Weird K-actions on U(g) for so(n,1) and su(n,1)

Let g0 be either so(n, 1) or su(n, 1), g its complexification, K a maximal compact subgroup of the adjoint group of g0, U(g) the universal enveloping algebra of g and U(g)K its subalgebra of K-invariants. A consequence of our results in [2] is that besides the usual adjoint action of K on U(g) there is another action of K commuting with the adjoint action and leaving U(g)K pointwise invariant. The case g0 = so(2, 1) ≃ su(1, 1) is trivial since K is commutative and the weird action of K coincides with the inverse of adjoint action. We investigate closely the weird action of K in the simplest nontrivial case g0 = so(3, 1)

The structure of the algebra (left (U(g)otimes C(p) right )^{K}) for the groups (SU(n,1)) and (SO_e(n,1))

The structure of the algebra of $K-$invariants in $cU(gg)otim C(pp)$ is important for constructing $(gg,K)-$modules by means of algebraic Dirac induction as developed in [5] and its variants in [8] and [10]. We show that for the groups $SU(n,1)$ and $SO_e(n,1)$ this algebra is a free $cU(gg)^K-$module of rank $dim C(pp)=2^{dimpp}.$ We also indicate a way of constructing a $cU(gg)^K-$basis in $(cU(gg)otim C(pp))^K.

On Landau\u27s theorems

In this paper we give some applications and special cases of a generalization of the Landau\u27s theorem for Frechet-differentiable functions

CHANGES IN SEX LIFE AFTER CHILDBIRTH

Background: Childbirth is major event in the life of closer and extended family. The aim of this study is to explore sex desire after childbirth and challenges for usual rhythm of intercourse. Subjects and methods: We studied 113 women who filled up questionnaire at the follow up examination. Inclusion criteria were: all women were secundigravidae and time between pregnancies was more than a year. Women anonymously filled out a survey with question on the time before first intercourse after delivery, frequency of sexual intercourse after delivery, sexual desire after delivery, sexual desire of partner after delivery, reasons for postponing sexual intercourse after delivery and frequency of intercourse in the first year after delivery. Results: Most women had same number of intercourse after delivery like before pregnancy (Hi-square test: Ȥ2(2)=22.04, p<0.0001). Significant proportion of women find their partners sexual desire to be the same like in the pre-pregnancy period (H i- square test: Ȥ2(2)=64.64, p<0.0001). Most women had intercourse once a week (several times a month) during first year after delivery (Hi-square test: Ȥ2(3)=91.93, p<0.001). Fatigue, sleep deprivation, bad mood and lack of time are the most common reasons for intercourse postponement. Most women find life conditions to be very good. They do not find that they neglect their children and partners find them attractive. Conclusion: Sex life after delivery is still taboo in most countries. Women should have the information that sex life after delivery will turn to normal after a certain time

Application of new drying techniques for the production of apple chips

U radu su analizirane sorte jabuke Cripps Pink, Granny Smith, Jonagold, Idared, Golden Delicious i Braeburn u svrhu pogodnosti plodova za sušenje. Rezultati istraživanja, odnosno polinomne jednadžbe krivulje sušenja, ukazuju da su neke sorte jabuka pogodnije za proizvodnju čipsa od jabuka (Cripps Pink, Golden Delicious, Idared). Kako bi se sačuvala kvaliteta listića (čips) i smanjili troškovi, nužno je prosec sušenja podijeliti u više faza. Priprema jabuka za dobivanje čipsa dosta je zahtjevna, što izravno utječe na troškove, pa je stoga nužno pripremne faze maksimalno mehanizirati.The paper analyzes the varieties of apples; Cripps Pink, Granny Smith, Jonagold, Idared, Golden Delicious and Braeburn for the purpose of amenities of fruits for drying. The research results, or polynomial equation of drying curve, indicate that some apple varieties suitable for the production of apple chips (Cripps Pink, Golden Delicious, Idared). In order to preserve the quality of slips (chips) and reduce costs, it is necessary to divide the drying process in several stages. Preparing for apple chips is getting quite challenging, which directly affects the cost, so it is necessary that the preparatory phase is maximally mechanize

