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Showing 1 - 200 of 2351 Journals sorted alphabetically
3D Research     Hybrid Journal   (Followers: 19, SJR: 0.214, h-index: 10)
4OR: A Quarterly J. of Operations Research     Hybrid Journal   (Followers: 10, SJR: 1.073, h-index: 25)
AAPS J.     Hybrid Journal   (Followers: 22, SJR: 1.192, h-index: 74)
AAPS PharmSciTech     Hybrid Journal   (Followers: 7, SJR: 0.718, h-index: 54)
Abdominal Imaging     Hybrid Journal   (Followers: 14, SJR: 0.723, h-index: 60)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3, SJR: 0.447, h-index: 12)
Academic Psychiatry     Full-text available via subscription   (Followers: 23, SJR: 0.492, h-index: 32)
Academic Questions     Hybrid Journal   (Followers: 8, SJR: 0.135, h-index: 6)
Accreditation and Quality Assurance: J. for Quality, Comparability and Reliability in Chemical Measurement     Hybrid Journal   (Followers: 26, SJR: 0.378, h-index: 30)
Acoustical Physics     Hybrid Journal   (Followers: 11, SJR: 0.355, h-index: 20)
Acoustics Australia     Hybrid Journal  
Acta Analytica     Hybrid Journal   (Followers: 7, SJR: 0.387, h-index: 6)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1, SJR: 0.624, h-index: 34)
Acta Biotheoretica     Hybrid Journal   (Followers: 4, SJR: 0.419, h-index: 25)
Acta Diabetologica     Hybrid Journal   (Followers: 16, SJR: 1.318, h-index: 46)
Acta Endoscopica     Hybrid Journal   (Followers: 1, SJR: 0.113, h-index: 8)
acta ethologica     Hybrid Journal   (Followers: 4, SJR: 0.465, h-index: 23)
Acta Geochimica     Hybrid Journal   (Followers: 7)
Acta Geodaetica et Geophysica     Hybrid Journal   (Followers: 2, SJR: 0.294, h-index: 13)
Acta Geotechnica     Hybrid Journal   (Followers: 7, SJR: 1.818, h-index: 22)
Acta Informatica     Hybrid Journal   (Followers: 5, SJR: 0.524, h-index: 32)
Acta Mathematica     Hybrid Journal   (Followers: 11, SJR: 8.021, h-index: 47)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2, SJR: 0.53, h-index: 29)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6, SJR: 0.406, h-index: 30)
Acta Mathematica Vietnamica     Hybrid Journal   (SJR: 0.451, h-index: 5)
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal   (SJR: 0.22, h-index: 20)
Acta Mechanica     Hybrid Journal   (Followers: 20, SJR: 0.898, h-index: 52)
Acta Mechanica Sinica     Hybrid Journal   (Followers: 5, SJR: 0.426, h-index: 29)
Acta Metallurgica Sinica (English Letters)     Hybrid Journal   (Followers: 6, SJR: 0.525, h-index: 18)
Acta Meteorologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.524, h-index: 14)
Acta Neurochirurgica     Hybrid Journal   (Followers: 6, SJR: 0.833, h-index: 73)
Acta Neurologica Belgica     Hybrid Journal   (Followers: 1, SJR: 0.348, h-index: 27)
Acta Neuropathologica     Hybrid Journal   (Followers: 5, SJR: 6.61, h-index: 117)
Acta Oceanologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.295, h-index: 17)
Acta Parasitologica     Hybrid Journal   (Followers: 10, SJR: 0.581, h-index: 28)
Acta Physiologiae Plantarum     Hybrid Journal   (Followers: 2, SJR: 0.551, h-index: 39)
Acta Politica     Hybrid Journal   (Followers: 13, SJR: 0.658, h-index: 20)
Activitas Nervosa Superior     Hybrid Journal  
adhäsion KLEBEN & DICHTEN     Hybrid Journal   (Followers: 5, SJR: 0.103, h-index: 4)
ADHD Attention Deficit and Hyperactivity Disorders     Hybrid Journal   (Followers: 23, SJR: 0.871, h-index: 15)
Adhesion Adhesives & Sealants     Hybrid Journal   (Followers: 8)
Administration and Policy in Mental Health and Mental Health Services Research     Partially Free   (Followers: 15, SJR: 0.795, h-index: 40)
Adsorption     Hybrid Journal   (Followers: 4, SJR: 0.774, h-index: 52)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3, SJR: 0.319, h-index: 15)
Advances in Atmospheric Sciences     Hybrid Journal   (Followers: 35, SJR: 0.959, h-index: 44)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18, SJR: 1.255, h-index: 44)
Advances in Contraception     Hybrid Journal   (Followers: 3)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 54, SJR: 1.113, h-index: 14)
Advances in Gerontology     Partially Free   (Followers: 8, SJR: 0.141, h-index: 3)
