The martingale problem for a class of nonlocal operators of diagonal type

We consider systems of stochastic differential equations of the form $$\begin{array}{c}\hfill d{X}_t^i=\sum _{j=1}^d{A}_{ij}\left(X_{t?}\right)d{Z}_t^j\end{array}$$ for $i=1,?,d$ with continuous, bounded and non‐degenerate coefficients. Here $Z_t^1,?,Z_t^d$ are independent one‐dimensional stable processes with ${\alpha }_1,?,{\alpha }_d\in (0,2)$. In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices.     

Development of Yttrium and Iron Oxide Thin Films via AACVD Method for Photooxidation of Water

Russian Journal of Applied Chemistry - Owing to high stability, metal oxide-based ceramic thin films are of great interest for photocatalytic oxidation of water. Therefore, the current research is...     

Ceramic fuel cells using novel proton-conducting BaCe0.5Zr0.3Y0.1Yb0.05Zn0.05O3-δ electrolyte

Journal of Solid State Electrochemistry - Protonic ceramic fuel cells have become extremely interesting due to their high power output at the intermediate temperature range...     

Organometallic assembling of chitosan‐Iron oxide nanoparticles with their antifungal evaluation against Rhizopus oryzae

The ever‐increasing resistance of plant microbes towards fungicides and bactericides has been causing serious threat to plant production in recent years. For the development of an effective antifungal agent, we introduce a novel hydrothermal protocol for synthesis of chitosan iron oxide nanoparticles (CH‐Fe₂O₃ NPs) using acetate buffer of low pH 5.0 for intermolecular interaction of Fe₂O₃ NPs and CH. The composite structure and elemental elucidation were carried out by using X‐ray power diffraction (XRD), Scanning Electron Microscopy (SEM), Energy Dispersive X‐ray (EDX), Transmission Electron Microscopy (TEM), Fourier Transformed Infrared Spectroscopy (FTIR) and Ultraviolet Visible Absorption Spectroscopy (UV–vis spectroscopy). Additionally, antifungal activity was evaluated both In vitro and In vivo against Rhizopus oryzae which is causing fruit rot disease of strawberry. We compared different concentrations (0.25%, 0.50%, 075% and 1%) of CH‐Fe₂O₃ NPs and 50% synthetic fungicide (Matalyxal Mancozab) to figure out suitable concentration for application in the field. XRD analysis showed a high crystalline nature of the NPs with average size of 52 nanometer (nm). SEM images revealed spherical shape with size range of 50–70 nm, whereas, TEM also revealed spherical shape, size ranging from 0 nm to 80 nm. EDX and FTIR results revealed presence of CH on surface of Fe₂O₃ NPs. The band gap measurement showed peak 317–318 nm for bare Fe₂O₃ NPs and CH‐Fe₂O₃ NPs respectively. Antifungal activity in both In vitro and In vivo significantly increased with increase in concentration. The overall results revealed high synergetic antifungal potential of organometallic CH‐Fe₂O₃ NPs against Rhizopus oryzae and suggest the use of CH‐Fe₂O₃ NPs against other Phyto‐pathological diseases due to biodegradable nature.     

Rapid Learning-Based and Geologically Consistent History Matching

Various types of data become available at different stages of a reservoir’s life. The production data are integrated into the flow simulation models through a process referred to as history matching. The history-matching process is iterative, and it usually involves a large number of simulation runs. Hence, this process requires significant computational time. In most history-matching methods, the initial geological assumptions in the reservoir model are destroyed or significantly altered in the process. Furthermore, they do not account for the information obtained during the previous trials, and lack learning from the previous failures. In this paper, we introduce a new methodology that maintains the geological realism. The candidate realizations are selected through a learning-based history-matching (LHM) algorithm by which all the previously successful patterns are preserved and used to assist the construction of the next realizations. The various pieces of matching regions are assembled together to make a pool of the successful candidates. Such regions are then utilized for making an auxiliary dataset in a multiscale framework by which the next model is generated. To prevent from trapping in local minima, ideas from the genetic algorithm is adapted. The LHM algorithm can be applied to both categorical and continuous distributions. The LHM provides a conditional map by which the new production data are immediately incorporated into the existing reservoir models. We apply the LHM algorithm to various 2D and 3D examples with very complex binary and continuous properties. The algorithm is shown to produce history-matched models with significantly smaller CPU times.     

GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space F N^s(·)p(·),h(·),q(R³)with s(·)=4-2α-3/p(·).We prove global well-posedness result with small initial data belonging to FN^4-2α-3/p(·)p(·),h(·)q(R³).The result of this paper extends some recent work.     

In memory of Professor Ali H. Nayfeh

Nonlinear Dynamics - In this paper, we propose and numerically study a nonlinear, asymmetric, passive metamaterial that achieves giant non-reciprocity with (i) broadband frequency operation and...