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Obesity and the Dysregulation of Fatty Acid Metabolism: Implications for Healthy AgingThe population of the world is aging. In 2010, an estimated 524 million people were aged 65 years or older presenting eight percent of the global population. By 2050, this number is expected to nearly triple to approximately 1.5 billion, 16 percent of the world’s population. Although people are living longer, the quality of their lives are often compromised due to illhealth. Areas covered. Of the conditions which compromise health as we age, obesity is at the forefront. Over half of the global older population were overweight or obese in 2010, significantly increasing the risk of a range of metabolic diseases. Although, it is well recognised excessive calorie intake is a fundamental driver of adipose tissue dysfunction, the relationship between obesity; intrinsic aging; and fat metabolism is less understood. In this review we discuss the intersection between obesity, aging and the factors which contribute to the dysregulation of wholebody fat metabolism. Expert Commentary. Being obese disrupts an array of physiological systems and there is significant crosstalk among these. Moreover it is imperative to acknowledge the contribution intrinsic aging makes to the dysregulation of these systems and the onset of disease.

On a degenerate nonlocal parabolic problem describing infinite dimensional replicator dynamicsWe establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for \[ u_t = u \Delta u + u \int_\Omega \nabla u^2 \] in bounded domains $\Om\sub\R^n$ which arises in game theory. We prove that solutions converge to $0$ if the initial mass is small, whereas they undergo blowup in finite time if the initial mass is large. In particular, it is shown that in this case the blowup set coincides with $\overline{\Omega}$, i.e. the finitetime blowup is global.

On hereditary reducibility of 2monomial matrices over commutative ringsA 2monomial matrix over a commutative ring $R$ is by definition any matrix of the form $M(t,k,n)=\Phi\left(\begin{smallmatrix}I_k&0\\0&tI_{nk}\end{smallmatrix}\right)$, $0<k<n$, where $t$ is a noninvertible element of $R$, $\Phi$ the compa\nion matrix to $\lambda^n1$ and $I_k$ the identity $k\times k$matrix. In this paper we introduce the notion of hereditary reducibility (for these matrices) and indicate one general condition of the introduced reducibility.

On some aspects of casual and neutral equations used in mathematical modellingThe problem that motivates the considerations here is the construction of mathematical models of natural phenomena that depend upon past states. The paper divides naturally into two parts: in the first, we expound the interconnection between ordinary differential equations, delay differential equations, neutral delaydifferential equations and integral equations (with emphasis on certain linear cases). As we show, this leads to a natural hierarchy of model complexity when such equations are used in mathematical and computational modelling, and to the possibility of reformulating problems either to facilitate their numerical solution or to provide mathematical insight, or both. Volterra integral equations include as special cases the others we consider. In the second part, we develop some practical and theoretical consequences of results given in the first part. In particular, we consider various approaches to the definition of an adjoint, we establish (notably, in the context of sensitivity analysis for neutral delaydifferential equations) roles for welldefined adjoints and ‘quasiadjoints’, and we explore relationships between sensitivity analysis, the variation of parameters formulae, the fundamental solution and adjoints.

On the behavior of the solutions for linear autonomous mixed type difference equationA class of linear autonomous mixed type difference equations is considered, and some new results on the asymptotic behavior and the stability are given, via a positive root of the corresponding characteristic equation.

On the decay of the elements of inverse triangular Toeplitz matricesWe consider half–infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that the elements of the inverse matrix, as well as the elements of the fundamental matrix, decay to zero. We provide a quantitative description of the decay of the fundamental matrix in terms of p–norms. The results add to the classical results of Jaffard and Vecchio, and are illustrated by numerical examples.

On the Dirichlet to Neumann Problem for the 1dimensional Cubic NLS Equation on the halflineInitialboundary value problems for 1dimensional `completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it requires the values of more boundary data than given for a wellposed problem. In the case of cubic NLS, knowledge of the Dirichet data su ces to make the problem wellposed but the Fokas method also requires knowledge of the values of Neumann data. The study of the Dirichlet to Neumann map is thus necessary before the application of the `Fokas transform'. In this paper, we provide a rigorous study of this map for a large class of decaying Dirichlet data. We show that the Neumann data are also su ciently decaying and that, hence, the Fokas method can be applied.

