Journal of the Indian Institute of Science, Bangalore 560 012, India
[Section B : Physical and Chemical Scicnees]
Volume 62
October 1980
Number 10
CONTENTS
ORLGINAL PAPERS
Page
Integral Equations
D~RIVAI'IOV
or
THC S.)I,UCION
O!' CI?RTAIN SIVGULAR LNrLOKAL EQUATIONS
Aloknatk Chakrabart~
147
Fluid Dynamics
O'J UrVSTEkDY
MUD bLOW PAST A I'OROUS P L A r E UNDEK PRESSURE ClRAUlENr
S T Revartkar and V. M . Ko~war
159
SHORT COMMUNICATIONS
Special Functron~
ON
NONLINE4R
OSClLLAllON
PROllLthl
P C Munot and Rcnu Murhur
167
Analytical Chemistry
TITRIMBTRIC
e j r r v % r m v or
PHOSPHI\.TE, MOLYUDATE AND SULPHATE WITH LEAD
NITRATBS3LUCIOV USING ~ - ( ~ ' - L E P I D Y L
A Z ~ ) - ~ - N A P H T H O ~ , - ~ - A M M OSULPHONATE
N~UM
(LANAS) AS VISUAL INDICATOR
R. C . Chadha, B. S. Garg, Swaran Lata and R . P. Singh
173
Oryanic Chemhtry
DEBENZYLATION
BY NI-AL
ALLOY
M. Venkar~a Naidu and G. S. Knsltna Rao
177
REVIEW PAPER
Organic Chemistry
T B ~CNEMSTKY 01; VEI.IYALENE-TYPE NAIIJRALLY
OCCUKIlING SBSQUI~ERPENOIDS
P. Anantha Reddy and G. S. Krishna Rao
181
BOOB REVIEWS
193
INDEX (Section B)
197
j,
Indian hst. Sci. 62 (B), Oct. 1980, Pp. 147-151
@
Indian Institute of Science, Printed
m India.
Derivation of the solution of certain singular integral equations
ALOKNATHCHAKRABARTX
Department of Applied Mathematics, Indian Institute of Science, Bangalore 560 012, India.
Received on April 11, 1980.
Abstract
It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulawhen made in a suitable manner
produces the s ~ l u t i a nof certain singular integral equations very quickly, thc method of arriving at
which, otherwise, is too complicaled. Two singular integral equations are considered. One of these
quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w
guide theory and the theory of dishcations.
Adifferent approach i? alw made here to solve the singular integralquation>of the waveguide theor?
ind this i ~ v o l v ethe
~ use of the inversion formula of the Cauchy-type singular integral e q u a h n and
dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to
obi& tbe closed form solutim of the irilegral equatlou at band.
The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral
equaticn of the waveguide theory knowr todate.
& words
: Singular integral equations, Cauch~~-type
kernel, Riemann Hilbert prrblem, wawguidc
them
1. htraductiou
The Poincare-Rertrand formula (PBF) is given by
where singular integrals are understood as their Cauchy principal values and where
is assumed to satisfy the HGlder condition used by Muskhelishvilib.
h e function g fx,
147
We shall use here the result (1) to solve first the singular integral equation fi,
Cauchy-type kernel and then a singular integral equation in wave-guide theory o,
which the work of William3" has come out recently. Wi&ams has investigated two
interesting features of the following equation in the wave-guide theory.
These features are :
(i) its relationship to the equation
j
-1
Y-i:
=
, f I < I.
(ii) The relationship between the solution of eqn. (2) for h E 1 ( p z - 1) and
the solution of the correqponding homogeneous equation with D replaced by - p
The work on the singular integral eqn. (2), and its gcnerdisation, by -win4, Bueck&
Biermannl and PetersR all involve very complicated complex variable methods asso.
ciated with the Hilbert problems and the Wieller-Hopf technique, except that Lev&,
has utilized some simple properties of the operator T defined by
to solve eqn. (2) in certain situations.
It is the Lcwin's form of the solution of eqn. (2) which has suggested utilizing the
PBF to such singular integral equations. This will be presented in the next section.
Jt is also observed that Pennline7, has tried to give an alternative approach to the
problem of solving (2) in the case when p = 112 and h = I . The approach of Pemlhie
involves the reduction of the problem (2) into a system of Hilbert problems, a closed
form solution of which is difficult to obtain and Pcnnline has obtained the solution
only by employing a special technique. What more we demonstrate here in the last
section of this paper is that, a reduction of eqn. (Z), after a simplz transformation and
an uaity of the inverse operator T-I obtained i n section 2, to a simple system of Hilbert
problems with constant coefficients for two unknowns, can be achieved relatively
cheaply and the h a 1 solution of eqn. (2) can be obtained in closed form for any realp.
5.
The me of the PBF
As a first use of the PBF to singular integral equations oC the first kind, we consider
the equation
SINGULAR INTEGRAL EQUATIONS
the functions
4
149
and f are assumed to satisfy the Halder conditions in (- 1 , 1).
Rewrite eqn. ( 5 ) as
Multiply both sides ol (6) by
= - 1 and + I, where 0 c Re (P)
Then interchanging the orders of integration by using the PBF (I), we obtain :
and integrate with respcct to x between x
If we now use the following result (see Gakhovs),
I
1.
150
ALOKNATH CHAKRABARTI
eqn. (7) takes the following form
(10) is satisfied by the solution d, of the integral ~cluations(5) for all fl $I&
The
that 0 < Re(B) < 1.
we have now to choose the unknown constant p(O < Re ( 8 ) < 1) in such a way
that (10) produces an inversion formula for (5). We observe thst the only choice is
that
P=
(W
f9
and then the function
4 is
recovered from (10) as
where
The reader is referred to the work of Peters8 for the comparison between the form of
the solution (12) of (5) and the solution obtained by Peters for the singular i n w
equation
We observe, from (12) and (13), that if
given by
We next consider eqn. (2),
d is a n
odd function, then the solution of (i) is
where
a2 = (I - p)/(i -i-p).
We now apply the PBF (I) to (16) in the following manner
Multiply both sides of (16) by
-
ee (- 1. 1) and integrate with respect to x between x = 1 to x = + 1 . Here fi $
a constant (0 < Re p r. 1) which will be chosen later on so that a solution of (16) is
finally arrived at. We obtain, after utilizing the PBF (I),
2
p-112
g ( x ) dx.
x-T
-1
If we now make use of the result (8) to evaluate the i w r integrals occurring in the
left of (18) and (20), we obtain
- (1 - o)
,(l +
t 8
(1
+ a2)n2a ( a +
*J a
sln(ZB)
-1
(YI
s
SINGULAR
INTEGRAL
EQUATIONS
153
Now noting that
m observe from (24), that the solution of the integral equation (16) will be obtained
rom (24) itself, if we choose b such that
a2cot (na>= tan nj?
s.,
tannp=\aI
md in that event, the solutior to (16) is given by
Yow, in our case, (6 is an odd function [cf. eqn. (1511 and, therefore, C = 0 and we
htain the solution of (16) as
i $4
ALOKNATH CIIAKRABARTI
where the functions gl and g , are defined as in (19) and (21). We observe that
form (27) of the solution of (16) agrees with that obtained by Lewin.
3. Reduction of equation (163 to a Hilbert problem and its solution
TQ reduce eqn. (16) to a simple system of Hilbert problems, we shall make use of tb
inverse operator T-I of the operator T i n (4), as given by (14).
Then, by (4) and (14), we obtain, since
4 is an add function,
BY (28) and (29), we then observe that eqn. (1 6) is equivalent to the following two
coupled integral equations for the two unknown funcliom 4(x) and X(x)
and
The two integral sqns. (30) and (31) can finally be reduced to a system of Hilbect
problems with constant coefficients by employing the usual method of such reduction as
explained in Mikhlin's book'
Setting
SINGULAR INTEGRAL EQUATIONS
155
the PlemeJj's formulae for the sectionally analytic functions Q ( z ) and
analytic in the complex z-plane, cut along the real axis between - 1 and + 1,
%e find that (30) and (31) reduce to the following Hilbert problem
sn,j
a Z n i[@+ ( x )
and
+ Q- ( x ) ] + n2 [X+( x ) - X- ( x ) ] = @-+A1)d&)
+
+
xi [X+(x)
X- (x)] [ 4,+ ( x ) - 4,- (x)] = 0
(33)
where F+ ( x ) are the limiting values of the sectionally analytic function F (z) on the
sides of the cut, as understood in the usual way (see Miklid).
We now decouple the system of Hibert problems (33) by definining
2 (z)
=
(a
+ i) [a @ (2) - n X (z)]
and
p(z) = ( a - i)[a@(z)+ n X ( z ) ] .
Then, in terms of the limiting values A+, 1.-, p+ and p-, the system (33) reduces to the
equivalent system,
A+ ( x ) + a'2
+ r A-:( x ) = nz.( p
+
2g ( x )
1) ( 1
-~
3 " ~
(35)
We note that, from (34),
2a (a"
1 ) 4, (2) = (a
- i) A ( z ) + ( a + i ) p (2)
Then using the Plernelj formulae in (36) and utilizing
-tion
(35), the solution of the integral
(16) can be expressed as,
*,
the problem of solving (16) reduces to that of determining the solution of the
sir@est of the Hilbert problems as given by (35), whose solution can be expressed
(m Muskhelishvili6) as
156
ALOKNATH CHAKRABARTI
and
J.,(=)
and p, ( z ) are the solutions, of the h o r u o ~ ~ i e o upvoblem
s
(39, given by
where fl is given by' the relation
Noting, then, that
2,: (x) = f 1
- AP'
eP?i*
(KX)
and
the solution (37) of eqn. (16) is given by
(a"
1)
a$
(x) =
-
+
+ )
P
I
+
1
- 2y
(=)
-13
1-x p
,>
j (
J
-1
g(t)
(1 - P
g (t)
'1
I
-t
1I
6
k t - P &
+t) t
) ]
-r
dt
(43)
-1
Note that the form of the solution (43) is not the same as those obtained in (27) and
by h w i n earlier. But this form of the solution does not have the apparent siBgulardy
as the form (27) is having at x = 1, which wa? felt and mentioned by Lewin.
SINGULAR INTEGRAL EQUAT~ONS
157
and
then. by (421,
4 (x)
is given by
The form (45) is exactly the one
as given
by (27).
A particular clash of singulas integral equations. SIAM J . AP,,~.
Math., 1971, 20, 99-109.
On a class of singular intepalequations, .
I
Mmlr.
.
Anal. nppl,c$.,
1966, 14, 392-426.
