Fluorescence spectroscopy for characterization and differentiation of beers
ABSTRACT J. Inst. Brew. 110(4), 267–275, 2004 Total luminescence and synchronous scanning fluorescence spectroscopic techniques were applied for characterization of the intrinsic fluorescence of eight different beers. Spectra were mea-sured using different geometries to reveal the presence of similar fluorescent components. The total luminescence and synchro-nous fluorescence spectra exhibit a relatively intense short-wavelength emission ascribed to aromatic amino acids and less intense emission in the long-wavelength region, which may originate from B vitamins. Classification of beers based on their synchronous fluorescence spectra was performed using non-parametrical k nearest neighbours method and linear discrimi-nant analysis. Very good discrimination was obtained in both methods with a low classification error. The results demonstrate the potential of fluorescence techniques to characterize and dif-ferentiate beers.
Article: Synchronous fluorescence spectroscopy of edible vegetable oils. Quantification of tocopherols.[show abstract] [hide abstract]
ABSTRACT: The study demonstrates the application of front face and right angle synchronous fluorescence spectroscopy for the characterization of edible oils. The method enables monitoring of tocopherols, pheophytins, and other fluorescent components in edible oils. Principal component analysis of synchronous fluorescence spectra revealed sample clustering according to the type of oil. Partial least-squares regression was utilized to develop calibration models between fluorescence spectra and total tocopherol content determined by HPLC. The regression models showed a good ability to predict tocopherol content. The best fitting results were obtained for 1% v/v diluted oils and for bulk samples using the entire spectrum, yielding the regression coefficient, r, of 0.991, and root mean square error of cross-validation of approximately 8%. The results presented confirm the capabilities of the fluorescence techniques as a tool for the analysis of edible oils.Journal of Agricultural and Food Chemistry 10/2005; 53(18):6988-94. · 2.82 Impact Factor
VOL. 110, NO. 4, 2004 267
Fluorescence Spectroscopy for
Characterization and Differentiation of Beers
Ewa Sikorska1,6, Tomasz Górecki2, Igor V. Khmelinskii3,
Marek Sikorski4 and Denis De Keukeleire5
J. Inst. Brew. 110(4), 267–275, 2004
Total luminescence and synchronous scanning fluorescence
spectroscopic techniques were applied for characterization of the
intrinsic fluorescence of eight different beers. Spectra were mea-
sured using different geometries to reveal the presence of similar
fluorescent components. The total luminescence and synchro-
nous fluorescence spectra exhibit a relatively intense short-
wavelength emission ascribed to aromatic amino acids and less
intense emission in the long-wavelength region, which may
originate from B vitamins. Classification of beers based on their
synchronous fluorescence spectra was performed using non-
parametrical k nearest neighbours method and linear discrimi-
nant analysis. Very good discrimination was obtained in both
methods with a low classification error. The results demonstrate
the potential of fluorescence techniques to characterize and dif-
Key words: Beer, discriminant analysis, synchronous fluores-
cence spectroscopy, total luminescence spectroscopy.
Beer is a very complex mixture of many constituents
varying widely in nature and concentration levels1–3. Raw
materials including water, yeast, malt, and hops contain a
wide range of different chemical components that react
and interact at all stages of the brewing process. The inter-
est in studying the chemical composition of beer is
prompted by its importance for the assessment of beer
quality. It is important to develop fast analytical methods
without sample pre-treatment. Multidimensional fluores-
cence techniques, such as total luminescence and synchro-
nous scanning fluorescence are particularly useful for the
analysis of complex food matrices4. Total luminescence
spectroscopy (TLS) involves simultaneous acquisition at
multiple excitation and emission wavelengths. The result-
ing emission-excitation data matrix (EEM) provides a to-
tal intensity profile of the sample over the range of ex-
citation and emission wavelengths scanned. Synchronous
fluorescence spectroscopy takes advantage of the ability to
vary both the excitation and the emission wavelengths dur-
ing analysis, thereby maintaining a constant wavelength
difference. Both techniques have been successfully used
in the analysis of crude oils, pharmaceuticals, polycyclic
aromatic hydrocarbons, motor oils, and humic matter in
water4–7. Fluorescence spectral data and lifetimes in di-
luted beers have been explored recently8. We have re-
ported on the application of total fluorescence spectros-
copy to characterize beers9. The objective of the present
study was to investigate the intrinsic fluorescence of beers
for the purpose of discrimination by applying statistical
methods to their synchronous fluorescence spectra.
