Decomposition of boundary representations on the Lobachevsky plane associated with linear bundles

2019 ◽  
pp. 368-375
Author(s):  
Larisa I. Grosheva
Keyword(s):  
Exceptional Case ◽  
Lobachevsky Plane ◽  
Canonical Representations ◽  
Boundary Representations

Earlier we described canonical (labelled by λ ∈C) and accompanying boundary representations of the group G = SU(1,1) on the Lobachevsky plane D in sections of linear bundles and decomposed canonical representations into irreducible ones. Now we decompose representations acting on distributions concentrated at the boundary of D. In the generic case 2λ ∉N they are diagonalizable, in the exceptional case Jordan blocks appear.

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 On the group of unit-valued polynomial functions

2021 ◽  
Author(s):  
Amr Ali Al-Maktry
Keyword(s):  
Commutative Ring ◽  
Semidirect Product ◽  
Polynomial Functions ◽  
Dual Numbers ◽  
Ring Of Integers ◽  
Group Of Units ◽  
Canonical Representations ◽  
Finite Commutative Ring

AbstractLet R be a finite commutative ring. The set $${{\mathcal{F}}}(R)$$ F ( R ) of polynomial functions on R is a finite commutative ring with pointwise operations. Its group of units $${{\mathcal{F}}}(R)^\times $$ F ( R ) × is just the set of all unit-valued polynomial functions. We investigate polynomial permutations on $$R[x]/(x^2)=R[\alpha ]$$ R [ x ] / ( x 2 ) = R [ α ] , the ring of dual numbers over R, and show that the group $${\mathcal{P}}_{R}(R[\alpha ])$$ P R ( R [ α ] ) , consisting of those polynomial permutations of $$R[\alpha ]$$ R [ α ] represented by polynomials in R[x], is embedded in a semidirect product of $${{\mathcal{F}}}(R)^\times $$ F ( R ) × by the group $${\mathcal{P}}(R)$$ P ( R ) of polynomial permutations on R. In particular, when $$R={\mathbb{F}}_q$$ R = F q , we prove that $${\mathcal{P}}_{{\mathbb{F}}_q}({\mathbb{F}}_q[\alpha ])\cong {\mathcal{P}}({\mathbb{F}}_q) \ltimes _\theta {{\mathcal{F}}}({\mathbb{F}}_q)^\times $$ P F q ( F q [ α ] ) ≅ P ( F q ) ⋉ θ F ( F q ) × . Furthermore, we count unit-valued polynomial functions on the ring of integers modulo $${p^n}$$ p n and obtain canonical representations for these functions.

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

scholarly journals An Exceptional Case of Intraparotid Plexiform Neurofibroma Originating from Autonomic Fibers of the Auriculotemporal Nerve

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Sarantis Blioskas ◽  
Sotiris Sotiriou ◽  
Katerina Rizou ◽  
Triantafyllia Koletsa ◽  
Petros Karkos ◽  
...  
Keyword(s):  
Parotid Gland ◽  
Plexiform Neurofibroma ◽  
Surgical Excision ◽  
Neurofibromatosis Type ◽  
Exceptional Case ◽  
Benign Tumors ◽  
First Case ◽  
Superficial Lobe ◽  
The Right ◽  
Auriculotemporal Nerve

Plexiform neurofibromas are benign tumors that tend to occur in patients suffering from neurofibromatosis type 1 (NF-1). This report addresses a rare case where the tumor affected the parotid gland, deriving almost exclusively from the peripheral portion of the facial nerve. A 6-year-old male was referred to us complaining about a gradually enlarging swelling over the right parotid area. Imaging localized the lesion to the superficial lobe of the parotid gland, suggesting a neurofibroma. Cosmetic disfigurement and a functional deficit led us to perform complete surgical resection. Meticulous surgical dissection as well as auriculotemporal nerve origin made complete extirpation possible with almost zero morbidity and ensured alleviation of both aesthetic impairment and pain. This is the first case of an intraparotid PN in a pediatric NF-1 patient, which originated from branches of the auriculotemporal nerve and particularly from fibers of the autonomic nervous system. Radical surgical excision was decided according to established decision-making algorithms.

