scholarly journals Interpolation and Sampling with Exponential Splines of Real Order

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Peter Massopust
Keyword(s):  
Positive Real ◽  
B Splines

AbstractThe existence of fundamental cardinal exponential B-splines of positive real order $$\sigma $$ σ is established subject to two conditions on $$\sigma $$ σ and their construction is implemented. A sampling result for these fundamental cardinal exponential B-splines is also presented.

scholarly journals The Use of Fractional B-Splines Wavelets in Multiterms Fractional Ordinary Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
X. Huang ◽  
X. Lu
Keyword(s):  
Differential Equations ◽  
Asymptotic Solution ◽  
Explicit Expression ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Differential Operators ◽  
Positive Real ◽  
B Splines ◽  
Fractional Differential ◽  
Linear Differential

We discuss the existence and uniqueness of the solutions of the nonhomogeneous linear differential equations of arbitrary positive real order by using the fractional B-Splines wavelets and the Mittag-Leffler function. The differential operators are taken in the Riemann-Liouville sense and the initial values are zeros. The scheme of solving the fractional differential equations and the explicit expression of the solution is given in this paper. At last, we show the asymptotic solution of the differential equations of fractional order and corresponding truncated error in theory.

Application of Cubic B-Splines for Synthesis of Selective Signals

2007 ◽  
Vol 66 (12) ◽  
pp. 1047-1056 ◽  
Author(s):  
I. V. Strelkovskaya
Keyword(s):  
B Splines

Robust Stabilization With Positive Real Uncertainty

1991 ◽  
Author(s):  
Waesim M. Haddad ◽  
Dennis S. Bernstein
Keyword(s):  
Robust Stabilization ◽  
Positive Real

B-splines on sparse grids for surrogates in uncertainty quantification

2021 ◽  
Vol 209 ◽  
pp. 107430
Author(s):  
Michael F. Rehme ◽  
Fabian Franzelin ◽  
Dirk Pflüger
Keyword(s):  
Uncertainty Quantification ◽  
Sparse Grids ◽  
B Splines

scholarly journals A positive real lemma for singular hybrid systems

2020 ◽  
Vol 53 (2) ◽  
pp. 2051-2056
Author(s):  
Chan-eun Park ◽  
In Seok Park ◽  
Nam Kyu Kwon ◽  
PooGyeon Park
Keyword(s):  
Hybrid Systems ◽  
Positive Real

scholarly journals SARS-CoV-2 infection in an infant with non-respiratory manifestations: a case report

2021 ◽  
Vol 69 (1) ◽  
Author(s):  
Muhammad Adel ◽  
Ahmed Magdy
Keyword(s):  
Computed Tomography ◽  
Aplastic Anemia ◽  
Rt Pcr ◽  
Positive Real ◽  
Case Presentation ◽  
Chest Computed Tomography ◽  
High Incidence ◽  
Laboratory Investigations ◽  
High Index Of Suspicion ◽  
Specific Symptoms

Abstract Background Coronavirus disease (COVID-19) presents in children usually with less severe manifestations than in adults. Although fever and cough were reported as the most common symptoms, children can have non-specific symptoms. We describe an infant with aplastic anemia as the main manifestation. Case presentation We describe a case of SARS-CoV-2 infection in an infant without any respiratory symptoms or signs while manifesting principally with pallor and purpura. Pancytopenia with reticulocytopenia was the predominant feature in the initial laboratory investigations, pointing to aplastic anemia. Chest computed tomography surprisingly showed typical findings suggestive of SARS-CoV-2 infection. Infection was later confirmed by positive real-time reverse transcription polymerase chain reaction assay (RT-PCR) for SARS-CoV-2. Conclusions Infants with COVID-19 can have non-specific manifestations and a high index of suspicion should be kept in mind especially in regions with a high incidence of the disease. Chest computed tomography (CT) and testing for SARS-CoV-2 infection by RT-PCR may be considered even in the absence of respiratory manifestations.

scholarly journals Multiple solutions for critical Choquard-Kirchhoff type equations

2020 ◽  
Vol 10 (1) ◽  
pp. 400-419 ◽  
Author(s):  
Sihua Liang ◽  
Patrizia Pucci ◽  
Binlin Zhang
Keyword(s):  
Critical Exponent ◽  
Critical Exponents ◽  
Sobolev Inequality ◽  
Multiple Solutions ◽  
Concentration Compactness ◽  
Positive Real ◽  
Multiplicity Results ◽  
Kirchhoff Type ◽  
Concentration Compactness Principle ◽  
Compactness Principle

Abstract In this article, we investigate multiplicity results for Choquard-Kirchhoff type equations, with Hardy-Littlewood-Sobolev critical exponents, $$\begin{array}{} \displaystyle -\left(a + b\int\limits_{\mathbb{R}^N} |\nabla u|^2 dx\right){\it\Delta} u = \alpha k(x)|u|^{q-2}u + \beta\left(\,\,\displaystyle\int\limits_{\mathbb{R}^N}\frac{|u(y)|^{2^*_{\mu}}}{|x-y|^{\mu}}dy\right)|u|^{2^*_{\mu}-2}u, \quad x \in \mathbb{R}^N, \end{array}$$ where a > 0, b ≥ 0, 0 < μ < N, N ≥ 3, α and β are positive real parameters, $\begin{array}{} 2^*_{\mu} = (2N-\mu)/(N-2) \end{array}$ is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality, k ∈ Lr(ℝN), with r = 2∗/(2∗ − q) if 1 < q < 2* and r = ∞ if q ≥ 2∗. According to the different range of q, we discuss the multiplicity of solutions to the above equation, using variational methods under suitable conditions. In order to overcome the lack of compactness, we appeal to the concentration compactness principle in the Choquard-type setting.

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