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Book_Pollack_1402049269_Proof1_April 28, 2006
CHAPTER 7
THE EFFECTS OF STATIC MAGNETIC FIELDS,
LOW FREQUENCY ELECTROMAGNETIC FIELDS
AND MECHANICAL VIBRATION ON SOME
PHYSICOCHEMICAL PROPERTIES OF WATER
SINERIK N. AYRAPETYAN∗, ARMINE M. AMYAN
AND GAYANE S. AYRAPETYAN
UNESCO Chair-Life Sciences International Postgraduate Educational Center, 31 Acharyan St.,
Yerevan, 375040, Armenia
Abstract: At present the biological effect of SMF and LF EMF can be considered as a proven
fact; however, the question how such a low-energy of EMF radiation could modulate the
functional activity of cell and organism still remains unanswered. Numerous hypotheses
on molecular mechanisms of the specific biological effect of EMF have been proposed,
but none have provided a reliable and exhaustive explanation of the experimental findings.
The oldest hypothesis is that EMF-induced structural changes of the cell bathing solution
could serve as a primary target for the biological effect of EMF. As water is the main
medium where the major part of biochemical reactions are taking place, it is predicted
that a slight changes of physico-chemical properties of both intracellular and extracellular
water could dramatically change the metabolic activity of cells and organisms
Therefore, extension of the knowledge on the mechanisms of SMF and EMF effects
on physicochemical properties of water seems extremely important for understanding the
biological effect of these factors, which are realized through water structural changes
Keywords: water structure; valence angle; distilled water; thermal capacity; melting point; specific
electrical conductivity
∗Corresponding author. UNESCO Chair-Life Sciences International Postgraduate Educational Center;
31 Acharyan St., Yerevan, 375040, Armenia. Tel.: +374 10 624170/612461; fax: +374 10 624170;
E-mail address: life@arminco.com (S.N. Ayrapetyan)
151
G. Pollack et al. (eds.), Water and the Cell, 151–164.
© 2006 Springer. Printed in the Netherlands.
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Book_Pollack_1402049269_Proof1_April 28, 2006
152 CHAPTER 7
1. GENERAL NOTES ON WATER STRUCTURE
The structure of a single water molecule is well described in literature. From 5 pairs
of electrons one pair is localized near the oxygen nucleus and the rest 4 pairs are
socialized between protons and oxygen nucleus. The oxygen nucleus partly attracts
to the electrons moving them away from the hydrogen nuclei. The latter acquires a
weak positive charge. The other two corners of the imaginary tetrahedron acquire
a weak negative charge near the oxygen atom. Moreover, 2 pairs are polarized
and directed to the peaks of the tetrad opposite the protons. These unshared pairs
of electrons have a crucial role in generation of intermolecular hydrogen bounds
(Figure 1). Hydrogen bounds continuously form and disrupt giving the “water
polymer” a high surface tension, high specific heat, high vaporization heat and high
dielectric constant (=80 at 20 C). According to the quant-mechanical calculations
the valence angle in water molecules between O-H bounds must be 90, however,
Figure 1. The theoretical conception of water structure. Each H2O is labile linked to other four molecules
with hydrogen bonds: the result is a polymeric structure of water
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Book_Pollack_1402049269_Proof1_April 28, 2006
EFFECTS OF SMF, LF EMF AND MV 153
in reality this valence angle is near 105, because in water, due to the strong polarity
of the H-O bounds, the minimal repulsion of the positively charged hydrogen atoms
increases the angle (Pullman and Pullman, 1963).
Because of the long hydrogen bound (0.28 nm) in water having an electrostatic
nature and a comparatively weak energy (14.2–20.9 k joule) the water structure
is very labile and sensitive to different environmental factors. The structure of
liquid water is being continuously changed from the moment of its forming. The
character of such changes depends on the physical and chemical characteristics of
the environmental medium. Even by keeping the distilled water in constant medium
its structure is being changed depending on its ‘aging’ (Stepanyan et al., 1999). AQ1
Therefore the structure of the water could be considered as a currier of a big
‘memory’ on the previous effects of various environmental factors.