Eight different beers (seven lagers, beers A–G, and one
ale, beer H) from different breweries were bought in a
local supermarket. Samples were degassed in an ultrasonic
bath and diluted in water. The pH values were between
3.5 and 4.5.
Phenylalanine, tyrosine, tryptophan and riboflavin were
purchased from Aldrich.
Fluorescence spectra were obtained on a Fluorolog 3-
11 Spex-Jobin Yvon spectrofluorometer. A xenon lamp
was used as an excitation source. Excitation and emission
slit widths were 2 nm. The acquisition interval and the
integration time were maintained at 1 nm and 0.1 s, re-
spectively. A reference photodiode detector at the excita-
tion monochromator stage compensated for source inten-
sity fluctuations. Individual spectra were corrected for the
wavelength response of the apparatus. The right-angled
geometry was used for diluted beer samples in a 10 mm
fused-quartz cuvette. Front-face and back-face geometries
were used for bulk beers and measurements were per-
formed in a triangular fused-quartz cuvette.
Three-dimensional spectra were obtained by measuring
the emission spectra in the range from 290 to 700 nm at
excitation wavelengths from 250 to 500 nm, spaced by
1 Faculty of Commodity Science, Poznań University of Economics,
al. Niepodległości 10, 60-967 Poznań, Poland.
2 Faculty of Mathematics and Computer Science, A. Mickiewicz
University, ul. Umultowska 87, 61-614 Poznań, Poland.
3 Universidade do Algarve, FCT, Campus de Gambelas, Faro 8005-
4 Faculty of Chemistry, A. Mickiewicz University, Grunwaldzka 6,
60-780 Poznań, Poland.
5 Ghent University, Faculty of Pharmaceutical Sciences, Laboratory
of Pharmacognosy and Phytochemistry, Harelbekestraat 72, B-
9000 Ghent, Belgium.
6 Corresponding author. E-mail: firstname.lastname@example.org
Publication no. G-2004-1213-234
© 2004 The Institute & Guild of Brewing
268 JOURNAL OF THE INSTITUTE OF BREWING
5 nm intervals in the excitation domain. Fully corrected
spectra were then concatenated into an excitation-emission
Synchronous fluorescence spectra were collected by
simultaneously scanning the excitation and emission
monochromators in the 250–600 nm range with constant
wavelength differences ∆λ. Fluorescence intensities were
plotted as a function of the excitation wavelength. Four
spectra were recorded for each sample with ∆λ of 10, 30,
60, and 80 nm, respectively.
For statistical analysis, twelve synchronous fluores-
cence spectra with different ∆λ (10, 30, 60, 80 nm) were
recorded for each sample. Two methods of discriminant
analysis were used for the purpose of multiple group clas-
sification: nearest neighbours method (kNN)10 and linear
discriminant analysis (LDA)11.
The k-nearest neighbours method (kNN) is a well-
known non-parametric classification method10. The test
object is assigned to the cluster, which is most repre-
sented in the set of k nearest training objects. For each
data point, the closest data points, called nearest neigh-
bours, are searched for and used in the analysis. The k
values were chosen between 1 and 10 due to the small
size of the sample set. The kNN non-parametrical method
was preferred, because parametrical methods, like linear
discriminant analysis and quadratic discriminant analysis,
are often unsuitable for datasets with a number of vari-
ables exceeding the number of objects, due to observation
matrix singularity or to non-orthogonality of the data set.
The kNN method allows performing analyses using entire
spectra, without any prior reduction of the spectral data.
Additionally, linear discriminant analysis (LDA) was
performed on reduced data sets. For this purpose, six
wavelengths were extracted from the synchronous spectra
recorded at a particular ∆λ and analysed. Discriminant
coordinates were determined for the purpose of graphical
presentation, with the two discriminant coordinates used
in the plots.
The bootstrap method was applied to estimate the clas-
sification error. The dataset was randomly split into two
independent sets (training and test). Version 0.632+ of this
method was used (low bias and variance) and 50 bootstrap
replications were performed. Larger numbers of bootstrap
replications gave no further improvement of the classifica-
tion error estimates12.
