Singularly Perturbed Population Models with Reducible Migration Matrix: 2. Asymptotic Analysis and Numerical Simulations

The paper is concerned with asymptotic analysis of a singularly perturbed system of McKendrick equations of population with age and geographical structure. It is assumed that the migration between geographical patches occurs on a much faster time scale than the demographic processes and is described by a reducible Kolmogorov matrix. We apply a novel regularizing technique which makes the error estimates easier than that in previous papers and provide a numerical illustration of theoretical results.     

MEROMORPHIC FUNCTIONS WITH BOUNDED BOUNDARY ROTATION

In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given.     

Normed spaces equivalent to inner product spaces and stability of functional equations

Let ${(X,\| \cdot \|)}$ be a normed space. If ${\| \cdot \|_i}$ is an equivalent norm coming from an inner product, then the original norm satisfies an approximate parallelogram law. Applying methods and results from the theory of stability of functional equations we study the reverse implication.     

Conducting Systems with Crystalline Ct Complexes

The method of reticulate doping previously used to obtain bulk-conducting macromolecular films is modified to yield surface-conducting materials. Morphology and properties of these systems, consisting of a conducting network of CT complex crystallites penetrating the bulk of an inert polymer matrix are briefly described, most of them being supposed to be common for bulk and surface-conducting films. Preparation of surface conducting films is discussed in terms of crystallization of the components of the CT complex initially molecular ly dispersed in the matrix due to a controlled increase of the molecular mobility in the surface layer of the film. Possible mechanisms responsible for the unusual effectiveness of the reticulate doping are discussed.     

Measurements of Energetic States Resulting from Ion Exchanges in the Isomorphic Crystals of Apatites and Bioapatites

Developments in the field of nanostructures open new ways for designing and manufacturing innovative materials. Here, we focused on new original ways of calculating energy changes during the substitution of foreign ions into the structure of apatites and bioapatites. Using these tools, the energetic costs of ion exchanges were calculated for the exemplary cases known from the literature. It was established that the most costly were ion exchanges of some cations inside apatites and of anions, and the least costly exchanges in tetrad channel positions. Real energy expenses for bioapatites are much smaller in comparison to mineral apatites due to the limited involvement of magnesium and carbonates in the structure of hard tissues. They are of the order of several electron volts per ion. The rigorous dependences of the energy changes and crystallographic cell volumes on the ionic radii of introduced cations were proved. The differentiation of the positioning of foreign ions in locations of Ca(I) and Ca(II) could be calculated in the case of a Ca-Pb reaction in hydroxyapatite. The energetic effects of tooth aging were indicated. The ability of energy change calculation during the ion exchange for isomorphic substances widens the advantages resulting from X-ray diffraction measurements.     

Effect of Bear Garlic Addition on the Chemical Composition,Microbiological Quality,Antioxidant Capacity,and Degree of Proteolysis in Soft Rennet Cheeses Produced from Milk of Polish Red and Polish Holstein-Friesian Cows

This study aimed to assess the effect of milk source and bear garlic addition on the selected properties of soft rennet cheese. Cheeses were produced from cow milk derived from two sources: Polish Red cows (PR) and Polish Holstein-Friesian cows (PHF) with a 0.5% (w/w) addition of bear garlic (Allium ursinum L.) dried leaves. Chemical composition and fatty acid profiles (GC) were determined in fresh cheeses. Fresh and stored for two weeks cheeses were subjected to microbiological studies, i.e., total aerobic bacteria count (TABC); count of Lactococcus sp., yeast and molds; coliforms; analysis of the proteolysis extension by means of o-phthaldialdehyde (OPA) assay and free amino acids content (HPLC); antioxidant capacity as 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging activity and ferric reducing antioxidant power (FRAP); as well as pH and water activity. Cheeses with bear garlic herbs were more prone to proteolysis but this was not accompanied by any effect on the microbial counts, water activity or pH. Cheeses produced from PR milk contained less monounsaturated fatty acids (MUFA) but were richer in n-3 PUFA and had a lower n-6/n-3 FA ratio than cheeses from PHF milk. Bear garlic addition increased DPPH anti-radical power but had less of an effect on the FRAP values.     

Direct observation of carbene and diazo formation from aryldiazirines by ultrafast infrared spectroscopy

Ultrafast laser flash photolysis (lambda(ex) = 270 nm) of phenyldiazirine produces transient infrared absorptions at 2040 and 1582 cm(-1). The first band is assigned to phenyldiazomethane, and the second is assigned to singlet phenylcarbene. This assignment is consistent with DFT calculations. Diazo band integration reveals that photoisomerization from diazirine to diazo occurs within a few picoseconds of the laser pulse. The majority of carbene produced is also formed instantaneously.     

Direct observation of a sulfonyl azide excited state and its decay processes by ultrafast time-resolved IR spectroscopy

The photochemistry of 2-naphthylsulfonyl azide (2-NpSO(2)N(3)) was studied by femtosecond time-resolved infrared (TR-IR) spectroscopy and with quantum chemical calculations. Photolysis of 2-NpSO(2)N(3) with 330 nm light promotes 2-NpSO(2)N(3) to its S(1) state. The S(1) excited state has a prominent azide vibrational band. This is the first direct observation of the S(1) state of a sulfonyl azide, and this vibrational feature allows a mechanistic study of its decay processes. The S(1) state decays to produce the singlet nitrene. Evidence for the formation of the pseudo-Curtius rearrangement product (2-NpNSO(2)) was inconclusive. The singlet sulfonylnitrene (1)(2-NpSO(2)N) is a short-lived species (τ ≈ 700 ± 300 ps in CCl(4)) that decays to the lower-energy and longer-lived triplet nitrene (3)(2-NpSO(2)N). Internal conversion of the S(1) excited state to the ground state S(0) is an efficient deactivation process. Intersystem crossing of the S(1) excited state to the azide triplet state contributes only modestly to deactivation of the S(1) state of 2-NpSO(2)N(3).     

trans‐(1R,2R)‐1‐Benzyl‐2‐phenylcyclopropanecarboxylic acid

The cyclopropane ring of the title compound, C₁₇H₁₆O₂, shows a high level of substituent‐induced bond‐length asymmetry. The carboxyl group adopts a conformation that prompts electron‐density transfer from the ring towards the carbonyl π system.     

Accurate ab initio potential energy surface and vibration‐rotation energy levels of hydrogen peroxide

The accurate ground‐state potential energy surface of hydrogen peroxide, H₂O₂, has been determined from ab initio calculations using the coupled‐cluster approach in conjunction with the correlation‐consistent basis sets up to septuple‐zeta quality. Results obtained with the conventional and explicitly correlated coupled‐cluster methods were compared. The core–electron correlation, scalar relativistic, and higher‐order valence–electron correlation effects were taken into account. The adiabatic effects were also discussed. The vibration–rotation energy levels of the H₂O₂, D₂O₂, and HOOD isotopologues were predicted, and the experimental vibrational fundamental wavenumbers were reproduced to 1 cm^?1 (“spectroscopic”) accuracy. © 2012 Wiley Periodicals, Inc.