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## Properties of real quadratic irrational numbers under the action of the group H = áx, y: x 2 = y 4 = 1ñ

Studia Scientiarum Mathematicarum Hungarica
Authors:
M. Aslam Malik
,
S. M. Husnine
, and
Abdul Majeed

Studying groups through their actions on different sets and algebraic structures has become a useful technique to know about the structure of the groups. The main object of this work is to examine the action of the infinite group \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $H = \langle x,y : x^{2} = y^{4} = 1\rangle$ \end{document} where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $x (z) = \frac{-1}{2z}$ \end{document} and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $y (z) = \frac{-1}{2(z+1)}$ \end{document} on the real quadratic field \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbb{Q}\left(\sqrt{n}\,\right)$ \end{document} and find invariant subsets of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbb{Q}\left(\sqrt{n}\,\right)$ \end{document} under the action of the group \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $H$ \end{document} . We also discuss some basic properties of elements of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbb{Q}\left(\sqrt{n}\,\right)$ \end{document} under the action of the group H.

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## On ambiguous numbers of an invariant subset \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$Q^{*} \left(\sqrt {k^2m}\,\right)$$ \end{document} of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$Q\left(\sqrt m\,\right)$$ \end{document} under the action of the modular group \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $${\rm PSL}\, (2,Z)$$ \end{document}

Studia Scientiarum Mathematicarum Hungarica
Authors:
S. M. Husnine
,
M. Aslam Malik
, and
Abdul Majeed

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n=k^2 m$ \end{document} , where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $m$ \end{document} is a square-free positive integer and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $k$ \end{document} is any non-zero integer. Then \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbb{Q}^{*}\big(\sqrt n\,\big)= \big\{\frac{a+\sqrt n}{c}\: a$ \end{document} , \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\frac{a^{2}-n}{c}$ \end{document} , \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $c\in \mathbb{Z}$ \end{document} , \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\big(a,\frac{a^2 -n}{c},c\big)=1\b\}$ \end{document} is a proper subset of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbb{Q}\big(\sqrt m\,\big)$ \end{document} for all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $k$ \end{document} . In this paper we determine, for each non square positive integer \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n$ \end{document} , the ambiguous numbers of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbb{Q}^{*}\big(\sqrt n\,\big)$ \end{document} which is invariant under the action of the modular group \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} ${\rm PSL}\, (2,\mathbb{Z}) =\langle x,y\colon x^2 =y^3 =1\rangle$ \end{document} where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $x\: C'\to C'$ \end{document} and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $y\: C' \to C'$ \end{document} are the Mobius transformations defined by: \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $x(z)=\frac{-1}{z}$ \end{document} , \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $y(z)=\frac{z-1}{z}$ \end{document} .

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## Radiological significance of Pakistani marble used for construction of dwellings

Journal of Radioanalytical and Nuclear Chemistry
Authors:
M. Aslam
,
S. Orfi
,
K. Khan
, and
A. Jabbar

## Abstract

Natural radioactivity in various types of marbles available in Rawalpindi/Islamabad industrial area have been assessed using HP(Ge) gamma-ray spectrometer. The concentration of 40K, 226Ra and 232Th ranges from 6.15 to 159.65 Bq.kg-1, 1.45 to 29.34 Bq.kg-1 and 1.16 to 6.28 Bq.kg-1, respectively. The radium equivalent activity lies between 5.56 to 33.42 Bq.kg-1. The average external and internal indices have been found to be 0.03 and 0.05, respectively. The average absorbed dose rate at 1 m was found to be 6.53 nGy.h-1. The estimated annual effective dose rate for whole body was found to be 0.04 mSv.y-1. These values are smaller than those predicted by UNSCEAR for normal background areas. The marbles analyzed pose less health hazard as compared to Pakistani baked bricks and other construction materials.

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## Neonatal hyperbilirubinemia: Background and recent literature updates on the diagnosis and treatment

Physiology International
Authors:
H. Nawaz
,
M. Aslam
, and
T. Rehman

## Abstract

Hyperbilirubinemia or jaundice has been studied by many researchers because of its diverse causes and potential for toxicity especially in the neonate but to a lesser extent beyond the neonate as well. Several studies have been performed on the normal metabolism and metabolic disorders of bilirubin in last decades of the 20th century. The recent advancement in research and technology facilitated for the researchers to investigate new horizons of the causes and treatment of neonatal hyperbilirubinemia. This review gives a brief introduction to hyperbilirubinemia and jaundice and the recent advancement in the treatment of neonatal hyperbilirubinemia. It reports modifications in the previously used methods and findings of some newly developed ones. At present, ample literature is available discussing the issues regarding hyperbilirubinemia and jaundice, but still more research needs to be done.

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## Silicon fertilization improves the maize (Zea mays L.) performance under limited moisture supply

Cereal Research Communications
Authors:
M. Amin
,
,
A. Ali
,
M. Aslam
, and
D.J. Lee

Field crops are subjected to numerous inconsiderate climatic hazards that negatively affect physiological processes, growth and yield. Drought is one of the major abiotic factors that limits the agricultural productivity especially in the arid and semi-arid areas of the globe. Silicon (Si) is a naturally occurring beneficial nutrient which modulates plant growth and development events and has been known to improve the crop tolerance to abiotic stresses. With the objective to investigate the role of silicon nutrition on maize hybrids under limited moisture supply, a two year field study was conducted during 2010–11 at Post Graduate Research Station (PARS), University of Agriculture Faisalabad, Pakistan. We evaluated growth of two maize hybrids P-33H25 and FH-810 under well watered (100% field capacity) and water deficit situation (60% field capacity) as affected by Si application. Silicon was added in soil @ 100 mg/kg using Calcium Silicate as source. Water deficit condition significantly reduced agro-morphological and physiological attributes of maize plants. Silicon application significantly increased the plant height, leaf area index, yield and related attributes along with improvement in photosynthetic rate, leaf water status and osmotic adjustment under limited moisture supply. It was concluded that silicon application to droughtstressed maize enhanced its growth and yield owing to improved photosynthetic rate, higher osmotic adjustment, increased water status and lowered transpiration.