Comparison of diagnostic imaging methods for intervertebral disc herniation in dogs

Hernijacija intervertebralnog diska jedna je od češćih bolesti međukralježničnog diska. Etiološki gledano, mnogi su uzroci ovoga stanja: degeneracije diska, traume, infekcije ili anatomske/razvojne anomalije. U dijagnostici hernijacije moguće je služiti se raznim metodama slikovne dijagnostike; najčešće nativnom rendgenografijom, mijelografijom, kompjuteriziranom tomografijom ili magnetnom rezonancijom. Prema dostupnim istraživanjima, najpouzdanija metoda pokazala se magnetna rezonancija koja omogućuje sigurnu dijagnostiku i lokalizaciju u 100 % slučajeva dok su za ostale metode postotci uspješnosti detekcije niži. Treba napomenuti da je korištenje određene metode slikovne dijagnostike u lokalizaciji i lateralizaciji mjesta hernijacije intervertebralnog diska u svakodnevnoj praksi najčešće ovisno o financijskim mogućnostima vlasnika, dostupnosti određene metode i hitnosti stanja. Shodno tome, rezultati pretraga variraju, kao i točnost lokalizacije hernijacije. Cilj je ovoga preglednog rada prikazati specifičnosti hernijacije intervertebralnog diska te mogućnosti dijagnostike slikovnim metodama raspoloživima u svakodnevnoj veterinarskoj praksi.Intervertebral disc herniation is a common disorder of the intervertebral disc. There are many causes of this condition: disc degeneration, trauma, infection, or anatomical/developmental abnormalities. In the diagnosis of herniation, various methods of diagnostic imaging can be applied, such as: survey radiography, myelography, computed tomography or magnetic resonance imaging. According to the literature, the most reliable method has proven to be magnetic resonance imaging, which allows for a sound diagnosis and localization in 100% of cases, while the success rates of detection for other methods are lower. It should be noted that the use of a particular imaging method in the localization and lateralization of the herniation site of the intervertebral disc in everyday practice is usually guided by the financial capacities of the owner, the availability of a particular method, and the urgency of the procedure. Consequently, the test results vary and thus the accuracy of the herniation localization. The aim of this review article is to show the specifics of intervertebral disc herniation and the methods for the most accurate diagnosis using imaging methods available in everyday veterinary practice

Management of patients with adrenal incidentaloma – 2019 update

Zadnjih desetak godina došlo je do značajnih promjena u zdravstvenom zbrinjavanju bolesnika s incidentalomima nadbubrežne žlijezde koje su rezultirale novim preporukama za dijagnostiku i liječenje ovih bolesnika napravljenim u suradnji Europskoga endokrinološkog društva i Europske mreže za istraživanje tumora nadbubrežne žlijezde. Na temelju navedenih preporuka i višegodišnjega vlastitog iskustva Referentni centar Ministarstva zdravstva Republike Hrvatske za bolesti nadbubrežne žlijezde predlaže izmjene i dopune preporuka za dijagnostiku i liječenje ovih bolesnika objavljenih u Liječničkom vjesniku 2010. godine.In the last decade, the clinical care of patients with adrenal incidentaloma has been significantly changed which prompted the European Society of Endocrinology and European Network for the Study of Adrenal Tumors to develop an updated clinical practice guideline for the management of these patients. In accordance with the aforementioned recommendations and based on its own experience, the Croatian Referral Center for adrenal gland disorders provides an update of the previous guideline for the clinical management of patients with adrenal incidentaloma published in Liječnički vjesnik in 2010

Practical guidelines for diagnosing arterial hypertension of the Croatian Society of Hypertension of Croatian Medical Association and the Working Group on Hypertension of the Croatian Cardiac Society.

