The electrostatics problem of a point charge next to a conducting plane is best solved by placing an image charge placed on the opposite side. For a charge between two parallel planes this can be solved with image charges outside the planes at evenly spaced intervals moving out to infinity. What is the corresponding image of a point charge is when placed on the axis of a cylinder?. The potential of a point charge in a cylinder is well known and may expressed in many forms involving integrals or series of Bessel functions, but none of which elude to an image. In fact the image consists of infinitely many rings on a disk with some complicated surface charge distribution. This manuscript attempts to describe the image as accurately as possible, and in doing so finds simple accurate approximations for the potential.

Abstract An approach to find the exact solution of ordinary, fractal and fractional Fokker-Planck equation FPE, based on transforming it to a system of first-order PDEs, together with using the extended unified method, is presented. Reduction of the fractal and fractional derivatives to the classical on's with time-dependent coefficient is performed via similarity transformations. Some explicit solutions of the classical, fractal and fractional time derivative FPE, are obtained . It is shown that the solution of the FPE is mixed Gaussian's. It is worthy to mention that the mixture of Gaussians is a powerful tool in machine learning. Further,it is found that the friction coefficient plays a significant role in lowering the magnitude of the distribution function. While changing the order of the fractal and fraction time derivative has a slight effects and the mean and mean square of the velocity vary slowly.

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.

A document by Bilender Pasaoglu. Click on the document to view its contents.

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.

In this work, we implement some analytical techniques such as Exp--Function method, Tan and Tanh methods, Extended Tan and Tanh methods, and Sech method for solving the fractional nonlinear partial differential equation with a truncated M-fractional derivative, which contain exponential terms its name, General Modified fractional Degasperis-Procesi-Camassa-Holm equation with a truncated M-fractional derivative. These methods can be used as an alternative to obtain exact solutions of different types of differential equations applied in engineering mathematics. Finally, we obtain the analytical solution of the M-fractional heat equation and present a graphical analysis.

Squalene is the gateway molecule for triterpene-based natural products and steroids-based pharmaceuticals. As a super lubricant, it has been used widely in health care industry due to its skin compatibility and thermostability. Squalene is traditionally sourced from shark-hunting or oil plant extraction, which is cost-prohibitive and not sustainable. Reconstitution of squalene biosynthetic pathway in microbial hosts is considered as a promising alternative for cost-efficient and scalable synthesis of squalene. In this work, we reported the engineering of the oleaginous yeast, Y. lipolytica, as a potential host for squalene production. We systematically identified the bottleneck of the pathway and discovered that the native HMG-CoA reductase led to the highest squalene improvement. With the recycling of NADPH from the mannitol cycle, the engineered strain produced about 180.3 mg/l and 188.2 mg/L squalene from glucose or acetate minimal media, respectively. By optimizing the C/N ratio, controlling the media pH and mitigating the acetyl-CoA flux competition from lipogenesis, the engineered strain produced about 502.7 mg/L squalene in shake flaks, a 28-fold increase compared to the parental strain (17.2 mg/L). We also profiled the metabolic byproducts citric acid and mannitol level and observed that they are reincorporated into cell metabolism at the late stage of fermentation. This work may serve as a baseline to harness Y. lipolytica as an oleaginous cell factory for production of squalene or terpene-based chemicals.

Sucrose metabolism, particularly the decomposition of sucrose by invertase, plays a central role in plants’ response to cold stress. Invertases inhibitors (INHs) evolved with higher plants as essential regulators of sucrose metabolism. By limiting invertase activity, INHs keep cellular sugar levels elevated, which provides enhanced protection for plants under stress. As the only vacuolar invertase (VIN) gene in peaches sensitive to chilling temperatures, our results showed that PpVIN2 expression increases significantly during cold storage, while VIN activity increases more modestly. We also found that peaches transiently overexpressing PpINH1 had decreased VIN activity. The interaction of PpINH1 and PpVIN2 was shown by yeast two-hybrid, bimolecular fluorescence complementation, and in vitro, with recombinant proteins. During cold storage, trehalose treated peaches had significantly increased PpINH1 expression, decreased VIN activity, and significantly higher sucrose content than untreated fruit. As a result, treated fruit had enhanced resistance to chilling injury. Collectively, our data show that the post-translational repression of VIN activity by PpINH1 helps maintain sucrose levels in peaches during cold storage, thereby improving resistance to chilling injury.

Polysorbates (PS) are surfactants commonly added in a therapeutic protein drug product as excipients to protect proteins from denaturation and aggregation during storage, transportation, and delivery. Significant degradation of PS in drug products could lead to shortened drug shelf lives and PS-degrading activity in drug products must be minimized. Identification of lipases that degrade PS could lead to better process control in drug manufacturing. In 2016, phospholipase B-like 2 (PLBD2) was proposed as a residual host cell protein responsible for degrading PS20 in a drug formulation. We have carried out a series of studies to verify the role of PLBD2 in degrading polysorbates in drug products purified from recombinant Chinese Hamster Ovary (CHO) cells. Genetic knock-out and immuno-depletion results showed that when PLBD2 was removed or depleted, the degradation of PS20 or PS80 was neither diminished nor reduced. In addition, a quantitative analysis of PLBD2 and PS20 degradation in multiple formulated mAb products did not establish a correlation between the amount of PLBD2 and the level of PS20 degradation. Collectively these results suggest that PLBD2 is not the primary cause of polysorbate degradation in formulated drug products purified using standard Protein A and ion exchange chromatography.

