Efficient spectral regulation in Ce:Lu3(Al,Cr)5O12 and Ce:Lu3(Al,Cr)5O12/Ce:Y3Al5O12 transparent ceramics with high color rendering index for high-power white LEDs/LDs

Realizing a high color rendering index (CRI) in Ce:LuAG transparent ceramics (TCs) with desired thermal stability is essential to their applications in white LEDs/LDs as color converters. In this study, based on the scheme of configuring the red component by Cr3+ doping, an efficient spectral regulation was realized in Ce,Cr:LuAG TCs. A unilateral shift phenomenon could be observed in both photoluminescence (PL) and photoluminescence excitation (PLE) spectra of TCs. By constructing TC-based white LED/LD devices in a remote excitation mode, luminescence properties of Ce,Cr:LuAG TCs were systematically investigated. The CRI values of Ce:LuAG TC based white LEDs could be increased by a magnitude of 46.2%. Particularly, by combining the as fabricated Ce,Cr:LuAG TCs with a 0.5 at% Ce:YAG TC, surprising CRI values of 88 and 85.5 were obtained in TC based white LEDs and LDs, respectively. Therefore, Ce,Cr:LuAG TC is a highly promising color convertor for high-power white LEDs/LDs applied in general lighting and displaying.

Efficient Spectral Regulation in Ce:Lu3(Al,Cr)5O12 and Ce:Lu3(Al,Cr)5O12/Ce:Y3Al5O12 Transparent Ceramics With High Color Rendering Index for High-Power White LEDs/LDs

Realizing a high color rendering index (CRI) in Ce:LuAG transparent ceramics (TCs) with desired thermal stability is essential to their applications in white LEDs/LDs as color converters. In this study, based on the scheme of configuring the red component by Cr3+ doping, an efficient spectral regulation was realized in Ce,Cr:LuAG TCs. A unilateral shift could be observed in both PL and PLE spectra. By constructing TC-based white LED/LD devices in a remote excitation mode, luminescence properties of Ce,Cr:LuAG TCs were systematically investigated. The CRI values of Ce:LuAG TC based white LEDs could be increased by a magnitude of 46.2%. Particularly, by combining Ce,Cr:LuAG TCs with a 0.5 at.% Ce:YAG TC, a surprising CRI values of 88 and 85.5 were obtained in TC based white LEDs and LDs, respectively. Therefore, Ce,Cr:LuAG TC is a highly promising color convertor for high-power white LEDs/LDs applied in general lighting and displaying.

On extended commuting operators

In this paper, we study properties of extended commuting operators. In particular, we provide the polar decomposition of the product of (?,?)-commuting operators where ? and ? are real numbers with ?? > 0. Furthermore, we find the restriction of ? for the product of (?,?)-commuting quasihyponormal operators to be quasihyponormal. We also give spectral and local spectral relations between ?-commuting operators. Moreover, we show that the operators ?-commuting with a unilateral shift are representable as weighted composition operators.

The invariant subspaces of S ⊕ S*

Using the tools of Sz.-Nagy–Foias theory of contractions, we describe in detail the invariant subspaces of the operator S ⊕ S*, where S is the unilateral shift on a Hilbert space. This answers a question of Câmara and Ross.

Conjugations in $$L^2$$ and their invariants

Conjugations in space $$L^2$$ L 2 of the unit circle commuting with multiplication by z or intertwining multiplications by z and $${{\bar{z}}}$$ z ¯ are characterized. We also study their behaviour with respect to the Hardy space, subspaces invariant for the unilateral shift and model spaces.

Some properties on extended eigenvalues and extended eigenvectors

In this paper, the study extended eigenvalues and extended eigenvectors, and we will investigate the and give for some concepts properties and result important, also we will find the and on the space, so U is Unilateral shift operator and . http://dx.doi.org/10.25130/tjps.24.2019.119

On the metrical theory of a non-regular continued fraction expansion

We introduced a new continued fraction expansions in our previous paper. For these expansions, we show the Brodén-Borel-Lévy type formula. Furthermore, we compute the transition probability function from this and the symbolic dynamical system of the natural number with the unilateral shift.

Heredity for triangular operators

A proof is given that if the lower triangular infinite matrix $T$ acts boundedly on $\ell^2$ and U is the unilateral shift, the sequence $(U^*)^nTU^n$ inherits from $T$ the following properties: posinormality, dominance, $M$-hyponormality, hyponormality, normality, compactness, and noncompactness. Also, it is demonstrated that the upper triangular matrix $T^*$ is dominant if and only if $T$ is a diagonal matrix.