Automata and logics over finitely varying functions

We extend some of the classical connections between automata and logic due to Büchi (1960) [5] and McNaughton and Papert (1971) [12] to languages of finitely varying functions or “signals”. In particular, we introduce a natural class of automata for generating finitely varying functions called View the MathML source’s, and show that it coincides in terms of language definability with a natural monadic second-order logic interpreted over finitely varying functions Rabinovich (2002) [15]. We also identify a “counter-free” subclass of View the MathML source’s which characterise the first-order definable languages of finitely varying functions. Our proofs mainly factor through the classical results for word languages. These results have applications in automata characterisations for continuously interpreted real-time logics like Metric Temporal Logic (MTL) Chevalier et al. (2006, 2007) [6] and [7].

Unsteady Natural Convection Flow over a Heated Cylinder Buried in a Fluid Saturated Porous Medium

Transient natural convection flow on a heated cylinder buried in a semi-infinite liquid-saturated porous medium has been studied. The unsteadiness in the problem arises due to the cylinder which is heated (cooled) suddenly and then maintained at that temperature. The coupled partial differential equations governing the flow and heat transfer are cast into stream function-temperature formulation, and the solutions are obtained from the initial time to the time when steady state is reached. The heat transfer is found to change significantly with increasing time in a small time interval immediately after the start of the impulsive change, and steady state is reached after some time. The average Nusselt number is found to increase with Rayleigh number When the surface of the cylinder is suddenly cooled, there is a change in the direction of the heat transfer in a small time interval immediately after the start of the impulsive change in the surface temperature;however when the surface temperature is suddenly increased, no such phenomenon is observed.

Identification of alpha- and beta-Hydroxy Acid Containing Cyclodepsipeptides in Natural Peptide Mixtures Using Negative Ion Mass Spectrometry

Natural peptide libraries often contain cyclodepsipeptides containing alpha or beta hydroxy residues. Extracts of fungal hyphae of Isaria yield a microheterogenous cyclodepsipeptide mixture in which two classes of molecules can be identified by mass spectral fragmentation of negative ions. In the case of isaridins, which contain an alpha-hydroxy residue and a beta-amino acid residue, a characteristic product ion corresponding to a neutral loss of 72 Da is obtained. hi addition, neutral loss of water followed by a 72 Da loss is also observed. Two distinct modes of fragmentation rationalize the observed product ion distribution. The neutral loss of 72 Da has also been obtained for a roseotoxin component, which is also an alpha-hydroxy residue containing cyclodepsipeptide. In the case of isariins, which contain a beta-hydroxy acid residue, ring opening and subsequent loss of the terminal residue as an unsaturated ketene fragment, rationalizes the observed product ion formation. Fragmentation of negative ions provide characteristic neutral losses, which are diagnostic of the presence of alpha-hydroxy or beta-hydroxy residues.

The RecA intein of Mycobacterium tuberculosis promotes cleavage of ectopic DNA sites. Implications for the dispersal of inteins in natural populations

The RecA intein of Mycobacterium tuberculosis, a novel double-stranded DNA endonuclease, requires both Mn(2+) and ATP for efficient cleavage of the inteinless recA allele. In this study, we show that Mg(2+) alone was sufficient to stimulate PI-MtuI to cleave double-stranded DNA at ectopic sites. In the absence of Mg(2+), PI-MtuI formed complexes with topologically different forms of DNA containing ectopic recognition sequences with equal affinity but failed to cleave DNA. We observed that PI-MtuI was able to inflict double-strand breaks robustly within the ectopic recognition sequence to generate either a blunt end or 1-2-nucleotide 3'-hydroxyl overhangs. Mutational analyses of the presumptive metal ion-binding ligands (Asp(122), Asp(222), and Glu(220)) together with immunoprecipitation assays provided compelling evidence to link both the Mg(2+)- and Mn(2+) and ATP-dependent endonuclease activities to PI-MtuI. The kinetic mechanism of PI-MtuI promoted cleavage of ectopic DNA sites proceeded through a sequential mechanism with transient accumulation of nicked circular duplex DNA as an intermediate. Together, these data suggest that PI-MtuI, like group II introns, might mediate ectopic DNA transposition and hence its lateral transfer in natural populations.

Chemical modifications of natural triterpenes—glycyrrhetinic and boswellic acids: evaluation of their biological activity

Synthetic analogues of naturally occurring triterpenoids; glycyrrhetinic acid, arjunolic acid, and boswellic acids, by modification of A-ring with a cyano- and enone-functionality, have been reported. A novel method of synthesis of α-cyanoenones from isoxazoles is reported. Bioassays using primary mouse macrophages and tumor cell lines indicate potent anti-inflammatory and cytotoxic activities associated with cyano-enones of boswellic acid and glycyrrhetinic acid.

Unsteady natural convection from a horizontal annulus filled with a porous medium

The unsteady natural convection flow from a horizontal cylindrical annulus filled with a non-Darcy porous medium has been studied. The unsteadiness in the problem arises due to the impulsive change in the wall temperature of the outer cylinder. The Navier–Stokes equations along with the energy equation governing the unsteady natural convection flow have been solved by the finite-volume method. The effect of time variation on the heat transfer is more pronounced only in a small time interval immediately after the start of the impulsive motion and the steady state is reached after certain time. The results show that the annulus completely filled with a porous medium has the best insulating effectiveness. Convection in the horizontal annulus is confined mostly at top and bottom regions. Hence, only these regions should be insulated. In case of annulus partially filled with a porous material, insulating the region near the outer cylinder is more effective than insulating the region near the inner cylinder. The effect of Darcy number on the heat transfer is more pronounced than that of the Grashof number.

