A new class of two-channel biorthogonal filter banks and wavelet bases

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters

Activating Magnesium Electrolytes through Chemical Generation of Free Chloride and Removal of Trace Water

Mg batteries are attractive next-generation energy storage systems due to their high natural abundance, inexpensive cost, and high theoretical capacity compared to conventional Li-ion based systems. The high energy density is achieved by electrodeposition and stripping of a Mg metal anode and requires the development of effective electrolytes enabled by a mechanistic understanding of the charge-transfer mechanism. The magnesium aluminum chloride complex (MACC) electrolyte is a good model system to study the mechanism as the solution phase speciation is known. Previously, we reported that minor addition of Mg(HMDS)₂ to the MACC electrolyte causes significant improvement in the Mg deposition and stripping voltammetry resulting in good Coulombic efficiency on cycle one and, therefore, negating the need for electrochemical conditioning. To determine the cause of the improved electrochemistry, here we probe the speciation of the electrolyte after Mg(HMDS)₂ addition using Raman spectroscopy, ²⁷Al nuclear magnetic resonance spectroscopy, and ¹H–²⁹Si heteronuclear multiple bond correlation spectroscopy on MACC + Mg(HMDS)₂ at various Mg(HMDS)₂ concentrations. Mg(HMDS)₂ scavenges trace H₂O, but it also reacts with MACC complexes, namely, AlCl₄⁻, to form free Cl⁻. We suggest that although both the removal of H₂O and the formation of free Cl⁻ improve electrochemistry by altering the speciation at the interface, the latter has a profound effect on electrodeposition and stripping of Mg

Tests of Basic Quantum Mechanics in Oscillation Experiments

According to standard quantum theory, the time evolution operator of a quantum system is independent of the state of the system. One can, however, consider systems in which this is not the case: the evolution operator may depend on the density operator itself. The presence of such modifications of quantum theory can be tested in long baseline oscillation experiments.Comment: 8 pages, LaTeX; no macros neede

Incidence and documentation of ear lobe numbness after parotidectomy: our 20 years' experience

Introduction: Parotidectomy carries a risk of postoperative complications including facial nerve palsy and Frey’s syndrome. Less attention, however, has been given to the management of the greater auricular nerve (GAN) during parotidectomy. Providing sensory supply to the auricle, the greater auricular nerve is often sacrificed for access to the parotid gland during surgery. This results in anaesthesia and paraesthesia of the ear lobe and significant patient morbidity. Aim: To review the electronically available documentation of post-parotidectomy ear lobe numbness in our follow-up clinic letters of the past 20 years. Methods: For this retrospective case series our departmental database of over 850 patients undergoing parotidectomy was used as the primary data source. The information collected from electronic records included documentation of intraoperative details, post-operative recovery and incidence of ear lobe numbness post-operatively. The current study was completed between October and November 2020. SPSS and Excel were used for data collection and analysis. Results: The incidence of ear lobe numbness was found to be higher in the patient cohort whose posterior branch of the GAN had been sacrificed during surgery (58% compared to 46%). This agrees with the published literature that preservation of the posterior branch of the GAN decreases the post-operative sensory deficit to the auricle. However, this audit was limited by the incomplete recording of GAN sacrifice intra-operatively and post-operative GAN dysfunction. Discussion: As any tissue removed, added or altered in surgery requires accurate record-keeping, the outcome of the greater auricular nerve during parotidectomy should always be included in the operation notes. A proforma made available within the department may allow for a standardised recording of recognised complications

Conditioning-Free Mg Electrolyte by the Minor Addition of Mg(HMDS)₂

Mg-based batteries are an attractive next-generation energy storage chemistry due to the high natural abundance and inexpensive cost of Mg, along with the high theoretical energy density compared to that of conventional Li-ion chemistry. The greater energy density is predicated on a Mg metal anode, and pathways to achieving reversible Mg electrodeposition and stripping are reliant on the development of Mg electrolytes. Although Mg electrolyte chemistry has advanced significantly from the reactive Grignards of the 1920s to the carboranes of this decade, there remains significant challenges in correlating the Mg metal anode electrochemistry with the composition of the electrolyte salts as a result of the complicated interface of Mg metal and the electrolyte. To probe the effect of the interface on Mg electrodeposition, we turn to an electrolyte with a known solution-phase composition: the magnesium aluminum chloride complex (MACC) electrolyte. The MACC electrolyte requires electrolytic conditioning to support reversible Mg electrodeposition and stripping. Here, we show that a small concentration (2–5 mM) of Mg(HMDS)₂ with respect to the MACC electrolyte salts suppresses Al³⁺ deposition and promotes reversible Mg electrodeposition and stripping in the first cycle. The significant effect of a small concentration of additive is attributed to changes to the electrode interface. The impact of the Mg interface on the observed electrochemical performance is discussed