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## An investigation into morphological and physiological approaches to screen maize (Zea mays L.) hybrids for drought tolerance

Cereal Research Communications
Authors:
M. Aslam
,
M.S.I. Zamir
,
S.A. Anjum
,
I. Khan
, and
M. Tanveer

A pot experiment was carried out in completely randomized design (CRD) having three replications to screen out six maize (Zea mays L.) hybrids viz; FH-810, 32-F-10, FH-782, 32-B-33, YH-1898, Monsanto-6525, R-2315 and R-3304 for drought tolerance. The study was carried out with objective to screen hybrids, when exposed to drought on the early phase of their vegetative growth. The moisture treatments comprised of 100% field capacity (FC), 75% FC and 50% FC. The results exhibited that all these hybrids varied substantially in their stability against drought tolerance. However, the results pertaining to interaction of maize hybrids with three moisture levels of 100% FC, 75% FC and 50% FC revealed that 32-F-10 performed comparatively better in contrast to other maize hybrids in plant height (79.74 cm, 47.02 cm and 41.65 cm), leaf area per plant (865.10 cm2, 405.7 cm2 and 178.60 cm2), relative water contents (81.23%, 69.79% and 65.98%), at 100%, 75% and 50% FC, respectively, while YH-1898 hybrid produced lowest values of these attributes in almost all water levels. However, a better stomatal conductance (gs), photosynthetic rate (A) and transpiration rate (E) were exhibited by 32-F-10 while YH-1898 revealed least gas-exchange values among all hybrids. The experimental results revealed that under drought conditions 32-F-10 performed best than all other maize hybrids and could be used for further investigation to screen out other drought tolerant-maize hybrids for maximum production.

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## Assessment of drought tolerance based impacts with over-expression of ZmLTP3 in maize (Zea mays L.)

Cereal Research Communications
Authors:
Y. Li
,
K. Zhou
,
M. Jiang
,
B. Zhang
,
M. Aslam
, and
H. Zou

Numerous studies showed that lipid transfer proteins (LTPs) play important roles in flower, development, cuticular wax deposition and pathogen responses; however, their roles in abiotic stresses are relatively less reported. This study characterized the function of a maize LTP gene (ZmLTP3) during drought stress. ZmLTP3 gene was transferred into maize inbred line Jing2416; subsequently the glyphosate and drought tolerance of the over-expression (OE) lines were analyzed. Analysis showed that OE lines could significantly enhance drought tolerance. Transgenic maize lines OE6, OE7 and OE8 showed lower cell membrane damage, higher chlorophyll contents, higher protective enzymes activities, better growth and development under drought condition. The results strongly indicated that overexpression of ZmLTP3 could increase drought tolerances in maize.

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## Salt stress induces genotype-specific DNA hypomethylation in ZmEXPB2 and ZmXET1 genes in maize

Cereal Research Communications
Authors:
F. Kaleem
,
,
G. Shabir
,
K. Aslam
,
S.M. Shah
, and
A.R. Khan

Maize, a moderately salt sensitive crop, first experiences osmotic stress that cause reduction in plant growth under salt stress. Fluctuation in cell wall elongation is one of the reasons of this reduction. Along with others, two important proteins expansins and xyloglucan endotransglucosylase are involved in regulation of cell wall elasticity, but the role of epigenetic mechanisms in regulating the cell wall related genes is still elusive. The present study was conducted with the aim of understanding the role of DNA methylation in regulating ZmEXPB2 and ZmXET1 genes. One salt sensitive and one salt tolerant maize cultivar was grown under hydroponic conditions at different levels of salt stress: T1 = 1 mM (control), T2 = 100 mM and T3 = 200 mM in three replicates. DNA and RNA were extracted from roots. After bisulfite treatment, Methyl Sensitive PCR was used for the DNA methylation analysis. It was revealed that fragment in promoter of ZmEXPB2 gene showed high level of DNA methylation under T1 in both varieties. Comparison of different stress treatments revealed decrease in DNA methylation with the increase in salt stress, significantly lower methylation appearing in T3. Similarly, the fragment in promoter of ZmXET1 gene also showed high levels of DNA methylation in T1. When different treatments were analysed, this gene significantly hypomethylated at T2 which continued to decrease in T3 in sensitive variety but remain stable in tolerant variety. Although, further in-depth analysis is required, our results demonstrate region-specific and genotype-specific methylation shift in the promoter of the ZmEXPB2 and ZmXET1 genes when subjected to the salt stress confirming the epigenetic regulation of these genes under stress conditions.

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## Terrestrial absorbed dose rate measurement in the Jhangar valley of Pakistan

Journal of Radioanalytical and Nuclear Chemistry
Authors:
Z. Chaudhry
,
H. Khan
,
K. Khan
,
M. Aslam
,
A. Jabbar
, and
S. Orfi

## Abstract

Specific activity of natural radionuclides; 226Ra, 232Th and 40K were measured in the agricultural soil of eastern salt range of Pakistan using gamma ray spectrometry. The soil samples were collected within the ploughing region (up to 12 cm depth) and processed before analysis. The average specific activities of different radionuclides in the dry mass of soil samples were: 40K, (666 Bq/kg), 226Ra (51 Bq/kg), and 232Th (59 Bq/kg). The average outdoor terrestrial absorbed dose rate in air from gamma radiation one meter above ground surface was found to be 93 nGy/h.

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