Riemannov teorem

U ovom radu dokazujemo Riemannov teorem koji dokazuje da svaka elementarna domena različita od skupa kompleksnih brojeva je konformno ekvivalenta jediničnom krugu.In this thesis, we prove Riemann’s theorem proving that each elementary domain is different from the set of complex numbers is conformally equivalent unit disk

The impact of climate change on biodiversity of freshwater insect

Vode na kopnu čine 0.8 % površine Zemlje, ali su stanište za otprilike 10 % poznatih vrsta čija je bioraznolikost stavljena na rizik u globalnoj razini. Veliku većinu takvih staništa sačinjavaju slatkovodni kukci. Najčesće susrećemo dvokrilce, vodencvjetove, vretenca, obalčare, polukrilce, muljare, tulare, opnokrilce, kornjaše i leptire. Oni su pod utjecajem abiotičkih uvjeta koji odražavaju gradijente širine, temperature i vlage te kemijskih karakteristika zraka i tla.Vodeni biomi se razlikuju po veličini, dubini, brzini protoka i morskom utjecaju (npr. jezera, potoci, rijeke, ušća). Uvjeti okoline nisu statični, već se mijenjaju sezonski i godišnje. Mnogi kukci imaju u velikoj mjeri neočekivanu fiziološku sposobnost za borbu s ekstremnim temperaturama i relativnom vlažnošću u najtežim ekosustavima planeta. Mnoge vrste pokazuju najmanje ograničenu homeostatsku sposobnost (tj. sposobnost reguliranja unutarnje temperature i sadržaja vode). Neke su vrste sposobne brzo regulirati tjelesnu toplinu ili sadržaj vode kontrakcijom mišića, uzdizanjem tijela iznad vrućih površina, traženjem sjene ili iskopavanjem. Biološka invazija vrsta toplijih područja, povišena koncentracija hranjivih tvari u vodama uslijed jačega ispiranja s kopna, povećana primarna produkcija i ostali poremećaji u hranidbenim lancima, pojačana eutrofikacija te smanjena koncentracija kisika u vodama su samo neki od poremećaja s kojima će se takvi ekosustavi u budućnosti boriti. Pred slatkovodnim ekosustavima dolazi velik izazov suprostavljanju klimatskim promjenama koje se događaju zadnjih 100 godina, a i nastavaljaju sve većim intezitetom kroz neodređeni period pod pretpostavkom povećanja temperature za 4 °C, abiotskog čimbenika na koji su kukci najviše osjetljivi.Onshore waters make up to 0.8 % of the Earth's surface, but they are home to approximately 10 % of known species whose biodiversity is at risk globally. The vast majority of such species are freshwater insects. Most often we find flies, mayflies, odonates, shorebirds, true bugs, megalopterans, casddisflies, hymenopterans, beetles and butterflies. They are influenced by abiotic conditions that reflect the gradients of latitude, temperature and humidity, and the chemical characteristics of air and soil. Aquatic habitats vary in size, depth, flow rate, and marine impact (e.g. lakes, streams, rivers, estuaries). Environmental conditions are not static, but change seasonally and annually. Many insects have a largely unexpected physiological ability to cope with extreme temperatures and relative humidity in the planet's most difficult ecosystems. Many species exhibit at least limited homeostatic ability (i.e. ability to regulate internal temperature and water content). Some of them are capable of quickly regulating body heat or water content by contracting muscles, lifting the body above hot surfaces, seeking shade, or excavating. Biological invasion of warm-area species, higher concentrations of nutrients in water followed by strong flushes with land, increased primary production and other disturbances in food chains, eutrophication occurred and decreased oxygen concentration in water are some of the disturbances that will such ecosystems face in future. Freshwater ecosystems face the great challenge of confronting climate change that has been occurring for the past 100 years, and continues to increase in intensity over an indefinite period with prediction of 4 °C temperature rise, abiotic condition that has most effects on insects

Riemannov teorem

U ovom radu dokazujemo Riemannov teorem koji dokazuje da svaka elementarna domena različita od skupa kompleksnih brojeva je konformno ekvivalenta jediničnom krugu.In this thesis, we prove Riemann’s theorem proving that each elementary domain is different from the set of complex numbers is conformally equivalent unit disk

