The Neumann boundary value problem (BVP) for the second order “stationary heat transfer” elliptic partial differential equation with variable coefficient is considered in two-dimensional bounded domain. Using an appropriate parametrix (Levi function) and applying the two-operator approach, this problem is reduced to some systems of boundary-domain integral equations (BDIEs). The two-operator BDIEs in 2D have special consideration due to their different equivalence properties as compared to higher dimensional case due to the logarithmic term in the parametrix for the associated partial differential equation. Consequently, we need to set conditions on the domain or function spaces to insure the invertibility of the corresponding layer potentials, and hence the unique solvability of BDIEs. Equivalence of the two operator BDIE systems to the original Neumann BVP, BDIEs solvability, uniqueness/non uniqueness of the solution, as well as Fredholm property and invertibility of the BDIE operator are analysed. Moreover, the two operator boundary domain integral operators for the Neumann BVP are not invertible, and appropriate finite-dimensional perturbations are constructed leading to invertibility of the perturbed operators.\\ \noindent\textbf{Key words:} Partial differential equation, Two-operator Boundary-Domain Integral Equations, finite-dimensional perturbations , equivalence, invertibility.

The formulation and analysis of two operator Boundary-Domain Integral Equation systems for variable coefficient mixed BVP with in two dimensional domain is discussed. To analyse the two-operator approach, we applied one of its linear versions to the mixed (Dirichlet-Neumann) BVP for a linear second-order scalar elliptic variable-coefficient PDE and reduced it to four different BDIE systems. %The two-operator BDIE systems are nonstandard systems of equations containing integral operators defined on the domain under consideration and potential type and pseudo-differential operators defined on open sub-manifolds of the boundary. Using the results as in CMN09 andAM11, a rigorous analysis of the two-operator BDIE systems is given and it is shown that they are equivalent to the mixed BVP and thus are uniquely solvable, while the corresponding boundary domain integral operators are invertible in the appropriate Sobolev-Slobodetski (Bessel potential) spaces.

In this paper, the Boundary-Domain Integral Equations (BDIEs) for the mixed boundary value problem(BVP) for a compressible Stokes system of partial differential equation (PDE) with variable coefficient in 2D is considered . An appropriate parametrix is used to reduce this BVP to the BDIEs. Although the theory of BDIEs in 3D is well developed, the BDIEs in 2D need a special consideration due to their different equivalence properties. As a result, we need to set conditions on the domain or on the spaces to ensure the invertibility of corresponding parametrix-based integral layer potentials and hence the unique solvability of BDIEs. The properties of corresponding potential operators are investigated. Equivalence of the BDIE systems to the mixed BVP and invertibility of the matrix operators associated with the BDIE systems in appropriate Sobolev spaces are proved.

In this paper, the Dirichlet and Neumann boundary value problems for the steady state Stokes system of partial differential equations for a compressible viscous fluid with variable viscosity coefficient is considered in two-dimensional bounded domain. Using an appropriate parametrix, this problem is reduced to a system of direct segregated boundary-domain integral equations (BDIEs). The BDIEs in the two dimensional case have special properties in comparison with the three dimension because of the logarithmic term in the parametrix for the associated partial differential equations. Consequently, we need to set conditions on the function spaces or on the domain to ensure the invertibility of corresponding parametrix-based hydrodaynamic single layer and hypersingular potentials and hence the unique solvability of BDIEs. Equivalence of the BDIE systems to the Dirichlet and Neumann BVPs and the invertibility of the corresponding boundary-domain integral operators in appropriate Sobolev spaces are shown.

The broad environmental, societal and animal welfare issues associated with large-scale animal protein production are well-documented, and cultivated meat represents a potentially more sustainable alternative protein form to conventional production methods. Some believe cultivated meat is years away from commercial success; however, computational modeling has real potential to reduce the timeline for commercial roll-out. In June, 2019, a diverse group of stakeholders attended the inaugural Cultivated Meat Modeling Consortium meeting in Seattle, Washington to develop a multiscale modeling framework for cultivated meat manufacturing. This whitepaper was created from the extensive brainstorming that occurred during the meeting and afterwards. The early stage framework presented here is meant only as a beginning, and our hope is that this paper will drive future discussions and generate more collaborations that maximize the utility of computational modeling in the areas outlined here and beyond.

