Dissertations / Theses on the topic 'Upper number'

Från en tidig ålder får barn lära sig att använda positiva tal. De kan lägga ihop två tal och få ett större tal eller dra ifrån ett tal från ett annat för att få ett mindre tal. Till exempel får småbarn lära sig att två plus två äpplen blir fyra äpplen och att om man har tre päron och tar bort två får man ett päron kvar. Man kan på ett konkret sätt se det framför sig. Något som inte är lika självklart är tal som t ex. fyra minus fem. Hur kan man ha fyra päron och dra ifrån fem? Negativa tal dyker sällan dyker upp i vardagliga problem, men det är fortfarande något som lärs ut i skolan. Syftet med arbetet som beskrivs i denna rapport är att undersöka gymnasieelevers uppfattningar om negativa tal och som teoretiskt ramverk används den fenomenografiska ansatsen. För att ta reda på vilka olika uppfattningar elever kan ha intervjuades åtta eleversom går sitt andra år på gymnasiet (och läser Matematik 2b). Undersökningen ämnade svarapå följande frågeställning: Hur uppfattar gymnasieelever negativa tal och vilka strategiersynliggörs i deras beräkningar? Vilka skilda beskrivnings-kategorier om negativa tal går detatt urskilja. En kvalitativ undersökning gjordes av materialet med hjälp av en fenomenografisk analys. Efter analysen gick det att särskilja fem distinkt olika beskrivningskategorier, där alla kategorier, utom den sista, leder till att eleven använder någon form av strategi för att underlätta beräkningar med negativa tal: (1) Minus minus blir plus, (2) Negativa tal förklaras med metaforer, (3) Uträkningar blir lättare om termerna i ett uttryck flyttas om, (4) Negativa tal håller till på andra sidan noll och (5) Upplever en osäkerhet kring negativa tal. Resultatet kan hjälpa matematiklärare förstå de utmaningar elever står inför beräkningar med negativa tal. Exempelvis att eleverna inte tycker det falla sig naturligt eller tillräckligt att beskriva ett tal som negativt, vilket kan bottna i att de är vana att matematik kan förklaras med konkreta exempel. Det är något som matematiklärare borde vara medvetna om.
From an early age we learn to use positive numbers. We can put two numbers together and get a bigger number or subtract a number from another to get a smaller number. For example,young children learn that two plus two apples will be four apples and that if you have three pears and remove two you have one pear left. It is easy to visualize the numbers in front of you. Something that is not as obvious is calculations such four minus five. How can one have four pears and subtract five? Negative numbers rarely appear in everyday problems, but it is still something we are required to learn in school. The purpose of the work described in this report is to examine the upper secondary school pupils' perceptions of negative numbers and as the theoretical framework a phenomenographic approach is used. To find out what different perceptions pupils may have about negative numbers, eight pupils were interviewed. They were all in their second year in upper secondary school and study mathematics at the (Swedish) level 2b. The survey intended to answer the following question: How do upper secondary school students perceive negative numbers and what strategies are made visible in their calculations? What different categories of descriptions about negative numbers can be distinguished? A qualitative study was preformed of the collected material using a phenomenographic analysis. After the analysis, five distinctly different description categories could be distinguished, where all categories, except the last one, results in the student using some form of strategy as help when performing calculations containing negative numbers: (1) Minus minus becomes plus, (2) Negative numbers are explained by metaphors, (3) Calculations become easier if the terms in an expression are moved around, (4) Negative numbers are on the other side zero, and (5) Experience of uncertainty about negative numbers. The results can help math teachers understand the challenges students face when calculating with negative numbers. For example, the pupils do not think it is natural or enough to describe a number as negative, which may be because they are used to mathematics which can beexplained by concrete examples. This is something that math teacher should be aware of.

