Report and Opinion
(Rep Oinion)
Volume
4  Issue 8, Cumulated 38, August 25, 2012, ISSN 15539873
Cover Page,
Introduction,
Contents, Call for
Papers,
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Welcome to send your
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CONTENTS
No.

Titles / Authors

Full Text

No.

1

Automorphic Functions And Fermat’s Last Theorem
(1)
ChunXuan Jiang
P.O. Box 3924, Beijing 100854,
China
jiangchunxuan@vip.sohu.com
Abstract:
In 1637 Fermat wrote:
“It is impossible to separate a cube into two cubes, or a
biquadrate into two biquadrates, or in general any power higher
than the second into powers of like degree: I have discovered a
truly marvelous proof, which this margin is too small to
contain.” This means:
has
no integer solutions, all different from 0 (i.e., it has only the
trivial solution, where one of the integers is equal to 0). It
has been called Fermat’s last theorem (FLT). It suffices to
prove FLT for exponent 4. and every prime exponent
.
Fermat proved
FLT for exponent 4. Euler proved FLT for exponent 3.
In this paper using automorphic
functions we prove FLT for exponents
and
,
where is
an odd prime. The proof of FLT must be direct. But indirect
proof of FLT is disbelieving.
[ChunXuan
Jiang. Automorphic Functions And Fermat’s Last Theorem (1).
Rep Opinion 2012;4(8):16].
(ISSN: 15539873).
http://www.sciencepub.net/report. 1
doi:10.7537/marsroj040812.01
Keywords:
automorphic function; cyclotomic field; Fermat; theorem 
Full Text 
1

2

Automorphic Functions And Fermat’s Last Theorem（2）
ChunXuan Jiang
P. O. Box 3924, Beijing 100854,
P. R. China
Jiangchunxuan@vip.sohu.com
Abstract:
In 1637 Fermat wrote: “It is impossible to separate a cube into two
cubes, or a biquadrate into two biquadrates, or in general any
power higher than the second into powers of like degree: I have
discovered a truly marvelous proof, which this margin is too
small to contain.” This means:
has
no integer solutions, all different from 0(i.e., it has only the
trivial solution, where one of the integers is equal to 0). It
has been called Fermat’s last theorem (FLT). It suffices to
prove FLT for exponent 4. and every prime exponent
.
Fermat proved
FLT for exponent 4. Euler proved FLT for exponent 3.
In this paper using automorphic
functions we prove FLT for exponents
and
,
where is
an odd prime. The proof of FLT must be direct .But indirect
proof of FLT is disbelieving.
[ChunXuan
Jiang. Automorphic Functions And Fermat’s Last Theorem（2）.
Rep Opinion
2012;4(8):710]. (ISSN:
15539873).
http://www.sciencepub.net/report. 2
doi:10.7537/marsroj040812.02
Keywords:
automorphic function; cyclotomic field; Fermat; theorem 
Full Text 
2

3

Automorphic Functions And Fermat’s Last Theorem（3）(Fermat’s
Proof of FLT)
ChunXuan Jiang
P. O. Box 3924, Beijing 100854,
P. R. China
jiangchunxuan@sohu.com
Abstract:
In 1637 Fermat wrote:
“It is impossible to separate a cube into two cubes, or a
biquadrate into two biquadrates, or in general any power higher
than the second into powers of like degree: I have discovered a
truly marvelous proof, which this margin is too small to
contain.” This means:
has
no integer solutions, all different from 0(i.e., it has only the
trivial solution, where one of the integers is equal to 0). It
has been called Fermat’s last theorem (FLT). It suffices to
prove FLT for exponent 4 and every prime exponent
.
Fermat proved
FLT for exponent 4. Euler proved FLT for exponent 3.
In this paper using automorphic
functions we prove FLT for exponents
and
,
where is
an odd prime. We rediscover the Fermat proof. The proof of FLT
must be direct. But indirect proof of FLT is disbelieving.
[ChunXuan
Jiang. Automorphic Functions And Fermat’s Last Theorem（3）(Fermat’s
Proof of FLT). Rep
Opinion
2012;4(8):1114]. (ISSN: 15539873).
http://www.sciencepub.net/report. 3
doi:10.7537/marsroj040812.03
Keywords:
automorphic function; cyclotomic field; Fermat; theorem 
Full Text 
3

