Let $R$ be an associative ring and let $M$ be a left $R$-module.Let $Spec_{R}(M)$ be the collection of all prime submodules of $M$ (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, t...

In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining  a new Hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

A composite spectral feature space is used to characterize the mixing properties of Sentinel 2 Multispectral Instrument (MSI) spectra over a wide diversity landscapes. Characterizing linearity and identifying bounding endmembers allows Substrate Vegetation Dark (SVD) mixture model previously developed for Landsat MODIS sensors be extended MSI sensors. The utility SVD its ability represent varie...

In this paper, exact formulæ of the input-output weight distribution function and its exponential growth rate are derived for truncated convolutional encoders. In particular, these weight distribution functions are expressed in terms of generating functions of error events associated with a minimal realization of the encoder. Although explicit analytic expressions can be computed for relatively...

\.{Z}uk proved that if a finitely generated group admits Cayley graph such the Laplacian on links of this has spectral gap $> \frac{1}{2}$, then property (T), or equivalently, every affine isometric action Hilbert space fixed point. We prove same holds for actions uniformly curved Banach (for example an $L^p$-space with $1 < p \infty$ interpolation between and arbitrary space) as soon two-sided...

We consider the problem of estimating the value of max cut in a graph in the streaming model of computation. At one extreme, there is a trivial 2-approximation for this problem that uses only O(log n) space, namely, count the number of edges and output half of this value as the estimate for max cut value. On the other extreme, if one allows Õ(n) space, then a near-optimal solution to the max cu...

MAX-2-SAT and MAX-2-CSP are important NP-hard optimization problems generalizing many graph problems. Despite many efforts, the only known algorithm (due to Williams) solving them in less than 2 steps uses exponential space. Scott and Sorkin give an algorithm with 2 2 d+1 ) time and polynomial space for these problems, where d is the average variable degree. We improve this bound to O∗(2 10/3 d...