Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces

MSC 2010: 26A33

Invariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras

2000 Mathematics Subject Classification: 16R10, 16R30.

On the Algebraic Properties of Convex Bodies

AMS subject classification: 52A01, 13C99.

Az európai gazdasági kormányzás előtt álló kihívások. A hármas tagadás lehetetlensége (Challenges of European economic governance. The impossible trinity of denial.)

Az európai gazdasági integráció folyamata olyan kényszerhelyzetekben formálódott a múltban, amelyek a közgazdaságtudományban jól ismert lehetetlen háromság alapján is leírhatók. Az Európai Monetáris Rendszer a rögzített árfolyam-mechanizmusra és önálló jegybanki politikára épített, korlátozva a tőkemozgásokat. A Gazdasági és Monetáris Unió ugyanakkor a tőke szabad áramlásával és az árfolyamok visszavonhatatlan rögzítésével felszámolta a tagállami szintű jegybanki autonómiát. Az euróövezet működése egyszersmind arra a háromszoros tagadásra épül(t), hogy 1. nem lehetséges az euróövezetből való kilépés, 2. nem engedélyezett a kimentés és 3. nem kerülhet sor államcsődre. A 2008-ban Európát is elérő pénzügyi és gazdasági válság azonban elemi erővel mutatott rá e hármas tiltás tarthatatlanságára. A gazdasági kormányzás körül kibontakozott viták így jól közelíthetők a három tiltó szabály egyidejű érvényesülése lehetetlenségének bemutatásával, számba véve az egyes opciók költségeit és lehetséges hasznait. / === / The process of economic integration in the EU has been shaped by the well-known theorem of the impossible trinity. Accordingly, the European Monetary System was built upon a mix of a fixed exchange-rate regime and an autonomous monetary policy, thereby constraining capital mobility. In launching the EMU project, the EU countries decided to fix national currencies irrevocably and maintain full capital mobility, in exchange for delegating their monetary policy upwards to a supranational level. The introduction of the Euro zone, however, has simultaneously meant denial of the following three elements: (1) exit, (2) bail-out, and (3) default. Nevertheless, the 2008–9 financial and economic crisis has demonstrated mercilessly that these three pillars are incompatible with each other. So the current debates on reshaping economic governance in the EU can be modelled by introducing the “impossible trinity of denial”, concentrating on the benefits and the costs of each option.

An analysis of the on-time graduation rate in the two-year program at National Taipei Institute of Technology in Taiwan

Taiwan's technical vocational educational system includes three levels: (1) institutes of technology (two and four year programs), (2) junior colleges (two, three and five year programs), and (3) senior vocational schools. Two-year junior colleges enroll their students through two channels: (1) based on results of the Particular Screening Entrance Examination (PSEE), (2) based on the Joint College Entrance Examination (JCEE). The PSEE has two categories: Category I includes on-time graduates with excellent performance, which means that they are within the top ten of their classes; Category II students include award-winning students in talent contests who have achieved a minimum grade point average of 75%. The JCEE is a regular entrance examination given to any senior vocation school graduate.^ Basic courses have a great impact on the students' academic performance. The purpose of the study was to focus on the effectiveness of teaching mathematics in two-year junior colleges and to analyze and correlate the results of two-year junior college students' performance in calculus and on-time graduation. The target group consisted of 521 students enrolled at National Taipei Institute of Technology in 1993.^ Calculus is a very important course for engineering majors in two-year junior colleges and has a great impact on the students' academic performance. This retrospective study showed that there was a correlation between students' performance in calculus and on-time graduation after two years of study.^ The conclusions of the study urge the Ministry of Education to reform two-year junior college curriculum standards to emphasize basic rudimentary courses. It is recommended that engineering majors receive three hours of calculus per week as the current requirement of only two hours per week is inadequate. The future job market will require a technologically advanced labor force that can be trained in a higher education system. More channels of higher education for two-year junior college graduates should be made available for those wishing to pursue bachelor degrees. Additional work in calculus will not only enhance the opportunities for two-year junior college graduates to continue their pursuit of an advanced academic degree, but also serve them well as they seek career advancement. ^

