Effects of ash fertilization and prescribed burning on macronutrient,
heavy metal, sulphur and
137Cs concentrations in lingonberries
(
Vaccinium vitis-idaea
)
Teuvo Levula
1,a, Anna Saarsalmi
b,*, Aino Rantavaara
2,caFinnish Forest Research Institute, Parkano Research Station, Kaironiementie 54, FIN-39700, Parkano, Finland bFinnish Forest Research Institute, Vantaa Research Centre, P.O. Box 18, FIN-01301, Vantaa, Finland
cRadiation and Nuclear Safety Authority (STUK), P.O. Box 14, FIN-00881, Helsinki, Finland
Received 2 October 1998; received in revised form 9 February 1999; accepted 16 February 1999
Abstract
The effects of ash fertilization and prescribed burning on the P, K, Ca, Mg, Mn, S, Fe, Al, Cu, Zn, Cd, Cr, Ni and137Cs concentrations in lingonberry (Vaccinium vitis-idaea L.) berries were investigated in a 100-year-old Scots pine (Pinus sylvestrisL.) stand growing on a dry site in central Finland. The treatments were control, prescribed burning and three ash-fertilizer doses of 1000, 2500 and 5000 kg haÿ1
. The size of the plots was 3030 m, and there were four replications per treatment. Lingonberries were collected two (1991) and seven (1996) growing seasons after the treatments. Ash fertilization had no effect on the heavy metal concentrations in the berries. Potassium was the only macronutrient whose concentration in the berries signi®cantly increased after ash fertilization (5000 kg haÿ1). Prescribed burning increased the berry Cd
concentrations, which, however, remained low even after prescribed burning. The berry137Cs concentrations decreased as a result of ash fertilization and prescribed burning. The reduction in137Cs concentrations caused by ash fertilization may be an
important ®nding especially for areas where the picking and consumption of berries has to be restricted as a result of radioactive fallout.#2000 Elsevier Science B.V. All rights reserved.
Keywords:Radiocaesium; Potassium; Forest soil
1. Introduction
Nutrient cycling in forests in the cool, humid con-ditions of the boreal coniferous forest zone is slow, and acidic humus material accumulates on the soil surface.
In addition to the slow, natural acidi®cation that occurs during the development of such soils, they are also sensitive to external inputs of acidifying compounds. For this reason, the atmospheric deposition of acid-ifying compounds is expected to gradually increase the leaching of base cations and soil acidi®cation. Attempts have been made to slow down the anthro-pogenic acidi®cation of forest soils by silvicultural means, e.g. by prescribed burning and ash fertiliza-tion.
1Tel. +358-3-44351, e-mail: teuvo.levula@metla.fi 2Tel.: +358-9-759881; e-mail: aino.rantavaara@stuk.fi
*Corresponding author. Tel.: 857051; fax: +358-9-8572575.
E-mail address:anna.saarsalmi@metla.fi (A. Saarsalmi).
In prescribed burning, logging residues, ground vegetation and part of the organic layer are burnt and the surface of the soil heats up (Viro, 1969). The maximum temperature of the soil surface during prescribed burning can momentarily be as high as 8008C (Vasander and Lindholm, 1985). Apart from the extremely high temperatures reached during burning, prescribed burning has a bene®cial effect on the longer term temperature conditions in the soil of the boreal forest. In addition to temperature, prescribed burning also affects the nutrient status of the soil. The mineral nutrients bound in the organic matter are converted into oxides during burning, many of which have an alkaline reaction. The hydroxyl ions formed after dissolution of these oxides have an immediate redu-cing effect on soil acidity, and the released base cations (Ca, Mg, K, Na) can increase the buffering capacity of the soil for decades (Viro, 1969; MaÈlkoÈnen and Levula, 1996).
Apart from N and S, wood ash contains mineral nutrients in almost the same proportions as in the stand biomass. Ash fertilization does not have the heating effect of prescribed burning, but in other respects the effects of ash fertilization are similar to those of prescribed burning. Wood ash has increased stand growth on N-rich peatlands (Silfverberg and Huikari, 1985; Silfverberg and Hotanen, 1989), but not on mineral soils (MaÈlkoÈnen and Levula, 1996; SikstroÈm, 1992). In the case of mineral soil sites, however, the bene®ts of using ash fertilization are associated with its role as an ameliorative agent and stimulator of the biological activity of the soil, rather than as a source of nutrients.