Advances in Health Sciences Education     Hybrid Journal   (Followers: 25, SJR: 1.397, h-index: 42)
Advances in Manufacturing     Hybrid Journal   (Followers: 3, SJR: 0.2, h-index: 4)
Advances in Polymer Science     Hybrid Journal   (Followers: 43, SJR: 0.637, h-index: 89)
Advances in Therapy     Hybrid Journal   (Followers: 5, SJR: 0.79, h-index: 44)
Aegean Review of the Law of the Sea and Maritime Law     Hybrid Journal   (Followers: 7)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2, SJR: 0.882, h-index: 23)
Aerobiologia     Hybrid Journal   (Followers: 2, SJR: 0.511, h-index: 36)
Aesthetic Plastic Surgery     Hybrid Journal   (Followers: 9, SJR: 0.821, h-index: 49)
African Archaeological Review     Hybrid Journal   (Followers: 16, SJR: 0.612, h-index: 24)
Afrika Matematika     Hybrid Journal   (Followers: 1, SJR: 0.248, h-index: 6)
AGE     Hybrid Journal   (Followers: 7, SJR: 1.358, h-index: 33)
Ageing Intl.     Hybrid Journal   (Followers: 7, SJR: 0.337, h-index: 10)
Aggiornamenti CIO     Hybrid Journal   (Followers: 1)
Aging Clinical and Experimental Research     Hybrid Journal   (Followers: 2, SJR: 0.529, h-index: 55)
Agricultural Research     Hybrid Journal   (Followers: 4)
Agriculture and Human Values     Hybrid Journal   (Followers: 14, SJR: 1.197, h-index: 49)
Agroforestry Systems     Hybrid Journal   (Followers: 19, SJR: 0.64, h-index: 56)
Agronomy for Sustainable Development     Hybrid Journal   (Followers: 11, SJR: 1.732, h-index: 59)
AI & Society     Hybrid Journal   (Followers: 6, SJR: 0.171, h-index: 19)
AIDS and Behavior     Hybrid Journal   (Followers: 13, SJR: 2.006, h-index: 71)
Air Quality, Atmosphere & Health     Hybrid Journal   (Followers: 4, SJR: 0.706, h-index: 19)
Akupunktur & Aurikulomedizin     Full-text available via subscription   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 4, SJR: 0.566, h-index: 18)
Algebra Universalis     Hybrid Journal   (Followers: 2, SJR: 0.388, h-index: 22)
Algebras and Representation Theory     Hybrid Journal   (Followers: 1, SJR: 0.868, h-index: 20)
Algorithmica     Hybrid Journal   (Followers: 8, SJR: 0.898, h-index: 56)
Allergo J.     Full-text available via subscription   (Followers: 1, SJR: 0.183, h-index: 20)
Allergo J. Intl.     Hybrid Journal   (Followers: 2)
Alpine Botany     Hybrid Journal   (Followers: 5, SJR: 0.729, h-index: 20)
ALTEX : Alternatives to Animal Experimentation     Open Access   (Followers: 3, SJR: 1.392, h-index: 32)
AMBIO     Hybrid Journal   (Followers: 15, SJR: 1.094, h-index: 87)
American J. of Cardiovascular Drugs     Hybrid Journal   (Followers: 16, SJR: 0.864, h-index: 39)
American J. of Community Psychology     Hybrid Journal   (Followers: 26, SJR: 1.237, h-index: 83)
American J. of Criminal Justice     Hybrid Journal   (Followers: 8, SJR: 0.634, h-index: 13)
American J. of Cultural Sociology     Hybrid Journal   (Followers: 15, SJR: 0.283, h-index: 3)
American J. of Dance Therapy     Hybrid Journal   (Followers: 4, SJR: 0.175, h-index: 13)
American J. of Potato Research     Hybrid Journal   (Followers: 3, SJR: 0.558, h-index: 35)
American J. of Psychoanalysis     Hybrid Journal   (Followers: 22, SJR: 0.293, h-index: 13)
American Sociologist     Hybrid Journal   (Followers: 14, SJR: 0.18, h-index: 13)
Amino Acids     Hybrid Journal   (Followers: 8, SJR: 1.362, h-index: 83)
AMS Review     Partially Free   (Followers: 4)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 7, SJR: 0.21, h-index: 37)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4, SJR: 0.665, h-index: 7)
Analysis in Theory and Applications     Hybrid Journal   (Followers: 1)
Analysis of Verbal Behavior     Hybrid Journal   (Followers: 5)
Analytical and Bioanalytical Chemistry     Hybrid Journal   (Followers: 31, SJR: 1.096, h-index: 123)
Anatomical Science Intl.     Hybrid Journal   (Followers: 2, SJR: 0.301, h-index: 26)
Angewandte Schmerztherapie und Palliativmedizin     Hybrid Journal  
Angiogenesis     Hybrid Journal   (Followers: 3, SJR: 2.212, h-index: 69)
Animal Cognition     Hybrid Journal   (Followers: 17, SJR: 1.122, h-index: 55)
Annales françaises de médecine d'urgence     Hybrid Journal   (Followers: 1, SJR: 0.156, h-index: 4)