BolcnrlZiry value problblems, Addison-Wilcy, 1963, p. 81.
o n the rewlution of a class of wave-mide discontinuity problems
by the use of singular integral Cquati-ms, L E E . Trans. MTT,
1961, 9, 321-332.
Integral equnlions, Pergamon, 1962, J . 126.
Some basic problem in the mathctnurical theor-v o f elnvtkicy+
P . Noordholr, Groningcn, 1963, ?p. 260 and 446.
A more tractable solution t9 a singular intesal equation obtained
by sdving a related Hilbert problem for two unknowrs, J Res.
Bur. St&. 1976, SOB (3), 403-414.
A note on the integral equation of the first kind with a Cauchy
kcmel, C m . Pure Appl. Ahths., 1963, 16, 57.41.
Pairs of Cawby singular integral equations and the kernel
[ b (2) -k a (c)l/(z - L), Co~mn.PEW AppL Muths. 1972, 25. 36%
402.
Note on a singular integral equation, J . Inst. Maths. Applies.,
1978, 22, 211-241.
On unsteady
flow past a porous plate under pressure gradient
S. T. REVANKAR A N D V. M. KORWAR
lXparlment of Physics, Karnatak University, Dharwad 580003, India.
Received on July 10. 1980; Rei'ised or. October 6, 1980.
Abstract
The problem of hMD two-dimensional flow past an iafinite porous plate with constant suction moving
with arbitrary time dependent velocity, under time dependent pressure gradient when initial distribution of velocity is an exponential form is studied. This ;roblem generalises aeveral earlier works
for the case when the motion has started frem rest with uniform pressure gradient as a result of the
plate movement in various aanicular ways.
Keg words :
Unsteady MHD flow, prwsure sradient, puroua plate, arbitrary t i e dependent iclocitr .
The incompressibie laminar viscous fluid flow between two stationary parallel iiat
plates with an arbitrary time varying pressure gradient and with an arbitrary initial
distribution of velocity has been studied by Hepworth and Rice1. The same problem
is studied by Prakash' under the same condition, but with the difference that the flow
is in between two stationary coaxial circular cylinders. The problem of viscous
incon~pressibleflow past a n infinite plate moving parallel to itself with an arbitrary
dependent velocity when the pressure is uniform and the initial distribution of
velocity is an exponential form has been discussed by Prakash3. Srivastava and Lal'
extended this problem in case of MHD flow. The present paper is concerned with
the Study of problem of incompressible laminar viscous electrically conducting fluid
flow past a n infinite flat porous plate moving parallel to itself with a n arbitrary time
dependent velocity with uniform suction at the plate, under constant pressure gradient,
when the initial distribution of velocity is an exponential form.
2. Formulation of the problem and solution
Consider an unsteady laminar viscous MHD flow past a n infinite porous flat insulated
Plate moving parallel to itself with arbitrary time depndent velocity with unifornl
159
suction V(p' > 0) under'tin~edependent pressure gradient, with initial distribution
velocity being in exponential form. We take x and y axes along 2,nd normal to the
*late and assume a uniform magnetic field H, acting along ?-axis. Then the soverning
equation of motion for this problem i s
where
= ? h; H:, = constant.
v is the kinematic viscosity and p is the pressure,
P
The initial and boundary conditions are
t=O;u=Aexp(-By)for
(2.2)
y>O
t>O: u=g(l)
for y
t>O:u=O
as
!.
=
0
+w
(2.3)
(2.1)
Here A, B are non-ncgdtiva constants and 4 ( t ) is bounded continuouv or piecewise
continuous arb~traryfunction of .I.
Now if we assume
- %'
2.K
= f ( t ) , (2.1) reduces to
We solve (2.1) with initial and boundary conditions (2.2)-(2.4), with Laplare trans.
Form techniqms and the solution, after assuming pressure gradient constant, i.e.,
where C is constant, is given by
UNSTEADY MHD FJ-OW PAST A POROUS PLAT6
C
t - (I
Pm
- e-"9
t A e x p { - By
+
-
FBI
- nit:,
161
(1. >
The steady state solution is obtained by taking limit of cqn. (2.6) as t
0)
(2.6)
+ oa.
3. Discussion
We find that s o l ~ ~ t i o(2.8)
n
is valid for both y ,
;0. However, this solution is derived
from solution ( 2 . 6 ) which is only valid for y s 0. This is due io discon~inuityin the
Bow at y = 0 since the start of motion.
From the solution ( 2 . 6 ) we note that velocity field dcpcnds on the initial distribution
OF velocity, motion of plate and on the pressure gradient, whereas the steniy state solution does not depend o n the initial distribution o l velocity but on plate motion and
pressure gradient. To see the effect of suction and ma.gnetic field on the velocity
profile we take the plate to be uniformly accelerated, i.e.. g ( t ) = at. B y giving the
values to constants. A, B. C, and a, as unity (= 1) and tzkiqg p = I (e.g., water) the
solution for velocity profile. eqns. ( 2 . 6 ) and (2.7) become
+exp(-q+t-V,t-mt)
21s
t
(q>O)
(v
= 0)
where
We plot the velocity profiles using eqns. (3.1) and (3.2). Figure 1 (a) and (bj show
the velocity profiles for t F 0.5 and f = I respectively.
We find from the figures that v is just f as given by eqn. (3.2) for q = 0. And for
increasing value of q the velocity decreases and for large value of 11, zr attains a
steady value determined by the magnetic field parametar m. For higher value of time
i, the steady value is attained quickly compared with lower Value of time t. With
increasing value of suction the value of u decreases before it attains steady state value.
The effect of magnetic field is more prominent; it decreases the velocity field and the
UNSTBADY MHD FLOW PAST A
IWROUS
PLATF
163
decrease in the value of the velocity at a point is more for higher magnetic field for the
0 difference in the value of lnap~lelicfield strength. This is also true for higher
value of time t .
J.
Special cases
(a) Solution For ordinary hydrodynamic flow (m = 0 ) :
If
m
=
Y~:H;
P
= 0,
then eqn. (2.6) becomes
- A
exp
Ct
:- B). + vR9 - Vw + .(J > 0 ) .
P
(4.1)
In the absence of pressure gradient this corresponds to the solution for hydrodynamic
Row given by Srivastav3.
(b) An infinite porous flat plate moving in Don-conducting fluid with time dependent
*locity U ( t ) with uniform suction V on the fluid at rest.
The solution for this problem is obtamed by putting g ( t ) = U ( t ) ,m = 0, A = 0,
p = 0,
0
(4.2)
This corresponds t o the expression given by Hasimoto6,
164
S. T. KEVANKAR AND
v. M.
ROKWAK
( c ) An infinite porous flat plate oscillating (linear harmonic) parallel to
itself Nith
velocity Ucos nt with uniform suction V in the fluid at rest.
ucosnt
The solution for this problem for large times is obtained by putting g ( t ) =
A=O,m=O,p=O.
with
q =
y/l/rn.
(4.31
This solution can be compared to the solution obtained by Srivastava and LalF. namely.
whore
(d) Stokes first problem
The classical Stokes first problem can be obtained by putting, 8 ( t )
V = 0, and p = 0.
=
U, A
= 0,
m = 0.
which i s the same as SchlictchingVsolution (Page 72, eqn. 5 . 22).
(e) Stokes second problem
Solution for Stokes second problem can be obtained with g ( t ) = U cos nt, A = 0.
m = 0, V = 0, p = 0. for large times, we have from (3.4),
which is equivalent to Schlicltingfi solution, (Page 75, eqn. 5.26)
5.
Conclusions
( I ) There
1s
dixontinuity in the flow at y
=
0, since the start of motion
(2) The velocity decreases with increase in the magnetic field strength and this decreag
is more with higher value of time i.
(3) The increase in the value of suction decreases the transient velocity
prose.
(4) The solution obtained is generalisation of several earlier works such as Stoka
problems,
UNSTEADY MED FLOW PAST A POROUS PLATE
ne authors
,,
wish t o thank the referees f o r their helpful suggestions.
H E ~ W ~H.KK.~ m
~ ,
RICE, W.
Laminar flow between parallel plates with arbitrary time vary&g
pressure gradient and arbitrary initial velocity, Tmm. ASME,
J. Appl. Mech., 1967, 34,215.
Laminar flow in an annulus with arbitrary time varying pressure
gradient and arbitrary velocity, Trum. ASME, J. Ap#I. Me&.,
1969, 36, 309.
Note on the problem of unsteady viswus flow past a flat plate,
Indian J. Pure Appl. Math., 1971, 2, 283.
On the problem >f unsteady magnetohydrodynamic v i m flow
past an i n b i t e flat plate, Rev. Roum. Marh. Pure AppL, 1977,
22, 1291.
On the problem of unsteady viscous M E D 03w past an infinite
porous flat plate with constant suction, Acra. Phys. Hung., 1976,
40, 139.
Boundary layer growth on a flat plate with suction or i n j e n i o ~
J. Phys. Sac. Japan, 1957, 12, 68.
On unsteady compressible &ow of suction near an oscillating
porous 5at plale, Japan J. Appl. Pkys., 1975, 14, 1249.
Boundary layer tkeory, McGraw-Hill Co., New York, I%&
pp. 72 and 75.
j,
]*din Inst. Sci. 62 (B), Oct. 1980, Pp. 167-171
Printed in India.
p Indian Institute of Science,
Short Communication
On nonlinear oscillation problem
P. C. MUNOT
AND
RENU MATHUR
DEpartment of Mathematics, University of Jodhpur, Jodhpur 342001, India.
Reeeibed on January 21, 1980; Revised on August 12, 1980; Re-rewed on September 29, 1980.
Abstract
In the present paper we have given the solution of the differential equatio~~
x+/(x)
J!
=- 0
the general free oscillations where,
by applying the linear orthogonal polynomial approximation.. The results obtained are of gmeral
hatter and include as particular cases many of the results given earlier by Garde and S a m and
Kushwaha.
bwords : Nonlinear oscillations, orthogonal polynomials, amplitude dependent approhimatimr,
Sneralised hypergeometric function, confluent hypcrgwmetric function.
1. Introduction
1959, by the application of Tchebicheff polynomial approximation to sin 0 in the
interval (- A, A), Denmannl obtained an amplitude dependent approximation t o the
fre¶uency o f the simple pendulum whose amplitude of motion is A. Later, in 1964,
Dmmann and Howard" m n m a n n and Liu8 have applied ultraspherical polynomials
the same prablem. Garde4 in 1965, applied Gegenbauer polynomials t o some forced
OKilhtion problem a n d in 1967, Jacobi polynomials to obtain a n approximate soluh depanding on the amplitude of the nonlinear oscillations defined by the differential equation
168
P. C . MUNOI AND KONU MATHUK
In 1970, Saxena and Kushwaha in two of their joint papers atteulpted ~ ~ ~
nomials to obtain the amplitude dependent linear approximate solution of the
differential eqnations
5
+ ax
-I- bx"
0
We have attempted in this paper a set of general orthogonal polyno~nials{$n[x)) to
an amplitude dependent linear approximate sohtion of a general daferentia~
equation
where r and s are positive integers and
efp"
; .. .
a ; & ]
b,, ht, . ., b,
is the gcneralised hypergeometric function5 (p. 73).
