Unique decomposition of lattices over orders

1975 ◽  
pp. 168-176
Author(s):  
H. Jacobinski
Keyword(s):  
Unique Decomposition

scholarly journals Linking the Spectra of Decomposing Litter to Ecosystem Processes: Tandem Close-Range Hyperspectral Imagery and Decomposition Metrics

2022 ◽  
Vol 14 (2) ◽  
pp. 370
Author(s):  
Cameron Proctor ◽  
Cedelle Pereira ◽  
Tian Jin ◽  
Gloria Lim ◽  
Yuhong He
Keyword(s):  
Remote Sensing ◽  
Spatial Scales ◽  
Ecosystem Processes ◽  
Carbon Dioxide Flux ◽  
Decomposition Process ◽  
Spectral Variation ◽  
Unique Decomposition ◽  
Decomposition Dynamics ◽  
Close Range ◽  
Surface Decomposition

Efforts to monitor terrestrial decomposition dynamics at broad spatial scales are hampered by the lack of a cost-effective and scalable means to track the decomposition process. Recent advances in remote sensing have enabled the simulation of litter spectra throughout decomposition for grasses in general, yet unique decomposition pathways are hypothesized to create subtly different litter spectral signatures with unique ecosystem functional significance. The objectives of this study were to improve spectra–decomposition linkages and thereby enable the more comprehensive monitoring of ecosystem processes such as nutrient and carbon cycles. Using close-range hyperspectral imaging, litter spectra and multiple decomposition metrics were concurrently monitored in four classes of naturally decayed litter under four decomposition treatments. The first principal component accounted for approximately 94% of spectral variation in the close-range imagery and was attributed to the progression of decomposition. Decomposition-induced spectral changes were moderately correlated with the leaf carbon to nitrogen ratio (R2 = 0.52) and sodium hydroxide extractables (R2 = 0.45) but had no correlation with carbon dioxide flux. Temperature and humidity strongly influenced the decomposition process but did not influence spectral variability or the patterns of surface decomposition. The outcome of the study is that litter spectra are linked to important metrics of decomposition and thus remote sensing could be utilized to assess decomposition dynamics and the implications for nutrient recycling at broad spatial scales. A secondary study outcome is the need to resolve methodological challenges related to inducing unique decomposition pathways in a lab environment. Improving decomposition treatments that mimic real-world conditions of temperature, humidity, insolation, and the decomposer community will enable an improved understanding of the impacts of climatic change, which are expected to strongly affect microbially mediated decomposition.

Valuation Rings and Rigid Elements in Fields

1981 ◽  
Vol 33 (6) ◽  
pp. 1338-1355 ◽  
Author(s):  
Roger Ware
Keyword(s):  
Quadratic Form ◽  
Nonzero Element ◽  
Discrete Valuation Ring ◽  
Binary Quadratic Form ◽  
Valuation Rings ◽  
Unique Decomposition ◽  
Complete Discrete Valuation Ring ◽  
Residue Class Field ◽  
Uniformizing Parameter ◽  
Anisotropic Quadratic Form

In [20], T. A. Springer proved that if A is a complete discrete valuation ring with field of fractions F, residue class field of characteristic not 2, and uniformizing parameter π then any anisotropic quadratic form q over F has a unique decomposition as q = q1 ⊥ 〈π〉q2, where q1 and q2 represent only units of A, modulo squares in F (compare [14, Satz 12.2.2], [19, §4], [18, Theorem 8.9]). Consequently the binary quadratic form x2 + πy2 represents only elements in Ḟ2 ∪ πḞ2, where Ḟ2 denotes the set of nonzero squares in F. Szymiczek [21] has called a nonzero element a in a field F rigid if the binary quadratic form x2 + ay2 represents only elements in Ḟ2 ∪ aḞ2.

Unique decomposition of low-order time series

2015 ◽  
Vol 45 (11) ◽  
pp. 3357-3366
Author(s):  
Eugene Seneta ◽  
Simon Ku
Keyword(s):  
Time Series ◽  
Unique Decomposition ◽  
Low Order

A UNIQUE DECOMPOSITION THEOREM FOR FACTORIAL LANGUAGES

2005 ◽  
Vol 15 (01) ◽  
pp. 149-160 ◽  
Author(s):  
S. V. AVGUSTINOVICH ◽  
A. E. FRID
Keyword(s):  
Decomposition Theorem ◽  
Canonical Decomposition ◽  
Unique Decomposition

We study decompositions of a factorial language to catenations of factorial languages and introduce the notion of a canonical decomposition. Then we prove that for each factorial language, a canonical decomposition exists and is unique.

scholarly journals Action of Finite Group Presentations on Signal Space

2021 ◽  
pp. 17-29
Author(s):  
D. Samaila ◽  
G. N. Shu’aibu ◽  
B. A. Modu
Keyword(s):  
Signal Processing ◽  
Finite Group ◽  
Finite Groups ◽  
Theoretic Approach ◽  
Signal Space ◽  
Unique Decomposition ◽  
Group Presentations ◽  
Different Types ◽  
Signal Processing Algorithms ◽  
Processing Algorithms

The use of finite group presentations in signal processing has not been exploit in the current literature. Based on the existing signal processing algorithms (not necessarily group theoretic approach), various signal processing transforms have unique decomposition capabilities, that is, different types of signal has different transformation combination. This paper aimed at studying representation of finite groups via their actions on Signal space and to use more than one transformation to process a signal within the context of group theory. The objective is achieved by using group generators as actions on Signal space which produced output signal for every corresponding input signal. It is proved that the subgroup presentations act on signal space by conjugation. Hence, a different approach to signal processing using group of transformations and presentations is established.

Sign in / Sign up

Export Citation Format

Share Document