Rh-Catalyzed Decarbonylative Cross-Coupling between o-Carboranes and Twisted Amides: A Regioselective,Additive-Free,and Concise Late-Stage Carboranylation

The convenient cross-coupling of sp² or sp³ carbons with a specific boron vertex on carborane cage represents significant synthetic values and insurmountable challenges. In this work, we report an Rh-catalyzed reaction between o-carborane and N-acyl-glutarimides to construct various B_cage−C bonds. Under the optimized condition, the removable imine directing group (DG) leads to B(3)− or B(3,6)−C couplings, while the pyridyl DG leads to B(3,5)−Ar coupling. In particular, an unexpected rearrangement of amide reagent is observed in pyridyl directed B(4)−C(sp³) formation. This scalable protocol has many advantages, including easy access, the use of cheap and widely available coupling agents, no requirement of an external ligand, base or oxidant, high efficiency, and a broad substrate scope. Leveraging the Rh^I dimer and twisted amides, this method enables straightforward access to diversely substituted and therapeutically important carborane derivatives at boron site, and provides a highly valuable vista for carborane-based drug screening.     

Probabilizing parking functions

We explore the link between combinatorics and probability generated by the question “What does a random parking function look like?” This gives rise to novel probabilistic interpretations of some elegant, known generating functions. It leads to new combinatorics: how many parking functions begin with i? We classify features (e.g., the full descent pattern) of parking functions that have exactly the same distribution among parking functions as among all functions. Finally, we develop the link between parking functions and Brownian excursion theory to give examples where the two ensembles differ.     

Quantitative estimation of constituents in fly ash by lithium tetraborate fusion

Silica is removed from fly ash sample by hydroflourination for its effective determination gravimetrically and the remaining residue is subjected to lithium tetraborate (Li₂B₄O₇) fusion followed by dissolution in dilute nitric acid to obtain a clear solution in which elements including aluminum (Al), iron (Fe), calcium (Ca), magnesium (Mg), sodium (Na), potassium (K), titanium (Ti), vanadium (V), chromium (Cr), manganese (Mn), nickel (Ni), copper (Cu) and zinc (Zn), have been determined by Flame Atomic Absorption Spectrometry (FAAS). Two fly ash samples analyzed by the proposed method have been received from the National Council of Cement and Building Materials (NCCBM), India (proposed CRM in future) and fly ash CRM 1633 (b) from NIST, USA. The validity of the method has been established by analyzing fly ash CRM 1633 (b) as reference standard. The standard deviation has been calculated for each measurement.     

Numerical solutions for jump-diffusions with regime switching

This paper is devoted to numerical solutions for a class of jump-diffusions with regime switching. After briefly reviewing the notion of jump-diffusions with regime switching, finite-difference procedures are constructed. Under simple conditions, it is proved that the algorithm converges to the desired limit by means of a martingale problem formulation. Numerical experiments are carried out to demonstrate the performance of the algorithm.     

DISCRETE UNIFORM STRUCTURES AND QUASITOPOI

It is known that no non-trivial subcategory of the category of topological spares is a quasitopos in the sense of Penon. The purpose of this note is to establish the existence of a proper class of sub-categories of the category of uniform spaces which are quasitopoi. These subcategories are generated by certain proximally discrete uniform spaces which correspond to each infinite regular cardinal.     

On algebraic Riccati equations associated with M-matrices

We consider the algebraic Riccati equation for which the four coefficient matrices form an M-matrix K. When K is a nonsingular M-matrix or an irreducible singular M-matrix, the Riccati equation is known to have a minimal nonnegative solution and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where K is a reducible singular M-matrix. Under a regularity assumption on the M-matrix K, we show that the Riccati equation still has a minimal nonnegative solution. We also study the properties of this particular solution and explain how the solution can be found by existing methods.     

A mean-reverting SDE on correlation matrices

We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright–Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a useful connection with Wishart processes that makes understand how we get the full SDE. Then, we focus on the simulation of this diffusion and present discretization schemes that achieve a second-order weak convergence. Last, we give a possible application of these processes in finance and argue that they could easily replace and improve the standard assumption of a constant correlation.     

Moduli spaces of arrangements of 10 projective lines with quadruple points

We classify moduli spaces of arrangements of 10 lines with quadruple points. We show that moduli spaces of arrangements of 10 lines with quadruple points may consist of more than 2 disconnected components, namely 3 or 4 distinct points. We also present defining equations to those arrangements whose moduli spaces are still reducible after taking quotients of complex conjugations.