The initial conditions of motion are x = A, 3 0 when t = 0, A being the amplitude of the motion under which the solution of the proposed problem will be obtained.
.
;
The main result of the paper is a generalisation of the results given by GardzQand
Saxena and Kushwahas, 9. The results obtained are believed to be new.
2. Orthogonal polynomials and liicar approljmation
Let 4, (x) be a polynomial of degree precisely n and (4. (x): forms a set of orthogonal
polynomials in the interval (a, b) with respect to the weight function w (x) > 0, then
It can be easily seen that the set of polynomials {#, (x/A)]arc orthogonal in the interval
(ad,bA) with weight function iv ( x / A ) .
Let LZ, be the class of functions f for which
~
b
d N NONLINEAR
OSClLLATIOPj PROBLEM
and let {#.(x)} be an orthonmmal SYsten1 of polynomials which bclong to L;.
,he system is closed and for every
169
Then
c~nyerges in mean to f
~n reference to the known solution of the differential equation
x+mx=n.
we obtain an approximate solution of the problen~
a+f(x) =o
by truncating the series (2.2) of f ( x ) after second term.
Thus the desired approxi-
mation o f f (x) in this problem is given by
3. Solution of the main problem
In this section we have solved the differential equation
a+f(x)= o
where
and
[ j ' ( ~ )=
],- K
+ K'xs.
where
-
K' = a,, + ale, K*') = a,
i = 0, I and
do = 1, dl
=c
d
z,
+ dx, K, are
'he integrals in a, exist since the series
defined by the relation (2.0).
f 70
Y. C. MUNOT AND RENU MATHUK
under the initial conditions w = A, .i
= 0 when 1 = 0. This solution is thaeforean
approximate solution of the prohlem (3.1 ) under these conditions.
Obviously it has the approximate period
Pcrrticdai cuses: ( i ) I f we take b,, (x)to be the Jacobi polynolniais [ref 7, p. 254; ref. 10,
p. 581, and use the integral [ref. 11, p. 4661, and [ref. 10, p. 711, Po(',@' (x)=l, P,'%PI
( x ) = 1(a + fi t 2) s
(a - /J!2. then the approximate solution o i the nonlinear
+
differential equation
a + f(r)=O
where
ON NONLINEAR OSCILLATION PROBLEM
-r-sj,
a+1
171
-
-8-r-sj
;
1).
The series for ?.2 a n d i*' are convergent for p < q
(ii) The a p p r o x i m a t e solutions of
.? + 11%: x
' ,F, (0:b ; exs) = 0
and f o r p = q
+1
if
I
[ < 1.
given by Saxena a n d K u s h w a h a y p . 295) and that of
P + ll'E x - ll$ cx3 = 0
b Garde6 (p. 112, 22) a r e SWn to b e easy consequences o f our main result.
4. Acknowledgement
The authors a r e highly thankful t o the worthy referee for his valuable suggestions for
tht improvement of t h e paper.
References
I. DENMANN,
H. H
2. DEW,
H. H. and
HOWARD,
J. E.
3. ~ M A N N H.
, H. AND
Llu, Y. K.
4. GARDE,R. M.
Amplitude de~ondencerf frequency in a linear a p p r o ~ i m t i ~ n
to simple pendulum equation, Am. J. Ph~s.. 1959, 27, 5%.
A-$plication of ultraspherical polynomials to nonlinear oscillations I.
Free oscillations of the pendulum, Q. Appl. Mmh., 1964,21,325-331.1.
Application of ultraspherical polynon?ials to nonlinear osdllations-11.
Free oscillations, O. Appl. Matlr., 1964.22, 173-292.
Application of Gegenbauer polynomials to nonlinear oscillations,
forced and free oscillations without damping, Indian 6. Math.,
1965, 7 (2), 111-117.
Application ~f Jacobi polynomials to nonlinear oscillatiocs-1.
Free oscillations, Pmc. Nut. Acnd. Sci. India, 1967, 37, 109-120.
The theory o f f u n c t i o ~of
~ ~o~ real varhble and the the0r.v of
Fourier's seyies, Dover Pub.. Inc. New York, 1926, Yol. 11.
Special functions, Macmillan and Co., New York. 1960.
Application of Jacobi pdynomials to nonlinear oscillations,
Proc. .Wt. Acad. Sci. Indin, 1970, 40, 65-72.
Application of Jacobi polynomials to nonlinear differential
equation associated with mntluer.t hypergeometric fundion,
pro,. Nat. Acnd. Sci., Ind;a, 1970, 40 (a), El,281-288.
Orthogonal polynomials, Am. Math. Soc. ColI. Pub. 1967.
Vol. m.
On sime integrals involving Jacobi yolynomials, Proc. Mot.
Acad. Sci.. India, 1966, 86, 465-468.
J.
bdiau Inst. Sci. 62 (B), Oct. 1980, Pp. 173-176.
0 Indim Institute of Science, Printed in India.
Short Communication
Titrimetric estimation of phosphate, molybdate and sulphate with lead
nitrate solution, using 2-(2'4epidyl azo)-l-naphthol-4-ammonium sulphonate (Lanas) as visual indicator
R. C. CHADHA, B. S. GARG*, SWARAN LATA AND R. P. SINGH
Department of Chemistry, University of Delhi, Delhi 110 007 (India).
Reeeived on September 20, 1980.
Abstract
2-(2'-Lepidylazo)-l-naphthol-4-ammoniumsulphonate (LANAS) forms a blue wloured complex with
PbflI) which is readily destroyed on addition of sulphate, phosphate and molybdate. Titrimetric
procedures for the estimtions of these ions have been developed. Large number of complehing
anions do not interfere.
Be? words : Titrimetric estimations, sulphate, phosphate and rnolybdate, LANAS as metallochromic
hdicator.
1. Introduction
Earlier LANAS has been found to be useful as a visual indicator in titration of metals1-'.
Tltrimetric estimation of molybdate, tungstate, phosphate and sulphate with lead
nitrate solution using LANAS as indicator under specified conditions is rapid and
sensitive. Sornmer and Janoscovas have established the condiioxs under which PAR,
TAR, TAMP and 1-PANAS can be used as mdlcators in titrimgtric estimation of
phosphate, molybdate, tungstate and sulphate. They have also mentioned the difliCult!? in the estimation of mugstate and sulphate. The present study shows that LAN&
can be used successfully as visual indicator for rapid titrimetrio estimation of these
anions by titration with lead nitrate solution. The titration is easy and 8OC~rateunder
Wified conditions prhich have been worked out in individual case.
'To whom au cwrcspondplce should bc addressed to.
173
2. Experimental
Indicator solution, 0 01% (wjv) in doubly dibtilled water, hexamine buffcrs of DH 6 0
and 7.0. and so&um acetate acid buffer of pH 4 5-5.5 were prepared. Anal>bal
grade reagents and doubly distilled water were used for the standard solutions.
LANAS was prepared1 by the condensation of 1, 2-naphthoquiuone-4.~odi,,
sulphonate with 2-hydrozino lepidine in thc presence of concentrated ammonia, ~h~
compound was isolated, purified and characterized by thin layer chromatographyand
elemental analysis.
3. Titration procedure
To a suitable aliquot containiny 0.96 to 100.0 mg of sulphate or 0.90 to 100.Omg
of phosphate or 0.80 to 160 mg of molybdate in a 100 ml conical flask, add 4 drops of
0.01% (wjv) indicator, followed by a few drops of wry dilute solution of nitric acid
to get yellow colour. Then add buffer solution dropwise till the pH is 6.0-7.5 (hexa.
mine/HNOd in the case of sulphate and phosphate ; 4.5-5.2 (NaAcIHAc) in the ca* of
molybdate. In the case of sulphate add the organic solvent (2.0 ml DMF and 2 . 0 ~ 1
isopropanol for 20.0 ml). Kaise the volume to 20.0 in1 and titrate with a standard
Pb(Q solution till the end point, orange or pink to blue colour is obtained. The
titrations can be done at room temperature in the case of sulphate and molybdate and
above 70" C in the case of phosphate. Detection of end point is easier even in the case
of sulphate at high temperature. Large amount of indicator obscure the end p o k
in the case or molybdate. The relative error is generally less than 1%.
4.
Effect of diverse ions
To ensure the suitability of the titration procedures, effects of diverse ions have
studied in detail. The tolerance limit (in ppm) of the ions which did not cause error
of more than 1% in the determination of 0.96 mg of sulphate or 0.90 mg of phosphate
or molybdate 1.6 mg per 20.0 ml are aummarised in Table I.
Sulphate, phospkdte and molybdate interfere with each other in the determinations.
Other anions which interfere in allcases are mugstate, oxalate, chromate and sulphite.
Metal ions, such as zinc/Q and manganese(I1) which give coloured complexes
LAN!$
also interfere in all cases28,
U N A S thus serves as a good vishal indicator for the precise titration of the ah*
anions in the presence of large number of other ions, The lead: phosphate ratio
the precipitate is 5 :3. he composition of the precipitate in the presence of chloride
is Pb5 (PO& C1(SP = 7.5 x 10-"1). h phosphate titration large amounts of cN0&
*
TITRIMETRIC BSTIMAT~ONOF PHOSPHATE, MOLYBDATE AND SULPHATB
175
Table 1
sect of diverse ions
-
Fareiw ion
Fluoride
Cblaride
Bromide
Iodide
Acetate
Thiosulphate
Nifrate
%trite
Borate
Citrate
Tartarate
TWanate
Cymide
Thourea
Hydroxylamine
Ascorbic acid
Cobalt* (U)
N~ckel*(II)
Mercury* &I)
Coyper* @)
hhpesium(T
Barium0
Aluminium (Ln)
Bismuthw*(m)
Tin 0
Aluminium*** @I)
* = masked
with cyanide,
Subhate
Phosphate
Molybdate
90
300
1000
100
5000
110
4000
60
100
400
1000
1500
1800
5000
200
4000
450
150
200
500
4000
2000
2000
700
200
400
125
500
90
400
40
30
104
600
130
95
400
1000
100
5000
1100
4000
2100
100
50
300
4000
2000
2000
2100
860
350
125
500
100
1000
1370
50
200
Interfereb
100
1400
2000
2000
350
100
500
150
500
100
400
Interferes
20
200
Interfere
100
"= masked with chloride,
Interferes
50
***
-
masked with flmride.
bromide, and acetate do not interfere like other known ligands. Molybdata could be
titrated at low pHs and interference of number of metal ions thus could ba avoided.
