Slant Lightlike Submanifolds of Indefinite Cosymplectic Manifolds

In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Cosymplectic manifold. We provide a nontrivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we give an example of a minimal slant lightlike submanifold of R⁹₂{R^{9}_{2}} and prove some characterization Theorems.     

Performance of CeO2–TiO2-admixed photoelectrode for natural dye-sensitized solar cell

Extracts from roots of Beta vulgaris were used as natural sensitizers of a wide-bandgap semiconductor (CeO₂–TiO₂) in photoelectrochemical solar cells. The natural dye, adsorbed onto the semiconductor surface, absorbs visible light and promotes electron transfer across the dye/semiconductor interface. We have applied CeO₂–TiO₂ to natural dye sensitizer solar cells as a photoelectrode to reduce the charge recombination rate by providing energy barrier at the interface between the photoanode and electrolyte which offers an improvement of photovoltaic efficiency. Short-circuit current density (J _sc) and open-circuit voltages (V _oc) of 9.0 mA cm^?2 and 680 mV, respectively, were obtained, and an effective energy conversion efficiency of 3.5?% was achieved. This simple and cheap technique of cell preparation opens up a perspective of commercial feasibility for inexpensive and environment-friendly dye cells.     

Hydroxo‐Bridged Dimers of Oxo‐Centered Ruthenium(III) Triangle: Synthesis and Spectroscopic and Theoretical Investigations

The homometallic hexameric ruthenium cluster of the formula [Ru^III₆(μ₃‐O)₂(μ‐OH)₂((CH₃)₃CCO₂)₁₂(py)₂] ( 1 ) (py=pyridine) is solved by single‐crystal X‐ray diffraction. Magnetic susceptibility measurements performed on 1 suggest that the antiferromagnetic interaction between the Ru^III centers is dominant, and this is supported by theoretical studies. Theoretical calculations based on density functional methods yield eight different exchange interaction values for 1 : J₁=?737.6, J₂=+63.4, J₃=?187.6, J₄=+124.4, J₅=?376.4, J₆=?601.2, J₇=?657.0, and J₈=?800.6 cm^?1. Among all the computed J values, six are found to be antiferromagnetic. Four exchange values (J₁, J₆, J₇ and J₈) are computed to be extremely strong, with J₈, mediated through one μ‐hydroxo and a carboxylate bridge, being by far the largest exchange obtained for any transition‐metal cluster. The origin of these strong interactions is the orientation of the magnetic orbitals in the Ru^III centers, and the computed J values are rationalized by using molecular orbital and natural bond order analysis. Detailed NMR studies (¹H, ¹³C, HSQC, NOESY, and TOCSY) of 1 (in CDCl₃) confirm the existence of the solid‐state structure in solution. The observation of sharp NMR peaks and spin‐lattice time relaxation (T1 relaxation) experiments support the existence of strong intramolecular antiferromagnetic exchange interactions between the metal centers. A broad absorption peak around 600–1000 nm in the visible to near‐IR region is a characteristic signature of an intracluster charge‐transfer transition. Cyclic voltammetry experiments show that there are three reversible one‐electron redox couples at ?0.865, +0.186, and +1.159 V with respect to the Ag/AgCl reference electrode, which corresponds to two metal‐based one‐electron oxidations and one reduction process.     

Multiplicative Lie algebras and Schur multiplier

In this paper, we attempt to study the structure of multiplicative Lie algebras, the theory of extensions, the second cohomology groups of multiplicative Lie algebras, and in turn the Schur multipliers. The Schur–Hopf formula is established for multiplicative Lie algebras. We also introduce the group of nontrivial relations satisfied by the Lie product in a multiplicative Lie algebra, and study it as a functor arising from the presentations of multiplicative Lie algebras. Some applications in K-theory are also discussed.     

Age-group-targeted testing for COVID-19 as a new prevention strategy

Nonlinear Dynamics - Robust testing and tracing are key to fighting the menace of coronavirus disease 2019 (COVID-19). This outbreak has progressed with tremendous impact on human life, society and...     

