A CFD model for oxygen permeation and partial oxidation of methane (POM) to syngas in a La0.6Sr0.4Co0.2Fe0.8O3-δ tubular membrane reactor was adopted to investigate the effects of the methane space velocity (MSV) and the feed composition on the reactor performance. It is shown that coupling POM reaction with carbon dioxide and steam reforming of methane (CRM and SRM), which is realized by co-feeding CH4 with CO2, H2O or CO2-H2O mixture into the reactor, can significantly enhance the methane conversion and syngas production rate and alter the H2/CO ratio as compared with feeding CH4 alone. For co-feeding CH4 with CO2, H2O or CO2-H2O mixture, the maximum syngas production rate is 2.3, 2 and 1.8 times that of feeding CH4 alone. Also, when POM is coupled with CRM and SRM, the temperature inside the reactor can be maintained above 973 K which is required for proper functioning of the membrane and catalyst.

Background and purpose: Muscarinic receptors contribute to both the facilitation and inhibition of levodopa-induced dyskinesia operated by striatal cholinergic interneurons, although the receptor subtypes and the mechanisms involved have not been clearly identified. Also muscarinic receptors in substantia nigra reticulata, activated by cholinergic midbrain afferents, regulate striatal functions although their role in levodopa-induced dyskinesia remains to be proven. Here, we investigate whether striatal and nigral muscarinic M1 and/or M4 receptors modulate dyskinesia expression and the underlying striato-nigral GABAergic pathway activation in 6-hydroxydopamine hemilesioned rats. Experimental approach: Reverse microdialysis allowed to deliver the M1 and M4 preferential antagonists telenzepine, PD-102807, tropicamide and the selective M4 positive allosteric modulator VU0152100 in striatum or substantia nigra, while levodopa was administered systemically. Dyskinetic movements were monitored along with nigral GABA (and glutamate) and striatal glutamate levels, taken as neurochemical markers of striato-nigral pathway activation. Key results: Intrastriatal telenzepine, PD-102807 and tropicamide alleviated dyskinesia and inhibited nigral GABA and striatal glutamate release. This was partially replicated by intrastriatal VU0152100 that, however, failed to inhibit striatal glutamate. The M2 preferential antagonist AFDX-116, used to elevate striatal acetylcholine levels, blocked the behavioral and neurochemical effects of PD-102807. Intranigral VU0152100 prevented levodopa-induced dyskinesia and its neurochemical correlates whereas PD-102807 was ineffective. Conclusions and Implications: Striatal M1 and M4, likely postsynaptic, receptors facilitate dyskinesia and striato-nigral pathway activation. Striatal M4 receptors, possibly located presynaptically, also inhibit dyskinesia. Potentiation of striatal and nigral M4 transmission leads to powerful multilevel inhibition of striato-nigral pathway providing a new strategy to tackle dyskinesia.

In this paper, we introduce the system of general equilibrium problem (SGEP) and new subgradient extragradient by using the concept of the set of solution of the modified variational inequality problem introduced by \cite{kangtunyakarn}. Then, we establish and prove weak and strong convergence theorem of the new subgradient extragradient algorithm for finding the set of the solutions of the SGEP under some suitable conditions of $\alpha_{n}$ and $\beta_{n}$ with $\alpha_{n}+\beta_{n}\leq 1$. Moreover, we apply our main theorem to prove weak and strong convergence theorems for finding solutions of the generalized equilibrium problem, the system of equilibrium problem, the variational inequality problem and the general system of variational inequality problem. In the last section, we give three numerical examples to support our main result.

This paper focuses on the cooperation mechanism between two retailers. To reduce the average processing cost, the supplier usually sets a threshold for trade credit to stimulate retailers' orders. Retailers can enjoy permissible delay in payments only when their order quantities are more than or equal to the given threshold. However, considering the diversity of retailers, the motivation effect of the threshold may be limited. To resolve the problem, the supplier can additionally provide retailers with a joint ordering policy under which two retailers can make delayed payments as long as their total order quantity meets the required threshold. Thus, the two retailers should decide whether to place a joint order or not and determine their respective order quantities simultaneously. We provide a mutually acceptable order-allocation scheme for retailers, and determine the optimal payment methods for them. In addition, an optimal threshold is identified for the supplier to maximize the total order quantity of retailers. Based on this, some managerial insights are obtained. A numerical experiment is performed to illustrate the validity of the model.