All statistical procedures were implemented in Mat-
RESULTS AND DISCUSSION
Total luminescence spectra
Undiluted beer exhibits high UV-Vis absorption, thus
fluorescence measured using the right-angled geometry is
severely distorted due to primary and secondary inner-
filter effects. Front-face geometry should avoid filter ef-
fects, although other phenomena including energy transfer
and collisional quenching are not eliminated. Appropriate
dilution of samples is, therefore, required. On the other
hand, dilution reduces fluorescence intensities arising from
such components, which are either present in low concen-
trations or have low fluorescence quantum yields. Bearing
in mind the advantages and disadvantages of the different
measurement techniques, we tested three different geome-
tries: front-face and back-face for bulk beers and right-
angled for diluted beers.
Fig. 1 shows the total luminescence spectra of a beer
for different instrumental arrangements. Contour maps of
beer luminescence were constructed such that one axis
Fig. 1. Contour maps of the fluorescence of a lager beer (Beer
G): (A) Front-face geometry, bulk beer; (B) Right-angled ge-
ometry, diluted beer, 3.2% in water (v/v); (C) Back-face geome-
try, bulk beer.
Fig. 2. Fluorescence intensity as a function of lager beer (Beer
G) concentration; right-angled geometry.
VOL. 110, NO. 4, 2004 269
represents the emission and the other axis the excitation
wavelengths, while the contours are plotted by linking
points of equal fluorescence intensity.
In the spectra of undiluted beer, Fig. 1A, measured us-
ing the front-face geometry, a relatively intense band with
excitation at about 250 nm and emission at 350 nm is ob-
served. Additionally, a distinct emission band with excita-
tion at 350 nm and emission at 420 nm is present, and a
less intense emission band is observed with excitation at
450 nm and emission at 520 nm. Fig. 1B shows the con-
tour map for a diluted beer sample (3.2% v/v in water).
The short-wavelength fluorescence with excitation at 250
nm and emission at 350 nm is clearly observed, while only
a very weak emission band exists with excitation at 350
nm and emission at 420 nm. This spectrum exhibits al-
most no fluorescence above 400 nm in excitation and 500
nm in emission. To observe this long-wavelength emis-
sion, we recorded the total luminescence of bulk beers
using the back-face geometry. In this scheme, the optical
path length of the exciting radiation is considerably re-
duced, resulting in a reduction of the primary inner-filter
effect. The emitted light is still absorbed, as the optical
path length for the emission is ca. 0.5 cm. However, the
absorption at longer emission wavelengths is considerably
lower than that at shorter excitation wavelengths. Fig. 1C
shows that the short-wavelength emission is completely
removed, while the longer-wavelength emission retains a
Fig. 2 shows the fluorescence intensity at three excita-
tion/emission wavelength pairs: 260/350 nm, 360/430
nm, and 450/540 nm, as a function of the beer concentra-
tion, obtained in the right-angled arrangement. The short-
wavelength emission has a maximum intensity at 1.6–
3.2% v/v concentrations, rapidly decreasing in more con-
centrated solutions. In contrast, the emission intensity of
the two longer wavelength excitation/emission pairs in-
creases with concentration (almost linearly for the longest
wavelength pair). Thus, due to the large differences in
fluorescence intensities of various fluorescent species, the
most complete fluorescent characteristics of the beers
were obtained by using the front-face geometry. However,
our system utilizes a configuration, in which front-face
illumination is performed using a triangular cuvette with
its front-face at 45° to the incident beam. The geometry
causes a large amount of light to be reflected directly into
the emission monochromator, thereby distorting the emis-
sion spectra. Further measurements were conducted in
diluted solutions to observe the intense short-wavelength
fluorescence. Back-face geometry was used for observa-
tion of the long-wavelength fluorescence.
The emission contour maps for some beers studied are
shown in Fig. 3. Although all beers exhibit very similar
fluorescence characteristics, differences in band positions,
shapes, and relative intensities are easily noticeable.
The intrinsic fluorescence characteristics of beers are
expected to be quite complex due to overlapping of emis-
sions from numerous species. Consequently, complete
assignment of the spectral features is difficult and beyond
the scope of this work. However, some tentative qualita-
tive assignments could be made, based on comparison of
the observed characteristic features with the well-known
fluorescent properties of particular beer constituents.
