Eigenvalue Problems

In natural sciences and engineering, are often used differential equations and systems of differential equations. Their solution leads to the problem of eigenvalues. Because of that, problem of eigenvalues occupies an important place in linear algebra. In this caption we will consider the problem of eigenvalues, and to linear and quadratic problems of eigenvalues. During the studying of linear problem of eigenvalues, we put emphasis on QR algorithm for unsymmetrical case and on minmax characterization of symmetric case. During the studying of quadratic problems of eingenvalue, we consider the linearization and variational characterization. We illustrate all with practical examples

Noncommutative groups and simplicial complexes

Предмет изучавања докторске дисертације су симплицијални комплекси при- дружени алгебарским објектима као што су циклотомични полиноми и иредуцибилни карактери решивих група. Приликом анализе придружених комплекса посебан нагласак је на некомутативности структура које се испитују. Алгебарском објекту као што је циклотомични полином може се придружити колек- ција симплицијалних комплекса. Хомотопски тип придружених симплицијалних ком- плекса у већини случајева даје потпуну информацију о коефицијентима циклотомичног полинома. Једини изузетак су циклотомични полиноми чији је степен једнак производу три различита проста броја и овај случај је у фокусу истраживања у овој докторској ди- сертацији. Хомотопски тип симплицијалног комплекса придруженог полиному Φpqr(x), где су p, q и r различити прости бројеви, одређује се помоћу дискретне теорије Морса, када је то могуће. Међутим, у посебним случајевима симплицијални комплекси придру- жени полиному Φpqr(x) имају некомутативну фундаменталну групу, чиме је обезбеђена нова некомутативна инваријанта оваквог типа полинома. Сложене презентације које се појављују као презентације фундаменталних група придружених симплицијалних ком- плекса анализирају се коришћењем Фоксовог рачуна. Други тип придруживања који се разматра јесте придруживање симплицијалног комплекса скупу иредуцибилних карактера коначне решиве групе. Придруживање се врши на два начина, као комплекс заједничког делиоца и комплекс простих делитеља. Проучавање фундаменталне групе оваквих типова симплицијалних комплекса обезбе- ђује боље разумевање структуре скупа иредуцибилних карактера коначних решивих група.This dissertation examines simplicial complexes associated with cyclotomic polynomials and irreducible characters of finite solvable groups. In the process of analysis of the associated objects special attention is paid to the noncommutativity of the examined structures. A collection of simplicial complexes can be associated to an algebraic object such as a cyclotomic polynomial. In most cases, the homotopy type of associated simplicial complexes gives us complete information about the coefficients of the cyclotomic polynomial. The only exceptions are cyclotomic polynomials whose degree is a product of three different prime numbers and this case is the focus of research in this doctoral dissertation. When it is possible, the homotopy type of a simplicial complex associated with the polynomial Φpqr(x), where p, q and r are different prime numbers, is determined by using the discrete Morse theory. However, in special cases, the simplicial complexes associated with the polynomial Φpqr(x) have a noncommutative fundamental group, thus providing a new noncommutative invariant of this type of polynomial. Complex presentations that appear as presentations of the fundamental groups of associated simplicial complexes are analyzed using Fox’s calculus. This thesis also focus on the study of simplicial complexes associated to a set of irreducible characters of a finite solvable group. Two types of simplicial complexes are attached to a set of irreducible characters of a finite solvable group — character degree complex and prime divisor complex. The examination of the fundamental group of these types of simplicial complexes provides better understanding of the structure of the irreducible characters of finite solvable groups

