295 research outputs found

    Bounds on changes in Ritz values for a perturbed invariant subspace of a Hermitian matrix

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    The Rayleigh-Ritz method is widely used for eigenvalue approximation. Given a matrix XX with columns that form an orthonormal basis for a subspace \X, and a Hermitian matrix AA, the eigenvalues of XHAXX^HAX are called Ritz values of AA with respect to \X. If the subspace \X is AA-invariant then the Ritz values are some of the eigenvalues of AA. If the AA-invariant subspace \X is perturbed to give rise to another subspace \Y, then the vector of absolute values of changes in Ritz values of AA represents the absolute eigenvalue approximation error using \Y. We bound the error in terms of principal angles between \X and \Y. We capitalize on ideas from a recent paper [DOI: 10.1137/060649070] by A. Knyazev and M. Argentati, where the vector of absolute values of differences between Ritz values for subspaces \X and \Y was weakly (sub-)majorized by a constant times the sine of the vector of principal angles between \X and \Y, the constant being the spread of the spectrum of AA. In that result no assumption was made on either subspace being AA-invariant. It was conjectured there that if one of the trial subspaces is AA-invariant then an analogous weak majorization bound should only involve terms of the order of sine squared. Here we confirm this conjecture. Specifically we prove that the absolute eigenvalue error is weakly majorized by a constant times the sine squared of the vector of principal angles between the subspaces \X and \Y, where the constant is proportional to the spread of the spectrum of AA. For many practical cases we show that the proportionality factor is simply one, and that this bound is sharp. For the general case we can only prove the result with a slightly larger constant, which we believe is artificial.Comment: 12 pages. Accepted to SIAM Journal on Matrix Analysis and Applications (SIMAX

    Mesopotamian Eye Disease Texts

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    This volume is the first English edition of the Nineveh Series on eye disease from the royal library of Ashurbanipal, 7th century BCE. It is the longest surviving ancient work on opthalmology, anticipating by centuries the Hippocratic treatise on the eye. The Nineveh series represents a systematic array of eye symptoms and therapies, also showing commonalities with Egyptian and Greco-Roman medicine

    ANTISTREPTOLYSIN `0` TITER IN PATIENTS WITH VIRAL HEPATITIS

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    Unruptured left coronary sinus of Valsalva aneurysm with bicuspid aortic valve stenosis and left ventricular inferior wall ischemia

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    Left coronary sinus of Valsalva aneurysm is a rare condition, and combination with aortic valve stenosis is veryun common. The diagnosis by transthoracic echocardiography (TTE) could be difficult and can easily be interpreted as aortic root dilatation only. Even the computed tomography of the chest (CTscan) and transesophageal echocardiography (TEE) will not give a definite diagnosis unless we think of this pathology. We report a case of unruptured left coronary sinus of Valsalva aneurysm (ULSVA) in 39-year-old male patient combined with stenosis of bicus pidaortic valve and complete heart block. He has a permanent pacemaker (PPM) implanted and was operated successfully with aortic valve replacement (AVR) and direct closure of the ULSVA

    ATTEMPT FOR HEPATIC LESION REPRODUCTION IN DOGS WITH BLOOD FROM HEPATITIS PATIENTS AND GLUCOCORTICOIDS

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    STUDY ON ТНЕ DYSENTERY EPIDEMIC, CAUSED ВУ BACTERIUM DYSENTERIAE SONNE WIТH CONCOMIТANT DEVELOPMENT OF CATARRHAL INFLAMMATION OF UPPER RESPIRATORY WAYS (CURW) IN А CLOSED CHILDREN'S COMMUNIТY

