversity and explore whether similar phenotypes may give rise to the same functional output (i.e. many-to-one mapping of form to function). We focused on the head shape of aquatically foraging snakes as they fulfil several fitness-relevant functions and show a large amount of morphological variability. We used 3D surface scanning and 3D geometric-morphometrics to compare the head shape of 62 species in a phylogenetic context. We first tested whether diet specialization and size are drivers of head shape diversification. Next, we tested for many-to-one mapping by comparing the hydrodynamic efficiency of head shapes characteristic of the main axis of variation in the dataset. We 3D printed these shapes and measured the forces at play during a frontal strike. Our results show that diet and size explain only a small amount of shape variation. Shapes did not functionally converge as more specialized aquatic species evolved a more efficient head shape than others. The shape disparity observed could thus reflect a process of niche specialization under a stabilizing selective regime.

Many eusocial insects, including ants, show complex colony structures, distributions, and reproductive strategies. In the ant Vollenhovia emeryi Wheeler (Hymenoptera: Myrmicinae), queens and males are produced clonally, while sterile workers arise sexually, unlike other ant species and Hymenopteran insects in general. Furthermore, there is a wing length polymorphism in the queen caste. Despite its ecological and evolutionary importance, little is known about the population dynamics and structure of this ant species, which may provide insight into its unique reproductive mode and polymorphic traits. We performed in-depth analyses of ant populations from Korea, Japan, and North America using three mitochondrial genes (COI, COII, and Cytb). The long-winged (L) morph is predominant in Korean populations, and the short-winged (S) morph is very rare. Interestingly, all L morphs were infected with Wolbachia, while all Korean S morphs lacked Wolbachia, demonstrating a novel association between a symbiont and a phenotypic trait. A phylogenetic analysis revealed that the S morph is derived from the L morph. We propose that the S morph is associated with potential resistance to Wolbachia infection, and that Wolbachia infection does not influence clonal reproduction.

The photocatalytic yield of the g-C3N4 for CO2 reduction was modified by phosphorus doping. The possible reaction pathways for CO2 reduction on the P-doped g-C3N4 (PCN) surface were investigated by DFT calculations for the first time. The experimental results showed that P doping improves the production of CH4 through the increase in the driving force of the electrons. The partial density of states of the PCN showed that the VBM and CBM are composed of px, py and s orbitals of the N atoms and pz states of carbon, nitrogen, and phosphorus, respectively and therefore, the P-doping increase carriers lifetime. Mechanism studies confirm that formic acid, formaldehyde, methanol and methane are the most probable products. The methane having positive adsorption energy can be easily desorbed from the PCN surface and the Gibbs activation energy of the final step is 1.98 eV. The formation of H2COOH is the rate-determining step.

The field of molecular magnetism has benefited from the fluid synergy between experimentalists and theoreticians for decades This has led to fundamental understanding of the processes that govern Single Molecule Magnets, allowing for the establishment of clear design criteria to control properties and the development of new synthetic methodologies, sophisticated magnetic measurements and innovative computational techniques. Herein we give an overview on the experimental and theoretical collaborative work we carried out as part of the synthesis group led by David Mills and the computational/theoretical team led by Nicholas Chilton at the University of Manchester. Together with this, we provide a perspective on collaborative work in molecular magnetism and how such collaborations are essential for advancing the field further.

We studied the ring opening of propylene oxide (PO) by salen-M coordinated OH- group [M = Al(Ⅲ), Sc(Ⅲ), Cr(Ⅲ), Mn(Ⅲ), Fe(Ⅲ), Co(Ⅱ), Co(Ⅲ), Ni(Ⅱ), Cu(Ⅱ), Zn(Ⅱ), Ru(Ⅲ) and Rh(Ⅲ)]. The results show that the ring opening energy barriers for M(II) complexes are much lower than those with M(III) complexes in the gas phase, and the barriers correlate linearly with the negative charges on the OH- group, the Fukui function condensed on the OH- group. The nucleophilicity ordering in gas phase can be rationalized by the ratio of formal positive charges/radius of M cations. Solvent effect greatly increases the barriers of M(II) complexes, but slightly changes the results of M(III) ones, making the barriers similar. Analysis indicates that the reaction heats are linearly proportional to the reverse reaction barriers. The relationships established here can be used to estimate the ring opening barriers and to screen epoxide ring opening catalysts.

