Filtry
wszystkich: 11132
-
Katalog
- Publikacje 4757 wyników po odfiltrowaniu
- Czasopisma 12 wyników po odfiltrowaniu
- Osoby 152 wyników po odfiltrowaniu
- Wynalazki 11 wyników po odfiltrowaniu
- Projekty 10 wyników po odfiltrowaniu
- Laboratoria 5 wyników po odfiltrowaniu
- Zespoły Badawcze 9 wyników po odfiltrowaniu
- Aparatura Badawcza 49 wyników po odfiltrowaniu
- Kursy Online 1436 wyników po odfiltrowaniu
- Wydarzenia 57 wyników po odfiltrowaniu
- Dane Badawcze 4634 wyników po odfiltrowaniu
wyświetlamy 1000 najlepszych wyników Pomoc
Wyniki wyszukiwania dla: G/G/1
-
An efficient algorithm for finding ideal schedules
PublikacjaPodejmujemy problem szeregowania zadań jednostkowych z zadanymi czasamy przybycia i zależnościami kolejnościowymi. Uszeregowanie jest idealne jeśli jednocześnie minimalizuje maksymalny oraz średni czas zakończenia zadania. Podajemy przyklad pokazujący, że uszeregowania idealne nie istnieją dla relacji zależności zadań będącej drzewem, gdy dopuścimy możliwość wystąpienia przerwań. Z drugiej strony podajemy algorytm o złożoności...
-
Mechanical properties of two-stage concrete modified by silica fume
PublikacjaAbstract. Two-stage concretes, despite the fact that they have proven themselves in various types of construction, have not been studied to the same extent as traditional heavy concretes. Therefore, the article developed the composition of frame concrete with various additives in the composition of the cement-sand mortar. A comparison of the mechanical characteristics of the developed compositions with the addition of silica fume...
-
Potential of nanocomposites of zero valent copper and magnetite with Eleocharis dulcis biochar for packed column and batch scale removal of Congo red dye
PublikacjaThe current study is the first attempt to prepare nanocomposites of Eleocharis dulcis biochar (EDB) with nano zero-valent Copper (nZVCu/EDB) and magnetite nanoparticles (MNPs/EDB) for batch and column scale sequestration of Congo Red dye (CR) from synthetic and natural water. The adsorbents were characterized with advanced analytical techniques. The impact of EDB, MNPs/EDB and nZVCu/EDB dosage (1–4 g/L), pH (4–10), initial concentration...
-
Fingerprint structure studies with semi-contact AFM
Dane BadawczeThe work [1] presents many, sometimes even surprising examples of the use of atomic force microscopy in modern forensics. Some of them are projectile tests using the characteristic scratch patterns created by the firing pin on the primer. There are more and more suggestions in the literature for the use of atomic force microscopy in dactyloscopy [2]....
-
Accelerated solvent extraction-gas chromatographic determination of acidic herbicides in soil
PublikacjaPrzyspieszona ekstrakcja rozpuszczalnikiem z wykorzystaniem wody jako ekstraktanta okazała się skutecznym sposobem izolacji herbicydów kwasowych (MCPP, MCPA, 2,4-D, 2,4,5-T, PCP, dinoseb, dinoterb) z próbek gleby. Wysoka zawartość substancji iłowych powodowała problemy techniczne, które udało się pokonać poprzez zwiększenie stosunku piasku do gleby w celce ekstrakcyjnej. Anality przenoszono z ekstraktu wodnego do rozpuszczalnika...
-
Cure kinetics of epoxy/MWCNTs nanocomposites: Nonisothermal calorimetric and rheokinetic techniques
PublikacjaNonisothermal calorimetric and isothermal rheokinetic analyses were used to study cure kinetics of epoxy/anhydride systems containing very low concentration of pristine and amine-functionalized multiwalled carbon nanotubes (MWCNTs). Isoconversional methods were applied in calorimetric modeling of cure kinetics. Eα vs. α dependency and autocatalytic nature of curing were identified for both types of nanocomposites by isoconversional...
-
Removal of cyclohexane and ethanol from air in biotrickling filters inoculated with Candida albicans and Candida subhashii
PublikacjaThis paper presents investigations on the removal of cyclohexane and ethanol from air in polyurethane- -packed biotrickling filters, inoculated with Candida albicans and Candida subhashii fungal species. Results on process performance together with flow cytometry analyses of the biofilm formed over packing elements are presented and discussed. The results indicate that the presence of ethanol enhances the removal efficiency of cyclohexane...
