Browsing Mathematics by Title
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Šarac, Marica (Belgrade)[more][less]
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Romano, Daniel (Belgrade , 1985)[more][less]
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Veljković, Kristina (Beograd , 2016)[more][less]
Abstract: Design of control chart for monitoring central tendency of nongaussian random variables with symmetric or positively skewed distributions is considered. In the case of nongaussian symmetric distributions, modified X bar control chart is proposed in this dissertation. For chosen Student, Laplace, logistic and uniform distributions, theoretical distribution of the standardized sample mean is calculated and approximated with Pearson type II or Pearson type VII distributions. Width of control limits and power of X bar control chart are established, for a given probability of type I error. The results imply that the corresponding Pearson distribution represents very good approximation of the distribution of the standardized sample mean. For implementation of X bar control chart in practice, measures of sample kurtosis are compared and the usage of proposed chart is illustrated on given data. In the case of positively skewed distributions, one sided median control chart for monitoring central tendency of quality characteristics is proposed in this dissertation. For chosen exponential, gamma and Weibull distributions, theoretical distribution of sample median is calculated and approximated with Pearson type I or Pearson type VI distributions. Calculated values of upper control limits and power of median control chart for theoretical distribution of sample median and corresponding Pearson distribution are very close. For implementation of median control chart in practice, measures of sample skewness and sample kurtosis are compared and then proposed median chart is constructed for given data. Besides the statistical design of control charts for monitoring central tendency of nongaussian random variables, their optimal economic statistical design is also considered. Use of genetic algorithms for constrained minimization of expected loss function is proposed in this dissertation. Same symmetric distributions as in the case of statistical design of the X bar control chart and positively skewed distributions as in the case of statistical design of median control chart are chosen. For all chosen distributions of quality characteristic, a corresponding Pearson distribution gives results very close to results based on the theoretical distribution of the standardized sample mean (sample median). URI: http://hdl.handle.net/123456789/4449 Files in this item: 1
Kristinateza.pdf ( 2.651Mb ) -
Dražić, Milan (Beograd , 1995)[more][less]
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Dražić, Milan (Beograd , 1995)[more][less]
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Takači, Arpad (Novi Sad , 1981)[more][less]
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Nikić, Mioljub (Belgrade)[more][less]
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Blažić, Novica (Belgrade)[more][less]
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Krstić, Sava (Belgrade)[more][less]
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Stević, Stevo (Belgrade , 2001)[more][less]
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Glišić, Zoran (Belgrade)[more][less]
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Stojaković, Zoran (Belgrade)[more][less]
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Mićić, Vladimir (Belgrade , 1973)[more][less]
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Stanojević, Vera (Belgrade , 1983)[more][less]
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Šili, Endre (Belgrade , 1985)[more][less]
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Petrović, Mihailo (Paris , 1894)[more][less]
URI: http://hdl.handle.net/123456789/3737 Files in this item: 1
Mik_Alas_Pariz_1894_high.pdf ( 23.25Mb ) -
Ababoub, Ali (Belgrade , 2013)[more][less]
Abstract: This thesis has been written under the supervision of my mentor Prof. Miodrag Mateljevi c, and my co-mentor dr. Vladimir Bo zin at the University of Belgrade in the academic year 2012-2013. The topic of this thesis is Complex analysis related with geometric function theory, more precisely the theory of quasiconformal mappings in the Euclidean n-dimensional space. For good survey of the eld, see F. W. Gehring [20] in the handbook of K uhnau [33] which also contains many other surveys on quasiconformal mappings and related topics. The main source in this dissertation is J. V ais al a [67]. The thesis is divided into three chapters. Chapter 1 is divided into 5 sections. In this chapter, we focus on quasiconformal mappings in Rn and discuss various equivalent de nitions. We give The Modulus of family of curves in the rst section, geometric de nition of quasiconformal space mappings in second section, analytic de nition of quasiconformal space mappings in third section, equivalence of the de nitions in fourth section, and the Beltrami equation in fth section. Chapter 2 is divided into 5 sections. We begin by generalizing the class of Lip ( ), 0 < 1, and some properties of that class. Chapter 2 is devoted to