The paper is devoted to the Stackelberg control of a linear parabolic equation with missing initial conditions. The strategy involves two controls called follower and leader. The objective of the follower is to bring the state to a desired state while the leader has to bring the system to rest at the final time. The results are obtained by means of Fenchel-Legendre transform and appropriate Carleman inequalities.

In this study, we firstly introduce a different type of directional Fermi-Walker transportations along with vortex lines of a non-vanishing vector field in three-dimensional space. Thus we conclude that geometric quantities, which are used to characterize vortex lines, are also associated with the geometric phase and angular velocity vector (Darboux vector) of the system. Then we present directional magnetic vortex lines by computing the Lorentz force. Hence, we reach a remarkable relation between directional magnetic vortex lines and angular velocity vector of vortex lines with a non-rotating frame. We later determine the directional electric vortex lines by considering the electromagnetic force equation. We finally investigate the conditions of being uniform for magnetic fields of directional magnetic vortex lines and we improve a remarkable approach to find the electromagnetic curvature, which contains many geometrical features belonging to directional electric vortex line.

In this paper, we use Schauder and Banach fixed point theorem to study the existence, uniqueness and stability of periodic solutions of a class of iterative differential equation $$\alpha x’‘(t)+\beta x’(t)+\gamma x(t)=\lambda_1(t)x(t)+\lambda_2(t)x(x(t))+\cdots+\lambda_n(t)x^{[n]}(t)+f(t).$$

Up to present, research on shout options remains only on the assumption that the underlying asset follows either Brownian motion or geometric Brownian motion. But it can not be evaluated accurately by PDE on geometric Brownian motion. To solve this problem this paper derives a new partial integro-differential inequality (PIDI) for shout options pricing on the assumption that the price of the underlying asset follows the jump-diffusion model and constructs the mathematical model by combining specific features and terminal conditions. On the basis of this model we obtain some results about shout options pricing. For this mathematical model this paper proposes a new competitive algorithm to choose two aspects. One is employing high-order difference for integral and partial derivative terms, the other is using Howard algorithm (also called policy iteration) for the complementarity problem. Numerical examples show that this algorithm yields an accurate technique and is more efficient than the traditional approaches in the case of geometric Brownian motion and jump-diffusion model, respectively.

Deepening and expanding the understanding of cyanide-degrading enzymes are the foundation of developing new technology for cyanide bioremediation. In this study, a putative cyanide-degrading enzyme gene from Alcaligenes sp. DN25(CGMCC 5734) was cloned and expressed in Escherichia coli. The purified recombinant enzyme named as cdE, consisting of a 38-kDa polypeptide, showed 99% amino acid sequence identity with cyanidase derived from Pseudomonas stutzeri AK61. However, the cdE was supposed to have both cyanide dihydratase (CynD) and cyanide hydratase (CHT) activities based on the findings that formate, ammonium and formamide were simultaneously generated during cyanide enzymatic degradation. The enzymatic properties of cdE were characterized with an optimal activity at a temperature of 30°C, pH of 7.0, and could even maintain approximately 50% activity at pH 9.0. More importantly, the selectivity of enzymatic reaction pathway was suggested related to the conformation stability of the cdE that affected by the modifications of amino acids near the active site as well as the degradation conditions, leading to produce different ratios of formate and formamide. As far as we know, this is the first report of a cyanide-degrading enzyme possessing bifunctional catalysis activity, which might become a supplement of cyanide-degrading enzyme databases.