The relatively intense band, observed in each beer stud-
ied in diluted solutions, with the excitation at ca. 250–300
nm and the emission at ca. 300–400 nm has been ascribed
to amino acids. Only the aromatic amino acids are fluo-
rescent: tryptophan (excitation/emission at 280/350 nm),
tyrosine (275/300 nm), and phenylalanine (260/280 nm).
Both tyrosine and tryptophan are fluorescent at 280–295
nm; however energy transfer from tryptophan to tyrosine
Fig. 3. Contour maps of fluorescence of various beers.
270 JOURNAL OF THE INSTITUTE OF BREWING
is quite common. Using excitation wavelengths above 295
nm, only tryptophan emits fluorescence. On the other
hand, the amino acids can be excited below 280 nm13. In
water, the quantum yield of phenylalanine fluorescence
(?Fl = 0.024) is relatively low compared with that of tryp-
tophan (?Fl = 0.13) and tyrosine (?Fl = 0.14)14. The fluor-
escence of amino acids is greatly affected by protonation
and pH. A typical content of fluorescent amino acids in
beer: tryptophan 3.1 mg/100 g, tyrosine 14.9 mg/100 g,
phenylalanine 5.9 mg/100 g3, although amounts may vary
widely depending on the choice of raw materials, the
brewing conditions, and the beer type.
The broad emission observed in bulk beer samples,
with decreased intensity upon dilution, originates presum-
ably from several fluorescent components. In particular,
compounds of the vitamin B group may contribute to this
emission. Beer is a rich source of water-soluble B-vitamins
and it typically contains: B1 (0.003–0.006 mg/100 g), B2
(0.02–0.04 mg/100 g), B3 (0.65–1.1 mg/100 g), and B6
(0.03–0.08 mg/100 g)2,3.
Vitamin B3 (niacin) includes nicotinic acid, nicotina-
mide and their coenzyme forms: nicotinamide adenine di-
nucleotide (NAD) and nicotinamide adenine dinucleotide
phosphate (NADP). Reduced forms NAD(P)H fluoresce
at around 470 nm with excitation maxima at 260 and 340
Vitamin B6 consists of three closely related pyridine de-
rivatives: pyridoxine, pyridoxal and pyridoxamine and their
corresponding phosphates. Vitamins B6 have the following
excitation/emission maxima: pyridoxine – (332,340) /400
nm, pyridoxal – 330/385 nm, and pyridoxamine – 335/400
nm, pyridoxic acid – 315/425 nm, pyridoxal 5?-phos-
phate – 330/400 nm. Vitamin B12 (cobalamin) emits at
The emission band at ca. 450/500–600 nm could be
ascribed to the vitamin B2 emission15. The principal forms
of vitamin B2 found in nature are flavin mononucleotide
(FMN) and flavin adenine dinucleotide (FAD). Vitamin B2
contents in beer were reported as: riboflavin – 169–508
µg/l; FAD – 19–65 µg/l; FMN – 8.1 µg/l16.
The spectral characteristics of the various beers studied
are generally similar to those reported previously by Ap-
person et al.8, who measured single-emission spectra. By
comparing the fluorescence spectra of beer with those of
tea and hops, they inferred that proteins, complex poly-
phenols, and iso-alpha-acids can contribute to the intrinsic
fluorescence of beer, although contribution of polyphenols
is minimal since their removal by polyvinylpolypyrroli-
done (PVPP) had not greatly affected the observed fluo-
rescence. The emission at 295/315 nm has been attributed
to tyrosine and not ?-catechin or epicatechin – the pro-
anthocyanidin monomers. The fluorescence maxima for
both catechin and epicatechin occur at 315 nm, when
excited at 265 and 280 nm, respectively, hence, they may
overlap tyrosine and tryptophan fluorescence8.
Synchronous fluorescence spectra
Synchronous scanning fluorescence spectroscopy is a
very useful technique for the analysis of mixtures of fluo-
rescent compounds. Both excitation and emission charac-
teristics are included in the spectrum by simultaneously
scanning excitation and emission wavelengths thereby
holding a constant difference between them. As a result,
the selectivity for individual components is considerably
improved and much additional information on mixtures of
fluorescent compounds is gained. The synchronous scan-
ning fluorescence method is a very simple and effective
means of obtaining data for several compounds present in
mixture in a single scan. Although it provides less informa-
tion than the TLS, in many cases, it may present a viable
alternative due to its inherent simplicity and rapidity.