Annales Henri Poincaré     Hybrid Journal   (Followers: 3, SJR: 1.377, h-index: 32)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annali dell'Universita di Ferrara     Hybrid Journal   (SJR: 0.504, h-index: 14)
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1, SJR: 1.167, h-index: 26)
Annals of Behavioral Medicine     Hybrid Journal   (Followers: 14, SJR: 2.112, h-index: 98)
Annals of Biomedical Engineering     Hybrid Journal   (Followers: 18, SJR: 1.182, h-index: 94)
Annals of Combinatorics     Hybrid Journal   (Followers: 3, SJR: 0.849, h-index: 15)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Dyslexia     Hybrid Journal   (Followers: 10, SJR: 0.857, h-index: 40)
Annals of Finance     Hybrid Journal   (Followers: 28, SJR: 0.686, h-index: 14)
Annals of Forest Science     Hybrid Journal   (Followers: 6, SJR: 0.929, h-index: 57)
Annals of Global Analysis and Geometry     Hybrid Journal   (Followers: 1, SJR: 1.136, h-index: 23)
Annals of Hematology     Hybrid Journal   (Followers: 16, SJR: 1.117, h-index: 62)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12, SJR: 0.593, h-index: 42)
Annals of Microbiology     Hybrid Journal   (Followers: 10, SJR: 0.402, h-index: 26)
Annals of Nuclear Medicine     Hybrid Journal   (Followers: 4, SJR: 0.68, h-index: 45)
Annals of Operations Research     Hybrid Journal   (Followers: 10, SJR: 1.186, h-index: 78)
Annals of Ophthalmology     Hybrid Journal   (Followers: 12)
Annals of Regional Science     Hybrid Journal   (Followers: 8, SJR: 0.405, h-index: 42)
Annals of Software Engineering     Hybrid Journal   (Followers: 13)
Annals of Solid and Structural Mechanics     Hybrid Journal   (Followers: 10, SJR: 0.553, h-index: 8)
Annals of Surgical Oncology     Hybrid Journal   (Followers: 14, SJR: 1.902, h-index: 127)
Annals of Telecommunications     Hybrid Journal   (Followers: 8, SJR: 0.315, h-index: 25)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1, SJR: 0.931, h-index: 31)
Antonie van Leeuwenhoek     Hybrid Journal   (Followers: 5, SJR: 0.992, h-index: 87)
Apidologie     Hybrid Journal   (Followers: 4, SJR: 1.14, h-index: 57)
APOPTOSIS     Hybrid Journal   (Followers: 8, SJR: 1.554, h-index: 87)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2, SJR: 0.354, h-index: 27)
Applications of Mathematics     Hybrid Journal   (Followers: 1, SJR: 0.274, h-index: 20)
Applied Biochemistry and Biotechnology     Hybrid Journal   (Followers: 42, SJR: 0.575, h-index: 80)
Applied Biochemistry and Microbiology     Hybrid Journal   (Followers: 16, SJR: 0.267, h-index: 26)
Applied Cancer Research     Open Access  
Applied Categorical Structures     Hybrid Journal   (Followers: 2, SJR: 0.361, h-index: 21)
Applied Composite Materials     Hybrid Journal   (Followers: 48, SJR: 0.705, h-index: 35)
Applied Entomology and Zoology     Partially Free   (Followers: 3, SJR: 0.554, h-index: 34)
Applied Geomatics     Hybrid Journal   (Followers: 4, SJR: 0.323, h-index: 9)
Applied Geophysics     Hybrid Journal   (Followers: 8, SJR: 0.541, h-index: 13)
Applied Intelligence     Hybrid Journal   (Followers: 11, SJR: 0.777, h-index: 43)
Applied Magnetic Resonance     Hybrid Journal   (Followers: 4, SJR: 0.358, h-index: 34)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6, SJR: 0.955, h-index: 33)
Applied Mathematics - A J. of Chinese Universities     Hybrid Journal   (SJR: 0.275, h-index: 8)
Applied Mathematics and Mechanics     Hybrid Journal   (Followers: 5, SJR: 0.37, h-index: 26)
Applied Microbiology and Biotechnology     Hybrid Journal   (Followers: 62, SJR: 1.262, h-index: 161)
Applied Physics A     Hybrid Journal   (Followers: 8, SJR: 0.535, h-index: 121)
Applied Physics B: Lasers and Optics     Hybrid Journal   (Followers: 24, SJR: 0.983, h-index: 104)
Applied Psychophysiology and Biofeedback     Hybrid Journal   (Followers: 8, SJR: 0.677, h-index: 47)
Applied Research in Quality of Life     Hybrid Journal   (Followers: 11, SJR: 0.288, h-index: 15)
Applied Solar Energy     Hybrid Journal   (Followers: 18, SJR: 0.251, h-index: 6)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5, SJR: 0.351, h-index: 9)