On the dynamics of a nonlocal parabolic equation arising from the GiererMeinhardt systemThe purpose of the current paper is to contribute to the comprehension of the dynamics of the shadow system of an activatorinhibitor system known as a GiererMeinhardt model. Shadow systems are intended to work as an intermediate step between single equations and reactiondiffusion systems. In the case where the inhibitor's response to the activator's growth is rather weak, then the shadow system of the GiererMeinhardt model is reduced to a single though nonlocal equation whose dynamics will be investigated. We mainly focus on the derivation of blowup results for this nonlocal equation which can be seen as instability patterns of the shadow system. In particular, a {\it diffusion driven instability (DDI)}, or {\it Turing instability}, in the neighbourhood of a constant stationary solution, which it is destabilised via diffusiondriven blowup, is obtained. The latter actually indicates the formation of some unstable patterns, whilst some stability results of globalintime solutions towards nonconstant steady states guarantee the occurrence of some stable patterns.

On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS controlWe consider a nonlocal parabolic model for a microelectromechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solution quenches, so that touchdown occurs in the device, in a situation where there is no steady state. It is also shown that quenching occurs at a single point and a bound on the approach to touchdown is obtained. Numerical simulations illustrating the results are given.

On the study of oil paint adhesion on optically transparent glass: Conservation of reverse paintings on glassReverse painting on glass is a technique which consists of applying a cold paint layer on the reverseside of glass. The main challenge facing these artworks is the fragile adhesion of the pictorial layer – a simple movement can modify the appearance of the painting. This paper details a study into the adhesion parameters of pigments on glass and the comparison between different pigments. The relationships between the binder (linseed oil) with pigments and the glass with or without the use of an adhesive are studied. Physical analyses by surface characterisation have been carried out to better understand the influence of the pigment. The use of a sessile drop device, optical microscopy, scanning electron microscopy (SEM), a surface 3D profiler and a pencil hardness scratch tester were necessary to establish a comparison of the pictorial layer adhesion. A comparison of the effect of two adhesives; namely ox gall and gum arabic, has shown that the adhesion is not only linked to the physical parameters but that possible chemical reactions can influence the results. Finally, a treatment based on humidityextreme storage has shown the weakness of some pictorial layers.

Online conductivity calibration methods for EIT gas/oil in water flow measurementElectrical Impedance Tomography (EIT) is a fast imaging technique displaying the electrical conductivity contrast of multiphase flow. It is increasingly utilised for industrial process measurement and control. In principle, EIT has to obtain the prior information of homogenous continuous phase in terms of conductivity as a reference benchmark. This reference significantly influences the quality of subsequent multiphase flow measurement. During dynamic industrial process, the conductivity of continuous phase varies due to the effects from the changes of ambient and fluid temperature, ionic concentration, and internal energy conversion in fluid. It is not practical to stop industrial process frequently and measure the conductivity of continuous phase for taking the EIT reference. If without monitoring conductivity of continuous phase, EIT cannot present accurate and useful measurement results. To online calibrate the electrical conductivity of continuous phase and eliminate drift error of EIT measurement, two methods are discussed in this paper. Based on the linear approximation between fluid temperature and conductivity, the first method monitors fluid temperature and indirectly calibrates conductivity. In the second method, a novel conductivity cell is designed. It consists of a gravitational separation chamber with refreshing bypass and grounded shielding plate. The conductivity of continuous phase is directly sensed by the conductivity cell and fed to EIT system for online calibration. Both static and dynamic experiments were conducted to demonstrate the function and accuracy the conductivity cell.

Optimal convergence rates for semidiscrete finite element approximations of linear spacefractional partial differential equations under minimal regularity assumptionsWe consider the optimal convergence rates of the semidiscrete finite element approximations for solving linear spacefractional partial differential equations by using the regularity results for the fractional elliptic problems obtained recently by Jin et al. \cite{jinlazpasrun} and Ervin et al. \cite{ervheuroo}. The error estimates are proved by using two approaches. One approach is to apply the duality argument in Johnson \cite{joh} for the heat equation to consider the error estimates for the linear spacefractional partial differential equations. This argument allows us to obtain the optimal convergence rates under the minimal regularity assumptions for the solution. Another approach is to use the approximate solution operators of the corresponding fractional elliptic problems. This argument can be extended to consider more general linear spacefractional partial differential equations. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

