Spatiotemporal pattern formation in a diffusive predator-prey system: an analytical approach

In this paper, we propose and analyse a mathematical model to study the mathematical aspect of reaction diffusion pattern formation mechanism in a predator-prey system. An attempt is made to provide an analytical explanation for understanding plankton patchiness in a minimal model of aquatic ecosystem consisting of phytoplankton, zooplankton, fish and nutrient. The reaction diffusion model system exhibits spatiotemporal chaos causing plankton patchiness in marine system. Our analytical findings, supported by the results of numerical experiments, suggest that an unstable diffusive system can be made stable by increasing diffusivity constant to a sufficiently large value. It is also observed that the solution of the system converges to its equilibrium faster in the case of two-dimensional diffusion in comparison to the one-dimensional diffusion. The ideas contained in the present paper may provide a better understanding of the pattern formation in marine ecosystem.     

Tail behavior for semigroups of measures on groups

Let (_t)_t>0 be a convolution semigroup of probability measures on a measurable group (G, ). In this paper, we provide precise information about the asymptotic behavior of _t{q>s, whereq is a measurable seminorm and (_t)_t>0 isq-continuous.     

Assignment of the Phosphorus,Proton and Carbon-NMR Spectra of [(Tetrahydro-2-hydroxy-5,5-dimethyl-4H-1,4,2-oxazaphosphorin-4-yl)methyl] phosphonic acid P-Oxide

The ¹H and ¹³C nmr signals of the methylene groups directly linked to the phosphorus atoms, namely P(2)-C(3)H₂ and P(8)-C(7)H₂ in 1a were assigned with the help of hetronuclear decoupling experiments and HETCOR spectrum.     

Spectral representations of infinitely divisible processes

Summary The spectral representations for arbitrary discrete parameter infinitely divisible processes as well as for (centered) continuous parameter infinitely divisible processes, which are separable in probability, are obtained. The main tools used for the proofs are (i) a polar-factorization of an arbitrary Lévy measure on a separable Hilbert space, and (ii) the Wiener-type stochastic integrals of non-random functions relative to arbitrary infinitely divisible noise.The research of both authors was supported partially by the AFSOR Grant No. 87-0136; the second named author was also supported partially by a grant from the University of Tennessee     

Trinuclear,Oxo-Bridged,Mixed-Valence Iron Mercaptocarboxylates

Mixed carboxylates and mercaptocarboxylates of mixed-valence Fe^IIFe^III with general formula [Fe^II-Fe^III ₂O(OOCR)₃(OOCRSH)₃L₃](where R = C₁₃H₂₇, C₁₅H₃₁ or C₁₇H₃₅; R= CH₂ or C₆H₄ and L = pyridine) were successfully prepared by substitution of [Fe^IIFe^III ₂O(OAc)₆(H₂O)₃] with straight chain carboxylic acids and mercaptocarboxylic acids. The title products have been characterized by elemental analyses, molar conductances and magnetic susceptibility measurements, i.r., electronic and Mössbauer spectral data. The i.r. spectra showed resolved bands arising from the _asym(OCO) and _sym(OCO) vibrations of the bridging carboxylate and mercaptocarboxylate ligands along with the _asym(Fe₃O) vibrations. Mössbauer spectroscopic studies revealed two resolved quadrupole doublets due to Fe^II and Fe^III at 80, 200 and 295 K, confirming the valence-localized type of compound. This fact has also been supported by the observed electronic spectral bands in the complexes. Magnetic susceptibility measurements showed net anti-ferromagnetic coupling related to mixed-valence pairs. A structure for the complexes has been established on the basis of physico-chemical studies.     