Aquaculture Intl.     Hybrid Journal   (Followers: 22, SJR: 0.613, h-index: 40)
Aquarium Sciences and Conservation     Hybrid Journal   (Followers: 1)
Aquatic Ecology     Hybrid Journal   (Followers: 32, SJR: 0.646, h-index: 44)
Aquatic Geochemistry     Hybrid Journal   (Followers: 4, SJR: 0.764, h-index: 39)
Aquatic Sciences     Hybrid Journal   (Followers: 13, SJR: 1.172, h-index: 53)
Arabian J. for Science and Engineering     Hybrid Journal   (Followers: 5, SJR: 0.345, h-index: 20)
Arabian J. of Geosciences     Hybrid Journal   (Followers: 1, SJR: 0.417, h-index: 16)
Archaeological and Anthropological Sciences     Hybrid Journal   (Followers: 23, SJR: 1.056, h-index: 15)
Archaeologies     Hybrid Journal   (Followers: 12, SJR: 0.397, h-index: 13)
Archiv der Mathematik     Hybrid Journal   (Followers: 1, SJR: 0.597, h-index: 29)
Archival Science     Hybrid Journal   (Followers: 56, SJR: 0.804, h-index: 22)
Archive for History of Exact Sciences     Hybrid Journal   (Followers: 8, SJR: 0.28, h-index: 15)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1, SJR: 0.946, h-index: 23)
Archive for Rational Mechanics and Analysis     Hybrid Journal   (SJR: 4.091, h-index: 66)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5, SJR: 0.865, h-index: 40)
Archives and Museum Informatics     Hybrid Journal   (Followers: 142)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5, SJR: 2.841, h-index: 40)
Archives of Dermatological Research     Hybrid Journal   (Followers: 7, SJR: 0.9, h-index: 65)
Archives of Environmental Contamination and Toxicology     Hybrid Journal   (Followers: 13, SJR: 0.846, h-index: 84)
Archives of Gynecology and Obstetrics     Hybrid Journal   (Followers: 16, SJR: 0.695, h-index: 47)
Archives of Microbiology     Hybrid Journal   (Followers: 8, SJR: 0.702, h-index: 85)
Archives of Orthopaedic and Trauma Surgery     Hybrid Journal   (Followers: 8, SJR: 1.039, h-index: 56)
Archives of Osteoporosis     Hybrid Journal   (Followers: 2, SJR: 1.092, h-index: 13)
Archives of Sexual Behavior     Hybrid Journal   (Followers: 10, SJR: 1.198, h-index: 74)
Archives of Toxicology     Hybrid Journal   (Followers: 17, SJR: 1.595, h-index: 76)
Archives of Virology     Hybrid Journal   (Followers: 5, SJR: 1.086, h-index: 90)
Archives of Women's Mental Health     Hybrid Journal   (Followers: 14, SJR: 1.264, h-index: 50)
Archivio di Ortopedia e Reumatologia     Hybrid Journal  
Archivum Immunologiae et Therapiae Experimentalis     Hybrid Journal   (Followers: 2, SJR: 1.2, h-index: 42)
ArgoSpine News & J.     Hybrid Journal   (SJR: 0.102, h-index: 3)
Argumentation     Hybrid Journal   (Followers: 5, SJR: 0.295, h-index: 18)
Arid Ecosystems     Hybrid Journal   (Followers: 3)
Arkiv för Matematik     Hybrid Journal   (Followers: 1, SJR: 0.948, h-index: 22)
Arnold Mathematical J.     Hybrid Journal   (Followers: 1)
Arthropod-Plant Interactions     Hybrid Journal   (Followers: 2, SJR: 0.797, h-index: 17)
Arthroskopie     Hybrid Journal   (Followers: 1, SJR: 0.145, h-index: 8)
Artificial Intelligence and Law     Hybrid Journal   (Followers: 11, SJR: 0.288, h-index: 25)
Artificial Intelligence Review     Hybrid Journal   (Followers: 14, SJR: 0.948, h-index: 48)
Artificial Life and Robotics     Hybrid Journal   (Followers: 8, SJR: 0.231, h-index: 14)
Asia Europe J.     Hybrid Journal   (Followers: 5, SJR: 0.247, h-index: 9)
Asia Pacific Education Review     Hybrid Journal   (Followers: 12, SJR: 0.371, h-index: 17)
Asia Pacific J. of Management     Hybrid Journal   (Followers: 16, SJR: 1.676, h-index: 50)
Asia-Pacific Education Researcher     Hybrid Journal   (Followers: 12, SJR: 0.353, h-index: 13)
Asia-Pacific Financial Markets     Hybrid Journal   (Followers: 2, SJR: 0.19, h-index: 15)
Asia-Pacific J. of Atmospheric Sciences     Hybrid Journal   (Followers: 20, SJR: 1.006, h-index: 14)
Asian Business & Management     Hybrid Journal   (Followers: 8, SJR: 0.41, h-index: 10)
Asian J. of Business Ethics     Hybrid Journal   (Followers: 8)
Asian J. of Criminology     Hybrid Journal   (Followers: 5, SJR: 0.263, h-index: 8)
AStA Advances in Statistical Analysis     Hybrid Journal   (Followers: 2, SJR: 0.681, h-index: 15)
