Automorphisms with annihilator condition in prime rings

Let R be a prime ring, I a nonzero ideal of R, and a ∈ R. Suppose that σ is a nontrivial automorphism of R such that a{(σ(x ∘ y))n − (x ∘ y)m} = 0 or a{(σ([x,y]))n − ([x,y])m} = 0 for all x,y ∈ I, where n and m are fixed positive integers. We prove that if char(R) > n + 1 or char(R) = 0, then either a = 0 or R is commutative

Solar global ultraviolet and broadband global radiant fluxes and their relationships with aerosol optical depth at New Delhi

The solar global ultraviolet (GUV) and broadband global (G) radiation flux obtained on a horizontal plane in Delhi, during April 2010 to March 2011 have been used to investigate the temporal variability of these radiations and their ratio, fraction of UV (FUV). For the first time the clearness index (KT) has been estimated over Delhi and its variability during different months of the year and season has been studied in detail. The impact of atmospheric aerosols on KT has also been studied. It has been found that for every unit increase in aerosol optical depth (AOD) at 340 nm, KT decreases by 0.06. A strong anti-correlation with correlation coefficient 0.75 is observed between AOD and KT. On the basis of our field experience and observations at Delhi it is found that for highly cloudy and overcast conditions 0KT0.15, for partial cloudy or hazy conditions 0.15KT0.21 and KT > 0.21 for clear sky conditions. In addition, during foggy days in winter we have found KT values lying in the range 0.120.18 at Delhi. The day-time daily-averaged fluxes GUV and G varied in the range 0.151.23 MJ m2 and 3.3627.02 MJ m2, respectively. The GUV and G showed similar pattern during the year except for the wet season when the FUV increased possibly due to an increase in water vapour concentration

Identity related to additive mappings on standard operator algebras

Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators of X and let A(X)⊆L(X) be a standard operator algebra. Suppose there exists a linear mapping T:A(X)→L(X) satisfying the relation T(An) = T(A)An−1 − AT(An−2)A − An−1T(A) for all A∈A(X), where n > 2 is some fixed integer. Then T is of the form: (i)T(A) = 0 for all A∈F(X) and (ii) T(A) = BA, for all A∈A(X) and some B∈L(X)

On generalized Jordan ∗-derivation in rings

Let n ⩾ 1 be a fixed integer and let R be an (n + 1)!-torsion free ∗-ring with identity element e. If F, d:R → R are two additive mappings satisfying F(xn+1) = F(x)(x∗)n + xd(x)(x∗)n−1 + x2d(x)(x∗)n−2+ ⋯ +xnd(x) for all x ∈ R, then d is a Jordan ∗-derivation and F is a generalized Jordan ∗-derivation on R

On commutativity of rings with generalized derivations

Let R be a prime ring, extended centroid C, Utumi quotient ring U, and m, n ≥ 1 are fixed positive integers, F a generalized derivation associated with a nonzero derivation d of R. We study the case when one of the following holds: (i) F(x)∘md(y)=(x∘y)n and (ii) (F(x)∘d(y))m=(x∘y)n, for all x, y in some appropriate subset of R. We also examine the case where R is a semiprime ring

Wavelength Dependence of the Aerosol Angstrom Exponent and Its Implications Over Delhi, India

The aerosol optical depth (AOD), Angstrom coefficients (α and β), and the second-order Angstrom exponent (α ) obtained by Microtops-II sun photometer have been analyzed in the spectral range 0.34–0.87 μm over the urban polluted city of Delhi, In- dia for the period 2007–2008, aiming at investigating the physical and optical properties of aerosols. The average values of AOD at 500 nm, α and β (in the range 340–870 nm) are found to be 0.78 ± 0.32, 0.78 ± 0.28, and 0.45 ± 0.21, respectively, for the entire period of observations. The AOD data show significant curvature in the lnτ versus lnλ relationship suggesting different dominant aerosol types depending on season. In order to analyze further the curvature effect and the relative dominance of aerosol size, α has been calculated in three wavelength bands, i.e., shorter (0.34–0.50 μm), longer (0.675–0.87 μm), and broad (0.34–0.87 μm) during four seasons, summer (April–June), monsoon (July–September), winter (October–January), and spring (February–March) accom-panied with calculations of α , which quantifies the deviation of logarithmic behavior of AOD with lnλ. The α values are found to be positive and higher in the months of October–December and mostly negative in February and March, while close to zero values of α are found in April–August. These results indicate that win-ter season exhibits dominance of fine-mode aerosols while summer relatively higher concentration of coarse-mode particles. On the other hand, monsoon and spring seasons revealed the presence of mixed type, both fine- and coarse-mode aerosols over Delhi

Effect of atmospheric black carbon aerosols over Delhi

136-139The atmospheric aerosols are the particles of solid or liquid phase that are found dispersed in the atmosphere. Aerosols by scattering andabsorption phenomenon contribute to direct forcing and indirect forcing by formation of cloud condensation nuclei. Black Carbon (BC)aerosols, the optically absorbing carbonaceous aerosols released from the incomplete combustion of almost all the fuels is an importantaerosol constituent. Its diameter is about 0.1 micron. In the present study changes in black carbon aerosols have been presented. Black carbonaerosols show spatial and temporal diurnal variation. BC exhibited highest concentration occurring 0630h to 0930h and again at around 2000htill midnight and low concentration from ~1000h while lowest concentration from 0930 to evening. The annual average BC concentration ofDelhi (January 2006 to December 2006) was 14.75 μg/m3. During winter months (December, January and February) concentration increasesto 25 μg/m3. Black carbon aerosols is about 6 % of RSPM

Variations in single scattering albedo and Angstrom absorption exponent during different seasons at Delhi, India

Simultaneous measurements of aerosol absorption and scattering coefficients for the PM2.5 aerosols particles were done at Delhi during April 2008–March 2009 to estimate the aerosol single scattering albedo (SSA) and the Angstrom absorption exponents at the surface. The annual average SSA at 0.55 μm was found to be 0.70 ± 0.07 with only slight variations during the four seasons, summer (0.63 ± 0.06), monsoon (0.69 ± 0.07), winter (0.74 ± 0.03) and spring (0.72 ± 0.04). However, large variations in average absorption and scattering coefficients were seen during these four seasons. The average absorption coefficients during summer, monsoon, winter and spring were found to be 62.47 ± 21.27, 50.95 ± 43.61, 189.65 ± 85.94 and 90.65 ± 33.06 Mm−1 respectively. The corresponding scattering coefficients were 110.46 ± 36.15, 95.34 ± 49.46, 565.59 ± 274.59 and 236.56 ± 96.25 Mm−1. The Angstrom absorption exponent (ασ(abs)) remained close to unity throughout the year averaging at 1.02 ± 0.08, 1.02 ± 0.10, 1.04 ± 0.11, and 1.03 ± 0.05 during summer, monsoon, winter and spring seasons respectively, strongly indicating that the absorption at Delhi aerosol is mainly due to the abundance of black carbon of fossil fuel origin