A classic combinatorics problem is: What is the probability that if n people randomly reach into a dark closet to retrieve their hats, no person will pick his own hat? Now there are n! ways to retrieve n hats if you didn't care which hat you got. But for this problem you need to determine how may different ways no person will pick his own hat. In this paper we expand on the original idea and consider two variations of this problem: If there are n elements and m distinguishable possibilities, in how many ways can you rearrange these elements. For example, if n men check their hats and k women check their hats, in how many ways will the men retrieve a different hat than the one he checked. The second problem is: if n people randomly reach into a dark closet to retrieve their hat but now there are m hats in the closet, how many different ways will no person retrieve his hat? In the second case m >= n.

在本論文中，令Dn是{1, 2,..., n}的錯排列所形成的集合，而讓dn代表Dn的個數。我們討論一個常用的遞迴關係式：dn=(n-1)(dn-1+dn-2)。針對這個公式，我們將會先給一個組合論證；而本文將提供一個更為簡潔的方式來證明這個遞迴關係式，就是構造出兩個函數，分別從類Dn-1和Dn-2的集合映射到Dn上，並且證明這兩個函數是對射的函數。 本文第一章先對錯排列作一個簡單的介紹，第二章則說明我們錯排列之間的映射是如何製造出來的，並且證明這樣的映射是沒有問題的，第三章則提供其他錯排列遞迴關係式的資訊，讓其他有興趣的夥伴們能一起探討。

O objetivo do presente estudo foi comparar dois métodos utilizados para determinar a posição do disco articular em boca fechada por meio de imagens sagitais corrigidas de Ressonância Magnética (RM). Um método analisa a localização da banda posterior em relação aos ponteiros de um relógio, e o outro analisa a localização da zona intermediária do disco articular em relação à cabeça da mandíbula e o tubérculo articular. Este estudo também avaliou a correlação entre o diagnóstico clínico e o diagnóstico obtido por cada método. Uma amostra de 20 pacientes com sinais e sintomas de disfunção temporomandibular foi examinada clinicamente e um diagnóstico clínico foi obtido. Imagens sagitais corrigidas de RM foram obtidas de ambas as articulações utilizando um aparelho de 0,3T com bobinas de superfície bilaterais. O método baseado nos ponteiros de horas de um relógio resultou numa maior percentagem de discos articulares com deslocamento anterior (52,5%) quando comparado ao segundo método (30,0%). Foi encontrada diferença estatisticamente significante entre os dois métodos. A concordância geral entre ambos os métodos foi de 77,5%, a concordância entre o diagnóstico clínico e o método do relógio foi de 70,0%, e a concordância entre o diagnóstico clínico e o método da zona intermediária foi de 87,5%. Não foi encontrada diferença estatisticamente significante entre o diagnóstico clínico e o método baseado na localização da zona intermediária. / The purpose of the present study was to compare two methods used to determine disc position with the mouth closed based on corrected sagittal Magnetic Resonance (RM) images. One method analyzes the posterior band location in terms of hours on a clock face, and the other analyzes the location of the intermediate zone of the disc in relation to the mandibular head and the articular tubercle. This study also evaluated the correlation between the clinical diagnosis with the diagnosis obtained by each method. A series of 20 patients with signs and symptoms of temporomandibular dysfunction was clinically examinated and a clinical diagnosis was reached. Corrected sagittal RM images were acquired for both joints using a 0.3T equipment with bilateral surface coils. The method based on the posterior band location in terms of hours on a clock face yielded a higher percentage of anterior displaced discs (52.5%) when compared with the second method (30.0%). Statistically significant difference between the two methods was found. The overall agreement between both methods was 77.5%, the agreement between the clinical diagnosis and the clock face method was 70.0%, and the agreement between the clinical diagnosis and the intermediate zone method was 87.5%. No statistically significant difference was found between the clinical diagnosis and the method based on the location of the intermediate zone.