The interior Dirichlet boundary value problem for the diffusion equation in non-homogeneous media is reduced to a system of Boundary-Domain Integral Equations (BDIEs) employing the parametrix obtained in different from . We further extend the results obtained in for the mixed problem in a smooth domain with L²(Ω) right hand side to Lipschitz domains and PDE right-hand in the Sobolev space H−1(Ω), where neither the classical nor the canonical co-normal derivatives are well defined. Equivalence between the system of BDIEs and the original BVP is proved along with their solvability and solution uniqueness in appropriate Sobolev spaces.

Nanofluid as a special thermal transporting medium has recently received unprecedented attention due to its improved heat transfer performance compared to conventional fluids. Numerous researches have been conducted on the natural convection characteristics of different nanofluids in various configurations of cavities due to the important applications of natural convection in environmental, petrochemical, medical, aviation and space technology, industrial and many more areas. The emergence of a magnetic field as a tool for the manipulation of convective flow and heat transfer behaviours of nanofluids in non-square enclosures has been extensively reviewed. The influence of several variables such as controlling parameters, heat distribution methods, thermal and concentration boundary conditions, magnetic field types, numerical methods, correlation types, nanofluid types, heaters types, numbers and length, and slip conditions, etc., on the magnetohydrodynamic (MHD) natural convection flow and heat transfer behaviours of nanofluid in non-square cavities has been given great attention and brought to the spotlight for discussion. The concepts of bioconvection, micro-polar nanofluid, bio-nanofluid (green nanofluid), ionic nanofluid, and hybrid nanofluid have also been discussed for the first time in relation to natural convection. Special cases of MHD natural convection in non-square cavities involving hybrid nanofluids and micro-polar nanofluids are also presented herein. The application of several numerical methods (which is the major approach studied so far) to investigate the hydromagnetic behaviours of nanofluids in non-square cavities is the focus of this work.

In this paper, we study the coupled nonlinear Schrödinger equation with variable coefficients (VCNLS) by means of modified Sine-Gordon equation method, the subsistence of some novel bright-dark solitons and dark-dark solitons are obtained. Moreover, some figures are simulated by computer to show the solutions are soliton solutions and how the evolution of soliton is determined by different values of variable group velocity dispersion terms, which can be used to simulate various phenomena.

The aim of this paper is to establish some strong coupled fixed point theorems via a new concept of cyclic contractive type mappings in the context of fuzzy metric spaces. Moreover, we ensure the existence of a common solution of the two Urysohn type integral equations:% for our result to get the existence theorem for common solution. The two Urysohn type integral equations are \begin{align*} &\xi(l)=\int_{a}^{b}K_1(l,s,\xi(s))ds+h_1(l),\\ &\xi(l)=\int_{a}^{b}K_2(l,s,\xi(s))ds+h_2(l), \end{align*} where $l\in[a,b]\subset\mathbb{R}$, $\xi,h_1,h_2\in C([a,b],\mathbb{R})$ and $K_1,K_2:[a,b]^2\times \mathbb{R}\to\mathbb{R}$

We apply the Bielecki metric on the space C([a, b]), to analyze the different types of stabilities of non-linear fractional integral equation corresponding to fractional boundary value problems. Sufficient conditions are obtained to prove stability results for fractional non-linear Volterra and Fredholm integral equations, given by Ulam, Hyer and Rassias. We extend the respective stability results to the fractional integral equations where the domain of integration is an unbounded interval. We provide numerical examples which asserts our stability results.

n this paper, we focus on the energy conservation for the weak solutions of inhomogeneous Navier-Stokes equations. It is proved that if the function of density belongs to $L^{\infty}(0,T;L^{\infty}(\mathbb{T}^N))\cap L^p(0,T;W^{1,p}(\mathbb{T}^N))$, and the function of velocity belongs to $L^s(0,T;L^r(\mathbb{T}^N))$ with $\f2s+\f2r=1$, then the energy equality holds. This result can be seen as a inhomogeneous version for Shinbrot’s criterion.

We establish nonexistence of nontrivial solutions (including sign-changing ones) for some partial differential inequalities of elliptic and parabolic type containing nonlinear terms that depend on the positive and negative part of the sought function in different ways. Systems of elliptic inequalities with similar structure are also considered. The proofs are based on the test function method.

