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