Vanishing theorems for higher-order Killing and Codazzi

Author(s):  
S. Stepanov ◽  
I. Tsyganok

A Killing p-tensor (for an arbitrary natural number p ≥ 2) is a symmetric p-tensor with vanishing symmetrized covariant derivative. On the other hand, Codazzi p-tensor is a symmetric p-tensor with symmetric covariant derivative. Let M be a complete and simply connected Riemannian manifold of nonpositive (resp. non-negative) sectional curvature. In the first case we prove that an arbitrary symmetric traceless Killing p-tensor is parallel on M if its norm is a Lq -function for some q > 0. If in addition the volume of this manifold is infinite, then this tensor is equal to zero. In the second case we prove that an arbitrary traceless Codazzi p-tensor is equal to zero on a noncompact manifold M if its norm is a Lq -function for some q  1 .

Author(s):  
Anna Varnayeva

Coordinative constructions are traditionally opposed to subordinative constructions. However, this opposition comes down to denial of dependence in coordinative constructions. Thereby the parity of these two constructions does not come to light: subordinative construction can be described without coordinative one. This situation is not improved by detection of a coordinative triangle in all coordinative constructions. The article shows a new approach in the study of coordinative constructions: a coordinative construction is a system; there are not only specific relations – a coordinative triangle, – but also specific elements. Novelty of the study consists in the address to extralinguistic facts, viz. a mathematical concept of a set and its elements. There are a lot of similarities between them. A set in mathematics includes generalizing elements and the composed row in coordinative constructions; in the first case the set is not partitioned, in the second case it is partitioned. In mathematics equivalent components in coordinative constructions correspond to the set elements. A characteristic property in mathematics is homogeneity in coordinative constructions and etc. It is firstly demonstrated, that coordinative and subordinative constructions are correlative and the study of one construction is impossible without the study of the other one. Their parity is shown in coordinative constructions with elements of one set, in subordinative ones with elements of different sets. Cf.: roses and tulips –red roses. In the coordinatiму construction elements of one set are called: «flowers »; in the subordinative construction there are elements of different sets: «flowers » and «colors». It should be noted that the mathematical concept of a set relates to so called logical aspect in linguistics or thinking about reality.


1994 ◽  
Vol 36 (1) ◽  
pp. 77-80 ◽  
Author(s):  
Leung-Fu Cheung ◽  
Pui-Fai Leung

For each p ∈ [2, ∞)a p-harmonic map f:Mm→Nn is a critical point of the p-energy functionalwhere Mm is a compact and Nn a complete Riemannian manifold of dimensions m and n respectively. In a recent paper [3], Takeuchi has proved that for a certain class of simply-connected δ-pinched Nn and certain type of hypersurface Nn in ℝn+1, the only stable p-harmonic maps for any compact Mm are the constant maps. Our purpose in this note is to establish the following theorem which complements Takeuchi's results.


PEDIATRICS ◽  
1948 ◽  
Vol 1 (3) ◽  
pp. 346-363
Author(s):  
I. WALLACE LEIBNER

Seven cases of brain tumors occurring in infants are presented. Six occurred in males and one was in a female. Three of them arose in the cerebellum while the other four were supratentorial. The tumors included two medulloblastomas, one [See Table II in Source Pdf] spongioblastoma polare, one ependymoma, one astrocytoma and one hemangioblastoma. The seventh case probably was also one of medulloblastoma. One of the proven medulloblastomas was supratentorial, which is unusual so faras location is concerned. The hemangioblastoma arose in the cerebrum. The location of this tumor is also a rare one and to my knowledge, it is the first case of its type reported in an infant in whom full recovery occurred following removal of the tumor. The diagnosis was unsuspected in four cases. Three of these infants were believed to be suffering from congenital hydrocephalus while the fourth was thought to be afflicted with encephalitis. The ways in which the correct diagnosis might have been made are discussed. Since bizarre clinical patterns are sometimes produced by brain tumors in infants and the diagnosis frequently overlooked, the possibility should be kept in mind by the pediatrician in considering the differential diagnosis of conditions producing signs referable to the nervous system.