Nonconforming h-p spectral element methods for elliptic problems

In this paper we show that we can use a modified version of the h-p spectral element method proposed in [6,7,13,14] to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal domains using nonconforming spectral element functions. A geometrical mesh is used in a neighbourhood of the corners. With this mesh we seek a solution which minimizes the sum of a weighted squared norm of the residuals in the partial differential equation and the squared norm of the residuals in the boundary conditions in fractional Sobolev spaces and enforce continuity by adding a term which measures the jump in the function and its derivatives at inter-element boundaries, in fractional Sobolev norms, to the functional being minimized. In the neighbourhood of the corners, modified polar coordinates are used and a global coordinate system elsewhere. A stability estimate is derived for the functional which is minimized based on the regularity estimate in [2]. We examine how to parallelize the method and show that the set of common boundary values consists of the values of the function at the corners of the polygonal domain. The method is faster than that proposed in [6,7,14] and the h-p finite element method and stronger error estimates are obtained.     

Evolving to the edge of chaos: Chance or necessity?

We show that ecological systems evolve to edges of chaos (EOC). This has been demonstrated by analyzing three diverse model ecosystems using numerical simulations in combination with analytical procedures. It has been found that all these systems reside on EOC and display short-term recurrent chaos (strc). The first two are non-linear food chains and the third one is a linear food chain. The dynamics of first two is dictated by deterministic changes in system parameters. In contrast to this, dynamics of the third model system (the linear food chain) is governed by both deterministic changes in system parameters as well as exogenous stochastic perturbations (unforeseen changes in initial conditions) of these dynamical systems.     

Chaotic population dynamics and biology of the top-predator

We study how the dynamics of a food chain depends on the biology of the top-predator. We consider two model food chains with specialist and generalist top-predators. Both types of food chains display same type of chaotic behavior, short-term recurrent chaos; but the generating mechanisms are drastically different. Food chains with specialist top-predators are dictated by exogenous stochastic factors. On the contrary, the dynamics of those with the generalist top-predator is governed by deterministic changes in system parameters. The study also suggests that robust chaos would be a rarity.     

Multiple attractors and crisis route to chaos in a model food-chain

An attempt has been made to identify the mechanism, which is responsible for the existence of chaos in narrow parameter range in a realistic ecological model food-chain. Analytical and numerical studies of a three species food-chain model similar to a situation likely to be seen in terrestrial ecosystems has been carried out. The study of the model food chain suggests that the existence of chaos in narrow parameter ranges is caused by the crisis-induced sudden death of chaotic attractors. Varying one of the critical parameters in its range while keeping all the others constant, one can monitor the changes in the dynamical behaviour of the system, thereby fixing the regimes in which the system exhibits chaotic dynamics. The computed bifurcation diagrams and basin boundary calculations indicate that crisis is the underlying factor which generates chaotic dynamics in this model food-chain. We investigate sudden qualitative changes in chaotic dynamical behaviour, which occur at a parameter value a₁=1.7804 at which the chaotic attractor destroyed by boundary crisis with an unstable periodic orbit created by the saddle-node bifurcation. Multiple attractors with riddled basins and fractal boundaries are also observed. If ecological systems of interacting species do indeed exhibit multiple attractors etc., the long term dynamics of such systems may undergo vast qualitative changes following epidemics or environmental catastrophes due to the system being pushed into the basin of a new attractor by the perturbation. Coupled with stochasticity, such complex behaviours may render such systems practically unpredictable.     

Magnetic and Rheological Characterization of Fe3O4 Ferrofluid: Particle Size Effects

Magnetite particles of different diameters were synthesized by chemical co-precipitation technique and the same are dispersed in dodecane to prepare a magnetic fluid. The results of X-ray diffraction, magnetization measurements, ac susceptibility and viscosity measurements are analyzed and discussed in the text.