4

Aotomorphic Functions And Fermat’s Last Theorem(4)
ChunXuan Jiang
P. O. Box 3924, Beijing 100854,
P. R. China
jiangchunxuan@sohu.com
Abstract:
1637 Fermat wrote: “It
is impossible to separate a cube into two cubes, or a biquadrate
into two biquadrates, or in general any power higher than the
second into powers of like degree: I have discovered a truly
marvelous proof, which this margin is too small to contain.”
This means: has
no integer solutions, all different from 0(i.e., it has only the
trivial solution, where one of the integers is equal to 0). It
has been called Fermat’s last theorem (FLT). It suffices to
prove FLT for exponent 4. and every prime exponent
.
Fermat proved FLT for exponent 4. Euler proved FLT for exponent
3. In this paper using automorphic functions we prove FLT for
exponents and
,
where is
an odd prime. We find the Fermat proof. The proof of FLT must be
direct. But indirect proof of FLT is disbelieving.
[ChunXuan
Jiang. Aotomorphic Functions And Fermat’s Last Theorem(4).
Rep Opinion 2012;4(8):1520]. (ISSN: 15539873).
http://www.sciencepub.net/report. 4
doi:10.7537/marsroj040812.04
Keywords:
automorphic function; cyclotomic field; Fermat; theorem 
Full Text 
4

5

Automorphic Functions And
Fermat’s Last Theorem（5）
ChunXuan Jiang
P. O. Box 3924, Beijing 100854,
P. R. China
jiangchunxuan@sohu.com
Abstract:
In 1637 Fermat wrote:
“It is impossible to separate a cube into two cubes, or a
biquadrate into two biquadrates, or in general any power higher
than the second into powers of like degree: I have discovered a
truly marvelous proof, which this margin is too small to
contain.” This means:
has
no integer solutions, all different from 0(i.e., it has only the
trivial solution, where one of the integers is equal to 0). It
has been called Fermat’s last theorem (FLT). It suffices to
prove FLT for exponent 4 and every prime exponent
.
Fermat proved
FLT for exponent 4. Euler
proved FLT for exponent 3[8]. In this paper using automorphic
functions we prove FLT for exponents
and
,
where is
an odd prime. The proof of FLT must be direct. But indirect
proof of FLT is disbelieving.
[ChunXuan
Jiang. Automorphic Functions And Fermat’s Last Theorem（5）.
Rep Opinion
2012;4(8):2124]. (ISSN:
15539873).
http://www.sciencepub.net/report. 5
doi:10.7537/marsroj040812.05
Keywords:
automorphic function; cyclotomic field; Fermat; theorem 
Full Text 
5

6

Automorphic Functions And Fermat’s Last Theorem（6）
ChunXuan Jiang
P. O. Box 3924, Beijing 100854,
P. R. China
jiangchunxuan@sohu.com
Abstract:
In 1637 Fermat wrote:
“It is impossible to separate a cube into two cubes, or a
biquadrate into two biquadrates, or in general any power higher
than the second into powers of like degree: I have discovered a
truly marvelous proof, which this margin is too small to
contain.” This means:
has
no integer solutions, all different from 0(i.e., it has only the
trivial solution, where one of the integers is equal to 0). It
has been called Fermat’s last theorem (FLT). It suffices to
prove FLT for exponent 4 and every prime exponent
.
Fermat proved
FLT for exponent 4. Euler
proved FLT for exponent 3[8]. In this paper using automorphic
functions we prove FLT for exponents
and
,
where is
an odd prime. The proof of FLT must be direct. But indirect
proof of FLT is disbelieving.
[ChunXuan
Jiang. Automorphic Functions And Fermat’s Last Theorem（6）.
Rep Opinion
2012;4(8):2527]. (ISSN:
15539873).
http://www.sciencepub.net/report. 6
doi:10.7537/marsroj040812.06
Keywords:
automorphic function; cyclotomic field; Fermat; theorem 
Full Text 
6

7

Jiang’s
function
in
prime distribution
ChunXuan Jiang
P. O. Box 3924, Beijing 100854,
P. R. China
jcxuan@sina.com
Abstract:
We define that prime
equations （5）are
polynomials (with integer coefficients) irreducible over
integers, where are
all prime. If Jiang’s function
then
（5）has
finite prime solutions. If
then
there are infinitely many primes
such
that are
primes. We obtain a unite prime formula in prime distribution
（8）.
Jiang’s function is accurate sieve function. Using Jiang’s
function we prove about 600 prime theorems [6]. Jiang’s function
provides proofs of the prime theorems which are simple enough to
understand and accurate enough to be useful.
[ChunXuan
Jiang. Jiang’s function
in
prime distribution.
Rep Opinion
2012;4(8):2834]. (ISSN: 15539873).
http://www.sciencepub.net/report. 7
doi:10.7537/marsroj040812.07
Keywords:
function; Jiang; Prime 
Full Text 
7