-
The influence of nanostructures size on V2O5 electrochemical properties as cathode materials for lithium ion battery
PublikacjaIn this paper, V2O5 nanostructures with a size depending on the annealing temperature are successfully synthesized by a sol-gel method. The crystal structure and morphology of samples are characterized by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), transmission electron microscopy (TEM), selected area electron diffraction (SEAD) and scanning electron microscopy (SEM), respectively. Electrochemical testing such...
-
The effect of boron concentration on the electrical, morphological and optical properties of boron-doped nanocrystalline diamond sheets: Tuning the diamond-on-graphene vertical junction
PublikacjaIn this paper, the effect of boron doping on the electrical, morphological and structural properties of free-standing nanocrystalline diamond sheets (thickness ~ 1 μm) was investigated. For this purpose, we used diamond films delaminated from a mirror-polished tantalum substrate following a microwave plasma-assisted chemical vapor deposition process, each grown with a different [B]/[C] ratio (up to 20,000 ppm) in the gas phase....
-
Ocena badań kinetycznych procesu usuwania azotu z odcieków w procesie nitryfikacji–denitryfikacji w reaktorze typu SBR
PublikacjaIstotnym źródłem azotu dopływającego do części biologicznej komunalnychoczyszczalni ścieków są odcieki pochodzące z beztlenowych komór fermentacji osadu.Ilościowo odcieki te stanowią zaledwie 1-2% dopływu ścieków do oczyszczalni, ale ładunekazotu kierowany wraz z nimi do ciągu głównego może wynosić nawet 10-30% ogólnegoładunku azotu. Dzięki zastosowaniu wydzielonych systemów oczyszczania odciekówmożliwe jest usunięcie nawet 90%...
-
Ocena badań kinetycznych procesu usuwania azotu z odcieków w procesie nitryfikacji–denitryfikacji w reaktorze typu SBR
PublikacjaIstotnym źródłem azotu dopływającego do części biologicznej komunalnychoczyszczalni ścieków są odcieki pochodzące z beztlenowych komór fermentacji osadu.Ilościowo odcieki te stanowią zaledwie 1-2% dopływu ścieków do oczyszczalni, ale ładunekazotu kierowany wraz z nimi do ciągu głównego może wynosić nawet 10-30% ogólnegoładunku azotu. Dzięki zastosowaniu wydzielonych systemów oczyszczania odciekówmożliwe jest usunięcie nawet 90%...
-
Laser Welding of UNS S33207 Hyper-Duplex Stainless Steel to 6061 Aluminum Alloy Using High Entropy Alloy as a Filler Material
PublikacjaThe high entropy alloy (HEA) filler used during the fabrication method determines the reliability of HEAs for steel-aluminum dissimilar alloy configuration. HEAs have a direct impact on the formation of intermetallic compounds (IMC) formed by the interaction of iron (Fe) and aluminum (Al), and influence the size of the joint’s interaction zone. A novel welding process for Fe-Al alloy joints was developed to prevent the development...
-
In Vitro Studies on the Relationship Between the Antioxidant Activities of Some Berry Extracts and Their Binding Properties to Serum Albumin
PublikacjaThe aim of this study was to investigate the possibility to use the bioactive components from cape gooseberry (Physalis peruviana), blueberry (Vaccinium corymbosum), and cranberry (Vaccinium macrocarpon) extracts as a novel source against oxidation in food supplementation. The quantitative analysis of bioactive compounds (polyphenols, flavonoids, flavanols, carotenoids, and chlorophyll) was based on radical scavenging spectrophometric assays...
-
Beta-galactosidase activity of Meiothermus ruber cells
PublikacjaFreeze-dried cells of Meiothermus ruber catalyses cleavage of o-nitrophenyl-b-D-galactopiranoside (oNPb-gal) and conversion of lactose into glucose and galactose. The permeabilization with 2%toluene,20%ethanol and 20%acetone increased enzymatic activity from 74.87 U/g of lyophilized cells up to 129.44,114.38 and 90.19 U/g,respectively. Ethanol was an effective permeabilizing agent and its efficiency was dependent on the concentration,...