Benthic macrofauna is regularly used in monitoring programmes, however the vast majority of benthic eukaryotic biodiversity lies mostly in microscopic organisms, such as meiofauna (invertebrates < 1 mm) and protists, that rapidly responds to environmental change. These communities have traditionally been hard to sample and handle in the laboratory, but DNA sequencing has made such work less time consuming. Compared to DNA sequencing that captures both alive and dead organisms, environmental RNA (eRNA) can be used to better target alive communities. Here, we assessed the biodiversity of three known bioindicator microeukaryote groups (nematodes, foraminifera, and ciliates) in sediment samples collected at seven coastal sites along an organic carbon (OC) gradient. We aimed to investigate if eRNA shotgun sequencing can be used to simultaneously detect differences in 1) biodiversity of multiple microeukaryotic communities, and 2) functional feeding traits of nematodes. Results showed that biodiversity was lower for nematodes and foraminifera in high OC (6.2–6.9 %), when compared to low OC sediments (1.2–2.8 %). The beta diversity for all three groups were different along the OC gradient, as well as the classified feeding type of nematode genera (with more non-selective deposit feeders in high OC sediment). High relative abundant genera included nematode Sabatieria and foraminifera Elphidium in high OC, and Cryptocaryon-like ciliates in low OC sediments. Considering that future sequencing technologies are likely to decrease in cost, the use of eRNA shotgun sequencing to assess biodiversity of living benthic microeukaryotes could be a powerful tool in recurring monitoring programmes.

Parental effects influence offspring phenotypes through pre- and post-natal routes but little is known about their molecular basis, and therefore their adaptive significance. Epigenetic modifications, which control gene expression without changes in the DNA sequence and are influenced by the environment, may contribute to parental effects. Taking advantage of the self-fertilising and inbred nature of the mangrove killifish Kryptolebias marmoratus, we investigated the effects of the rearing environment on parents and offspring by comparing neophobia, metabolic rate and brain epigenetic (DNA methylation) patterns of genetically identical fish reared in enriched or barren environments. Parental fish reared in enriched environments had lower cortisol levels, lower metabolic rates and were more active and neophobic than those reared in barren environments. They also differed in 1,854 methylated cytosines (DMCs). Offspring activity and neophobia were determined by the parental environment and we also found evidence of, limited but significant, parental influence on the DNA methylation patterns of the offspring. Among the DMCs of the parents, 98 followed the same methylation patterns in the offspring, three of which were significantly influenced by parental environments irrespective of their own rearing environment. Our results suggest that the environment experienced by the parents influences the behaviour and, to some extent, brain DNA methylation patterns of the offspring in an environment-specific manner.

Interfacial tension is an essential physical property in two phase flow and it changes due to the mass transfer. The measurement of dynamic interfacial tension (DIFT) in such condition is a difficult problem. In previous study (Zhou at al., Chem Eng Sci. 2019; 197:172-183), we presented the quantitative relation between the droplet breakup frequency function (DBFF) and interfacial tension. It is found that the DBFF is highly depends on interfacial tension. Therefore the DBFF is a suitable parameter to quantitatively characterize the interfacial tension. Based on this concept, the DIFT in the column is determined by regression method after the DBFF under mass transfer condition is measured. It is found that the DIFT is smaller than the static interfacial tension. This result indicates that interphase mass transfer leads to decreasing of the interfacial tension. The decreasing extent of the DIFT has a positive correlation with the mass transfer flux.

Temperature is one of the most important abiotic factors defining the yield potential of temperate cereal crops such as barley. The regulators of heat shock response (HSR); Heat shock factors (HSFs) modulate the transcription level of heat responsive genes in order to protect the plants against heat stress. In the present study, a heat shock factor from wheat (TaHSFA6b) is overexpressed in barley for providing thermotolerance. Transgenic barley lines overexpressing TaHSFA6b showed significant improvement in thermotolerance. The constitutive overexpression of TaHSFA6b gene upregulated the expression of major heat shock protein genes as well as other abiotic stress responsive genes. RNA-seq and qRT-PCR analysis showed upregulation of HSPs, chaperonins, DNAJ, LEA proteins and genes related to anti-oxidative enzymes in transgenic lines. Excessive generation and accumulation of ROS occurred in wild type plants during heat stress; however, the transgenic lines reflected improved ROS homeostasis mechanisms in the form of significantly low ROS accumulation under high temperature. There were no negative phenotypic changes in overexpression lines. The present study suggests that TaHSFA6b is one of the major regulators of HSR as it showed the capacity to alter the expression patterns of main defense related genes and enhance the thermotolerance of this cereal crops.

