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  • 1
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    Unknown
    Hindawi
    Publication Date: 2013-06-27
    Description: The paper investigates the risk factors for the severity of orthodontic root resorption. The multidimensional scaling (MDS) visualization method is used to investigate the experimental data from patients who received orthodontic treatment at the Department of Orthodontics and Dentofacial Orthopedics, Faculty of Dentistry, “Carol Davila” University of Medicine and Pharmacy, during a period of 4 years. The clusters emerging in the MDS plots reveal features and properties not easily captured by classical statistical tools. The results support the adoption of MDS for tackling the dentistry information and overcoming noise embedded into the data. The method introduced in this paper is rapid, efficient, and very useful for treating the risk factors for the severity of orthodontic root resorption.
    Print ISSN: 1024-123X
    Electronic ISSN: 1563-5147
    Topics: Mathematics , Technology
    Published by Hindawi
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Czechoslovak journal of physics 50 (2000), S. 17-22 
    ISSN: 1572-9486
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The connection between Killing tensors and Lax operators are presented. The Toda lattice case and the Rindler system are analyzed in details.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Czechoslovak journal of physics 50 (2000), S. 1189-1194 
    ISSN: 1572-9486
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the Lax tensors of the separable coordinates in (2+1) dimensions. The Lax tensors of the dual manifolds are investigated.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    General relativity and gravitation 31 (1999), S. 497-509 
    ISSN: 1572-9532
    Keywords: DUAL METRICS SYMMETRIES
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we study the symmetries of thedual Taub-nut metrics. Generic and non-genericsymmetries of dual Taub-nut metrics are investigated.The existence of the Runge-Lenz type symmetry isanalyzed for dual Taub-nut metrics. We find that in somecases the symmetries of the dual metrics are the samewith the symmetries of Taub-nut metric.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    General relativity and gravitation 30 (1998), S. 195-207 
    ISSN: 1572-9532
    Keywords: KILLING-YANO TENSORS
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we investigate the geodesic motion of the pseudo-classical spinning particle for the extended Taub-NUT metric. The generalized equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We find only two types of extended Taub-NUT metrics with Kepler type symmetry admitting Killing-Yano tensors. The solutions for the lowest components of generalized Killing equations are presented for a particular form of extended Taub-NUT metric.
    Type of Medium: Electronic Resource
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  • 6
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    Unknown
    SpringerOpen
    Publication Date: 2014-11-01
    Description: In this manuscript we investigate the existence of the fractional finite difference equation (FFDE) Δμ−2μx(t)=g(t+μ−1,x(t+μ−1),Δx(t+μ−1)) via the boundary condition x(μ−2)=0 and the sum boundary condition x(μ+b+1)=∑k=μ−1αx(k) for order 1
    Print ISSN: 1687-1839
    Electronic ISSN: 1687-1847
    Topics: Mathematics
    Published by SpringerOpen
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  • 7
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    Unknown
    Hindawi
    Publication Date: 2015-03-27
    Description: The existence and the uniqueness theorems play a crucial role prior to finding the numerical solutions of the fractional differential equations describing the models corresponding to the real world applications. In this paper, we study the existence of solutions for a time-fractional integrodifferential equation via three-point boundary value conditions.
    Print ISSN: 1024-123X
    Electronic ISSN: 1563-5147
    Topics: Mathematics , Technology
    Published by Hindawi
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  • 8
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    Unknown
    MDPI Publishing
    In: Entropy
    Publication Date: 2015-02-17
    Description: In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
    Published by MDPI Publishing
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  • 9
    facet.materialart.
    Unknown
    MDPI Publishing
    In: Entropy
    Publication Date: 2014-11-29
    Description: In this paper, based on fixed entropy, the adiabatic equation of state in fractal flow is discussed. The local fractional wave equation for the velocity potential is also obtained by using the non-differential perturbations for the pressure and density of fractal hydrodynamics.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
    Published by MDPI Publishing
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  • 10
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    Unknown
    Springer
    Publication Date: 2015-09-18
    Description: The existence criterion has been extensively studied for different classes in fractional differential equations (FDEs) through different mathematical methods. The class of fractional order boundary value problems (FOBVPs) with p-Laplacian operator is one of the most popular class of the FDEs which have been recently considered by many scientists as regards the existence and uniqueness. In this scientific work our focus is on the existence and uniqueness of the FOBVP with p-Laplacian operator of the form: D γ ( ϕ p ( D θ z ( t ) ) ) + a ( t ) f ( z ( t ) ) = 0 , 3 〈 θ , γ ≤ 4 , t ∈ [ 0 , 1 ] , z ( 0 ) = z ‴ ( 0 ) , η D α z ( t ) | t = 1 = z ′ ( 0 ) , ξ z ″ ( 1 ) − z ″ ( 0 ) = 0 , 0 〈 α 〈 1 , ϕ p ( D θ z ( t ) ) | t = 0 = 0 = ( ϕ p ( D θ z ( t ) ) ) ′ | t = 0 , ( ϕ p ( D θ z ( t ) ) ) ″ | t = 1 = 1 2 ( ϕ p ( D θ z ( t ) ) ) ″ | t = 0 , ( ϕ p ( D θ z ( t ) ) ) ‴ | t = 0 = 0 , where 0 〈 ξ , η 〈 1 and D θ , D γ , D α are Caputo’s fractional derivatives of orders θ, γ, α, respectively. For this purpose, we apply Schauder’s fixed point theorem and the results are checked by illustrative examples.
    Print ISSN: 1687-2762
    Electronic ISSN: 1687-2770
    Topics: Mathematics
    Published by Springer
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