This thesis is developed as a proposal for heating for a primary school and kindergarten in the region of Brno-countryside. For the insulated building, a combination of heating and air-conditioning is proposed. The concept is designed so that the air-conditioning preheats the exterior air and the heating system warms the incoming air to a comfortable temperature. For the required thermal performance, sources of heat (for gas and pellets) and a layout solution for the boiler room is designed. Drainage of combustion products is proposed for both solutions. The project solution is per the extent of the construction permit. The theoretical part is linked with the practical part through the condensation boilers, their function and division, and drainage of combustion products. The experiment for the given topic was conducted on the drainage of combustion products. The pressure loss of the reverse knob was determined in relation to the flow rate of air in the condensation boilers as this loss is essential in assessing the drainage of combustion products.

碩士
明志科技大學
工業工程與管理系碩士班
102
The k-rainbow domination is a variant of the classical domination problem in graphs and is defined as follows. Given an undirected graph G = (V, E), we have a set C with k colors and assign an arbitrary subset of these colors to each vertex of G. If a vertex is assigned an empty set, then the union of color sets of its neighbors must be C. This assignment is called the k-rainbow dominating function of G. The minimum sum of numbers of assigned colors over all vertices of G is called the k-rainbow domination number of G. In this paper, we give some algorithms to determine the k-rainbow dominating sets on Sierpiński graphs with k ∈ {2, 3, 4}, and we have the upper bounds of k-rainbow domination number on Sierpiński graph where k ∈ {2, 3, 4}.

碩士
大葉大學
資訊工程學系碩士在職專班
94
In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski ([15]) developed a graph transformation that transforms a graph G into a new graph (G), we now call the Mycielskian of G. For t2, . The problem of determining the circular chromatic numbers of these graphs has been investigated in many papers. In this thesis, we shall study the range of c(Mt(G)), especially when G is a complete graph (Kn) or a circular complete graph . In [3], Chang, Huang, and Zhu proved that if cG)  G) r with r=1/2 or 1/3, then cM2tG))  M2tG)) r for every positive integer t. We find that this property is also true for r = 2/3. That is, when cG) is close to G) cM2tG)) will also be close to M2tG))  for every positive integer t.

碩士
淡江大學
中等學校教師在職進修數學教學碩士學位班
104
The routing number rt(G) of a connected graph G is the minimum integer r so that every permutation of vertices can be routed in r steps by swapping the ends of disjoint edges. In this paper, we study and prove the routing number of circular complete graph K_(p/q) is rt(K_(p/q) )≤2q， "for all" p≥3q，p,q∈Z^+.

We are interested in investigating the number of integral points on quadrics. First, we consider non-degenerate plane conic curves defined over Z. In particular we look at two types of conic sections: hyperbolas with two rational points at infinity, and ellipses. We give upper bounds for the number of integral points on such curves which depends on the number of divisors of the determinant of a given conic. Next we consider quadratic surfaces of the form q(x, y, z) = k, where k is an integer and q is a non-degenerate homogeneous quadratic form defined over Z. We give an upper bound for the number of integral points (x, y, z) with bounded height.

博士
國立中央大學
數學系
105
In 1966, P. M. Cohn introduced the concept of a generalized Euclidean ring, inspired by the property that any invertible matrix over a Euclidean ring can be row-reduced to the dentity matrix by elementary matrices. In 1984, Dennis, Magurn and Vaserstein proved that the integral group ring ZCm of finite cyclic group Cm is generalized Euclidean. It is well known that a Euclidean ring is quasi-Euclidean and a quasi-Euclidean ring is generalized Euclidean. In this thesis, we construct a finitely generated nonprincipal ideal of ZG for nontrivial abelian group G to show that ZG is neither Euclidean nor quasi-Euclidean. Moreover, we give an upper bound for the number of generators of an ideal in ZCm. The case m being a power of a prime is treated more seriously. In the final chapter, following the Wedderburn-Artin Theorem, we give a more accessible proof than Bass' to show that a semilocal ring has stable rank one, hence it is a generalized Euclidean ring.