2. THE EFFECT LF EMF, LF MV AND SMF ON THERMAL
PROPERTIES OF WATER
From the point of present knowledge on water structure, the LF EMF could modify
the water structure by two pathways: a) by changing the valence angle in water
molecules and b) by mechanical vibration (MV) of dipole molecules of water. To
estimate the role of each of these pathways in EMF-induced water structure changes
the effects of SMF and MV on water physicochemical properties were studied.
It is suggested that SMF effect would imitate the valence angle changes, while
the effect of MV – the mechanical vibration of dipole molecules of water. It is
predicted that EMF- and MV-induced water structure changes would accompanied
by the thermal release in the result of broken hydrogen bounds between water
molecules.
A special setup allowing the treatment of distilled water by SMF, ELF EMF
and LF MV was assembled (Institute of Radiophysics and Electronics (IRPhE) of
Armenian NAS, Yerevan, Armenia). The block scheme of the setup is presented in
Figure 2.
Glass test tube (1) with diameter 10 mm and volume 10ml, was used. The vibrator
was controlled by the sine-wave generator (6) (GZ-118, Made in Russian Feder-
ation), the signal went to the double pole switch (8): in position I the generator
functions as EMF and LF MV sources, while in position II – as LF MV sources. To
obtain MV waves the vibrating device (3) was used generating vertical vibrations
by set frequency and intensity. The vibrator was constructed in the department of
engineering at LSIPEC on the basis of the IVCh-01 device (Russian production)
To keep vibration intensity constant (30 dB) at different frequencies, a coil (4) with
a feedback amplifier system (IRPhE, Yerevan, Armenia) was used. Thus, MV was
transmitted to the test tube containing DW with insignificant power dissipation.
For concordance of high impedance output of generator to low impedance input
of vibrator, a special power amplifier (IRPhE, Yerevan, Armenia) was used. MV
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Book_Pollack_1402049269_Proof1_April 28, 2006
154 CHAPTER 7
Figure 2. The setup for treatment of DW by LF EMF, SMF and LF MV. 1. Glass test tube with diameter
10 mm and volume 10 ml. 2. Platinum electrodes. 3. Mobile part of the vibrator. 3. Motionless part of
the vibrator. 4. The coil. 5. The device for the measurement of DW SEC (conductometer). 6. Generator
of sinusoid vibration. 7. The low-noise amplifier. 8. The switch (has 2 positions: I and II, where I- EMF
and MV and II- EMF). 9. Personal Computer. 10. The generator of a constant field
frequency was controlled by a cymometer (CZ-47D, production of Russian Feder-
ation), while the intensity was measured by a measuring device (IRPhE, Yerevan,
Armenia) having a sensor on the vibration table. It was possible to keep the intensity
of MV on stable level at all frequencies, including resonance frequency (more than
200 Hz for the given setup).
EMF was generated by the controlled generator (6) and low-noise amplifier
(7) on the coil (4) (IRPhE, Yerevan, Armenia). The coil had a cylindrical form
with 154 mm in diameter and 106 mm in height. The coil consisted of Helmholtz
rings generating the homogeneous magnetic field. Rings of Helmholtz were formed
by two equal ring coils located coaxially and parallel. The distance between ring
coils was equal to their radius (77 mm). The magnetic field created by these rings
had high homogeneity, for example, at a distance of 0.25sm from the center of an
axis strength differs from computed by formula only on 05%H=716··I
R.
SMF was generated by the generator of a static field (10) and transferred to
the coil.
For determination of the thermal characteristics of DW during EMF exposure
the following works were performed: new created DW (10 ml.) was placed into
the Helmholtz rings for EMF exposure. A needle thermo-sensor of the measuring
device Biophys-TT (LSIPEC, Armenia) was placed in the test-tube. During the EMF
exposure the following frequencies were used: 4,10,15,20 and 50 Hz. The device
Biophys-TT was connected to the personal computer through Digidata 1322A data
acquisition system (Axon Instruments, USA). The data recording was carried out
with the help of computer program Axsoscope 8.1.
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Book_Pollack_1402049269_Proof1_April 28, 2006
EFFECTS OF SMF, LF EMF AND MV 155
Time (min.)
0510 15 20 25 30 Control 4 Hz
4 HzControl 10 Hz 15 Hz 20 Hz 50 Hz
t°C
A
10 Hz 15 Hz 20 Hz 50 Hz
12,9
12,8
12,7
12,6
12,5
12,4
12,3
12,2
12,1
12
11,9
Time (min.)
