In this paper, we have addressed three major problems of uniform linear array in case of a sensor failure at any position. We assume that sensor position is known. The problems include increase in sidelobe levels, displacement of nulls and diminishing of null depth. The desired null depth is achieved by making the weight of symmetrical counterpart element passive. Genetic algorithm (GA) along w...

We establish the Gaussian Multi-Bubble Conjecture: least Gaussian-weighted perimeter way to decompose $\mathbb{R}^n$ into $q$ cells of prescribed (positive) measure when $2\le q\le n+1$, is use a ``simplicial cluster," obtained from Voronoi equidistant points. Moreover, we prove that simplicial clusters are unique isoperimetric minimizers (up null-sets). In particular, case $q=3$ confirms Doubl...

Automated chromosome classification is an essential task in cytogenetics. The genetic disorders and abnormalities that occur to the future generation can be predicted through analysing the various characteristics of the chromosomes. The chromosome classification is mainly based on geometric and morphological features. An effective algorithm for chromosome geometric feature extraction is present...

Three issues regarding sensor failure at any position in the antenna array are discussed. We assume that sensor position is known. The issues include raise in sidelobe levels, displacement of nulls from their original positions, and diminishing of null depth. The required null depth is achieved by making the weight of symmetrical complement sensor passive. A hybrid method based on memetic compu...

We prove the following theorem: For a partially ordered set Q such that every countable subset of Q has a strict upper bound, there is a forcing notion satisfying the countable chain condition such that, in the forcing extension, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in ...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

Acoustic scattering by three-dimensional obstacles is considered, using boundary integral equations, null-field equations and the T-matrix. Connections between these techniques are explored. It is shown that solving a boundary integral equation by a particular Petrov–Galerkin method leads to the same algebraic system as obtained from the null-field equations. It is also emphasised that the T-ma...

We deal with only finite point sets P in the plane in general position. A point set is convex or in convex position if it determines a convex polygon. A convex subset Q of P is said to be empty if no point of P lies inside the convex hull of Q. An empty convex subset of P with k elements is also called a k-hole of P . Let P be an n planar point set in general position. For a subset Q of P , den...

Classically, null designs were defined on the poset of subsets of a given finite set (boolean algebra). A null design is defined as a collection of weighted k-subsets such that the sum of the weights of ksubsets containing a t-subset is 0 for every t-subset, where 0 ≤ t < k ≤ n. Null designs are useful to understand designs or to construct new designs from a known one. They also deserve researc...