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EPR of Vanadyl Ion Impurities in Single Crystals of RbHC_2O_4

100%

Singh V. , Jain V.

Acta Physica Polonica A

2002

tom 102

nr 6

795-799

The EPR of VO^{2+} in RbHC_2O_4 single crystals has been studied in X-band at≈290 K. Three sites have been observed. VO^{2+} enters the lattice at substitutional and interstitial sites. Spin-Hamiltonian parameters are evaluated.

Convolution theorems for starlike and convex functions in the unit disc

80%

Anbudurai M. , Parvatham R. , Ponnusamy S. , Singh V.

nr 1

27-39

Let A denote the space of all analytic functions in the unit disc Δ with the normalization f(0) = f'(0) − 1 = 0. For β < 1, let $P⁰_{β} = {f ∈ A: Re f'(z) > β, z ∈ Δ}$. For λ > 0, suppose that 𝓕 denotes any one of the following classes of functions: $M^{(1)}_{1,λ} = {f ∈ 𝓐 : Re{z(zf'(z))''} > -λ, z ∈ Δ}$, $M^{(2)}_{1,λ} = {f ∈ 𝓐 : Re{z(z²f''(z))''} > -λ, z ∈ Δ}$, $M^{(3)}_{1,λ} = {f ∈ 𝓐 : Re{1/2 (z(z²f'(z))'')' - 1} > -λ, z ∈ Δ}$. The main purpose of this paper is to find conditions on λ and γ so that each f ∈ 𝓕 is in $𝓢_{γ}$ or $𝒦_{γ}$, γ ∈ [0,1/2]. Here $𝓢_{γ}$ and $𝒦_{γ}$ respectively denote the class of all starlike functions of order γ and the class of all convex functions of order γ. As a consequence, we obtain a number of convolution theorems, namely the inclusions $M_{1,α} ∗ 𝓖 ⊂ 𝓢_{γ}$ and $M_{1,α} ∗ 𝓖 ⊂ 𝒦_{γ}$, where 𝓖 is either $𝓟⁰_{β}$ or $M_{1,β}$. Here $M_{1,λ}$ denotes the class of all functions f in 𝓐 such that Re(zf''(z)) > -λ for z ∈ Δ.

Third-Order Nonlinear Optical Properties and Reverse Saturable Absorption in 2,3-Butanedione Dihydrazone Using z-Scan Technique

80%

Singh V. , Aghamkar P. , Lal B.

nr 1

39-44

Using chemical route a 2,3-butanedione dihydrazone (BDDH) compound was prepared. The third-order nonlinear optical properties of BDDH were investigated by using single beam z-scan technique with Q-switched, frequency doubled Nd:YAG laser (λ = 532 nm) at 5 ns pulse. Effect of excitation intensity on nonlinear optical properties has been studied and found that experimental and computed values are well in agreement. Also, we found the measured nonlinear optical coefficients are nearly ten times larger than the reported. The excited state absorption cross-section of BDDH was found to be larger than that of the ground state absorption cross-section, indicating the reverse saturable absorption.