The Evolution of Mathematical Programming Systems

Computer programs to solve linear programming problems by the simplex method have existed since the early 1950s. They remain the central feature of today's mathematical programming systems. There has been a steady increase in the size of problem that can be solved: this has been due as much to a better understanding of how to exploit sparseness as to larger and faster computers. There has been a steady increase in the type of problem that can be solved: this has been due as much to new concepts, such as separable programming, integer variables and special ordered sets, as to new algorithms. There has been a steady increase in the extent to which the application of mathematical programming has become more automatic. This applies both to the use of computerized matrix generators and report writers and to the mathematical formulation itself, in that we rely less on the user producing a well-scaled linear programming problem and are starting on the process of automatically sharpening the formulation of integer programming problems.Important new work is being done on all these aspects of computational mathematical programming.     

A convergent boundary integral method for three-dimensional water waves

We design a boundary integral method for time-dependent, three-dimensional, doubly periodic water waves and prove that it converges with accuracy, without restriction on amplitude. The moving surface is represented by grid points which are transported according to a computed velocity. An integral equation arising from potential theory is solved for the normal velocity. A new method is developed for the integration of singular integrals, in which the Green's function is regularized and an efficient local correction to the trapezoidal rule is computed. The sums replacing the singular integrals are treated as discrete versions of pseudodifferential operators and are shown to have mapping properties like the exact operators. The scheme is designed so that the error is governed by evolution equations which mimic the structure of the original problem, and in this way stability can be assured. The wavelike character of the exact equations of motion depends on the positivity of the operator which assigns to a function on the surface the normal derivative of its harmonic extension; similarly, the stability of the scheme depends on maintaining this property for the discrete operator. With grid points, the scheme can be implemented with essentially operations per time step.

     

A General Method for Estimating Dynamic Parameters of Spatial Mechanisms

Dynamic equations of motion require a large number of parameters for each element of the system. These can include for each part their mass, location of center of mass, moment of inertia, spring stiffnesses and damping coefficients. This paper presents a technique for estimating these parameters in spatial mechanisms using any joint type, based on measurements of displacements, velocities and accelerations and of external forces and torques, for the purpose of building accurate multibody models of mechanical systems. A form of the equations of spatial motion is derived, which is linear in the dynamic parameters and based on multibody simulation code methodologies. Singular value decomposition is used to find the essential parameter set, and minimum parameter set. It is shown that a simulation of a four-bar mechanism (with spherical, universal, and revolute joints) and based on the estimated parameters gives accurate response.     

Search for third-generation scalar leptoquarks in pp at square root s=1.96 TeV

We report on a search for charge-1/3 third-generation leptoquarks (LQ) produced in pp collisions at square root s =1.96 TeV using the D0 detector at Fermilab. Third-generation leptoquarks are assumed to be produced in pairs and to decay to a tau neutrino and a b quark with branching fraction B. We place upper limits on sigma(pp --> LQLQ)B2 as a function of the leptoquark mass M(LQ). Assuming B=1, we exclude at the 95% confidence level third-generation scalar leptoquarks with M(LQ)<229 GeV.     

Implementation of a combined SAXS/WAXS/QEXAFS set‐up for time‐resolved in situ experiments

It has previously been shown that there are many benefits to be obtained in combining several techniques in one in situ set‐up to study chemical processes in action. Many of these combined set‐ups make use of two techniques, but in some cases it is possible and useful to combine even more. A set‐up has recently been developed that combines three X‐ray‐based techniques, small‐ and wide‐angle X‐ray scattering (SAXS/WAXS) and quick‐scanning EXAFS (QEXAFS), for the study of dynamical chemical processes. The set‐up is able to probe the same part of the sample during the synthesis process and is thus able to follow changes at the nanometre to micrometre scale during, for example, materials self‐assembly, with a time resolution of the order of a few minutes. The practicality of this kind of experiment has been illustrated by studying zeotype crystallization processes and revealed important new insights into the interplay of the various stages of ZnAPO‐34 formation. The flexibility of this set‐up for studying other processes and for incorporating other additional non‐X‐ray‐based experimental techniques has also been explored and demonstrated for studying the stability/activity of iron molybdate catalysts for the anaerobic decomposition of methanol.     

Phenolics from Medicinal and Aromatic Plants: Characterisation and Potential as Biostimulants and Bioprotectants

Biostimulants and bioprotectants are derived from natural sources and can enhance crop growth and protect crops from pests and pathogens, respectively. They have attracted much attention in the past few decades and contribute to a more sustainable and eco-friendly agricultural system. Despite not having been explored extensively, plant extracts and their component secondary metabolites, including phenolic compounds have been shown to have biostimulant effects on plants, including enhancement of growth attributes and yield, as well as bioprotectant effects, including antimicrobial, insecticidal, herbicidal and nematicidal effects. Medicinal and aromatic plants are widely distributed all over the world and are abundant sources of phenolic compounds. This paper reviews the characterisation of phenolic compounds and extracts from medicinal and aromatic plants, including a brief overview of their extraction, phytochemical screening and methods of analysis. The second part of the review highlights the potential for use of phenolic compounds and extracts as biostimulants and bioprotectants in agriculture as well as some of the challenges related to their use.