DEA models for ratio data:convexity consideration

Data envelopment analysis (DEA) is defined based on observed units and by finding the distance of each unit to the border of estimated production possibility set (PPS). The convexity is one of the underlying assumptions of the PPS. This paper shows some difficulties of using standard DEA models in the presence of input-ratios and/or output-ratios. The paper defines a new convexity assumption when data includes a ratio variable. Then it proposes a series of modified DEA models which are capable to rectify this problem.

On a Convexity Preserving Integral Operator

MSC 2010: 30C45, 30A20, 34C40

Convexity, C-convexity and Pseudoconvexity

Николай М. Николов - Разгледани са характеризации на различни понятия за изпъкналост, като тези понятия са сравнени.

Convexity around the Unit of a Banach Algebra

2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.

Uniform G-Convexity for Vector-Valued Lp Spaces

2000 Mathematics Subject Classification: 46B20.

Viable solutions to nonautonomous inclusions without convexity

The existence of viable solutions is proven for nonautonomous upper semicontinuous differential inclusions whose right-hand side is contained in the Clarke subdifferential of a locally Lipschitz continuous function.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Efeitos do aparelho Jasper Jumper no tratamento da má oclusão de Classe II

OBJETIVO: o objetivo deste estudo foi avaliar os efeitos esqueléticos e dentoalveolares do tratamento de pacientes com má oclusão de Classe II com o aparelho Jasper Jumper associado ao aparelho ortodôntico fixo, comparados a um grupo controle não-tratado. MÉTODOS: a amostra foi constituída por 47 indivíduos, divididos em dois grupos: Grupo 1, contendo 25 pacientes com idade média de 12,72 anos, tratados com o aparelho Jasper Jumper por um tempo médio de 2,15 anos; Grupo 2 (controle), composto por 22 indivíduos com idade média de 12,67 anos, não-submetidos a tratamento ortodôntico e com má oclusão de Classe II, observados por um período médio de 2,12 anos. Foram avaliadas as telerradiografias ao início e ao final do tratamento ortodôntico para o Grupo 1 e do período de observação para o Grupo 2. As variáveis cefalométricas iniciais, finais e as alterações com o tratamento foram comparadas entre os grupos por meio do teste t independente. RESULTADOS: em comparação ao grupo controle, o grupo Jasper Jumper apresentou maior restrição do deslocamento anterior da maxila e maior retrusão maxilar, melhora da relação maxilomandibular, diminuição da convexidade facial, maior protrusão e intrusão dos incisivos inferiores e maior extrusão dos molares inferiores, além de maior diminuição dos trespasses horizontal e vertical e maior melhora da relação molar. CONCLUSÃO: a correção da Classe II no grupo tratado com o Jasper Jumper e aparelhagem fixa se deu principalmente devido à restrição do crescimento maxilar, protrusão e intrusão dos incisivos inferiores e extrusão dos molares inferiores.

Avaliação dos fatores determinantes da estética do perfil facial

OBJETIVO: avaliar a influência da idade, do sexo, da relação oclusal sagital, do Padrão Facial e de 8 medidas do perfil facial sobre a estética do perfil. MÉTODOS: foram utilizadas tabelas de contingência, o Teste Qui-quadrado e o coeficiente de Cramér para avaliar a possível associação entre a nota dada por 32 avaliadores (14 ortodontistas, 12 leigos e 6 artistas) para a estética do perfil de 100 brasileiros - adultos, leucodermas, portadores de selamento labial passivo - e a idade, o sexo, a relação oclusal sagital, o Padrão Facial e as variáveis da análise facial numérica do perfil. RESULTADOS: não foi observada associação entre a idade, o sexo e a relação oclusal sagital e a estética do perfil facial. A associação foi observada entre a nota recebida para a estética do perfil e o Padrão Facial, o ângulo de convexidade facial e o ângulo do terço inferior da face. CONCLUSÃO: o Padrão Facial, definido na avaliação do perfil pela convexidade do perfil facial, e a projeção anterior do mento foram, entre os fatores avaliados, os determinantes para a estética do perfil facial.

Estudo das características cefalométricas em adolescentes brasileiros portadores de Padrão Face Longa

OBJETIVO: definir valores cefalométricos esqueléticos e dentários para adolescentes brasileiros com Padrão Face Longa. MÉTODOS: a amostra foi constituída de telerradiografias em norma lateral de 30 pacientes com Face Longa, sendo 17 do sexo feminino e 13 do masculino; e 30 pacientes face Padrão I, 15 do sexo masculino e 15 do feminino, no estágio de dentadura permanente durante a adolescência. As características do Padrão Face Longa foram definidas clinicamente, pela análise facial. As seguintes grandezas cefalométricas foram avaliadas: (1) Comportamento sagital das bases apicais (SNA, SNB, ANB, NAP, Co-A, Co-Gn); (2) Comportamento vertical das bases apicais (SN.PP, SN.PM, ângulo goníaco, AFAT, AFAI, AFAM, AFP, AFATperp, AFAIperp); (3) Comportamento dentoalveolar (1-PP, 6-PP, 1-PM, 6-PM, 1.PP, IMPA); e (4) Proporção entre as alturas faciais (AFAIPerp/AFATPerp, AFAI/AFAT, AFAM/AFAI). RESULTADOS E CONCLUSÕES: o erro vertical na Face Longa concentra-se no terço inferior. A maxila apresenta uma maior altura dentoalveolar e a mandíbula, com morfologia mais vertical, mostra maior rotação no sentido horário. Essas características morfológicas e espaciais acarretam alterações sagitais e verticais no esqueleto e alterações verticais dentoalveolares. No sentido sagital, os ângulos de convexidade facial estão aumentados. No sentido vertical, as alturas faciais anteriores total e inferior estão aumentadas. O componente dentoalveolar está mais longo.

