- Zeitschriftendaten
- Format
- Zeitschrift
- eISSN
- 2300-133X
- Erstveröffentlichung
- 11 Dec 2014
- Erscheinungsweise
- 1 Hefte pro Jahr
- Sprachen
- Englisch

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Uneingeschränkter Zugang

#### An extensive note on various fractional-order type operators and some of their effects to certain holomorphic functions

Seitenbereich: 7 - 15

#### Zusammenfassung

The aim of this paper is to present background information in relation with some fractional-order type operators in the complex plane, which is designed by the fractional-order derivative operator(s). Next we state various implications of that operator and then we show some interesting-special results of those applications.

#### Schlüsselwörter

- complex plane
- holomorphic function
- series expansion
- fractional-order calculus
- operators in certain domains
- argument properties

Uneingeschränkter Zugang

#### Compactness of quadruple band matrix operator and geometric properties

Seitenbereich: 17 - 32

#### Zusammenfassung

In this work, we characterize the class of compact matrix operators from _{0}(_{∞} (_{0}, _{∞}, respectively, with the notion of the Hausdorff measure of noncompactness. Moreover, we determine some geometric properties of the sequence space _{p}

#### Schlüsselwörter

- matrix transformations
- matrix domain
- compact operators
- Hausdorff measure of noncompactness
- matrix classes

Uneingeschränkter Zugang

_{γµ} ℋ-compactness in GTS

_{γµ}

Seitenbereich: 33 - 42

#### Zusammenfassung

Using the notion of operations on a generalized topological space (_{γµ}_{γµ}_{γµ}_{γµ}

#### Schlüsselwörter

- -open set
- operation
- Hereditary class
- ℋ-compact

Uneingeschränkter Zugang

#### On Traczyk’s BCK-sequences

Seitenbereich: 43 - 49

#### Zusammenfassung

BCK-sequences and

#### Schlüsselwörter

- BCK-algebra
- BCK-sequence
- variety

Uneingeschränkter Zugang

#### A simpler method to get only the true solutions of cubic and quartic equations using Tschirnhaus transformation

Seitenbereich: 51 - 56

#### Zusammenfassung

The classic method of solving the cubic and the quartic equations using Tschirnhaus transformation yields true as well as false solutions. Recently some papers on this topic are published, in which methods are given to get only the true solutions of cubic and quartic equations. However these methods have some limitations. In this paper the author presents a method of solving cubic and quartic equations using Tschirnhaus transformation, which yields only the true solutions. The proposed method is much simpler than the methods published earlier.

#### Schlüsselwörter

- Tschirnhaus transformation
- true solutions
- cubic equations
- quartic equations
- false solutions

Uneingeschränkter Zugang

#### Solution to algebraic equations of degree 4 and the fundamental theorem of algebra by Carl Friedrich Gauss

Seitenbereich: 57 - 70

#### Zusammenfassung

Since

#### Schlüsselwörter

- Nonlinear algebraic equations
- Niccolo Tartaglia
- Johann Faulhaber
- resolvente
- fundamental theorem of algebra

Uneingeschränkter Zugang

#### On a certain characterisation of the semigroup of positive natural numbers with multiplication

Seitenbereich: 71 - 92

#### Zusammenfassung

In this paper we continue our investigation concerning the concept of a

#### Schlüsselwörter

- Beurling numbers
- distribution of prime numbers
- Cauchy translation equation
- numerical semigroups
- Apéry sets

Uneingeschränkter Zugang

#### Deductive systems of pseudo-M algebras

Seitenbereich: 93 - 116

#### Zusammenfassung

The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, pseudo-CI algebras and many other algebras of logic. In this paper, the notion of deductive system in a pseudo-M algebra is introduced and its elementary properties are investigated. Closed deductive systems are defined and studied. The homomorphic properties of (closed) deductive systems are provided. The concepts of translation deductive systems and R-congruences in pseudo-M algebras are introduced and investigated. It is shown that there is a bijection between closed translation deductive systems and R-congruences. Finally, the construction of quotient algebra 𝒜/

#### Schlüsselwörter

- pseudo-M
- pseudo-CI
- pseudo-BCH
- pseudo-BCK algebra
- (translation) deductive system
- congruence
- quotient algebra