How metal (hydr)oxides are protonated in aqueous media: the (n+1) rule and the role of the interfacial potential

The mechanism of the protonation of solid metal (hydr)oxides in aqueous media, which is closely interrelated to many processes of great technological and environmental importance, has been elucidated using simulation and experimental work. The electrical potential, smeared out at the interfacial region, changes the concentration of the H+ ions on the surface of the (hydr)oxide, thus promoting or hindering protonation. This is manifested by the shifts of the protonation peaks of the various kinds of surface sites and the appearance of an extra peak in the differential potentiometric titration curve.     

Versions of Normality and Some Weak Forms of the Axiom of Choice

We investigate the set theoretical strength of some properties of normality, including Urysohn's Lemma, Tietze-Urysohn Extension Theorem, normality of disjoint unions of normal spaces, and normality of F_σ subsets of normal spaces.     

Reactivity of 2‐Methyl‐4H‐3,1‐benzoxazin‐4‐ones and 2‐Methyl‐4H‐pyrido[2,3‐d][1,3]oxazin‐4‐one under Microwave Irradiation Conditions

The reactivity of variably substituted 2‐methyl‐4H‐3,1‐benzoxazin‐4‐ones and 2‐methyl‐4H‐pyrido[2,3‐d][1,3]oxazin‐4‐one towards carbon and oxygen nucleophiles under microwave irradiation conditions was investigated. Optimization of the reaction conditions of oxazinones with carbon nucleophiles led to the synthesis of a series of 4‐hydroxy‐quinolin‐2‐ones and 4‐hydroxy‐1,8‐naphthyridin‐2‐ones in high yields, whereas reaction with a variety of alcohols proceeded smoothly to the formation of the corresponding N‐acetyl‐anthranilates and nicotinates.     

Countable compact Hausdorff spaces need not be metrizable in ZF

We show that the existence of a countable, first countable, zero-dimensional, compact Hausdorff space which is not second countable, hence not metrizable, is consistent with ZF.

     

Some weak forms of the Baire category theorem

We show that the statement (K12) “separable, countably compact, regular spaces are Baire” is deducible from a strictly weaker form than AC, namely, CAC(?) (the axiom of choice for countable families of non‐empty subsets of the real line ?). We also find some characterizations of the axiom of dependent choices.     

Disjoint Unions of Topological Spaces and Choice

We find properties of topological spaces which are not shared by disjoint unions in the absence of some form of the Axiom of Choice.     

Coherent state transfer between an electron and nuclear spin in (15)N@C(60)

Electron spin qubits in molecular systems offer high reproducibility and the ability to self-assemble into larger architectures. However, interactions between neighboring qubits are "always on," and although the electron spin coherence times can be several hundred microseconds, these are still much shorter than typical times for nuclear spins. Here we implement an electron-nuclear hybrid scheme which uses coherent transfer between electron and nuclear spin degrees of freedom in order to both effectively turn on or off interqubit coupling mediated by dipolar interactions and benefit from the long nuclear spin decoherence times (T(2n)). We transfer qubit states between the electron and (15)N nuclear spin in (15)N@C(60) with a two-way process fidelity of 88%, using a series of tuned microwave and radio frequency pulses and measure a nuclear spin coherence lifetime of over 100 ms.     

The Boolean prime ideal theorem and products of cofinite topologies

We show:

1. The Boolean Prime Ideal theorem is equivalent to each one of the statements:
   1. “For every family of compact spaces, for every family of basic closed sets of the product with the fip there is a family of subbasic closed sets () with the fip such that for every ”.
   2. “For every compact Loeb space (the family of all non empty closed subsets of has a choice function) and for every set X the product is compact”.
2. (: the axiom of choice restricted to families of finite sets) implies “every well ordered product of cofinite topologies is compact” and “every well ordered basic open cover of a product of cofinite topologies has a finite subcover”.
3. (: the axiom of choice restricted to countable families of finite sets) iff “every countable product of cofinite topologies is compact”.
4. (: every filter of extends to an ultrafilter) is equivalent to the proposition “for every compact Loeb space having a base of size and for every set X of size the product is compact”.

     

On null geodesically complete spacetimes under NEC and NGC: Is the Gao-Wald “time dilation” a topological effect?

We review a theorem of Gao-Wald on a kind of a gravitational “time delay” effect in null geodesically complete spacetimes under NEC and NGC, and we observe that it is not valid anymore throughout its statement, as well as a conclusion that there is a class of cosmological models where particle horizons are absent, if one substituted the manifold topology with a finer (spacetime) topology. Since topologies of the Zeeman-Göbel class incorporate the causal, differential, and conformal structure of a spacetime and there are serious mathematical arguments in favour of such topologies and against the manifold topology, there is a strong evidence that “time dilation” theorems of this kind are topological in nature rather than having a particular physical meaning.