In this work, we study a weakly singular Volterra integro differential equation with Caputo type fractional derivative. First, we derive a sufficient condition for the existence and uniqueness of the solution of this problem based on the maximum norm. It is observed that the condition depends on the domain of definition of the problem. Thereafter, we show that this condition will be independent of the domain of definition based on an equivalent weighted maximum norm. In addition, we have also provided a procedure to extend the existence and uniqueness of the solution in its domain of definition by partitioning it. We also derive a sufficient condition under which the model problem will provide an analytic solution. Next, we introduce a operator based parameterized method to generate an approximate solution of this problem. Convergence analysis of this approach is established here. Next, we have optimized this solution based on least square method. For this, residual minimization is used to obtain the optimal values of the auxiliary parameter. In addition, we have also provided an error bound based on this technique. Several numerical examples are produced to clarify the effective behavior of the convergence of the present method. Comparison of the standard method and optimized method based on residual minimization signify the better accuracy of modified one. In addition, we also consider an equivalent form of weakly singular integro differential equation of a Heat transfer problem to show the effectiveness of the present approach.

In this paper, a class of nonautonomous SEIRS epidemic models with vaccination and nonlinear incidence is investigated. Under some quite weak assumptions, a couple of new threshold values in the form of integral, i.e., $R_1$, $R^*_1$, $R_2$ and $R^*_2$ on the extinction and permanence of disease for the model are established. As special cases of our model, the autonomous, periodic and almost periodic circumstances are discussed respectively. The nearly necessary and sufficient criteria of threshold on the extinction and permanence of disease for above cases are obtained as well. Numerical examples and simulations are presented to illustrate the analytic results.

A mixed boundary value problem for the L\’ame equation in a thin layer $\Omega^h:\cC\times[-h,h]$ around a surface $\cC$ with the Lipshitz boundary is investigated. The main goal is to find out what happens when the thickness of the layer tends to zero $h\to0$. To this end we reformulate BVP into an equivalent variational problem and prove that the energy functional has the $\Gamma$-limit being the energy functional on the mid-surface $\cC$. The corresponding BVP on $\cC$, considered as the $\Gamma$-limit of the initial BVP, is written in terms of G\”unter’s tangential derivatives on $\cC$ and represents a new form of the shell equation. It is shown that the Neumann boundary condition from the initial BVP on the upper and lower surfaces transforms into a right-hand side term of the basic equation of the limit BVP.

The identification of the mechanisms underlying co-occurrence patterns of species is a way to identify which processes (niche, neutral or both) structure metacommunities. In this paper, our goals are to identify patterns of co-occurrence in neotropical stream fish and determine which processes structure the metacommunity and the gradients that underlie this structure. Our results pointed out that the metacommunity formed by the total pool of species is structured by a nested pattern (Hyperdispersed Species Loss) of co-occurrence and the mass effect mechanism. On the other hand, a set of core species displays a Clementisian pattern and is structured by the species sorting mechanism. Both, hyperdispersed species loss and the Clementisian patterns point to a discrete set of communities in the metacommunity. These communities could be isolated by physicochemical conditions, or physical barriers, like dams or waterfalls.

In this study, the viscosity of MgO-Water nanofluid in a different volume fraction of nanoparticles, temperatures, and shear rates has been predicted by Artificial Neural Networks (ANNs) and surface methods. In the ANN method, an algorithm is proposed to select the best neuron number for the hidden layer. In the fitting method, a surface is proposed for each volume fraction of nanoparticles, and finally, the results of ANN and surface fitting method have been compared. It can be observed that, increasing the volume fraction from 0.07% to 1.25% at temperatures of 25, 30, 40, 50, and 60 °C resulted in about two-fold increase in viscosity. Also, the best network has 24 neurons in the hidden layer. It can be seen that for a network with 24 neurons in the hidden layer has the best overall correlation, and this coefficient is 0.999035. The mean absolute value of errors in ANN and fitting method are 0.0118 and 0.0206, respectively.

We calculate the concerted pathway of 1, 2-bromochloroethane monocation to C2H4+ and BrCl using the Minnesota density functional M06-2X and the def2-TZVP basis set. We also calculate the elimination channel of 1, 2-bromochloroethane monocation to C2H4 and BrCl+ for the reason that positive charge can be assigned to either moiety in the fragmentation process of 1,2-C2H4BrCl+. Our results demonstrate that the elimination channel of 1, 2-bromochloroethane monocation to C2H4+ and BrCl is preferred, and the singly charged 1,2-bromochloroethane ions surpass two energy barriers and then separate into C2H4+ + BrCl by an asynchronous concerted process. Experimentally, we confirm that this elimination channel is from the dissociative ionization process of 1,2-bromochloroethane monocation by dc-slice imaging technique. Besides, we can see in laser-induced time-of-flight mass spectra of 1,2-bromochloroethane that fragment ion C2H4+ occur at the laser intensity of 6.0×1013 W/cm2 while BrCl+ occur at a higher laser intensity, which is consistent with the theoretical results that appearance energy of ion C2H4+ should be lower than that of BrCl+, and this is the reason why the low-velocity component of ion BrCl+ is absent from our sliced images.

