scholarly journals On Semi- c -Periodic Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
M. T. Khalladi ◽  
M. Kostić ◽  
M. Pinto ◽  
A. Rahmani ◽  
D. Velinov
Keyword(s):  
Complex Number ◽  
Periodic Functions ◽  
Absolute Value ◽  
Nonzero Complex Number

The main aim of this paper is to indicate that the notion of semi- c -periodicity is equivalent with the notion of c -periodicity, provided that c is a nonzero complex number whose absolute value is not equal to 1.

scholarly journals On lp-Complex Numbers

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 877
Author(s):  
Wolf-Dieter Richter
Keyword(s):  
Symmetry Group ◽  
Complex Number ◽  
Common Property ◽  
Complex Numbers ◽  
Trigonometric Functions ◽  
Absolute Value ◽  
Basic Properties ◽  
The Common

Dispensing with the common property of distributivity and replacing classical trigonometric functions with their l p -counterparts in Euler’s trigonometric representation of complex numbers, classes of l p -complex numbers are introduced and some of their basic properties are proved. The collection of all points that leave the l p -absolute value of each l p -complex number invariant under l p -complex numbers multiplication is shown to be a group of elements that have l p -absolute value one but not the symmetry group.

scholarly journals Expressions for the g-Drazin inverse in a Banach algebra

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3845-3854
Author(s):  
Huanyin Chen ◽  
Marjan Sheibani
Keyword(s):  
Banach Algebra ◽  
Complex Number ◽  
Block Matrix ◽  
Explicit Representation ◽  
Drazin Inverse ◽  
Operator Matrices ◽  
Nonzero Complex Number ◽  
Generalized Drazin Inverse

We explore the generalized Drazin inverse in a Banach algebra. Let A be a Banach algebra, and let a,b ? Ad. If ab = ?a?bab? for a nonzero complex number ?, then a + b ? Ad. The explicit representation of (a + b)d is presented. As applications of our results, we present new representations for the generalized Drazin inverse of a block matrix in a Banach algebra. The main results of Liu and Qin [Representations for the generalized Drazin inverse of the sum in a Banach algebra and its application for some operator matrices, Sci. World J., 2015, 156934.8] are extended.

ON REAL PARTS OF POWERS OF COMPLEX PISOT NUMBERS

2016 ◽  
Vol 94 (2) ◽  
pp. 245-253 ◽  
Author(s):  
TOUFIK ZAÏMI
Keyword(s):  
Finite Number ◽  
Algebraic Number ◽  
Complex Number ◽  
Convergent Sequence ◽  
Pisot Number ◽  
Pisot Numbers ◽  
Limit Points ◽  
Nonzero Complex Number

We prove that a nonreal algebraic number $\unicode[STIX]{x1D703}$ with modulus greater than $1$ is a complex Pisot number if and only if there is a nonzero complex number $\unicode[STIX]{x1D706}$ such that the sequence of fractional parts $(\{\Re (\unicode[STIX]{x1D706}\unicode[STIX]{x1D703}^{n})\})_{n\in \mathbb{N}}$ has a finite number of limit points. Also, we characterise those complex Pisot numbers $\unicode[STIX]{x1D703}$ for which there is a convergent sequence of the form $(\{\Re (\unicode[STIX]{x1D706}\unicode[STIX]{x1D703}^{n})\})_{n\in \mathbb{N}}$ for some $\unicode[STIX]{x1D706}\in \mathbb{C}^{\ast }$. These results are generalisations of the corresponding real ones, due to Pisot, Vijayaraghavan and Dubickas.

scholarly journals COLORED JONES POLYNOMIALS WITH POLYNOMIAL GROWTH

2008 ◽  
Vol 10 (supp01) ◽  
pp. 815-834 ◽  
Author(s):  
KAZUHIRO HIKAMI ◽  
HITOSHI MURAKAMI
Keyword(s):  
Irreducible Representation ◽  
Complex Number ◽  
Polynomial Growth ◽  
Jones Polynomial ◽  
The Other ◽  
Absolute Value ◽  
Volume Conjecture ◽  
Jones Polynomials ◽  
Dimensional Irreducible Representation ◽  
Colored Jones Polynomials

The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;ℂ) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near [Formula: see text]. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alexander polynomial evaluated at exp c. In this paper we study cases where it grows polynomially.

