On certain q-analogue of Sz��sz Kantorovich operators

In the present paper we propose q-analogue of the well known Sz??sz-Kantorovich operators. We study local approximation as well as weighted approximation properties of these new operators.     

ON THE RATE OF CONVERGENCE OF BEZIER VARIANT OF SZASZ—DURRMEYER OPERATORS

In the present paper, we introduce Szasz-Durrmeyer-Bezier operators M.,.(f,x) , which generalize the Szasz-Durrmeyer operators. Here we obtain an estimate on the rate of convergence of Mn,a(f,x) for functions of bounded variation. Our result extends and improves that of Sahai and Prasad and Gupta and Pant.     

Synthesis,characterisation, luminescence and defect centres in solution combustion synthesised CaZrO3:Tb3+ phosphor

Tb³⁺ doped CaZrO₃ has been prepared by an easy solution combustion synthesis method. The combustion derived powder was investigated by X-ray diffraction, Fourier-transform infrared spectrometry and scanning electron microscopy techniques. A room temperature photoluminescence study showed that the phosphors can be efficiently excited by 251 nm light with a weak emission in the blue and orange region and a strong emission in green light region. CaZrO₃:Tb³⁺ exhibits three thermoluminescence (TL) glow peaks at 126 °C, 200 °C and 480 °C. Electron Spin Resonance (ESR) studies were carried out to study the defect centres induced in the phosphor by gamma irradiation and also to identify the centres responsible for the TL peaks. The room temperature ESR spectrum of irradiated phosphor appears to be a superposition of two distinct centres. One of the centres (centre I) with principal g-value 2.0233 is identified as an O^? ion. Centre II with an axial symmetric g-tensor with principal values g_=1.9986 and g_?=2.0023 is assigned to an F⁺ centre (singly ionised oxygen vacancy). An additional defect centre is observed during thermal annealing experiments and this centre (assigned to F⁺ centre) seems to originate from an F centre (oxygen vacancy with two electrons). The F centre and also the F⁺ centre appear to correlate with the observed high temperature TL peak in CaZrO₃:Tb³⁺ phosphor.     

EPR and photoluminescence properties of green light emitting LaAl11O18:Mn phosphors

The LaAl₁₁O₁₈:Mn²⁺ powder phosphor has been prepared using a self-propagating synthesis. Formation and homogeneity of the LaAl₁₁O₁₈:Mn²⁺ phosphor has been verified by X-ray diffraction and energy dispersive X-ray analysis respectively. The EPR spectra of Mn²⁺ ions exhibit resonance signals with effective g values at g≈4.8 and g≈1.978. The signal at g≈1.978 exhibits six-line hyperfine structure and is due to Mn²⁺ ions in an environment close to tetrahedral symmetry, whereas the resonance at g≈4.8 is attributed to the rhombic surroundings of the Mn²⁺ ions. It is observed that the number of spins participating in resonance for g≈1.978 increases with decreasing temperature obeying the Boltzmann law. Upon 451 nm excitation, the photoluminescence spectrum exhibits a green emission peak at 514 nm due to ⁴T₁ (G)→⁶A₁ (S) transition of Mn²⁺ ions. The crystal field parameter Dq and Racah inter-electronic repulsion parameters B and C have been evaluated from the excitation spectrum.     

Approximation by the Complex form of a Link Operator Between the Phillips and the Szász–Mirakjan Operators

Results in Mathematics - The link operator $${P_{\alpha}^\rho(f,x)=\sum_{k=1}^\infty s_{\alpha,k}(x)\int_0^\infty \theta_{\alpha,k}^\rho(t)f(t)dt+e^{-\alpha x}f(0)}$$ , $${\alpha, \rho >...     

Infrared and visible emission of Er in combustion-synthesized CaAl2O4 phosphors

New near-infrared luminescent, monoclinic CaAl₂O₄:Er³⁺ phosphor was prepared by using the combustion route at furnace temperatures as low as 500 °C in a few minutes. Combustion synthesized phosphor has been well characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy-dispersive analysis of X-ray (EDAX) mapping studies. The luminescence spectra of Er³⁺-doped calcium aluminate were studied at UV (380 nm), vis (488 nm) and IR (980 nm) excitation. Upon UV and vis excitation, the CaAl₂O₄:Er³⁺ phosphor exhibits emission bands at ~523 nm and at ~547 nm, corresponding to transitions from the ²H_11/2 and ⁴S_3/2 erbium levels to the ⁴I_15/2 ground state. A strong luminescence at 1.55 μm in the infrared (IR) region due to ⁴I_13/2→⁴I_15/2 transition has been observed in CaAl₂O₄:Er³⁺ phosphor upon 980 nm CW pumping. In the spectrum of IR-excited up-conversion luminescence, green (~523 and ~547 nm) and red (662 nm) luminescence bands were present, the latter associated with the ⁴F_9/2→⁴I_15/2 transitions of Er³⁺ ions. Both excited state absorption and energy transfer may be proposed as processes responsible for the population of the ⁴S_3/2 and ⁴F_9/2 erbium levels upon IR excitation. The mechanisms responsible for the up-conversion luminescence are discussed.     

Infrared emission and defect centres in Er and Yb codoped Y3Al5O12 phosphors

YAG phosphor powders doped/codoped with Er³⁺/(Er³⁺ + Yb³⁺) have been synthesised by using the solution combustion method. The effect of direct pumping into the ⁴I_11/2 level under 980 nm excitation of doped/codoped Er³⁺/Yb³⁺−Er³⁺ in Y₃Al₅O₁₂ (YAG) phosphor responsible for an infrared (IR) emission peaking at ∼1.53 μm corresponding to the ⁴I_13/2→⁴I_15/2 transition has been studied. YAG exhibits three thermally-stimulated luminescence (TSL) peaks at around 140°C, 210°C and 445°C. Electron spin resonance (ESR) studies were carried out to identify the centres responsible for the TSL peaks. The room temperature ESR spectrum of irradiated phosphor appears to be a superposition of two distinct centres. One of the centres (centre I) with principal g-value 2.0176 is identified as O⁻ ion, while centre II with an isotropic g-factor 2.0020 is assigned to an F⁺ centre (singly ionised oxygen vacancy). An additional defect centre is observed during thermal-annealing experiments and this centre (assigned to F⁺ centre) seems to originate from an F-centre (oxygen vacancy with two electrons) and these two centres appear to correlate with the observed high-temperature TSL peak in YAG phosphor.