-
Chemical characterization of wild populations of Brassica oleracea complex species (n=9) for the content of their bioactive compounds
PublikacjaThe wild species belonging to Brassica oleracea complex species (n=9) are widespread in the Mediterranean basin and represent the relative species of several vegetable crops, such as broccoli, cauliflower, kale, cabbage. They are characterized by the high level of bioactive compounds, such as glucosinolates (GLSs), known for their benefits for human health. Four accessions were evaluated: B. macrocarpa (BM) from Favignana (Trapani),...
-
Service time distribution influence on end-to-end call setup delay calculation in networks with Session Initiation Protocol
PublikacjaThe most important GoS parameter for networks with SIP protocol is end-to-end call setup delay. So far there were no coherent models allowing calculation of these parameters for networks with SIP protocol. Few models were developed but they are insufficient. In the paper we propose model which allows end-to-end call setup delay calculation for networks with SIP protocol. The model is using chain of M/G/1/K models and is applicable...
-
Enhanced supercapacitor materials from pyrolyzed algae and graphene composites
PublikacjaThis study focuses on the synthesis and characterization of supercapacitor materials derived from pyrolyzed natural compounds. Four compounds were investigated: methylcellulose with lysine (ML), methylcellulose with lysine-graphene composite (MLG), algae (A), and algae-graphene composite (AG). The pyrolysis process was utilized to convert these natural compounds into carbon-based materials suitable for supercapacitor applications....
-
Exploiting multi-interface networks: Connectivity and Cheapest Paths
PublikacjaLet G = (V,E) be a graph which models a set of wireless devices (nodes V) that can communicate by means of multiple radio interfaces, according to proximity and common interfaces (edges E). The problem of switching on (activating) the minimum cost set of interfaces at the nodes in order to guarantee the coverage of G was recently studied. A connection is covered (activated) when the endpoints of the corresponding edge share at...
-
Mercury concentration and the absolute and relative sizes of the internal organs in cormorants Phalacrocorax carbo (L. 1758) from the breeding colony by the Vistula Lagoon (Poland)
PublikacjaThis work analyses the effect of mercury on the condition of cormorants (Phalacrocorax carbo) from an extensive breeding colony in northern Poland, the largest in Europe. A total of 55 birds (44 adults and 11 immature) were obtained. Total mercury (Hg) concentrations were measured in the liver, kidneys, breast muscles, heart, gullet (oesophagus), stomach, intestines, trachea, lungs and eyeballs. The total body mass (TBM) and empty...
-
Differences between selected volatile aromatic compound concentrations in sludge samples in various steps of wastewater treatment plant operations
PublikacjaSewage sludge, one of the main wastes generated during wastewater treatment, constitutes an important source of emissions of volatile chemical compounds such as volatile aromatic compounds These substances may undergo various changes as a result of operations and unit processes, which affects their concentrations in sewage sludge. An important factor determining the potential hazardousness of volatile organic compounds is the quality...
-
Kinetics of cyclohexane removal by Candida subhashii and Fusarium solani
Dane BadawczeDataset presents cyclohexane biodegradation in gas phase using two species of microorganisms: Candida Subhashii and Fusarium solani. Biodegradation was carried out in sealed chambers with a capacity of 1000 ml. In each of them there are two discs inhabited with microorganisms, made of polyurethane foam, 80 mm in diameter and 20 mm thick.
-
Chlorek poliglinu w likwidacji skutków rozwoju bakterii nitkowatych
PublikacjaW pracy przedstawiono wyniki badań nad wpływem dawkowania polichlorku glinu na likwidację skutków rozwoju bakterii nitkowatych w gminnej oczyszczalni ścieków w Lubaniu. Wykazano, że w ciągu 10 dni wprowadzania polichlorku glinu przy wielkości dawki ok. 3 g Al3+/(kgsm*d) możliwe było całkowite usunięcie piany biologicznej i znaczne ograniczenie populacji bakterii Microthrix parvicella. Kontynuacja wprowadzania reagenta przez kolejne...
-
Rate performance of the V2O5 nanocrystals as cathode material in Li-ion batteries
Dane BadawczeThe DataSet contains the galvanostatic charge/discharge curves of the V2O5 nanocrystals obtained by the sol-gel method. The battery tests of the samples were performed using the Atlas-Sollich 0961 (Atlas-Sollich, Poland) with different current densities in the voltage range between 2.0 V and 4.0 V vs. Li/Li+. Here 1C is 294 mAh g-1.
