Extending the π-Conjugated System in Spiro-Type Hole Transport Material Enhances the Efficiency and Stability of Perovskite Solar Modules

Hole transport materials (HTMs) are a key component of perovskite solar cells (PSCs). The small molecular 2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenyl)-amine-9,9′-spirobifluorene (spiro-OMeTAD, termed “Spiro”) is the most successful HTM used in PSCs, but its versatility is imperfect. To improve its performance, we developed a novel spiro-type HTM (termed “DP”) by substituting four anisole units on Spiro with 4-methoxybiphenyl moieties. By extending the π-conjugation of Spiro in this way, the HOMO level of the HTM matches well with the perovskite valence band, enhancing hole mobility and increasing the glass transition temperature. DP-based PSC achieves high power conversion efficiencies (PCEs) of 25.24 % for small-area (0.06 cm²) devices and 21.86 % for modules (designated area of 27.56 cm²), along with the certified efficiency of 21.78 % on a designated area of 27.86 cm². The encapsulated DP-based devices maintain 95.1 % of the initial performance under ISOS-L-1 conditions after 2560 hours and 87 % at the ISOS-L-3 conditions over 600 hours.     

Subspaces with Equal Closure

We take a new and unifying approach toward polynomial and trigonometric approximation in topological vector spaces used in analysis on R ⁿ . The idea is to show in considerable generality that in such a space a module, which is generated over the polynomials or trigonometric functions by some set, necessarily has the same closure as the module which is generated by this same set, but now over the compactly supported smooth functions. The particular properties of the ambient space or generating set are, to a large degree, irrelevant for these subspaces to have equal closure. This translation—which goes in fact beyond modules—allows us, by what is now essentially a straightforward check of a few properties, to replace many classical results in various spaces by more general statements of a hitherto unknown type. Even in the case of modules with one generator the resulting theorems on, e.g., completeness of polynomials are then significantly stronger than the classical statements. This extra precision stems from the use of quasi-analytic methods (in several variables) rather than holomorphic methods, combined with the classification of quasi-analytic weights. In one dimension this classification, which then involves the logarithmic integral, states that two well-known families of weights are essentially equal. As a side result we also obtain an integral criterion for the determinacy of multidimensional measures which is less stringent than the classical version. The approach can be formulated for Lie groups and this interpretation then shows that many classical approximation theorems are actually theorems on the unitary dual of R ⁿ , thus inviting to a change of paradigm. In this interpretation polynomials correspond to the universal enveloping algebra of R ⁿ and trigonometric functions correspond to the group algebra. It should be emphasized that the point of view, combined with the use of quasi-analytic methods, yields a rather general and precise ready-to-use tool, which can very easily be applied in new situations of interest which are not covered by this paper.     

The -module structure of -modules

Let be a regular ring, essentially of finite type over a perfect field . An -module is called a unit -module if it comes equipped with an isomorphism , where denotes the Frobenius map on , and is the associated pullback functor. It is well known that then carries a natural -module structure. In this paper we investigate the relation between the unit -structure and the induced -structure on . In particular, it is shown that if is algebraically closed and is a simple finitely generated unit -module, then it is also simple as a -module. An example showing the necessity of being algebraically closed is also given.

     

Universal homogeneous derivations of graded ϵ-commutative algebras

Let K be a commutative ring, let ? be an abelian group, and let ?:?x?→K be a commutation factor over ?.A ? graded K-algebra is said to be ?-commutative if its ?-bracket is identically zero, (K,?) derivations from a given ?-commutative ?-graded K-algebra A into bimodules are studied. It is proved that for each λ?? there exists a universal initial (k,?)-derivation of degree λ of A. For each λ?? a natural module of (K, ?, λ)-differentials of A along with a differential map is constructed. It is proved that each derivation of A canonically equipps this module with a structure of differential module. Applications and examples are given. It is shown that the first order exterior differentials which are known from the theory of smooth graded manifolds are universal initial homogeneous derivations of the sort considered hereby.     

Some Properties of Minimal Splines

S. G. Mikhlin was the first to construct systematically coordinate functions on an equidistant grid solving a system of approximate equations (called “fundamental relations”, see [5]; Goel discussed some special cases earlier in 1969; see also [1, 4, 6]). Further, the idea was developed in the case of irregular grids (which may have finite accumulation points, see [1] ). This paper is devoted to the investigation of A-minimal splines, introduced by the author; they include polynomial minimal splines which have been discussed earlier. Using the idea mentioned above, we give necessary and sufficient conditions for existence, uniqueness and g-continuity of these splines. The application of these results to polynomial splines of m-th degree on an equidistant grid leads us, in particular, to necessary and sufficient conditions for the continuity of their i-th derivative (i = 1, ?, m). These conditions do not exclude discontinuities of other derivatives (e.g. of order less than i). This allows us to give a certain classification of minimal spline spaces. It turns out that the spline classes are in one-to-one-correspondence with certain planes contained in a hyperplane.     

具有可积伸张同胚的边界扩张

研究了具有可积伸张的同胚，证明了在一定条件下这类同胚可以连续扩张到边界．     

Representations over PID's with three distinguished submodules

Let be a principal ideal domain. The -representations with one distinguished submodule are classified by a theorem of Gaußin the case of finite rank, and by the ``Stacked Bases Theorem" of Cohen and Gluck in the case of infinite rank. Results of Hill and Megibben carry this classification even further. The -representations with two distinguished pure submodules have recently been classified by Arnold and Dugas in the finite-rank case, and by the authors for countable rank. Although wild representation type prevails for -representations with three distinguished pure submodules, an extensive category of such objects was recently classified by Arnold and Dugas. We carry their groundbreaking work further, simplifying the proofs of their main results and applying new machinery to study the structure of finite- and infinite-rank representations with two, three, and four distinguished submodules. We also apply these results to the classification of Butler groups, a class of torsion-free abelian groups that has been the focus of many investigations over the last sixteen years.

     

Performance optimization of hollow fiber reverse osmosis membranes. Part II. Comparative study of flow configurations

Sensitivity evaluation of overall performance of hollow fiber membranes was performed to study the effects of such operating parameters as pressure, packing density, and fiber diameter. It is shown that in a wide range of operating conditions, fiber productivity and selectivity as dependent upon hollow fiber length exhibit a similarity property. This is demonstrated in all three flow configurations of concurrent, countercurrent, and flow inside hollow fibers.     

Types in a mixed language system

As a support for writing software, a comprehensive set of problem oriented languages appears preferable to any so-called universal language, as soon as static checking is sufficient to ensure type correctness of the mixed language program. We lay the basis for a mixed language system where this requirement is fulfilled. The general outline of the system is first sketched. Detailed consideration is then given to our basic constructs for establishing communication between languages, namely standard types and foreign types. Abstract types, such as defined in CLU, are finally shown to be a particular class of foreign types.