Arithmeticity for periods of automorphic forms

A cuspidal automorphic representation \pi of a group G is said to to be distinguished with respect to a subgroup H if the integral of f along H is nonzero for a cusp form f in the space of \pi. Such period integrals are related to (non)vanishing of interesting L-values and also to Langlands functoriality. This article discusses a general principle, labelled arithmeticity, which roughly states that "\pi is H-distinguished if and only if any Galois conjugate of \pi is H-distinguished." We study this principle via several examples; starting with GL(2) and leading up to more complicated situations where the ambient group is a higher GL(n) or a classical group.Comment: 32 pages. The final version is to appear in the proceedings of the International Colloquium on Automorphic Representations and L-functions, held in TIFR, Mumbai, January 201

Matrimid-JUC-62 and Matrimid-PCN-250 mixed matrix membranes displaying light-responsive gas separation and beneficial ageing characteristics for CO2/N2 separation

The performance of two generation-3 light-responsive metal-organic framework (MOF), namely JUC-62 and PCN-250, was investigated in a mixed matrix membrane (MMM) form. Both of them were incorporated inside the matrimid as the polymer matrix. Using our custom-designed membrane testing cell, it was observed that the MMMs showed up to 9% difference in CO2 permeability between its pristine and UV-irradiated condition. This shows that the light-responsive ability of the light-responsive MOFs could still be maintained. Thus, this finding is applicable in designing a smart material. Apart from that, the MMMs also has the potential to be applied for post-combustion carbon capture. At loadings up to 15 wt%, both CO2 permeability and CO2/N2 ideal selectivity could be significantly improved and surpassed the value exhibited by most of the MOF-matrimid MMM. Lastly the long term performance of the MMM was also evaluated and it was observed that both MMM could maintain their performance up to 1 month with only a slight decrease in CO2 permeability observed for 10 wt% PCN-250-matrimid. This study then opens up the possibility to fabricate a novel anti-aging multifunctional membrane material that is applicable as a smart material and also in post combustion carbon capture applications

Robust Control of Bipedal Humanoid (TPinokio)

AbstractA stable walking motion requires effective gait balancing and robust posture correction algorithms. However, to develop and implement such intelligent motion algorithms remain a challenging task for researchers. In order to minimize the modeling errors and disturbances, this paper presents an alternative approach in generating a stable Centre-of-Mass (CoM) trajectory by applying augmented model predictive control. The propose approach is to apply Augmented Model Predictive Control (AMPC) algorithm with on-line time shift and look ahead to process future data to optimize a control signal by minimizing a cost function so that the system is able to track the reference Zero Moment Point (ZMP) as close as possible, and at the same time to limit the motion jerk in order to improve the robot walking stability

Quasi-residual quasi-symmetric designs

AbstractIt is shown that for each λ ⩾ 3, there are only finitely many quasi-residual quasi-symmetric (QRQS) designs and that for each pair of intersection numbers (x, y) not equal to (0, 1) or (1, 2), there are only finitely many QRQS designs.A design is shown to be affine if and only if it is QRQS with x = 0. A projective design is defined as a symmetric design which has an affine residual. For a projective design, the block-derived design and the dual of the point-derivate of the residual are multiples of symmetric designs

Measuring Imputed Cost in the Semiconductor Equipment Supply Chain

We consider the order-fulfillment process of a supplier producing a customized capital good, such as production equipment, commercial aircraft, medical devices, or defense systems. As is common in these industries, prior to receiving a firm purchase order from the customer, the supplier receives a series of shared forecasts, which are called “soft orders.” Facing a stochastic internal manufacturing lead time, the supplier must decide at what time to begin the fulfillment of the order. This decision requires a trade-off between starting too early, leading to potential holding or cancellation costs, and starting too late, leading to potential delay costs. We collect detailed data of shared forecasts, actual purchase orders, production lead times, and delivery dates for a supplier-buyer dyad in the semiconductor equipment supply chain. Under the assumption that the supplier acts rationally, optimally balancing the cancellation, holding, and delay costs, we are able to estimate the corresponding imputed cost parameters based on the observed data. Our estimation results reveal that the supplier perceives the cost of cancellation to be about two times higher and the holding costs to be about three times higher than the delay cost. In other words, the supplier is very conservative when commencing the order fulfillment, which undermines the effectiveness of the overall forecast-sharing mechanism