understanding the properties by introducing the notion of Linearity, Di erentiability, and majorants. A majorant function is a certain generalization of the power functions t , this is done in the rst section. In the second section we introducing the notion of moduli of continuity with its Some Properties which gotten from I.M. Kolodiy, F. Hildebrand paper [39]. In third section we produced harmonic mapping as preliminary for the fourth section which including subharmonicity of jfjq of harmonic quasiregular mapping in space. In the last section we introducing estimation of the Poisson kernel which were extracted from Krantz paper [42]. Chapter 3 is divided into 3 sections. This chapter is include the main result in this dissertation. In this chapter we prove that !u( ) C!f ( ), where u : ! Rn is the harmonic extension of a continuous map f : @ ! Rn, if u is a K-quasiregular map and is bounded in Rn with C2 boundary. Here C is a constant depending only on n, !f and K and !h denotes the modulus of continuity of h. We also prove a version of this result for !-extension domains with c-uniformly perfect boundary and quasiconformal mappings, and we state some results regarding HQC self maps of the quadrant Q = fz : z = x + iy; x; y > 0g. URI: http://hdl.handle.net/123456789/3048 Files in this item: 1
Ali Ababaoub Li ... asicionformal Mappings.pdf ( 501.4Kb ) -
Dautović, Šejla (Beograd , 2022)[more][less]
Abstract: The goal of this dissertation is to develop logics with the aim of formalizing Bayesian confirmation theory. As such, the very topic of this dissertation is in the field of probabilistic logic. In Bayesian theory there are qualitative and quantitative concepts of confirmation. Ac- cording to the first of these two terms, the event E probabilistically confirms the second event F if the conditional probability of the event F (with the condition E) is greater than unconditional probabilities. On the other hand, the quantitative approach studies the degree to which E confirms F , which is formalized by relevance measures of confirmation, binary functions with arguments E and F . Carnap used the notion of the degree of confirmation as the basic term for the formal apparatus of inductive logic. The main results of the dissertation are probabilistic logics with operators of confirma- tion that correspond to existing measures of relevance from the literature, and theoretical predictions related to these logics, such as deduction and completeness theorems, as well as decision results. The importance of the development of such logical systems, except in the direct formalization of important Bayesian concepts, lies in their expressiveness: for each measure of relevance that will be logically formalized, the resulting logical language is rich enough to express many basic operators of probabilistic logic from the literature, which are the operators of standard probability, qualitative confirmation and independence. The com- pleteness of these logical systems is proven in relation to the standard class of measurable models, which consist of Kripke’s structures in which the accessibility relation is replaced by a probabilistic measure defined over all possible worlds. The second part of the dissertation is about dynamic aspect of confirmation in the sense that we monitor how much the realization of an event affects the realization of another event in the future. Accordingly, in this dissertation we constructed a branching-time temporal logic with ac- tions and probabilistic confirmation operators. The results of the first part were successfully modified to obtain the completeness result of this logic URI: http://hdl.handle.net/123456789/5452 Files in this item: 1
Doktorska_disertacija_sdautovic.pdf ( 1.181Mb ) -
Rašković, Miodrag (Belgrade , 1983)[more][less]
Abstract: The results from this thesis contributed to the development of model theory for probability logic with values in {0,+∞}. The thesis consists of three chapters. The basic notions and theorems from nonstandard analysis and the measure theory are given in Chapter 1. Also, by using the methods of nonstandard analysis, it is proved that if a function f, f:f→R is Lebesque measurable, a function f:R^4→R is continuous and equation f(x+y)=g(f(x),f(y),x,y) holds, then the function f is also continuous. The logics L_ωM, L_ω1M. L_AM and L^5_AM are defined in Chapter 2. The main characteristic of these logics is that their models are σ-finite. Some of the axioms of these logics are modifications of known axioms and some of them are new, as the axioms of σ-finiteness. The property of completeness, Barwise's completeness and compactness for L_AM are proved. Moreover, the theorem of elementary equivalence, the theorem of Robinson’s coexistence, several theorems of interpolation, upper Skolem-Lőwenheim theorem and the theorem of normal form are proved. In Chapter 3 of the thesis Loeb measure is founded in the alternative set theory. The theorems which are analogous to some theorems from nonstandard analysis are proved and some limitations of the alternative set theory are presented. Finally, a new proof of the well-known Lusin's theorem is given. URI: http://hdl.handle.net/123456789/288 Files in this item: 1
phdMRaskovic.pdf ( 3.730Mb ) -
Mršević, Mila (Belgrade)[more][less]