The synchronous fluorescence spectra of a lager beer
(undiluted and diluted in water, 3.2% v/v) are shown in
Fig. 4. As is evident from Fig. 4, the shape and intensity
of synchronous spectra depend on the difference between
the excitation and emission wavelengths ∆λ, which de-
fines overlapping of absorption and emission bands. An
effective bandwidth reduction is observed at the smallest
?? = 10 nm, when compared to the emission band. Syn-
chronous fluorescence spectra of a diluted beer in the
right-angled geometry obtained at a small ?? (?? = 10
nm) show a sharp, intense band with a maximum at 283
nm and a very weak band with a maximum at 384 nm.
The short-wavelength emission band is broadened at ?? =
30 nm and its maximum is shifted to 275 nm, accompa-
nied by an increased intensity of both this band and of the
Fig. 4. Synchronous fluorescence spectra of a lager beer (Beer G)
recorded at ?? = 10 nm, 30 nm, 60 nm, and 80 nm: (A) Diluted
beer, 3.2% in water (v/v); (B) Bulk beer.
VOL. 110, NO. 4, 2004 271
bulk samples; (C) ?? = 60 nm, diluted samples, 3.2% in water (v/v); (D) ??
= 60 nm, bulk samples.
Fig. 5. Comparison of synchronous fluorescence spectra of beers measured,
at (A) ?? = 10 nm, diluted samples, 3.2% in water (v/v); (B) ?? = 10 nm,
272 JOURNAL OF THE INSTITUTE OF BREWING
broad band between 300 nm and 450 nm. Further increas-
ing the ?? values to 60 nm and 80 nm led to a decrease of
fluorescence intensity at 275 nm; simultaneously, the long-
wavelength broad band grows in intensity and its maxi-
mum shifts to the blue.
Fig. 4B shows the synchronous spectra of undiluted
beer samples recorded using the back-face geometry. As
was shown for the total luminescence spectra, the short-
wavelength emission is not observed when using this ge-
ometry, due to the high absorption of both the excitation
and the emission light. Three overlapping bands with
maxima at 386, 428, and 489 nm are observed at ?? =
10 nm. An increased ∆λ of 30 nm results in increased
fluorescence intensity of all the bands and in changes of
their relative intensities, while their maxima were slightly
shifted to the blue, to 380, 422, and 480 nm, respectively.
A further increase of intensity and broadening of bands
are observed at ?? = 60 nm and 80 nm, accompanied by
disappearance of the 422 nm band and appearance of a
295 nm band.
Similar spectral profiles were obtained for the other
beers, see Fig. 5. In the same way as in the previous dis-
cussion of the total luminescence spectra, the intense
short-wavelength emission band for diluted beer samples
was attributed to amino acid fluorescence. The long-wave-
length emission in the synchronous spectra of bulk beers
should originate in the vitamin B group. The existence of
more than one band suggests that several substances emit
in this region. To test this assignment, synchronous fluo-
rescence spectra of standard compounds were measured
in aqueous solutions, at pH = 4.
Fig. 6. shows spectra of three aromatic amino acids
and vitamin B2 recorded at ?? = 10 nm. Phenylalanine,
tyrosine and tryptophan exhibit single, narrow bands in
the short-wavelength region with respective maxima at
263, 283 and 296 nm. Riboflavin emission occurs in the
long-wavelength region with a maximum at 489 nm. The
very good matching of fluorescence of tyrosine and ribo-
flavin with the respective emission bands of beers pro-
vides support for the identification of these two fluoro-
phores. Further studies are needed to confirm assignments
of the other fluorescent bands as well as to establish a
quantitative relationship between the chemical composi-
tion of a beer and its fluorescence characteristics.
Despite their general similarity, the profiles of synchro-
nous fluorescence spectra of individual beers vary signifi-
cantly, producing unique spectral patterns. Apart from
qualitative distinctions, the samples also differ in fluores-
cence intensities of particular components. These differ-
ences may reflect variation in the contents of fluorescent
compounds in a particular beer; however, due to the com-
plexity of the system, quantitative predictions require fur-
The ale beer measured in diluted aqueous solutions ex-
hibited considerably lower fluorescence intensities than
lager beers, which is evident from the higher absorbance
of the ale beer. No fluorescence signal could be observed
in the bulk ale beer.