Bt°C
0510 15 20 25
12,9
12,8
12,7
12,6
12,5
12,4
12,3
12,2
12,1
12
11,9
30
4 Hz
10 Hz
15 Hz
20 Hz
50 Hz
Control
4 HzControl 10 Hz 15 Hz 20 Hz 50 Hz
Figure 3. The time- and frequency-dependent heat release from the water samples treated by EMF
(2.5 mT) (A), MV (B) and MV (30dB) after 30 min pre-treated by SMF (12mT) (C). Initial temperature –
119C
As it can be seen from the presented data in Figure 3, the character of frequency-
dependency of heat release is changed during EMF (A) and MV (B) exposure, as
well as it could be modulated by preliminary exposure to SMF (C).
These data strongly suggest that the sensitivity of water structure to these factors
depends on the preliminary state of the water.
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Book_Pollack_1402049269_Proof1_April 28, 2006
156 CHAPTER 7
Time (min.)
Ct°C
0510 15 20 25
12,9
12,8
12,7
12,6
12,5
12,4
12,3
12,2
12,1
12
11,9
30
4 Hz
10 Hz
15 Hz
20 Hz
50 Hz
Control
4 HzControl 10 Hz 15 Hz 20 Hz 50 Hz
Figure 3. (Continued)
The results of studying the melting processes of water pretreated by EMF, MV
and SMF after freezing in liquid N2brought us to the same conclusion.
For studying the time-dependence changes of thermal capacity of EMF-
, MV- and SMF-pretreated DW after freezing in liquid N2the following
method was used: the plastic tube (Vol. 1 ml) with a hermetic cup having a
thermo-sensor at the bottom was fixed in another plastic tube (vol. 100 ml)
and was inserted into the well containing liquid N2. After withdrawing the
tube from the liquid N2the hermetic cup of the tube was opened and left for
melting at room temperature. The temperate recording was performed by extra
sensitive thermometer Biophys-TT (production of LSIPEC, Armenia), connected
to the PC through Digidata 1322A data acquisition system (Axon Instru-
ments, USA).
The family of curves of time-dependent temperature raising at room temper-
ature (18 C) of EMF- (A and A*), MV- (B and B*) and SMF- (C and
C*) pretreated 1 ml water after its freezing in liquid N2are demonstrated in
Figure 4.
As it can be seen from the presented data the melting point (when the temperature
keeps constant) and the time of reaching to 0 C (marker for the thermal capacity
of frozen crystals), as well as thermal capacity and thermal anomaly properties
of liquid water are frequency (A,B) and intensity (C)-dependant. Comparing the
family of curves of the left and right columns, the “aging” effect on frequency and
intensity-dependence of the water thermal properties can be seen. From these data
we can conclude that water “memory” on the effect of various factors could be
modified by water ‘aging’.
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Book_Pollack_1402049269_Proof1_April 28, 2006
EFFECTS OF SMF, LF EMF AND MV 157
Control 10Hz 15Hz 20Hz 50Hz4Hz
Control 10Hz 15Hz 20Hz 50Hz4Hz
Control 1.25mT 2.5mT 3.75mT
C C*
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0
0
5 101520253035404550
t ˚C
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0
05 101520253035404550
t ˚C
Time (min) Time (min)
B*B
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0
0
5 101520253035404550
t ˚C
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0
05 101520253035404550
t ˚C
Time (min) Time (min)
A
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0 5 10 15 20 25 30 35 40 45 50
t ˚C
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0 5 10 15 20 25 30 35 40 45 50
t ˚C
A*
Time (min) Time (min)
Figure 4. Time-dependent temperature rising of EMF- (A and A*), MV- (B and B*) and SMF- (C and C*)
pretreated 1 ml DW at room temperature (18C) after freezing in liquid N2. In the left column (A,B,C) –
the one-hour water was 30 minutes treated by EMF, MV, SMF and immediately frozen in liquid N2. In the
right column (A*, B* and C*) – 30 minutes EMF, MV and SMF-treated water was frozen after 72 hours
remaining at room temperature. EMF and MV have intensity 2.5 mT and 30 dB, correspondingly
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Book_Pollack_1402049269_Proof1_April 28, 2006
158 CHAPTER 7
3. THE EFFECT LF EMF, LF MV AND SMF ON SPECIFIC
ELECTRICAL CONDUCTIVITY OF WATER
As SEC of water depends on the degree of its dissociation, SEC can be considered as
a marker for studying the effect of different factors on water structure
AQ1
(Klassen, 1982; Ayrapetyan, 1994a). To estimate the contribution of valence angle
changes and mechanical vibration of dipole moments of water molecules in LF
EMF-induced water structure changes, the SMF, LF MV and LF EMF effects on
SEC of DW were studied (Ayrapetyan, 1994a; Stepanyan et al., 1999; Hakobyan
and Ayrapetyan, 2001).