The impact of climate change on biodiversity of freshwater insect

Vode na kopnu čine 0.8 % površine Zemlje, ali su stanište za otprilike 10 % poznatih vrsta čija je bioraznolikost stavljena na rizik u globalnoj razini. Veliku većinu takvih staništa sačinjavaju slatkovodni kukci. Najčesće susrećemo dvokrilce, vodencvjetove, vretenca, obalčare, polukrilce, muljare, tulare, opnokrilce, kornjaše i leptire. Oni su pod utjecajem abiotičkih uvjeta koji odražavaju gradijente širine, temperature i vlage te kemijskih karakteristika zraka i tla.Vodeni biomi se razlikuju po veličini, dubini, brzini protoka i morskom utjecaju (npr. jezera, potoci, rijeke, ušća). Uvjeti okoline nisu statični, već se mijenjaju sezonski i godišnje. Mnogi kukci imaju u velikoj mjeri neočekivanu fiziološku sposobnost za borbu s ekstremnim temperaturama i relativnom vlažnošću u najtežim ekosustavima planeta. Mnoge vrste pokazuju najmanje ograničenu homeostatsku sposobnost (tj. sposobnost reguliranja unutarnje temperature i sadržaja vode). Neke su vrste sposobne brzo regulirati tjelesnu toplinu ili sadržaj vode kontrakcijom mišića, uzdizanjem tijela iznad vrućih površina, traženjem sjene ili iskopavanjem. Biološka invazija vrsta toplijih područja, povišena koncentracija hranjivih tvari u vodama uslijed jačega ispiranja s kopna, povećana primarna produkcija i ostali poremećaji u hranidbenim lancima, pojačana eutrofikacija te smanjena koncentracija kisika u vodama su samo neki od poremećaja s kojima će se takvi ekosustavi u budućnosti boriti. Pred slatkovodnim ekosustavima dolazi velik izazov suprostavljanju klimatskim promjenama koje se događaju zadnjih 100 godina, a i nastavaljaju sve većim intezitetom kroz neodređeni period pod pretpostavkom povećanja temperature za 4 °C, abiotskog čimbenika na koji su kukci najviše osjetljivi.Onshore waters make up to 0.8 % of the Earth's surface, but they are home to approximately 10 % of known species whose biodiversity is at risk globally. The vast majority of such species are freshwater insects. Most often we find flies, mayflies, odonates, shorebirds, true bugs, megalopterans, casddisflies, hymenopterans, beetles and butterflies. They are influenced by abiotic conditions that reflect the gradients of latitude, temperature and humidity, and the chemical characteristics of air and soil. Aquatic habitats vary in size, depth, flow rate, and marine impact (e.g. lakes, streams, rivers, estuaries). Environmental conditions are not static, but change seasonally and annually. Many insects have a largely unexpected physiological ability to cope with extreme temperatures and relative humidity in the planet's most difficult ecosystems. Many species exhibit at least limited homeostatic ability (i.e. ability to regulate internal temperature and water content). Some of them are capable of quickly regulating body heat or water content by contracting muscles, lifting the body above hot surfaces, seeking shade, or excavating. Biological invasion of warm-area species, higher concentrations of nutrients in water followed by strong flushes with land, increased primary production and other disturbances in food chains, eutrophication occurred and decreased oxygen concentration in water are some of the disturbances that will such ecosystems face in future. Freshwater ecosystems face the great challenge of confronting climate change that has been occurring for the past 100 years, and continues to increase in intensity over an indefinite period with prediction of 4 °C temperature rise, abiotic condition that has most effects on insects