Биосорпција јона никла на тканинама од јуте: кинетичка и изотермска испитивања

Raw jute fabric was chemically modified with 1 % NaOH for 30 min, 17.5 % NaOH for 5 min or with 0.7 % NaClO2 for 30 and 60 min to study the influence of changes in the chemical composition of the fabrics and quantity of carboxyl groups on the biosorption capacity of the fabrics for nickel ions. The effects of contact time and initial concentration of nickel ions on the biosorp- tion capacity of the fabrics were also investigated. The obtained results rev- ealed that the biosorption of nickel ions can be explained by the pseudo-sec- ond-order kinetic model, while the experimental isotherm data fit better with the Langmuir model. The calculated ratios between maximal biosorption cap- acity (6.30–12.06 mg g-1) of the jute fabrics and carboxyl group quantity indi- cated that approximately half of the carboxyl groups of the fabrics’ would be involved in binding nickel ions during biosorption. Therefore, the quantity of carboxyl groups can be used to predict the maximal biosorption capacity of jute fabrics toward nickel ions. In the case of oxidized jute fabrics, the lignin rem- oval, and consequently increased content of cellulose and hemicelluloses, also contributed to a higher biosorption capacity.Сирова тканина од јуте је хемијски модификована 1 % NaOH у току 30 min, 17,5 % NaOH у току 5 min или 0,7 % NaClO2 у току 30 и 60 min у циљу испитивања утицаја промена хемијског састава и садржаја карбоксилних група на биосорпциони капацитет тканина према јонима никла. Такође, испитиван је и утицај времена контакта тканина са раствором NiSO4 и почетне концентрације раствора никла на биосорпциони капацитет тканина од јуте. Добијени резултати указују на то да се процес биосорпције никла може описати кинетичким моделом псеудо-другог реда, а равнотежне вредности добијене за сорпцију никла се боље слажу са Langmuir адсорпционом изотермом. Израчунати однос између максималних биосорпционих капацитета тканина од јуте (6,30–12,06 mg g-1) и садржаја карбоксилних група указују на то да ће приближно половина карбоксилних група учествовати у везивању јона никла током биосорпције. Према томе, садржај карбоксилних група се може користити као индикатор максималног биосорпционог капацитета тканина од јуте према јонима никла. Код оксидисане тканине, уклањање лигнина које је праћено са повећањем садржаја целулозе и хемицелулоза је такође допринело већем биосорпционом капацитету

Shift Strategy for Non-overdamped Quadratic Eigen-problems

ABSTRACT In this paper we study properties of non-overdamped quadratic eigenproblems. For the non-overdamped Eigen-value problems we cannot apply variational characterization in full. One of the subintervals of the interval in which we can apply variational characterization for Eigen-values of a negative type is known. In this paper we expand this subinterval by giving better right boundry of the variational characterization interval. This is achieved by getting bigger lower boundary for δ +. New strategy is seen in fact that we join suitably selected hyperbolic quadratic pencil to non-overdamped quadratic pencil. From the variational characterization of the hyperbolic eigenproblem we get better lower boundary for δ +

The concentrations of Fe, Cu and Zn in selected wines from South-East Serbia

Fruits and vegetables constitute the cheapest source of essential trace elements for the majority of people living in developing countries. The Cu, Fe and Zn contents in twenty selected wine samples produced in the South-East region of Serbia were determined by flame atomic absorption spectrometry. The Cu concentrations varied from 0.07 to 0.57 ppm in wines, and the Fe concentrations fluctuated from 2.93 to 36.2 ppm, while the Zn levels were in the range from 0.21 to 0.67 ppm. The established contents of Cu and Zn showed that wines from this part of the world could serve as good dietary sources of the essential trace metals, and the determined values were within the allowed me¬tals levels in wines for human consumption

Obtaining colored antioxidant cotton and cotton/linen fabrics using green tea aqueous extract

Green tea aqueous extract was prepared and characterized regarding total flavonoids and total phenolic contents as well as antioxidant activity (assessed by ABTS method). The characterized aqueous extract was used for dyeing and functionalization of 100% cotton and cotton/linen (47%/53% and 70%/30%) fabrics. Fabric color strength (K/S) values and their antioxidant activities before and after washing were compared. The obtained results revealed that 100% cotton (GTI), 47%/53% cotton/linen (GTII), and 70%/30% cotton/linen (GTIII) fabrics have K/S values ranging between 8.33 and 10.85. After one washing cycle, these values decreased significantly. On the other hand, dyed fabrics showed excellent (100 %) ABTS radical scavenging ability which remained excellent (GTII) or decreased to medium (GTI and GTIII) levels after one washing cycle. Based on the obtained results, it can be concluded that 47%/53% cotton/linen fabric is the most suitable for functional clothing capable of trapping the free radial of oxygen species. The current paper represents a step towards a more sustainable textile industry that could undoubtedly contribute to overcoming the environmental problems caused by the textile industry