The block scheme of the setup for these studies is presented in Figure 2. Three
glass test tubes (1) with diameter of 10 mm and volume of 10 ml, with two platinum
electrodes inside were used. Platinum electrodes-plates with the area 100 mm2,
located on 5 mm distance from each other, were connected with the conductivity-
measuring device (5) capable to determine SEC of water at currents less than the
10−9A. As the conductivity of water was measured in micro power modes, the
application of low-noisy voltage amplifier of alternating current in the device raises
the accuracy of measurement due to exception of self-heating influence. For the
continuous recording of SEC the output of a measuring device was connected to
the PC (9) through Digidata 1322A data acquisition system.
The presented data in Figure 5 show that EMF at 4, 10, 20 and 50 Hz has
depressing effect on SEC of one-day DW, while in case of six-day DW only 4 and
20 Hz EMF has depressing effect on it. It is extremely interesting that the 20 Hz
frequency ‘window’ was less pronounced at higher intensity of EMF (>10 mT)
(Stepanyan et al., 2000).
AQ1
The similar frequency ‘windows’ were observed by studying the LF MV
effect on SEC of DW (Figure 7). However, in case of MV effect on SEC of
one-day DW, comparing to EMF, 15 Hz also has depressing effect on water SEC
(Figure 7A).
As in case of EMF effect, MV at 20 Hz has less expressed depressing effect on
water SEC at higher intensity (75 dB) (Figure 8) than at a weak intensity (30 dB)
(Figure 7).
SMF also had a depressing effect on SEC of DW however, this effect was less
sensitive to water ‘aging’, than in case of EMF and MV (Figure 9).
In order to find out whether these factors have specific effect on water SEC,
the combined effect of 4 Hz EMF (2,5 mT), 4 Hz MV (30 dB) and SMF (2,5 mT)
in different orders was investigated on one-day DW. These results are shown in
Figure 10.
As it can be seen on the presented data there are no significant differences
between various combinations of factors-induced depressing effect on SEC of DW,
which shows that all these three factors lead to the packing of the water molecules
that brings to the decrease of SEC of DW. However, whether the LF EMF-, LF MV-
and SMF-induced decrease of SEC of DW has the same biological mining, could
serve as a subject for future investigations.
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Book_Pollack_1402049269_Proof1_April 28, 2006
EFFECTS OF SMF, LF EMF AND MV 159
A
Specific Electrical Conductivity
%
120
100
80
60
40
20
0
B
Specific Electrical Conductivity
%
120
100
80
60
40
20
0
Control
Control
4 Hz
ELF EMF
10 Hz 15 Hz 20 Hz 50 Hz 100 Hz
Control 4 Hz 10 Hz 15 Hz 20 Hz 50 Hz 100 Hz
Control ELF EMF
*** p < 0.001
*** p < 0.001
** p < 0.01
*p < 0.05
*
*
*
*
*
*
*
*
*
*
**
*
**
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
Figure 5. The effect of EMF (2,5mT) exposure at different frequencies on specific electrical conductivity
of one-day (A) and six-day (B) distilled water at 18 C
AQ2
80
85
90
95
100
105
C SMF 4 Hz 10 Hz 20 Hz 50 Hz
G.%
Figure 6. The effect of EMF (12 mT) exposure at different frequencies on specific electrical conductivity
of one-day distilled water at 18 C
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Book_Pollack_1402049269_Proof1_April 28, 2006
160 CHAPTER 7
A
Specific Electrical Conductivity
%
120
100
80
60
40
20
0
B
Specific Electrical Conductivity
%
120
100
80
60
40
20
0
Control
Control
4 Hz
LF MV
10 Hz 15 Hz 20 Hz 50 Hz 100 Hz
Control
Control
4 Hz
LF MV
10 Hz 15 Hz 20 Hz 50 Hz 100 Hz
*** p < 0.001
*** p < 0.001
** p < 0.01
*p < 0.05
*
*
*
***
*
*
*
**
**
*
*
*
*
*
**
*
**
*
*
*
*
*
*
*
*
Figure 7. The effect of EL MV exposure at different frequencies on specific electrical conductivity of
one-day (A) and six-day (B) distilled water at 18 C
The preliminary studies of our laboratory have shown that LF EMF-, LF MV-
and SMF-induced water structure changes have different biological effects on
growth and development of Escherichia Coli (Stepanyan et al., 2000; Ayrapetyan
et al., 2001) and plant seed germination potentials (Amyan and Ayrapetyan, 2004).