O objetivo do presente estudo foi comparar dois métodos utilizados para determinar a posição do disco articular em boca fechada por meio de imagens sagitais corrigidas de Ressonância Magnética (RM). Um método analisa a localização da banda posterior em relação aos ponteiros de um relógio, e o outro analisa a localização da zona intermediária do disco articular em relação à cabeça da mandíbula e o tubérculo articular. Este estudo também avaliou a correlação entre o diagnóstico clínico e o diagnóstico obtido por cada método. Uma amostra de 20 pacientes com sinais e sintomas de disfunção temporomandibular foi examinada clinicamente e um diagnóstico clínico foi obtido. Imagens sagitais corrigidas de RM foram obtidas de ambas as articulações utilizando um aparelho de 0,3T com bobinas de superfície bilaterais. O método baseado nos ponteiros de horas de um relógio resultou numa maior percentagem de discos articulares com deslocamento anterior (52,5%) quando comparado ao segundo método (30,0%). Foi encontrada diferença estatisticamente significante entre os dois métodos. A concordância geral entre ambos os métodos foi de 77,5%, a concordância entre o diagnóstico clínico e o método do relógio foi de 70,0%, e a concordância entre o diagnóstico clínico e o método da zona intermediária foi de 87,5%. Não foi encontrada diferença estatisticamente significante entre o diagnóstico clínico e o método baseado na localização da zona intermediária. / The purpose of the present study was to compare two methods used to determine disc position with the mouth closed based on corrected sagittal Magnetic Resonance (RM) images. One method analyzes the posterior band location in terms of hours on a clock face, and the other analyzes the location of the intermediate zone of the disc in relation to the mandibular head and the articular tubercle. This study also evaluated the correlation between the clinical diagnosis with the diagnosis obtained by each method. A series of 20 patients with signs and symptoms of temporomandibular dysfunction was clinically examinated and a clinical diagnosis was reached. Corrected sagittal RM images were acquired for both joints using a 0.3T equipment with bilateral surface coils. The method based on the posterior band location in terms of hours on a clock face yielded a higher percentage of anterior displaced discs (52.5%) when compared with the second method (30.0%). Statistically significant difference between the two methods was found. The overall agreement between both methods was 77.5%, the agreement between the clinical diagnosis and the clock face method was 70.0%, and the agreement between the clinical diagnosis and the intermediate zone method was 87.5%. No statistically significant difference was found between the clinical diagnosis and the method based on the location of the intermediate zone.

Integruojant vaikus, turinčius elgesio ir emocijų sutrikimų į bendrojo lavinimo mokyklas susiduriama su lėta integracija, kuri lydima įvairių sunkumų. Remiantis teorine, moksline literatūra ir atlikto tyrimo duomenimis parengti modeliai darbui su vaikais, turinčiais elgesio ir emocijų sutrikimų, padėtų sėkmingiau vaikams socializuotis, o mokytojams ugdymo procesą padarytų patrauklesnį. Vilniaus Šeškinės pradinėje mokykloje 2006/2007 m.m. įsteigta pirmoji Lietuvoje specialioji klasė vaikams, turintiems elgesio ir emocijų sutrikimų. Įsteigta specialioji klasė vaikams, turintiems elgesio ir emocijų sutrikimų, Vilniaus Šeškinės pradinėje mokykloje, ir darbas joje, iniciavo gilinimąsi į šią problemą ir sprendimo suradimą. Siekiant ištirti ugdymo proceso organizavimo ir valdymo tobulinimo galimybes, integruojant vaikus, turinčius elgesio ir emocijų sutrikimų analizuojami nagrinėjamos problemos moksliniai, teoriniai pagrindai. Siekiama išsiaiškinti mokytojų ir mokyklų vadovų, vaikų ir tėvų požiūrį į vaikų, turinčių elgesio ir emocijų sutrikimų, mokymąsi bendrojo lavinimo mokykloje, specialioje klasėje. / The main problem of the work is slow integration of children with derangements in their behaviour and emotions. According to nonfiction, theoretical literature and the data of the research models for work with children, who has derangements in their behaviour and emotions were formulated. These models would help the children to socialize and make the education process more attractive. The special class for the children who has derangements in their behaviour and emotions was established in 2006/2007 school year in Vilnius at Seskines primary school. This class is the first in Lithuania. This class and work there initiated to go deeper into the problem and discover the decision. On purpose to explore the possibilities how to improve the planning and management of the education process integrating the children with derangements in their behaviour and emotions, scientific and theoretical basics of the problem are analysed. The opinion of teachers, headmasters, children and parents about the children with derangements in their behaviour and emotions learning at school in special class is being found out in this work.

