Nonlinear conjugate gradient method is very popular in solving large-scale unconstrained minimization problems due to its simple iterative form and lower storage requirement. In the recent years, it was successfully extended to solve higher-dimension monotone nonlinear equations. Nevertheless, the research activities on conjugate gradient method in symmetric equations are just beginning. This s...

The strong truncated Hamburger moment problem (STHMP) of degree (?2k1,2k2) asks to find necessary and sufficient conditions for the existence a positive Borel measure, supported on R, such that ?i=?xid?(?2k1?i?2k2). first solution STHMP, covering also its matrix generalization, was established by Simonov [60], who used operator approach described all solutions in terms self-adjoint extensions c...

<p style='text-indent:20px;'>Computational techniques for the construction of quasi-symmetric block designs are explored and applied to case with <inline-formula><tex-math id="M2">\begin{document}$ 56 $\end{document}</tex-math></inline-formula> points. One new id="M3">\begin{document}$ (56,16,18) many id="M4">\begin{document}$ (56,16,6) discovered, non-existe...

We suggest using spatially modulated strain for control of a spin wave propagating inside bulk magnet. The modulation with the vector $q=2k$, by virtue magnetoelasticity, mixes waves vectors near $k$ and $-k$. This leads to lifting degeneracy symmetric antisymmetric eigenstate combinations these waves. resulting picture reminds one tunneling particle in double-well potential. Here, moving being...

Assume Mn is the n-dimensional permutation module for the symmetric group Sn, and let M n be its k-fold tensor power. The partition algebra Pk(n) maps surjectively onto the centralizer algebra EndSn(M ⊗k n ) for all k, n ∈ Z≥1 and isomorphically when n ≥ 2k. We describe the image of the surjection Φk,n : Pk(n) → EndSn(M ⊗k n ) explicitly in terms of the orbit basis of Pk(n) and show that when 2...