Toeplitz operators of finite interval type and the table method

We solve a Riemann-Hilbert problem with almost periodic coefficient G, associated to a Toeplitz operator T-G in a class which is closely connected to finite interval convolution equations, based on a generalization of the so-called table method. The explicit determination of solutions to that problem allows one to establish necessary and sufficient conditions for the invertibility of the corresponding Toeplitz operator, and to determine an appropriate factorization of G, providing explicit formulas for the inverse of T-G. Some unexpected properties of the Fourier spectrum of the solutions are revealed which are not apparent through other approaches to the same probleminfo:eu-repo/semantics/acceptedVersio

Riemann–Hilbert problems, Toeplitz operators and Q-classes

We generalize the notion of Q-classes C(Q1,Q2) , which was introduced in the context of Wiener–Hopf factorization, by considering very general 2 × 2 matrix functions Q1, Q2. This allows us to use a mainly algebraic approach to obtain several equivalent representations for each class, to study the intersections of Q-classes and to explore their close connection with certain non-linear scalar equations. The results are applied to various factorization problems and to the study of Toeplitz operators with symbol in a Q-class. We conclude with a group theoretic interpretation of some of the main results.Fundação para a Ciência e a Tecnologia (FCT/Portugal), through Project PTDC/MAT/121837/2010 and Project Est- C/MAT/UI0013/2011. The first author was also supported by the Center for Mathematical Analysis, Geometry, and Dynamical Systems and the second author was also supported by the Centre of Mathematics of the University of Minho through the FEDER Funds Programa Operacional Factores de Competitividade COMPET

Kernels of unbounded Toeplitz operators and factorization of symbols

We consider kernels of unbounded Toeplitz operators in Hp(C+) in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in Hp(C+), we describe the kernels of Toeplitz operators whose symbol possesses a certain factorization involving two different Hardy spaces and we establish relations between the kernels of two operators whose symbols differ by a factor which corresponds, in the unit circle, to a non-integer power of z. We apply the results to describe the kernels of Toeplitz operators with non-vanishing piecewise continuous symbols.This work was partially supported by FCT/Portugal through UID/MAT/04459/2020. The research of M. T. Malheiro was partially supported by Portuguese Funds through FCT/Portugal within the Projects UIDB/00013/2020 and UIDP/00013/2020

Model spaces and Toeplitz kernels in reflexive Hardy spaces

This paper considers model spaces in an Hp setting. The existence of unbounded functions and the characterisation of maximal functions in a model space are studied, and decomposition results for Toeplitz kernels, in terms of model spaces, are establishedFCT/Portuga

Endodontic Treatment of a Geminated Maxillary Left First Premolar: a Case Report

Morfološke nepravilnosti zuba izazov su svakom specijalistu endodoncije. Kako bi ih se uspješno lociralo i tretiralo, treba biti svjestan svih anatomskih varijacija korijenskih kanala. Svrha ovog prikaza jest opisati nekirurško liječenje prvog lijevoga maksilarnog premolara s geminacijom. Dvadesetogodišnja pacijentica poslana je na endodontski tretman prvog lijevoga maksilarnog premolara. Nakon kliničke i radiološke obrade specijalist endodoncije je dijagnosticirao nekrozu pulpe s kroničnim apikalnim parodontitisom te geminaciju zuba. Korijenski kanali obrađeni su instrumentima ProTaper Universal™. – za bukalni kanal odabran je F3, a za palatalni F4. Nakon toga osušeni su sterilnim papirnatim pointom i napunjeni tehnikom hladne lateralne kondenzacije gutaperkom ProTaper te punilom AH-plus. Na kontrolnom pregledu nakon dvanaest mjeseci zub je bio asimptomatičan i na radiološkoj slici nije se vidjela periapikalna radiolucencija. Treba istaknuti da se čak i kod zuba s iznimno kompleksnom morfologijom korijenskih kanala može postići adekvatno cijeljenje bez komplikacija, ako se odaberu uobičajene endodontske metode bez kirurških zahvata.Morphological aberrations in teeth present challenges to root-canal treatment. In such cases, an awareness of the possible anatomical variations is essential to localize and successfully treat the entire root-canal system. The purpose of this case report was to describe a nonsurgical treatment of a maxillary left first premolar with gemination. A 20-year-old female patient was referred for endodontic treatment of her maxillary left first premolar. Based on the clinical and radiographic examination, pulp necrosis and chronic apical periodontitis and a geminated tooth were diagnosed. The root canals were instrumented using the ProTaper Universal™ rotary system up to F3 and F4 instruments, respectively, for the buccal and palatal root canals. The root canals were dried with sterile paper points and filled with ProTaper gutta-percha points and AH Plus Sealer using a cold lateral condensation technique. At the 12-month follow-up, the tooth was asymptomatic and there was no radiolucency around the apical region. Even in a tooth with extremely complex root canal morphology, a conventional endodontic treatment without surgical intervention can result in adequate healing without any complications

Dietas contendo fenos de leucena ou estilosantes para cabras Anglo-Nubianas de tipo misto em lactação.

Com o intuito de avaliar dietas para cabras Anglo-Nubianas do tipo misto em lactação, foram utilizadas oito cabras com peso médio 37,9 ± 1,72 kg, entre a 2ª e 4ª ordem de lactação, no terço médio da lactação, distribuídas em duplo quadrado latino 4 x 4. A ordenha foi realizada as 7 e 16 h. Os tratamentos consistiram de quatro dietas formuladas com diferentes volumosos (silagem de capim-elefante associada ou não aos fenos de leucena ou de estilosantes) e milho em grão, acrescidas ou não do farelo de soja

Comparison of two extraction methods for evaluation of volatile constituents patterns in commercial whiskeys: Elucidation of the main odour-active compounds

An analytical procedure based on manual dynamic headspace solid-phase microextraction (HS-SPME) method and the conventional extraction method by liquid–liquid extraction (LLE), were compared for their effectiveness in the extraction and quantification of volatile compounds from commercial whiskey samples. Seven extraction solvents covering a wide range of polarities and two SPME fibres coatings, has been evaluated. The highest amounts extracted, were achieved using dichloromethane (CH2Cl2) by LLE method (LLECH2Cl2)(LLECH2Cl2) and using a CAR/PDMS fibre (SPMECAR/PDMS) in HS-SPME. Each method was used to determine the responses of 25 analytes from whiskeys and calibration standards, in order to provide sensitivity comparisons between the two methods. Calibration curves were established in a synthetic whiskey and linear correlation coefficient (r ) were greater than 0.9929 for LLECH2Cl2LLECH2Cl2 and 0.9935 for SPMECAR/PDMS, for all target compounds. Recoveries greater than 80% were achieved. For most compounds, precision (expressed by relative standard deviation, R.S.D.) are very good, with R.S.D. values lower than 14.78% for HS-SPME method and than 19.42% for LLE method. The detection limits ranged from 0.13 to 19.03 μg L−1 for SPME procedure and from 0.50 to 12.48 μg L−1 for LLE. A tentative study to estimate the contribution of a specific compound to the aroma of a whiskey, on the basis of their odour activity values (OAV) was made. Ethyl octanoate followed by isoamyl acetate and isobutyl alcohol, were found the most potent odour-active compounds

Ação inibidora de óleos essenciais sobre o crescimento micelial de Botrytis cinerea.

Assim, o objetivo deste trabalho foi testar diferentes óleos essenciais no controle de B. cinerea