On Spectral Properties of Matrices with Positive Characteristic Vectors

Canadian Journal of Mathematics ◽

10.4153/cjm-1968-133-1 ◽

1968 ◽

Vol 20 ◽

pp. 1332-1343

Author(s):

Kulendra N. Majindar

Keyword(s):

Spectral Properties ◽

Positive Characteristic ◽

Real Numbers

Unless stated otherwise, all our matrices (denoted by capital letters) are square matrices of size n × n and composed of real numbers. A' denotes the transpose of A. The characteristic or eigenvectors of matrices are written as column vectors having n coordinates. If ζ is a vector, ζ’ denotes its transpose.

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Hypertranscendental elements of a formal power-series ring of positive characteristic

Nagoya Mathematical Journal ◽

10.1017/s0027763000003913 ◽

1992 ◽

Vol 125 ◽

pp. 93-103 ◽

Cited By ~ 2

Author(s):

Kayoko Shikishima-Tsuji ◽

Masashi Katsura

Keyword(s):

Power Series ◽

Formal Power Series ◽

Positive Characteristic ◽

Rational Numbers ◽

Natural Numbers ◽

Real Numbers ◽

Power Series Ring ◽

Series Ring ◽

Formal Power Series Ring ◽

Formal Power

Throughout this paper, we denote by N, Q and R the set of all natural numbers containing 0, the set of all rational numbers, and the set of all real numbers, respectively.

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Quantitative properties of the non-properness set of a polynomial map, a positive characteristic case

Journal of Algebra and Its Applications ◽

10.1142/s0219498820501923 ◽

2019 ◽

Vol 19 (10) ◽

pp. 2050192

Author(s):

Zbigniew Jelonek ◽

Michał Lasoń

Keyword(s):

Upper Bound ◽

Positive Characteristic ◽

Manuscripta Math ◽

Geometric Proof ◽

Real Numbers ◽

Affine Spaces ◽

Polynomial Curves ◽

Polynomial Map ◽

Characteristic Case ◽

Quantitative Properties

Let [Formula: see text] be a generically finite polynomial map of degree [Formula: see text] between affine spaces. In [Z. Jelonek and M. Lasoń, Quantitative properties of the non-properness set of a polynomial map, Manuscripta Math. 156(3–4) (2018) 383–397] we proved that if [Formula: see text] is the field of complex or real numbers, then the set [Formula: see text] of points at which [Formula: see text] is not proper is covered by polynomial curves of degree at most [Formula: see text]. In this paper, we generalize this result to positive characteristic. We provide a geometric proof of an upper bound by [Formula: see text].

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A version of p-adic minimality

Journal of Symbolic Logic ◽

10.2178/jsl/1333566641 ◽

2012 ◽

Vol 77 (2) ◽

pp. 621-630 ◽

Cited By ~ 5

Author(s):

Raf Cluckers ◽

Eva Leenknegt

Keyword(s):

Positive Characteristic ◽

Quantifier Elimination ◽

Cell Decomposition ◽

Real Numbers ◽

Valued Fields ◽

The Real ◽

Definable Sets ◽

A Cell ◽

Definable Functions

AbstractWe introduce a very weak language on p-adic fields K, which is just rich enough to have exactly the same definable subsets of the line K that one has using the ring language. (In our context, definable always means definable with parameters.) We prove that the only definable functions in the language are trivial functions. We also give a definitional expansion of in which K has quantifier elimination, and we obtain a cell decomposition result for -definable sets.Our language can serve as a p-adic analogue of the very weak language (<) on the real numbers, to define a notion of minimality on the field of p-adic numbers and on related valued fields. These fields are not necessarily Henselian and may have positive characteristic.

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Model of multicomponent narrow-band periodical non-stationary random signal

Information extraction and processing ◽

10.15407/vidbir2020.48.017 ◽

2020 ◽

Vol 2020 (48) ◽

pp. 17-24

Author(s):

I.M. Javorskyj ◽

◽

R.M. Yuzefovych ◽

P.R. Kurapov ◽

◽

...

Keyword(s):

Time Series ◽

Real Time ◽

Hilbert Transform ◽

Spectral Properties ◽

Narrow Band ◽

Analytic Signal ◽

Random Signal ◽

Hilbert Transformation ◽

The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

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