2018 ◽  
Vol 301 ◽  
pp. 44-52
Author(s):  
Tomasz Kowalski ◽  

The aim of the article to present the role of analysing the manner of generating fingermarks in the investigative proceedings. These examinations are based on the analysis of the location of the marks on a given background and aim at providing the requesting party additional information about the circumstances of the investigated incident. The Author refers to two unusual cases, in which Voivodeship Police Command Forensic Laboratory issued expert opinions in the area of fingerprint identification. In the first case, at the initial stage of the proceedings the circumstances and recovered evidential fingermarks indicated a fatal accident or manslaughter by means of a firearm. In the other case at the preliminary stage recovered evidence did not allow identification of the perpetrator due to incorrectly selected exhibits. These cases would not be off special interest to us without the significant role of proper recovering of fingermarks and their analysis in a broader context than just identification.


2009 ◽  
Vol 22 (1) ◽  
pp. 49-78 ◽  
Author(s):  
Francesco Giglio

Restitution for civil wrongs, also known as restitutionary damages, is a legal response through which the defendant’s wrongful gain is awarded to the claimant. James Edelman has recently advocated two different restitutionary responses for wrongs. One response, termed ‘restitutionary damages’, would aim to compel the wrongdoer to give back to the victim a wrongful gain, whereas the other response, ‘disgorgement damages’, would oblige the wrongdoer to give up a wrongful gain for the benefit of the claimant.In the first case, the claimant would obtain what should have never left his assets. In the second case, the claimant would be the beneficiary of a judicial decision according to which a wrongful gain should not be kept by the wrongdoer. In this essay, I seek to demonstrate that this taxonomy cannot be accepted. I argue that Edelman’s ‘disgorgement damages’ are the only true example of restitution for wrongs, whereas his ’restitutionary damages’ are simply compensatory damages which are quantified in a particular fashion. Edelman’s ‘restitutionary damages’ might appear to deprive the defendant of his gain, and thus to achieve a restitutionary goal. Yet they nullify the victim’s loss and therefore have a compensatory nature. They are ‘pseudo-restitutionary damages’. In opposition to the dual theory, I submit a model of restitutionary damages based upon a single response which is coherent with the tenets of corrective justice. Given that it deals mainly with Edelman’s ‘restitutionary damages’, this article is not so much about restitution for wrongs but rather about compensation, which is what Edelman’s ‘restitutionary damages’ really concerns. The theory which I propose, based upon a single restitutionary response for wrongs, solves the taxonomic incoherence of Edelman’s dual theory. It also reflects the law as we find it, being supportable by reference to the available judicial authorities.


2013 ◽  
Vol 15 (03) ◽  
pp. 1350007
Author(s):  
XIAOLE SU ◽  
HONGWEI SUN ◽  
YUSHENG WANG

Let △p1p2p3 be a geodesic triangle on M, a complete 2-dimensional Riemannian manifold of curvature ≥ k, and let [Formula: see text] be its comparison triangle on [Formula: see text] (a complete and simply connected 2-dimensional manifold of constant curvature k). Our main result is that if △p1p2p3 is areable, then its area is not less than that of [Formula: see text].


1994 ◽  
Vol 4 (4) ◽  
pp. 390-394 ◽  
Author(s):  
Jassim M. Abdulhamed ◽  
Saad Al Yousef ◽  
Mohamed A. Ali Khan ◽  
Martin O'Laughlin

AbstractThree patients aged five years, five years four months and 14 years with obstruction of the systemic venous baffle following the Mustard operation were treated with balloon dilation and implantation ofstents. Balloon dilation of the baffle obstruction was performed initially in the first two cases. In the third case, the obstruction was complete and was punctured with atranseptal needle via a 6 French transeptal sheath followed by a balloon dilation. in all three patients, a Palmaz stent (Johnson & Johnson, Summerville, New Jersey, USA) was loaded onto the balloon catheter and delivered into the stenotic area. There was complete relief of obstruction in allcases. The first case developed supraventricular tachycardia at the time ofcatheterization, the morning following implantation of the stent and thentwo weeks after that. There were no complications with catheterization and noshort-term side effects in the other cases. These cases illustrate the use of endovascular stents in the treatment of baffle obstruction.