Addressing the environmental problems of wastewater: reducing the pollution while providing multifunctional wool fabrics

The reduction of water pollution represents one of the priority topics of the EU’s goal to achieve climate neutrality by 2050. Considering this, the concept of reusing the same dyebath for multiple dyeing cycles is proposed. For this purpose, two pyridinium-based azo pyridone dyes with improved solubility and affinity towards different fibers, are used for dyeing wool fabric. It is demonstrated that the dye concentration in wastewater could be reduced up to four times by recirculation of the same dyebath 5 times. The dyed fabrics obtained in each cycle are further characterized regarding color strength (K/S) and ultraviolet protection factor (UPF), while their antioxidant potential is evaluated by ABTS (2,2’-azino-bis(3-ethylbenzothiazoline-6-sulphonic acid)) test. The results revealed that the proposed concept could be used for obtaining multifunctional wool fabrics by following the principles of sustainable development of reducing the effluent load in wastewater

Informality and cultural landscape in Belgrade Riverside

By considering regulations defined by laws, plans and decisions on different levels related to urban development of Belgrade riverside, specific conditions of privatization of land, changes in legislation and insufficiently defined planning procedures have been recognized, which reflect the informal practice of land use development. The example of such coastal areas can be found along the Sava and Danube riverside, including the illegal appropriation of the aquatory, which are regarded in this research as a specific practice of creating a unique cultural landscape. This practice reflects a spontaneous urban development of the riverside through the formal and informal establishment of temporary and permanent housing, numerous commercial and recreational activities in different scale along the 200km of Belgrade riverbank. The shaping of the cultural landscape of Belgrade riverside will be analyzed through the comparison of the advantages and disadvantages of different approaches to the ongoing riverside urbanization, which manifest the complex linkage between formal institutions, and members of the local community. The importance of closer examination of cultural, economic, environmental and spatial aspects of this process is in the recognition of indigenous building regulations and relations to the natural resources. The main goal of the research is to understand different levels on which this informal practice persists and to outline the possibilities for the improvement of the current planning of Belgrade riverbank through their institutionalisation

Transferring COVID-19 Challenges into Learning Potentials: Online Workshops in Architectural Education

The paper addresses the shift in architectural education regarding the need to develop new approaches in teaching methodology, improve curricula, and make advancements in new learning arenas and digital environments. The research is based on the assumption that online workshops could offer a unique learning experience for students in higher education. Accordingly, workshops are considered an essential element in teaching emergency design. As a result, this can produce broader and more innovative solutions to COVID-19 challenges regarding social distancing, limited movements, regulated use of public space, and suspended daily activities. The theoretical notions of emergency design and education for sustainable design enabled the identification of research perspectives and spatial levels to be taken as a starting point of the workshop “COVID-19 Challenges: Architecture of Pandemic” that was conducted by the University of Belgrade—Faculty of Architecture in April 2020. The critical review of the workshop’s procedural and substantial aspects led to identifying four main COVID-19 design challenges perceived in performance, innovation, alteration, and inclusion. Additionally, the paper’s findings concern the identification of learning potentials and limitations arising from a current topic affecting global society, for which neither solutions nor adequate answers in the field of architecture and urbanism have been found

Drivers' Preference for the Color of LED Street Lighting

The purpose of this paper was to initiate broad research aimed to establish the preferred color of light of LEDs from a driver's point of view. Two street lighting installations (one with 3000 K and the other with 4000 K LEDs) were evaluated both objectively and subjectively. The objective evaluation, realized using a CCD camera, included detection of small targets and pedestrians. A slight advantage was identified for the 3000 K lighting installation regarding both types of target. As for subjective evaluation (realized through a questionnaire), the task of the participants (drivers) was to choose the more appropriate between the two lighting installations regarding six lighting parameters, as well as the overall visibility. The 3000 K LED installation was evaluated as a better solution for most analyzed parameters, as well as for the overall visibility. However, only the results regarding the color of the light (in favor of the 3000 K LEDs) and the detection of small light-colored obstacles (in favor of 4000 K LEDs) were convincing, which was confirmed by the statistical analysis. Due to the obtained mild preference for the 3000 K LEDs and several limitations/challenges of the conducted surveys, it was concluded that additional research is needed in order to decide on the preferred color of light of LEDs from a driver's perspective