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Convex Analysisの二,三の進展について

There is still an ongoing effort to search for sustainable, clean and highly efficient energy generation to satisfy the energy needs of modern society. Among various advanced technologies, electrocatalysis for the oxygen evolution reaction (OER) plays a key role and numerous new electrocatalysts have been developed to improve the efficiency of gas evolution. Along the way, enormous effort has been devoted to finding high-performance electrocatalysts, which has also stimulated the invention of new techniques to investigate the properties of materials or the fundamental mechanism of the OER. This accumulated knowledge not only establishes the foundation of the mechanism of the OER, but also points out the important criteria for a good electrocatalyst based on a variety of studies. Even though it may be difficult to include all cases, the aim of this review is to inspect the current progress and offer a comprehensive insight toward the OER. This review begins with examining the theoretical principles of electrode kinetics and some measurement criteria for achieving a fair evaluation among the catalysts. The second part of this review acquaints some materials for performing OER activity, in which the metal oxide materials build the basis of OER mechanism while non-oxide materials exhibit greatly promising performance toward overall water-splitting. Attention of this review is also paid to in situ approaches to electrocatalytic behavior during OER, and this information is crucial and can provide efficient strategies to design perfect electrocatalysts for OER. Finally, the OER mechanism from the perspective of both recent experimental and theoretical investigations is discussed, as well as probable strategies for improving OER performance with regards to future developments.

Electrocatalysis for the oxygen evolution reaction: recent development and future perspectives

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

Sunlight is by far the most plentiful renewable energy resource, providing Earth with enough power to meet all of humanity's needs several hundred times over. However, it is both diffuse and intermittent, which presents problems regarding how best to harvest this energy and store it for times when the sun is not shining. Devices that use sunlight to split water into hydrogen and oxygen could be one solution to these problems, because hydrogen is an excellent fuel. However, if such devices are to become widely adopted, they must be cheap to produce and operate. Therefore, the development of electrocatalysts for water splitting that comprise only inexpensive, earth-abundant elements is critical. In this Review, we investigate progress towards such electrocatalysts, with special emphasis on how they might be incorporated into photoelectrocatalytic water-splitting systems and the challenges that remain in developing these devices. Splitting water is an attractive means by which energy — either electrical and/or light — is stored and consumed on demand. Active and efficient catalysts for anodic and cathodic reactions often require precious metals. This Review covers base-metal catalysts that can afford high performance in a more sustainable and available manner.

Earth-abundant catalysts for electrochemical and photoelectrochemical water splitting

Introduction to linear and nonlinear programming

In photosynthesis, water is oxidized at a protein-bound Mn4Ca complex. Artificial water-oxidation catalysts that are similarly efficient and based on inexpensive and abundant materials are of great interest. Recently, assembly of a catalyst as an amorphous layer on inert cathodes by electrodeposition starting from an aqueous solution of cobalt ions and potassium phosphate has been reported. X-ray absorption spectroscopy on the cobalt catalyst film (CoCF) suggests that its central structural unit is a cluster of interconnected complete or incomplete CoIII−oxo cubanes. Potassium ligation to Co-bridging oxygens could result in Co3K(μ-O)4 cubanes, in analogy to the Mn3Ca(μ-O)4 cubane motif proposed for the photosynthetic Mn complex. The similarities in function and oxidative self-assembly of CoCF and the catalytic Mn complex in photosynthesis are striking. Our study establishes a close analogy also with respect to the metal−oxo core of the catalyst.

Cobalt−Oxo Core of a Water-Oxidizing Catalyst Film

A class of mixing processes arising in the theory of identification of linear systems will be introduced. The main results of the paper are: a moment inequality, a uniform law of large numbers and its analogue when arithmetic mean is replaced by exponential smoothing.

On a class of mixing processes

Identification of ARX systems with non-stationary inputs - asymptotic analysis with application to adaptive input design

It is proved that the sequence of recursive estimators generated by Ljung’s scheme combined with a suitable restarting mechanism converges under certain conditions with rate $O_M (n^{{{ - 1} / 2}} )$, where the rate is measured by the $L_q $-norm of the estimation error for any $1 \leq q < \infty $.

Rate of convergence of recursive estimators

The active site of photosynthetic water oxidation by Photosystem II (PSII) is a manganese-calcium cluster (Mn(4)CaO(5)). A postulated catalytic base is assumed to be crucial. CP43-Arg357, which is a candidate for the identity of this base, is a second-sphere ligand of the Mn(4)-Ca cluster and is located near a putative proton exit pathway, which begins with residue D1-D61. Transient absorption spectroscopy and time-resolved O(2) polarography reveal that in the D1-D61N mutant, the transfer of an electron from the Mn(4)CaO(5) cluster to Y(Z)(OX) and O(2) release during the final step of the catalytic cycle, the S(3)-S(0) transition, proceed simultaneously but are more dramatically decelerated than previously thought (t(1/2) of up to ~50 ms vs a t(1/2) of 1.5 ms in the wild type). Using a bare platinum electrode to record the flash-dependent yields of O(2) from mutant and wild-type PSII has allowed the observation of the kinetics of release of O(2) from extracted thylakoid membranes at various pH values and in the presence of deuterated water. In the mutant, it was possible to resolve a clear lag phase prior to the appearance of O(2), indicating formation of an intermediate before the onset of O(2) formation. The lag phase and the photochemical miss factor were more sensitive to isotope substitution in the mutant, indicating that proton efflux in the mutant proceeds via an alternative pathway. The results are discussed in comparison with earlier results obtained from the substitution of CP43-Arg357 with lysine and in regard to hypotheses concerning the nature of the final steps in photosynthetic water oxidation. These considerations led to the conclusion that proton expulsion during the initial phase of the S(3)-S(0) transition starts with the deprotonation of the primary catalytic base, probably CP43-Arg357, followed by efficient proton egress involving the carboxyl group of D1-D61 in a process that constitutes the lag phase immediately prior to O(2) formation chemistry.

The D1-D61N mutation in Synechocystis sp. PCC 6803 allows the observation of pH-sensitive intermediates in the formation and release of O₂ from photosystem II.

László Gerencsér

Papers

Cobalt−Oxo Core of a Water-Oxidizing Catalyst Film

On a class of mixing processes

Identification of ARX systems with non-stationary inputs - asymptotic analysis with application to adaptive input design

Rate of convergence of recursive estimators

The D1-D61N mutation in Synechocystis sp. PCC 6803 allows the observation of pH-sensitive intermediates in the formation and release of O₂ from photosystem II.