AStA Wirtschafts- und Sozialstatistisches Archiv     Hybrid Journal   (Followers: 5, SJR: 0.195, h-index: 5)
ästhetische dermatologie & kosmetologie     Full-text available via subscription  

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Journal Cover Advances in Applied Clifford Algebras
  [SJR: 0.319]   [H-I: 15]   [3 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1661-4909 - ISSN (Online) 0188-7009
   Published by Springer-Verlag Homepage  [2351 journals]
  • Generalization of Superalgebras to Color Superalgebras and Their
    • Authors: Naruhiko Aizawa
      Abstract: For a given Lie superalgebra, two ways of constructing color superalgebras are presented. One of them is based on the color superalgebraic nature of the Clifford algebras. The method is applicable to any Lie superalgebras and results in color superalgebra of \( {\mathbb Z}_2^{\otimes N} \) grading. The other is discussed with an example, a superalgebra of boson and fermion operators. By treating the boson operators as “second” fermionic sector we obtain a color superalgebra of \({\mathbb Z}_2 \otimes {\mathbb Z}_2\) grading. A vector field representation of the color superalgebra obtained from the boson–fermion system is also presented.
      PubDate: 2018-02-26
      DOI: 10.1007/s00006-018-0847-x
      Issue No: Vol. 28, No. 1 (2018)
  • Symplectic Field Theories: Scalar and Spinor Representations
    • Authors: Caroline Costa; Marcia R. Tenser; Ronni G. G. Amorim; Marco C. B. Fernandes; Ademir E. Santana; J. David M. Vianna
      Abstract: Using elements of symmetry, as gauge invariance, aspects of field theories represented in symplectic space are introduced and analyzed under physical bases. The states of a system are described by symplectic wave functions, which are associated with the Wigner function. Such wave functions are vectors in a Hilbert space introduced from the cotangent-bundle of the Minkowski space. The symplectic Klein–Gordon and the Dirac equations are derived, and a minimum coupling is considered in order to analyze the Landau problem in phase space.
      PubDate: 2018-02-26
      DOI: 10.1007/s00006-018-0840-4
      Issue No: Vol. 28, No. 1 (2018)
  • The Monogenic Cauchy–Kovalevskaya Extension in Two Vector Variables
    • Authors: David Eelbode; Tim Janssens; Matthias Roels
      Abstract: The Cauchy–Kovalevskaya extension for polynomials in several variables is a crucial result in Clifford analysis which describes theoretically how to construct simplicial monogenics in m dimensions starting from certain polynomial spaces in \(m-1\) dimensions, hereby using the so-called branching rules. In [13] it was shown that the Cauchy–Kovalevskaya extension map is an isomorphism of the kernel of the wedge operator onto the space of spherical monogenics in two variables. The aim of this paper is to show that this extension maps simplicial polynomials of the kernel of the wedge operator just onto the simplicial monogenics.
      PubDate: 2018-02-24
      DOI: 10.1007/s00006-018-0846-y
      Issue No: Vol. 28, No. 1 (2018)
  • The Hyperbolic Spinor Representation of Transformations in $$\mathbb
           {R}_1^3$$ R 1 3 by Means of Split Quaternions
    • Authors: Mustafa Tarakçioğlu; Tülay Erişir; Mehmet Ali Güngör; Murat Tosun
      Abstract: In this study, firstly, we give a different approach to the relationship between the split quaternions and rotations in Minkowski space \(\mathbb {R}_1^3\) . In addition, we obtain an automorphism of the split quaternion algebra \(H'\) corresponding to a rotation in \(\mathbb {R}_1^3\) . Then, we give the relationship between the hyperbolic spinors and rotations in \(\mathbb {R}_1^3\) . Finally, we associate to a split quaternion with a hyperbolic spinor by means of a transformation. In this way, we show that the rotation of a rigid body in the Minkowski 3-space \(\mathbb {R}_1^3\) expressed the split quaternions can be written by means of the hyperbolic spinors with two hyperbolic components. So, we obtain a new and short representation (hyperbolic spinor representation) of transformation in the 3-dimensional Minkowski space \(\mathbb {R}_1^3\) expressed by means of split quaternions.