Arterijska je hipertenzija glavni neovisni čimbenik rizika za kardiovaskularni pobol i smrtnost. Prevalencija hipertenzije u većini zemalja pokazuje tendenciju rasta. Unatoč dostupnosti svih razreda antihipertenziva, kontrola liječenih hipertoničara nije zadovoljavajuća, za što postoji niz razloga i objašnjenja. Jedan od razloga jest i jaz između smjernica koje se temelje na činjenicama te mogućnostima njihova provođenja u stvarnome životu, što kao posljedicu ima lošu kontrolu hipertenzije i velik broj prijevremenih kardiovaskularnih događaja i smrti. Prvi korak u zbrinjavanju hipertoničara jest racionalna dijagnostika, što znači da pri tako masovnoj kroničnoj bolesti nepotrebnim pretragama ne povećavamo troškove, a s druge strane da pristupom na najmanju mjeru smanjimo propuste. Svrha je ovih smjernica za dijagnosticiranje arterijske hipertenzije da budu praktične i korisne u svakodnevnome radu. U njima je naglasak na konkretnim postupcima i podatcima s točno navedenim graničnim vrijednostima. Budući da je cilj smjernica ne samo usmjeriti i olakšati razmišljanja u svakodnevnome kliničkome radu nego i educirati, uz postupnike podsjećamo na neka temeljna znanja. U smjernicama ima nekoliko posve novih elemenata (upute o frekvenciji srca, mjesto i uloga mjerenja centralnoga arterijskoga tlaka i brzine pulsnoga vala, procjena bubrežne funkcije, zatim informatička tehnologija, tj. telemonitoriranje, primjena aplikacija za „pametne mobitele“). Na kraju smjernica uvršteno je nekoliko dodataka koji mogu biti korisni u svakodnevnome kliničkome radu, kao što su npr. upitnici za sindrom apneje u snu, upitnik o erektilnoj i seksualnoj disfunkciji, upitnik o kognitivnoj disfunkciji i drugi. U ovim smo smjernicama željeli biti praktični, precizni i realni s obzirom na mogućnosti koje nam pruža sredina u kojoj živimo. Svrha je bila na jednome mjestu obuhvatiti i prikazati što više konkretnih postupaka i podataka koji će biti korisni u radu, tako da liječnik ne mora gubiti vrijeme tražeći podatke bilo u samim smjernicama bilo u literaturi.Arterial hypertension is the main independent risk factor for cardiovascular morbidity and mortality. The prevalence of hypertension is increasing in most countries. Despite the availability of all classes of antihypertensive drugs, the rate control in hypertension treatment is insufficient, for which there are abundant explanations. One of the main reasons is the gap between evidence-based guidelines and their applicability in practice, a gap which leads to poor rate control in hypertension and increases the number of premature cardiovascular events and death. The first step in the management of a hypertensive patient is rational diagnosis, i.e., to avoid increasing the expenses of treating this mass chronic disease by unnecessary tests and to minimize errors. The aim of these practical guidelines for diagnosis of hypertension is for them to be practical and useful in everyday practice. There is an emphasis on particular procedures and data with exact cut-off values. The aim of these guidelines is not only to guide and simplify our decision-making process in everyday work, but also to educate. We thus provide reminders on some fundamental knowledge. There are some novel elements (instructions of heart rate, place and role of central blood pressure and pulse wave velocity measurement, estimation of renal function, IT e.g. telemonitoring, and the use of smartphone apps). At the end of the guidelines, we provide several appendices which could be useful in everyday clinical work, such as questionnaires for sleep apnea syndrome, questionnaires for erectile and sexual dysfunction, cognitive dysfunction questionnaires, and others. In these guidelines, we wanted to be practical, precise, and realistic given the options available in our work setting. The objective was to show and cover as many specific facts and procedures as possible that we find useful in everyday work, so that the clinician does not have to waste time searching the guidelines or literature

The structure of the algebra (left (U(g)otimes C(p) right )^{K}) for the groups (SU(n,1)) and (SO_e(n,1))

The structure of the algebra of $K-$invariants in $cU(gg)otim C(pp)$ is important for constructing $(gg,K)-$modules by means of algebraic Dirac induction as developed in [5] and its variants in [8] and [10]. We show that for the groups $SU(n,1)$ and $SO_e(n,1)$ this algebra is a free $cU(gg)^K-$module of rank $dim C(pp)=2^{dimpp}.$ We also indicate a way of constructing a $cU(gg)^K-$basis in $(cU(gg)otim C(pp))^K.