Rice and Rice‐Shapiro Theorems for transfinite correction grammars

Hay and, then, Johnson extended the classic Rice and Rice‐Shapiro Theorems for computably enumerable sets, to analogs for all the higher levels in the finite Ershov Hierarchy. The present paper extends their work (with some motivations presented) to analogs in the transfinite Ershov Hierarchy. Some of the transfinite cases are done for all transfinite notations in Kleene's important system of notations, $\mathcal {O}$. Other cases are done for all transfinite notations in a very natural, proper subsystem $\mathcal {O}_{\mathrm{Cantor}}$ of $\mathcal {O}$, where $\mathcal {O}_{\mathrm{Cantor}}$ has at least one notation for each constructive ordinal. In these latter cases it is open as to what happens for the entire set of transfinite notations in $(\mathcal {O} -\mathcal {O}_{\mathrm{Cantor}})$.     

Fluorescent zinc(II) complex exhibiting "on-off-on" switching toward Cu2+ and Ag+ ions

Binuclear zinc(II) and copper(II) complexes based on a new Schiff base ligand N,N'-bis(2-hydroxybenzilidene)-2,4,6-trimethylbenzene-1,3-diamine (H(2)L) have been synthesized. The ligand H(2)L and complexes under investigation have been characterized by elemental analyses, spectral (FT-IR, (1)H, (13)C NMR, ESI-MS, electronic absorption, emission), and electrochemical studies. The structures of H(2)L and complexes [{Zn(C(23)H(18)N(2)O(2))}(2)] (1) and [{Cu(C(23)H(18)N(2)O(2))}(2)]·H(2)O (2) have been determined crystallographically. Selective "On-Off-On" switching behavior of the fluorescent complex 1 has been studied. The fluorescence intensity of 1 quenches (turns-off) upon addition of Cu(2+), while enhances (turns-on) in the presence of Ag(+) ions. The mechanisms of "On-Off-On" signaling have been supported by (1)H NMR, ESI-MS, electronic absorption, and emission spectral studies. Job's plot analysis supported 1:1 and 1:2 stoichiometries for Cu(2+) and Ag(+) ions, respectively. Association and quenching constants have been estimated by the Benesi-Hildebrand method and Stern-Volmer plot. Moreover, 1 mimics a molecular keypad lock that follows correct chemical input order to give maximum output signal.     

Synthesis of fused bicyclic systems with nitrogen atom at the bridgehead, including indolizidines and quinolizidines

Monocyclic as well as fused bicyclic systems with a nitrogen 10 atom at the bridgehead, including indolizidines and quinolizidines, can be prepared in four steps from N-Boc β-lactams. These easily prepared, highly robust, and flexible building blocks allow the incorporation of chirality and structural diversity, rendering the method feasible for diversity- as well as target-oriented synthesis.     

Density functional theory calculations and vibrational spectral analysis of 3,5-(dinitrobenzoic acid)

The FT-IR and Raman spectra of 3,5-dinitrobenzoic acid (DNBA) have been recorded and analyzed. The equilibrium geometry, various bonding and harmonic vibrational wavenumbers have been calculated with the help of density functional theory (DFT) method. Most of the vibrational modes are observed in the expected range. Mulliken population analysis shows the interactions C-N-O?H-C and C-O?H-C. The most possible interaction is explained using natural bond orbital (NBO) analysis. The strengthening and polarization of the CO bond increases due to the degree of conjugation. HOMO-LUMO energy and the thermodynamic properties are also evaluated.     

Dietary Flavonoids: Cardioprotective Potential with Antioxidant Effects and Their Pharmacokinetic,Toxicological and Therapeutic Concerns

Flavonoids comprise a large group of structurally diverse polyphenolic compounds of plant origin and are abundantly found in human diet such as fruits, vegetables, grains, tea, dairy products, red wine, etc. Major classes of flavonoids include flavonols, flavones, flavanones, flavanols, anthocyanidins, isoflavones, and chalcones. Owing to their potential health benefits and medicinal significance, flavonoids are now considered as an indispensable component in a variety of medicinal, pharmaceutical, nutraceutical, and cosmetic preparations. Moreover, flavonoids play a significant role in preventing cardiovascular diseases (CVDs), which could be mainly due to their antioxidant, antiatherogenic, and antithrombotic effects. Epidemiological and in vitro/in vivo evidence of antioxidant effects supports the cardioprotective function of dietary flavonoids. Further, the inhibition of LDL oxidation and platelet aggregation following regular consumption of food containing flavonoids and moderate consumption of red wine might protect against atherosclerosis and thrombosis. One study suggests that daily intake of 100 mg of flavonoids through the diet may reduce the risk of developing morbidity and mortality due to coronary heart disease (CHD) by approximately 10%. This review summarizes dietary flavonoids with their sources and potential health implications in CVDs including various redox-active cardioprotective (molecular) mechanisms with antioxidant effects. Pharmacokinetic (oral bioavailability, drug metabolism), toxicological, and therapeutic aspects of dietary flavonoids are also addressed herein with future directions for the discovery and development of useful drug candidates/therapeutic molecules.     

Spherically symmetric, self-similar spacetimes

In this paper, we show that self-similarity with respect to the existence of a (purely radial) homothetic Killing vector field for spherically symmetric spacetimes implies the separability of the spacetime metric in terms of the co-moving coordinates (and vice versa) and that the metric is, uniquely, the one recently reported in (Class. Quantam Grav. 18: 2147–2162; 2001). This spacetime, in general, has non-vanishing energy flux and shear. An interesting feature of this spacetime, in contrast to other self-similar spherically symmetric spacetimes (not reducible to our form) is that it has an arbitrary radial distribution of matter.     

Rat pups and random robots generate similar self‐organized and intentional behavior

Biorobotic research continually demonstrates that behavior and cognition can be the emergent products of (1) embodied agents that are (2) dynamically embedded within an environment and (3) equipped with simple sensorimotor rules. Thigmotaxis is an orientation response to contact manifested in infant rats by wall following, corner burrowing, and group aggregation. Orientation responses have been long thought to be mediated only by sensory or central processes. Here we show that a random control architecture in a morphologically similar robot embedded in a scaled environment can reproduce thigmotaxic behaviors seen in infant rats. We conclude that (1) and (2) may play a larger role than previously thought in the generation of complex behaviors. © 2006 Wiley Periodicals, Inc. Complexity 12: 53–66, 2006