Singular valuations and the Hadwiger theorem on convex functions

We give a new proof of the Hadwiger theorem on convex functions derived from a characterization of smooth rotation invariant valuations. We also give a description of the construction of singular Hessian valuations using integration over the differential cycle and provide a new representation of these functionals as principal value integrals with respect to the Hessian measures.Comment: 37 pages, new representation formula for singular Hessian valuation

Monge-Amp\`ere operators and valuations

Two classes of measure-valued valuations on convex functions related to Monge-Amp\`ere operators are investigated and classified. It is shown that the space of all valuations with values in the space of complex Radon measures on $\mathbb{R}^n$ that are locally determined, continuous, dually epi-translation invariant as well as translation equivariant, is finite dimensional. Integral representations of these valuations and a description in terms of mixed Monge-Amp\`ere operators are established, as well as a characterization of $\mathrm{SO}(n)$-equivariant valuations in terms of Hessian measures.Comment: 36 page

Hatch Success and Population Modeling for the Critically Endangered Bog Turtle in North Carolina

Recent literature suggests that several North Carolina bog turtle (Glyptemys muhlenbergii) populations are in decline, and many of these populations have few remaining individuals with low annual survival probability. Most populations appear dominated by older adults with few juveniles encountered; however, the proportion of juveniles encountered at two populations is dramatically higher. The reason for this variability is unknown. We conducted a nest monitoring study in 2016 and 2017 to test the hypothesis that nest survival patterns explain the observed population age structure. We collected the largest dataset yet compiled on the fate of naturally-incubated bog turtle eggs as well as the first study of its kind in North Carolina. Predation was the primary driver of nest failure across all sites. Populations with more juvenile encounters had substantially higher egg survival. These observations support the hypothesis that variation in egg survival may be linked to observed variation in recruitment patterns. We subsequently incorporated site-specific population parameters, including site-specific egg survival, into a stage-based matrix model to estimate population growth rates and to assess potential management scenarios for five bog turtle populations. Only two of the five populations modeled were stable or growing under current vital rates. Our results demonstrated that management scenarios targeting increased recruitment (especially a head-start scenario) may substantially contribute to some populations reaching stability. Population growth rates will likely be higher when recruitment augmentation coincides with wetland restoration efforts that increase survival and site fidelity at other life stages

The scope of functions delegated to the engineering department of a typical, progressive metal mine

Nearly every conscientious engineering student will subject his college courses to an occasional critical analysis in an effort to assure himself that the studies he is pursuing will be a valuable aid to him in future practice. Possibly this skeptical attitude is accentuated by published letters of graduate mining engineers who decry the courses of mining schools in general and clamor for more practicability and higher specialization. Pure science as it is taught may at times seem to be very remote from any possible practical application. Mathematics may appear to be highly abstract. It seems quite logical that the degree of enthusiasm with which a student will apply himself will be considerably dependent upon the conviction he acquires concerning the practical value of his studies. It is the purpose of this thesis, therefore, to offer concrete evidence that a thorough and fundamental training in pure and applied sciences, mathematics, English, and drawing is indispensable to the practicing mining engineer. To be sure, a cursory examination of a good mining textbook or handbook might acquaint any prospective engineer with the wide range of problems and tasks which are peculiar to that branch of service. Although these sources are available, they do not apparently completely convince the student engineer that all of his work is essential. However, just as a ship\u27s log reveals the course and events of a voyage, so also might a collection of field notes, drawings, reports, assignments, and problems selected from the log or a typical mining engineering department over a period of a few years acquaint the reader not only with the scope of functions delegated to that department, but also with the range of science and mathematics which is employed in the performance of engineering work --Introduction, pages 1-2

Equivariant Endomorphisms of Convex Functions

Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the origin, and of finite convex functions are established. Moreover, all continuous, additive, monotone endomorphisms of the same spaces, which are equivariant with respect to rotations and dilations, are characterized. Finally, all continuous, additive endomorphisms of the space of finite convex functions of one variable are characterized.Comment: 33 page