Deciphering the genetic basis of phenotypic plasticity and genotype x environment interaction (GxE) is of primary importance for plant breeding in the context of global climate change. Tomato is a widely cultivated crop that can grow in different geographical habitats and which evinces a great capacity of expressing phenotypic plasticity. We used a multi-parental advanced generation intercross (MAGIC) tomato population to explore GxE and plasticity for multiple traits measured in a multi-environment trial (MET) design comprising optimal cultural conditions and water deficit, salinity and heat stress over 12 environments. Substantial GxE was observed for all the traits measured. Different plasticity parameters were estimated through the Finlay-Wilkinson and factorial regression models and used together with the genotypic means for quantitative trait loci (QTL) mapping analyses. Mixed linear models were further used to investigate the presence of interactive QTLs (QEI). The results highlighted a complex genetic architecture of tomato plasticity and GxE. Candidate genes that might be involved in the occurrence of GxE were proposed, paving the way for functional characterization of stress response genes in tomato and breeding for climate-adapted crop.

Jatropha (Jatropha curcas L.) is an oil bearing crop growing in tropical and subtropical parts of the world. The present study was undertaken to establish a protocol for in vitro callusing of three Jatropha accessions namely; Metema, Adami Tulu and Shewa Robit accession from leaf explants. The experiment was laid out in CRD with five replications in factorial arrangement. The medium supplemented with combination of 1.0 mg/L BAP and 1.0 mg/L 2,4-D resulted in maximum percentage of callus (100%) formed for all accessions. The maximum shoot regeneration (66.67%) from callus with 10.13 number of shoot was obtained from Shewa Robit accession in MS medium fortified with TDZ (0.5 mg/L) and IBA (0.1 mg/L). The presence of TDZ in the shoot regeneration medium has greater influence on the induction of adventitious shoot buds, whereas MS supplemented with BAP alone and combination with IBA did not induce shoot regeneration from callus culture. The results obtained in the present study would facilitate the high callus induction and regeneration responses in Jatropha for its improvement using biotechnological tools.

In this research, the specification of 3-dimensional flow stagnation point of hybrid Nano fluids passing through circular cylinder with sinusoidal radius are analyzed. C2H6O2, H2O and Engine oil are used as an ordinary liquid, while nano-particles include SWCNT and MWCNT. Fluid stream is taken into account with/without considering the effect of thermal slippage. Higher order non-linear phrases are transformed to ordinary prime-order differential equations and then solved applying the Analytical Method (HPM) in Matlab-14 software. Graphical analysis of the impressive parameters like: Prandtl number, thermal slip parameter, CNTs volume fraction is precisely checked on the profiles of velocity and temperature for various carbon nano-tubes. Consequences display that: cooling process or heat transfer rate can be increased by employing smaller thermal slippage parameter. Further, due to the better thermal conductivity of SWCNT carbon nanotube, the temperature increase in these carbon nanotubes is more than that of MWCNT.

The aim of this work is to present new approach to study weighted pseudo almost periodic functions with infinite delay using the measure theory. We study the existence and uniqueness of (μ,ν)-pseudo almost periodic solutions of infinite class for some neutral partial functional differential equations in a Banach space when the delay is distributed on ]-∞,0].

The aim of this article to propose some generalization of Meir-Keeler fixed point theorem with the help of an $\alpha$-admissible mapping. Further we prove the existence of solution of an infinite system of integral equations by using this generalized fixed point theorem involving measure of noncompactness in Banach space and illustrate the results with the help of an example. Finally, apply an iterative algorithm we find an approximate solution of an infinite system of integral equations.

This paper aims to construct new mixed-type periodic and lump-type solutions via the dependent variable transformation and the Hirota’s bilinear form (general bilinear techniques). This study will be investigated by considering the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation which describes the weakly dispersive waves in a homogenous medium in fluid dynamics. The obtained solutions contain abundant physical structure. Consequently, the dynamical behaviors of these solutions are graphically discussed for different choices of the free parameters through 3D- and contour plots.