8

The
HardyLittlewood prime ktuple conjecture is false
ChunXuan Jiang
P. O. Box 3924, Beijing 100854,
P. R. China
jcxuan@sina.com
Abstract:
Using Jiang function
we prove Jiang prime
tuple
theorem. We prove that the HardyLittlewood prime
tuple
conjecture is false. Jiang prime
tuple
theorem can replace the HardyLittlewood prime
tuple
conjecture.
[ChunXuan
Jiang. The HardyLittlewood prime ktuple conjecture
is false. Rep Opinion 2012;4(8):3538]. (ISSN:
15539873).
http://www.sciencepub.net/report. 8
doi:10.7537/marsroj040812.08
Keywords:
function; Jiang; prime; theorem; conjecture 
Full Text 
8

9

Solid
waste management at Mansa Devi and Chandi Devi temples in
the Shiwalik foothills, during Kumbh Mela at Haridwar
(Uttarakhand)
Sudhanshu Kaushik* & B. D. Joshi
*Dev Sanskriti
Vishwavidyalaya, Haridwar (Uttarakhand)
Department of zoology and
Environmental sciences, Gurukula Kangri University,
Haridwar
Abstract:
The present study
deals about solid waste generation over the Mansa Devi and
Chandi Devi hillock at Haridwar during the Kumbh festival of
2010. Total amount of solid waste generated for seven days
of collection was 7615.0 Kg and 4992.7 Kg at Mansa Devi and Chandi Devi temples, respectively. The composition of solid
waste was about 64.7% biodegradable waste and 12.3% non
biodegradable and 23.0% miscellaneous waste at Mansa Devi
hillock. On the other hand Chandi Devi hillock had 62.1%
biodegradable, 12.3% non biodegradable and 25.6%
miscellaneous wastes, while during normal non festive days
62.7% biodegradable, 10.2% non biodegradable, 27.1%
miscellaneous solid waste was found at Mansa Devi and 62.2%
biodegradable, 13.4% non biodegradable and 24.4%
miscellaneous was found at Chandi Devi hillock.
[Sudhanshu
Kaushik & B. D. Joshi.
Solid waste management at Mansa Devi and Chandi Devi temples
in the Shiwalik foothills, during Kumbh Mela at Haridwar
(Uttarakhand).
Rep Opinion
2012;4(8):3942].
(ISSN: 15539873).
http://www.sciencepub.net/report.
9
doi:10.7537/marsroj040812.09
Keywords:
Bio degradable, Non biodegradable, Kumbh, Festive and Non
festive days

Full Text 
9

10

Ecophysiological Responses of Grey Mangrove (Avicennia marina)
(Forssk.) Vierh. to Oil Pollution at Ras Mohammed Protective
Area
Amal A. Morsy; Amira A. Hassanein and Hawa O. ElRefaai
Botany Department, Faculty of Science, Ain shames
UniversityEgypt
Abstract:
The current study was undertaken to investigate the adverse
effect of oil spills on the performance of Avicennia marina
grow in Ras Mohammed protected Area.
The plant materials were collected from four different plots of
studied area. The
effects of oil pollution on the sediment analysis,_{ }
photosynthetic pigments, lipid
peroxidation as
malondialdehyde accumulation, enzyme activities, amino acids,
total phenols, total soluble proteins, carbohydrates, and
organic acids, of Avicennia marina grow in Ras Mohammed
protected Area were analyzed.
The data cleared significant decrease in the content chlorophyll
a, chlorophyll b, and carotenoids, in
Avicennia marina. The Most significant decrease was observed in plot1 and the
highest one in plants growing in plot 4.
The
significant increasing malondialdehyde (MDA) contents in
Avicennia marina growing in plot (1) in compassion to
Avicennia marina growing in plot (4) sites.
The activity of peroxidase was significantly increased under oil
pollution in Avicennia marina. The highest value was
detected in plot (1) and lowest value was cleared in plot (4)
plants. On the other hand, the activity of catalase, superoxide
dismutase and glutathione reductase significantly decreased in
Avicennia marina growing in plots 1. The highest activity
of these enzymes detected in plants growing in plots 4 of the
studied area of Ras Mohammed.
Avicennia
marina
growing in plots (3,4) contained higher concentrations of
aspartic acid, serine, glutamic acid, glycine, alanine, valine,
leucine, lysine, threonine, isoleucine, argnine and ammonia than
plots (1,2), while Phenylalanine detected only in plant growing
in plots (3,4). Proline content was increased in Avicennia
marina plants growing in plots (1, 2) as compared to
Avicennia marina plants growing in plots (3, 4).
The most significant increases in total phenols, total soluble
protein and carbohydrate in Avicennia marina plants
growing in plot1 and the significant decreases was observed in
plants growing in plots 4. The total carbohydrate contents show
a reverse pattern.
Oil pollution caused significant increase in the contents of citric
acid, jasmonic acid and salicylic acid.
The highest value was determined
in
Avicennia marina plants growing in
plot 1 and the lowest value was cleared in plants growing in
plot (4).
These changes were discussed in relation to plant performance
under environmental pollution.
[Amal
A. Morsy; Amira A. Hassanein and Hawa O. ElRefaai.
Ecophysiological Responses of Grey Mangrove (Avicennia marina)
(Forssk.) Vierh. to Oil Pollution at Ras Mohammed Protective
Area. Rep Opinion
2012;4(8):4356].
(ISSN: 15539873).
http://www.sciencepub.net/report.
10
doi:10.7537/marsroj040812.10
Key words:
Avicennia marina,
oil spills, Ras Mohammed protected area. 
Full Text 
10