碩士
國立東華大學
應用數學系
103
Let G be a graph and f : V (G) → N be a coloring on G. Define f(G)=∑_(x∈V(G))f(x).Suppose for all α∈{1,2,...,f(G)} there is a connected subgraph H of G, that ∑_(x∈V(H))f(x)=α , then f is said to be an IC-coloring of G.And the IC-index M(G) is defined as M(G) = max{f(G)|f is an IC-coloring of G}. Let us focus on the case that G = P_n, a path of length n. Previous results gives us the upper bound n(n+1)/2 -1 of M(P_n), which is a loose estimation. In this study,we introduce a new approach, exploiting the property of repeat- number, to make a tighter estimation of the upper bound of M(P_n),that M(Pn) <= n(n+1)/2 − 23 if n <= 14.

In der oberen Troposphäre und untersten Stratosphäre (OT/US) beeinflussen Aerosolpartikel im Submikrometerbereich den Strahlungshaushalt der Erde direkt und, was noch wichtiger ist, indirekt, da sie als Kondensationskern für Wolken dienen und somit die Spurengaskonzentrationen durch heterogene chemische Prozesse ändern können. Seit 1997 gibt es regelmäßige in situ Messungen der OT/US Partikel durch das Leibniz-Institut für Troposphärenforschung in Leipzig, Deutschland. Diese Messungen werden an Bord eines Passagierflugzeugs mit dem weltweit einzigartigen IAGOS-CARIBIC Messcontainer durchgeführt (www.iagos.org/iagos-caribic). In der vorliegenden Arbeit wurden die Partikelanzahlkonzentration und die Partikelgrößenverteilung im Submikrometerbereich der vergangenen Jahre ausgewertet. Dafür wurden die Daten von drei Kondensationspartikelzählern (CPC, Condensation Particle Counter) und einem optischen Partikelgrößenspektrometer (OPSS, Optical Particle Size Spectrometer) verwendet. Zunächst wurde im Labor eine umfangreiche Charakterisierung des IAGOS-CARIBIC OPSS hinsichtlich der Zähleffizienz durchgeführt. Weiterhin wurde eine Kalibrierung mit Polystyrol-Latex im geräterelevanten Bereich von 140 nm bis 1050 nm vorgenommen und daraus mit Hilfe der Mie-Streuung eine Funktion zur Datenauswertung für die OT/US entwickelt. Die statistische Analyse der IAGOS-CARIBIC OPSS und CPC Daten gibt einen guten Überblick über die in der OT/US vorkommenden Partikelanzahlkonzentrationen und stellt sicher, dass ein statistisch fundierter Datensatz für die Analyse zur Verfügung steht. Auf dieser Grundlage wurde zum ersten Mal eine detaillierte Analyse der raumzeitlichen Verteilung der Aitkenmode- und Akkumulationsmode-Partikelanzahlgrößenverteilung in der OT/US vorgenommen. Diese Analyse beinhaltet Weltkarten mit Medianwerten, Wahrscheinlichkeitsdichtefunktionen für spezielle Flugrouten und Partikelgrößenverteilungen entlang der Längengrade. Außerdem wurden die Partikelanzahlkonzentrationen zum ersten Mal mit dem globalen Klimamodell ECHAM-HAM verglichen. Dabei ergab sich, dass die Partikelanzahlkonzentration hauptsächlich von großräumigen Strömungsverhältnissen beeinflusst wird, was im Großen und Ganzen gut vom Modell wiedergegeben wird. Für die einzelnen Jahreszeiten wurden mit Hilfe der potentiellen Temperatur und äquivalenten Breitengrade die vertikalen Profile ausgewertet. Für die Analyse in Bezug auf die Aerosol-Mikrophysik und den Transport durch die Tropopause wurden auch die in IAGOS-CARIBIC gemessenen Spurengase, wie z.B. Ozon und Wasserdampf, hinzugezogen. Die Auswertung zeigt ebenfalls deutlich den Einfluss von Wolken in der oberen Troposphäre und verschiedene Austauschprozesse zwischen der Stratosphäre und Troposphäre. Außerdem wurde der Einfluss verschiedener Austauschprozesse auf die Partikelanzahlkonzentration untersucht: die Brewer-Dobson Zirkulation, warm conveyor belts, Isentropentransport und der Transport durch tropische, hochreichende konvektive Bewölkung. In der Vergangenheit wurde diese Analyse nur für atmosphärische Spurengase durchgeführt, und nun zum ersten Mal auch für Aerosolpartikel. Die hier präsentierten Ergebnisse zeigen eine umfangreiche Charakterisierung der Aitken- und Akkumulationsmode-Partikelanzahlkonzentration in der OT/US und den Einfluss von Austauschprozessen der Stratosphäre und Troposphäre auf die Partikel. Die Auswertungen tragen maßgeblich zum Verständnis und zur Vorhersage der Partikelanzahlkonzentration in Klimamodellen und damit schlussendlich zur Berechnung des Strahlungshaushalts der Erde und dessen zeitlicher Veränderung bei.
