Equivalent Binary Quadratic Form and the Extended Modular Group

Extended modular group $\bar{\Pi}=$, where R:z\rightarrow -\bar{z}, \sim T:z\rightarrow\frac{-1}{z},\simU:z\rightarrow\frac{-1}{z +1} , has been used to study some properties of the binary quadratic forms whose base points lie in the point set fundamental region $F_{\bar{\Pi}}$ (See \cite{Tekcan1, Flath}). In this paper we look at how base points have been used in the study of equivalent binary quadratic forms, and we prove that two positive definite forms are equivalent if and only if the base point of one form is mapped onto the base point of the other form under the action of the extended modular group and any positive definite integral form can be transformed into the reduced form of the same discriminant under the action of the extended modular group and extend these results for the subset \QQ^*(\sqrt{-n}) of the imaginary quadratic field \QQ(\sqrt{-m}).Comment: Paper contains two figures and twelve page

Do government schools improve learning for poor students? Evidence from rural Pakistan

Pakistan’s Punjab province has witnessed numerous education reforms in recent years. Many of these reforms have been aimed at improving the well-documented low levels of learning by focusing on improving teaching quality. The rhetoric suggests that government schools, particularly those in rural areas with a more disadvantaged pupil base, are especially ineffective at imparting learning. This paper seeks to investigate whether children in rural Punjab are learning literacy and numeracy over the course of a year, and if so, are some pupils progressing more than others. Using recently collected data, it finds that children in our sample are making progress. Variation in progress is found to be greater within schools rather than across them. The competence and qualifications of a teacher also makes a significant difference to a child’s academic progress. The paper further finds differential progress for rich and poor students within schools, suggesting an important role for education policy to put in place targeted support towards those from disadvantaged backgrounds to ensure improvements in their learning keep pace with their peers.Department for International Development (DFID

Direction of Arrival Estimation in the presence of Scatterer in noisy environment

We present an algorithm to estimate direction of arrival (DOA) of an incoming wave received at an array antenna in the scenario where the incoming wave is contaminated by the additive white Gaussian noise and scattered by arbitrary shaped 3D scatterer(s). We present different simulation examples to show the validity of the proposed method. It is observed that the proposed algorithm is capable of closely estimating the DOA of an incoming wave irrespective of the shape of the scatterer provided the decision is made over multiple iterations. Moreover, presence of noise affects the estimate especially in the case of low signal-to-noise ratio (SNR) that gives a relatively large estimation error. However, for larger SNR the DOA estimation is primarily dependent on the scatterer only

A strong construction of S-box using Mandelbrot set an image encryption scheme

The substitution box (S-box) plays a vital role in creating confusion during the encryption process of digital data. The quality of encryption schemes depends upon the S-box. There have been several attempts to enhance the quality of the S-box by using fractal chaotic mechanisms. However, there is still weakness in the robustness against cryptanalysis of fractal-based S-boxes. Due to their chaotic behavior, fractals are frequently employed to achieve randomness by confusion and diffusion process. A complex number-based S-box and a chaotic map diffusion are proposed to achieve high nonlinearity and low correlation. This study proposed a Mandelbrot set S-box construction based on the complex number and Chen chaotic map for resisting cryptanalytic attacks by creating diffusion in our proposed algorithm. The cryptosystem was built on the idea of substitution permutation networks (SPN). The complex nature of the proposed S-box makes it more random than other chaotic maps. The robustness of the proposed system was analyzed by different analysis properties of the S-box, such as nonlinearity, strict avalanche criterion, Bit independent criterion, and differential and linear probability. Moreover, to check the strength of the proposed S-box against differential and brute force attacks, we performed image encryption with the proposed S-box. The security analysis was performed, including statistical attack analysis and NIST analysis. The analysis results show that the proposed system achieves high-security standards than existing schemes

Acetone sensor based on solvothermally prepared ZnO doped with Co3O4 nanorods

This paper describes a reliable and sensitive method for sensing dissolved acetone using doped nanomaterials. Large-scale synthesis of ZnO nanorods (NRs) doped with Co(3)O(4) was accomplished by a solvothermal method at low temperature. The doped NRs were characterized in terms of their morphological, structural, and optical properties by using field-emission scanning electron microscopy coupled with energy-dispersive system, UV-Vis., Fourier transform IR, X-ray diffraction, and Xray photoelectron spectroscopy. The calcinated (at 400 °C) doped NRs are shown to be an attractive semiconductor nanomaterial for detecting acetone in aqueous solution using silver electrodes. The sensor exhibits excellent sensitivity, stability and reproducibility. The calibration plot is linear over a large concentration range (66.8 μM to 0.133 mM), displays high sensitivity (~3.58 μA cm(−2) mM(−1)) and a low detection limit (~14.7 ± 0.2 μM; at SNR of 3). [Figure: see text

Influence of additives (inorganic/organic) on the clouding behavior of amphiphilic drug solutions: Some thermodynamic studies

AbstractHerein we provide a detailed result about the effect of various additives, viz. inorganic salts, quaternary ammonium bromides (QABs) and amino acids on clouding behavior of amphiphilic drug amitriptyline hydrochloride (AMT). The continuous increase in the cloud point (CP) of drug by increase in inorganic salt concentration and the magnitude of increases rely upon the position of the salts in Hofmeister series and hydrated radii. The QABs also influence continuous increase in the CP, which is illustrated in terms of the alkyl chain length of peculiar QAB. The effect of amino acids on CP of the drug solution is dependent upon the characteristics (acidic, basic, polar or nonpolar) of particular amino acids. The overall behavior of additives has been analyzed and discussed on the basis of electrostatic repulsion or interaction, micellar growth, and mixed micelle formation between the ingredients. In addition to this, thermodynamic parameters are also evaluated