This thesis consists of both theoretical and practical parts. The aim of the theoretical part is to present the basic concepts of this field of research, then discuss the types of nourishment intake defects, their causes and treatment, and also to define the term "pubescent". The entire theoretical part is based on the examined professional literature. The practical part focuses on research which ascertains pubescents´ awareness of the topic and the possible influence and occurrence of the nourishment intake defects in pubescents. Following the practical part, there is a summary and evaluation of the results based on the questionnaire method.

關於錯排列(Derangements)│D_n│=n│D_n-1│+(-1)ⁿ 的證明可用代數方法證出，甚至│D_n│的個數亦可由生成函數求出，因此我們希望能藉用更直接的觀點加以探討和證明，並找出彼此的對應。 　　當我們確定了D_n→n D_n-1的對應方式，它可以做為密碼的利用，當我們傳送一個D_n中的碼，可由譯碼的過程（即對應方式），對應到D_n-1中的一個碼（而且是1對1），因此在機密性方面有很大的幫助。 　　本文章節安排如下： 　　第一章錯排列的簡介 　　第二章如何製造錯排列 　　第三章錯排列的對應

Au cours des deux dernières décennies, des travaux actifs ont été menés pour étendre des résultats classiques liés au groupe symétrique à d'autres groupes plus généraux. Cette thèse a pour objectif d’étendre aux produits en couronne les résultats concernant le tableau de différence d’Euler. Elle est divisée en cinq chapitres. Le tableau de différence d’Euler lié à la suite {n!} conduit naturellement à la formule du nombre de dérangements. Nous étudions dans les deux premiers chapitres, le tableau de différence d’Euler associé à la suite {rnn!} et la généralisation du problème de dérangements. Pour les coefficients de ce dernier tableau, nous donnons des interprétations combinatoires en termes de k-successions sur les produits en couronne. Clarke et al. ont introduit un q-analogue du tableau de différence d’Euler sur le groupe symétrique. Dans le troisième chapitre, nous étendons leurs résultats sur les produits en couronne. En généralisant leur bijection, nous montrons que « (fix, exc, fmaj) » et « (fix, exc, fmaf) » sont équidistribués sur les produits en couronne où «fmaf» est une nouvelle statistique mahonienne. D’autre part, Foata et Han ont récemment construit deux transformations. Nous prouvons dans le quatrième chapitre que ses bijections fournissent une factorisation de la bijection de Clarke et al.. Dans le cinquième chapitre nous donnons une extension de la seconde transformation fondamentale de Foata sur les mots r-colorés. Nous prouvons l’équidistribution sur les produits en couronne de « (fmaj , des*) » et « (finv , col) » où « col » est la somme des couleurs et « des* » une nouvelle statistique. / In the last two decades, much effort has been made to extend various enumerative results on symmetric groups to other more general groups. The main objective of this thesis is to extend to wreath products the results that concern the Euler's difference table. It is divided into five chapters. Euler's difference table associated to the sequence {n!} leads naturally to the counting formula for the derangements. In the first two chapters, we study Euler's difference table associated to the sequence {rnn!} and the generalized derangement problem. For the coefficients appearing in the later table, we give the combinatorial interpretations in terms of k-successions on wreath products. Clarke et al. introduced a q-analogue of Euler's difference table on symmetric group. In the third chapter, we extend their results to wreath products. By generalizing their bijection, we prove the equidistribution of the triple statistics “(fix, exc, fmaj)” and “(fix, exc, fmaf)” on wreath products, where “fmaf” is a new mahonian statistic on wreath products. On the other hand, Foata and Han have recently constructed two new transformations. We prove in fourth chapter that their two bijections provide a factorization of Clarke et al.'s bijection. In the fifth chapter we give an extension of Foata’s second fundamental transformation on r-colored words. We show that the bistatistics “(fmaj , des*)” and “(finv , col)” are equidistributed on wreath products, where “col” is the sum of color and “des*” a new statistic.