The authors are thankful to the University of Delhi, Chemistry Department, for
Providing necessary facilities and to Dr. S. K. Mehrotra for helpful discussions.
References
1. CHADHA,R. C., SINOH, I.,
GARG,B. S. AND
SINQH.R. P.
Analytical potentialities of a new heterocyclic au, dye:
zU'-
1epidylazo)-1-naphthol-4-ammanium sulphonate (LANU) as a
metallo-indicator for titrimetric determination of mercuq
EDTA, Curr. Sci., 1976, 45, 830-832.
(n) l,h
GARG,BB.
s. AND
SWGH,R. P.
~omplnrometricestimation of some transition elements (hay&
3d6 to 3dSelectronic configuration) wing LANAS as visual metallocbromic indicator, Indian Naf. Sci. Acad., 1979, 45, 20-2~.
3.
CHADHA,
R. C., GARO.B. S.
AND SIXGH,R. P.
Ammonium 2-(2'-le~id~law)-l-na~hthol-4-sul~honate
as indiobr
in mercurimetric determination of halides, Talanta, 1979, 26,313.
4.
C
2. CHADHA,
R. C..
H ~R. , C., GARG,B. S.
SINGR,R . P.
AND
2-(2'-lepidylazo)-l-naphthol-4-ammonium sulphonate (LAN&)
as visual metallochromic indicator in complexomtric determi.
nation of lead (I[), Curr. Sci., 1979, 48, 15.
5 . so-,
L. AND
JANOSCOVA,
L.
Contribution to the determination of some anions by titr&nq,
with lead @I) nitrate using heterocyclic am dyes as indicator.
Coll. Czech. Chem. Commun., 1974, 39, 101-109.
6. CHADRA,
R. C., LATA,S . ,
GARG, B. S . AND
SIXGH,R. P.
LANAS as a metallocluomic indicator in complexometricesti.
mation of zinc, cadmium and mercury, Indian Ckeni. Soc., 1980
(communicated).
j. ~ ~ d i aInst.
n
Sci. 62 @I, Oct. 1980, Pp. 177-180.
0 Indian Institute
of Science, Printed in India.
Short Communication
Debenzylation by Ni-A1 alloy
M. VENKAMA NA1DU"m
G. S. KRISHNA RAO**;
Department of Organic Chemistry, Indian Institute of Science, Bangalorc 560 012.
Received o n O c ~ o b e r 21, 1980
Abstract
Nickel-aluminum alloy in aqueous sodium hydroxide-ethanol medium brings about facile hydro~enolrsisof benzyl ether function in substrates carrying a vicinal methoxy group. Simplicity of the
reaction conditions and cheapness of the reagent are some of the advanrages of the procedure.
Additionally, carbonyl functions when present are untouched and alkaline medium of the reaction
makes it compatible with the presence of acid-sensitite groups.
lie). words : Ni-A1 alloy, benzyl ether cleavage, hydrogenolyw, debenzylalion.
1. Introduction
Introduced by Schwenk and co-workersl-6 nickel-aluminium alloy' (1 : 1) in aqueous
alkali has proved to be quite useful in several reduction reactions because of cheapness
of the reagent and operational simplicity of the reaction. a, 19-Unsaturated acids
with5, ' and withouts, 6 2 1 % 11 aryl substitution. y-aryl-fl, ;i-unsaturated acids'?-l5
chlorinated polyene acidsle and neutral substrates like benzyl alcohols', aldehydes
and ketones?, 0.17, aromatic halides43 18, nitroaromatics3, oximesla and nitrileszo have
been reduced by Ni-Al alloy essentially under aqueous conditions. Displacement of
some groups (sulphonic acid and alkoxy groups) was also encountered in some cased.
Our recent finding of facile hydrogenolysis of benzyl ethers with vicinal nrethoxy function constitutes a useful addition to the above list of applications of Wi-A1 alloy in
*
.*
Prevent address : Department of Chemistry, Rice University, Houston, Texns 77001 (U.S.A.1.
T o whom all correspondence should be addressed.
177
.M. VENKAMA NAIOU AND G. S. KRISHNA
178
RAO
organic synthesib. Thus 3-n~ethox~-4-ben~~lox~t@luene
(I), 3 - m e t h o ~ y - 4 . b ~ ~ ~ ] ~ ~ ~ .
propanoic acid
benmldehyde (11) and 3-(2'-1nethyl-4'-methoxy-5'-benzyloxybenzoyl)
(111) under%,ent debenzylation in excellent yield on stirring with Ni-A1 alloy pouder
in elkanolio sodiuin hydroxide to afford the corresponding hydrogenolysis products 11'.
V and V I respectively. The hydrogenolysis of compounds 11 and 111 is
noteworthy in that the carbonyl function4 are left in tact, whereas literature reca&
reduction of the carbony1 group, in nmst cases. to the carbinol or to the inethybnest&@,
depending o n reaction temperature" G 3 ".
Recently Kanztani ef al" "ported cleavage of benzyl ethers with sodium his (2.
methoxyethoxy) aluminium hydtide in refluxing xylene. Thus benzyl vanillin afforded
(i) a mixture of the phenol (IV) nnd the alcohol (VII) (reaction t h e 6 hr) and (ii) exch.
sively the phenoi (IV) (reaction time 10 hr), the a l d e h y d ~function in either case reduced
patially or coinpletdy depending on the length of time of the reaction. On the other.
hand Ni-A1 alloy. as found by us, does not reduce the carbonylfunction while cleaving
the benzyl ether (TZ + V ; I11 + Vl). However, as observed by Kametani r t a!", a
vicinal methoxy function appears to he essential for debenzylation in the case of Ni-Al
alloy too, as shown by the complete recovery of 4-benzyloxytoluene under identical
experimental conditions. Suhject to this limitation, Ni-A1 alloy seems to score an
advantage over some of the alternate catalytic2', metal hydrideY3, and alkoxy meial
hydride" debenzylation techniques, as the reagent (Ni-A1 alloy) is accessible even
to a low-budget laboratory. It nlso demands no special handling (except for keep'ing
the pyrophoric nickel wet till disposal) and storage precautions and the reaction is
conducted in alkaline aqueous ethanolic medium, compatible with acid sellskive
functions.
IV
v
VI
Vll
DEBENZYLATIOh
BY N1-AL
ALLOY
179
3. Typical cxyerirnental pracedure
a solution of the benzyl ether (IIIi/III) (0.01 mol) dissolved in ethanolic sodium
amount of water and the volunie made
hydroxide [NaOH (1 g) dissolved in nliili~nu~n
up to 10 1111 with cthanol] and maintained at gentle reflux. Ni-A1 alloy pcr5dcr (1 : 1 ,
1 g) was added under stirring in sriall lots, keeping the frothing under control by
adjusting the rate of addition of the alloy. After compbtioti of addition, the reaction
mixture was stirred fcr 6 hr, allowed to cool and the nickel was filtered off. taking care
to see that it is maintained wet. Most of the ethanol From the Alaate was distilled
off under suction and the residue was acjdifred with dilute hydrochloric acid ( 1 : I).
The product was thoroughly extracted with ether and the cxtract was washed with
brine and dried over anhydrous sodium sulphate. Removal of solvent rurnished the
debenzylated products IV (95";), V (60;,;). VI (95%;) yield. identified by L.1. and spectral
comparison (i.r. and p.m.r.) with authentic materials".
TO
4. Acknawledgement
MVN thanks the UGC, New Delhi. for a research fellowship.
References
2.
PAPA,D., SCLWEKK.
E.
WHITMAN,
B.
AND
4.
SC~WENK,
E., PAPA,D..
WHITMAN,
B. AND
GINSBERG,H.
5. SCHW~NK,
E., PAPA,D.,
WH~TMAN,
B. AND
GINSBERG,
H.
J. Org. Cicenr., 1944, 9, 175.
6 . S C ~ W E ~E.,
K PAPA.
,
D,
mNm, H. AND
Org. S.vwh., 1955, Coll.
Val.
3, 742.
GINSBERO,
H.
Rengerils fur. Orgunic Synthesis, John Wiley. New York. 1967.
1, 718; 1969, 2, 289; 1974, 4, 350.
Ow. Synth., 1963, Coll. Vol. 4, 136.
180
Y.
M. VEYLAMA NkIDU AND G .
SANK,P.
S.
KRISEINA RAO
J'.,
KULI(AKNI,
H. S.,
VAIDYA,A. S . AND
RAO,A . S.
10.
JOHN,
T. K. AND
KNSRNARAO,G.
S
P1z.D. Thesiv, Indian bstilutc of Science, Ban&ye,
1979.
J. lidiun Chem Soc., 1955, 32, 5 1 5 .
J. brdiatz Chem Soc., 1959, 36, I .
14. GUPTA.
A S.,
M u ~ m u ,K
Sum
L.
A*ID
DEV
J . Clieni. SOL. Perkin I. 1975, p . 1275.
16.
ROEDIG,
A,, MARIL, G
AND S C ~ ~ A y.
AL,
17. COOK,P...I
Ucr., 1962, 95, 2284.
I. Org. Chenr., 1962, 27, 3893.
Ber., 1963, 96, 1441.
J. Clre,,~.Soe. (C), 1966. P . 6 5 5 .
21. KAWNI, T ,
HUASG,S. P., IIIAR*, M.
AND F~KUMOTO,
K.
Pi-otcclivs group\ i,i orgnrik clte,rri,~li~v,McOmic, J .
Plenum Prcsb, London, 1973, p . 145.
J. Am Chem. Suc., 1957, 79, 5463.
r. W.
(Ed.)
J.
9
Indian Inst. Sci. 62 (B), Oct. 1980, Pp. 181-192.
[ndian Instihlte of Science. Printed in India.
The chemistry of vetivalene-type naturally occurring sesqufterpenoids
P. ANANTHA REDDY"
AND
ti. S. KRISHNA RAO""
Department o r Organic Chemistry. Indian Instituw of Science, Rangaior~560 OIZ.
Received o n August 29. 1980.
Abstract
Vetivalene, 1,4-dimetiiyl-6-isopropylnaphl1tlmlenc(1) represents a new sesquiterpene skelcton which 15
presumed to originate from eudesmane by a shift of the angular nicthyl group. Novel sesquiterpenm
related to vetivalene have been isolated from plant sources ill ~ s c e o igears. A suriey dealing xith
the chemistry (structure, synthesis and configuration) of members of this interesting new class OF yesquiterpenes, coniprising occidol, risbitinol and the various ernmotinn is presented.
