Karakterizacije unitarnih prostora

Cilj ovog rada je izložiti različite karakterizacije unitarnih prostora među normiranim prostorima. Osnovna karakterizacija je dana Jordan - von Neumannovim teoremom prema kojem je norma izvedena iz skalarnog produkta ako i samo ako ona zadovoljava jednakost paralelograma $$||x+y||^2+||x-y||^2=2||x||^2+2||y||^2.$$ Poopćenjem te jednakosti jezikom funkcijskih jednadžbi dobiju se brojne funkcijske jednadžbe koje karakteriziraju unitarne prostore, a najvažnija je kvadratna funkcijska jednadžba $$f(x+y)+f(x-y)=2f(x)+2f(y).$$ Jedno poopćenje jednakosti paralelograma je i jednakost $$||x+y+z||^2=||x+y||^2-||z||^2+||y+z||^2-||x||^2+||z+x||^2-||y||^2,$$ a iz nje je izvedena Frechétova funkcijska jednadžba: $$f(x+y+z)=f(x+y)-f(z)+f(y+z)-f(x)+f(z+x)-f(y).$$The aim of this thesis is to expose various characterizations of inner product spaces among normed spaces. A basic characterization is given by the Jordan - von Neumann theorem according to which a norm is derived from an inner product if and only if it satisfies the parallelogram identity $$||x+y||^2+||x-y||^2=2||x||^2+2||y||^2.$$ Numerous functional equations characterizing inner product spaces are obtained by generalizing this identity to the language of functional equations. The most important is the quadratic functional equation $$f(x+y)+f(x-y)=2f(x)+2f(y).$$ Another generalization of the parallelogram identity is the identity $$||x+y+z||^2=||x+y||^2-||z||^2+||y+z||^2-||x||^2+||z+x||^2-||y||^2,$$ from which the Frechét’s functional equation is derived: \[ f(x+y+z)=f(x+y)-f(z)+f(y+z)-f(x)+f(z+x)-f(y). \

Karakterizacije unitarnih prostora

Cilj ovog rada je izložiti različite karakterizacije unitarnih prostora među normiranim prostorima. Osnovna karakterizacija je dana Jordan - von Neumannovim teoremom prema kojem je norma izvedena iz skalarnog produkta ako i samo ako ona zadovoljava jednakost paralelograma $$||x+y||^2+||x-y||^2=2||x||^2+2||y||^2.$$ Poopćenjem te jednakosti jezikom funkcijskih jednadžbi dobiju se brojne funkcijske jednadžbe koje karakteriziraju unitarne prostore, a najvažnija je kvadratna funkcijska jednadžba $$f(x+y)+f(x-y)=2f(x)+2f(y).$$ Jedno poopćenje jednakosti paralelograma je i jednakost $$||x+y+z||^2=||x+y||^2-||z||^2+||y+z||^2-||x||^2+||z+x||^2-||y||^2,$$ a iz nje je izvedena Frechétova funkcijska jednadžba: $$f(x+y+z)=f(x+y)-f(z)+f(y+z)-f(x)+f(z+x)-f(y).$$The aim of this thesis is to expose various characterizations of inner product spaces among normed spaces. A basic characterization is given by the Jordan - von Neumann theorem according to which a norm is derived from an inner product if and only if it satisfies the parallelogram identity $$||x+y||^2+||x-y||^2=2||x||^2+2||y||^2.$$ Numerous functional equations characterizing inner product spaces are obtained by generalizing this identity to the language of functional equations. The most important is the quadratic functional equation $$f(x+y)+f(x-y)=2f(x)+2f(y).$$ Another generalization of the parallelogram identity is the identity $$||x+y+z||^2=||x+y||^2-||z||^2+||y+z||^2-||x||^2+||z+x||^2-||y||^2,$$ from which the Frechét’s functional equation is derived: \[ f(x+y+z)=f(x+y)-f(z)+f(y+z)-f(x)+f(z+x)-f(y). \