Transmission electron tomography: quality assessment and enhancement for three-dimensional imaging of nanostructures

Nanotechnology has revolutionised humanity's capability in building microscopic systems by manipulating materials on a molecular and atomic scale. Nan-osystems are becoming increasingly smaller and more complex from the chemical perspective which increases the demand for microscopic characterisation techniques. Among others, transmission electron microscopy (TEM) is an indispensable tool that is increasingly used to study the structures of nanosystems down to the molecular and atomic scale. However, despite the effectivity of this tool, it can only provide 2-dimensional projection (shadow) images of the 3D structure, leaving the 3-dimensional information hidden which can lead to incomplete or erroneous characterization. One very promising inspection method is Electron Tomography (ET), which is rapidly becoming an important tool to explore the 3D nano-world. ET provides (sub-)nanometer resolution in all three dimensions of the sample under investigation. However, the fidelity of the ET tomogram that is achieved by current ET reconstruction procedures remains a major challenge. This thesis addresses the assessment and advancement of electron tomographic methods to enable high-fidelity three-dimensional investigations. A quality assessment investigation was conducted to provide a quality quantitative analysis of the main established ET reconstruction algorithms and to study the influence of the experimental conditions on the quality of the reconstructed ET tomogram. Regular shaped nanoparticles were used as a ground-truth for this study. It is concluded that the fidelity of the post-reconstruction quantitative analysis and segmentation is limited, mainly by the fidelity of the reconstructed ET tomogram. This motivates the development of an improved tomographic reconstruction process. In this thesis, a novel ET method was proposed, named dictionary learning electron tomography (DLET). DLET is based on the recent mathematical theorem of compressed sensing (CS) which employs the sparsity of ET tomograms to enable accurate reconstruction from undersampled (S)TEM tilt series. DLET learns the sparsifying transform (dictionary) in an adaptive way and reconstructs the tomogram simultaneously from highly undersampled tilt series. In this method, the sparsity is applied on overlapping image patches favouring local structures. Furthermore, the dictionary is adapted to the specific tomogram instance, thereby favouring better sparsity and consequently higher quality reconstructions. The reconstruction algorithm is based on an alternating procedure that learns the sparsifying dictionary and employs it to remove artifacts and noise in one step, and then restores the tomogram data in the other step. Simulation and real ET experiments of several morphologies are performed with a variety of setups. Reconstruction results validate its efficiency in both noiseless and noisy cases and show that it yields an improved reconstruction quality with fast convergence. The proposed method enables the recovery of high-fidelity information without the need to worry about what sparsifying transform to select or whether the images used strictly follow the pre-conditions of a certain transform (e.g. strictly piecewise constant for Total Variation minimisation). This can also avoid artifacts that can be introduced by specific sparsifying transforms (e.g. the staircase artifacts the may result when using Total Variation minimisation). Moreover, this thesis shows how reliable elementally sensitive tomography using EELS is possible with the aid of both appropriate use of Dual electron energy loss spectroscopy (DualEELS) and the DLET compressed sensing algorithm to make the best use of the limited data volume and signal to noise inherent in core-loss electron energy loss spectroscopy (EELS) from nanoparticles of an industrially important material. Taken together, the results presented in this thesis demonstrates how high-fidelity ET reconstructions can be achieved using a compressed sensing approach.