      PubDate: 2018-02-24
      DOI: 10.1007/s00006-018-0844-0
      Issue No: Vol. 28, No. 1 (2018)
  • Bilinear Forms Derived from Lipschitzian Elements in Clifford Algebras
    • Authors: Jacques Helmstetter
      Abstract: In every Clifford algebra \({\mathrm {Cl}}(V,q)\) , there is a Lipschitz monoid (or semi-group) \({\mathrm {Lip}}(V,q)\) , which is in most cases the monoid generated by the vectors of V. This monoid is useful for many reasons, not only because of the natural homomorphism from the group \({\mathrm {GLip}}(V,q)\) of its invertible elements onto the group \({\mathrm {O}}(V,q)\) of orthogonal transformations. From every non-zero \(a\in {\mathrm {Lip}}(V,q)\) , we can derive a bilinear form \(\phi \) on the support S of a in V; it is q-compatible: \(\phi (x,x)=q(x)\) for all \(x\in S\) . Conversely, every q-compatible bilinear form on a subspace S of V can be derived from an element \(a\in {\mathrm {Lip}}(V,q)\) which is unique up to an invertible scalar; and a is invertible if and only if \(\phi \) is non-degenerate. This article studies the relations between a, \(\phi \) and (when a is invertible) the orthogonal transformation g derived from a; it provides both theoretical knowledge and algorithms. It provides an effective tool for the factorization of lipschitzian elements, based on this theorem: if \((v_1,v_2,\ldots ,v_s)\) is a basis of S, then \(a=\kappa \,v_1v_2\ldots v_s\) (for some invertible scalar \(\kappa \) ) if and only if the matrix of \(\phi \) in this basis is lower triangular. This theorem is supported by an algorithm of triangularization of bilinear forms.
      PubDate: 2018-02-24
      DOI: 10.1007/s00006-018-0842-2
      Issue No: Vol. 28, No. 1 (2018)
  • Determinantal Representations of Solutions to Systems of Quaternion Matrix
    • Authors: Ivan Kyrchei
      Abstract: Within the framework of the theory of quaternion column–row determinants and using determinantal representations of the Moore–Penrose inverse previously obtained by the author, we get explicit determinantal representation formulas of solutions (analogs of Cramer’s rule) to the systems of quaternion matrix equations \( \mathbf{A}_{1}{} \mathbf{X}=\mathbf{C}_{1}\) , \( \mathbf{X}\mathbf{B}_{2}=\mathbf{C}_{2} \) , and \( \mathbf{A}_{1}{} \mathbf{X}=\mathbf{C}_{1}\) , \(\mathbf{A}_{2} \mathbf{X}=\mathbf{C}_{2} \) .
      PubDate: 2018-02-23
      DOI: 10.1007/s00006-018-0843-1
      Issue No: Vol. 28, No. 1 (2018)
  • Discretization of Maxwell’s Equations for Non-inertial Observers
           Using Space-Time Algebra
    • Authors: Mariusz Klimek; Stefan Kurz; Sebastian Schöps; Thomas Weiland
      Abstract: We employ classical Maxwell’s equations formulated in space-time algebra to perform discretization of moving geometries directly in space-time. All the derivations are carried out without any non-relativistic assumptions, thus the application area of the scheme is not restricted to low velocities. The 4D mesh construction is based on a 3D mesh stemming from a conventional 3D mesh generator. The movement of the system is encoded in the 4D mesh geometry, enabling an easy extension of well-known 3D approaches to the space-time setting. As a research example, we study a manifestation of Sagnac’s effect in a rotating ring resonator. In case of constant rotation, the space-time approach enhances the efficiency of the scheme, as the material matrices are constant for every time step, without abandoning the relativistic framework.
      PubDate: 2018-02-14
      DOI: 10.1007/s00006-018-0841-3
      Issue No: Vol. 28, No. 1 (2018)
  • Finite Motion Analysis of Parallel Mechanisms with Parasitic Motions Based
           on Conformal Geometric Algebra
    • Authors: Xinming Huo; Yimin Song
      Abstract: Finite motion analysis of parallel mechanisms (PMs) denotes formulating the map between finite motion of end-effector and those of its component limbs. By employing conformal geometric algebra (CGA), this paper presents an analytical and accurate method to analyze the finite motions of PMs with parasitic motions. Herein, parasitic motions are defined as the dependent motions in the constraint Degrees-of-Freedom (DoFs) of PMs. Firstly, description of rigid body transformations based on CGA is reviewed. Then, the intersection algorithm of finite motions is introduced by exploiting the algebraic properties of CGA. Based on this, a method to formulate the finite motions of PMs with parasitic motions is proposed. Finally, Z3 mechanism is sketched as example by utilizing the approach. This method facilitates the invention of new mechanisms and can also be applied in the finite motion analysis of other kinds of PMs.
      PubDate: 2018-02-12
      DOI: 10.1007/s00006-018-0832-4
      Issue No: Vol. 28, No. 1 (2018)
  • Non-anti-hermitian Quaternionic Quantum Mechanics
    • Authors: Sergio Giardino
      Abstract: The breakdown of Ehrenfest’s theorem imposes serious limitations on quaternionic quantum mechanics (QQM). In order to determine the conditions in which the theorem is valid, we examined the conservation of the probability density, the expectation value and the classical limit for a non-anti-hermitian formulation of QQM. The results also indicated that the non-anti-hermitian quaternionic theory is related to non-hermitian quantum mechanics, and thus the physical problems described with both of the theories should be related.