Key words: Vctivalenc,
configuration
sesquitcrpcno~ds, occidol,
rishitinol, emmotins,
s1ruciul.e.
sgn~hecis,
1. lutroduction
In recent years, about a dozen sesquiterpenes huvz been isolated which may be
regarded as derivatives of 1,4-dimethyl-6-isopropylnaphthalene (I), called vetiva1ene.l
Vetivalene (1) represents a new sesquiterpene skeleton which is presumed to originate
fram eudesmane (Fig. 1 ) by a shift of the angnlar methyl group. The present survey
deals with the chemistry (structure, synthesis and confiyration) of members of this
interesting new class of sesqujtcrpenes. comprising occidol, rishitinol and the various
emmotins.
* Present address : Department of Cbrmiclry, Uni\er';ity Coliepe or Swanscn, Singlelon ?ark.
Swansea SAZ 8PP (U.K.I.
** Address for correspandcnce.
181
182
2.
P. ANANTHA REDDY AND G. S. KRISNNA R 4 0
Occidol (2)
A major sesquiterpene alcohol (C,&&)
( 2 ) named occidoi, 111.p. 69-70", [,I$ + 1 6 3 , ~ ~
(CHCI$ was i s o l a t e d ~ r o ~the
n essential oil of T h i n occidmtalis L. along with ocei.
dental01 (3) (Fig. 2 ) . The structure depicted as (2J for occidol was elucidated bg ~i~~~~
and Nakatsuka2 and was confirn~edby a number of syntheses.
The synthesis of occidol (2) by Hirose and Nakatsuka3 (Fig. 3) starts from p.nylenp
and proceeds ria the tetralone (4). The tetralone wa.3 converted to I*)-occidol (2) in
six steps.
A &es of three syntheses of' occidol have been reported by Hoa--"duriug 1971-73
(Figs. 4-6). Unaware of the earlier synthesiss, Ho reported4 in 1971 a more or leg%
identical synthesis of Occidol (2) from identical intermediates (Fig. 4).
Tnfhis second synthesis of occidol Ho5 started with 3,6-diunethylphthalicanhydride (7)
(Fig. 5). Its reduction to thc diol(8) with LAM, Collowzd by treatment with phospho~s
tribromide, gave the dibromide (9) which was converted to the o-quinodimethane (10).
Diels-Alder reaction of (10) with methyl acrylate gave the tetralin ester (6). Reaction
vf the ester (6) with methyllithium gavc (A)-occidol (2).
VETIVALENE-TYPE N.4TUR4LLY OCCURRING SESQL~ITERPEUrlIDS
ls.1
In his third synthesis', of occidol, Ho utilized transition meial catalysi, to carboxylate
the dihydronaphthalenc (13) (obtained by the route indicated in Fig. hl by photoreaction with nickel carbonyl. Reaction of the resulting tetralin ester (61 with methyl
lithium completed the synthesis of (&)-occidol (2).
The synthesis of ( i l - o ~ c i d oby
~ l Dauben' as depicted i n Fig. 7 Ftarta from the wrhon~ethoxy acetylcylclohexene (14), prepared by Friedel-Crafts azyhtion of methyl
zyclohex-3-enecarboxylate. The bicyclic diene estei (15) obtained from the keto estei
(14) by treatment with 2-hutenylidene triphenylphosphorane was dehydrogenated to the
tdralin ester (6) from which (t)-occidol (2) was obtained in the usual way.
Wolinsky's%ynthesis of (&)-oceidol starts from 9-chloro-I-p-menthen* (161 derived
from (+)-limanene. Its condensation with vinylacetyl chloride (Fig. 8) gave the chloronaphthalenone (17) as one of the products in 33% yield, resulting from n sequence of
hydride and metl~yyl shifts. Addition of nuethylmagnesium iodide to the ketone (17)
W a s accompanied by dehydration in the work-up, giving the diene (18). its WmatiZation, followed by dehydrochl~ri~ation
gave the isopropenyltetralin (19) which afforded
(+)-omidol (2) o n oxymercuration-demercuration sequence of reactions.
w< Q-%coci
16
=I
-
'17
a
18
@-CL
19
-
hrn
[+j-&<m
184
P. ANANTHA REDDY AND G. S. KRISHNA RAO
The synthesis of (i)-occidol developed i n our laboralorysJu exploits the s y n t h ~
potential of Vilsmeier reaction in the key-step. Thus the dihydr~naphthaldeh~d~
(21,
obtained from 5,s-dimethyl-1-telralol (20) on Vilsmeier reaction, was Converted tb th;
methyl dihydronaphthoate (22) (Fig. 9). Its hydrogenation gave the tetralin erter (6,,
the well-known precursor for (+I-occidol (2).
CHO
OH
The absolute configuration (R) of the chiral Centre at C, of occidol was established
by correlatianll-"" with (-pantonin (23) as outlined in Fig. 10.
Hyposantonous acid (24a) prepared from (-pantonin (23) was converted ta
(+)-occidol i n six steps via the chiral ketone (25) which established identical
configurations at C-6 of both (-)+antonin and (+)-occidol.
The conversion of emn~otin-A and enmotin-F (vide supra) to (i-)-occidol by
Olivej~aef all3 is yet anothei interesting exercise in configurational correlation involving
occidol.
Emmotin-A diacetate (26) and ernmotin-F diacetate (27) were reduced by zinc to the
keto acetate (26) (Fig. I I). Catalytic hydrogenolysis and saponification of the acaoxytetralone (28) gave (+)-omidol.
A possible bjogenetic origin of occidol is delineated in Fig. 12. The cyclodecadiene
$4) representing the product of initial ring closure of traits-trai~s-facnesylpyrophosphae
(29) may be visualised as a precursor for occidol. The charge bearing isopropyl group
in (30) accepts a hydroxyl group to give the side chain as in (31). a situation encounrered in a number of sesquiterpene alcohols. Dehydrogenation of the dienol(31) could
dye the 1,3,5-cyclodecatriene system (32). Its further transformation may occur via
is valence tautomer, occidental01 (3) and finally to occidol (2) involving methyl shifr
and aromatization or its equivalent on intermediate oxidation states.
3. Rishitinol (33)
From the infected tuber tissues of white potatoes (Solaizum fuberosum and S. demLs.wtn)
Katsui et 0114J5
isolated a sesquiterpene alcohol, rishitinol (33) along with rishitin (34).
Rishitinol (CIsH,,O3 (33), m.p. 127-129", [a] + 47" (CHC13, M+-(234) was shown
a tetrasubstituted benzene with two vicinal hydrogens. Its failure to undergo
oxidation with periodic acid and its co-occurrence with rishitin (34) suggested that
iishitinol be represented by one of the structures (33 a), (33 b) and (33 C) (Fig. 13).
Since, these structures would represent rishitinol as a hydroxy derivative of occidol (2).
the PMR spectra of occidol and its synthetic intermediates were compared with that
of rishitinol. The structures (33 b) and (33 c) with hydroxyls peri to the methyl groups
were excluded and the structure (33 a) was p f e r r e d Tor rishitinol and the assignrnenc
Was confirmed by syuthesisl4~'~.
lo contain
The tetralone carboxylic acid ( 3 3 , re pared starting fromp-xylene in several Steps.
was esterified and reduced to the hydroxy esters (36) which on dehydration gave the
dihydronaphthalene ester (37). It was converted to the oxyisopropyl derivatiw (3%
which on hydrobaration followed by oxidation afforded a mixture of isomeric 1,3- and
Lbdiols (39 and 40). The required 1,3-diol, viz., (i)-rishitjnol (33) was obtained from
this mixture after elaborate chromatographic purification. In the PMR spectra of the
epimeric alcohols (39) the CHOH proton of one appeared as a multiplet with Wafs o f
25 Hz Centred a t 6 3.5 (trans), while in that of the other epimer corresponding to (33)
it appeared as a broad singlet with W,, of 7 Hz at d 4.76 (cis).
Comparative study of the absolute configurations of ridtiniB-l8 (34) and o~cidol"'.
(2) indicated that the biogenetically selated rishitinol (33) also would Possess Wim*d
Hence rishitinol was most fayourably represented as (33).
O W ~ P ~ * Pgroup.
Y~
! 86
P. \luh\iTMA REDDY 4ND G. S . KRISHKA R40
,
hydroaromatic bicgclic szsquiterpene methyl ether (C,,,H,,O.,). m.p 72".51- (2ii:.
was isolated from the trunk wood of Ein~mtz~i)?
nitens (Iraciizu~eue)by Oliveira et a ! ' .
The sesquirerpene called emmotin-h constituted one of a group of four compoundi.
vir., enlmotins-A, B: C and D with closely' related structures occurring in the same planr.
The presence of an avylketone moiety in emmotin-A was inferred from its UY and 1R
spectra, a-hile its PMR spectrum exhibjted characteristic signals for (a) two aromatii
ortho hydrogens, (b) one aromatic methyl, (c) one mnerhoxymeth.yl group prri To a
carbonyl function. ((1) a hydsoxyisopropyl group and (e) a secoadary hydroxyl u- 10
a carbonyl. The a-ketol function -COCFIOH- was also confirmed from chemical
evidence. Based o n these chemical and spectral (PMR) evidence of the sesquitetpene
and its derivatives (acetylation, dehydration and reduction products), StructUie? (49
and (42) (Fig. 14) were considered for emmotin-A. of which the former was preferred
on biogenetic grounds. as well as from CMR spectral support.
41
FIG. 14
The determination of molecular weight (by MS) of emmotin-BlQhowed it to be 0 4 WmmXin-A (C1,H,,OJ. Its PMR spectrum resembled closely that of emmotin4 (41),
differing mainly i n the replacement of Ar-CH, (b 2 . 3 2 ) by As-CSOH (6 4.67).
Presence of an extra OH group in emmotin-B was also revealed by the forrnaUoa'oi
VETIVALENE-TYPE NATURALLY OCCURRING SESQUITERPENOIDS
187
,,riacetae. Further insight into the structure of ernnlotin-B
was provided by CMR.
ifomparativestudy of the chemical shifts of the non-aromatic ~arbo!,.~of emmotins-A
m d - ~by application of the theory2", of chenucal shifts, and biogenetic considerdtions
titabfishedthe structure (43) (Fig. 15) for emmotin-B, excluding the &ternate
su~tufe(44).
"
The third constituent from Emnzofiim izite~lswas named emmotin-Cl" (C,,H,,O3, m.p.
