We prove that an alternating e-form on a vector space over a quasialgebraically closed field always has a singular (e − 1)-dimensional subspace, provided that the dimension of the space is strictly greater than e. Here an (e−1)-dimensional subspace is called singular if pairing it with the e-form yields zero. By the theorem of Chevalley and Warning our result applies in particular to finite bas...

We study the normalization of integrable analytic vector fields with a nilpotent linear part. We prove that such an analytic vector field can be transformed into a certain form by convergent transformations when it has a non-singular formal integral. In particular, we show that a formally linearizable analytic vector field with a nilpotent linear part is linearizable by convergent transformatio...

In this paper, experimental responses of the clamped mild steel, copper, and aluminium circular plates are presented subjected to blast loading. The GMDH-type neural networks (Group Method of Data Handling) are then used for the modelling of the mid-point deflection thickness ratio of the circular plates using those experimental results. The aim of such modelling is to show how the mid-point de...

Non Uniform Rational B-splines (NURBs) are proved to be very promising for metamodeling in engineering problems, because they have unique properties such as local modification scheme, strong convex hull property, and infinitely differentiability, etc. Since NURBs are defined by control points, knot vector, and weights associated with control points, the precision of NURBs is influenced by all o...

The singular vectors of a chemical transport model are the directions of maximum perturbation growth over a finite time interval. They have proved useful for the estimation of error growth, the initialization of ensemble forecasts, and the optimal placement of adaptive observations. The aim of this paper is to address computational aspects of singular vector analysis for atmospheric chemical tr...

HAMID HASSANPOUR School of Information Technology and Computer Engineering, Shahrood University of Technology. ___________________________________________________________________________________ Abstract: In this paper, a new method is presented for noise reduction in signal using partial differential equations. In this approach, the signal is initially represented as a matrix. Then using singu...

‎this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$‎. ‎some applications to these inequalities are also given‎. ‎in addi...

Abstract We study the topology of moduli spaces weighted stable tropical curves Δ g , w with fixed genus and unit volume. The space arises as dual complex divisor singular in Hassett’s M curves. When is positive, we show that simply connected for any choice weight vector . also give a formula Euler characteristic terms combinatorics vector.

Position-specific scoring matrices (PSSMs) are useful for detecting weak homology in protein sequence analysis, and they are thought to contain some essential signatures of the protein families. In order to elucidate what kind of ingredients constitute such family-specific signatures, we apply singular value decomposition to a set of PSSMs and examine the properties of dominant right and left s...

Abstract We consider a singular holomorphic vector field in neighborhood of 0∈ C3and suppose that there is foliation codimension one (outside its set, given by decomposition this into complex surfaces, called leaves) to which it tangent. This means that, when both objects are non-singular, the orbits contained leaves foliation. First we desingularizations objects, trying relate their final mode...