Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Incidence of breast cancer in the five-year period (2001-2006) in patients treated surgically in the Cantonal Hospital in Zenica

Breast cancer is currently one of the most common malignant tumors of human race and at the same it is the most frequent cancer of female population. The war and post-war migrations of population have significantlychanged the demographic and age structure in Bosnia and Herzegovina. Absence of a National Cancer Register and a unique database on malignant diseases makes monitoring of breast cancer even more difficult.Theobjectiveof this retrospective study was to analyze the incidence of breast cancer in Zenica-Doboj Canton, to conduct a survey based on the age of patients in the five-year period starting from 1 January 2001 until 30 November 2005 and results of the study have been compared with 1990. All the patients were treated surgically with pre-surgical clinical examination, ultra-sound examination and mamography, and pathohistological verification of cancer and pathologically determined size of tumor. A total of 297 patients were treated out of the series of 583 breast surgeries.During this five-year survey a continuous increase of breast cancers in Zenica-Doboj Canton was noted.Therehas been an increased incidence of breast cancer in women aged 30-45, the average size of tumor has decreased, and there has been no change in the relationship between the pathohistological types of tumors and tendencies in surgical treatments to use breast conserving surgical methods. The program of early detection of breast cancer or screening of healthy women and search for “small” cancers (screening programs) will enable a wider use of breast conserving surgical methods and it requires a more active involvement of the state and society

Complete pancreas traumatic transsection

This report presents a case of a twenty-year old male with complete pancreas breakdown in the middle of its corpus, which was caused by a strong abdomen compression, with injuries of the spleen, the firstjejunumcurve,mesocolon transversum, left kidney, and appereance of retroperitoneal haemathoma. Surgical treatment started 70 minutes after the injury. The treatment consisted of left pancreatectomy with previous spleenectomy, haemostasis of ruptured mesocolon transversum blood vessels, left kidney exploration, suturing of the firstjejunumcurvelession and double abdomen drainage. Posttraumatic pancreatitis which appeared on the second postoperative day and prolonged drain secretion were successfully solved by conservative treatment

Breech deliveries in the Cantonal Hospital Zenica in the five-yearperiod(1999-2003)

In this retrospective study we analysed the influence of gestation age,parity and the way of a delivery completion on postpartum vitality of new born infants in breech deliveries of singleton fetal pregnancies and none-malformed fetuses in the five-yearperiod.Out of the total number of 13431 deliveries, 502 ofthem(3.7%)were completed by breech delivery in the period from 1999 to 2003. Breech deliveries are classified according to gestation age,parity and the way of delivery completion. Each delivery is further classified in one of the three groups of postpartum vitality, according to the method of Virginia Apgar (regular Apgar, mild and heavy hypoxia). Out of 502 breech deliveries, 211 (42%) were delivered vaginally, and 291 (58%) in sectio Caesarean. 98 (19,5%) new born babies were delivered in mild hypoxia, and 33 (6.6%) in heavier hypoxia. All infants with heavier hypoxia, 24 of them (72.7%), were delivered vaginally. Preterm born infants made 78,8% of children who were born in heavy hypoxia. Analysis based on parity does not show any significant difference in postpartum vitality of new born infants. Sectio Caesarea participated in significantly better postpartum vitality of newborn childrenin particular gestational age and parity groups. It should be preferred at term breech deliveries of the primiparas, and preterm breech deliveries of 33-37 weeks of gestational age regardless of parity