The impact of climate change on biodiversity of freshwater insect

Vode na kopnu čine 0.8 % površine Zemlje, ali su stanište za otprilike 10 % poznatih vrsta čija je bioraznolikost stavljena na rizik u globalnoj razini. Veliku većinu takvih staništa sačinjavaju slatkovodni kukci. Najčesće susrećemo dvokrilce, vodencvjetove, vretenca, obalčare, polukrilce, muljare, tulare, opnokrilce, kornjaše i leptire. Oni su pod utjecajem abiotičkih uvjeta koji odražavaju gradijente širine, temperature i vlage te kemijskih karakteristika zraka i tla.Vodeni biomi se razlikuju po veličini, dubini, brzini protoka i morskom utjecaju (npr. jezera, potoci, rijeke, ušća). Uvjeti okoline nisu statični, već se mijenjaju sezonski i godišnje. Mnogi kukci imaju u velikoj mjeri neočekivanu fiziološku sposobnost za borbu s ekstremnim temperaturama i relativnom vlažnošću u najtežim ekosustavima planeta. Mnoge vrste pokazuju najmanje ograničenu homeostatsku sposobnost (tj. sposobnost reguliranja unutarnje temperature i sadržaja vode). Neke su vrste sposobne brzo regulirati tjelesnu toplinu ili sadržaj vode kontrakcijom mišića, uzdizanjem tijela iznad vrućih površina, traženjem sjene ili iskopavanjem. Biološka invazija vrsta toplijih područja, povišena koncentracija hranjivih tvari u vodama uslijed jačega ispiranja s kopna, povećana primarna produkcija i ostali poremećaji u hranidbenim lancima, pojačana eutrofikacija te smanjena koncentracija kisika u vodama su samo neki od poremećaja s kojima će se takvi ekosustavi u budućnosti boriti. Pred slatkovodnim ekosustavima dolazi velik izazov suprostavljanju klimatskim promjenama koje se događaju zadnjih 100 godina, a i nastavaljaju sve većim intezitetom kroz neodređeni period pod pretpostavkom povećanja temperature za 4 °C, abiotskog čimbenika na koji su kukci najviše osjetljivi.Onshore waters make up to 0.8 % of the Earth's surface, but they are home to approximately 10 % of known species whose biodiversity is at risk globally. The vast majority of such species are freshwater insects. Most often we find flies, mayflies, odonates, shorebirds, true bugs, megalopterans, casddisflies, hymenopterans, beetles and butterflies. They are influenced by abiotic conditions that reflect the gradients of latitude, temperature and humidity, and the chemical characteristics of air and soil. Aquatic habitats vary in size, depth, flow rate, and marine impact (e.g. lakes, streams, rivers, estuaries). Environmental conditions are not static, but change seasonally and annually. Many insects have a largely unexpected physiological ability to cope with extreme temperatures and relative humidity in the planet's most difficult ecosystems. Many species exhibit at least limited homeostatic ability (i.e. ability to regulate internal temperature and water content). Some of them are capable of quickly regulating body heat or water content by contracting muscles, lifting the body above hot surfaces, seeking shade, or excavating. Biological invasion of warm-area species, higher concentrations of nutrients in water followed by strong flushes with land, increased primary production and other disturbances in food chains, eutrophication occurred and decreased oxygen concentration in water are some of the disturbances that will such ecosystems face in future. Freshwater ecosystems face the great challenge of confronting climate change that has been occurring for the past 100 years, and continues to increase in intensity over an indefinite period with prediction of 4 °C temperature rise, abiotic condition that has most effects on insects

Riemannov teorem

U ovom radu dokazujemo Riemannov teorem koji dokazuje da svaka elementarna domena različita od skupa kompleksnih brojeva je konformno ekvivalenta jediničnom krugu.In this thesis, we prove Riemann’s theorem proving that each elementary domain is different from the set of complex numbers is conformally equivalent unit disk

Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture

There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy for the chess KRK endgame. The final, machine verifiable, result presented in this paper is that there is a winning strategy for white in the KRK endgame generalized to $n \times n$ board (for natural $n$ greater than $3$). We demonstrate that different approaches for computer-based theorem proving work best together and in synergy and that the technology currently available is powerful enough for providing significant help to humans deriving complex proofs

Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture

There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy for the chess KRK endgame. The final, machine verifiable, result presented in this paper is that there is a winning strategy for white in the KRK endgame generalized to $n \times n$ board (for natural $n$ greater than $3$). We demonstrate that different approaches for computer-based theorem proving work best together and in synergy and that the technology currently available is powerful enough for providing significant help to humans deriving complex proofs

Ponašanje pri savijanju toplinski obrađenih aluminijskih pjena

Metalne pjene su porozni, ćelijasti materijali s vrlo nejednolikom strukturom. Upravo ta struktura značajno utječe na njihova mehanička svojstva. Glavni cilj ovog rada bio je ispitivanje savojnih svojstava uzoraka okruglog profila, jednakog olumena i gustoće, napravljenih od aluminijske pjene legure AlMgSi0, 6 s zatvorenim ćelijama, a koji su toplinski obrađeni. Zbog toga su provedena ispitivanja mehaničke otpornosti pri savijanju na kidalici uzoraka od kojih je polovica hlađena u vodi, a polovica na zraku. Dio uzoraka ohlađenih na zraku podvrgnuti homogenizaciji i umjetnom dozrijevanju, a dio ohlađenih u vodi umjetnom dozrijevanju