Evolving Views of Islamic Law in Turkey

2013 ◽  
Vol 28 (2) ◽  
pp. 467-487 ◽  
Author(s):  
Russell Powell
Keyword(s):  
Islamic Law ◽  
Empirical Studies ◽  
Exceptional Case ◽  
Legal Norms ◽  
Muslim Countries ◽  
Law And Politics ◽  
Legal Opinions ◽  
Turkish Constitution ◽  
The Relationship

The tradition of Kemalist secularism (laiklik) in Turkey is often cited to distinguish Turkey as an exceptional case among predominantly Muslim countries. While it is true that the Turkish Constitution, laws, and legal opinions approach the relationship between the state and religion very differently than those of Iran, Saudi Arabia, Egypt, or even Indonesia, it would be wrong to underestimate the role that religion plays in the formation of Turkish legal norms, including citizen understanding of those norms. There is a wealth of literature describing the nature of Turkish secularism and its evolution. A number of both quantitative and qualitative studies inquire about the preference forShari'aamong Turkish voters. The typical question asks whether respondents favor the establishment of aShari'astate. Over the past fifteen years, these surveys have received response rates ranging between five and twenty-five percent in favor of such a state. However, these results are extremely problematic, because they do not provide any context or meaning for “the establishment of aShari'astate,” either for those who favor it or for those who oppose it. This study begins to unpack the range of possible meanings attributed toShari'awithin Turkey, both among voters and among intellectuals, as a framework for future empirical studies and as a basis for deeper understandings of the role of Islam within Turkish law and politics.

Pyroxene-type compounds NaM3+Ge2O6, withM= Ga, Mn, Sc and In

2014 ◽  
Vol 70 (9) ◽  
pp. 852-857 ◽  
Author(s):  
Günther J. Redhammer ◽  
Gerold Tippelt
Keyword(s):  
Ambient Pressure ◽  
Tetrahedral Site ◽  
Exceptional Case ◽  
Temperature Structure ◽  
Present Sample ◽  
Teller Distortion ◽  
Octahedral Sites ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
The Individual

The four title compounds, namely sodium gallium germanate, NaGaGe2O6, sodium manganese vanadate germanate, NaMnV0.1Ge1.9O6, sodium scandium germanate, NaScGe2O6, and sodium indium germanate, NaInGe2O6, adopt the high-temperature structure of the pyroxene-type chain germanates, with monoclinic symmetry and space groupC2/c. The lattice parameters, the individual and average bond lengths involvingM1, and the distortion parameters scale well with the ionic radius of theM1 cation. NaGaGe2O6has more distortedM1 sites and more extended tetrahedral chains than NaInGe2O6, in which a high degree of kinking is required to maintain the connection between the octahedral and tetrahedral building units of the pyroxene structure. An exceptional case is NaMnGe2O6, in which the strong Jahn–Teller effect of Mn3+results in more distorted octahedral sites than expected according to linear extrapolation from the other NaM3+Ge2O6pyroxenes. In contrast with the literature, minor incorporations of V5+in the tetrahedral site and a corresponding reduction of Mn3+to Mn2+in the octahedral sites in the present sample lower the Jahn–Teller distortion and stabilize the Mn-bearing pyroxene, even allowing its synthesis at ambient pressure.

The Palestinians – lessons from the Arab Spring†

2013 ◽  
Vol 6 (3) ◽  
pp. 422-437 ◽  
Author(s):  
As'ad Ghanem
Keyword(s):  
Arab Spring ◽  
Arab World ◽  
Exceptional Case ◽  
The Arab Spring

This paper examines the implications of the Arab Spring for the Palestinians. The aim is to point out the basic lessons and implications of the transformations occurring in the Arab world for the Palestinians as an exceptional case, due to their situation under occupation and exile. Cause for optimism is discerned in the anticipated increase in broad and practical Arab support for the Palestinians. However, the contention here is that Palestinians themselves have derived too limited a lesson from the Arab revolutions by focusing only on the call for unity between the competing Palestinian factions. Their reconciliation is only about their self-preservation and that of the system which has served them hitherto. The recommendations posited here are for the Palestinians to embrace the full message of the Arab Spring and make peaceful protest en masse and across the whole Palestinian people their path to liberation.

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