:I-124' M+ (244) and shown to be structurally related to emmotins-A and -B. The
PUR spectrum of emmotis-C exhibited the characteristic signals: 3xAr-H, 3x05.
CEO. Ar-Cg, and C g (Ctl,),. Together with this information, the pr~babl~biogene~ic
&ion~hip of emmotin-C with emmotin-A (41) suggested structure (45) (Fig. 16) for
:minotin-C. Hydrogen bonded nature of an aldehyde carbonyl (0-H. . .O=C-HJ
jlR: c,,3440 (OH) and 1650 cm-' (C=O); PMR: 6 9.66 (CHO) and 12.35 (OH) 1,
u h o deihielded hydrogen (6 7.79, d, H3 coupled strongly = SHz) to another hydro.
!to (8 7 -24, d J = 8Hz.
and WH,,?of this Proton (H,)
-- signal (3' 7.24) revealing we&
.dog ran@ coupling with the neighbouring Ar-CH, (0' 2.77 bs) are in agreement ivith
9e structure (45) for emm0tin-C.
.
(1
188
P. ANANTHA RBDDY AND G . S. KRISHNA RAO
spectruln and that of its diacetate and its aryl methyl ether indicated the
of a Y-lactone unit (IR: v,. 1745 cm-I).
The PMR spectra of emmotiil-D and its derivatives revealed two aromati or,hn
hydrogens, one isolated aromatic hydrogen, an aromatic methyl g~oup,two hydioy
functions one of which is part of an oxyisopropyl group. These spectral data andbo;
genetic considerations indicated the structure (46) for emmotin-D.
A hydroaromatic bicyclic sesquiterpene (C,,H,,O$ isolated by Oliveira et alla fromtb
heartwood of Emmotum nitens and named emmotin-F, was found to co-occur along&
two other closely related compounds (emmotins-G and -H).
The three oxygen atoms of emmotin-F (47) were assigned to one carbonyl andm
hydraxy functions (reduction to a trio1 and formation of a diacetate). The U V d
IR spectra as well as the ease of catalytic hydrogenolysis of emmotin-F to a diol(&~
showed that the carbony1 function is flanked on either side by an aromatic res~dued
a hydroxyl function (Fig. IS). The presence of -CHOHCO- grouping was endcu
from the formation of a red a-quinone (49) upon dehydrogenation, the structureoftlx
a-quinone being confirmed by derivatization to the quinoxaline (50). The W q
carbinol of emmotin-F formed part of a hydroxy-isopropyl group. These facts 1s
conjunction with similar PMR spectra of emmoons-F,-A (41) and-B (43) led to tk
tentative assignment of enmotin-F also as a tetralone (47) (Fig. 18).
VETIVALENE TYPE-NATURALLY OCCURRING
SESQUITERPENOIDS
189
The diacetates (27 and 26) of emmotins-F (47) and-A (41) were reduced with zinc
ad the product (28) (Fig. 11) gave (+)-occidol (2) on hydrogenolysib and saponifivaion. While this correlation established the carbon skeleton of einmotin-F (47), the
diaxial relationship of 3 and
as indicated by the PMR data, fixed the C-6 and
C-7 configurations of emmotin-F (47).
5,
The ORD curve of emmotin-F was found to be superimposable on those of ernnlo@.A (41) and -B (43) i n which the substituents at C 6 and C-7 are trans, showing
?hatall the three tetralone emmotins-A, -B and -F (41, 43 and 47) possess identical
absolute configurations.
~
Emmotin-G, a sesquiterpene naphthol (Cs,HSsOJ was isolated from E m t n o t u ~ niiat1s'3,
mp. 112-115', Mi (229), IR: ?ha.3473 and 3125 cm-I (OH), UV (EtOH): i.,,,243
(52.900), shifted i n the presence of NaOH to >,. 254 nm ( c 55.200) (naphthol), PMR:
two orfho (8 7.08 and 7.18, dd,J = 8 Hz) and two paru (8 7'42 and 7.73, s) aromatic,
protons.
As expected, acetylation of emnlotin-G (51 a) caused a strong paramagnetic shift
(-0.59 6) of the 5 singlet and oxidation with Fremy's salt gave the naphthoquinone
ammotin-HsS (52) (Fig. 19).
The Syntheses of en~morin-G (51 a) and its methyl e t h e ~ + ~(5, 16)
' ~ have recently been
achieved i n our laboratory. The key-sbp in these syntheses is the Vilsmeier formyladon of 1,4-dimethyl-6-methoxytetralin(53) (Fig. 19) to the coriesponding forrnyl
Wralin (54) which on subsequent dehydrognation to the naphthaldehyde (5% followed
by oxidation and esterification gave the naphthol ester (56b). The hydroxy- (56a)
and the mtliaxy- (56b) naphthoic esters were converted to emmotin-G (51a) and its
methyl ether (51b) respectively.
h ortho naphthoquinone (C,5~L,03,m.p. 178-18O0, MT (246) isolatedL3 from Emmo265 nm ( e 40,800) and IR : v,,
W nitens was called emmotin-H (52) [UV: &.,
The intense red colour of emmotin-H was slowly discharged by tlre addiion of aqueous sodium dithionate. In the aromatic region of its PMR s p t r u m it
W i t e d two ortho protons (6 7.13 and 7.36, dd, L = 8 Hz) and a pert Proton
1649 om-7.
190
P. 4NhNTIIA RPDDY kND 6 . S. KRISHNA R A O
(J 7.86,
.). Thcse observationS led to the l"orn1ulation or the structure or tile
nat,lri
product as (52) (Fig. 20).
Reductive acetylation of emmllnlotin-H (52) or dehydration of its quinoxalill delivatnp
(57) gave the isopropenyl cornpounds (58) and (50) mpectively. Since the anby$".
quinoxalin adduct (50) could be prcl?ared from all thc three emmotin-f ( 4 7 ) ; ~
and-H (52). they were presumed t o hdvc doscly rclated structl~ralfeatures aud ihc
same carbon skeleton as in occidol (2).
The structure (52) of emmotill-H has been confirnied by its synthesis" i n our labo.
ratory. The tetralone ester (59) (Fig. 20) was oxidized by selenium dioxidc to thr.
corresponding o-quinone ester (60). Its reductive acetylaiion atlbrded ti,.: dincstohy
naphthoic ester (61). Grignard reaction on the ester (61) with excess or CH.,Mgl gair
emmoLiil-H (521, presulnablp through aerial oxidation or the intermediate unit.able
trio1 (62).
11. Conclusion
From the above account i t is seen that the structuvei and configurations of' ocdd~l.
rishitinol and the emmatins are closcly related. The co-occurrence of occidol (2) in
Tlzuju occidentalis'%vith occidental01 (3, a sesquiterpnic alcohol of the general eudei.
mane skeletan, and the co-occurrence of all the structnrally similar enimatins in another
source (Emnzotsnr niter~s) arc striking. A m t h y l shift in the parent eudesmane (31.
accompanied by a diene-benzene 1-earrangemmt seems to characterize all these newvlv
discovered vetivalene-type sesquiterpenes.
Acknowledgement
P. A. R. thanks the authorities of the Indian Institute of Science, Bangalore, for tb
award of a research fellowsllip.
References
J. Am. Chem. Soc., 1968, 81, 1963
1. Bijcm, G.,
W ~ N A UM.
. S . V.
W ~ E D.
, M.
AND
VETIVALENE-TYPE
NATURALLY OCCUKllING SESQUITEKPENOIDb
Bull. &i.
1, Hi~osc,Y . AND
Cl~eni.Sue. Jupriiz, 1959, 23, 143.
NAKATSUKA, T.
Bull. Axui. Cliem. Soc. Japair, 1959, 23, 253.
3. HROSE,Y . A N D
NKA.TSUKA, T.
4. Ho, T.-L.
Clfem. ntrd h i d , 1971, p. 487.
5. Ho, T.-L.
Cm. J. Cl~enr.,1972, 50. 1098.
6. Ho, T.-L.
7. DAUBEN,
W. G.,
H.UT, 9. .I.,
IPAKTSCHI,J. A ~ D
Koz1nowsKI, A. P.
J. C h n . Soc. Pcrkin-I, 1973, p. 3579.
Tetvahcdi-on Left., 1973, p. 4425.
8. MACKEUZIE,
B. D.,
ANGELO, M. M. AND
WOLINSKY,
J.
9. ANANTHA
REDDY,P.
10. AVANTHA
REDDY,P.
KRISHNARAO,G. S .
Synihefic siudies in terperroid~and Mlsineier formylrrrbrr ~ J I I sumr
hyrlrorznphfaen sjwenu, P1i.D. Thesis, Indian Institute of
Science, Bangalore, 1978.
AND
Indioii J. Cl~em.,1980, 19B, 753.
11. NAKAZAKI, M .
CIIenr. und Znd., 1962, p. 413.
12. NAKAZAKI,M.
BUN. Che~n.Sor. Jupun, 1962, 35, 1387.
13. .DE OLIVEIRA,A. B.,
Pil~.rotIren~.,
1976, 15, 1267.
DE OLIVEIRA,G. G.,
LIBERALLI, C. T. M.,
GOTTLBB, 0. R. AND
MAGALHAES,M. T.
Tct~aliedronLett., 1971, p. 83.
14. KATSUI,N.,
MATSUNAGA,
A.,
IMAIZUMI,K.,
MASAMUNE,T. AND
T O ~ A M K.
.~,
u.
KATSUI, N.,
MATSUNAGA,A,,
Bull. C h m . Soc. Jupair, 1972, 45, 2871.
~huuzuhnr, K.,
MAUMVNE, T. AND
TOMIYM, K.,
16. KATSUI,N., M u m , A,,
Cl~em.Comm.. 1968, P. 43.
TAK~SUGI,
M.,
I M A ~ M I , K.,
MASAMUNE,
T. AND
ToMrYAMA, K.
J. Am. Chem. Soc., 1969, 91, 3989.
192
P. ANANTHA KEDDY AND C. S . RRISHKA ~ A O
18. BUKHARI,S. T. K.
AND
GUIHRIE,R. D.
19. DL OLLVEIKA,
A. B.,
FERNANDES,
M. ut L. M.,
GOTTLEB,
0. R.,
HAC+AMAN,
E. W. AND
WXNKERT,
E.
'"C-NMR spe~lro&cupy.Academic Press, New York, 1972.
21. LEVY, G . C. AND
NELSON,
G. L
'"C-NMR for
o q v w i ~dremi.rtr, W i l e y - I n l e ~ s c i c ~New
~ ~ ~york,
,
1972.
Commiu~icaledLO 111diuiiJ. Clreni.
Iildiu~t .I. CIzem, 1980, 19B, 578.