Oral Health among Young Adults and the Middle-aged in Iran

The aim of the present study was to assess oral health and treatment needs among adult Iranians according to socio-demographic status, smoking, and oral hygiene, and to investigate the relationships between these determinants and oral health. Data for 4448 young adult (aged 18) and 8301 middle-aged (aged 35 to 44) Iranians were collected in 2002 as part of a national survey using the World Health Organization (WHO) criteria for sampling and clinical diagnoses, across 28 provinces by 33 calibrated examiners. Gender, age, place of residence, and level of education served as socio-demographic information, smoking as behavioural and modified plaque index (PI) as the biological risk indicator for oral hygiene. Number of teeth, decayed teeth (DT), filled teeth (FT), decayed, missing, filled teeth (DMFT), community periodontal index (CPI), and prosthodontic rehabilitation served as outcome variables of oral health. Mean number of DMFT was 4.3 (Standard deviation (SD) = 3.7) in young adults and 11.0 (SD = 6.4) among middle-aged individuals. Among young adults the D-component (DT = 70%), and among middle-aged individuals the M-component (60%) dominated in the DMFT index. Among young adults, visible plaque was found in nearly all subjects. Maximum (max) PI was associated with higher mean number of DT, and higher periodontal treatment needs. A healthy periodontium was a rare condition, with 8% of young adults and 1% of middle-aged individuals having a max CPI = 0. The majority of the CPI findings among young adults consisted of calculus (48%) and deepened periodontal pockets (21%). Respective values for middle-aged individuals were 40% and 53%. Having a deep pocket (max CPI = 4) was more likely among young adults with a low level of education (Odds ratio (OR) = 2.7, 95% Confidence interval (CI) = 1.9–4.0) than it was among well-educated individuals. Among middle-aged individuals, having calculus or a periodontal pocket was more likely in men (OR = 1.8, 95% CI = 1.6–2.0) and in illiterate subjects (OR = 6.3, 95% CI = 5.1–7.8) than it was for their counterparts. Among young adults, having 28 teeth was more (p < 0.05) prevalent among men (72% vs. 68% for women), urban residents (71% vs. 67% for rural residents), and those with a high level of education (73% vs. 60% for those with a low level). Among middle-aged individuals, having a functional dentition was associated with younger age (OR = 2.0, 95% CI = 1.7−2.5) and higher level of education (OR = 1.8, 95% CI = 1.6−2.1). Of middle-aged individuals, 2% of 35- to 39-year-olds and 5% of those aged 40 to 44 were edentulous. Among the dentate subjects (n = 7,925), prosthodontic rehabilitation was more prevalent (p < 0.001) among women, urban residents, and those with a high level of education than it was among their counterparts. Among those having 1 to 19 teeth, a removable denture was the most common type of prosthodontic rehabilitation. Middle-aged individuals lacking a functional dentition were more likely (OR = 6.0, 95% CI = 4.8−7.6) to have prosthodontic rehabilitation than were those having a functional dentition. In total, 81% of all reported being non-smokers, and 32% of men and 5% of women were current smokers. Heavy smokers were the most likely to have deepened periodontal pockets (max CPI ≥ 3, OR = 2.9, 95% CI = 1.8−4.7) and to have less than 20 teeth (OR = 2.3, 95% CI = 1.5−3.6). The findings indicate impaired oral health status in adult Iranians, particularly those of low socio-economic status and educational level. The high prevalence of dental plaque and calculus and considerable unmet treatment needs call for a preventive population strategy with special emphasis on the improvement of oral self-care and smoking cessation to tackle the underlying risk factors for oral diseases in the Iranian adult population.

Uniform algebras generated by holomorphic and close-to-harmonic functions

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc (D) over bar generated by z and h, where h is a nowhere-holomorphic harmonic function on D that is continuous up to partial derivative D, equals C((D) over bar). The abstract tools used by Axler and Shields make harmonicity of h an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if h is replaced by h + R, where R is a non-harmonic perturbation whose Laplacian is ``small'' in a certain sense.

