Fredholmness of Toeplitz operators on the Fock space

The Fredholm property of Toeplitz operators on the $p$-Fock spaces $F_\alpha^p$ on $\mathbb{C}^n$ is studied. A general Fredholm criterion for arbitrary operators from the Toeplitz algebra $\mathcal{T}_{p,\alpha}$ on $F_\alpha^p$ in terms of the invertibility of limit operators is derived. This paper is based on previous work, which establishes corresponding results on the unit balls $\mathbb{B}^n$

Reply to Elmendorf and Ettinger: Photoperiod playsa dominantand irreplaceable role in triggering secondary growth resumption

In their Letter, Elmendorf and Ettinger (1) question the dominant role of photoperiod in driving secondary growth resumption (hereafter referred to as xylem formation onset) of the Northern Hemisphere conifers, recently reported by Huang et al. (2). Their opinions are grounded on the following three aspects, including 1) the seasonality of the photoperiod, 2) the dependence of the predictor variables (e.g., photoperiod, forcing, and chilling) on the response variable (the date of onset of xylem formation, day of the year [DOY]), and 3) the limited value of the obtained models for interannual forecasting. We think they bring up an interesting issue that deserves further discussion and clarification. Photoperiod is acknowledged to regulate spring bud swelling while wood formation starts (3, 4). Although photoperiod seasonality occurs at each site, its influence is marginal in our study given that the analysis involved comparisons among sites across the Northern Hemisphere. Our conclusion that photoperiod plays a dominant role was built upon the combination of several coherent pieces of evidence, rather than “the crux of Huang et al….” as they pointed out. First, we clearly stated that model 2, which modeled DOY as a function of the mean annual temperature of the site (MAT), forcing, chilling, and soil moisture, was considered the best model in terms of parsimony according to minimum Akaike information criterion and Bayesian information criterion, rather than R2 as referred to in their Letter. Second, photoperiod interacted with MAT and can explain 61.7% of the variance of MAT alone (2). Therefore, we concluded that secondary growth resumption was driven primarily by MAT and photoperiod or by their interaction, which is challenging to be disentangled without experimental data, we agree. In terms of biological functioning, they play an ..

Woody biomass production lags stem-girth increase by over one month in coniferous forests

Wood is the main terrestrial biotic reservoir for long-term carbon sequestration1, and its formation in trees consumes around 15% of anthropogenic carbon dioxide emissions each year2. However, the seasonal dynamics of woody biomass production cannot be quantified from eddy covariance or satellite observations. As such, our understanding of this key carbon cycle component, and its sensitivity to climate, remains limited. Here, we present high-resolution cellular based measurements of wood formation dynamics in three coniferous forest sites in northeastern France, performed over a period of 3 years. We show that stem woody biomass production lags behind stem-girth increase by over 1 month. We also analyse more general phenological observations of xylem tissue formation in Northern Hemisphere forests and find similar time lags in boreal, temperate, subalpine and Mediterranean forests. These time lags question the extension of the equivalence between stem size increase and woody biomass production to intra-annual time scales3–6. They also suggest that these two growth processes exhibit differential sensitivities to local environmental conditions. Indeed, in the wellwatered French sites the seasonal dynamics of stem-girth increase matched the photoperiod cycle, whereas those of woody biomass production closely followed the seasonal course of temperature. We suggest that forecasted changes in the annual cycle of climatic factors7 may shift the phase timing of stem size increase and woody biomass production in the future

Xylem formation in Fagus sylvatica during one growing season

The study analyses the activity of cambium and the increment of wood during one growing season of European beech (Fagus sylvatica L.) in the central part (region) of the Drahanská vrchovina, Czech Republic. The research plot was situated at an altitude of 630ma.s.l. The following parameters were studied: the beginning and end of cambial activity, differentiation of wood fibres and vessels and the total increment of wood during the growing season in six trees. Samples were taken during the growing season of 2010 in weekly intervals from the beginning of April to the end of October. The dormant cambium consisted of 5.3 cells on average; their number rose gradually after reactivation. The maximum number of cells (10 to 14, 9.1 on average) in the cambial zone persisted for 8 weeks; in mid-August the cambium ended its division activity, while the differentiation process continued till mid-September. The first fully lignified vessels were formed 5 to 6 weeks after their formation in the cambial zone. Vessels and adjacent wood fibres were the first elements to become fully lignified. The maximum production of cells (wood increment) was recorded from June 11 to June 24. 57% of the total ring width was formed in June. The mean ring width calculated by means of Gompertz function is 1777 μm (ranging from 1226 μm to 2423 μm)

Nine-year monitoring of cambial seasonality and cell production in Norway spruce

We analyzed the relationship between weather conditions and year-to-year (1981-1989) variation in the seasonal dynamics of cambial cell production (CCP) in Norway spruce in a monoculture forest area in the Czech Republic. We found that the timing of CCP greatly varied among the studied years. The onset of CCP occurred at the beginning of May and was strongly correlated with the April mean temperature. CCP ceased by the end of August. The timing of the cessation of CCP was more variable among trees and among years than its onset. The amount of precipitation positively influenced the duration of CCP and the average rate of cell production positively correlated to the minimum temperature in January-April, as well as the maximum temperature during the growing period. Our results show that the timing and the rate of CCP of xylem cells are influenced by temperature and precipitation. However, weather-xylem growth relations of spruce from temperate forests under climatic conditions are complex, since trees are known to respond less strongly to climatic average variation than influences of extreme conditions

Monitoring of xylem formation in Picea abies under drought stress influence

The effect of drought stress on regular cambium activity and wood formation in stems of two different clones of Norway spruce (Picea abies (L.) Karst.) was investigated. Tissue samples were taken during the growing season from May to September 2010. Artificial drought stress, induced by long-term sheltering of the soil, was significantly manifested in clone 15. In the stressed individual, the period of cambium activity was shorter, the total number of formed cells was lower and the resulting tree ring was narrower. The number of cells in the phases of postcambial growth and secondary cell wall formation was significantly lower in comparison to the control tree. The tracheid lignification process was slower in the tree stressed by water deficit and the first mature tracheids were observed later. On the other hand, in clone 18 probably genetic dispositions played an important role as no considerable deviations in the cambium activity and new wood cells production were observed. Fitting xylem increments to the Gompertz function showed that the period of the most intensive cell formation was at the turn of June and July and the maximum daily production of new cells was higher in non-stressed individuals than in the stressed ones. The results of the experiment lead us to the conclusion that drought stress can significantly affect the cambium activity of some clones, the differentiation process of anatomical elements, and thus also the resulting tree ring width