Dielectric Response of Bi4Ti3O12/PVDF Composite Electrodes for Energy Storage

This study is reporting the role of embedded ferroelectric ceramics Bi₄Ti₃O₁₂ (BTO = 1–5 wt%) into the polyvinylidene fluoride (PVDF) composites on its structural, bonding, surface morphology, and dielectric response. Especially lead free flexible composite electrodes have lot of attention due to its high dielectric permittivity and energy storage density. X-ray diffraction spectra confirms monophasic orthorhombic structure of composites, while Fourier transform infrared (FTIR) spectra confirms the bonding behavior. Scanning electron microscopy (SEM) images surface morphology of homogeneously distributed ceramic particles with interconnected network. Dielectric constant has been found to be improved from 9.56 to 13.73 for BTO_5%PVDF_95% composites at frequency of 1 kHz attributes promoted interfacial polarization of PVDF and effectively limited the charge leakage in the composites, implying promising applications in flexible electronic devices.     

Bamford-Stevens reaction assisted synthesis of styrene C-glycosides

Modification of carbohydrates and their analogs is hindered due to multi-step synthetic methodologies involving selective protection and deprotection of multiple hydroxyl groups present in the molecule. A highly efficient route for the synthesis of 1-phenyl-2-(β-D-glycopyranosyl)ethenes has been developed from native sugars, which neither requires protection/deprotection of the hydroxyl groups nor use of any metal/metal ions. The key step of the developed methodology is the use of Bamford-Stevens reaction which led to the formation of the desired compounds in moderate to high yields in three steps only.     

PHOSPHONOMETHYLATION OF AMINOALKANOLS PREPARATION OF 4-(PHOSPHONOMETHYL)-2-HYDROXY-2-OXO-1,4,2-OXAZAPHOSPHORINANES1

Abstract

Treatment of aminoalkanols 1 with phosphorous acid and formaldehyde in presence of conc. hydrochloric acid gave mixtures of [(2-hydroxy alkyl)imino] dimethylene diphosphonic acids 3 and 4-(phosphonomethyl)-2-hydroxy-2-oxo-1,4,2-oxazaphosphorinanes 2 from which 2 were isolated as crystalline solids. Similar treatment of 2-amino-2-methyl-1,3-propanediol 8 gave a complex mixture from which dimethylene diphosphonic acid of 5-amino-5-methyl-1,3-dioxane 9 was isolated. 2-Aminoethanethiol, when subjected to phosphonomethylation. gave an unexpected novel quarternary nitrogen product 11. N-Alkylaminoalkanols 4 on phosphonomethylation gave 3:1 mixtures of [N-alkyl-N-(2-hydroxyalkyl)amino] methane phosphonic acid 6 and N-alkyl-2-hydroxy-2-oxo-1,4,2-oxazaphosphorinane 5. Treatment of the crude mixtures of 5 and 6 with aqueous sodium hydroxide gave disodium salts of [N-alkyl-N-(2-hydroxyalkyl)amino] methanephosphonic acid 7. The ratio of the cyclic to the open chain structures obtained as well as the formation of any unexpected novel products is dependent on the structure of the aminoalkanol that is phosphonomethylated. The ¹H, ¹³C and ³¹P spectra are reported for all new compounds.     

The role of top predator interference on the dynamics of a food chain model

In this paper, the effects of top predator interference on the dynamics of a food chain model involving an intermediate and a top predator are considered. It is assumed that the interaction between the prey and intermediate predator follows the Volterra scheme, while that between the top predator and its favorite food depends on Beddington–DeAngelis type of functional response. The boundedness of the system, existence of an attracting set, local and global stability of non-negative equilibrium points are established. Number of the bifurcation and Lyapunov exponent bifurcation diagrams is established. It is observed that, the model has different types of attracting sets including chaos. Moreover, increasing the top predator interference stabilizes the system, while increasing the normalization of the residual reduction in the top predator population destabilizes the system.     

Development of tBu-phenyl Acetamide Appended Thiacalix[4]arene as “Turn-ON” Fluorescent Probe for Selective Recognition of Hg(II) Ions

Journal of Fluorescence - Herein, a novel N-(4-(tert-butyl)-phenyl)-2-chloroacetamide functionalized thiacalix[4]arene architecture, viz TCAN2PA has been synthesized and the sensing behaviour...