Optimisation and management of energy generated by a multifunctional MFCintegrated composite chassis for rail vehiclesWith the advancing trend towards lighter and faster rail transport, there is an increasing interest in integrating composite and advanced multifunctional materials in order to infuse smart sensing and monitoring, energy harvesting and wireless capabilities within the otherwise purely mechanical rail structures and the infrastructure. This paper presents a holistic multiphysics numerical study, across both mechanical and electrical domains, that describes an innovative technique of harvesting energy from a piezoelectric micro fiber composites (MFC) builtin composite rail chassis structure. Representative environmental vibration data measured from a rail cabin have been critically leveraged here to help predict the actual vibratory and power output behaviour under service. Time domain mean stress distribution data from the Finite Element simulation were used to predict the raw AC voltage output of the MFCs. Conditioned power output was then calculated using circuit simulation of several stateoftheart power conditioning circuits. A peak instantaneous rectified power of 181.9 mW was obtained when eightstage Synchronised Switch Harvesting Capacitors (SSHC) from eight embedded MFCs were located. The results showed that the harvested energy could be sufficient to sustain a selfpowered structural health monitoring system with wireless communication capabilities. This study serves as a theoretical foundation of scavenging for vibrational power from the ambient state in a rail environment as well as to pointing to design principles to develop regenerative and power neutral smart vehicles.

Optimization of antiwear and antibacterial properties of beta TiNb alloy via controlling duty cycle in openair laser nitridingA multifunctional beta TiNb surface, featuring wearresistant and antibacterial properties, was successfully created by means of openair fibre laser nitriding. Beta TiNb alloy was selected in this study as it has low Young’s modulus, is highly biocompatible, and thus can be a promising prosthetic joint material. It is, however, necessary to overcome intrinsically weak mechanical properties and poor wear resistance of beta TiNb in order to cover the range of applications to loadbearing and/or shearing parts. To this end, openair laser nitriding technique was employed. A control of single processing parameter, namely duty cycle (between 5% and 100%), led to substantially different structural and functional properties of the processed beta TiNb surfaces as analyzed by an array of analytical tools. The TiNb samples nitrided at the DC condition of 60% showed a most enhanced performance in terms of improving surface hardness, antifriction, antiwear and antibacterial properties in comparison with other conditions. These findings are expected to be highly important and useful when TiNb alloys are considered as materials for hip/knee articular joint implants

Optomechanical switching of adsorption configurations of polar organic molecules by UV radiation pressureUsing photoemission spectroscopy (PES), we have systematically investigated the behavior of polar organic molecule, chloroaluminum phthalocyanine (ClAlPc), adsorbed in the Cldown configuration on the Ag(111) substrate at low temperature − 195 °C under UV irradiation with a range of different photon fluxes. Judging from the evolution of photoemission spectral line shapes of molecular energy states, we discovered that the Cl atoms are so robustly anchored at Ag(111) that the impinging photons cannot flip the ClAlPc molecules, but instead they crouch them down due to radiation pressure; we observe that the phthalocyanine (Pc) lobes bend down to interact with Ag atoms on the substrate and induce charge transfer from them. As photon flux is increased, radiation pressure on the Pc plane initiates tunneling of the Cl atom through the molecular plane to turn the adsorption configuration of ClAlPc from Cldown to an upheld Clup configuration, elucidating an optomechanical way of manipulating the dipole direction of polar molecules. Finally, work function measurements provide a distinct signature of the resulting upheld Clup configuration as it leads to a large increase in vacuum level (VL), ~ 0.4 eV higher than that of a typical flaton Clup configuration driven by thermal annealing.

Orthogonality for a class of generalised Jacobi polynomial $P^{\alpha,\beta}_{\nu}(x)$This work considers gJacobi polynomials, a fractional generalisation of the classical Jacobi polynomials. We discuss the polynomials and compare some of their properties to the classical case. The main result of the paper is to show that one can derive an orthogonality property for a subclass of gJacobi polynomials $P^{\alpha,\beta}_{\nu}(x)$ The paper concludes with an application in modelling of ophthalmic surfaces.

Oscillatory and stability of a mixed type difference equation with variable coefficientsThe goal of this paper is to study the oscillatory and stability of the mixed type difference equation with variable coefficients \[ \Delta x(n)=\sum_{i=1}^{\ell}p_{i}(n)x(\tau_{i}(n))+\sum_{j=1}^{m}q_{j}(n)x(\sigma_{i}(n)),\quad n\ge n_{0}, \] where $\tau_{i}(n)$ is the delay term and $\sigma_{j}(n)$ is the advance term and they are positive real sequences for $i=1,\cdots,l$ and $j=1,\cdots,m$, respectively, and $p_{i}(n)$ and $q_{j}(n)$ are real functions. This paper generalise some known results and the examples illustrate the results.