395 research outputs found
A remark about positive polynomials
The following theorem is proved.
{\bf Theorem.} {\it Let be a polynomial with
positive coefficients. If the inequalities hold for all then
for every .}
We show that the constant in this theorem
could not be increased. We also present some corollaries of this theorem.Comment: Submitted to the journal "Mathematical Inequalities and Applications"
on September 29, 200
On sufficient conditions for the total positivity and for the multiple positivity of matrices
The following theorem is proved:
Suppose be a matrix with positive entries and
Then The constant in this Theorem is sharp. A few other results concerning
totally positive and multiply positive matrices are obtained.
Keywords: Multiply positive matrix; Totally positive matrix; Strictly totally
positive matrix; Toeplitz matrix; Hankel matrix; P\'olya frequency sequence.Comment: 15 page
A note on zero sets of absolutely monotonic functions
A new necessary condition for a set to be the zero set of an absolutely monotonic function is given
Zero sets of entire absolutely monotonic functions
The paper is devoted to the problem of characterization of the class of subsets of which can serve as zero
sets of entire absolutely monotonic functions
A note on zero sets of absolutely monotonic functions
A new necessary condition for a set to be the zero set of an absolutely monotonic function is given
The first light of Mini-MegaTORTORA wide-field monitoring system
Here we describe the first light of the novel 9-channel wide-field optical
monitoring system with sub-second temporal resolution, Mini-MegaTORTORA, which
is being tested now at Special Astrophysical Observatory on Russian Caucasus.
The system is able to observe the sky simultaneously in either wide (~900
square degrees) or narrow (~100 square degrees) fields of view, either in clear
light or with any combination of color (Johnson B, V or R) polarimetric filters
installed, with exposure times ranging from 100 ms to 100 s. The primary goal
of the system is the detection of rapid -- with sub-second characteristic
time-scales -- optical transients, but it may be also used for studying the
variability of the sky objects on longer time scales.Comment: 9 pages, 9 figures, based on the talk presented on "Modern stellar
astronomy-2014" (Rostov-on-Don
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