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Mathematics, Volume 2, Issue 1 (March 2014), Pages 1-67

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Research

Open AccessArticle One-Dimensional Nonlinear Stefan Problems in Storm’s Materials
Mathematics 2014, 2(1), 1-11; doi:10.3390/math2010001
Received: 17 October 2013 / Revised: 12 December 2013 / Accepted: 20 December 2013 / Published: 27 December 2013
Cited by 1 | PDF Full-text (224 KB) | HTML Full-text | XML Full-text
Abstract
We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material x > 0; with phase change temperature Tf : We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. In the first case, we assume a
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We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material x > 0; with phase change temperature Tf : We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. In the first case, we assume a heat flux boundary condition of the type q(t) = q 0 t , and in the second case, we assume a temperature boundary condition T = Ts < Tf at the fixed face. Solutions of similarity type are obtained in both cases, and the equivalence of the two problems is demonstrated. We also give procedures in order to compute the explicit solution. Full article
(This article belongs to the Special Issue Mathematics on Partial Differential Equations)
Open AccessArticle On the Folded Normal Distribution
Mathematics 2014, 2(1), 12-28; doi:10.3390/math2010012
Received: 10 October 2013 / Revised: 26 January 2014 / Accepted: 26 January 2014 / Published: 14 February 2014
Cited by 5 | PDF Full-text (351 KB) | HTML Full-text | XML Full-text
Abstract
The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback–Leibler from the normal and half normal distributions are approximated using Taylor series. The accuracy of the results are also
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The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback–Leibler from the normal and half normal distributions are approximated using Taylor series. The accuracy of the results are also assessed using different criteria. The maximum likelihood estimates and confidence intervals for the parameters are obtained using the asymptotic theory and bootstrap method. The coverage of the confidence intervals is also examined. Full article
Open AccessArticle Some New Integral Identities for Solenoidal Fields and Applications
Mathematics 2014, 2(1), 29-36; doi:10.3390/math2010029
Received: 31 December 2013 / Revised: 7 February 2014 / Accepted: 19 February 2014 / Published: 3 March 2014
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Abstract In spaces Rn, n ≥ 2, it has been proved that a solenoidal vector field and its rotor satisfy the series of new integral identities which have covariant form. The interest in them is explained by hydrodynamics problems for an ideal fluid. Full article
(This article belongs to the Special Issue Mathematics on Partial Differential Equations)
Open AccessArticle Bounded Gaps between Products of Special Primes
Mathematics 2014, 2(1), 37-52; doi:10.3390/math2010037
Received: 23 August 2013 / Revised: 18 February 2014 / Accepted: 25 February 2014 / Published: 3 March 2014
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Abstract
In their breakthrough paper in 2006, Goldston, Graham, Pintz and Yıldırım proved several results about bounded gaps between products of two distinct primes. Frank Thorne expanded on this result, proving bounded gaps in the set of square-free numbers with r prime factors for
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In their breakthrough paper in 2006, Goldston, Graham, Pintz and Yıldırım proved several results about bounded gaps between products of two distinct primes. Frank Thorne expanded on this result, proving bounded gaps in the set of square-free numbers with r prime factors for any r ≥ 2, all of which are in a given set of primes. His results yield applications to the divisibility of class numbers and the triviality of ranks of elliptic curves. In this paper, we relax the condition on the number of prime factors and prove an analogous result using a modified approach. We then revisit Thorne’s applications and give a better bound in each case. Full article
Open AccessArticle Convergence of the Quadrature-Differences Method for Singular Integro-Differential Equations on the Interval
Mathematics 2014, 2(1), 53-67; doi:10.3390/math2010053
Received: 22 December 2013 / Revised: 20 February 2014 / Accepted: 21 February 2014 / Published: 4 March 2014
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Abstract
In this paper, we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with the Cauchy kernel on the interval (–1,1). We consider equations of zero, positive and negative indices. It is shown that the method converges to an
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In this paper, we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with the Cauchy kernel on the interval (–1,1). We consider equations of zero, positive and negative indices. It is shown that the method converges to an exact solution, and the error estimation depends on the sharpness of derivative approximations and on the smoothness of the coefficients and the right-hand side of the equation. Full article
(This article belongs to the Special Issue Mathematics on Partial Differential Equations)

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