It was shown that pretreatment of wort by EMF and SMF has depressing effect
on growth and development of microbes (Stepanyan et al., 2000), while MV has
activation effect on it (Ayrapetyan et al., 2001). Different effects of the mentioned
factors on plant seed germination potential have also been observed. The metabolic-
depended seed hydration was elevated in EMF-treated DW, while in MV-treated
DW seed hydration was decreased (Amyan and Ayrapetyan, 2004). The comparative
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Book_Pollack_1402049269_Proof1_April 28, 2006
EFFECTS OF SMF, LF EMF AND MV 161
FREQUENCY OF ACOUSTIC WAVES, Hz
WATER SEC, %
0
70
75
80
85
90
95
100
105
3
10
6
5
4
100
50
25
20
15
250
200
150
500
1000
5000
2500
CONTROL
Figure 8. The effect of mechanical vibrations at different frequencies (at the intensity of 75 dB) on the
specific electrical conductivity (SEC) of distilled water of the intermediate age
Specific Electrical Conductivity,
%
120
100
80
60
40
20
0
Control
Control
SMF I SMF III
SMF
SMF VI
*** p < 0.001
*
*
*
*
*
*
*
*
*
Figure 9. The effect of SMF exposure on specific electrical conductivity of one-day (I), three-day (III)
and six-day (VI) distilled water at 18 C
study of the biological effect of EMF and MV on high-level organized organisms
could be the subject for future investigation.
As in reality water contains its dissociation products and soluble gasses, it is
predicted that its structure could be extremely sensitive to the effect of any environ-
mental factors. Water can be considered as an open thermo-dynamical system with
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Book_Pollack_1402049269_Proof1_April 28, 2006
162 CHAPTER 7
Specific Electrical Conductivity,
%
120
100
80
60
40
20
0
Control
Control
+
EMF
LF MV
EMF + LF MV
+
EMF
SMF
EMF + SMF
+
SMF
EMF
SMF + EMF
+
SMF
LF MV
SMF + LF MV
+
LF MV
EMF
LF MV + EMF
+
LF MV
SMF
LF MV + SMF
Figure 10. The combined effect of 4 Hz EMF (2.5mT), 4 Hz MV (30 dB) and SMF (2.5mT) on one-day
DW at 18 C exposed in different order. The exposure time for each factor was 30 min. The interval
between exposures was less than 1 min
energy and substances exchange with the medium leading to continuous structural
changes. The latter could appear even without breaking the hydrogen bounds, just
by their deformation (Klassen, 1982). Therefore it is extremely difficult to suggest
the exact value of energy which is necessary to change the water structure, however
it should be less than the energy of hydrogen bounds (167-251 kDj). Such
variability of water properties is the main barrier for precise reproduction of the
experimental results in water studies. This picture becomes more complicated in
case of water solutions containing electrolytes, non-electrolytes, solid particles and
air-bladders. The increase of a number of ions in water leads to the increase of its
entropy, instead of its predicted decrease, because of the hydration-induced disorders
of the water structure. Two groups of ions could be distinguished depending
on their effect on water structure: ordering and disordering the water structure
(Kireev, 1968). As velocity and chemical activity of ions are determined by the
degree of their hydration, the knowledge on the effect of magnetic fields on ions
hydrations is important to understand the mechanism of its effect. It was shown
that the hydration of ions is highly sensitive to the effect of EMF. The hydration of
diamagnetic ions is decreased, while in case of paramagnetic ions it is increased.
