Abstract:
The properties of aerosols present in the atmosphere are often influenced by the environment in which they are being disbursed. Subsequently, the variation in the environmental conditions may severely affect the aerosol size and distribution. Thus it is quite exciting to investigate the spatial and temporal variations of AOD that are being affected by the significant changes in the environment to a large extent. This paper presents preliminary observations of diurnal variation of Aerosol Optical Depth (AOD) over two distinct locations in Kannur, India. The AOD over a location which has strong marine influence shows the presence of coarse particles while that on a valley of Western Ghats reveals the combined influences of both land and the ocean. The correlation between AOD measured from the ground and that retrieved from MODIS is fairly good. The AODs retrieved from ground based observation is validated with that estimated from MODIS in the context of meteorological parameters observed during the period of this observation.

Abstract:
The solar UV radiation has prominent impacts on human life, animals and plants with positive and negative effects. Atmospheric ozone, which is formed from the photodissociation of molecular oxygen mainly in the stratosphere, absorbs a significant factor of solar UV radiation. The ozone in the stratosphere acts as a protective layer to prevent UV radiation reaching on the surface of the earth. Hence the intensity of solar UV radiation on the surface has a strong dependence on the Total Ozone Column (TOC). The UV irradiance on earth surface depends on geometrical factors such as solar zenith angle, altitude, latitude and other atmospheric parameters as well. This is an attempt to study the variation of solar UV flux at its four discrete wavelengths ranging from 305 - 380 nm at Kannur, which is located in the north of Kerala in India. Hence such a correlation of TOC and UV irradiance is relevant to realize the radiation budget at this location (12.3N, 75.4E) using AURA OMI data. This paper reveals the correlation of day to day, month to month temporal variation of total ozone column (in DU) and UV irradiance (w/m2). From the analysis, the anti-correlation between UV and TOC is revealed and its impact in the solar radiation budget is established.

Abstract:
The Circular Restricted Three-Body Problem (CRTBP) with more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries is considered to generate the halo orbits around L1 and L2 for the seven satellites (Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus) of Saturn in the frame work of CRTBP. It is found that the oblateness effect of Saturn on the halo orbits of the satellites closer to Saturn has significant effect compared to the satellites away from it. The halo orbits L1 and L2 are found to move towards Saturn with oblateness.

Abstract:
This work is on the Cauchy problem for critical wave maps coupled to Einstein's equations of general relativity. The main result of this work is the proof that the energy of the Einstein-equivariant wave map system does not concentrate during the Cauchy evolution. A key ingredient in the proof is the use of the fact that geometric mass at infinity of the Einstein-equivariant wave map system is conserved during the evolution. However, this observation has some subtle local implications which have been used to estimate the energy locally. For instance, we construct a divergence-free vector field which gives monotonicity of energy in the past null cone of any point. In addition, this vector has also been used to prove that the energy does not concentrate away from the axis of the domain manifold. Later, estimating the divergence of a Morawetz vector on a truncated past null cone, we prove that the kinetic energy does not concentrate. Finally, assuming that the target manifold satisfies the Grillakis condition, we proceed to prove the non-concentration of energy for the critical Einstein-equivariant wave map system. Keeping track of various quantities of wave map relative to the evolving null geometry of the background manifold is a recurring theme throughout the course of this work. Apart from a purely mathematical interest, the motivation to study critical self-gravitating wave maps is that they occur naturally in 3+1 Einstein's equations of general relativity. Therefore, studying critical self-gravitating wave maps could be a fruitful way of understanding the ever elusive global behaviour of Einstein's equations. This work is a step in this endeavour.

Abstract:
We consider linear delay differential equations at the verge of instability, i.e. a pair of roots of the characteristic equation are on the imaginary axis of the complex plane and all other roots have negative real parts. When nonlinear and noisy perturbations are present, it is shown that the error in approximating the dynamics of the delay system by certain two dimensional stochastic differential equation without delay is small with high probability. Two cases are considered: (i) linear perturbations and multiplicative noise (ii) cubic perturbations and additive noise. The two-dimensional system without-delay is related to the projection of the delay equation onto the space spanned by the eigenfunctions corresponding to the imaginary roots of the characteristic equation. This is an attempt to relax the Lipschitz restriction imposed on the coefficients in arXiv:1311.4532. Examples without rigorous proofs are worked in arXiv:1403.3029.

Abstract:
We consider the Cauchy problem of 2+1 equivariant wave maps coupled to Einstein's equations of general relativity and prove that it disperses to a linearized equation in the large. Global asymptotic behaviour of 2+1 Einstein-wave map system is relevant because the system occurs naturally in 3+1 vacuum Einstein's equations.

Abstract:
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. We deal with linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic equation (eigenvalues) lie on the imaginary axis of the complex plane, and all other roots have negative real parts. We show that, when the system is perturbed by small noise, under an appropriate change of time scale, the law of the amplitude of projection onto the critical eigenspace is close to the law of a certain one-dimensional stochastic differential equation (SDE) without delay. Further, we show that the projection onto the stable eigenspace is small. These results allow us to give an approximate description of the delay-system using an SDE (without delay) of just one dimension. The proof is based on the martingale problem technique.

Abstract:
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic equation lie on the imaginary axis of the complex plane, and all other roots have negative real parts. It is shown that, when small noise perturbations are present, the probability law of the dynamics can be approximated by the probability law of a one dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDE are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

Abstract:
We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data.Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any b

Abstract:
The present study was was conducted in the University Livestock farm and Fodder Research and Development scheme (ULF and FRDS), Kerala Agricultural University Mannuthy, Thrissur from February to May 2008, covering the hottest part of the summer on twelve healthy crossbred cows in mid lactation, to study the effect of feeding during cooler hours of summer season on physiological and hematological parameters of crossbred cows in mid lactation. Animals were divided into two groups of six each. The T1 animals were maintained on routine management protocol whereas the T2 animals were maintained on concentrate mixture and green grass as roughage with 1/3rd of the concentrate and roughage fed during the day time (10.a.m) and rest in evening (6.00 p.m) and early morning (5.00 a.m) hours. Various physiological and hematological parameters of the two groups were recorded. From the present study it was concluded that the cool hour feeding of the animals during summer season did not show much significant differences in physiological and hematological parameters of mid lactation cross bred cows. On statistical analysis a significant difference (P< 0.05) in plasma cortisol was obtained between the two groups during the first and second fortnights. The overall average plasma cortisol level was significantly higher in the T1 in comparison to T2. [Vet. World 2010; 3(1.000): 21-22]