Fractional partial differential equations with boundary conditions

We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show well-posedness of the associated Cauchy problems in $C_0(\mathrm{\Omega })$ and $L_1(\mathrm{\Omega })$. In order to do so we develop a new method of embedding finite state Markov processes into Feller processes on bounded domains and then show convergence of the respective Feller processes. This also gives a numerical approximation of the solution. The proof of well-posedness closes a gap in many numerical algorithm articles approximating solutions to fractional differential equations that use the Lax–Richtmyer Equivalence Theorem to prove convergence without checking well-posedness.     

On a class of smooth Frechet subalgebras of C * -algebras

The paper contributes to understanding the differential structure in a C ^*-algebra. Refining the Banach $(D_p^*)$ -algebras investigated by Kissin and Shulman as noncommutative analogues of the algebra C ^p [a,b] of p-times continuously differentiable functions, we investigate a Frechet $(D_\infty^*)$ -subalgebra $\ensuremath{{\mathcal B}}$ of a C ^*-algebra as a noncommutative analogue of the algebra C ^?∞?[a,b] of smooth functions. Regularity properties like spectral invariance, closure under functional calculi and domain invariance of homomorphisms are derived expressing $\ensuremath{{\mathcal B}}$ as an inverse limit over n of Banach $(D^*_n)$ -algebras. Several examples of such smooth algebras are exhibited.     

Lewis Acid Directed Regioselective Metalations of Pyridazine

Mono‐ or bidentate boron Lewis acids trigger a regioselective magnesiation or zincation of pyridazine in position C3 (ortho product) or C4 (meta product). The regioselectivity of the metalation was rationalized with the help of calculated pK_a values of both pyridazine and pyridazine/Lewis acid complexes.     

Automatic correction of in-plane bulk motion artifacts in self-navigated radial MRI

Radial MRI is typically used for scans that are sensitive to unavoidable motion. While the translational motion artifact can be easily removed from the radial trajectory data by phase correction, correction of rotational motion still remains a challenge in radial MRI. We present a novel method to refocus the image corrupted by view-to-view motion in the view-interleaved radial MRI data. In this method, the error in rotational view angles was modeled as a polynomial function of the view order and the model parameters were estimated by minimizing the self-navigator image metrics such as image entropy, gradient entropy, normalized gradient squared and mean square difference. Translational motion correction was conducted by aligning the projection profiles. Simulation studies were conducted to demonstrate the robustness of both translational and rotational motion correction methods in different noise levels. The proposed method was successfully applied to correct for motion of healthy subjects. Substantial motion correction with relative error of less than 5% was achieved by using either first- or second-order model with the image metrics. This study demonstrates the potential of the method for motion-sensitive applications.     

Multi-targeted molecular docking,drug-likeness and ADMET studies of derivatives of few quinoline- and acridine-based FDA-approved drugs for anti-breast cancer activity

Structural Chemistry - Quinoline- and acridine-based drugs are widely used as anti-breast cancer agents. These drugs act through various mechanisms of action; for example, neratinib acts on...     

Analysis of atypical orbits in one-dimensional piecewise-linear discontinuous maps

In this paper, boundary regions of 1-D linear piecewise-smooth discontinuous maps are examined analytically. It is shown that, under certain parameter conditions, maps exhibit atypical orbits like a continuum of periodic orbits and quasi-periodic orbits. Further, we have derived the conditions under which such phenomenon occurs. The paper also illustrates that there exists a specific parameter region where as the parameter is varied, there is a transition from stable to unstable periodic orbits. Moreover, we have derived an expression for the value of parameter at which this transition from stable to unstable periodic orbits occurs. Additionally, the dynamics concerning this value of parameter is also given.

     

Symbiotic organism search algorithm for simulation of <Emphasis Type="Italic">J</Emphasis>-<Emphasis Type="Italic">V</Emphasis> characteristics and optimizing internal parameters of DSSC developed using electrospun TiO<Subscript>2</Subscript> nanofibers

In the present investigation, the recently developed, simple, robust, and powerful metaheuristic symbiotic organism search (SOS) algorithm was used for simulation of J-V characteristics and optimizing the internal parameters of the dye-sensitized solar cells (DSSCs) fabricated using electrospun 1-D mesoporous TiO₂ nanofibers as photoanode. The efficiency (η =?5.80%) of the DSSC made up of TiO₂ nanofibers as photoanode is found to be ～ 21.59% higher compared to the efficiency (η =?4.77%) of the DSSC made up of TiO₂ nanoparticles as photoanode. The observed high efficiency can be attributed to high dye loading as well as high electron transport in the mesoporous 1-D TiO₂ nanofibers. Further, the validity and advantage of SOS algorithm are verified by simulating J-V characteristics of DSSC with Lambert-W function.