3-MANIFOLD GROUPS, KÄHLER GROUPS AND COMPLEX SURFACES

Let G be a Kahler group admitting a short exact sequence 1 -> N -> G -> Q -> 1 where N is finitely generated. (i) Then Q cannot be non-nilpotent solvable. (ii) Suppose in addition that Q satisfies one of the following: (a) Q admits a discrete faithful non-elementary action on H-n for some n >= 2. (b) Q admits a discrete faithful non-elementary minimal action on a simplicial tree with more than two ends. (c) Q admits a (strong-stable) cut R such that the intersection of all conjugates of R is trivial. Then G is virtually a surface group. It follows that if Q is infinite, not virtually cyclic, and is the fundamental group of some closed 3-manifold, then Q contains as a finite index subgroup either a finite index subgroup of the three-dimensional Heisenberg group or the fundamental group of the Cartesian product of a closed oriented surface of positive genus and the circle. As a corollary, we obtain a new proof of a theorem of Dimca and Suciu in Which 3-manifold groups are Kahler groups? J. Eur. Math. Soc. 11 (2009) 521-528] by taking N to be the trivial group. If instead, G is the fundamental group of a compact complex surface, and N is finitely presented, then we show that Q must contain the fundamental group of a Seifert-fibered 3-manifold as a finite index subgroup, and G contains as a finite index subgroup the fundamental group of an elliptic fibration. We also give an example showing that the relation of quasi-isometry does not preserve Kahler groups. This gives a negative answer to a question of Gromov which asks whether Kahler groups can be characterized by their asymptotic geometry.

Revisiting the Fourier transform on the Heisenberg group

A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on R-n as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. In this note we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group.

On Hermite pseudo-multipliers

In this article we deal with a variation of a theorem of Mauceri concerning the L-P boundedness of operators M which are known to be bounded on L-2. We obtain sufficient conditions on the kernel of the operator M so that it satisfies weighted L-P estimates. As an application we prove L-P boundedness of Hermite pseudo-multipliers. (C) 2014 Elsevier Inc. All rights reserved.

A papaína no tratamento da periodontite crônica

A raspagem subgengival e o alisamento radicular constituem o "padrão ouro" e o tratamento de eleição para a periodontite; porém, é um procedimento difícil de ser executado, que requer um intenso treinamento e que pode expor a dentina, causando hipersensibilidade dentinária pela remoção excessiva de cemento, ou produzir defeitos, como sulcos e ranhuras, além de deixar cálculo residual e não conseguir atingir toda as superfície radicular. Recentemente, um gel a base de papaína e cloramina foi introduzido no mercado (Papacárie), utilizado no tratamento da remoção de dentina cariada. Este gel poderia auxiliar na remoção do cálculo subgengival com menor desgaste do cemento. O objetivo deste trabalho foi comparar a eficácia e analisar a superfície radicular na utilização de um gel à base de papaína e cloramina, associado ao alisamento radicular, na região subgengival. Após receberem instruções de higiene oral, raspagem supragengival e polimento coronário, 18 pacientes com periodontite crônica, 6 mulheres e 12 homens, com idade média de 51 anos (8) foram tratados num modelo de boca dividida. O tratamento-teste foi constituído pela aplicação do gel na área subgengival por 1 min., seguida pelo alisamento radicular; o tratamento-controle foi constituído pela raspagem subgengival e alisamento radiculares. A terapia foi executada por 3 operadoras e os exames inicial, de 28 dias e 3 meses, foram realizados por um único examinador. Quatro dentes nunca tratados de dois outros pacientes (2 incisivos centrais inferiores e 2 premolares), com indicação para extração, foram submetidos ao tratamento teste e controle e, após a exodontia, analisados em microscopia eletrônica de varredura (MEV). Ao longo dos 3 meses, os resultados demonstraram significativa melhora nos parâmetros clínicos: sangramento à sondagem, profundidade de bolsa e ganho de inserção, tanto no lado-teste, como no lado-controle, principalmente aos 28 dias; mas não foi observada significância estatística quando ambas as formas de terapia foram comparadas. O índice de placa médio permaneceu alto ao longo do estudo. A análise do MEV demonstrou que o tratamento-teste deixou uma maior quantidade de cálculo residual sobre a superfície radicular; porém, áreas livres de cálculo também foram observadas. No tratamento-controle, verificaram-se regiões mais profundas não atingidas pelas curetas, áreas livres de cálculo e um sulco produzido pela cureta. Concluiu-se que tanto o tratamento-teste, como o controle, foram eficazes no tratamento da periodontite crônica nos 3 meses observados.