In addition to base cations, wood ash also contains heavy metals (e.g. Cu, Zn, Mn, Pb, Cd, Cr, Hg, Ni). Some of these metals (Mn, Cu, Zn) are essential trace elements for plants. It has been suspected that these heavy metals may be harmful for soil microbial activity and nutrient cycling, and represent a health hazard for people collecting edible products from the forest such as berries and fungi. The most harmful heavy metals are Cd, Hg and Pb, of which Cd is the only metal of any practical importance. However, when moderate doses are applied, the normal range of Cd concentrations in wood ash has no detrimental effects on organic matter decomposition or on the rate of nutrient mineralization (Fritze et al., 1994). In laboratory experiments, the respiration of soil, treated
with ash fertilizer,was reduced only on a Cd addition of 0.4 mg kgÿ1
of soil, as compared to that of the controls (Fritze et al., 1995).
In nature, Cd concentrations are normally very low. However, owing to its severe toxicity and relatively high mobility and enrichment, it is considered to be perhaps the most problematic of the heavy metals. Normally the Cd concentrations in wood ash vary from 4 to 20 mg kgÿ1
(Anonymous, 1993). In Finland, the application to agricultural soil of ash which contains >3 mg kgÿ1
Cd is prohibited (Anon-ymous, 1994), but this restriction does not hold for forest soils.
Wood ash fertilization results in lush development of the ground vegetation on N-rich, drained peatlands (Silfverberg and Huikari, 1985; Silfverberg and Hotanen, 1989), while on infertile drained peatlands it has only slight effects on the ground vegetation, apart from a reduction in the coverage of Sphagnum
spp. (Vasander et al., 1988). No signi®cant changes in the ground vegetation have been observed on mineral soils following ash fertilization (Gyllin and Kruuse, 1996; RuÈhling, 1996).
Following the Chernobyl nuclear accident (1986), attention started to be paid in Finland to the levels of radioactive Cs, primarily137Cs, in forest ecosystems (Dahlgaard et al., 1994). Caesium, which occurs naturally in the bedrock, is not known to have any signi®cance as a nutrient, but it may, to a small extent, replace K in the metabolism of animals and plants, and thus be transferred from the soil to living organisms (Koljonen et al., 1992). The radioactive Cs which is formed in nuclear reactions behaves, when it enters the nutrient cycle, in the same way as the natural isotope of Cs and expose, via the food chain, humans to radiation.
The radiocaesium concentrations of forest berries and fungi in Finland have been monitored regularly since 1986 (Rantavaara, 1990). Plants take up Cs from forest soil much more ef®ciently than from agricul-tural land. This has been demonstrated by the Finnish studies on137Cs concentrations in moose (Alces alces
Fertilization has been found to reduce 137Cs con-centrations in many crop plants (Fredriksson, 1963). In Finland, the effects of fertilization on the radio-caesium transfer in forests has been emphasized in radioecological research (Raitio and Rantavaara, 1994).
The aim of this study is to determine the effects of ash fertilization and prescribed burning on the macro-nutrient, heavy metal, sulphur and 137Cs concentra-tions in the berries of lingonberry (Vaccinium vitis-idaeaL.) growing in a Scots pine stand on a dry site.
2. Material and methods
A ®eld experiment was established in a 100-year-old Scots pine (Pinus sylvestrisL.) stand at Kuorevesi (62820
N, 248500
E, 130 m asl), central Finland, in the spring of 1990. At the time of establishment the stem number of the stand was 300 stems haÿ1
, mean height 21 m, and the volume including bark 180 m3haÿ1
. The site was of the dry site type, the soil texture sorted sand and the soil type iron podsol. The thickness of the humus layer was 3 cm. The organic matter content of the humus layer was 75%.