-
Rate performance of the V2O5 nanorods as cathode material in Li-ion batteries
Dane BadawczeThe DataSet contains the galvanostatic charge/discharge curves of the V2O5 nanorods obtained by the sol-gel method. The battery tests of the samples were performed using the Atlas-Sollich 0961 (Atlas-Sollich, Poland) with different current densities in the voltage range between 2.0 V and 4.0 V vs. Li/Li+. Here 1C is 294 mAh g-1.
-
Tuning of microstructure in engineered poly (trimethylene terephthalate) based blends with nano inclusion as multifunctional additive
PublikacjaImmiscible blends and their composites are heterogeneous and have variable morphology due to variation in mesophase regions. Tuning, i.e. controlling the phase dimension is important, thereof we report a “super-combo” effect of multiwalled carbon nanotubes (MWCNTs) in poly (trimethylene terephthalate)/polypropylene (PTT/ PP) blend system. MWCNTs act as a good reinforcing agent and compatibilizer in the otherwise immiscible PTT/...
-
Interspecific and intraspecific variation in organochlorine pesticides and polychlorinated biphenyls using non-destructive samples from Pygoscelis penguins
PublikacjaAs humans are present in Antarctica only for scientific and tourism-related purposes, it is often described as a pristine region. However, studies have identified measurable levels of Persistent Organic Pollutants (POPs), such as organochlorine pesticides (OCPs) and polychlorinated biphenyls (PCBs), in the Antarctic region. These are highly toxic anthropogenic compounds with tendency to travel long distances and reach remote environments, where...
-
Effect of dendrimer-based interlayers for enzyme immobilization on a model electrochemical sensing system for glutamate
PublikacjaIn this paper, we discuss dendrimer usage in enzyme-based electrochemical biosensors, particularly with respect to biomolecule loading on the sensing surface. A novel approach to design bioactive layers with immobilized enzymes for electrochemical biosensors using the surface plasmon resonance (SPR) method in combination with electrochemical impedance spectroscopy was presented. The gold surface was modified with linear linkers...
-
Sample preparation procedure using extraction and derivatization of carboxylic acids from aqueous samples by means of deep eutectic solvents for gas chromatographic-mass spectrometric analysis
PublikacjaThe paper presents a new procedure for the determination of organic acids in a complex aqueous matrixusing ultrasound-assisted dispersive liquid–liquid microextraction followed by injection port derivati-zation and GC–MS analysis. A deep eutectic solvent (choline chloride: 4-methylphenol in a 1:2 mol ratio)was used both as an extracting solvent and as a derivatizing agent to yield ion pairs which were next con-verted to methyl...
-
Phenolic compounds from Nerium oleander leaves: microwave assisted extraction, characterization, antiproliferative and cytotoxic activities
PublikacjaA microwave-assisted extraction (MAE) method was used for the extraction of phenolic compounds from Nerium oleander leaves. The influence of variables such as ethanol concentration, microwave power, irradiation time and liquid/solid ratio on polyphenol extraction was modelled using a second-order regression equation based on response surface methodology (RSM). The optimal conditions for MAE were: extraction solvent 35% ethanol...
-
Postępy technik w elektronice
Kursy OnlinePostępy technik w elektronice [moduł dyscyplinarny, do wyboru Grupa A] Prowadzący: Prof. Marcin Gnyba, Prof. Małgorzata Jędrzejeska-Szczerska, Prof. Piotr Jasiński, Prof. Janusz Smulko, Prof. Sebastian Molin, Prof. Łukasz Kulas Terminy: 15.04 (g. 14-16), 16.04 (g. 12-14), 14.05 (g. 13-15), 19.05 (g.17-19), 26.05 (g. 17-19) 27.05 (g.10-12 ) 28.05 (10-13) Tematyka realizowanego przedmiotu obejmuje: Czujniki elektroniczne...
-
Mapping the spatial distribution of global anthropogenic mercury atmospheric emission inventories
PublikacjaW pracy przedstawiono procedury zastosowane do przygotowania map emisji rtęci ze źrodeł antropogennych na skale globalna i przedyskutowano wyniki obliczeń przedstawione na tych mapach. Dane o emisji użyte do przygotowania map zostały obliczone i opublikowane przez Pacyna et al. (2006). W niniejszej pracy przedstawiono mapy emsji dla roku 2000 oraz zmodyfikowane mapy emisji dla roku 1995.Mapy z rozkladem emisji w układzie gridów:...
