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

The Rayleigh-Ritz method is widely used for eigenvalue approximation. Given a matrix $X$ with columns that form an orthonormal basis for a subspace \X, and a Hermitian matrix $A$, the eigenvalues of $X^HAX$ are called Ritz values of $A$ with respect to \X. If the subspace \X is $A$-invariant then the Ritz values are some of the eigenvalues of $A$. If the $A$-invariant subspace \X is perturbed to give rise to another subspace \Y, then the vector of absolute values of changes in Ritz values of $A$ 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 $A$. In that result no assumption was made on either subspace being $A$-invariant. It was conjectured there that if one of the trial subspaces is $A$-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 $A$. 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

Нозологична структура на смъртността в р България в периода 1990-2012 г

Вредица наши и чужди проучвания се посочва, че единот основните елементи на социалното и биологично равновесие е смъртността с нейните характеристики - равнище, причини, фактори, тенденции. Тя също е и определящ показател за здравното състояние на населението като цяло и на отделни негови възрастови, полови, социални, професионални и други групи, формирани по определени критерии

ANTIGENIC UNITY BETWEEN PHYTOHEMAGGLUTININ OF PHASEOLUS VULGARIS AND SOME BACTERIA AND VIRA

No abstract

ANTISTREPTOLYSIN `0` TITER IN PATIENTS WITH VIRAL HEPATITIS

No abstract

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

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

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

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

Evaluation of the yield and the yield stability of perspective lines of barley

The study was carried out in the Experimental field of the Department of Genetics and Plant Breeding – Agricultural University, Plovdiv during the period 2009-2011. New breeding lines were investigated using block design with 4 replications and 20 m2 plot size. The aim of the investigation was to estimate barley lines by yield, stability and some important traits, using Obzor as a standard. Applying biometrical and cluster analysis and index of yield stability, it has been established that some  breeding lines: numbers 21411003, 21401409 and 21001008, respectively, had better traits in comparison with the standard cultivar “Obzor” as well as stable yields regardless of differences in the climatic conditions over the years. These lines can be certified as new cultivars according to the government’s requirements for cultivar testing

Inclusive production of charged pions in p+C collisions at 158 GeV/c beam momentum

The production of charged pions in minimum bias p+C interactions is studied using a sample of 377000 inelastic events obtained with the NA49 detector at the CERN SPS at 158 GeV/c beam momentum. The data cover a phase space area ranging from 0 to 1.8 GeV/c in transverse momentum and from -0.1 to 0.5 in Feynman x. Inclusive invariant cross sections are given on a grid of 270 bins per charge thus offering for the first time a dense coverage of the projectile hemisphere and of the cross-over region into the target fragmentation zone.Comment: 31 pages, 30 figures, submitted to European Journal of Physic

Upper Limit of D0 Production in Central Pb-Pb Collisions at 158A GeV

Results are presented from a search for the decays D0 -> Kmin piplus and D0bar -> Kplus pimin in a sample of 3.8x10^6 central Pb-Pb events collected with a beam energy of 158A GeV by NA49 at the CERN SPS. No signal is observed. An upper limit on D0 production is derived and compared to predictions from several models.Comment: REVTEX 5 pages, 4 figure