Postsynthetic modification of zirconium metal-organic frameworks

Metal-organic frameworks (MOFs) have been in the spotlight for a number of years due to their chemical and topological versatility. As MOF research has progressed, highly functionalised materials have become desirable for specific applications, and in many cases the limitations of direct synthesis have been realised. This has resulted in the search for alternative synthetic routes, with postsynthetic modification (PSM), a term used to collectively describe the functionalisation of pre-synthesised MOFs whilst maintaining their desired characteristics, becoming a topic of interest. Advances in the scope of reactions performed are reported regularly; however reactions requiring harsh conditions can result in degradation of the framework. Zirconium-based MOFs present high chemical, thermal and mechanical stabilities, offering wider opportunities for the scope of reaction conditions that can be tolerated, which has seen a number of successful examples reported. This microreview discusses pertinent examples of PSM resulting in enhanced properties for specific applications, alongside fundamental transformations, which are categorised broadly into covalent modifications, surface transformations, metalations, linker and metal exchange, and cluster modifications

The Gerby Gopakumar-Mari\~no-Vafa Formula

We prove a formula for certain cubic $\Z_n$-Hodge integrals in terms of loop Schur functions. We use this identity to prove the Gromov-Witten/Donaldson-Thomas correspondence for local $\Z_n$-gerbes over \proj^1.Comment: 43 pages, Published Versio

Dense gap-junction connections support dynamic Turing structures in the cortex

The recent report by Fukuda et al [1] provides convincing evidence for dense gap-junction connectivity between inhibitory neurons in the cat visual cortex, each neuron making 60 +/- 12 gap-junction dendritic connections with neurons in both the same and adjoining orientation columns. These resistive connections provide a source of diffusive current to the receiving neuron, supplementing the chemical-synaptic currents generated by incoming action-potential spike activity. Fukuda et al describe how the gap junctions form a dense and homogeneous electrical coupling of interneurons, and propose that this diffusion-coupled network provides the substrate for synchronization of neuronal populations. To date, large-scale population-based mathematical models of the cortex have ignored diffusive communication between neurons. Here we augment a well-established mean-field cortical model [2] by incorporating gap-junction-mediated diffusion currents, and we investigate the implications of strong diffusive coupling. The significant result is the model prediction that the 2D cortex can spontaneously generate centimetre-scale Turing structures (spatial patterns), in which regions of high-firing activity are intermixed with regions of low-firing activity (see Fig. 1). Since coupling strength decreases with increases in firing rate, these patterns are expected to exchange contrast on a slow time-scale, with low-firing patches increasing their activity at the expense of high-firing patches. These theoretical predictions are consistent with the slowly fluctuating large-scale brain-activity images detected from the BOLD (blood oxygen-level-dependent) signal [3]

Employee Heterogeneity and Within-Firm Experience-Earnings Profiles: A Nonparametric Analysis

Abstract Motivated by a priori uncertainty with respect to the parametric specification of the earnings function, I model the earnings function as semiparametric partially linear model and follow the estimation approach described in Robinson (1988). Using data from the personnel records of a large major UK based financial sector employer, I let years of within-firm and pre-firm experience form the nonparametrically modelled component of the earnings function. It is shown that the estimated within-firm experience earnings profiles, which are conditional upon a given number years of pre-firm experience accumulated before entry, converge and even overtake as years of pre-firm experience increases. This result can be explained with the recognition of unobservable explanatory variables, such as the match and individual quality of the employees, both of which are a function of years of within- and pre-firm experience and wages

Skew-closed categories

Spurred by the new examples found by Kornel Szlach\'anyi of a form of lax monoidal category, the author felt the time ripe to publish a reworking of Eilenberg-Kelly's original paper on closed categories appropriate to the laxer context. The new examples are connected with bialgebroids. With Stephen Lack, we have also used the concept to give an alternative definition of quantum category and quantum groupoid. Szlach\'anyi has called the lax notion {\em skew monoidal}. This paper defines {\em skew closed category}, proves Yoneda lemmas for categories enriched over such, and looks at closed cocompletion.Comment: Version 2 corrects a mistake in axiom (2.4) noticed by Ignacio Lopez Franco. Only the corrected axiom was used later in the paper so no other consequential change was needed. A few obvious typos have been corrected. Some material on weighted colimits, composite modules and skew-promonoidal categories has been added. Version 3 adds Example 23 and corrects a few typos.

How Prices are Determined

PDF pages: 2

DASH: Delivering and Serving Hope

The main purpose of DASH is to reach out to the community with simple acts such as giving food, giving service, and helping those in need.https://digitalscholarship.unlv.edu/educ_sys_202/1082/thumbnail.jp