Jensen inequalities for tunneling probabilities in complex systems

The Jensen theorem is used to derive inequalities for semiclassical tunneling probabilities for systems involving several degrees of freedom. These Jensen inequalities are used to discuss several aspects of sub-barrier heavy-ion fusion reactions. The inequality hinges on general convexity properties of the tunneling coefficient calculated with the classical action in the classically forbidden region.

A test of competing explanations of compensation demanded

We find that prospect theory behavior is significantly more prevalent than utility theory behavior in experiments involving multiple, real items. In the experiments, subjects were endowed with three items and asked the minimum payments they required to be willing to return one, two, or three of them. Our key observation is that prospect theory implies concavity of compensation demanded, whereas utility theory implies convexity. We examine whether the compensation demanded is convex or concave in the number of items returned. (JEL C91).

Cephalometric evaluation in different phases of Jasper jumper therapy

Introduction: The aim of this study was to evaluate the dentoskeletal and soft-tissue effects of Class II malocclusion treatment with the Jasper jumper followed by Class II elastics at the different stages of therapy. Methods: The sample comprised 24 patients of both sexes (11 boys, 13 girls) with an initial age of 12.58 years, treated for a mean period of 2.15 years. Four lateral cephalograms were obtained of each patient in these stages of orthodontic treatment: at pretreatment (T1), after leveling and alignment (T2), after the use of the Jasper jumper appliance and before the use of Class II intermaxillary elastics (T3), and at posttreatment (T4). Thus, 3 treatment phases could be evaluated: leveling and alignment (T1-T2), use of the Jasper jumper (T2-T3), and use of Class II elastics (T3-T4). Dependent analysis of variance (ANOVA) and Tukey tests were used to compare the durations of the 3 treatment phases and for intragroup comparisons of the 4 treatment stages. Results: The alignment phase showed correction of the anteroposterior relationship, protrusion and labial inclination of the maxillary incisors, and reduction of overbite. The Jasper jumper phase demonstrated labial inclination, protrusion and intrusion of the mandibular incisors, mesialization and extrusion of the mandibular molars, reduction of overjet and overbite, molar relationship improvement, and reduction in facial convexity. The Class II elastics phase showed labial inclination of the maxillary incisors; retrusion, uprighting, and extrusion of the mandibular incisors; and overjet and overbite increases. Conclusions: The greatest amount of the Class II malocclusion anteroposterior discrepancy was corrected with the Jasper jumper appliance. Part of the correction was lost during Class II intermaxillary elastics use after use of the Jasper jumper appliance. (Am J Orthod Dentofacial Orthop 2011;140:e77-e84)

Evaluation of anterior open-bite treatment with occlusal adjustment

Introduction: The purpose of this study was to evaluate the cephalometric and occlusal changes, the functional occlusion, and the dentinal sensitivity of anterior open-bite treatment with occlusal adjustment. Methods: The sample comprised 20 patients who experienced relapse of the anterior open bite (mean, -1.06 mm). Occlusal adjustment was performed until a positive overbite was established. Cephalometric changes were evaluated on lateral cephalograms taken before and after the occlusal adjustment. The functional occlusion analysis consisted of evaluating immediate anterior and canine guidance and the number of teeth in contact before and after the procedure. Dentinal sensitivity was evaluated before, shortly after, and 4.61 months after the occlusal adjustment. Pretreatment and posttreatment cephalometric changes and the number of teeth in contact were compared with dependent t tests. Percentages of anterior and canine guidance before and after the adjustment procedure were compared with the McNemar test. To compare dentinal sensitivity at several stages, the nonparametric Friedman test was used, followed by the Wilcoxon test. Results: Significant increases in overbite and mandibular protrusion were seen, as were significant decreases in apical base discrepancy, facial convexity, and growth pattern angles. The percentages of immediate anterior and canine guidance increased significantly, as did the number of teeth with occlusal contacts. Dentinal sensitivity increased immediately after the adjustment but decreased to normal levels after 4.61 months. Conclusions: Occlusal adjustment is a viable treatment alternative for some open-bite patients; it establishes positive vertical overbite and improves the functional occlusion with only transient dentinal sensitivity.

Biaxial failure model for fiber reinforced concrete

Steel fiber reinforced concrete (SFRC) is widely applied in the construction industry. Numerical elastoplastic analysis of the macroscopic behavior is complex. This typically involves a piecewise linear failure curve including corner singularities. This paper presents a single smooth biaxial failure curve for SFRC based on a semianalytical approximation. Convexity of the proposed model is guaranteed so that numerical problems are avoided. The model has sufficient flexibility to closely match experimental results. The failure curve is also suitable for modeling plain concrete under biaxial loading. Since this model is capable of simulating the failure states in all stress regimes with a single envelope, the elastoplastic formulation is very concise and simple. The finite element implementation is developed to demonstrate the conciseness and the effectiveness of the model. The computed results display good agreement with published experimental data.