-
Red Algae – An Alternative Source of Carbon Material for Energy Storage Application
PublikacjaNew electrode material obtained by pyrolysis of aquatic biomass macro (red algae) soaked with glucose solution has been characterized by SEM, EDX and Raman spectroscopy. Graphitized carbon was identified by Raman spectroscopy. Galvanostatic cyclic polarization of the materials in contact with 1M LiPF6 electrolyte in EC:DMC (1:1 v/v) and Li as a counter electrode was performed. Specific capacity of the novel material was enhanced...
-
Efficiency of pollutant removal by five multistage constructed wetlands in a temperate climate
PublikacjaIn recent years, an increase in interest in hybrid constructed wetland systems (HCWs) has beenobserved. These systems are composed of two or more filters with different modes of sewage flow.Based on over eight years of monitoring, carried out at five local HCWs located in the PomeraniaRegion of Northern Poland, the effective removal of organic matter (from 74.9 to 95.5% COD) in theloading range 1.5-17.0 g COD·m-2·d-1 was confirmed....
-
On extremal sizes of locally k-tree graphs
PublikacjaA graph G is a locally k-tree graph if for any vertex v the subgraph induced by the neighbours of v is a k-tree, k>=0, where 0-tree is an edgeless graph, 1-tree is a tree. We characterize the minimum-size locally k-trees with n vertices. The minimum-size connected locally k-trees are simply (k + 1)-trees. For k >= 1, we construct locally k-trees which are maximal with respect to the spanning subgraph relation. Consequently, the...
-
Ocena odporności na zużycie ścierne stopów Ti na elementy pary trącej endoprotez stawu kolanowego
PublikacjaNajczęściej stosowanym biomateriałem tytanowym na elementy endoprotez stawu kolanowego jest stop Ti6Al4V. Z uwagi na zawartość wanadu, zaliczanego do pierwiastków o dużej toksyczności podejmowane są działania w kierunku zastąpienia wskazanego stopu - stopami bezwanadowymi. Jednym z najbardziej obiecujących jest stop Ti13Nb13Zr zawierający w swoim składzie jedynie pierwiastki witalne, niewywołujące stanów zapalnych i odczynów...
-
Study on Dry Sliding Wear and Friction Behaviour of Al7068/Si3N4/BN Hybrid Composites
PublikacjaHybrid aluminium metal matrix composites have the potential to replace single reinforced aluminium metal matrix composites due to improved properties. Moreover, tribological performance is critical for these composites, as they have extensive application areas, such as the automotive, aerospace, marine and defence industries. The present work aims to establish the tribological characteristics of Al7068/Si3N4/BN hybrid metal matrix...
-
Multianalyte Calibration Methods for Potentiometric Integrated Sensors System for Determination of Ions Concentration in a Body Fluids
PublikacjaIn recent years, integration and miniaturization of ion-selective electrodes (ISEs) have brought many benefits resulting in the possibility of simultaneous determination of the ions concentration in a small sample volume. One of the key problems related to the preparation of integrated sensors systems (ISSs) is a calibration procedure due to the necessity to calibrate each particular sensor separately. The main aim of the research...
-
Surface Chemistry & Experimental Techniques
Kursy Onlinewykłady prowadzone przez prof. G. Jerkiewicza
-
Corrigendum to “Blood pressure disturbances and endothelial dysfunction markers in children and adolescents with type 1 diabetes” [Atherosclerosis 237 (2014) 129–134]
Publikacja -
Polychlorinated biphenyls (PCBs) and polychlorodibenzo-p-dioxins (PCDDs) determination in disposable baby diapers with the application of natural deep eutectic solvent
PublikacjaIn this work a new method involving solvent extraction of porous membrane-packed solid samples (SE-PMSS) coupled to gas chromatography-mass spectrometry (GC–MS) has been developed for the determination of six polychlorinated biphenyls (PCBs) and five polychlorodibenzo-p-dioxines (PCDDs) in disposable baby diapers. In that aim, a terpenoid-based natural deep eutectic solvent (NADES) composed of carvone and camphor in a 1:1 M ratio...