      PubDate: 2018-02-12
      DOI: 10.1007/s00006-018-0819-1
      Issue No: Vol. 28, No. 1 (2018)
  • Kinematic Optimal Design of a 2-DoF Parallel Positioning Mechanism
           Employing Geometric Algebra
    • Authors: Xinming Huo; Panfeng Wang; Wanzhen Li
      Abstract: This paper proposes a geometric algebra (GA) based approach to carry out inverse kinematics and design parameters of a 2-degree-of-freedom parallel mechanism with its topology structure 3-RSR&SS for the first time. Here, R and S denote respectively revolute and spherical joints. The inverse solutions are obtained easily by utilizing special geometric relations of 3-RSR&SS parallel positioning mechanism, which are proven by calculating relations among point, line and plane in virtue of operation rules. Three global indices of kinematic optimization are defined to evaluate kinematic performance of 3-RSR&SS parallel positioning mechanism in the light of shuffle and outer products. Finally, the kinematic optimal design of 3-RSR&SS parallel positioning mechanism is carried out by means of NSGA-II and then a set of optimal dimensional parameters is proposed. Comparing with traditional kinematic analysis and optimal design method, the approach employing GA has following merits, (1) kinematic analysis and optimal design would be carried out in concise and visual way by taking full advantage of the geometric conditions of the mechanism. (2) this approach is beneficial to kinematic analysis and optimal design of parallel mechanisms in automatic and visual manner using computer programming languages. This paper may lay a solid theoretical and technical foundation for prototype design and manufacture of 3-RSR&SS parallel positioning mechanism.
      PubDate: 2018-02-12
      DOI: 10.1007/s00006-018-0829-z
      Issue No: Vol. 28, No. 1 (2018)
  • Schwarzschild Black Hole in Anti-De Sitter Space
    • Authors: Miguel Socolovsky
      Abstract: We review several aspects of anti-De Sitter (AdS) spaces in different dimensions, and of four dimensional Schwarzschild anti-De Sitter (SAdS) black hole.
      PubDate: 2018-02-08
      DOI: 10.1007/s00006-018-0822-6
      Issue No: Vol. 28, No. 1 (2018)
  • Generalized Quaternion Rings over $$\mathbb {Z}/n\mathbb {Z}$$ Z / n Z for
           an Odd $$\varvec{n}$$ n
    • Authors: José María Grau; Celino Miguel; Antonio M. Oller-Marcén
      Abstract: We consider a generalization of the quaternion ring \(\Big (\frac{a,b}{R}\Big )\) over a commutative unital ring R that includes the case when a and b are not units of R. In this paper, we focus on the case \(R=\mathbb {Z}/n\mathbb {Z}\) for and odd n. In particular, for every odd integer n we compute the number of non R-isomorphic generalized quaternion rings \(\Big (\frac{a,b}{\mathbb {Z}/n\mathbb {Z}}\Big )\) .
      PubDate: 2018-02-07
      DOI: 10.1007/s00006-018-0839-x
      Issue No: Vol. 28, No. 1 (2018)
  • An Extended Implementation Framework for Geometric Algebra Operations on
           Systems of Coordinate Frames of Arbitrary Signature
    • Authors: Ahmad Hosny Eid
      Abstract: There is a steadily increasing interest in applying Geometric Algebra (GA) in diverse fields of science and engineering. Consequently, we need better software implementations to accommodate such increasing demands that widely vary in their possible uses and goals. For large-scale complex applications having many integrating parts, such as Big Data and Geographical Information Systems, we should expect the need for integrating several GAs to solve a given problem. Even within the context of a single GA space, we often need several interdependent systems of coordinates to efficiently model and solve the problem at hand. Future GA software implementations must take such important issues into account in order to scale, extend, and integrate with existing software systems, in addition to developing new ones, based on the powerful language of GA. This work attempts to provide GA software developers with a self-contained description of an extended framework for performing linear operations on GA multivectors within systems of interdependent coordinate frames of arbitrary metric. The work explains the mathematics and algorithms behind this extended framework and discusses some of its implementation schemes and use cases. If properly implemented, the extended framework can significantly reduce the memory requirements for implementing Geometric Algebras with larger dimensions, especially for systems based on the symbolic processing of multivector scalar coefficients.
      PubDate: 2018-02-07
      DOI: 10.1007/s00006-018-0827-1
      Issue No: Vol. 28, No. 1 (2018)
  • Novel Uncertainty Principles for Two-Sided Quaternion Linear Canonical
    • Authors: Yan-Na Zhang; Bing-Zhao Li
      Abstract: The uncertainty principle, which offers information about a function and its Fourier transform in the time-frequency plane, is particularly powerful in mathematics, physics and signal processing community. In this paper, based on the fundamental relationship between the quaternion linear canonical transform (QLCT) and quaternion Fourier transform (QFT), we propose two different uncertainty principles for the two-sided QLCT. It is shown that the lower bounds can be obtained on the product of spreads of a quaternion-valued function and its two-sided QLCT from newly derived results. Furthermore, an example is given to verify the consequences. Finally, some possible applications are provided to demonstrate the usefulness of new uncertainty relations in the QLCT domain.