Sustentabilidade no Paraná agrícola: reflexão jurídica

RESUMOO presente artigo objetiva promover a reflexão acerca do problema da sustentabilidade ambiental e energética do estado do Paraná, a partir do respeito ao direito ao desenvolvimento sustentado, ao meio ambiente ecologicamente equilibrado, ao  princípio da erradicação da pobreza e da marginalização, ao direito fundamental à moradia, do direito fundamental à saúde, do princípio da valorização do trabalho humano e da livre iniciativa e da dignidade da pessoa humana, constitucionalmente garantidos  em face à realidade da demarcação das APPs em torno dos lagos artificiais e seus impactos locais e regionais. PALAVRAS-CHAVE: Sustentabilidade ambiental – APPs – Paraná – Direito Fundamental – Dignidade da pessoa humana ABSTRACTThis article aims to promote reflection about the issue of environmental sustainability and energy on the state of Paraná, from respect for the right to sustainable development, to an ecologically balanced environment, the principle of eradication of poverty and marginalization,  the fundamental right to housing, the fundamental right to health, the principle of appreciation of human labor and free enterprise and the dignity of the human person, constitutionally guaranteed to face the reality of demarcation of APPs aroundartificial lakes and their local and regional impacts.KEYWORDS: Ambiental Sustainability – APPs – Paraná – Fundamental Rights – Human Dignit

THE POLICE POWER AND COMPLIANCE IN A LEGAL STATE AND THEIR INFLUENCE ON THE ANTI-CORRUPTION LAW (LAW 12,846 DATED AUGUST 1, 2013).

ABSTRACT   This scientific paper deals with the intensity and extent of police power exercised by the State of Law on issues relating to anti-corruption practices that should be adopted by companies and their managers, especially in light of Law 12,846 dated August 1, 2013, formal introducer in Brazil of compliance practices. Compliance is evidence of self-regulation granted by the State to the companies for the effectiveness of the police power internally in companies, for themselves, through compliance programs containing the code of conduct and ethics and internal policies to spread the good conduct and ethics in business and preventing acts of corruption.   KEYWORDS: Compliance; Anti-Corruption Act; Police Power; Ethics.   RESUMO   O presente artigo científico aborda a intensidade e extensão do poder de polícia exercido pelo Estado de Direito nos temas relativos às práticas anticorrupção que devem ser adotadas pelas empresas e seus administradores, especialmente diante da Lei n º 12.846 de 1º de agosto de 2013, introdutora formal no Brasil das práticas de compliance. O compliance é a evidência da autorregulação conferida pelo Estado às empresas, para que o poder de polícia seja exercido internamente nas empresas, por elas mesmas, através de programas de compliance contendo código de conduta e ética e políticas internas, com o objetivo de disseminar a boa conduta e ética nos negócios e coibir atos de corrupção.   PALAVRAS-CHAVE: Compliance; Lei Anticorrupção; Poder de Polícia; Ética

A FORMAÇÃO DO ESTADO NA CONTEMPORANEIDADE A PARTIR DA REVOLUÇÃO RUSSA – UM SÉCULO DETERMINANTE DOS NOVOS RUMOS DA SOCIEDADE E DO DIREITO

In revisiting the history of Russia in relation to the revolutionary movement, this article aims to draw a parallel with the formation of a state in continuous transformation and / or revolution originating from ideological, political and economic convictions. With a brief historical retrospective, the article visits the formation of the state (patrimonialist or bureaucratic) also in the light of Max Weber. This is followed by the transition from the Liberal to the Social State with the assumptions of freedoms, rights and guarantees that surpass sovereignty in order to grant it the legal duty to provide public services. Consequently, this transformation has repercussions on the law and becomes a protagonist in the construction of a new state model. For the development of this article, the historiography portrayed relies on the bibliographical methodology, which contributes to the understanding of the formation of the contemporary state and law.Ao revisitar a história da Rússia no que tange o movimento revolucionário, o presente artigo objetiva traçar um paralelo com a formação de um Estado em contínua transformação e/ou revolução oriunda de convicções ideológicas, políticas e econômicas. Com breve retrospecto histórico, o artigo visita a formação do Estado (patrimonialista ou burocrático) também à luz de Max Weber. Trata-se, na sequência, da transição do Estado liberal ao Social com pressupostos de liberdades, direitos e garantias que superam a soberania a fim de outorgar-lhe o dever legal de prestar serviços públicos. Por conseguinte, essa transformação repercute no direito e passa a ser protagonista na construção de um novo modelo de Estado. Para o desenvolvimento deste artigo, a historiografia retratada se vale da metodologia bibliográfica, a qual contribui para a compreensão da formação do Estado e direito contemporâneos