We study the Liouville theorem for steady Q-tensor system of liquid crystal in $\R^3$. Assuming that $u\in L^{\frac 92, \infty}(\R^3)\cap \dot{H}(\R^3)$ and $Q\in H^2(\R^3)$, we show that the steady system admits only trivial solution $u=0, Q=0$.

One of the fundamental research problems in the theory of generalized inverses of matrices is to establish reverse order laws for generalized inverses of matrix products. Under the assumption that $A$, $B$, and $C$ singular matrices of the appropriate sizes, two reverse order laws for generalized inverses of the matrix products $AB$ and $ABC$ can be written as $(AB)^{(i,\ldots,j)} = B^{(i_2,\ldots,j_2)}A^{(i_1,\ldots,j_1)}$ and $(ABC)^{(i,\ldots,j)} = C^{(i_3,\ldots,j_3)}B^{(i_2,\ldots,j_2)}A^{(i_1,\ldots,j_1)}$, or other mixed reverse order laws. These equalities do not necessarily hold for different choices of generalized inverses of the matrices. Thus it is a tremendous work to classify and derive necessary and sufficient conditions for the reverse order law to hold because there are all 15 types of $\{i,\ldots, j\}$-generalized inverse for a given matrix according to combinatoric choices of the four Penrose equations. In this paper, we shall establish several decades of mixed reverse order laws for $\{1\}$- and $\{1,2\}$-generalized inverses of $AB$ and $ABC$, and give a classified investigation to a family of reverse order laws $(ABC)^{(i,\ldots,j)} = C^{-1}B^{(k,\ldots,l)}A^{-1}$ for the eight commonly-used types of generalized inverses by means of the block matrix representation method (BMRM) and the matrix rank method (MRM). A variety of consequences and applications these reverse order laws are presented.

Recently, much attention has been given to multi-granulation rough sets (briefly, MGRS) and different kinds of multi-granulation rough set models have been developed from various viewpoints. In this paper, we propose two types of MGRS models under neighborhood systems from the topological view, where a target concept is approximated by employing the j-neighborhoods and j-adhesion neighborhoods of objects in a given universe set. Therefore, we investigate some of the basic properties of the two types of MGRS models and discuss the relationships and differences among the classical MGRS model and some other new models. Also, for each new MGRS model, an algorithm will be presented.

The present article is devoted to developing the Legendre wavelet operational matrix method (LWOMM) to find the numerical solution of two-dimensional hyperbolic telegraph equations (HTE) with appropriate initial time boundary space conditions. The Legendre wavelets series with unknown coefficients has used for approximating the solution in both of the spatial and temporal variables. The basic idea for discretizing two-dimensional HTE is based on differentiation and integration of operational matrices. By implementing LWOMM on HTE, HTE is transformed into algebraic generalized Sylvester equation. Numerical experiments are provided to illustrate the accuracy and efficiency of the presented numerical scheme. Comparisons of numerical results associated with the proposed method with some of the existing numerical methods confirm that the method is easy, accurate and fast experimentally. Moreover, we have investigated the convergence analysis of multidimensional Legendre wavelet approximation.

The aim of the present paper is to extract the exact traveling wave solutions of the chiral nonlinear Schr\”{o}dinger’s equation (cNLSE). The $(\frac{G’}{G^{2}})-$expansion method and the first integral method along with symbolic computation package has been exerted to celebrate the exact solutions. As a consequence, the obtained solutions can be categorized into trigonometric, hyperbolic and rational with some free parameters of the problem studied. In addition, these types of the solutions lead to understand the physical phenomena of the problem such as solitary, periodic, complex function, singular optical solitons and dark-singular combo solitons.

This article analyze singular optimal control problems (SOCP) from different areas of engineering and applied mathematics. We use the notion of partial Hamiltonian and we show that every singular optimal control problem can be written in the form of current value or standard Hamiltonian. The partial Hamiltonian approach is used to compute the partial Hamiltonian operators and first integrals. Then these first integrals are utilized to construct the closed-form solutions of hybrid vehicle optimal energy management model, optimal harvesting mathematical model and model of membrane filtration system. We explain how one can use partial Hamiltonian approach for both finite horizon and infinite horizon systems. This study provides a new way of solving singular optimal control problems.

