Goldbach's Problem in the Ring M n (Z)

Wang, Jun

doi:10.2307/2324122

Cited by 3 publications

(2 citation statements)

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“…Lenard and colleagues worked on phosphors, and they used different rare earth ions in addition to heavy metal ions as luminescent ions in different host materials. 57 Frank Condon, Fonger, and Struck are significant personalities who have aided in the comprehension of some of the temporal characteristics of luminescence. During this period of time there were only few literatures on the phosphor-based thermometry until 2000. later in 2002, Wang et al, 58 published a work of using luminescent nanophosphors for thermometry application.…”

Section: History Of Phosphor-based Optical Thermometersmentioning

confidence: 99%

Review—Structural and Optical Interpretations on Phosphor-Based Optical Thermometry

Tejas Chennappa,

Kamath

2024

ECS J. Solid State Sci. Technol.

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This comprehensive review article discusses the brief history, development, and applications of phosphor-based optical thermometers, which have become increasingly important in various fields due to their ability to measure temperature remotely and with high precision. The article highlights the importance of choosing the suitable phosphor material for a given application, considering factors such as crystal structure and mode of thermometry. It then delves into the structural importance of phosphors, discussing their luminescent properties. The review focuses particularly on fluorescence-based temperature-dependent techniques, including the fluorescence intensity ratio method, which has garnered significant attention due to its straightforward implementation, affordability, and self-referential nature. The article discusses the mathematical formulations underlying this method, including the Boltzmann distribution and the effective lifetime calculation. The review also explores the concept of dual-mode thermometry, which involves the use of multiple luminescent centers to enhance sensitivity and thermal stability. This approach is particularly useful in applications where single-emitter thermometers are vulnerable to variations in excitation intensity or detector stability. The article highlights the advantages, limitations, and future developments of phosphor-based thermometers, including their ability to measure temperature remotely and with high precision.

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Section: History Of Phosphor-based Optical Thermometersmentioning

confidence: 99%

Review—Structural and Optical Interpretations on Phosphor-Based Optical Thermometry

Tejas Chennappa,

Kamath

2024

ECS J. Solid State Sci. Technol.

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“…In 1965, Hayes [4] proved that every polynomial in Z[x] of degree d 1 is expressible as the sum of two irreducible polynomials in Z[x], each of degree d. This result was later rediscovered by Rattan and Stewart in [8], and its various generalizations and specializations (for monic polynomials, for polynomials in the ring R [x], where R is not necessarily Z, for matrices, etc.) have been given in [1,3,5,7,[11][12][13]. In particular, for a monic polynomial f in the ring Z[x], there is an asymptotical formula for the number of representations of f by the sum of several irreducible monic polynomials, each of height at most T (see [2,6,9]).…”

Section: Representations By a Linear Formmentioning

confidence: 99%