Submicrometer aerosol particles in the upper troposphere and lowermost stratosphere (UT/LMS) influence the Earth's radiation budget directly and, more important, indirectly, by acting as cloud condensation nuclei and by changing trace gas concentrations through heterogeneous chemical processes. Since 1997, regular in situ measurements of UT/LMS particles have been conducted by the Leibniz Institute for Tropospheric Research, Leipzig, Germany, using the world-wide unique IAGOS-CARIBIC observatory (www.iagos.org/iagos-caribic) onboard a passenger aircraft. In this thesis, UT/LMS aerosol particle number concentrations and the submicrometer aerosol particle size distribution as measured by three condensation particle counters (CPCs) and one Optical Particle Size Spectrometer (OPSS) are discussed. Before analyzing the measurement data from the UT/LMS region a throughout characterization of the IAGOS-CARIBIC OPSS with respect to the counting efficiency was carried out in the laboratory for the OPSS-relevant particle size range of 140 nm to 1040 nm diameter. After calibration with polystyrene latex (PSL) particles a theoretical response function, representative for the UT/LMS, was calculated with Mie theory to ensure a correct data analysis. The statistical analysis of the IAGOS-CARIBIC OPSS and CPC data gives a good overview of existing particle number concentrations in the UT/LMS and ensures a statistically sound data analysis. On this basis a detailed characterization of the spatio-temporal distribution of Aitken and accumulation mode particle number concentrations in the UT/LMS was carried out for the first time. This analysis includes global maps with median values, probability density functions for specific flight routes, and longitudinal distributions of the particle size distribution. Also a first comparison with the global climate model ECHAM-HAM was conducted. The analysis showed that the aerosol distributions are mainly influenced by large-scale circulation patterns which were, in gererel terms, well reflected by the global climate model. Moreover, seasonal vertical cross-sections for particle number concentrations, the potential temperature, and the equivalent latitude were generated. The results are interpreted with respect to aerosol microphysics and cross-tropopause transport using IAGOS-CARIBIC trace gases like ozone and water vapor. The influence of clouds in the troposphere and the different stratosphere-troposphere exchange processes are clearly visible. Furthermore, the influence of the major transport processes into the UT/LMS region on the aerosol particle number concentrations was investigated: the Brewer-Dobson circulation, warm conveyor belts, isentropic transport, and tropical deep convective cloud outflow. In the past this was done only for atmospheric trace gases, but now for the first time for aerosol particles. The findings presented in this study represent a comprehensive characterization of the Aitken and accumulation mode particle number concentration in the UT/LMS and the influence of stratospheric-tropospheric exchange processes on these particles. These findings may help to evaluate and improve predictions of particle number concentrations by climate models and finally the calculation of the Earth's radiation budget and its change over the years.

