Biodegradable polymers have attracted much attention from an environmental point of view. Optically pure lactic acid that can be prepared by fermentation is one of the important raw materials for biodegradable polymer. The separation and purification of lactic acid from the fermentation broth are the major portions of the production costs. We proposed the application of supported ionic liquid membranes to recovering lactic acid. In this paper, the effect of ionic liquids, such as Aliquat 336, CYPHOS IL-101, CYPHOS IL-102, CYPHOS IL-104, CYPHOS IL-109 and CYPHOS IL-111 on the lactic acid permeation have been studied. Aliquat 336, CYPHOS IL-101 and CYPHOS IL-102 were found to be the best membrane solvents as far as membrane stability and permeation of lactic acid are concerned. CYPHOS IL-109 and CYPHOS IL-111 were found to be unsuitable, as they leak out from the pores of the supported liquid membrane (SLM), thereby allowing free transport of lactic acid as well as hydrochloric acid. CYPHOS IL-102 was found to be the most adequate (Permeation rate = 60.41%) among these ionic liquids as far as the separation of lactic acid is concerned. The permeation mechanisms, by which ionic liquid-water complexes act as the carrier of lactate and hydrochloric acid, were proposed. The experimental permeation results have been obtained as opposed to the expected values from the solution-diffusion mechanism.

Development of economical and high-performance electrocatalysts for the oxygen evolution reaction (OER) is of tremendous interest for future applications as sustainable energy materials. Here, a unique member of efficient OER electrocatalysts has been developed based upon structurally versatile dumbbell-shaped ternary transition-metal (Cu, Ni, Co) phosphates with a three-dimensional (3D) (Cu2(OH)­(PO4)/Ni3(PO4)2·8H2O/Co3(PO4)2·8H2O) (CNCP) structure. This structure is prepared using a simple aqueous stepwise addition of metal ion source approach. Various structural investigations demonstrate highly crystalline nature of the composite structure. Apart from the unique structural aspect, it is important that the CNCP composite structure has proved to be an excellent electrocatalyst for OER performance in comparison with its binary or constituent phosphate under alkaline and neutral conditions. Notably, the CNCP electrocatalyst displays a much lower overpotential of 224 mV at a current density of 10 mA cm–2 and a lower Tafel slope of 53 mV dec–1 with high stability in alkaline medium. In addition, X-ray photoelectron spectroscopy analysis suggested that the activity and long-term durability for the OER of the ternary 3D metal phosphate are due to the presence of electrochemically dynamic constituents such as Ni and Co and their resulting synergistic effects, which was further supported by theoretical studies. Theoretical calculations also reveal that the incredible OER execution was ascribed to the electron redistribution set off in the presence of Ni and Cu and the most favorable interaction between the *OOH intermediate and the active sites of CNCP. This work may attract the attention of researchers to construct efficient 3D ternary metal phosphate catalysts for various applications in the field of electrochemistry.

As lithium-ion battery technology becomes widely popular with increasing demand for efficient energy-storage devices for a wide range of applications, the scarcity of lithium resources poses a concern for increasing costs. Replacing lithium with much more abundant sodium in combination with abundant transition metals such as iron (instead of traditionally used cobalt or nickel) as the charge compensation center in the cathode materials is expected to make large-scale battery technology a reality. To activate iron as a reversible redox center, oxyanions (XO4) n− have been introduced to stabilize the structures and raise the redox potentials, and silicates (X = Si, n = 4) form the best candidate group in terms of abundance and cost. In this regard, we explored the Na2O-FeO-SiO2 pseudoternary system and identified a new phase, Na2Fe2Si2O7, with an efficient chemical composition for charge accumulation (Na/Fe = 1), providing a large one-electron theoretical capacity of 164.5 mAhg–1 as a sodium-ion battery cathode.

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It is well-known that overparametrized neural networks trained using gradient-based methods quickly achieve small training error with appropriate hyperparameter settings. Recent papers have proved this statement theoretically for highly overparametrized networks under reasonable assumptions. These results either assume that the activation function is ReLU or they crucially depend on the minimum eigenvalue of a certain Gram matrix depending on the data, random initialization and the activation function. In the later case, existing works only prove that this minimum eigenvalue is non-zero and do not provide quantitative bounds. On the empirical side, a contemporary line of investigations has proposed a number of alternative activation functions which tend to perform better than ReLU at least in some settings but no clear understanding has emerged. This state of affairs underscores the importance of theoretically understanding the impact of activation functions on training. In the present paper, we provide theoretical results about the effect of activation function on the training of highly overparametrized 2-layer neural networks. A crucial property that governs the performance of an activation is whether or not it is smooth. For non-smooth activations such as ReLU, SELU and ELU, all eigenvalues of the associated Gram matrix are large under minimal assumptions on the data. For smooth activations such as tanh, swish and polynomial, the situation is more complex. If the subspace spanned by the data has small dimension then the minimum eigenvalue of the Gram matrix can be small leading to slow training. But if the dimension is large and the data satisfies another mild condition, then the eigenvalues are large. If we allow deep networks, then the small data dimension is not a limitation provided that the depth is sufficient. We discuss a number of extensions and applications of these results.