A synchronous spectrum contains more information
than conventional single-excitation or single-emission
spectra, as it depends on both excitation and emission
profiles of the respective fluorescent components. The
synchronous fluorescence spectrum is, in fact, a spectral
signature of the particular sample and may be used, for
example, in qualitative analysis, for beer identification,
Fig. 6. Synchronous fluorescence spectra, recorded at ?? = 10
nm, of phenylalanine (Ph) tyrosine (Ty) tryptophan (Tr) and
riboflavin (Rf) in water, at pH = 4; fluorescence intensity nor-
malized to 1.
Table I. Classification of beers using entire synchronous fluorescence
spectra in the k nearest neighbours method (diluted beers).
Table II. Classification of beers using entire synchronous fluorescence
spectra in the k nearest neighbours method (bulk beers).
VOL. 110, NO. 4, 2004 273
Fig. 7. Classification of beers by linear discriminant analy-
sis. Top panels: bulk beers at ?? = 10 nm and at ?? = 60 nm;
bottom panels: diluted beers at ?? = 10 nm and at ?? =
274 JOURNAL OF THE INSTITUTE OF BREWING
quality monitoring or for authentication purposes. Visual
comparison of spectra could be insufficient for such appli-
cations; hence, multivariate statistical methods should be
Classification of beers using synchronous
The possibility of discriminating different beers on the
basis of their synchronous fluorescence spectra was in-
vestigated by using two statistical methods: the k nearest
neighbours method and the linear discriminant analysis.
The k nearest neighbours method was applied using the
entire spectra as input. In the linear discriminant analysis,
selected excitation/emission wavelength pairs were used
for classification purposes.
Tables I and II present the results of the k nearest
neighbours method applied to diluted and bulk samples,
respectively. Discrimination between different beers using
this method was very good, with zero or very low classifi-
cation error and low standard deviation values. The best
discrimination was achieved using synchronous fluores-
cence spectra of bulk beers measured at ?? = 10 and 60
nm and diluted beers measured at ?? = 10 nm. Discrimi-
nation using spectra of diluted beers at ?? = 60 nm was
still very good.
Further, linear discriminant analysis was applied to a
set of selected wavelength pairs from the synchronous
spectra. Such analysis, although simplified and limited to
only six excitation/emission wavelength pairs, produced a
satisfactory discrimination between different beers (low
error and standard deviation values). These results show
that it is not even necessary to record the entire synchro-
nous spectra in order to discriminate between beers. In-
stead, the fluorescence intensity could be measured at
selected excitation/emission wavelengths and then sub-
jected to linear discriminant analysis.
The results of the LDA analysis are visualized on the
maps plotted by using the two discriminant coordinates,
DV1 and DV2 (Fig. 7).
The bulk beers could be correctly classified by using
only two principal discriminant coordinates, both at ?? =
10 and 60 nm values, with very good separation between
all beers. For diluted beers at ?? = 10 and 60 nm, some of
the beers were located too close to each other.
The results indicate that, although both techniques
could be applied for beer discrimination, the spectra of
bulk samples appear to be more reliable than those of di-
luted beers. This may result from the more pronounced
variations in vitamin-B contents (long-wavelength bands)
than in the amino acid contents. Despite these effects, we
confirmed that both the short-wavelength UV-emission
and the long-wavelength visible emission can be applied
to discriminate various beers.
Total luminescence and synchronous fluorescence spec-
troscopic techniques were used for direct beer analyses.
Fluorescence spectroscopy provides information on the
overall beer characteristics thereby enabling identification
of some beer constituents. Although unambiguous attribu-
tion of fluorescence bands to beer components requires
further studies, the present results show that distinct spec-
tral ranges, such as those corresponding to amino acids
and to compounds of the vitamin-B group, may be identi-
fied in the spectra and used as markers for differentiation
of beers. Synchronous scanning fluorescence spectroscopy
was successfully used to characterize and discriminate
various beer samples. We demonstrated that it is possible
to classify various beers using single synchronous fluores-
cence scans or even selected excitation/emission wave-
It would be interesting to correlate the spectral char-
acteristics of beers to known beer classifications and spe-
cific beer properties. Such investigation is currently in
The grant No. 2P06T 112 26 from the Polish State Commit-
tee for Scientific Research is gratefully acknowledged.
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(Manuscript accepted for publication October 2004)