A total synthesis of the epoxyquinone based antifungal natural product (±)-ambuic acid

A total synthesis of the recently isolated polyketide natural product (+/-)-ambuic acid has been accomplished from the readily available Diels-Alder adduct of cyclopentadiene and 2-allyl-p-benzoquinone through a simple sequence with sound stereocontrol. (c) 2005 Elsevier Ltd. All rights reserved.

Effect of static deflection on natural frequency of non-linear spring mass system by direct linearization method

An exact expression for the frequency of a non-linear cubic spring mass system is obtained considering the effect of static deflection. An alternative expression for the approximate frequency is also obtained by the direct linearization procedure; it is shown that this is very accurate as compared with the exact method. This approximate frequency equation is used to explain a “dual behaviour” of the frequency amplitude curves.

Ferrolysis induced soil transformation by natural drainage in Vertisols of sub-humid South India

In sub-humid South India, recent studies have shown that black soil areas (Vertisols and vertic Intergrades), located on flat valley bottoms, have been rejuvenated through the incision of streambeds, inducing changes in the pedoclimate and soil transformation. Joint pedological, geochemical and geophysical investigations were performed in order to better understand the ongoing processes and their contribution to the chemistry of local rivers. The seasonal rainfall causes cycles of oxidation and reduction in a perched watertable at the base of the black soil, while the reduced solutions are exported through a loamy sand network. This framework favours a ferrolysis process, which causes low base saturation and protonation of clay, leading to the weathering of 2:1 then 1:1 clay minerals. Maximum weathering conditions occur at the very end of the wet season, just before disappearance of the perched watertable. Therefore, the by-products of soil transformation are partially drained off and calcareous nodules, then further downslope, amorphous silica precipitate upon soil dehydration. The ferrolysed area is fringing the drainage system indicating that its development has been induced by the streambed incision. The distribution of C-14 ages of CaCO3 nodules suggests that the ferrolysis process started during the late Holocene, only about 2 kyr B.P. at the studied site and about 5 kyr B.P. at the watershed outlet. The results of this study are applied to an assessment of the physical erosion rate (4.8x10(-3) m/kyr) since the recent reactivation of the erosion process. (C) 2010 Elsevier B.V. All rights reserved.

Natural frequencies and modes of tapered skew plates

The vibration of simply supported skew plates having a linear variation in thickness in one direction is considered. Approximate analysis is made by using Lagrange's equations employing the double Fourier sine series in oblique co-ordinates to represent the deflected surface. Natural frequencies are obtained for rhombic plates for several ranges of thickness variation and skew angle. The nodal patterns plotted for a few typical configurations show interesting metamorphoses with variation in thickness and skew angle.

Steroids and related natural products. VIII. Synthesis of oxasteroids

Peroxydisulfuric acid oxidation of testosterone propionate, progesterone, and cholest-4-en-3-one has been shown to yield 3-oxo-17β-hydroxy-4-oxa-5α-androstane (I, after saponification), 3,20-dioxo-4-oxa-5α-pregnane (V) and 3-oxo-4-oxa-5α-cholestane (VII) respectively. Boron trifluoride etherate-lithium aluminum hydride reduction of δ-lactones I, V, and VII led to the corresponding tetrahydropyran derivatives (IIb, VIa, and VIII). Similar reduction of 3β-hydroxy-17-oxo-17a-oxa-D-homo-5α-androstane (XI) gave 3β-hydroxy-17a-oxa-D-homo-5α-androstane (XIIa). Diborane-boron trifluoride etherate was also found to reduce lactones to cyclic ethers, while reduction with diborane gave hemiacetals. Evidence in support of the structures and stereochemistry assigned to the lactones and their unusual reduction products has been summarized. A tentative mechanism is proposed for lactone → ether reduction employing diborane-boron trifluoride etherate.

Steroids and related natural products. VII. Boron trifluoride etherate-lithium aluminum hydride reduction of smilagenin acetate

Reduction of smilagenin acetate (Va) using a boron trifluoride etherate-lithium aluminum hydride reagent, followed by hydrogen peroxide oxidation and acetylation, was found to yield: 3β-ethoxysmilagenin (Vb), 3β-ethoxydihydrosmilagenin acetate (VIa), dihydrosmilagenin diacetate (VIb), and a complex mixture of partially acetylated products. Similar reaction conditions were employed to convert dihydrodiosgenin (II) to dihydrochlorogenin (III). Boron trifluoride etherate-lithium aluminum hydride reduction of 3β-acetoxy-5α-cholestane and 3β-acetoxy-5α-lanostane (VIIIa) was shown to yield the corresponding 3β-ethoxy (e.g., VIIIb) derivatives.

Natural history and behaviour of the primitively eusocial wasp Ropalidia marginata (Hymenoptera: Vespidae): a comparison of the two sexes

We report the natural history and behaviour of the primitively eusocial wasp Ropalidia marginata with a special reference to the males. We found that just as nests of this species are found throughout the year, so are the males. Females spend all their life in their nests but males stay in their natal nests only for 1-12 days and leave to lead a nomadic life. Males maintained in the laboratory can live for up to 140 days. Like all eusocial hymenopteran males, R. marginata males also do not perform any colony maintenance activities. We found that males did not forage or feed larvae. Compared with females, males showed fewer dominance and subordinate behaviours and being solicited behaviour and more feeding self and soliciting behaviours. By comparing males with young females, we found similar differences, except that the males showed similar rates of feeding self and higher rates of subordinate behaviour.