this paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

Let L ⊂ V = R be a maximally isotropic subspace. It is shown that any simply connected Lie group with a bi-invariant flat pseudo-Riemannian metric of signature (k, l) is 2-step nilpotent and is defined by an element η ∈ Λ3L ⊂ Λ3V . If η is of type (3, 0)+(0, 3) with respect to a skew-symmetric endomorphism J with J2 = ǫId, then the Lie group L(η) is endowed with a left-invariant nearly Kähler s...

We study the complexity of solving the generalized MinRank problem, i.e. computing the set of points where the evaluation of a polynomial matrix has rank at most r. A natural algebraic representation of this problem gives rise to a determinantal ideal: the ideal generated by all minors of size r+1 of the matrix. We give new complexity bounds for solving this problem using Gröbner bases algorith...

Protozoan parasites of the order Kinetoplastida cause severe diseases primarily in the tropical and subtropical areas. The enormous development of molecular and cellular biology in recent times have provided opportunities for discovering newer molecular targets for drug designing, which now form a rational basis for the development of improved anti-parasitic therapy. DNA topoisomerases play a k...

Let Z be the set of integers, and for a prime p let Zp denote the set of those rational numbers whose denominator is not divisible by p. Let (p ) be the Legendre symbol. Suppose that p is an odd prime and a ∈ Zp. In [7] the author investigated congruences for ∑[p/4] k=0 (4k 2k ) ak modulo p, where [x] is the greatest integer not exceeding x. For k ∈ {0, 1, . . . , p − 1} it is easily seen that ...

The design of magnetic nanoparticles by incorporation of iron oxide colloids within gelatine/silica hybrid nanoparticles has been performed for the first time through a nanoemulsion route using the encapsulation of pre-formed magnetite nanocrystals and the in situ precipitation of ferrous/ferric ions. The first method leads to bi-continuous hybrid nanocomposites containing a limited amount of w...

Modern methods for H2-optimal model order reduction include the Iterative Rational Krylov Algorithm (IRKA, [Gugerkin, Antoulas, and Beattie, 2008]) and Parameterized Model Reduction (PMOR, [Baur, Beattie, Benner, and Gugercin, 2011]). In every IRKA or PMOR iteration, two sequences of shifted linear systems need to be solved, one for the shifted matrices and one for their adjoint, using the same...

Computer-based aids for writing assistance have been around since at least the early 1980s, focussing primarily on aspects such as spelling, grammar and style. The potential audience for such tools is very large indeed, and this is a clear case where we might expect to see language processing applications having a significant real-world impact. However, existing comparative evaluations of appli...

Direct arguments are presented showing that for rational series in several com muting variables the rational series problem is non computable and closure under Hadamard product fails

We study the connections between rational series with coeecients in a semiring and their languages.