The experiment was laid out in a random block design, with ®ve treatments in four blocks. The treat-ments within each block were performed on 3030 plots with a control, three levels of ash fertilization (1000, 2500 and 5000 kg haÿ1
) and a prescribed burning treatment. The ash used was derived from the ignited bark (850±10008C for ca. 30 min) mechanically stripped from the stems of Scots pine and Norway spruce (Picea abies(L.) Karsten) during processing for saw timber. According to current knowledge, 5000 kg haÿ1
is a relatively high dose of wood ash. The composition of the bark ash used in the experiment was, on a dry weight basis, as follows: P, 13; K, 36; Ca, 280; Mg, 21; and Mn, 16 g kgÿ1
; and Fe, 4300; Al, 9400; Cu, 90; Zn, 630; Cd, 1.4; and Pb, 19 mg kgÿ1
. The approximate concentration of137Cs in ash, ranging from 5000 to 10 000 Bq kgÿ1
, was derived from the data on ash origin, namely the regional 137Cs deposited in the delivery area of timber (Arvela et al., 1990) and from the data on radioactivity of Finnish timber, and parti-cularly bark of pine and spruce (Rantavaara, 1996). The original surface density of the137Cs activity at the
site was ca. 50 000 Bq mÿ2
(1 October, 1991). The ash was spread on the plots on 21±22 May, 1990. The prescribed burning treatment was prepared as follows. Pine and spruce cutting residues (ca. 19 t haÿ1
, dry weight) from a neighbouring cutting area were spread on the plots to carry a ®re and ensure burning of the ground vegetation. With the cutting residues, roughly 1000 Bq137Cs mÿ2
was added to the plots. Prescribed burning was performed on 14 May, 1990. All the trees on the experimental area were left standing.
Samples were taken from the humus layer in 1990, one growing season after the treatments. Fifteen sub-samples were taken systematically from each plot using a cylinder (d5.8 cm). The thickness of the humus layer was measured at the same time. The subsamples were combined to give one composite sample per plot. The samples were air-dried and milled to pass through a 2-mm sieve. Exchangeable and extractable nutrients (P, K, Ca, Mn and Zn) were determined by extraction with 1 M ammonium acetate (pH 4.65) and analyzed by inductively coupled plasma atomic emission spectrometry (ICP/AES), total N on a CHN analyser (LECO), and pH from a water suspen-sion (Halonen et al., 1983). The Al concentration was determined by titration following extraction with 1 M KCl.
Lingonberry samples were collected from each plot in autumn 1991 and 1996. The berries were collected when ripe using protective gloves. In 1991 there were no berries on the burnt plots. The dried berries (608C, 5 days) were milled in an ultracentrifuge mill. The element (P, K, Ca, Mg, Mn, S, Fe, Al, Cu, Zn, Cr, Cd, Ni) concentrations were determined by wet digestion (HNO3H2O2) (Huang and Schulte, 1985). The Cd
concentration was determined by ¯ameless AAS, and the other elements by ICP/AES.
The 137Cs concentration was determined from the lingonberry samples using a low-background semi-conductor spectrometer calibrated for the analysis of environmental radioactivity. A standard sample geo-metry was used. The gamma spectra were analyzed using the GAMMA-83 computer code developed at STUK. The method has been tested in several inter-national and Nordic comparison programmes for gamma spectrometric radiocaesium determinations (Rantavaara et al., 1994). For a realistic comparison of the concentration of 137Cs in the two samplings (1991 and 1996), the effect of radioactive decay on the
concentrations was eliminated by correcting all the
137
Cs concentrations to correspond to the activity in October 1991.
The coverage of the ground vegetation was studied in August 1995. Eight 1-m2 quadrats were system-atically marked out on each plot, and the coverage of ®eld and bottom layer species estimated.
The effects of the treatments on the element concentrations in the humus layer and berries and on the coverage of species were tested using analysis of variance. Tukey's paired t-test was used to test the statistical signi®cance of differences between the treatments (BMDP statistical software, 1985).
3. Results
3.1. Acidity and nutrient content of the humus layer
The total N, extractable P and exchangeable Mg concentrations on the control plots were slightly lower, the K concentrations about the same, and the Ca concentrations higher than the mean values for this site type in Southern Finland (Fig. 1) (cf. Tamminen, 1991). Ash fertilization and burning decreased the acidity of the humus layer and increased the base cation concentrations. The Ca and Mg concentrations were, after one growing season, somewhat higher on the burned plots than on the plots given 1000 kg ash haÿ1
, but clearly lower than after the addition of 5000 kg ash haÿ1
. After the largest ash dose, the exchangeable nutrient concentrations increased to a level higher than the average for herb-rich sites in southern Finland (cf. Tamminen, 1991). The exchangeable Al concentration in the humus layer decreased along with the increase in pH. There was no exchangeable Al at all on the plots that were burnt or given 5000 kg ash haÿ1
.
