An iterative method for a Cauchy problem for the heat equation

An iterative method for reconstruction of the solution to a parabolic initial boundary value problem of second order from Cauchy data is presented. The data are given on a part of the boundary. At each iteration step, a series of well-posed mixed boundary value problems are solved for the parabolic operator and its adjoint. The convergence proof of this method in a weighted L2-space is included.

An iterative method for reconstruction of temperature

An iterative method for the reconstruction of a stationary three-dimensional temperature field, from Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L 2-space is include

Towards the in silico identification of class II restricted T-cell epitopes:a partial least squares iterative self-consistent algorithm for affinity prediction

Motivation: The immunogenicity of peptides depends on their ability to bind to MHC molecules. MHC binding affinity prediction methods can save significant amounts of experimental work. The class II MHC binding site is open at both ends, making epitope prediction difficult because of the multiple binding ability of long peptides. Results: An iterative self-consistent partial least squares (PLS)-based additive method was applied to a set of 66 pep- tides no longer than 16 amino acids, binding to DRB1*0401. A regression equation containing the quantitative contributions of the amino acids at each of the nine positions was generated. Its predictability was tested using two external test sets which gave r pred =0.593 and r pred=0.655, respectively. Furthermore, it was benchmarked using 25 known T-cell epitopes restricted by DRB1*0401 and we compared our results with four other online predictive methods. The additive method showed the best result finding 24 of the 25 T-cell epitopes. Availability: Peptides used in the study are available from http://www.jenner.ac.uk/JenPep. The PLS method is available commercially in the SYBYL molecular modelling software package. The final model for affinity prediction of peptides binding to DRB1*0401 molecule is available at http://www.jenner.ac.uk/MHCPred. Models developed for DRB1*0101 and DRB1*0701 also are available in MHC- Pred

A Perturbed Iterative Method for a General Class of Variational Inequalities

The generalized Wiener-Hopf equation and the approximation methods are used to propose a perturbed iterative method to compute the solutions of a general class of nonlinear variational inequalities.

An Iterative Method for the Matrix Principal n-th Root

In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.

Solving Fractional Diffusion-Wave Equations Using a New Iterative Method

Mathematics Subject Classification: 26A33, 31B10

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.

An Iterative Procedure for Solving Nonsmooth Generalized Equation

2000 Mathematics Subject Classification: 47H04, 65K10.

Probing crystallisation of a fluoro-apatite - mullite system using neutron diffraction

Real-time small angle neutron scattering and wide angle neutron scattering studies were undertaken concurrently on a glass ionomer of nominal composition 4.5(SiO2)-3(Al2O3)-1.5(P2O5)-3(CaO)-2(CaF2). Neutron studies were conducted as a function of temperature to investigate the crystallisation process. No amorphous phase separation was observed at room temperature and the onset of crystallisation was found to occur at 650°C, which is 90°C lower than previously reported. The first crystalline phase observed corresponded to fluorapatite; it was only upon further heating was the mullite phase became present. The crystallite size at 650°C was found to be ~115Å and the result was consistent across all measurements.

Probing the Role of Thermally Reduced Graphene Oxide in Enhancing Performance of TiO2 in Photocatalytic Phenol Removal from Aqueous Environments

We thank the INSA-RSE bilateral exchange programme for financial assistance (PD) and the Petroleum Technology Development Fund (PTDF, Nigeria) for the award of PhD scholarship, as well as Abubakar Tafawa Balewa University, Bauchi-Nigeria for the granted fellowship (H.A).

Probing the Role of Thermally Reduced Graphene Oxide in Enhancing Performance of TiO2 in Photocatalytic Phenol Removal from Aqueous Environments

We thank the INSA-RSE bilateral exchange programme for financial assistance (PD) and the Petroleum Technology Development Fund (PTDF, Nigeria) for the award of PhD scholarship, as well as Abubakar Tafawa Balewa University, Bauchi-Nigeria for the granted fellowship (H.A).

Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.