ALGEBRAIC INDEPENDENCE OF CERTAIN MAHLER FUNCTIONS AND OF THEIR VALUES

2014 ◽  
Vol 98 (3) ◽  
pp. 289-310 ◽  
Author(s):  
PETER BUNDSCHUH ◽  
KEIJO VÄÄNÄNEN
Keyword(s):  
Rational Function ◽  
Complex Number ◽  
Functional Equations ◽  
Algebraic Independence ◽  
Lucas Numbers ◽  
Mahler Functions ◽  
Independence Results ◽  
Nonzero Complex Number ◽  
Fibonacci And Lucas Numbers ◽  
Reciprocal Sums

This paper considers algebraic independence and hypertranscendence of functions satisfying Mahler-type functional equations $af(z^{r})=f(z)+R(z)$, where $a$ is a nonzero complex number, $r$ an integer greater than 1, and $R(z)$ a rational function. Well-known results from the scope of Mahler’s method then imply algebraic independence over the rationals of the values of these functions at algebraic points. As an application, algebraic independence results on reciprocal sums of Fibonacci and Lucas numbers are obtained.

On the Skitovich–Darmois theorem for complex and quaternion random variables

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Gennadiy Feldman
Keyword(s):  
Complex Number ◽  
Random Variables ◽  
Wide Sense ◽  
Narrow Sense ◽  
Gaussian Random Variables ◽  
Linear Forms ◽  
Nonzero Complex Number

AbstractWe prove the following theorem. Let {\alpha=a+ib} be a nonzero complex number. Then the following statements hold: (i) Let either {b\neq 0} or {b=0} and {a>0}. Let {\xi_{1}} and {\xi_{2}} be independent complex random variables. Assume that the linear forms {L_{1}=\xi_{1}+\xi_{2}} and {L_{2}=\xi_{1}+\alpha\xi_{2}} are independent. Then {\xi_{j}} are degenerate random variables. (ii) Let {b=0} and {a<0}. Then there exist complex Gaussian random variables in the wide sense {\xi_{1}} and {\xi_{2}} such that they are not complex Gaussian random variables in the narrow sense, whereas the linear forms {L_{1}=\xi_{1}+\xi_{2}} and {L_{2}=\xi_{1}+\alpha\xi_{2}} are independent.

scholarly journals Fixed points of differences of meromorphic functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zhaojun Wu ◽  
Jia Wu
Keyword(s):  
Meromorphic Function ◽  
Fixed Points ◽  
Finite Order ◽  
Complex Number ◽  
Meromorphic Functions ◽  
Acta Math ◽  
Transcendental Meromorphic Function ◽  
Nonzero Complex Number ◽  
Discrete Analogues

Abstract Let f be a transcendental meromorphic function of finite order and c be a nonzero complex number. Define $\Delta _{c}f=f(z+c)-f(z)$ Δ c f = f ( z + c ) − f ( z ) . The authors investigate the existence on the fixed points of $\Delta _{c}f$ Δ c f . The results obtained in this paper may be viewed as discrete analogues on the existing theorem on the fixed points of $f'$ f ′ . The existing theorem on the fixed points of $\Delta _{c}f$ Δ c f generalizes the relevant results obtained by (Chen in Ann. Pol. Math. 109(2):153–163, 2013; Zhang and Chen in Acta Math. Sin. New Ser. 32(10):1189–1202, 2016; Cui and Yang in Acta Math. Sci. 33B(3):773–780, 2013) et al.

scholarly journals Linear mappings preserving square-zero matrices

1993 ◽  
Vol 48 (3) ◽  
pp. 365-370 ◽  
Author(s):  
Peter Šemrl
Keyword(s):  
Complex Number ◽  
Linear Mapping ◽  
Dimensional Case ◽  
Complex Matrices ◽  
Infinite Dimensional ◽  
Nonzero Complex Number

Let sln denote the set of all n × n complex matrices with trace zero. Suppose that ø: sln → sln is a bijective linear mapping preserving square-zero matrices. Then ø is either of the form ø(A) = cUAU-1 or ø(A) = cUAtU-1 where U is an invertible n × n matrix and c is a nonzero complex number. The same result holds if we assume that ø is a linear mapping preserving square-zero matrices in both directions. Applying this result we prove that a linear mapping ø defined on the algebra of all n × n matrices is an automorphism if and only if it preserves zero products in both directions and satisfies ø(I) = I. An extension of this last result to the infinite-dimensional case is considered.

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