Neurological diseases and anesthesia

Postoji više od 600 neuroloških bolesti od kojih boluje diljem svijeta stotine milijuna ljudi. Manifestacije neurološke bolesti mogu uključivati motorne i senzorne deficite, ali i autonomnu disfunkciju. Starenje populacije je jedan od glavnih faktora rizika za nastanak neurodegenerativnih bolesti. Bolesnici s neurodegenerativnim kao i drugim neurološkim bolestima predstavljaju populaciju koja ima potrebu kako za velikim tako i za malim kirurškim intervencijama. Postoji nekoliko veoma važnih činjenica vezanih za ovu grupu bolesnika: priroda i trajanje oboljenja, terapija, sposobnost bolesnika za samostalan život. Neurološke bolesti mogu se pogoršati poslije opće i regionalne anestezije. Regionalna anestezija može se koristiti u bolesnika s nekim neurološkim bolestima, dok kod drugih dovodi do egzacerbacije njihove bolesti ili je kontraindicirana. Također ovi bolesnici pokazuju atipičan odgovor na nedepolarizirajuće i depolarizirajuće mišićne relaksanse. Prekid terapije može dovesti do pogoršanja. Kod ovih bolesnika postoji zajednički rizik od značajnih kardiorespiratornih komplikacija. To je od izuzetne važnosti u procjeni operativnog rizika, za preoperativnu pripremu kao i za postoperativni oporavak i ishod kirurškog liječenja. Pored utjecaja anesteziološke tehnike na tok bolesti, postoji i međusobni utjecaj lijekova korištenih tijekom anestezije i lijekova koji se koriste u liječenju neurološke bolesti. Nedijagnosticirane bolesti mogu biti otkrivene tek nakon anesteziološke i kirurške intevencije.There are more than 600 neurologic diseases of which hundreds of millions of people worldwide are affected. Manifestations of neurological disease may include motor and sensory deficits, but autonomic dysfunction also may be present. Ageing of population has significant contribution as one of the major risk factor for neurodegenerative disorders. The patients with neurodegenerative as well as other neurological diseases presented the population with possible great need either of big or small surgical intervention. There are several important issues in patients with neurological diseases: the nature, disease duration, therapy, the patients abilitiy to live without assistance. Neurological disease may become worst by general and regional anesthesia. Regional anesthesia may be used in patients with certain neurological diseases, but in others it may exacerbate their disease or be contraindicated. These patients may exhibit an atypical response to nondepolarizing and depolarizing muscular blockers. Stopping therapy may lead to worsening. One of the main common threat is the risk of significant cardiorespiratory complications. It is of great importance in assessing operational risk, preoperative preparation as well as for postoperative recovery and outcome of surgical treatment. Besides the effect of the anesthetic technique upon the course of the disease, there is also the interaction of drugs administered during anesthesia and patient medication. Several undiagnosed diseaases may be disclosed following a anesthetic and surgical intervention

Neurological diseases and anesthesia

Postoji više od 600 neuroloških bolesti od kojih boluje diljem svijeta stotine milijuna ljudi. Manifestacije neurološke bolesti mogu uključivati motorne i senzorne deficite, ali i autonomnu disfunkciju. Starenje populacije je jedan od glavnih faktora rizika za nastanak neurodegenerativnih bolesti. Bolesnici s neurodegenerativnim kao i drugim neurološkim bolestima predstavljaju populaciju koja ima potrebu kako za velikim tako i za malim kirurškim intervencijama. Postoji nekoliko veoma važnih činjenica vezanih za ovu grupu bolesnika: priroda i trajanje oboljenja, terapija, sposobnost bolesnika za samostalan život. Neurološke bolesti mogu se pogoršati poslije opće i regionalne anestezije. Regionalna anestezija može se koristiti u bolesnika s nekim neurološkim bolestima, dok kod drugih dovodi do egzacerbacije njihove bolesti ili je kontraindicirana. Također ovi bolesnici pokazuju atipičan odgovor na nedepolarizirajuće i depolarizirajuće mišićne relaksanse. Prekid terapije može dovesti do pogoršanja. Kod ovih bolesnika postoji zajednički rizik od značajnih kardiorespiratornih komplikacija. To je od izuzetne važnosti u procjeni operativnog rizika, za preoperativnu pripremu kao i za postoperativni oporavak i ishod kirurškog liječenja. Pored utjecaja anesteziološke tehnike na tok bolesti, postoji i međusobni utjecaj lijekova korištenih tijekom anestezije i lijekova koji se koriste u liječenju neurološke bolesti. Nedijagnosticirane bolesti mogu biti otkrivene tek nakon anesteziološke i kirurške intevencije.There are more than 600 neurologic diseases of which hundreds of millions of people worldwide are affected. Manifestations of neurological disease may include motor and sensory deficits, but autonomic dysfunction also may be present. Ageing of population has significant contribution as one of the major risk factor for neurodegenerative disorders. The patients with neurodegenerative as well as other neurological diseases presented the population with possible great need either of big or small surgical intervention. There are several important issues in patients with neurological diseases: the nature, disease duration, therapy, the patients abilitiy to live without assistance. Neurological disease may become worst by general and regional anesthesia. Regional anesthesia may be used in patients with certain neurological diseases, but in others it may exacerbate their disease or be contraindicated. These patients may exhibit an atypical response to nondepolarizing and depolarizing muscular blockers. Stopping therapy may lead to worsening. One of the main common threat is the risk of significant cardiorespiratory complications. It is of great importance in assessing operational risk, preoperative preparation as well as for postoperative recovery and outcome of surgical treatment. Besides the effect of the anesthetic technique upon the course of the disease, there is also the interaction of drugs administered during anesthesia and patient medication. Several undiagnosed diseaases may be disclosed following a anesthetic and surgical intervention