3.2. Element composition of the lingonberries
Ash fertilization (5000 kg haÿ1
) increased the K concentrations of the lingonberries compared to the controls in both the sampling years (Table 1). In contrast, the Mn concentrations after seven growing seasons were signi®cantly lower on both, the burnt and ash-fertilized plots than on the controls. Burning increased the Cd and Al concentrations in the berries. The change in the Al concentration was statistically only indicative (p< 0.1). Neither burning nor ash-fertilization had any signi®cant effect on the concentrations of other macronutrients. The Ca con-centration was higher, but the Al concon-centration was lower, in the berries in all the treatments in 1996 as compared to 1991. There were no statistical differ-ences in other element concentrations between the sampling years.
3.3. Cs concentrations of lingonberries
Prescribed burning and ash-fertilization reduced the 137Cs concentrations in the berries (Fig. 2), which were higher after seven growing seasons on
the controls and ash-fertilized (1000 kg haÿ1
) plots than after two growing seasons. There were no differences in the berry 137Cs concentrations in the other ash-fertilizer treatments between the sampling years. Seven growing seasons after the treatments, the
137
Cs concentrations were signi®cantly lower on the burnt and ash-fertilized (2500 and 5000 kg haÿ1
) plots than on the control or ash-fertilized (1000 kg haÿ1
) plots.
The 137Cs concentrations in the berries clearly correlated inversely with the pH of the humus layer and the exchangeable macronutrient concentrations (Fig. 3). The 137Cs concentration of the berries was best explained by the exchangeable Mg concentration in the humus layer (R20.88).
3.4. Ground vegetation
The dominant ®eld layer species on the control and ash-fertilized plots were lingonberry (Vaccinium vitis-idaea) and crowberry (Empetrum nigrum), and the bottom layer species red-stemmed feather moss (Pleurozium schreberi) and wavy fork moss ( Dicra-num polysetum) (Table 2). The dominant species on the burnt plots were lingonberry and purple-fruiting heath moss (Ceratodon purpureus). Crowberry, red-Fig. 2. 137Cs concentration (dry matter basis) in the lingonberries
in becquerels (Bq kgÿ1) two (in 1991) and seven (1996) growing
seasons after prescribed burning or wood ash-fertilization. Mean values with the same letter do not differ significantly from each other according to the F-test (p< 0.5). Standard deviation is marked on the columns by bars.
stemmed feather moss or wavy fork moss had not reappeared on the burnt plots even after six growing seasons. The coverage of lingonberry on both, the burnt and control plots was 17%. Ash fertilization
reduced the coverage of lingonberry to some extent. On the plot given the largest dose of ash (5000 kg haÿ1
) the coverage of lingonberry was only 8%.
Table 1
Element concentrations in the lingonberries two (in 1991) and seven (in 1996) growing seasons after prescribed burning or wood-ash fertilization.
Nutrient Year Control Burnede Ashe(kg haÿ1) F-value
1000 2500 5000
P (g kgÿ1) 1991 1.1 Ðd 1.2 1.1 1.2 3.1
1996 1.2 1.1 1.1 1.1 1.2 1.2
K (g kgÿ1) 1991 6.0a Ðd 6.8ab 6.6a 7.6b 11.2***c
1996 6.3a 6.4ab 6.1a 6.4ab 7.2b 4.3*a
Ca (g kgÿ1) 1991 1.3 Ðd 1.2 1.3 1.3 0.3
1996 1.6 1.3 1.5 1.5 1.6 2.0
Mg (g kgÿ1) 1991 0.5 Ðd 0.6 0.6 0.6 1.4
1996 0.6 0.6 0.6 0.6 0.7 1.2
Mn (mg kgÿ1) 1991 253 Ðd 241 254 261 0.2
1996 274b 261a 249a 204a 178a 3.7*a
S (mg kgÿ1) 1991 747 Ðd 758 720 755 1.0
1996 781 711 735 714 752 0.9
Fe (mg kgÿ1) 1991 15 Ðd 15 13 15 1.1
1996 14 14 14 13 14 0.7
Al (mg kgÿ1) 1991 32 Ðd 30 27 30 1.1
1996 24 29 24 19 18 2.6
Cu (mg kgÿ1) 1991 5.7 Ðd 5.9 5.0 5.3 3.3
1996 5.8 5.2 5.9 5.1 5.4 1.5
Zn (mg kgÿ1) 1991 11 Ðd 11 11 11 0.6
1996 11 11 11 11 11 1.0
Cd (mg kgÿ1) 1991 0.004 Ðd 0.004 0.003 0.005 1.1
1996 0.003a 0.009b 0.003a 0.003a 0.003a 5.1**b
Cr (mg kgÿ1) 1991 0.2 Ðd 0.2 0.2 0.2 0.2
1996 0.2 0.2 0.2 0.2 0.2 0.7
Ni (mg kgÿ1) 1991 0.3 Ðd 0.3 0.3 0.3 1.4
1996 0.4 0.3 0.3 0.3 0.3 2.9
a*p< 0.05. b**p< 0.01. c***p< 0.001.