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.

La misura delle emissioni da odori e delle concentrazioni di sostanze odorigene si inserisce in uno scenario in cui i cattivi odori sono tra le principali fonti di disturbo per la popolazione esposta. Tali scenari vengono associati a condizioni di pericolo per la salute e per la qualità dell’aria. L’impatto da odori rappresenta una criticità degli impianti industriali come quelli di trattamento delle acque reflue, specialmente quando sono localizzati in zone fortemente urbanizzate, in tali circostanze risulta opportuna l’analisi dell’impatto odorigeno. La stima degli odori avviene con metodi analitici e sensoriali. Si propone la correlazione tra i suddetti metodi integrando la soggettività sensoriale con l’oggettività analitica. Nel presente articolo si mostrano varie applicazioni della comparazione dei metodi, adoperando diverse tecniche uliti per gestire e manutenere un impianto e per individuare nuove sostanze responsabili di odori sgradevoli.

Orbital vibronic coupling parameters for C60+ were derived by using frozen-phonon approach via density functional theory calculations with hybrid B3LYP and CAM-B3LYP functional. Based on these derived vibronic coupling parameters, the static Jahn-Teller effect of C60+ were analyzed. At the global minima of adiabatic potential energy surface (APES), the Jahn-Teller deformation shows a D5d structure with stabilization energies of 110 and 129 meV with B3LYP and CAM-B3LYP respectively. These stabilization energies are two times larger than that in C60-, suggesting the crucial role of the dynamical Jahn-Teller effect in C60+. Present coupling parameters enable us to assess the actual situation of dynamical Jahn-Teller effect in C60+ and also that of excited C60 in combination with the established coupling parameters for C60-.

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 consider a non-linear two-phase unidimensional Stefan problem, which consists on a solidification process, for a semi-infinite material x > 0, with phase change temperature T₁, an initial temperature T₂ > T₁ and a convective boundary condition imposed at the fixed face x = 0 characterized by a heat transfer coefficient h > 0. We assume that the volumetric heat capacity and the thermal conductivity are particular nonlinear functions of the temperature in both solid and liquid phases and they verify a Storm-type relation. A certain inequality on the coefficient h is established in order to get an instantaneous phase change process. We determine sufficient conditions on the parameters of the problem in order to prove the existence and uniqueness of a parametric explicit solution for the Stefan problem.

We derive an approximate solution for hypersingular integrals of the first kind. Chebyshev polynomials of the second kind are used to construct the interpolating polynomial. In turn, this polynomial approximates the crack opening displacement function of the density function. A collocation method is implemented, with the zeros of the Chebyshev polynomial of the first kind as the collocation points. As a result of these implementations, the whole integral equation is approximated by a system of algebraic equations which is mathematically tractable. The application and accuracy of the present method are illustrated with some relevant examples.

Abstract Objective: To research the safety and effect of the simultaneous abdominal aorta balloon occlusion without radiation exposure during caesarean section in placenta percreta patients. Design: A retrospective case study. Setting: A class A tertiary comprehensive hospital in Beijing of China. Population or Sample: 28 pregnant women from September 1st, 2015, to January 31st, 2019 Methods: The medical records of 28 patients with placenta percreta, who undertook the simultaneous abdominal aortic balloon occlusion without radiation exposure during caesarean section, were retrospective studied. Main Outcome Measures: The intra-operative blood loss, transfusion requirements, hysterectomy rate, the duration of operation, length of Intensive Care Unit time and postoperative hospital stay. Results: The technical success rate was 100%. The amount of blood loss was 600 - 6500 (3094 ± 1502) ml. The duration of operation was 123 - 488 (285 ± 102) min. The mean Intensive Care Unit time and postoperative hospital stay were 2.0 (1.0 - 2.8) days and 7.0 (7.0 - 9.0) days respectively. Hysterectomy was carried out in 12 (42.9%) cases. No maternal and neonatal deaths. The complication included 7 cases of local thrombosis of right femoral artery. Thrombectomy was successfully performed through the femoral artery incision on the operating table simultaneously. There was no other complication. Conclusions: The simultaneous abdominal aorta balloon occlusion without radiation exposure during caesarean section in placenta percreta patients is a safe and effective procedure for hemorrhage control. It is an easy-to-implement procedure by a well-trained surgeon which performed in the general operation room.

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.

In this research paper, the HIV-1 infection of CD4+ T-cells fractional mathematical model with the effect of antiviral drug therapy is handled by applying three new computational schemes to this biological model to investigate its analytical explicit wave solutions. This mathematical model is used to predict the evolution of the population dynamical systems involving virus particles. The modified Khater method, the extended simplest equation method, and sech–tanh method with a new fractional operator (Atangana–Baleanu derivative operator) is employing to find the analytical solutions in various distinct new formulas of the biological suggested model. Moreover, the stability of the obtained solutions is investigated by using the characterizes of the Hamiltonian system to show their applicability in making the antivirals that protect our human life. Some plots are explained under specific conditions of the contained constants to reveal the dynamical behavior of the evolution of the population dynamical systems involving virus particles. A comparison between our results and that obtained in previous work is also represented and discussed in detail to show the novelty for our solutions. The performance of the used methods shows power, practical, and ability to apply to other nonlinear partial differential equations.