Karakterizacije unitarnih prostora

Cilj ovog rada je izložiti različite karakterizacije unitarnih prostora među normiranim prostorima. Osnovna karakterizacija je dana Jordan - von Neumannovim teoremom prema kojem je norma izvedena iz skalarnog produkta ako i samo ako ona zadovoljava jednakost paralelograma $$||x+y||^2+||x-y||^2=2||x||^2+2||y||^2.$$ Poopćenjem te jednakosti jezikom funkcijskih jednadžbi dobiju se brojne funkcijske jednadžbe koje karakteriziraju unitarne prostore, a najvažnija je kvadratna funkcijska jednadžba $$f(x+y)+f(x-y)=2f(x)+2f(y).$$ Jedno poopćenje jednakosti paralelograma je i jednakost $$||x+y+z||^2=||x+y||^2-||z||^2+||y+z||^2-||x||^2+||z+x||^2-||y||^2,$$ a iz nje je izvedena Frechétova funkcijska jednadžba: $$f(x+y+z)=f(x+y)-f(z)+f(y+z)-f(x)+f(z+x)-f(y).$$The aim of this thesis is to expose various characterizations of inner product spaces among normed spaces. A basic characterization is given by the Jordan - von Neumann theorem according to which a norm is derived from an inner product if and only if it satisfies the parallelogram identity $$||x+y||^2+||x-y||^2=2||x||^2+2||y||^2.$$ Numerous functional equations characterizing inner product spaces are obtained by generalizing this identity to the language of functional equations. The most important is the quadratic functional equation $$f(x+y)+f(x-y)=2f(x)+2f(y).$$ Another generalization of the parallelogram identity is the identity $$||x+y+z||^2=||x+y||^2-||z||^2+||y+z||^2-||x||^2+||z+x||^2-||y||^2,$$ from which the Frechét’s functional equation is derived: \[ f(x+y+z)=f(x+y)-f(z)+f(y+z)-f(x)+f(z+x)-f(y). \

Intensive cyclic chemotherapy and transplantation of autologous peripheral blood progenitor cells (PBPC) or whole blood in high-risk breast cancer — follow up at 10 years

Aim: The main aim of our paper is to contribute to objectification of currently widely discussed results of overall survival (OS), disease free survival (DFS) and time from relapse to tumor progression (TTP) in women with breast cancer. Methods: Forty consecutive patients fulfilling the eligibility criteria were admitted to the study. Fifty-six women were included in the control group. All patients received 6 cycles of adjuvant intensive cyclic combined chemotherapy with epirubicin 150 mg/m2 and cyclophosphamide 1250 mg/m2 (EC) applied each 14 days. To overcome haematological toxicity transplantations of autologous peripheral blood progenitor cells (PBPCs) or whole blood enriched of PBPC were used. Results: We found statistically significant difference in OS regardless of the stage of the disease to the benefit of women treated by intensive cyclic EC chemotherapy when compared with the control group. In evaluation of DFS no statistically significant difference was found in survival between the control group and the group with all stages of the disease. TTP in women without relation to the stage was statistically significantly longer than in the control group. Conclusion: In our study intensive cyclic EC chemotherapy did not show better curative effect when compared with conventional dosage chemotherapy.Цель:объективизация широко обсуждаемых результатов по общей выживаемости (OВ), периода ремиссии (ПР) и продолжительности периода от рецидива к опухолевой прогрессии (ПРОП) у больных раком молочной железы. Методы: обследовано 40 больных, отвечающих установленным критериям отбора, и 56 здоровых женщин, составивших контрольную группу. У всех больных проведено 6 циклов адъювантной интенсивной циклической комбинированной химио­терапии (эпирубицин — 150 мг/м2 и циклофосфамид — 1250 мг/м2 (ЭЦ)), проводимой каждые 14 дней. Для преодоления гематологической токсичности применяли трансплантацию клеток-предшественников периферической крови (КППК) или цельной крови, обогащенной КППК. Результаты: выявлены статистически значимые различия в ОВ, не зависящие от стадии заболевания, у пациенток, получавших интенсивную циклическую химиотерапию ЭЦ, по сравнению с контрольной группой. При оценке ПР не выявлено статистически значимых различий выживаемости между контрольной группой и больными во всех стадиях заболевания. ПРОП у пациенток независимо от стадии заболевания статистически значимо выше, чем таковой контрольной группы. Выводы: по результатам исследования, интенсивная циклическая химиотерапия ЭЦ не имеет лечебных преимуществ по сравнению со стандартной дозовой химиотерапией