4. Discussion
Changes in soil acidity affect the chemical and biological properties of the soil, thus in¯uencing the uptake of nutrients by plants. The increase in the pH of the substrate caused by ash fertilization may have a detrimental effect on the functioning of the mycor-rhizas of berry species (Moberg and TidstroÈm, 1985). According to RuÈhling (1996), the fungi which form mycorrhizal associations decrease after ash fertiliza-tion, while fungi that decompose litter increase. According to Swedish studies, a reduction in lingon-berry stands was not observed on mineral soil sites 2±9
years after ash fertilization (Gyllin and Kruuse, 1996). In this study, however, the dwarf shrub stand was slightly reduced by the application of 5000 kg ash haÿ1
.
Changes in the ground vegetation after prescribed burning are long-lasting. According to Viro (1969), 10 years after burning the coverage of mosses was about one-third and that of dwarf shrubs about half that on unburnt plots. On the burnt plots in this study crow-berry plants, red-stemmed feather moss or wavy fork moss had not reappeared at all after six growing seasons, but the coverage of lingonberry was already the same as on the control plots.
Fig. 3. Dependence of137Cs concentration in the lingonberries on nutrient concentrations and pH
(water)in the humus layer in 1991.
The nutrient concentrations of the lingonberries in this study were of the same level as those reported in earlier studies (Silfverberg and Issakainen, 1991; Laine et al., 1993; RuÈhling, 1996). The Cd concentra-tions in this study were lower than those reported by Silfverberg and Issakainen (1991), but of the same level as those obtained by RuÈhling (1996). The natural Cd concentrations in berries are <1 mg kgÿ1
(Varo et al., 1980; Silfverberg and Issakainen, 1991; Laine et al., 1993; Eriksson, 1996; RuÈhling, 1996; Nilsson and Eriksson, 1998). In earlier studies, the Cd concentra-tions of lingonberries have varied between 0.004 to 0.3 mg kgÿ1
, which is of the same magnitude or slightly higher than those in blueberry (Vaccinium myrtillus L.), but clearly lower than those in cloud-berry (Rubus chamaemorus L.) (Varo et al., 1980; Silfverberg and Issakainen, 1991; RuÈhling, 1996). Fungi have clearly higher Cd concentrations than berries, ceps (Boletus edulis Fr.) even reaching 12 mg kgÿ1
(Kojo and Lodenius, 1989; RuÈhling, 1996). Although differences have been found in the natural element concentrations of berry species, the type of site (peatland or mineral soil) has only a minor effect on the nutrient concentrations of berries (Silf-verberg and Issakainen, 1991).
The Cd in ash can remain in an insoluble form for a long time owing to the pH-increasing effect of the ash (Eriksson, 1991). The Cd concentration of the wood ash used in this study was low, 1.4 mg kgÿ1
, and the amount of Cd applied in the ash (totalling 2±7 g haÿ1
) had no effect on the Cd concentrations in the lingon-berries even seven growing seasons after application. Wood ash with a normal range of Cd concentrations has not increased the Cd concentrations in the leaves and berries of lingonberry and blueberry (Silfverberg and Issakainen, 1991; Rehell, 1991; Eriksson, 1996; RuÈhling, 1996; Nilsson and Eriksson, 1998). Thus, it would appear that wood-ash fertilization does not increase the concentrations of other heavy metals even in the berries of lingonberry, as has been also con-cluded in earlier studies (Silfverberg and Issakainen, 1991; Eriksson, 1996; RuÈhling, 1996).