In this aspect Ca ions play a crucial role in realization of biological effect of
EMF, because of forming the aqua-complexes CaH2O62+in water making it
very sensitive to EMF. Therefore the character of magnetic field effect on water
structure depends on the concentration of Ca ions. Early our works have shown that
the direction of SMF-induced changes of water SEC could be changed depending
on CaCl2concentration in water (Ayrapetyan, 1994a).
The sensitivity of water structure to EMF and MV significantly depends on the
effect of solute gases in it. The solubility of even neutral gazes in water leads
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Book_Pollack_1402049269_Proof1_April 28, 2006
EFFECTS OF SMF, LF EMF AND MV 163
Figure 11. The kinetics of IR-specter of magnetized bi-distilled (1), distilled (2) and natural water (3)
after SMF exposure
to the deformation of hydrogen bounds in result of which the formation of new
hydrogen bounds is taking place. The degree of solubility of CO2and O2in water
is very sensitive to EMF and MV (Stepanyan et al., 1999). It was shown that
SMF has depressing effect on CO2and elevation effect on O2solubility in water
(Klassen, 1982).
AQ3
The ‘memory’ of EMF-induced water structure changes from the point of its
biological effects is extremely important. From the point of equilibrium thermo-
dynamic system, it is predicted that after EMF expose, its effect on water should
disappear immediately, however, the experimental results show that the ‘trace’
effect of EMF stays incomparably longer than the exposure time. This memory is
much longer in water solutions than in pure water (Klassen, 1982).
As can be seen in the presented Figure the rate of SMF effect on be-distillated
water in IR-specters (magnetic susceptibility) is higher than in case of distillate and
natural water, and the spontaneous relaxing period after SMF-exposure for natural
water is much longer than for bi-distilled and distilled waters.
REFERENCES
Amyan AM, Ayrapetyan SN (2004) On the modulation effect of pulsing and static magnetic fields and
mechanical vibrations on barley seed hydration. Physiol Chem Phys Med NMR 36:69–84
Ayrapetyan SN, Avanesian AS, Avetisian T, Majinian S (1994a) Physiological effects of magnetic fields
may be mediated through actions on the state of calcium ions in solution. In: Carpenter D, Ayrapetyan
SN (eds) Biological effects of electrical and magnetic fields, vol 1, pp 181–192, Academic Press
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Book_Pollack_1402049269_Proof1_April 28, 2006
164 CHAPTER 7
Ayrapetyan SN, Stepanyan RS, Oganesyan HG, Barseghyan AA, Alaverdyan ZhR, Arakelyan AG,
Markosyan LS (2001) Effect of mechanical vibration on the lon mutant of Escherichia coli K-12.
Microbiology 70:248–252 (in Russian)
Hakobyan SN, Ayrapetyan SN (2001) The effect of EMF on water specific electrical conductivity and
wheat sprouting. WHO Meeting on EMF Biological Effects and Standards Harmonization in Asia
and Oceania, 123
Kireev V (1968) Physical chemistry. Higher School Publishing House, Moscow
Klassen VI (1982) Magnetizing of water systems. Chemistry Press, Moscow, 296 (in Russian)
Pullman B, Pullman A (1963) Quantum biochemistry. Interscience Publisher, New York
Stepanyan RS, Ayrapetyan GS, Arakelyan AG, Ayrapetyan SN (1999) The effect of mechanical vibration
on the water conductivity. Biophysics 2(44):197–202 (in Russian)
Stepanyan RS, Alaverdyan ZhR, Oganesyan HG, Markosyan LS, Ayrapetyan SN (2000) The effect of
magnetic fields on lon mutant of Escherichia coli K-12 growth and division. Radiational Biology,
Radioekology 3(40):319–322 (in Russian)
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Book_Pollack_1402049269_Proof1_April 28, 2006
QUERIES TO BE ANSWERED (SEE MARGINAL MARKS)
IMPORTANT NOTE: Please mark your corrections and answers to these
queries directly onto the proof at the relevant place. Do NOT mark your
corrections on this query sheet.
Chapter-07
Query No. Page No. Line No. Query
AQ1 153 10 The author name ‘Stepanian’ has
been changed to‘Stepanyan’ as per
the references section. Is this ok?
158 9, 25
AQ2 159 Figure 6 Please provide citation inside the text
AQ3 163 Figure 11 Please provide citation inside the text