M.Sc.
In this dissertation we study two types of colourings, namely line-distinguishing colourings and harmonious colourings. A line-distinguishing colouring of a graph G is a k-colouring of the vertices of G such that no two edges have the same colour. The line-distinguishing chromatic number G is defined as the smallest k such that G has a line-distinguishing k-colouring. A harmonious colouring of a graph G is a proper k-colouring of the vertices of G such that no two edges have the same colour, i.e. no two adjacent vertices can have the same colour. The harmonious chromatic number hG is defined as the smallest k such that G has a line-distinguishing k-colouring. In Chapter 0 we discuss some of the terminology and definitions used later on in our study. In Chapter 1 we introduce line-distinguishing colourings and consider the line-distinguishing chromatic number of certain familiar classes of graphs such as trees, paths, cycles and complete graphs. We also consider graphs with line-distinguishing chromatic number G equal to the usual chromatic number G, and we compare G with the chromatic index G of a graph. In Chapter 2 we mostly discuss minimal line-distinguishing (MLD) colourings. We consider minimal line-distinguishing colourings and graphs of diameter two as well as classes of regular MLD-colourable graphs. We also introduce the concept of distance regular graphs and discuss minimal line-distinguishing colourings in these graphs. In Chapter 3 we introduce a new parameter, namely the upper line-distinguishing chromatic number H G of a graph. We investigate H G for paths and cycles, and consider graphs with small upper line-distinguishing chromatic numbers. In Chapter 4 we consider the second type of colouring studied in this dissertation, namely harmonious colourings. We define the harmonious chromatic number hG and determine hG for certain classes of graphs such as paths, trees, cycles and complete graphs. In Chapter 5 we discuss upper and lower bound for hG. In Chapter 6 we discuss the upper harmonious chromatic number HG of a graph, and we determine HG for paths and cycles. We also consider graphs satisfying HG  G  1. The purpose of this study is to compile a resource which will give a thorough and well-integrated background on line-distinguishing and harmonious colourings. It is also intended to lay the groundwork for further doctoral studies in the field of colourings.

碩士
國立中正大學
資訊工程研究所
90
In this paper we give new upper bounds on feedback vertex numbers in butterflies and toroidal butterflies. The graphs considered are undirected graphs of bounded degree and widely used as inter- connection networks. We give algorithms to find approximating minimum feedback vertex sets. The new upper bounds are better than previous results.

碩士
國立中央大學
數學系
82
Neumann (cf.Feller(1950,p.210),或 Chow 和 Teicher (1988,p61))證 明一個關於連段數定理, 但是它並不一定被任何的子序列所滿足, Quall(1974)The law of the iterated logarithm on arbitrary sequences for stationary Gaussian processes and Browian motion. Ann.Probab. 5,724-739.提出 "Thinner Subsequences" 之觀念,經由 Chow, Teicher, Wei 和 Yu (1981) Iterated logarithm laws with random subsequences, Z. Wahr- scheinlichkeitstheorie verw. Geb. 57,235-251,的論文, 我們亦利用稀疏子序列來證明滿足Neumann 結果的 子序列成立之充要條件. Neumann (cf.Feller(1950,p.210),or Chow and Teicher (1988,p61)) proved that a theorem on Numbers Of Runs, but it not satisfied by any subsequences, by Qualls(1974) "The law of the iterated logarithm on arbitrary sequences for stationary Gaussian processes and Browian motion. Ann. Probab. 5,724-739" appending the concept about "Thinner Subsequences" and pattern after Chow, Teicher, Wei and Yu (1981) "Iterated logarithm laws with random subsequences, Z. Wahrscheinlichkeitstheorie verw. Geb. 57,235-251", we also use thinner subsequences to prove a theorem about Neumann's result that satisfies sufficient and necessary conditions.

We consider a simplified model based on the Navier-Stokes-Fourier system coupled to a transport equation and the Maxwell system, proposed to describe radiative flows in stars. We establish global- in-time existence for the associated initial-boundary value problem in the framework of weak solutions. Next, we study a hydrodynamical model describing the motion of internal stellar layers based on compressible Navier-Stokes-Fourier-Poisson system. We suppose that the medium is electrically charged, we include energy exchanges through radiative transfer and we assume that the system is steadily rotating. We analyze the singular limit of this system when the Mach number, the Alfven number, the Peclet number and the Froude number go to zero in a certain way and prove convergence to a 3D incompressible MHD system with a stationary linear transport equation for transport of radiation intensity. Finally, we show that the energy equation reduces to a steady equation for the temperature corrector.