In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural genera...

‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...

the stolt (f-k) migration algorithm is a direct (i.e. non-recursive) fourier-domain technique based on a change of variables (or equivalently, a mapping) that converts the input spectrum to the output spectrum. the algorithm is simple and efficient but limited to constant velocity. a v(z)(f-k) migration method, capable of very high accuracy for vertical variations of velocity, can be formulated...

the complex of ce(iii), [ ce (phensc) (h 0) ] (c10 ) , was synthesized using the phensc, a hexadentate ligand,2,9-diformyl-1,lo- phenanthroline bis (semicarbazone), and characterized by x-ray diffraction. the cerium atom has an unusual coordination number of ten involving six donor atoms of the planar ligand in the equatorial plane and four oxygen atoms from four axial water molecules. the comp...

We prove a sufficient condition for finite clique complex to collapse k-dimensional complex, and use this exhibit thresholds (k+1)-collapsibility in sparse random complex. In particular, if every strongly connected, pure (k+1)-dimensional subcomplex of X has vertex degree at most 2k+1, then is (k+1)-collapsible. the model X(n,p) complexes an Erdős–Rényi graph G(n,p), we show that any fixed k≥0,...

The complexation of Alkali metal cations by the water-soluble p-sulfonic acid calix(4)arenewas thermodynamically characterized using spectrophotometeric data which are consistentwith the formation of a 1:1 complex resulting from electrostatic interactions between thesulfonato groups and alkali metal cations. In this study, we determined the formationconstants (log K) of the complexes and have c...

‎Hensel [K‎. ‎Hensel‎, ‎Deutsch‎. ‎Math‎. ‎Verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎Fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{Z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎Then $|x...

The present study was performed to determine whether or not spontaneous K-complexes are induced by sensory stimuli. In the first part of the present study, sound stimuli were prescribed during sleep in 7 healthy, young, adult subjects. EEG segments in stage 2 sleep were averaged separately according to the presence or absence of an evoked K-complex appearing after each stimulus. The sound stimu...

The cooling of molecules during the adiabatic expansion of supersonic seeded molecular beams is reviewed and illustrated by the example of NO -molecules. The reduction of the Doppler width by collimation of the beam and the cooling to low rotational temperatures brings a significant simplification of the complex NO -absorption spectrum and allows its assignment. The measured rotational tem...