Discrete equations of convolution type in an exceptional case

1970 ◽  
Vol 11 (1) ◽  
pp. 66-74 ◽  
Author(s):  
N. K. Karapetyants
Keyword(s):  
Exceptional Case ◽  
Convolution Type ◽  
Discrete Equations

An Exceptional Case of Atrial Fibrillation Arrhythmia Induced by Etoposide

2013 ◽  
Vol 8 (4) ◽  
pp. 287-289 ◽  
Author(s):  
Wala Kridis ◽  
Afef Khanfir ◽  
Faten Triki ◽  
Mounir Frikha
Keyword(s):  
Atrial Fibrillation ◽  
Exceptional Case

Posttraumatic Delayed Jugular Foramen Syndrome in a Toddler

2021 ◽  
Author(s):  
Cristina Toledo-Gotor ◽  
Nerea Gorría ◽  
Miren Oscoz ◽  
Katia Llano ◽  
Pablo la Fuente Rodríguez-de ◽  
...  
Keyword(s):  
Physical Examination ◽  
Cranial Nerves ◽  
Jugular Foramen ◽  
Exceptional Case ◽  
Cerebellar Tonsil ◽  
Occipital Condyle ◽  
Lower Cranial Nerve ◽  
Cranial Nerve Palsies ◽  
Blunt Head Trauma ◽  
Condyle Fracture

Abstract Background Multiple lower cranial nerve palsies have been attributed to occipital condyle fractures in older children and adults, but no clinical details of other possible mechanisms have been described in infants. Case Report A 33-month-old boy suffered blunt head trauma. A bilateral skull base fracture was diagnosed, with favorable outcome during the first days after trauma. On the sixth day, the patient began to refuse drinking and developed hoarseness. Physical examination and additional investigations revealed paralysis of left VII, IX, X, and XI cranial nerves. A follow-up computed tomography (CT) scan disclosed a left petrous bone fracture involving the lateral margin of the jugular foramen, and a cranial magnetic resonance imaging (MRI) study showed a left cerebellar tonsil contusion. He improved after methylprednisolone was started. Three months later, he was asymptomatic, although mild weakness and atrophy of the left sternocleidomastoid and trapezius muscles remained 1 year later. Discussion A posttraumatic “jugular foramen syndrome” is rare in children, but it has been reported shortly after occipital condyle fracture, affecting mainly IX, X, and XI cranial nerves. In this toddler, delayed symptoms appeared with unilateral involvement. While an occipital fracture was ruled out, neuroimaging findings suggest the hypothesis of a focal contusion as a consequence of a coup-contrecoup injury. Conclusion This exceptional case highlights the importance of gathering physical examination, anatomical correlation, and neuroimaging to yield a diagnosis.

scholarly journals A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

2021 ◽  
Vol 47 (3) ◽  
Author(s):  
Timon S. Gutleb
Keyword(s):  
Open Source ◽  
Spectral Method ◽  
Jacobi Polynomial ◽  
Numerical Experiments ◽  
Exponential Convergence ◽  
Analytic Solutions ◽  
Convolution Type ◽  
Volterra Equations ◽  
Polynomial Bases ◽  
Sparsity Structure

AbstractWe present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods.

scholarly journals The Calderón–Zygmund Theorem with an $$L^1$$ Mean Hörmander Condition

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Soichiro Suzuki
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Acta Math ◽  
Limited Range ◽  
Singular Integral Operators ◽  
Convolution Type ◽  
Worst Case ◽  
Hörmander Condition

AbstractIn 2019, Grafakos and Stockdale introduced an $$L^q$$ L q mean Hörmander condition and proved a “limited-range” Calderón–Zygmund theorem. Comparing their theorem with the classical one, it requires weaker assumptions and implies the $$L^p$$ L p boundedness for the “limited-range” instead of $$1< p < \infty $$ 1 < p < ∞ . However, in this paper, we show that the $$L^q$$ L q mean Hörmander condition is actually enough to obtain the $$L^p$$ L p boundedness for all $$1< p < \infty $$ 1 < p < ∞ even in the worst case $$q=1$$ q = 1 . We use a similar method to that used by Fefferman (Acta Math 124:9–36, 1970): form the Calderón–Zygmund decomposition with the bounded overlap property and approximate the bad part. Also we give a criterion of the $$L^2$$ L 2 boundedness for convolution type singular integral operators under the $$L^1$$ L 1 mean Hörmander condition.

scholarly journals The Exceptional Case of Post-Bailout Portugal: A Comparative Outlook

2020 ◽  
Vol 25 (2) ◽  
pp. 127-150
Author(s):  
Elisabetta De Giorgi ◽  
José Santana-Pereira
Keyword(s):  
Exceptional Case
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