Stopping land degradation is one of the biggest challenges worldwide and particularly in Burundi, which currently faces unprecedented rates of soil loss and food insecurity. This paper proposes a different development discourse on how to stop land degradation, and presents results and lessons learned of a bottom-up inclusive approach implemented since 2014 in Burundi: the Integrated Farm Planning approach (PIP) approach. This approach aims to build a solid foundation for sustainable change towards enhanced food production and good land stewardship, based on three foundation principles (motivation, stewardship and resilience) and three guiding principles (empowerment, integration and collaboration). Findings from an impact study on the PIP approach and testimonies of farmers from a qualitative study show profound changes in land management practices and diversity of activities on the farm, as well as in the social cohesion in households and villages. Based on a vision and a plan, nearly 80,000 motivated households are currently actively involved to stop land degradation and make their farms more productive, while in all PIP villages concrete collective action is undertaken for sustainable land stewardship. Given that these actions are widespread and come along with a change in mind-set rooted in all three foundation principles, the paper concludes that the PIP approach is able to effectively build a foundation for sustainable change. Five key lessons from this experience reveal the key elements of a different development discourse that actually motivates and mobilises farmers to stop land degradation.

In this paper, the Laplace transform combined with the local discontinuous Galerkin method is used for distributed-order time-fractional diffusion-wave equation. In this method,at first, we convert the equation to some time-independent problems by Laplace transform.Then we can solve these stationary equations by the local discontinuous Galerkin method to discretize diffusion operators at the same time. Then, by using a numerical inversion of the Laplace transform we can find the solutions of the original equation. One of the advantages of this procedure is its parallel implementation. Another advantage of this approach is that the number of stationary problems that should be solved is much less than that are needed in time-marching methods. Finally, some numerical experiments have been provided to show the accuracy and efficiency of the method.

This study is concerned with the optimal time rates of weak solutions for the 2D magneto-micropolar equations with only micro-rotational dissipation and magnetic diffusion. Due to some new observations, we obtain the optimal time decay rates of weak solutions $\|\nabla u(t)\|_{L^2}+\|\nabla w(t)\|_{L^2}\le C(1+t)^{-2}$ and $ \|\nabla b(t)\|_{L^{p}}\le C(1+t)^{-\frac12-(1-\frac1p)}$ with $p\in[2,\infty)$.

We consider the following quasilinear Keller-Segel system \left\{ {l} u_t = \Delta u - \nabla (u \nabla v) + g(u), \quad &(x,t)\in \Omega \times [0,T_{max}) ,\\[6pt] 0= \Delta v - v + u, \qquad \quad &(x,t)\in \Omega \times [0,T_{max}), \\[6pt] \right. on a ball $\Omega \equiv B_R(0)\subset^n$, $n\geq 3$, $R>0$, under homogeneous Neumann boundary conditions and non negative initial data. The source term $g(u)$ is superlinear and of logistic type i.e. $g(u)=\lambda u - \mu u^k,\ k>1, \ \mu >0$, $\lambda \in $ and $T_{max}$ is the blow-up time.\\ The solution $(u,v)$ may or may not blow up in finite time. Under suitable conditions on data, we prove that the function $u$, which blows up in $L^{\infty} (\Omega)$-norm , blows up also in $L^p(\Omega)$-norm for some $p>1$. Moreover a lower bound of the lifespan (or blow-up time when it is finite) $T_{max}$ is derived. \\ In addition, if $\Omega \subset ^3$ a lower bound of $T_{max}$ is explicitly computable.

The present paper is focused on the analysis on the existence of positive solutions of a second order differential system with two delays \left \{{lcr} x_1''(t)-a_1(t)x_1(t)+m_1(t)f_1(t,x(t),x_\tau(t))=0,\ \ t>0,\\ x_2''(t)-a_2(t)x_2(t)+m_2(t)f_2(t,x(t),x_\tau(t))=0,\ \ t>0,\\ x_1(t)=0,\ \ -\tau_1\ \leq t \leq 0,\;\; x_1(t)=0,\\ x_2(t)=0,\ \ -\tau_2\ \leq t \leq 0,\;\; x_2(t)=0 \right. by using two well-known fixed point theorems.

By using some real analysis techniques, We study the structural characteristics of a multi-parameter Hilbert-type integral inequality with the hybrid kernel, and obtain some equivalent conditions for this inequality. We also consider the operator expression of the equivalent inequalities. The conclusions not only integrates some results of references, but also nds some new Hilbert-type integral inequalities with simple form by choosing suitable parameter values.

The present article deals with the similarity method to tackle the fractional Schrӧdinger equation where the derivative is defined in the Riesz sense. Moreover the procedure of reducing a fractional partial differential equation (FPDE) into an ordinary differential equation (ODE) has been efficiently displayed by means of suitable scaled transform to the proposed fractional equation. Furthermore the ODEs are treated effectively via the Fourier transform. The graphical solutions are also depicted for different fractional derivatives .