      PubDate: 2018-02-06
      DOI: 10.1007/s00006-018-0828-0
      Issue No: Vol. 28, No. 1 (2018)
  • Division Algebras, Clifford Algebras, Periodicity
    • Authors: Geoffrey Dixon
      Abstract: The dimensions 2, 8 and 24 play significant roles in lattice theory. In Clifford algebra theory there are well-known periodicities of the first two of these dimensions. Using novel representations of the purely Euclidean Clifford algebras over all four of the division algebras, \({\mathbf{R}}\) , \({\mathbf{C}}\) , \({\mathbf{H}}\) , and \({\mathbf{O}}\) , a door is opened to a Clifford algebra periodicity of order 24 as well.
      PubDate: 2018-02-05
      DOI: 10.1007/s00006-018-0820-8
      Issue No: Vol. 28, No. 1 (2018)
  • A New Algebraic Technique for Quaternion Constrained Least Squares
    • Authors: Tongsong Jiang; Zhaozhong Zhang; Ziwu Jiang
      Abstract: This paper studies the constrained least squares problems of quaternion matrices by means of complex representation of quaternion matrices, and derive a novel algebraic technique for the quaternion equality constrained least squares (LSE) and quadratic inequality constrained least squares (LSQI) problems by generalized singular values decomposition (GSVD) of complex matrices.
      PubDate: 2018-02-05
      DOI: 10.1007/s00006-018-0838-y
      Issue No: Vol. 28, No. 1 (2018)
  • Elementary Functions and Factorizations of Zeons
    • Authors: G. Stacey Staples; Alexander Weygandt
      Abstract: Algebraic properties of zeons are considered, including the existence of elementary factorizations and homogeneous factorizations of invertible zeons. A “zeon division algorithm” is established, showing that every nontrivial invertible zeon can be written as a sum of homogeneously decomposable zeons. Elementary functions (exponential, logarithmic, hyperbolic, and trigonometric) are extended to zeons, and a number of properties and identities are revealed. Finally, fast computation of logarithms is discussed for homogeneously decomposable zeons.
      PubDate: 2018-02-05
      DOI: 10.1007/s00006-018-0836-0
      Issue No: Vol. 28, No. 1 (2018)
  • On T-Magnetic Biharmonic Particles with Energy and Angle in the Three
           Dimensional Heisenberg Group H
    • Authors: Talat Körpinar
      Abstract: In the present paper, we define new particles by using biharmonic particles in Heisenberg group \(\mathbf{H}\) . We obtain energy and angle of T magnetic biharmonic particles and some vector field. Finally, we draw energy and angle value in terms of Frenet fields in the Heisenberg group \(\mathbf{H}\) .
      PubDate: 2018-02-02
      DOI: 10.1007/s00006-018-0834-2
      Issue No: Vol. 28, No. 1 (2018)
  • The Fermi–Walker Derivative and Non-rotating Frame in Dual Space
    • Authors: Tevfik Şahin; Fatma Karakuş; Yusuf Yaylı
      Abstract: In this study, we defined Fermi–Walker derivative in dual space \(\mathbb {D}^3\) . Fermi–Walker transport, non-rotating frame and Fermi–Walker termed Darboux vector by using Fermi–Walker derivative are given in dual space \(\mathbb {D}^3\) . Being conditions of Fermi–Walker transport and non-rotating frame are investigated along any dual curve for dual Frenet frame, dual Darboux frame and dual Bishop frame.
      PubDate: 2018-02-02
      DOI: 10.1007/s00006-018-0837-z
      Issue No: Vol. 28, No. 1 (2018)
  • Introduction to Hybrid Numbers
    • Authors: Mustafa Özdemir
      Abstract: In this study, we define a new non-commutative number system called hybrid numbers. This number system can be accepted as a generalization of the complex \(\left( {\mathbf {i}}^{2}=-1\right) \) , hyperbolic \(\left( {\mathbf {h}} ^{2}=1\right) \) and dual number \(\left( \varvec{\varepsilon }^{2}=0\right) \) systems. A hybrid number is a number created with any combination of the complex, hyperbolic and dual numbers satisfying the relation \(\mathbf { ih=-hi=i}+\varvec{\varepsilon }.\) Because these numbers are a composition of dual, complex and hyperbolic numbers, we think that it would be better to call them hybrid numbers instead of the generalized complex numbers. In this paper, we give some algebraic and geometric properties of this number set with some classifications. In addition, we examined the roots of a hybrid number according to its type and character.
      PubDate: 2018-02-02
      DOI: 10.1007/s00006-018-0833-3
      Issue No: Vol. 28, No. 1 (2018)
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