Tamely Ramified Towers and Discriminant Bounds for Number Fields

The root discriminant of a number field of degree n is the nth root of the absolute value of its discriminant. Let R _2m be the minimal root discriminant for totally complex number fields of degree 2m, and put ₀ = lim inf _m R _2m . One knows that ₀ 4e 22.3, and, assuming the Generalized Riemann Hypothesis, ₀ 8e 44.7. It is of great interest to know if the latter bound is sharp. In 1978, Martinet constructed an infinite unramified tower of totally complex number fields with small constant root discriminant, demonstrating that ₀ < 92.4. For over twenty years, this estimate has not been improved. We introduce two new ideas for bounding asymptotically minimal root discriminants, namely, (1) we allow tame ramification in the tower, and (2) we allow the fields at the bottom of the tower to have large Galois closure. These new ideas allow us to obtain the better estimate ₀ < 83.9.     

A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

A NONLINEAR MICROBEAM MODEL BASED ON STRAIN GRADIENT ELASTICITY THEORY

A micro scale nonlinear beam model based on strain gradient elasticity is developed.Governing equations of motion and boundary conditions are obtained in a variational framework.As an example,the nonlinear vibration of microbeams is analyzed.In a beam having a thickness to length parameter ratio close to unity,the strain gradient effect on increasing the natural frequency is predominant.By increasing the beam thickness,this effect decreases and geometric nonlinearity plays the main role on increasing the natural frequency.For some specific ratios,both geometric nonlinearity and size effects have a significant role on increasing the natural frequency.     

A new model for automatic normalization of multitemporal satellite images using Artificial Neural Network and mathematical methods

Relative Radiometric Normalization is often required in remote sensing image analyses particularly in the land cover change detection process. Normalization process minimizes the radiometric differences between two images caused by inequalities in the acquisition conditions rather than changes in surface reflectance. A wide range of RRN methods have been developed to adjust linear models. This paper proposes an automated Relative Radiometric Normalization (RRN) method to adjust a non-linear model based on an Artificial Neural Network (ANN) and unchanged pixels. The proposed method includes the following stages: (1) automatic detection of unchanged pixels based on a new idea that uses CVA (Change Vector Análysis) method, PCA (Principal Component Analysis) transformation and K-means clustering technique, (2) evaluation of different architectures of perceptron neural networks to find the best architecture for this specific task and (3) use of the aforementioned network for normalizing the subject image. The method has been implemented on two images taken by the TM sensor. Experimental results confirm the effectiveness of the presented technique in the automatic detection of unchanged pixels and minimizing imaging condition effects (i.e., atmosphere and other effective parameters).     

Some Properties On Isoclinism in n-Lie Algebras

The concept of n-Lie algebra were introduced by Filippov in 1987. One notes that not all properties of Lie algebras can be carried over to n-Lie algebras, as Williams showed in 2009. In the present article, among other results it is shown that the notions of isoclinism and isomorphism for two finite dimensional n-Lie algebras of the same dimension are equivalent. This was already done for ordinary Lie algebras by Moneyhun in 1994.     

Microwave Assisted Deprotection of N,N-Dimethylhydrazones in Water Using Palladium Chloride–Tin Chloride as Catalyst

Summary.  N,N-Dimethylhydrazones of ketones and aldehydes undergo facile cleavage to the corresponding carbonyl compounds upon exposure to microwaves in water containing a catalytic amount of PdCl₂–SnCl₂ in high yields. Corresponding authors. E-mail: rahman@umz.ac.ir Received December 27, 2001. Accepted (revised) February 6, 2002     

High-valent [Sn(Br8TPP)(OTf)2] as a highly efficient and reusable catalyst for selective methoxymethylation of alcohols and phenols: The effect of substituted bromines on the catalytic activity

High-valent tin(IV)octabromotetraphenylporphyrinato trifluoromethanesulfonate, [Sn^IV(Br₈TPP)(OTf)₂], was used for selective methoxymethylation of alcohols and phenols with formaldehyde dimethyl acetal (FDMA) at room temperature. Different primary, secondary and tertiary alcohols as well as phenols were converted to their corresponding methoxymethyl ethers with FMDA in the presence of an electron deficient tin(IV) porphyrin. The catalyst was reused several times without significant loss of its activity.     

Analysis of xylene in aqueous media using needle‐trap microextraction with a carbon nanotube sorbent

This paper describes a new extraction technique with needles and a sorbent based on carbon nanotubes to analyze trace amounts of three isomers of xylenes in aqueous samples. In this research, results have been compared with one commercial sorbent. The synthesized sorbent was prepared using sol–gel technology and was packed into 20 gauge needles, and the same size needle was used for packing the commercial sorbent. In the extraction process, a purge and trap sampling methodology is developed, so purging and trapping cycles were performed by a sampling pump. Optimized conditions for standard xylene samples have been obtained, and eight urine samples from workers that were exposed to xylene in the workplace were collected and analyzed. Experimental parameters such as limits of detection and quantification were investigated, and these two parameters were <1 μg/L.     

Supported N-propylsulfamic acid on magnetic nanoparticles used as recoverable and recyclable catalyst for the synthesis of 2, 3-dihydroquinazolin-4(1H)-ones in water

An efficient and eco-friendly method is reported for the synthesis of 2-substituted-2,3-dihydroquinazolin -4（1 H）-ones from direct cyclocondensation of anthranilamide with aldehydes and ketones using N-propylsulfamic acid supported onto magnetic Fe₃O₄ nanoparticles（MNPs-PSA） as a recoverable and recyclable nanocatalyst in good to excellent yields in water at 70℃.The catalyst was readily separated using an external magnet and reusable without significant loss of their catalytic efficiency.