Multiplication in Riesz spaces

A.G. Vulih has shown how an essentially unique intrinsic multiplication can be defined in certain types of Riesz spaces (vector lattices) L. In general, the multiplication is not universally defined in L, but L can always be imbedded in a large space L^# in which multiplication is universally defined.

If ф is a normal integral in L, then ф can be extended to a normal integral on a large space L₁(ф) in L^#, and L₁(ф) may be regarded as an abstract integral space. A very general form of the Radon-Nikodym theorem can be proved in L₁(ф), and this can be used to give a relatively simple proof of a theorem of Segal giving a necessary and sufficient condition that the Radon-Nikodym theorem hold in a measure space.

In another application, the multiplication is used to give a representation of certain Riesz spaces as rings of operators on a Hilbert space.

On the Lyapunov transformation for stable matrices

The matrices studied here are positive stable (or briefly stable). These are matrices, real or complex, whose eigenvalues have positive real parts. A theorem of Lyapunov states that A is stable if and only if there exists H ˃ 0 such that AH + HA* = I. Let A be a stable matrix. Three aspects of the Lyapunov transformation L_A :H → AH + HA* are discussed.

1. Let C₁ (A) = {AH + HA* :H ≥ 0} and C₂ (A) = {H: AH+HA* ≥ 0}. The problems of determining the cones C₁(A) and C₂(A) are still unsolved. Using solvability theory for linear equations over cones it is proved that C₁(A) is the polar of C₂(A*), and it is also shown that C₁ (A) = C₁(A^-1). The inertia assumed by matrices in C₁(A) is characterized.

2. The index of dissipation of A was defined to be the maximum number of equal eigenvalues of H, where H runs through all matrices in the interior of C₂(A). Upper and lower bounds, as well as some properties of this index, are given.

3. We consider the minimal eigenvalue of the Lyapunov transform AH+HA*, where H varies over the set of all positive semi-definite matrices whose largest eigenvalue is less than or equal to one. Denote it by ψ(A). It is proved that if A is Hermitian and has eigenvalues μ₁ ≥ μ₂…≥ μ_n ˃ 0, then ψ(A) = -(μ₁-μ_n)²/(4(μ₁ + μ_n)). The value of ψ(A) is also determined in case A is a normal, stable matrix. Then ψ(A) can be expressed in terms of at most three of the eigenvalues of A. If A is an arbitrary stable matrix, then upper and lower bounds for ψ(A) are obtained.

Uma proposta para introdução de noções de Cálculo no ensino médio

A presente dissertação tem o objetivo de propor a reinclusão de elementos de Cálculo no ensino médio, pois no passado o Cálculo fazia parte do currículo e foi abolido após uma reforma no ensino da matemática. O trabalho apresenta os resultados de um levantamento estatístico sobre os índices de reprovação na disciplina Cálculo Diferencial e Integral I nos períodos mais recentes da Universidade do Estado do Rio de Janeiro (UERJ) e, também, uma pesquisa quantitativa com quarenta professores de matemática com o objetivo de analisar a viabilidade do projeto e os problemas a serem enfrentados. Por fim, a dissertação conta com uma série de atividades comentadas sobre o tema de limites, que é o foco do trabalho. Tais atividades podem ser incluídas já no 1 ano do ensino médio, paralelamente ao conteúdo de funções, e visam proporcionar aos estudantes o contato com elementos de Cálculo em uma linguagem acessível, e orientar o professor nesta tarefa