-
The Influence of the Electrodeposition Parameters on the Properties of Mn-Co-Based Nanofilms as Anode Materials for Alkaline Electrolysers
PublikacjaIn this work, the influence of the synthesis conditions on the structure, morphology, and electrocatalytic performance for the oxygen evolution reaction (OER) of Mn-Co-based films is studied. For this purpose, Mn-Co nanofilm is electrochemically synthesised in a one-step process on nickel foam in the presence of metal nitrates without any additives. The possible mechanism of the synthesis is proposed. The morphology and structure...
-
Białka aktywne biologicznie obecne w soku pokrochmalnianym
PublikacjaPodczas przetwarzania 1 tony ziemniaków na skrobię powstaje od 5 do 12 m3 odpadów ciekłych, które zawierają 300-410 g białek na 1 kg suchej masy. Trzy główne grupy białek to: białka typu patatyny, inhibitory proteaz o charakterze zasadowym, grupa białek złożonych o wielkości 22 kDa. Białka te mogą zostać wyizolowane z soku pokrochmalnianego w formie natywnej, a następnie wykorzystane jako: środki ochrony roślin, dodatki do żywności...
-
Isolation and some properties of collagen from the backbone of Baltic cod(Gadus morhua)
PublikacjaOssein from Baltic cod backbone was obtained after extraction of non-collagenous protein with 0.1 M NaOH solution and demineralization with 1.0 M HCl solution. The extractions were performed at 4 C for24, 48 and 72 h using a solid/solution ratio from 1:4 to 1:8 (w/v). After 48 h of extraction in 0.5 M acetic acid only about 25% of collagen was dissolved. After 48 h of extraction at optimal concentration of pepsin(4 mg/g ossein)...
-
Confined granular flow in silos with inserts - full-scale experiments
PublikacjaArtykuł omawia wyniki doświadczalne przepływów silosowych w silosach w naturalnej skali ze wstawkami. Podczas doświadczeń pomierzono przemieszczenia oraz napór na ściany. Zastosowano różne typy wstawek położone na różnej wysokości. Wyniki badań doświadczalnych porównano z przepływami bez wstawek.
-
Konkurencyjność międzynarodowa krajów
PublikacjaZa podstawę badań autorskich nt. konkurencyjności międzynarodowej przyjęto raporty World Economic Forum (WEF). W rozdziale pierwszym przedstawiono rozważania związane z teoretycznymi aspektami konkurencyjności międzynarodowej oraz zaproponowano autorską definicję pojęcia konkurencyjności międzynarodowej kraju. W rozdziale drugim omówiono metodologię pomiaru Global Competitiveness Index (GCI). Podjęto próbę krytycznej oceny GCI,...
-
Updated 24-year trend of Type 1 diabetes incidence in children in Poland reveals a sinusoidal pattern and sustained increase
Publikacja -
Michał Tomasz Kucewicz dr
OsobyMichal Kucewicz was born in 1986 in Gdansk. In 2005 he completed International Baccalaureate programme in Topolowka (III High School in Gdańsk). Thanks to the G. D. Fahrenheit scholarship, he moved to the United Kingdom to study neuroscience. He received his Bachelor’s and Master’s degree from the Cambridge University, and his doctoral degree from the University of Bristol specializing in electrophysiology of memory and cognitive...
-
An analysis of the prevalence of thyroid autoantibodies: thyroid peroxidase antibodies (ATA) and thyroglobulin antibodies (ATG) in children with newly diagnosed diabetes mellitus type 1 during 2000–2004 in the Upper Silesia region, Poland
Publikacja -
Waste materials assessment for phosphorus adsorption toward sustainable application in circular economy
PublikacjaPhosphorus is the main determinant of nutrient enrichment in the water bodies. Many resources including nutrients may be shortly exhausted, assuming current consumption. This scenario leads to growing interest in resources recovery and/or reuse, which together with sustainable energy consumption and waste reduction are the main courses of the circular economy. Usage of coagulants in wastewater treatment plants (WWTP) does not allow...
-
Classification of homotopy classes of equivariant gradient maps
PublikacjaNiech V będzie ortogonalną reprezentacją zwartej grupy Liego Gi niech S(V),D(V) oznaczają sferę jednostkową i kulę jednostkową V.Jeżeli F jest G-niezmienniczą funkcją rzeczywistą klasy C^1 na Vto mówimy, że grad F (gradient F) jest dopuszczalny, jeżeli(grad F)(x) jest różny od zera dla x należących do S(V). Pracapoświęcona jest homotopijnej klasyfikacji dopuszczalnychG-niezmienniczych odwzorowań gradientowych.