In this study, K was the only nutrient which increased signi®cantly after ash fertilization (cf. also Silfverberg and Issakainen, 1991). Because K is a highly mobile nutrient, it moves rapidly from the soil into the plants. The decrease in the Mn concentrations in the lingonberries as a result of ash fertilization and prescribed burning is connected to the reduction in soil acidity. Mn is in an easily soluble form in acidic soils, Table 2
Coverage of plant species six growing seasons after prescribed burning or wood ash fertilization
Plant species Coverage (%)
controla burneda asha(kg haÿ1)
1000 2500 5000
Lichens
Cladonia rangiferina(L.) Weber ex F. H. Wigg. 7 0 5 3 1
Cladonia arbuscula(Wallr.) Flot. 1 0 0 1 0
Mosses
Ceratodon purpureus(Hedw.) Brid. 0 18 0 0 0
Dicranum polysetumSw. 22a 0b 25a 19a 11a
Hylocomium splendens(Hedw.) 2 0 3 5 2
Pleurozium schreberi(Brid.) Mitt. 50a 0b 52a 57a 68a
Pohlia nutans(Hedw.) Lindb. 0 5 0 0 0
Polytrichum juniperumHedw. 0 5 0 0 0
Vascular species
Calluna vulgaris(L.) 2 2 3 2 3
Empetrum nigrumL. 13a 0b 15a 11a 9a
Epilobium angustifoliumL. 0 1 0 0 0
Vaccinium vitis-idaeaL. 17 16 14 12 8
and it is transported in large amounts to different parts of the plants.
No signi®cant changes were observed in the Al concentrations of the lingonberries, even though ash fertilization signi®cantly reduced both, the acidity of the humus layer and the concentrations of exchange-able Al (cf. also Silfverberg and Issakainen, 1991). On the burnt plots, where the humus layer contained no exchangeable Al at all, the Al concentrations in the lingonberries were even higher than those in the other treatments. The Al concentrations in pine needles have also been reported to increase after prescribed burning (Levula, 1991; MaÈlkoÈnen and Levula, 1996).
The ash treatments and prescribed burning reduced the concentration of137Cs in the lingonberries despite an additional dose of 1±10% of137Cs to the soil in connection with the treatments. The effect of ash, and particularly K, was similar to the ®ndings in earlier studies on agricultural systems (Fredriksson, 1963). The addition of exchangeable K, with smaller ionic radius than its chemical analogue Cs, decreases the uptake of Cs by plants. The reduction in137Cs con-centrations appeared to be clearly dependent on the acidity and exchangeable Mg, Ca, K and extractable P concentrations of the humus layer. However, it is not possible on the basis of this study to conclude which of the nutrients added in the ash or burning were respon-sible for the observed reduction in lingonberry137Cs concentrations. The effect of ash fertilization in low-ering lingonberry137Cs concentrations may be impor-tant in relation to the picking and consumption of berries, particularly in areas that have suffered large-scale radioactive fallout.
Owing to the volatile nature of Cs, the losses of
137
Cs to the atmosphere during burning of forest organic material are unknown but probable (Horrill et al., 1995). The observed decline in lingonberry
137
Cs concentrations after the prescribed burning treatment may partially be due to smoke losses of Cs from the humus layer. Part of the caesium so released to the atmosphere will probably be deposited locally, increasing the137Cs content of the lingonber-ries close to the burned plots, including the control plots. This may have partially caused the observed delayed increase in 137Cs concentrations in lingon-berries collected from the controls and ash fertilized plots (1000 kg haÿ1
) in 1996. Nevertheless, the experiment did show a reduction in137Cs uptake by
the lingonberries in both, the ash fertilized and burned plots.
The recycling of wood ash back to the forest, thus, does not appear to be problematic from the point of view of the nutrient or heavy metal concentrations in berries. The amounts of ash applied in this study are hardly likely to create long-term problems, because no increases in lingonberry heavy-metal concentrations were observed seven growing seasons after the ash application. However, spreading large amounts of ash in the forest may be a questionable practice if the reduction in the stand of lingonberries observed in this study following the application of 5000 kg of ash haÿ1
is likely to occur on other sites.
Acknowledgements
We are grateful to Prof. Eino MaÈlkoÈnen and Klaus Silfverberg, Ph.D. for valuable comments on the manuscript, and to John Derome, Lic. For for translat-ing the text into English.
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