J , Chenr. Soc. Perkiir-I, 1979, p. 237.
J. Ow. Chen~.,1969, 34, 736.
Added in press
Manicol (2-isoprepenyl-5-methyl-7-hyctroxy-1,2,3,4-tetrahydro--naphtloic
acidj recentl)
isolated [J. Polonsky, Z. Varon, H. Jacqnemin, D. M. X. DonneUy and M. J. Megan,
J . Chem. Soc. Perkiiz -1, 2065 (1980)] From the root bark of a Guyanan tree (D~dacm
guianwsis) is the latest member to be added t o the vetivalcnc scsquiterpcne family.
Manicol has been reported to possess moderate antileukemic activity. Its structure and
absolute stcreochemistry (R-configuration) were assigned on the basis of spectrosopk
evidence and partial synthesis.
BOOK REVIEWS
~~ricultural
Statistics-A Handbook for Developiu,o Countries by N. M. Idaikkadar,
pergdmon Press, 1979, pp. xii 5 139, £ 4.50.
This book is written by a former statistician of the FAO. It contains 14 chapters,
2 appendices, a list of relevant publications and an index. It covers the Methodology
of Development, Agricultural Production (AP)--General Ideas, AP-Crop Yields, A p
(Crops)-Area,
AP (Crops)-Forecasting,
AP-Livestock
and Livestock Products,
Index Numbers of Agricultural Production, Supplv/Utilization accounts (Food Balance
Sheers), Census of Agricultme, Survey and Sampling Methods, Price Statistics, Statistics
for Agricultural Planning, Staff Organisation. Appendices give typical forms for
~easonalcollection of aata on the cost of productiol~used a t sub-district level in an
African country and monthly collection of data on cropp-d areas at sub-district level
in an Asian country.
The book is based on the lectures given by the author in some Asian and African
countries and especially on the course ow Third Wo~ld A~riculkural Stat~s'ics and
Survey and Sampling Methods to M.Sc. students of Agricultural Statistics at Oxford.
The aimsand scope of ths book are: (a) to provide guidelines to those in charge of agritultural statistics in developing countries, for improving th-ir statistics in a systematic
way, to know their priorities and to havz clear objectives; (b) to provide for planers,
policy maksrs and senior statisticians a handbook on the methodology of agricultural
statistics; (c) to emphasize the use of objective methods for colIection of data ; (a') to
emphasize the importancs of collecting data independent of farmers to overcome their
subjective at~itudeto data collection; (e) to use samp!ing with its zccompanying benefits,
in data collection.
The book is written in the first instance for use in the statistics departments, ministries of agriculture and planning departments of the developing countries. Senior
officers in these departments would be interested in tho methodology while the juniors
may prefer the practical approach. The book will be also useful for students of statistics,
economics and agriculture.
The book displays a good blend of theoretical aspects of the subject with the pract:c%I
experience of the author and largely deals with current agricultural statiskiss.
The author takes the practical approach that ' no grandiose expansion of the statistical
staff should be requested all at cnce from a Government nor a request for large funds '
and that 'the process of development of statistics has to be gradual and acceplabl"
to the government concerned'. Hence the author rightly advocates ' t o give top
priority for replacement of existing subjectiv; methods that give m s l errors and for
statistics where the country's economy is most concerned
".
193
The author has pointed out how the old concept or census of agriculture nleaning
an jnvmtory of africulture for the whole coulltry at %: point of time has gradually
expanded in recent times and bases his discussion filrcher on that. It is i q o r t a n rto
note as pointed out by the author that ' i n developed countries, sampling-plimrilv
opens the way tosavings and better accuracy while other techniques may be eguall;
pvailabie. In developing countries, however, the use of sampling methods is
times the only way t o collect agricultural statistics '. Statistics of ptices conneckd
with the agrisultual indust~yare very important, but lllang d~veloping countries have
nut accorded the conipiialioi~of meaningful and adequate price statistics th: same
attention as Lhat given to other statistics such as cropped a r e s and yield rate?.
such the discussicn in the chapter on Price Statistics will be usrf~rl. Un&r Staff
and Organisation the author discusses thz asp;.cts of selection and trsbing, field
o~ganisation, public relations, ~ t c .
The printmg and g-t-up of the book 1s very good. The bcok has met reasonably
well the aims and scope kept belore him by the aurhor.
Proceedings of the Ninth Lunar and Planetary Science Conference (1978). Vok. I, 11
and LIL, Pergamon Press, Oxford, P r m $ 200.
These three bulky volamea, that arc a supplement of thc GcochimicC osmocliemica Acta:
constitute an exhaustive review of the investigations and current state of the art in
this important topic that started with the investigation of the samples recovered from
the lunar flights, but have expandcd into the much wider area of structure, coinposition
and history of the planets of the solar system.
The first volume deals with geochemical and petrogenetic studies on lunar and
meteoritic samples that provide pertineat information on the crustal evolution and
constraints that have to be met by any model. The second volume deals with trace
eleo~ents,isotopic, radiometric, chronologizal and related studies that are relatedto the
imp& phenomena, soil and mare formation on the moon with other implications as
well. The third volume deals with the structure and tectonics, as well as other physical
properties obtained hy seicmic, remote sensing and other techniques that have a general
bearing on the development of the inner solar system. Since all the general research
groups working in this area have contributed to the conference one obtains a synoptic
view of the present state of the art.
In Volun~eI tracc element data and calculationq are piescntcd @p. 1-119) ejpzcially
on the lunar highlands and non-mare rocks with inlplications on the lanar origin. The
1%
BOOK REVIEWS
Qolution of the mare basalis is tieated in the next scction (pp. 219-337) fiom gittlcral
cvidencs. A more detailed study of' thz mare basaltr fullo~vswith trrct: elelllent correlations, i s ~ t o p i cdata and experimentnl studies relating to paxition coefficients of rare
art;,., ctc. (pp. 33.547). Tflc :lmt section (pp. 629-7731 is KREEPK (I) ~ . ; r chh c ~ n i ~ a l
a n d ; a d i ~ ~ h r ~ n ~ l ~ $(including
ica.l
the new S m N d method) data on thc K R E E P sa~nplcs
(ie., enriched in K, rare earths, phosphorus etc.), that ?.re found in the lunar highlands.
I
Special interest a t t x h e d to the " Breccias " that are iiriigmee.n-lndcn melt semple,
formed in the lunar b.si3-f~rmillgimpact events and the study of their ptiiology. major
and trace element cherniatry sad tho new: 39Ai-,1UArdati.~gt h ~ piovi&~
t
inform~tion
on the tharmal history of the samples (pp. 773-959).
The concluding section of Vol. I (pp. 977-1137) is devoted to the stud:: or meteorites,
which ere the earliest bodies of the solar system, and in particular, ::re ' Allcndc "
meteorite. Detailed studies of major and trace elemeat c!lendsiry. isotopis a~iomalie~.
ion-microprobe stdie;, etc., of these samples that appear to have recordcd some of t l a
earliest events of the solar system formation, 4.6 billion yews aga. arc prcrcxtcd.
The secand volume starts with a systematic study of the lunar 'reyolith' or top
surface. A characteristic feature is the presence of glossy dioplets of all sizes, and
they are studied in detail to establish their formation, e.g., au spray melts splashed by
meteorite impact (pp. 1449-1551). The effects of thc 'solar wind i.r.. particlei
emitted from the solai plasma are prominent on the lunar regolith and have been
studied by mass-spectrometric and also the ' particle tresk ' teckriques where the
tracks are enlarged by suitable etching and observed on a microscope. The possiblc
effects of sputtering and associated fractionation effects is also discussed (pp. 15711765). D;ill cores from the regolith have also been annlysed. The results from thc
cores in the Descartes region pcovide information obtained o : ~in-sit11 reworking and
lateral transport on the surface. The study of dynamic mixing processej (Sun-tan ages
as referred to by Prof. La1 and co-workers) by the use of cosmic ray produced mdionuclides, and the application of such studies to soil maturation and agglutination
processes have also becn studied in great detail. Volatiles in lunar r o c b and soils also
provide related information while 2QAr,P0Aryield the chronologies. Possible effects of
solar flare; have also been investigated.
'.
.
the various aspects of impact
In the last section of this volume ( ~ p 2469-2805),
phenomenz. on the lunar and terrestrial surfaces have been studied. The shapes of
impact miorocraters, composition variztions in shocked glasses and other materials
have been studied. On the teirestiial scale, the investigations relate to known craters
and impact structures-the special features of structures. trace element contents. etc.
Volume I11 begins with remote sensing studies mainly in optical and infra-red but
also in the X- and p r a y ranges (pp. 2825-3057). Reflectance of plagioclasc feldspars
Ud pyroxenes, measurement of 16-concentrations, Mg-A1 ratios and other possibilities
196
BOOK REVIEWS
have been examined. Lunar and ~nartianmawetic fields, their interactions with
solar wind, aud dynamo-type core-motion origins and related questions are covered
in the next section (pp. 3057-3165).
The geological processes, so thorou~hly investigate* under terrestrial conditic2%.
arc next considered i n tho lunar and martian context. The morphology of the mart,an
topography of volcanism and rock emplacement, and the volcanic featutes
of telascopicaliy-known formations on moo11 and mars belong to this category (pp,
3181-3459). This leads on to the t e c t ~ n i c - ~ t r ~ crelationships
t~re
observed for the
lunar graben systems, and mare-rids orientations a.nd the ' mascons' related to the
subsidence of mare basins and exhibiting themselves by gravily anoinalies. Seismology
has
important contributious to our know led^ of lunar structure (a well-knom
aueh0r reFerred to the identity of 5eismk velocities in the upper lunar surface and the
acoustic velocities in green cheese !), and a review of the scismic structure, the current
statuu
the passive seismic experiments, and related topics ale given next (pp. 35753651).
Craters have been a well-recognized feature of the moon, and thc conditions, physical
properties, morphology and related parameters of these impact-created structures are
investigated in detail in the last section (pp. 3651-3935). Models of impact cratering
lead to evaluation of crater volumes, size-distribution, cratcr-shapes, energy-inputs, etc.
Computer-simulations are also made.
The volumcs clearly illustrate how the availability of such a wealth of precise quantitative data on actual samples have supplanted pure speculations in this ficld that has
been the subject of interest for such a long time. The criterion of success of models
in such a multi-disciplinary field. ! t i t . , the convergence of results obtained from
different disciplines has also been amply illustra.tcd.