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    Dysentery epidemics, caused bу Васt. dysenteriae Sonne have been described rather oflen in the past decade, especially аmong children groups. More rаrеlу а combined course of the dysentery epidemic is reported with epidemic caused bу adenoviral or other etiological factors. In this country, Sheljazkov and Radev, Slanishev, Nedialkova and Belova have observed clinical angina in patients with dysentery. In the literature reviewed wе couldn't find evidence for simultaneous development of dysentery epidemic - Sоnnе and catarrhal inflammation of the upper respiratory ways (CURW). The latter combination was observed in the boarding school of the village G. nеаг Vаrnа.The first dysentery cases occurred on 3 February, 1964 аnd spread rapidly, reaching the peak on 11 February; the illness was controlled on 15 February. The cases with CURW almost coincide with the dynamics just described.lnformation concerning dysentery discase аnd CURW show that CURW morbidity rаtе is higher than that of dysentery. ln part of the patieпts а combination was disclosed of the two affections. The analysis of the widespreading of the illnesses according to classes, sex аnd dormitories enabled us of establishing the following characteristic features:Boys and girls of the lower classes аге involved in а greater degree bу dysentery affections аnd less bу CURW. The contrary is valid for the children of the upper classes. The morbidity гаtе of dysentery among girls is higher as compared to boys, whereas morbidity of CURW - higher among boys and lower among girls.The involvement of children bу dysentery аnd CURW according to dormitories is reverse. For instaпce, in II dormitory where girls live mainly of III and IV classes, the dysentery cases are 60% and CURW - 36%. whereas in IV dormitory, where boys from the VII class lived, the affected bу dysentery аге 25% and bу CURW - 75%

    EPIDEMIOLOGICAL, CLINICA.L AND VIROLOGICAL STUDIES ON INFLUENZA MORBIDITY RATES FOR ТНЕ PERIOD APRIL 1962 – МАY 1963 IN ТНЕ СIТУ OF VARNA

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    Тhe epidemic process of influenza acquires vaгious forms in its couгse: pandemics, epidemics аnd sporadic morbidity inbetween epidemics. Wе dispose of mоrе precise data оn its course in Bulgaria since 1952. Мorе scanty аrе the data which characteгize influenza epidemics in the city of Vагnа up to 1955 which is seen on Diagr. 1. From the latter it becomes evident that influenza morbidity rates in the city of Vагnа run parallel to morbidity rates in the whole country, being occasionally morе intensive - 1959, 1962. Тlie diаgrаm reveals high level for influenza morbldity rates fог the countгy and the city of Vаrnа in 1956 and аn epidemic peak in 1957, 1959 аnd 1962. Тhe epidemic peak in 1962 is due to аn influenza outbreak caused bу virus А2 which started at the end of January and continued till Магсh, the same уеаr.After the epidemics а period was established, characteгized bу а low level of influenza morbldity rates in the city of Varna. Stress should bе laid оn the fact that determination of actual levels of influenza morbidity rates inbetween epidemics is particularly difficult owing to the imperfect diagnosis and the diversity of clinical forms of influenza

    Висівні машини та системи на основі елементів пневмоніки

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    On the basis of the research results it is established that to increase the productivity and quality, as well as to reduce the work intensity of planting machines it is necessary to unite the metering and timing system on one principle – the principle of discrete action. The rational basis for this is using of control and power fluidic devices, and active distribution of pneumatic devices and pneumatic power systems. On this basis, pneumatic seeding systems on the row and one grain sowing were developed, which also allows distributing seeds differentially when this seeding technology is used for precision farming. На підставі результатів досліджень встановлено, що для підвищення продуктивності і якості, зниження енергоємності роботи посівних машин необхідно об'єднання висівного апарату і системи синхронізації на одному принципі – дискретної дії, а раціональною основою для цього є застосування керуючих і силових струменевих елементів, а також активних пневматичних розподільних пристроїв і пневматичної системи живлення. Виходячи з цього, розроблено пневмоструминні висіваючі системи для рядової і однозернової сівби, що також дозволяють диференційовано розподіляти насіння при сівбі по технології точного землеробства

    Improving dental epithelial junction on dental implants with bioengineered peptides

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    Introduction: The functionalization of titanium (Ti) and titanium alloys (Ti6Al4V) implant surfaces via material-specific peptides influence host/biomaterial interaction. The impact of using peptides as molecular linkers between cells and implant material to improve keratinocyte adhesion is reported.Results: The metal binding peptides (MBP-1, MBP-2) SVSVGMKPSPRP and WDPPTLKRPVSP were selected via phage display and combined with laminin-5 or E-cadherin epithelial cell specific peptides (CSP-1, CSP-2) to engineer four metal-cell specific peptides (MCSPs). Single-cell force spectroscopy and cell adhesion experiments were performed to select the most promising candidate. In vivo tests using the dental implant for rats showed that the selected bi functional peptide not only enabled stable cell adhesion on the trans-gingival part of the dental implant but also arrested the unwanted apical migration of epithelial cells.Conclusion: The results demonstrated the outstanding performance of the bioengineered peptide in improving epithelial adhesion to Ti based implants and pointed towards promising new opportunities for applications in clinical practice
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