scholarly journals Calculating a function of a matrix with a real spectrum

2021 ◽  
Author(s):  
P. Kubelík ◽  
V. G. Kurbatov ◽  
I. V. Kurbatova
Keyword(s):  
Real Spectrum

scholarly journals More about solar g modes

2018 ◽  
Vol 612 ◽  
pp. L1 ◽  
Author(s):  
E. Fossat ◽  
F. X. Schmider
Keyword(s):  
Cross Correlation ◽  
Previous Analysis ◽  
Model Parameters ◽  
Real Spectrum ◽  
Space Observatory ◽  
Correlation Peak ◽  
Similar Frequency ◽  
Precise Estimation ◽  
The One ◽  
Additional Constraints

Context. The detection of asymptotic solar g-mode parameters was the main goal of the GOLF instrument onboard the SOHO space observatory. This detection has recently been reported and has identified a rapid mean rotation of the solar core, with a one-week period, nearly four times faster than all the rest of the solar body, from the surface to the bottom of the radiative zone. Aim. We present here the detection of more g modes of higher degree, and a more precise estimation of all their parameters, which will have to be exploited as additional constraints in modeling the solar core. Methods. Having identified the period equidistance and the splitting of a large number of asymptotic g modes of degrees 1 and 2, we test a model of frequencies of these modes by a cross-correlation with the power spectrum from which they have been detected. It shows a high correlation peak at lag zero, showing that the model is hidden but present in the real spectrum. The model parameters can then be adjusted to optimize the position (at exactly zero lag) and the height of this correlation peak. The same method is then extended to the search for modes of degrees 3 and 4, which were not detected in the previous analysis.Results. g-mode parameters are optimally measured in similar-frequency bandwidths, ranging from 7 to 8 μHz at one end and all close to 30 μHz at the other end, for the degrees 1 to 4. They include the four asymptotic period equidistances, the slight departure from equidistance of the detected periods for l = 1 and l = 2, the measured amplitudes, functions of the degree and the tesseral order, and the splittings that will possibly constrain the estimated sharpness of the transition between the one-week mean rotation of the core and the almost four-week rotation of the radiative envelope. The g-mode periods themselves are crucial inputs in the solar core structure helioseismic investigation.

scholarly journals Magnetic resonance imaging-monitored conservative management of traumatic spinal epidural hematomas

1999 ◽  
Vol 6 (1) ◽  
pp. E8 ◽  
Author(s):  
Giovanni La Rosa ◽  
Domenico d'Avella ◽  
Alfredo Conti ◽  
Salvatore Cardali ◽  
Domenico La Torre ◽  
...  
Keyword(s):  
Magnetic Resonance Imaging ◽  
Magnetic Resonance ◽  
Nonsurgical Treatment ◽  
Spine Injury ◽  
Real Spectrum ◽  
Mri Imaging ◽  
Resonance Imaging ◽  
Traumatic Injuries ◽  
Lumbar Vertebral Body ◽  
Spinal Epidural

Spinal epidural hematomas (SEHs) are uncommon complications caused by traumatic injuries to the spine. Emergency surgical evacuation is the standard treatment. Although recognized in the literature, the possibility of nonsurgical treatment of traumatic SEHs is far from being codified. The authors report on the treatment of four patients whose traumatic SEHs were diagnosed by magnetic resonance (MRI) imaging and managed conservatively with excellent results. All patients had suffered severe spine injury with fracture of a lumbar vertebral body, were admitted within 12 hours of trauma, and exhibited only minimal neurological disturbances on admission. Magnetic resonance imaging studies were performed within 24 hours of trauma. Hematomas appeared isointense/slightly hyperintense on T1- and heterogeneous on T2-weighted MR images. Clot thickness varied between 0.8 cm and 1 cm, width between 1 cm and 1.8 cm, and length between 2.7 and 9 cm. In light of each patient's fairly good neurological condition a conservative approach was taken. In all cases serial MR imaging documented progressive clot resolution, which was completed within 8 to 10 days of trauma. At discharge all patients were neurologically intact. The conservative treatment option of traumatic SEH should be reserved for exceptional cases whose deficits are minimal, when neurological deterioration is followed by early and sustained spontaneous recovery, and when there are clear medical contraindications for surgery. The results of the present study confirm that nonsurgical treatment is feasible in a subgroup of minimally symptomatic patients who harbor moderate-sized SEHs. Although the authors' experience shows a good spontaneous outcome of some traumatic SEH, further studies are necessary to understand the real spectrum of nonsurgical treatment of such lesions.