Journal of the
Indian Institute of Science
Volume 62 (B), 1980
INDEX
Indian Institute of Science
Bangalore 560 012
JOURNAL OF
THE INDIAN INSTITUTE OF SCIENCE
Volume 62, 1980
SECTION B
Title Index
Algorithms for integer fractional programming
C. R. SESHANAND V. G. TIKBKAR9
An algorithm for ranking the extreme
points for a linear fractional objective
function
C. R. SESHAN
119
Wbration for studying microstructure of
clouds sampled from an aircraft
S. K. PAUL,S. K. SHARMA
AND R. K.
KAPOOR
83
The chemistry of vetivalene type naturally
occurring sesquiterpenoids
P. ANTH HA REDDYAND G. S. KRIsHNA
RAO
181
Debenzylation by Ni-A1 alloy
M. VENKAMA
NAIDUAND G. S. KRISHNA
R\o
177
Derivation of the solution of certain
singular integral equations
ALOKNATH CHAKRABAR~
147
External features of vegetation as hydrologic indicators in Varahamilrira's
Brihat Samhita
E. A. V. PRASAD
123
Investigation of the utility of some
synthetic magnesium silicates in radioactive waste treatment
SATYA
BRATAND N. S. SUNDER
RAJAN1
On Lauricella's n-variable function F f i
P. C. MUNOT
AND P. A. PADMANABHAM
17
On nonlinear oscillation problem
167
P. C. MUNOTAND RENUMATHLTR
On umteady MHD flow p a t a porous
plate under pressure gradient
S. T. REVANKAR
AND V. M. KORWAR
159
Mesospheric influences on linkages
between solar activity and lower atmospheric phenomena
RAMANI
SESHAMANI
35
A note on diffrarrion by a strip under
mixed boundary conditions
A. CHAKRABARTI
AND V. V. S. S. SASTRY
25
Photometric study of manganne 2nd
potassium dichromate reaction in strong
sulphuric acid medium
N. SUBBARAMI
BDDY
AND D. VBNKATA
R~DDY
51
progress of research on .the Raman
k n a t i o n constants of Schiff bases
<. SIVARAMAPRASAD, P. VASANTHA Effect: A statistical analysls
53
R. S. KRISHNAN
AND R. K. SHANKAR
CWR AND M. C. CHOWDARY 101
INDEX
200
Author Index
BWATTACHARYY
Z, PANCII.~WAN
Uilsteady lsnunn Row in a channel wrth
porous bed
89
CHOWDARY,
M. C.
See Sivarama Prasad. K., Vaiantha
Kumal, P. and Chowdar), M. C 101
BRAT,SATYAAND SUNDER
RAIAN,N. S.
hwtigation of the ut~Lty of some
synthetic magnesium silicates in rad~o1
active waste treatlnent
GARG,5. S.
See Chadha., R. C., Garg B. S., Lata.
Swaran and Singh, R. P.
173
CHADB4, R. C., GARG, B. S., LATA,
AND SINOH,R. P.
SWARAN
Titrim:tric estimation of phosphate.
molybdate and sulphste with lead
nitrate solution, using 2-(2-lepidyl a m - I naphthol-4-ammoniumsulphonatz
(Lanas)
as visual indicator
173
CHAERABARTI,
ALOKNATH
Dxivation of the solurion of certnin
147
singular integral equations
CH~KRABARTI.
A. AND SASTRY,
V. V. S. S.
A not* on diffraction by a strip under
mixed boundary conditions
25
KAYOOR,
R. K.
See Paul, S. K., Sharma, S. K. and
81
Kapoor, R. K.
RORWARV. M.
See Revinkar, S. T. and Korwar, V. IS9
M.
K R I S H N ~R. S. AND SHANKAN,
R. K.
Progress bf research on ? ~ e l+.dm
EtTect : A statistical analysis
3
INDEX
LATA,SWARAN
See Chadha, R. C., Garg, B. S., Lata,
Swaran and Singh, R. P.
173
MATHUR,
RENU
See Munot, P. C . and Mathur, Renu
167
MUNOT,P. C. AND MATHUR, RENU
167
On nonlincar oscillation problem
MUNOT, P. C. AND PADMANABHAM,
P. A.
On L%lric:lla's n-variable function F;)
17
NAIDU,M. VENKAMAAND RAO, G. S.
KRISHNA
177
Debanzylation by Ni-A1 alloy
PADUNABHAM,
P. A.
See Munot, P. C. and Padmanabham,
P. A.
17
PAUL,S. K., SHARMA,
S. K.
AND
KAPOOR,
R K
20 1
PRASAD,
K. R. K. K. V. AND SESHAGIRI.
I'.
Thermil, infrared 2nd nl?.gletic ~ t u d yof
addnzts of C>(II) rea~etopl~enone
oximste colllples with nitrogen bases 107
Rho. G. S. KRISI-IVA
See Anmh?. Rlzdd:', P. and Krishna Rao,
G. S.
181
Venkam Naidu, M. a l ~ dRao. G. S.
Kri:hna
177
REDDY,P. ANAXTHA
ASD
RAO, G. S .
KRISIINA
The chemistry 0,: vctivalene type naturall!.
181
occurring sesqu~icrpcnoids
Spt.
REDDY,N. SUBBARAMI
AND REDDY,D.
VEXKATA
Photometric study of manganese and
potasium dichromate reaction in strong
51
sulphuric acid medium
Spectrophotometric determination of
micro amounts of vanadium(V) with
resasetophenone-indirect
method
47
chibration for studying microstructure
of clouds sampled from an aircraft 83
REDDY,13. VENKATA
See Subbsrami Reddy, N . and Venkata
Reddy, D.
47, 51
PRASAD,
E. A. V.
External fe?.tures of vegetation as hydrologic indicators
in Varahamihira's
Brihat Samhita
123
SATYAKUMAR
See Hjmtnt Kulshreshtha, Satyn Kumar
and Singh, R. P.
113
RAW, USHA
Solution9 of f-gravity coupled to So(3)
73
gauge field
REVANKAR,
S. T. AND KORWAR,V. M.
On unsteady MHD flow past a porous
plate under pressure gradient
159
SESHAGIRI,
V.
See Prasad, K. R. K. H. V. and
107
Seshagiri, V.
SESHAN,C . R.
An algorithm for ranking the extreme
points for a linear fractional objective
119
function
W R Y , V. V. S. S.
See Chskrabxrti, A and Sa~try,V. V. S. S.
25
SESHAMANI,
RAMANI
lMasospheric influence on linkages between
solar activity and lower atmospheric
35
phenomena
SENGUPTA.PRARIRKUMAR
The spectrum of a matrix differential
43
operator
SESHAN,C. R. AND TIKEKAR,V. G.
Algorithm? for integer fractional programming
Y
a
202
INDEX
R. K.
SHANKAR,
See Krishnan, R. S. and Shankar, R. K.
53
SIVARAM*
PRASAD,K., VASANT~A
K
~
P. AND CHOWDARK,
M. C.
Formation constants of Schiff banes lo1
SHARMA,
S. K.
See Paul, S. K., Sharma, S. K. and2
Kapoor, R. K.
83
SUNDERRAJAN,N. S.
See Brat, Satya and Sunder Raja,,, N, S,
1.
TIKEKAR,
V. G.
See Seshan, C. R.and Tikekar, V, G. g
SINGH,R. P.
R' C', Garg' B' S"
See
Swaran and Singh, R. P.
y;j
SINGH,R. P.
seeHornant Kulshreshtha, Satya Kumar
and Singh, R. P.
113
VASANTHA
KUMAR,P.
See Sivarama Prasad, . K., V2Santha
Kumar, P. and Chowdary, M. C. 101
Key Word Index
Adduct formation
Aircraft
Alloys
Amplitude dependent approximation
Analytical reagent
Aniline
Arbitrary time dependent velocity
107
83
113
167
107
101
159
~ e n z y lether cleavage
Binudear structure
173
107
Calibration
Cauchy-type kernel
Chromium(V1)
Cloud microstructure
Configuration
Confluent hypergeometric function
Copper
83
147
51
83
181
167
113
~econtknination
1
Di-2-pyridylglyoxal-2-quinolylhydrazone
113
6"IPRZntiatial operator
43
Diffraction
25
Formation constant
101
Gauge field
Generalised hypergeometricfunction
Generalised Laguerre polynomial
Geobotany
Gomory method
Higher order approximation
Hydrogenolysis
Hydrologic indicator plants
73
161
17
123
9
25
173
123
Ion exchange
Integral equations
Jacobi polynomial
17
LANAS as meta~ochrbmicindicator 113
LauriceUa's n-variable function F$' 17
Linear fractional programming 9,
Maenerium oxide
~aGganese0
Manganese(l1I)-sulphate complex
Mesosphere
Mixed boundary conditiom
Modified Job's method
Ni-A1 alloy
Nonlinear oscillations
Number of eigenvalues
83
51
?:
JJ
25
lQ1
177
161
4
~
~
~ccidol
orthogonal polynolnials
Oxidation
paraUel channel
pararn:tnc Integer programming
phosphate and molybdate
photometry
phyllitic minerals
pochhammcr symbol
porous medium
porous plate
pressure gradient
pseudo-monotonic
Radio active wastes
Raman Effect
Ranking extreme points
Resacetophenone
Rieman Hilbert problem
Risbitinol
Sorprion
Spectrophotomcter
Spectrophotometric determination
Spectrophotonletry
Soactrum
solar activity
Statistical analysis of trends in
research
Stevensite
Strong gravity
Strong interaction
Structure
Sulphate
Sul phuric acid
Sun-weather relationships
Synthesis
Titrimetric estimat'ons
Unsteady flow
Unsteady MHD flow
Upper stratosphcre
Sxlicylaldehyde
hlicylidene aniline
Wff base
Sesquiterpenoids
Siliconc oil
Singular integral equations
Sl1pflow
Soot
Vanadium(%
Vandermonde's theorem
Vetivalene
Wave-guide theory
Weight matrix
Book Review Index
Ag~cultural statistics-A handbook for
dzvelopingcountries by N. M. Idaikkadar.
193
reviewed by V. G. Tikekar
Chemistrv for the eneineerinr and applied
sciences by W. ~teedman, B. Suedden
bylii
and 1. E. Anderson,
Gopalakrishnan
The common sense of science by J.
Bronowski, reviewed by K. P. Sinha 69
*
vwuianics and heat (' , Level
Volume I), by M. Chapple, reviewed by
The observer's book of rocks and
m m a l s by Richard and ~ r a n c i r
Atkinson. rewewed by Ci. V. Anantha
Tver
7
.1-,problems of linear electron (polaron)
transport theory in semiconductors by
M. I. Klinger, reviewed by G. Suryan 70
Proceedings of the Ninth Lunar Planetary Science Conference (1978), Vok. 1.
JI and 111, reviewed by V. S. Venkatasubranlanian
194