Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and$I\subset S$ be a monomial ideal with a LINEARRESOLUTION. Let$\frak{m}=(x_1,\ldots,x_n)$ be the unique homogeneous maximal ideal and $I\frak{m}$ be apolymatroidal ideal. We prove that if either $I\frak{m}$ is polymatroidal with strongexchange property, or $I$ is a monomial ideal in at most 4variables, then $I$ is polymatroidal. We also show that the firsthomological shift ideal of polymatroidal ideal is againpolymatroidal.

I In this paper, we propose an algorithm base on decomposition technique for solving the mixed integer LINEAR multiplicative-LINEAR bilevel problems. In fact, this algorithm is an application of the algorithm given by G. K. Saharidis et al for the case in which the first level objective function is LINEAR multiplicative. We use properties of quasi-concave of bilevel programming problems and decompose the initial problem into two subproblems named RMP and SP. The lower and upper bound provided from the RMP and SP are updated in each iteration. The algorithm converges when the difference between the upper and lower bound is less than an arbitrary tolerance. In conclusion, some numerical examples are presented in order to show the efficiency of algorithm.

The aim of this paper is to present an algebraic method which is called Wu's method for solving fuzzy complex systems of LINEAR equations. Wu's method is used as a solution procedure for solving the crisp polynomial equations system. This algorithm leads to solving characteristic sets that are amenable to easy solution. First, the system of fuzzy complex systems of LINEAR equations is transformed to an equivalent crisp polynomial equations system. Then, using Wu's method an algorithm for  nding fuzzy solutions of original system is introduced. One of the great bene ts of our approach is that gives all solutions at a time. To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed.

In this paper, an improved sample of capacitive-type LINEAR encoder with untethered slider is presented that has higher RESOLUTION and lower error. This encoder has a simple structure consisting of two main parts, stator and slider. Both parts are made of hard PCB. The stator has a sequence of four-phase receiver electrodes and the slider contains two-phase transmitter electrodes. The electrical energy is supplied to transmitter electrodes by the electrostatic induction. Therefore, there is no need to connect any wire to the slider. These features make the encoder to use in limited spaces. By improving RESOLUTION, smooth and precise movement of motors is facilitated in the closed loop systems. Thus, the improved encoder is equipped with two ground electrodes between the receiver electrodes and induction electrodes on the stator board to reduce electrostatic interface between these electrodes. As, output error goes down. In addition, the step of electrodes are reduced to increase RESOLUTION. Making an experimental sample of improved encoder and testing it, showed 15μ m error in 1μ m RESOLUTION. This indicates, the error and RESOLUTION are improved than the previous one.

In geophysical inverse problems with increasing number of data and model parameters or increasing level of data errors (noise), we have many problems about model instability and inversion of bad condition matrixes. Progressive methods can be use for achieving desire convergence and precision in mentioned systems base on real geological reality.Most geophysical inverse problems can be solved by minimizing a misfit function between observed data and theoretical estimations. In inverse problems studying model stability and independence of model parameters can be done by Error analysis and RESOLUTION matrix. Other important factors for evaluating inverse methods are rate of convergence, running time of computer codes and number of iterations. This paper had focused on Marquardt-Levenberg (ridge regression) as one of conventional and efficient geophysical inverse method against subspace inversion to invert Magnetic data. In subspace inversion, Spanning original model parameters space to some subspaces can be done in two essential manner respects to physical dimension of model parameters.The efficiency of subspace method is demonstrated by comparing quality of RESOLUTION matrixes and error analysis in Marquardt-Levenberg with subspace inversion method. Comparison results show that the subspace method has fast and stable convergence compare to conventional method.

Background and Aim: Fluorscence Tomography is Emerging as an important alternative to molecular imaging. Simultaneous detection of several biological processes in vivo is a common requirement in molecular imaging. Application of multiple fluorophores and multispectral approaches have been widely used for distinguishing fluorescence signals. But, in case of spectral overlapping isolation of signals requires using unmixing algorithms. In this study, the researchers used blind source unmixing method, Non-Negative Matrix Factorization (NMF), to decompose contributions of different fluorescent probes in Fluorescence Molecular Tomography (FMT) images.Methods: A cylinder tissue-like phantom containing 2 transparent tube with 0.5 millimeter inner diameter filled with different fluorophores (fluorescine and rhodamine). It was imaged by using experimental FMT setup at three different wavelengths. We performed NMF algorithm on multispectral measurement to resolve the relative contributions of fluorescent dyes. Multispectral projection was simulated and used as input of unmixing algorithms in simulation part of study. The projection images of each probes was simulated and used as reference data to evaluate performance of unmixing algorithm for simulated images.Results: Two set of data, each of them corresponded to isolated contribution of each fluorophore, were obtained as the result of performing the algorithm on multispectral measurements. The "root mean square error" (RMSE) was calculated between original reference and related unmixed images. The difference between "Peak signal to noise ratio" (PSNR) values was statistically significant for each reference image (p<0.01). It shows that the proposed algorithm works in an accurate manner. The correlation coefficient between unmixed images and related reference image was more than 97% in simulation study. Unmixing method based on NMF can be used as an efficient technique to unmix contribution of different florophores. The 3-D location of each florophore can be obtained separately by reconstructing of these unmixed image.

Along with commercial accessibility of high RESOLUTION satellite images in recent decades, the issue of extracting accurate 3D spatial information in many fields became the centre of attention and applications related to photogrammetry and remote sensing has increased. To extract such information, the images should be geo-referenced. The procedure of georeferencing is done in four main steps of extracting some control information such as point, line or areal features, matching, transformation function estimation and finally resampling. Among different control features, the lines are more considered due to their unique characteristics such as easier procedure of automatically extracting and matching as well as abundance of LINEAR features in satellite images especially in urban areas. To reach an automatic georeferencing procedure, it is inevitable to automate the matching step as one of the most challenging process especially in heterogonous spaces such as image and map spaces. So, in this paper, the automatic matching procedure is performed and assessed using a new structural LINEAR feature-based matching method with no need to any initial information. This method is based on using the most inherent conceivable information of the extracted features. The purpose of this paper is to find all possible match-lines through finding the correspondence of two specific patterns. The proposed method is done in three main phases of high quality pattern selection, matching as well as the final-phase. Additionally, new concepts of mathematically-generated-lines which are produced by extension and intersection of line-segments in two spaces as well as mathematically-generated-points which are the keypoints of that lines are introduced and used to find the match-lines. In this paper, the impact of different numbers of stopping-criteria as well as one of the thresholds is studied experimentally. The results show the high potential of the proposed method to find more than 80 percentages of match-lines with 100 percentages of accuracy and reliability in a low computational time.