Charged clay surfaces can impact storage and mobility of hydrocarbon and water mixtures. Here, we use equilibrium molecular dynamics (MD) and nonequilibrium MD simulations to investigate hydrocarbon-water mixtures and their transport in slit-shaped illite nanopores. We construct two illite pore models with different surface chemistries: potassium-hydroxyl (P-H) and hydroxyl-hydroxyl (H-H) structures. In H-H nanopore, we observe water adsorption on the clay surfaces. In P-H nanopores, however, we observe the formation of water bridges or columns between the top and bottom pore surfaces. This is because of the existence of a local, long-range electric field within the P-H pore causing water molecules to align in a specific direction promoting the formation of a water bridge. Our NEMD simulations demonstrate that the velocity profiles across the pore depends strongly on the presence or absence of the water bridge. This study provides a theoretical basis for understanding of nanofluidics with charged surfaces.

β-carotene is a natural pigment and health-promoting metabolite, and has been widely used in the nutraceutical, feed and cosmetic industries. Here, we engineered a GRAS yeast Saccharomyces cerevisiae to produce β-carotene from xylose, the second most abundant and inedible sugar component of lignocellulose biomass. Specifically, a β-carotene biosynthetic pathway containing crtYB, crtI and crtE from Xanthophyllomyces dendrorhous were introduced into a xylose-fermenting S. cerevisiae. The resulting strain produced β-carotene from xylose at a titer three-fold higher than from glucose. Interestingly, overexpression of tHMG1, which has been reported as a critical genetic perturbation to enhance metabolic fluxes in the mevalonate (MVA) pathway and β-carotene production in yeast when glucose is used, did not further improve the production of β-carotene from xylose. Through fermentation profiling, metabolites analysis and transcriptional studies, we found the advantages of using xylose as a carbon source instead of glucose for β-carotene production to be a more respiratory feature of xylose consumption, a larger cytosolic acetyl-CoA pool, and up-regulated expression levels of rate-limiting genes in the β-carotene producing pathway, including ACS1 and HMG1. As a result, 772.81 mg/L of β-carotene was obtained in a fed-batch bioreactor culture with xylose feeding. Considering the inevitable production of xylose at large scales when cellulosic biomass-based bioeconomy is implemented, our results suggest xylose utilization is a promising strategy for overproduction of carotenoids and other isoprenoids in engineered S. cerevisiae.

The fermentation conditions for the production of “pupuru” are enhanced at optimized conditions using response surface methodology (RSM). A Central Composite Design (CCD) with three independent variables; mass of root (2 to 6 kg), fermentation temperature (28 to 32 oC) and fermentation time (72 to 120 h) are used to study the response variables pH and Total Titratable Acidity (TTA) of fermented cassava. The design gives nineteen runs, 5 centre points, 14 non centre points. A face centred central composite second - order design is used to evaluate the combined effect of the independent variables. The results indicate that the generated regression model represents the relationship between the independent variables and responses. All linear terms, two quadratic terms (fermentation time and fermentation temperature) and all interactive terms had insignificant (p < 0.05) effect on pH and TTA. The optimum conditions for fermentation are achieved at 28 oC for 105 h to obtain pH of 3.99 and TTA of 0.25% Lactic acid which shows no significant difference (p>0.05) from the response surface methodology predicted pH and TTA of 3.96 and 0.22% Lactic acid.

Most digesters in industrial-scale operate in deficient level and almost nominal due to inefficient process. Optimization of the process may rectify the issue but required a valid method that does not just improve the process yet able to unravel the eventuality of the intricate process if the adjustment needed. A proper tool is required. The central composite design (CCD) was implemented in this study to investigate the suitability of this tool for optimization of anaerobic digestion (AD) process. The main effect of pH and HRT studied in CCD acquired from the screening process show the importance of having neutral pH value and long retention period for a better biogas yield. The process with pH 7.0 and HRT 15.7 days, IP 33%, TS 4% and FR 4% found to be the optimum setting for the process. The new setting successfully improved the production output up to 60% compared with baseline (existing setting), while allowing 50% more sludge to be processed. The X2 goodness-of-fit test indicates that the mathematical model applied in this study is valid at 95% of confidence level with R2 of 0.9. The results presented in the paper demonstrate the reliability of CCD as optimization tools for AD process in the industrial scale sewage treatment plant (STP).