Path components of the space of gradient vector fields on the two-dimensional disc

We present a short proof that if two gradient maps on the two-dimensional disc have the same degree, then they are gradient homotopic.     

Regular partitions of dual polar spaces

We describe several classes of regular partitions of dual polar spaces and determine their associated parameters and eigenvalues. We also give some general methods for computing the eigenvalues of regular partitions of dual polar spaces.     

Supplier quality improvement: The value of information under uncertainty

We consider supplier development decisions for prime manufacturers with extensive supply bases producing complex, highly engineered products. We propose a novel modelling approach to support supply chain managers decide the optimal level of investment to improve quality performance under uncertainty. We develop a Poisson–Gamma model within a Bayesian framework, representing both the epistemic and aleatory uncertainties in non-conformance rates. Estimates are obtained to value a supplier quality improvement activity and assess if it is worth gaining more information to reduce epistemic uncertainty. The theoretical properties of our model provide new insights about the relationship between the degree of epistemic uncertainty, the effectiveness of development programmes, and the levels of investment. We find that the optimal level of investment does not have a monotonic relationship with the rate of effectiveness. If investment is deferred until epistemic uncertainty is removed then the expected optimal investment monotonically decreases as prior variance increases but only if the prior mean is above a critical threshold. We develop methods to facilitate practical application of the model to industrial decisions by a) enabling use of the model with typical data available to major companies and b) developing computationally efficient approximations that can be implemented easily. Application to a real industry context illustrates the use of the model to support practical planning decisions to learn more about supplier quality and to invest in improving supplier capability.     

Polymer Nanocontainers for Intracellular Delivery

Carriers for intracellular delivery are required to overcome limitations of therapeutic agents such as low specificity, systemic toxicity, high clearance rate, and low therapeutic index. Nanocontainers comprised of an aqueous core and a polymer shell have received increasing attention because they readily combine stimuli response to improve intracellular payload release and surface modification to enhance selectivity towards the desired region of action. This Minireview summarizes the design and properties of polymer nanocontainers for intracellular delivery, classified according to the polymer architecture.     

Growth Actuated Bending and Twisting of Single Crystals

Crystals of a variety of substances including elements, minerals, simple salts, organic molecular crystals, and high polymers forgo long‐range translational order by twisting and bending as they grow. These deviations have been observed in crystals ranging in size from nanometers to centimeters. How and why so many materials choose dramatic non‐crystallographic distortions is analyzed, with an emphasis on crystal chemistries that give rise to stresses operating either on surfaces of crystallites or within the bulk.     

Bootstrap robust prescriptive analytics

Mathematical Programming - We address the problem of prescribing an optimal decision in a framework where the cost function depends on uncertain problem parameters that need to be learned from...     

Surface functionalized N-C-TiO2/C nanocomposites derived from metal-organic framework in water vapour for enhanced photocatalytic H2 generation

Surface-functionalized nitrogen/carbon co-doped polymorphic TiO2 phase junction nanoparticles uniformly distributed in porous carbon matrix were synthesized by ...