Synthesis and Structure Elucidation of New Regioisomeric 2‐Alkylamino‐6‐aryl‐8,9‐dihydropyrimido[4,5‐b][1,4]diazepin‐4(7H)‐ones

Novel 2‐Alkylamino‐6‐aryl‐8,9‐dihydropyrimido[4,5‐b][1,4]diazepin‐4(7H)‐ones 5a , 5b , 5c , 5d , 5e , 5f , 5g , 5h , 5i , 5j , 5k , 5l , 5m , 5n , 5o were prepared regioselectively by the reaction of 2‐alkylamino‐5,6‐diaminopyrimidin‐4(3H)‐ones 3a , 3b , 3c and dimethylamino propiophenones (Mannich bases) 4a , 4b , 4c , 4d , 4e , 4f . The combination of conventional heating and microwave irradiation approaches provided the possibility of working with both stable and sensitive diaminopyrimidines by controlling parameters such as reaction rates, temperature, and power of irradiation. All products were fully characterized by detailed NMR measurements.     

The Gamow vectors and the Schwinger effect

We introduce a ‘proper time’ formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field-theoretic problem to a quantum mechanical one in a higher dimension. The instability results from the inverted oscillator structure which appears in the Hamiltonian. We show that the ‘proper time’ unitary evolution splits into two semigroups. The semigroup associated with decaying Gamov vectors is related to the Feynman boundary conditions for the Green functions and the semigroup associated with growing Gamov vectors is related to the Dyson boundary conditions.     

On the favorable estimation for fitting heavy tailed data

Assessment of heavy tailed data and its compound sums has many applications in insurance, auditing and operational risk capital assessment among others. In this paper, we compare the classical estimators (maximum likelihood, QQ and moment estimators) with the recently introduced robust estimators of “generalized median”, “trimmed mean” and estimators based on t-score moments. We derive the exact distribution of the likelihood ratio tests of homogeneity and simple hypothesis on the tail index of a two-parameter Pareto model. Such exact tests support the assessment of the performance of estimators. In particular, we discuss some problems that one can encounter when misemploying the log-normal assumption based methods supported by the Basel II framework. Real data and simulated examples illustrate the methods.     

Trapping an intensely bright, stable sonoluminescing bubble

Previous works on single bubble sonoluminescence in sulfuric acid solutions have stressed the fact that the sonoluminescence (SL) emissions are the highest ever found, but at the same time the bubble moves in orbits. We have fixed the SL bubble spatially and at the same time we have reached higher SL emissions using another harmonic acoustic signal to produce the acoustic excitation. Multiple harmonic excitation produces up to a fourfold increase in SL emissions, reaching the peak value of about 40 microW for a moving bubble and 15 microW for a nonmoving bubble. The ability to have a bright stationary bubble also opens new research opportunities. In particular, we develop a new method to measure the absolute radius evolution of the bubble that exploits this stability.     

On some families of subsemigroups of a numerical semigroup

Semigroup Forum - To a given numerical semigroup S we associate a family of subsemigroups $$\{\partial ^nS\}$$ , $$n\in {\mathbb {N}}$$ , that permits us to understand some of the structure of S....     

Molecular structure of trans-[Co(NH3)4(NH2CH3)Cl](ClO4)2

The title compound crystallizes in the orthorhombic space group Pnma, with a = 7.9209(5), b = 9.818(1), c = 16.867(2) Å, and Z = 4. The structure was solved employing 1864 independent x-ray reflections with I>2(I) by Patterson and difference Fourier techniques and refined by full-matrix least-squares to R = 0.036. The trans-[CO(NH₃)₄(NH₂CH₃)Cl](ClO₄)₂ molecule is on a crystallographic mirror plane. The cobalt ion is in an elongated octahedral coordination with four equatorial ammonia ligands [average Co–N distance equal to 1.966(2) Å], an axial methylamine [Co–N=1.965(3)Å], and an axial chlorine ion [Co–Cl=2.2771(9)Å]. Kinetic steric effects of the complex are interpreted in terms of structural results.     

Herringbone Pattern and CH–π Bonding in the Crystal Architecture of Linear Polycyclic Aromatic Hydrocarbons

The herringbone pattern is a pervasive structural motive found in most molecular crystals involving aromatic compounds. A plot of the experimental sublimation enthalpies of members of increasing size of the acene, phenacene and p‐phenyl families versus the number of carbons uncovers a linear relationship between the two magnitudes, suggesting a major role of CH–π bonding. In this work we undertake the task of evaluating the relevance of the edge‐to‐face interaction (or CH–π bond) in the overall reticular energy of the crystal, to quantitatively assess the importance of this structural element. Following a heuristic approach, we considered the series of acenes, phenacenes and p‐phenyls and analyzed the edge‐to‐face interaction between the molecules as they occur in the experimental crystal network. Isolation of the relevant molecular dimers allows to incorporate some of the most sophisticated tools of quantum chemistry and get a reliable picture of the isolated bond. When compared to the experimental sublimation energy, our results are conclusive: this sole interaction is the largest contribution to the lattice energy, and definitively dictates the crystal architecture in all the studied cases. Elusive enough, the edge‐to‐face interaction is mainly dominated by correlation interactions, specifically in the form of dispersion and, to a less extent, of charge‐transfer terms. A suggestive picture of the bond has been obtained by displaying the differences in local electron densities calculated by either correlated or non‐correlated methods.     

Pore size distributions in polyelectrolyte multilayers determined by nuclear magnetic resonance cryoporometry

Polyelectrolyte multilayers (PEMs) are thin films, which are assembled one molecular layer at a time, by alternatingly adsorbing polycations and polyanions making use of their attractive electrostatic interaction. Since the porosity of PEMs is one of the properties of major interest, in the current work the first pore size distribution of PEMs in samples consisting of silica particles coated with poly(allylamine hydrochloride) and poly(sodium 4-styrenesulfonate) is presented. To this end, the nuclear magnetic resonance (NMR) cryoporometry technique was applied. The proton NMR signal of liquid water is analyzed assuming a log normal distribution of motional correlation times. From the results, it is possible to determine the size of water sites in the layers to around 1 nm. In addition, a slight variation with the number of layers is found. The average pore size agrees with cutoff sizes found in permeation experiments.