11

OVERVIEW OF COPPER TOXICITY TO AQUATIC LIFE
Okocha RO and Adedeji OB
Veterinary Public Health and
Preventive Medicine University of Ibadan, Nigeria
roobee27_okocha@yahoo.com, +23428183240
ABSTRACT:
Copper
is an essential element required by all living
organisms, but it can be toxic to aquatic species when present
at elevated concentrations. This document is an overview of
copper toxicity and its effects on aquatic organisms. The
subtopics include history: the copper age; general sources and
uses; basic copper chemistry;
environmental factors; effects on aquatic organisms; public
health implication; proposed criteria for the protection of
aquatic life and human health and recommendations.
[Okocha RO and Adedeji OB.
OVERVIEW OF COPPER TOXICITY TO AQUATIC LIFE.
Rep Opinion
2012;4(8):5767].
(ISSN: 15539873).
http://www.sciencepub.net/report.
11
doi:10.7537/marsroj040812.11
Keywords :
Aquatic organisms, Copper, Toxicity, Aquatic Poll 
Full Text 
11

12

Similarity solution for natural convection from a moving
vertical plate with internal heat generation and a convective
boundary condition in the presence of thermal radiation and
viscous dissipation
Olanrewaju, P.O.
Department of Mathematics,
Covenant University, Ota, Nigeria.
oladapo_anu@yahoo.ie,
philip.olanrewaju@covenantuniversity.edu.ng
Abstract:
In this paper we analyze the
influences of thermal radiation, viscous dissipation, buoyancy
force and internal heat generation on steady laminar convection
flow over a semimoving vertical plate in the presence of a
convective surface boundary condition. In the analysis, we
assumed that the left surface of the plate is in contact with a
hot fluid while the cold fluid on the right surface of the plate
contains a heat source that decays exponentially with the
classical similarity variable. We utilized similarity variable
to transform the governing nonlinear partial differential
equations into a system of ordinary differential equations,
which are solved numerically by applying shooting iteration
technique alongside with sixth order RungeKutta integration
scheme for better accuracy. The effects of the local Biot
number, the Prandtl number, the internal heat generation
parameter, the thermal radiation, the local Grashof number and
the Eckert number on the velocity and temperature profiles are
illustrated and interpreted in physical terms. A comparison with
previously published results on similar special cases showed
excellent agreement. Finally, numerical values of physical
quantities, such as the local skinfriction coefficient and the
local Nusselt number are presented in tabular form.
[Olanrewaju,
P.O. Similarity solution for natural convection from a moving
vertical plate with internal heat generation and a convective
boundary condition in the presence of thermal radiation and
viscous dissipation. Rep Opinion 2012;4(8):6876].
(ISSN: 15539873).
http://www.sciencepub.net/report. 12
doi:10.7537/marsroj040812.12
Key words:
: viscous dissipation; thermal radiation; moving vertical
plate; local Grashof number; local Biot number; Eckert number;
convective surface boundary condition. 
Full Text 
12

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