A well known issue in metabolic flux analysis with labelling experiments is the structural identifiability analysis. It comes from the fact that some enrichment measurement sets cannot uniquely elucidate all intracellular fluxes. To the best of our knowledge, the structural identifiability analysis of dynamic isotope experiments is not available in the literature. In this work, it is shown that if one measurement plan makes the dynamic isotopic fractions balance equations structurally identifiable then for any arbitrary small time interval the plan also makes the equations structurally identifiable. Based on the fact, in order to resolve the local structural identifiablity problem of the dynamic isotopic fractions balance equations approximated with piecewise affine intracellular fluxes, one should check the local structural identifiablity for the corresponding cascaded linear time invariant system at each sampling point with the approach proposed in our earlier work (Lin \emph{et al.}, Math Biosci. 2018; 300:122-129).

Although species delimitation can be highly contentious, the development of reliable methods to accurately ascertain species boundaries is an imperative step in cataloguing and describing Earth’s quickly disappearing biodiversity. Spider species delimitation remains largely based on morphological characters; however, many mygalomorph spider populations are morphologically indistinguishable from each other yet have considerable molecular divergence. The focus of our study, Antrodiaetus unicolor species complex which contains two sympatric species, exhibits this pattern of relative morphological stasis with considerable genetic divergence across its distribution. A past study using two molecular markers, COI and 28S, revealed that A. unicolor is paraphyletic with respect to A. microunicolor. To better investigate species boundaries in the complex, we implement the cohesion species concept and employ multiple lines of evidence for testing genetic exchangeability and ecological interchangeability. Our integrative approach includes extensively sampling homologous loci across the genome using a RADseq approach (3RAD), assessing population structure across their geographic range using multiple genetic clustering analyses that include STRUCTURE, PCA, and a recently developed unsupervised machine learning approach (Variational Autoencoder). We evaluate ecological similarity by using large-scale ecological data for niche-based distribution modeling. Based on our analyses, we conclude that this complex has at least one additional species as well as confirm species delimitations based on previous less comprehensive approaches. Our study demonstrates the efficacy of genomic-scale data for recognizing cryptic species, suggesting that species delimitation with one data type, whether one mitochondrial gene or morphology, may underestimate true species diversity in morphologically homogenous taxa with low vagility.

In this paper we investigate the size of a bi-dimensional fragmentation process. A rectangle of dimensions x and y is considered, it is split into four sub-rectangles with some probability that depends on x and y, we iterate until the stop of the process. The total number of the all the obtained rectangles at the end of the process satisfies some equality in distribution which is resolved , using some tools on integral equations, via the contraction method.

In this paper, we consider a viscoelastic kirchhoff equation with a delay term in the internal feedback. By using the Faedo-Galarkin approximation method we prove the well-posedness of the global solutions. Introducing suitable energy, we prove the general uniform decay results

A 2-dimension linguistic lattice implication algebra (2DL-LIA) can build a bridge for logical algebras and 2-dimension fuzzy linguistic information. In this paper, the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed. Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated. Moreover, it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

In this paper, we study the solvability of a nonlinear two-parametric quantum difference equation Dirichlet boundary value problem. At first, we provide and prove the formula of changing the order of integration for (p,q)-double integral. Second, We obtain the existence and uniqueness criteria of solutions for this kind of boundary value problem by using Banach contraction mapping principle, Leray-Schauder nonlinear alternative theorem and Leray-Schauder continuation theorem. At last, we give two examples to illustrate our results.

Crowd-based hydrological observations can supplement existing monitoring networks and allow data collection in regions where otherwise no data would be available. In the citizen science project CrowdWater, repeated water level observations using a virtual staff gauge approach result in time series of water level classes. To investigate the quality of these observations, we compared the water level class data for a number of locations where water levels were also measured and assessed when these observations were submitted. We analysed data for nine locations where citizen scientists reported multiple observations using a smartphone app and stream level data were also available. At twelve other locations, signposts were set up to ask citizens to record observations on a form that could be left in a letterbox. The results indicate that the quality of the data collected with the app was higher than for the forms. A possible explanation is that for each app location, most contributions were made by a single person, whereas at the locations of the forms almost every observation was made by a new contributor. On average, more contributions were made between May and September than during the other months. Observations were submitted for a range of flow conditions, with a higher fraction of high flow observations for the data collected with the app. Overall, the results are encouraging for citizen science approaches in hydrology and demonstrate that the smartphone application with its virtual staff gauge is a promising approach for crowd-based water level class observations.