Algebra, Analysis, and Associated Topics

Preface
Contents
Contributors
1 Maximal Rotational Hypersurfaces Having Spacelike Axis, Spacelike Profile Curve in Minkowski Geometry
	1.1 Introduction
	1.2 Preliminaries
	1.3 Spacelike Rotational Hypersurfaces Having Spacelike Axis, Spacelike Profile Curve
	1.4 Maximal Rotational Hypersurface Having Spacelike Axis, Spacelike Profile Curve Satisfying ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper Delta bold x equals script upper A bold x) /StPNE pdfmark [/StBMC pdfmarkx=Axps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
	1.5 Conclusion
	References
2 On the Generalized k-Horadam-Like Sequences
	2.1 Introduction
		2.1.1 The Catalan Transform
	2.2 Generalized k-Horadam Sequences
		2.2.1 Generalized k-Horadam Sequence of Second Order (When  h(k)=0 )
		2.2.2 Catalan Transformation and Generating Function
		2.2.3 The Hankel Transform
	2.3 Generalized k-Horadam Sequences of Order 3 (When h(k) ≠0 )
		2.3.1 Generating Function of Extended Generalized
k-Horadam Sequences {Hk,n}n∈N
		2.3.2 Binet Formula
		2.3.3 Binet Formula for Tribonacci Sequence by Direct Method
	References
3 
New Results on (p1,p2, ··· ,pn, k)
Analogue of Lauricella Function with
Transforms and Fractional Calculus
Operator
	3.1 Introduction
	3.2 (p1,p2, ··· ,pn, k) Analogue of Lauricella Function
	3.3 Integral Representations
	3.4 Integral Transforms
	3.5 Fractional Calculus
	3.6 Concluding Remarks
	References
4 Absolute Linear Method of Summation for Orthogonal Series
	4.1 Introduction
	4.2 Notable Results
	4.3 Main Results
	4.4 Proof of the Theorems
	4.5 Special Cases of the Main Theorems
		4.5.1 Case I: ϕ(n) = nγ (δ+1−1
k )
		4.5.2 Case II: ϕ(n) = n(δ+1−1
k )
		4.5.3 Case III [15] ϕ(n) = n1−1
k
		4.5.4 Case IV: ϕ(n) = n1−1
k and pv = 1 or qv = 1
	4.6 Conclusion
	References
5 Derivations and Special Functions Over Fields
	5.1 Basic Conventions
	5.2 Liouvillian Extensions
	5.3 Liouville's Theorem
	5.4 Error Functions
	5.5 Logarithmic Integrals
	5.6 Dilogarithmic Integrals
	References
6 On Equalities of Central Automorphism Group with Various Automorphism Groups
	6.1 Introduction
	6.2 Equalities of Central Automorphisms
		6.2.1 Equalities with Group of All Automorphisms
		6.2.2 Equalities with Group of Inn(G) and Z(Inn(G))
		6.2.3 Equalities with Class-Preserving Automorphisms
		6.2.4 Equalities with Absolute Central and IA Automorphisms
		6.2.5 Equalities with Central Automorphisms Fixing the Center Elementwise
	References
7 Automorphism Group and Laplacian Spectrum of a Graph Over Brandt Semigroups
	7.1 Introduction
	7.2 Premliminary
	7.3 Main Results
		7.3.1 Laplacian Spectrum of Pe(Bn)
		7.3.2 Distance Spectrum of Pe(Bn)
	References
8 Unified Iteration Scheme in CAT(0) Spaces and Fixed Point Approximation of Mean Nonexpansive Mappings
	8.1 Introduction
	8.2 Analysis of Existing Iteration Schemes and Unified Iteration Scheme
	8.3 Tools and Notations
	8.4 Definitions and Preliminaries
	8.5 Main Results
	References
9 Semigroups of Completely Positive Maps
	9.1 Hilbert Space Theory
	9.2 C*-Algebras
	9.3 von Neumann Algebras
	9.4 Completely Positive Maps
	9.5 One-Parameter Semigroups
		9.5.1 Strongly Continuous (C0)-Semigroups
	9.6 Quantum Dynamical Semigroups
	References
10 On Sumset Problems and Their Various Types
	10.1 Introduction
	10.2 Sum of Dilated Set of Integers
	10.3 An Approach to Cardinality of h(r)A
	10.4 Signed and Restricted Signed Sumset Problems
	10.5 Sumsets in Groups
	References
11 Vector-Valued Affine Bi-Frames on Local Fields
	11.1 Introduction
	11.2 The Auxiliary Results
	11.3 Main Results
	References
12 A New Perspective on I2-Statistical Limit Points and I2-Statistical Cluster Points in Probabilistic Normed Spaces
	12.1 Introduction
	12.2 Main Results
	12.3 Conclusion
	References
13 Evaluation of Integral Transforms in Terms of Humbert and Lauricella Functions and Their Applications
	13.1 Introduction and Preliminaries
	13.2 Main Results
	13.3 Special Cases
		13.3.1 Case of μ = −ν = 12
		13.3.2 Case of μ = ν = 12
		13.3.3 Let s = ∓r and ξ = −r − 12
		13.3.4 Case of s = ±

12
− r

and ξ = r
		13.3.5 Case of s = ±

a+1
2
+ b

and ξ = a
2
		13.3.6 Case of s=0 and ξ=r
		13.3.7 Case of s = 0 and ξ = 12
		13.3.8 Case of s = a + 14
and ξ = −14
		13.3.9 Case of s = a + 34
and ξ = 14
		13.3.10 Case of s = r − 12
and ξ = r
		13.3.11 Case of s = −14
and ξ = 14
	13.4 Numerical Simulations
	13.5 Application
	13.6 Conclusion
	References
14 Some Spaces in Neutrosophic e-Open Sets
	14.1 Introduction
	14.2 Preliminaries
	14.3 Neutrosophic e Connected Spaces
	14.4 Neutrosophic e Separated Sets
	14.5 Neutrosophic e Compact Spaces
	14.6 Conclusion
	Reference
15 Generalized Finite Continuous Ridgelet Transform
	15.1 Introduction
	15.2 Wμ,ν (I ) as Testing Function Space with Its Dual
W

μ,ν (I )
	15.3 Inversion Theorem
	15.4 Operational Calculus
	15.5 Applications
	References