Reverse Young and Heinz inequalities for matrices

We give reverses of the classical Young inequality for positive real numbers and we use these to establish reverse Young and Heinz inequalities for matrices.     

Bounds and a majorization for the real parts of the zeros of polynomials

We apply some eigenvalue inequalities to the real parts of the Frobenius companion matrices of monic polynomials to establish new bounds and a majorization for the real parts of the zeros of these polynomials.

     

Some decomposition results for companion matrices

Let C(p) denote the Frobenius companion matrix of the monic polynomial p with complex coefficients. The singular value decomposition and the QR-decomposition of C(p) are computed.     

Entropy generation in nonlinear mixed convective flow of nanofluid in porous space influenced by Arrhenius activation energy and thermal radiation

This paper focuses on an experimental study of the surface tension of nanofluids based on ethylene glycol with various types of nitride nanoparticles. Samples were prepared using a two-step method with mass content between 1 and 5% of particles. Nanofluids contain three types of nitride nanoparticles: aluminum nitride, silicon nitride and titanium nitride with various particle average sizes. Surface tension of nanofluids was investigated at a constant temperature of 298.15 K with two different techniques: du Noüy ring method and pendant drop method. It is presented that experimental values obtained with both methods are in good agreement with each other. Also, results obtained during this study show that the addition of this type of nanoparticles does not have a significant impact on the surface tension of base fluid for the concentrations and diameters of nitride nanoparticles considered.

     

Some inequalities for commutators and an application to spectral variation. II

Inequalities that compare unitarily invariant norms of A - B and those of AΓ - ΓB and Γ^-1A - B Γ^-1 are obtained, where both A and B are either Hermitian or unitary or normal operators and Γ is a positive definite operator in a complex separable Hilbert space. These inequalities are then applied to derive bounds for spectral variation of diagonalisable matrices. Our new bounds improve substantially previously published bounds.     

Bounds and Majorization Relations for the Zeros of Polynomials

We use matrix inequalities to prove several bounds and majorization relations for the zeros of polynomials. Our results generalize the classic bound of Montel and improve some other known bounds.     

Fixed-time synchronization of four-dimensional energy resource systems with mismatched parameters

In this paper, we establish sufficient conditions for the existence of positive solutions for a class of higher order Riemann–Liouville fractional initial value problems. First, we construct an appropriate Banach space and prove the equivalence between the posed problem and the associated Volterra integral equation, then by means of Guo–Krasnoselskii fixed point theorem, we investigate the existence of at least one positive solution under sublinearity conditions.     

Norm Inequalities for Sums of Positive Operators. II

It is shown that if A and B are positive operators on a separable complex Hilbert space, then for every unitarily invariant norm. When specialized to the usual operator norm ||·|| and the Schatten p-norms ||·||_p, this inequality asserts that and These inequalities improve upon some earlier related inequalities. Other norm inequalities for sums of positive operators are also obtained.     

Improved Young and Heinz inequalities for matrices

We give refinements of the classical Young inequality for positive real numbers and we use these refinements to establish improved Young and Heinz inequalities for matrices.     

A Hopfield neural network with multiple attractors and its FPGA design

Neural network is important for a wide range of applications. Especially, a small neural network can display various complex behaviors. In this work, the investigations of a Hopfield neural network and its field programmable gate array (FPGA) implementation have been reported. The considered Hopfield neural network is simple because it includes only three neurons. It is interesting that we observed chaos and numerous coexisting attractors in such a network. In addition, the network has been implemented via an FPGA platform to verify its feasibility.