Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

Synthesis and characterization of a new sulphate derivative of hydrazine, N2H5HSO4

Hydrazinium(1 +) hydrogensulphate, N2H5HSO4, has been prepared for the first time by the reaction of solid ammonium hydrogensulphate with hydrazine monohydrate. The compound has been characterized by chemical analysis, infrared spectra, and X-ray powder diffraction. Thermal properties of N2H5HSO4 have been investigated using differential thermal analysis and thermogravimetric analysis and compared with those of N2H6SO4 and (N2H5)2SO4.

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

Synthesis and characterization of a new sulfate derivative of hydrazine, n2h5hso4

Hydrazinium(1 +) hydrogensulphate, N2H5HS04, has been prepared for the first time by the reaction of solid ammonium hydrogensulphate with hydrazine monohydrate. The compound has been characterized by chemical analysis, infrared spectra, and X-ray powder diffraction. Thermal properties of N2H5HS04 have been investigated using differential thermal analysis and thermogravimetric analysis and compared with those of N2H6S04 and (N2H5)2S04.

The impact of a streamlined funding application process on application time: Two cross-sectional surveys of Australian researchers

Objective: To examine if streamlining a medical research funding application process saved time for applicants. Design: Cross-sectional surveys before and after the streamlining. Setting: The National Health and Medical Research Council (NHMRC) of Australia. Participants: Researchers who submitted one or more NHMRC Project Grant applications in 2012 or 2014. Main outcome measures: Average researcher time spent preparing an application and the total time for all applications in working days. Results: The average time per application increased from 34 working days before streamlining (95% CI 33 to 35) to 38 working days after streamlining (95% CI 37 to 39; mean difference 4 days, bootstrap p value <0.001). The estimated total time spent by all researchers on applications after streamlining was 614 working years, a 67-year increase from before streamlining. Conclusions: Streamlined applications were shorter but took longer to prepare on average. Researchers may be allocating a fixed amount of time to preparing funding applications based on their expected return, or may be increasing their time in response to increased competition. Many potentially productive years of researcher time are still being lost to preparing failed applications.

The global burden of injury: Incidence, mortality, disability-adjusted life years and time trends from the Global Burden of Disease study 2013

Background The Global Burden of Diseases (GBD), Injuries, and Risk Factors study used the disability-adjusted life year (DALY) to quantify the burden of diseases, injuries, and risk factors. This paper provides an overview of injury estimates from the 2013 update of GBD, with detailed information on incidence, mortality, DALYs and rates of change from 1990 to 2013 for 26 causes of injury, globally, by region and by country. Methods Injury mortality was estimated using the extensive GBD mortality database, corrections for ill-defined cause of death and the cause of death ensemble modelling tool. Morbidity estimation was based on inpatient and outpatient data sets, 26 cause-of-injury and 47 nature-of-injury categories, and seven follow-up studies with patient-reported long-term outcome measures. Results In 2013, 973 million (uncertainty interval (UI) 942 to 993) people sustained injuries that warranted some type of healthcare and 4.8 million (UI 4.5 to 5.1) people died from injuries. Between 1990 and 2013 the global age-standardised injury DALY rate decreased by 31% (UI 26% to 35%). The rate of decline in DALY rates was significant for 22 cause-of-injury categories, including all the major injuries. Conclusions Injuries continue to be an important cause of morbidity and mortality in the developed and developing world. The decline in rates for almost all injuries is so prominent that it warrants a general statement that the world is becoming a safer place to live in. However, the patterns vary widely by cause, age, sex, region and time and there are still large improvements that need to be made.

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Frechet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography. (C) 2010 Optical Society of America.

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T

PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.

Chemistry in Confined Spaces: High-Energy Conformer of a Piperidine Derivative is Favored Within a Water-Soluble Capsuleplex

Propyloxy-substituted piperidine in solution adopts a conformation in which its alkoxy group is equatorially positioned Surprisingly, two conformers of it that do not interconvert in the NMR time scale at room temperature have been found within an octa-acid capsule The serendipitous finding of the axial conformer of propyloxy-substituted piperidine within a supramolecular capsule highlights the value of confined spaces in physical organic chemistry.

Impact of metal binding on the antitumor activity and cellular imaging of a metal chelator cationic imidazopyridine derivative

A new water soluble cationic imidazopyridine species, viz. (1E)-1-((pyridin-2-yl)methyleneamino)-3-(3(pyridin-2-yl) imidazo1,5-a]pyridin-2(3H)-yl)propan-2-ol (1), as a metal chelator is prepared as its PF6 salt and characterized. Compound 1 shows fluorescence at 438 nm on excitation at 342 nm in Tris-HCl buffer giving a fluorescence quantum yield (phi) of 0.105 and a life-time of 5.4 ns. Compound 1, as an avid DNA minor groove binder, shows pUC19 DNA cleavage activity in UV-A light of 365 nm forming singlet oxygen species in a type-II pathway. The photonuclease potential of 1 gets enhanced in the presence of Fe2+, Cu2+ or Zn2+. Compound 1 itself displays anticancer activity in HeLa, HepG2 and Jurkat cells with an enhancement on addition of the metal ions. Photodynamic effect of 1 at 365 nm also gets enhanced in the presence of Fe2+ and Zn2+. Fluorescence-based cell cycle analysis shows a significant dead cell population in the sub-G1 phase of the cell cycle suggesting apoptosis via ROS generation. A significant change in the nuclear morphology is observed from Hoechst 33258 and an acridine orange/ethidium bromide (AO/EB) dual nuclear staining suggesting apoptosis in cells when treated with 1 alone or in the presence of the metal ions. Apoptosis is found to be caspase-dependent. Fluorescence imaging to monitor the distribution of 1 in cells shows that 1 in the presence of metal ions accumulates predominantly in the cytoplasm. Enhanced uptake of 1 into the cells within 12 h is observed in the presence of Fe2+ and Zn2+.

A novel structural derivative of natural alkaloid ellipticine, MDPSQ, induces necrosis in leukemic cells

DNA intercalating molecules are promising chemotherapeutic agents. In the present study, a novel DNA intercalating compound of pyrimido4',5':4,5]selenolo(2,3-b)quinoline series having 8-methyl-4-(3 diethylaminopropylamino) side chain is studied for its chemotherapeutic properties. Our results showed that 8-methyl-4-(3 diethylaminopropylamino) pyrimido 4',5':4,5] selenolo(2,3-b)quinoline (MDPSQ) induces cytotoxicity in a time- and concentration-dependent manner on leukemic cell lines. Both cell cycle analysis and tritiated thymidine assays revealed that MDPSQ affects DNA replication. Treatment with MDPSQ resulted in both elevated levels of DNA strand breaks and repair proteins, further indicating its cytotoxic effects. Besides, Annexin V/PI staining revealed that MDPSQ induces cell death by triggering necrosis rather than apoptosis.