A Shapley-based Groves mechanism: when the mechanism designer plays the wise man

We define two mechanisms. The first one implements the Shapley value to define some monetary transfers, but it is not incentive compatible. The second one implements only in expectation the same solution and it is a Groves mechanism. While inheriting all the properties of this family, it is also budget-balanced (still in expectation). The trick is to ask the mechanism designer to insert/remove some utility and to take/give it back at the end.     

REPRESENTATIONS OF A LOOP LIE ALGEBRA ASSOCIATED WITH QUANTUM PLANE

In this article,some modules over a loop Lie algebra associated to quantum plane are constructed.The isomorphism classes among these modules are also determined.     

The Motion of a Quantum Mechanical Particle Under the Inverse Square Potential

We consider the motion of a quantum mechanical particle under the inverse square potential k /(|x| 2 ), where k is a constant and x ] R N . Applying the method of the Friedrichs extension, we show that there exists the motion of such a particle as long as k > m N /4. Our treatment gives the best possible value of k when 1 h N h 4.     

Partial Decomposition Bases and Global Warfield Groups

The class of abelian groups with partial decomposition bases was developed by the first author in order to generalize Barwise and Eklof's classification of torsion groups in L_∞ω. In this article, we continue to explore algebraic characteristics of this class and establish a uniqueness theorem, extending our previous work on mixed p-local groups to the global case. It is shown that groups with partial decomposition bases are characterized in terms of Warfield groups and k-groups of Hill and Megibben. In fact, we prove that the class of groups with partial decomposition bases is identical to the class of k-groups, and, as such, closed under direct summands, and that every finitely generated subgroup of a k-group is locally nice. Also, we introduce and explore subgroups possessing a partial subbasis. As an application, it is shown that isotype k-subgroups of abelian groups are k-groups.     

On a New High Dimensional Weisfeiler-Lehman Algorithm

We investigate the following problem: how different can a cellular algebra be from its Schurian closure, i.e., the centralizer algebra of its automorphism group? For this purpose we introduce the notion of a Schurian polynomial approximation scheme measuring this difference. Some natural examples of such schemes arise from high dimensional generalizations of the Weisfeiler-Lehman algorithm which constructs the cellular closure of a set of matrices. We prove that all of these schemes are dominated by a new Schurian polynomial approximation scheme defined by the m-closure operators. A sufficient condition for the m-closure of a cellular algebra to coincide with its Schurian closure is given.     

Inequalities for two type potential operators on differential forms

The purpose of this paper is to derive some strong-type inequalities for convolution type potential operator applied on differential forms. Caccioppoli-type inequalities for integral type potential operator acting on A-harmonic tensor are also obtained.     

Potential measures for spectrally negative Markov additive processes with applications in ruin theory

The Markov additive process (MAP) has become an increasingly popular modeling tool in the applied probability literature. In many applications, quantities of interest are represented as functionals of MAPs and potential measures, also known as resolvent measures, have played a key role in the representations of explicit solutions to these functionals. In this paper, closed-form solutions to potential measures for spectrally negative MAPs are found using a novel approach based on algebraic operations of matrix operators. This approach also provides a connection between results from fluctuation theoretic techniques and those from classical differential equation techniques. In the end, the paper presents a number of applications to ruin-related quantities as well as verification of known results concerning exit problems.     

Impact of Electrostatic Interaction on Non-radiative Recombination Energy Losses in Organic Solar Cells Based on Asymmetric Acceptors

Reducing non-radiative recombination energy loss (ΔE₃) is one key to boosting the efficiency of organic solar cells. Although the recent studies have indicated that the Y-series asymmetric acceptors-based devices featured relatively low ΔE₃, the understanding of the energy loss mechanism derived from molecular structure change is still lagging behind. Herein, two asymmetric acceptors named BTP-Cl and BTP-2Cl with different terminals were synthesized to make a clear comparative study with the symmetric acceptor BTP-0Cl. Our results suggest that asymmetric acceptors exhibit a larger difference of electrostatic potential (ESP) in terminals and semi-molecular dipole moment, which contributes to form a stronger π–π interaction. Besides, the experimental and theoretical studies reveal that a lower ESP-induced intermolecular interaction can reduce the distribution of PM6 near the interface to enhance the built-in potential and decrease the charge transfer state ratio for asymmetric acceptors. Therefore, the devices achieve a higher exciton dissociation efficiency and lower ΔE₃. This work establishes a structure-performance relationship and provides a new perspective to understand the state-of-the-art asymmetric acceptors.