scholarly journals Repurposing of Drugs: Radiological Aspect

2019 ◽  
pp. 70-73 ◽  
Author(s):  
Nikolay Kolotilov ◽  
A. Alekseenko ◽  
Irina Andrushchenko ◽  
S. Anton
Keyword(s):  
Succinic Acid ◽  
Medical Practice ◽  
Economic Resources ◽  
Real Spectrum ◽  
Term Administration ◽  
Radiological Aspect ◽  
Term Maintenance

Repurposing or re-positioning of drugs applied in medical practice is a trend under a new adequate and clearly understood term that existed before (for example, application of known drugs for a new purpose). The purpose of the article is to state, within the framework of repurposing and future sudden relevance and demand, the information on budget drugs for a long-term maintaining of increased body radioresistance. Drugs for the long-term maintenance of increased body radioresistance are described: riboxin and succinic acid. The possibility of long-term administration is an important advantage of riboxin and succinic acid. The knowledge of the full real spectrum of available drugs, undoubtedly, allows prevention of polypharmacy and conservation of economic resources.

Mesozonation of the Italian territory for the definition of real spectrum-compatible accelerograms

2012 ◽  
Vol 10 (5) ◽  
pp. 1357-1375 ◽  
Author(s):  
M. Rota ◽  
E. Zuccolo ◽  
L. Taverna ◽  
M. Corigliano ◽  
C. G. Lai ◽  
...  
Keyword(s):  
Real Spectrum ◽  
Definition Of ◽  
Italian Territory

scholarly journals Real Tropicalization and Analytification of Semialgebraic Sets

2020 ◽  
Author(s):  
Philipp Jell ◽  
Claus Scheiderer ◽  
Josephine Yu
Keyword(s):  
Inverse Limit ◽  
Point Of View ◽  
General Point ◽  
Real Spectrum ◽  
Closed Field ◽  
Topological Properties ◽  
Absolute Value ◽  
The Real ◽  
Semialgebraic Set ◽  
Refined Version

Abstract Let $K$ be a real closed field with a nontrivial non-archimedean absolute value. We study a refined version of the tropicalization map, which we call real tropicalization map, that takes into account the signs on $K$. We study images of semialgebraic subsets of $K^n$ under this map from a general point of view. For a semialgebraic set $S \subseteq K^n$ we define a space $S_r^{{\operatorname{an}}}$ called the real analytification, which we show to be homeomorphic to the inverse limit of all real tropicalizations of $S$. We prove a real analogue of the tropical fundamental theorem and show that the tropicalization of any semialgebraic set is described by tropicalization of finitely many inequalities, which are valid on the semialgebraic set. We also study the topological properties of real analytification and tropicalization. If $X$ is an algebraic variety, we show that $X_r^{{\operatorname{an}}}$ can be canonically embedded into the real spectrum $X_r$ of $X$, and we study its relation with the Berkovich analytification of $X$.

Gyroscopically Stabilized Systems: A Class Of Quadratic Eigenvalue Problems With Real Spectrum

1991 ◽  
Vol 44 (1) ◽  
pp. 42-53 ◽  
Author(s):  
Lawrence Barkwell ◽  
Peter Lancaster ◽  
Alexander S. Markus
Keyword(s):  
Hilbert Space ◽  
Real Line ◽  
Spectral Properties ◽  
Eigenvalue Problems ◽  
Real Spectrum ◽  
Hyperbolic Operator ◽  
Quadratic Operator ◽  
Distribution Of Eigenvalues ◽  
Quadratic Eigenvalue Problems ◽  
Quadratic Eigenvalue

AbstractEigenvalue problems for selfadjoint quadratic operator polynomials L(λ) = Iλ2 + Bλ+ C on a Hilbert space H are considered where B, C∈ℒ(H), C >0, and |B| ≥ kI + k-l C for some k >0. It is shown that the spectrum of L(λ) is real. The distribution of eigenvalues on the real line and other spectral properties are also discussed. The arguments rely on the well-known theory of (weakly) hyperbolic operator polynomials.

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