Subordination,rank, and determinism of multivariate stationary sequences

Necessary and sufficient conditions for an arbitrary q-variate stationary sequence x_t, t ∈ $\text{Z}$, to be deterministic are presented. A characterization of the rank r(x) of x_t, t ∈ $\text{Z}$, and a method to construct the Wold-Cramér decomposition for x_t, t ∈ $\text{Z}$, are given. Subordination of q-variate bounded orthogonally scattered vector measures is considered.     

UV/VIS Spectrophotometric Studies on the Antileukemic Agent Glyoxal bis(Amidinohydrazone) [‘Glyoxal bis(Guanylhydrazone)’]

Glyoxal bis(amidinohydrazone) (GBG) and several analogs thereof are compounds of considerable pharmacological interest, and a variety of HPLC and MECC methods have been developed for their analysis. In these methods, detection is invariably based on the strong UV absorption of the compound. Yet, almost nothing has been known of their UV and VIS spectral properties. In the present paper the UV and VIS Spectroscopy of GBG has been studied in several solvent systems (water, 0. 03 M aqueous sodium acetate buffer, 0. 1 inM aqueous NaOH and dimethylsulfoxide). In the case of solutions in bare water, the shape of the UV spectrum depends drastically on concentration, probably because of changes in the species distribution of GBG as a function of concentration. The spectrum comprises one maximum at ca. 200 nm, and between ca. 250 nin and 400 nm an absorption region with distinctly higher absorbance. In the case of aqueous sodium acetate as well as NaOH solutions, one strong maximum can be detected (at ca. 285–288 nm and 332–337 nm, respectively). In both cases, the maximum occurs at constant wavelength, being independent of concentration. In dimethylsulfoxide, the spectrum of GBG contains an absorption band at distinctly higher wavelengths (λ_max 354 nm) than in any one of the aqueous solvents studied, indicating that solvent effects are considerable in the UV spectrum of GBG. In no case, distinct absorption could be detected at wavelengths higher than 400 nm. The results indicate that if aqueous media are used as elements in HPLC analyses of bis(amidinohydrazones) or as solvents in direct UV analysis, they must be buffered.     

Highly Robust but Surface‐Active: An N‐Heterocyclic Carbene‐Stabilized Au25 Nanocluster

Surface organic ligands play a critical role in stabilizing atomically precise metal nanoclusters in solutions. However, it is still challenging to prepare highly robust ligated metal nanoclusters that are surface‐active for liquid‐phase catalysis without any pre‐treatment. Now, an N‐heterocyclic carbene‐stabilized Au₂₅ nanocluster with high thermal and air stabilities is presented as a homogenous catalyst for cycloisomerization of alkynyl amines to indoles. The nanocluster, characterized as [Au₂₅(ⁱPr₂‐bimy)₁₀Br₇]²⁺ (ⁱPr₂‐bimy=1,3‐diisopropylbenzimidazolin‐2‐ylidene) ( 1 ), was synthesized by direct reduction of AuSMe₂Cl and ⁱPr₂‐bimyAuBr with NaBH₄ in one pot. X‐ray crystallization analysis revealed that the cluster comprises two centered Au₁₃ icosahedra sharing a vertex. Cluster 1 is highly stable and can survive in solution at 80 °C for 12 h, which is superior to Au₂₅ nanoclusters passivated with phosphines or thiols. DFT computations reveal the origins of both electronic and thermal stability of 1 and point to the probable catalytic sites. This work provides new insights into the bonding capability of N‐heterocyclic carbene to Au in a cluster, and offers an opportunity to probe the catalytic mechanism at the atomic level.     

Self-passivating edge reconstructions of graphene

Planar reconstruction patterns at the zigzag and armchair edges of graphene were investigated with density-functional theory. It was unexpectedly found that the zigzag edge is metastable and a planar reconstruction spontaneously takes place at room temperature. The reconstruction changes electronic structure and self-passivates the edge with respect to adsorption of atomic hydrogen from a molecular atmosphere.     

Cortical sensitivity to periodicity of speech sounds

Previous non-invasive brain research has reported auditory cortical sensitivity to periodicity as reflected by larger and more anterior responses to periodic than to aperiodic vowels. The current study investigated whether there is a lower fundamental frequency (F0) limit for this effect. Auditory evoked fields (AEFs) elicited by natural-sounding 400 ms periodic and aperiodic vowel stimuli were measured with magnetoencephalography. Vowel F0 ranged from normal male speech (113 Hz) to exceptionally low values (9 Hz). Both the auditory N1m and sustained fields were larger in amplitude for periodic than for aperiodic vowels. The AEF sources for periodic vowels were also anterior to those for the aperiodic vowels. Importantly, the AEF amplitudes and locations were unaffected by the F0 decrement of the periodic vowels. However, the N1m latency increased monotonically as F0 was decreased down to 19 Hz, below which this trend broke down. Also, a cascade of transient N1m-like responses was observed in the lowest F0 condition. Thus, the auditory system seems capable of extracting the periodicity even from very low F0 vowels. The behavior of the N1m latency and the emergence of a response cascade at very low F0 values may reflect the lower limit of pitch perception.     

Water Activity and Freezing Points in Aqueous Solutions of Manganese Nitrate: Experimental and Modeling

The water activities of manganese nitrate solutions were measured using a humidity sensor instrument up to almost the saturation molality at 298.15 K; the thermodynamic properties of the system were described by the Pitzer model and specific interaction theory (SIT). The evaluation of the ion interaction parameters for the Pitzer model and SIT were carried out using experimental freezing points and osmotic coefficients of manganese nitrate aqueous solutions, collected from the open literature, and the water activity data measured in this work. A set of Pitzer and SIT parameters were estimated using a temperature dependency, that enables us to cover wider temperature ranges, and consequently calculate system properties to higher molalities. Both approaches represent very satisfactorily, and with similar accuracy, the experimental data and the calculated manganese nitrate molal activity coefficients are comparable to those already published for analogous systems. Additionally, the Pitzer model was also able to calculate the ice curve and the solubility branch of manganese nitrate hexahydrate up to a salt solution 6.5 mol·kg^?1.     

Atomically Precise Nanocluster Assemblies Encapsulating Plasmonic Gold Nanorods

The self‐assembled structures of atomically precise, ligand‐protected noble metal nanoclusters leading to encapsulation of plasmonic gold nanorods (GNRs) is presented. Unlike highly sophisticated DNA nanotechnology, this strategically simple hydrogen bonding‐directed self‐assembly of nanoclusters leads to octahedral nanocrystals encapsulating GNRs. Specifically, the p‐mercaptobenzoic acid (pMBA)‐protected atomically precise silver nanocluster, Na₄[Ag₄₄(pMBA)₃₀], and pMBA‐functionalized GNRs were used. High‐resolution transmission and scanning transmission electron tomographic reconstructions suggest that the geometry of the GNR surface is responsible for directing the assembly of silver nanoclusters via H‐bonding, leading to octahedral symmetry. The use of water‐dispersible gold nanoclusters, Au_≈250(pMBA)_n and Au₁₀₂(pMBA)₄₄, also formed layered shells encapsulating GNRs. Such cluster assemblies on colloidal particles are a new category of precision hybrids with diverse possibilities.