Hierarchical Dobinski-type relations via substitution and the moment problem

We consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form exp(x (a*)^r a), r=1,2,..., under the composition of their exponential generating functions (egf). They turn out to be of Sheffer-type. We demonstrate that two key properties of these sequences remain preserved under substitutional composition: (a)the property of being the solution of the Stieltjes moment problem; and (b) the representation of these sequences through infinite series (Dobinski-type relations). We present a number of examples of such composition satisfying properties (a) and (b). We obtain new Dobinski-type formulas and solve the associated moment problem for several hierarchically defined combinatorial families of sequences.Comment: 14 pages, 31 reference

Primary interhemispheric subdural empyemas: A report of three cases and review of literature

Background: Interhemispheric subdural empyema is an uncommon condition and is considered neurosurgical emergency. These are generally seen following neglected otorhinological infection, but may be posttraumatic or iatrogenic in origin. The source of infection can be frequently found, but in few cases no source of infection can be identified, called idiopathic empyemas. These idiopathic interhemispheric subdural empyemas are even rare. They can present with a rapid progression of symptoms and can carry poor prognosis. Early intervention with craniotomy and appropriate antibiotics can improve the condition of these patients. Materials and Methods: We present three cases of idiopathic interhemispheric empyemas who underwent emergency craniotomy and evacuation followed by antibiotics for 6 weeks. Results: All the patients had excellent recovery on mean follow-up of 10 years. Conclusion: Early diagnosis and treatment of interhemisheric subdural empyema can lead to excellent recovery and outcome

Electrochemical Performance of Li2TiO3//LiCoO2 Li-Ion Aqueous Cell with Nanocrystalline Electrodes

A challenge in developing high-performance lithium batteries requires a safe technology without flammable liquid electrolytes. Nowadays, two options can satisfy this claim: all-solid-state batteries and aqueous-electrolyte batteries. Commercially available Li-ion batteries utilize non-aqueous electrolytes (NAE) owing to a wide potential window (>3 V) that achieves high energy density but pose serious safety issues due to the high volatility, flammability, and toxicity of NAE. On the contrary, aqueous electrolytes are non-flammable, low-toxic, and have a low installation cost for humidity control in the production line. In this scenario, we develop a new aqueous rechargeable Li-ion full-cell composed of high-voltage cathode material as LiCoO2 (LCO) and a safe nanostructured anode material as Li2TiO3 (LTO). Both pure-phase LTO and LCO nanopowders are prepared by hydrothermal route and their structural and electrochemical properties are studied in detail. Simultaneously, the electrochemical performances of these electrodes are tested in both half- and full-cell configurations in presence of saturated 1 mole L−1 Li2SO4 aqueous electrolyte medium. Pt//LCO and Pt//LTO half-cells deliver high discharge capacities of 142 and 133 mAh g−1 at 0.5 C rate with capacity retention of ~95% and 94% after 50 cycles with a Coulombic efficiency of 98.25% and 99.89%, respectively. The electrochemical performance of a LTO//LCO full cell is investigated for the first time. It reveals a discharge capacity of 135 mAh g−1 at 0.5 C rate (50th cycle) with a capacity retention of 94% and a Coulombic efficiency of 99.7%

Electrochemical Performance of Li₂TiO₃//LiCoO₂ Li-Ion Aqueous Cell with Nanocrystalline Electrodes

A challenge in developing high-performance lithium batteries requires a safe technology without flammable liquid electrolytes. Nowadays, two options can satisfy this claim: all-solid-state batteries and aqueous-electrolyte batteries. Commercially available Li-ion batteries utilize non-aqueous electrolytes (NAE) owing to a wide potential window (>3 V) that achieves high energy density but pose serious safety issues due to the high volatility, flammability, and toxicity of NAE. On the contrary, aqueous electrolytes are non-flammable, low-toxic, and have a low installation cost for humidity control in the production line. In this scenario, we develop a new aqueous rechargeable Li-ion full-cell composed of high-voltage cathode material as LiCoO2 (LCO) and a safe nanostructured anode material as Li2TiO3 (LTO). Both pure-phase LTO and LCO nanopowders are prepared by hydrothermal route and their structural and electrochemical properties are studied in detail. Simultaneously, the electrochemical performances of these electrodes are tested in both half- and full-cell configurations in presence of saturated 1 mole L−1 Li2SO4 aqueous electrolyte medium. Pt//LCO and Pt//LTO half-cells deliver high discharge capacities of 142 and 133 mAh g−1 at 0.5 C rate with capacity retention of ~95% and 94% after 50 cycles with a Coulombic efficiency of 98.25% and 99.89%, respectively. The electrochemical performance of a LTO//LCO full cell is investigated for the first time. It reveals a discharge capacity of 135 mAh g−1 at 0.5 C rate (50th cycle) with a capacity retention of 94% and a Coulombic efficiency of 99.7%