A Hausdorff-Young theorem for rearrangement-invariant spaces

The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1 <_ p <_ 2, p[-1] + q[-1] = 1, and if X is a rearrangement-invariant space on the circle T with indices equal to p[-1], it is shown that there is a rearrangement-invariant space X on the integers Z with indices equal to q[-1] such that the Fourier transform is a bounded linear operator from X into X. Conversely, for any rearrangement-invariant space Y on Z with indices equal to q[-1], 2 < q <__ oo, there is a rearrangement-invariant space Y on T with indices equal to p[-1] such that J is bounded from Y into Y. Analogous results for other groups are indicated and examples are discussed when X is L[p] or a Lorentz space L[pr]

A crank-kinematics based engine cylinder pressure reconstruction model

A new inverse model is proposed for reconstructing steady-state and transient engine cylinder pressure using measured crank kinematics. An adaptive nonlinear time-dependent relationship is assumed between windowed-subsections of cylinder pressure and measured crank kinematics in a time-domain format (rather than in crank-angle-domain). This relationship comprises a linear sum of four separate nonlinear functions of crank jerk, acceleration, velocity, and crank angle. Each of these four nonlinear functions is obtained at each time instant by fitting separate m-term Chebychev polynomial expansions, where the total 4m instantaneous expansion coefficients are found using a standard (over-determined) linear least-square solution method. A convergence check on the calibration accuracy shows this initially improves as more Chebychev polynomial terms are used, but with further increase, the over-determined system becomes singular. Optimal accuracy Chebychev expansions are found to be of degree m=4, using 90 or more cycles of engine data to fit the model. To confirm the model accuracy in predictive mode, a defined measure is used, namely the ‘calibration peak pressure error’. This measure allows effective a priori exclusion of occasionally unacceptable predictions. The method is tested using varying speed data taken from a 3-cylinder DISI engine fitted with cylinder pressure sensors, and a high resolution shaft encoder. Using appropriately-filtered crank kinematics (plus the ‘calibration peak pressure error’), the model produces fast and accurate predictions for previously unseen data. Peak pressure predictions are consistently within 6.5% of target, whereas locations of peak pressure are consistently within ± 2.7˚ CA. The computational efficiency makes it very suitable for real-time implementation

Weak randomness completely trounces the security of QKD

In usual security proofs of quantum protocols the adversary (Eve) is expected to have full control over any quantum communication between any communicating parties (Alice and Bob). Eve is also expected to have full access to an authenticated classical channel between Alice and Bob. Unconditional security against any attack by Eve can be proved even in the realistic setting of device and channel imperfection. In this Letter we show that the security of QKD protocols is ruined if one allows Eve to possess a very limited access to the random sources used by Alice. Such knowledge should always be expected in realistic experimental conditions via different side channels

A unified approach to engine cylinder pressure reconstruction using time-delay neural networks with crank kinematics or block vibration measurements

Closed-loop combustion control (CLCC) in gasoline engines can improve efficiency, calibration effort, and performance using different fuels. Knowledge of in-cylinder pressures is a key requirement for CLCC. Adaptive cylinder pressure reconstruction offers a realistic alternative to direct sensing, which is otherwise necessary as legislation requires continued reductions in CO2 and exhaust emissions. Direct sensing however is expensive and may not prove adequately robust. A new approach is developed for in-cylinder pressure reconstruction on gasoline engines. The approach uses Time-Delay feed-forward Artificial Neural Networks trained with the standard Levenberg-Marquardt algorithm. The same approach can be applied to reconstruction via measured crank kinematics obtained from a shaft encoder, or measured engine cylinder block vibrations obtained from a production knock sensor. The basis of the procedure is initially justified by examination of the information content within measured data, which is considered to be equally important as the network architecture and training methodology. Key hypotheses are constructed and tested using data taken from a 3-cylinder (DISI) engine to reveal the influence of the data information content on reconstruction potential. The findings of these hypotheses tests are then used to develop the methodology. The approach is tested by reconstructing cylinder pressure across a wide range of steady-state engine operation using both measured crank kinematics and block accelerations. The results obtained show a very marked improvement over previously published reconstruction accuracy for both crank kinematics and cylinder block vibration based reconstruction using measurements obtained from a multi-cylinder engine. The paper shows that by careful processing of measured engine data, a standard neural network architecture and a standard training algorithm can be used to very accurately reconstruct engine cylinder pressure with high levels of robustness and efficiency

Implementation of the Multiple Point Principle in the Two-Higgs Doublet Model of type II

The multiple point principle (MPP) is applied to the non--supersymmetric two-Higgs doublet extension of the Standard Model (SM). The existence of a large set of degenerate vacua at some high energy scale caused by the MPP results in a few relations between Higgs self-coupling constants which can be examined at future colliders. The numerical analysis reveals that these MPP conditions constrain the mass of the SM--like Higgs boson to lie below 180 GeV for a wide set of MPP scales $\Lambda$ and $\tan\beta$.Comment: 26 pages, 3 figures, some minor changes to the tex