2018 ◽  
pp. 359-372
Author(s):  
Agata Strzelczyk
Keyword(s):  

This article is about Russian Empress Catherine the Great, her relations with her son Paul and grandson Alexander and role that she played in their upbringings. When Paul, Catherine’s only legal son was born, he was taken from her by Empress Elizabeth. That – and the fact, that Paul blamed Catherine for the death of his father – resulted in the fact, that they never develops proper, familial relation. On the other hand, Catherine was very active and affectionate grandmother, primarily for her oldest grandson, Alexander. She wanted to raise him to become ideal enlightened monarch. She took care of his education and even wrote fairy tales for him herself. Paul hated mother with bitter passion. Alexander loved her, but her influence shaped also his negative features. Catherine had undoubtedly great impact on both her son’s and grandson’s lives, but in the first case – impact was definitely negative and in second case – only arguably positive.


2013 ◽  
pp. 241-264
Author(s):  
Ignacio Del Valle Dávila

Resumo No final dos anos sessenta, ocorreu uma eclosão do cinema folclórico-histórico na Argentina e em Cuba. No primeiro caso, isso se deu principalmente devido ao interesse da ditadura de Onganía em utilizar os mitos fundadores da nação como uma metáfora legitimadora do regime. Contrários a essa tendência, o Grupo Cine Liberación elaborou representações desses relatos que buscavam adaptá-los à contingência, especialmente nos filmes La hora de los hornos (1968) e Los hijos del Fierro (1976). Em Cuba, o centenário da Guerra Grande (1868-1878) e a maior rigidez ideológica em matéria cultural durante o Quinquênio Gris (1971-1976) levaram a que se fomentasse a produção de um cinema histórico que representava a Revolução de 1959 como o produto de um século de luta. Os cineastas cubanos e Cine Liberación coincidiram em sua busca por renovar a forma de representação cinematográfica da História, enquanto o cinema comercial argentino apostou em adaptações distantes desse revisionismo. Résumé À la fin des années soixante s’est produit en Argentine et Cuba une éclosion du cinéma folklorique-historique. Dans le premier cas, ceci est dû principalement à l’intérêt de la dictature d’Onganía à se servir des mythes fondateurs de la nation avec l’objectif d’élaborer des métaphores légitimatrices du régime. Face à cela, Grupo Cine Liberación a élaboré des représentations de ces récits tout en cherchant à les adapter à la contingence, notamment dans les films L’heure des brasiers (1968) et Les fils de Fierro (1976). À Cuba le centenaire de la Guerre des dix ans (1968-1878) ainsi qu’une plus grande rigidité idéologique dans le domaine culturel pendant le Quinquennat Gris (1971-1976), ont conduit à l’encouragement de la production d’un cinéma historique où la révolution de 1959 est représentée comme la conclusion d’un siècle de lutte. Les cinéastes cubains et Cine Liberación ont partagé leur intérêt de renouveler les représentations cinématographiques de l’Histoire, tandis que le cinéma commercial argentin a misé sur des adaptations éloignées du révisionnisme.Abstract At the end of the sixties, there was a growth of historical-folkloric cinema in Argentina and Cuba. In the first case, it happened mainly because of the interest of the Onganía’s dictatorship in making use of the nation’s founding myths to develop metaphors to legitimize this regime. On the other hand, Grupo Cine Liberación elaborated representations of these narratives trying to adapt them to the contingency, especially in the movies The hour of the furnaces (1968) and Los hijos del Fierro (1976). In Cuba, the centenary of the War of ten years (1868-1878), as well as an increase of ideological rigidity in the cultural domain during the Grey Quinquennium (1971-1976), encouraged the production of a historical cinema where the revolution of 1959 has been represented as the conclusion of a century of struggle. Cuban filmmakers and Cine Liberación shared their interest in renewing the filmic representations of History, whereas the Argentinean commercial cinema supported adaptations far from this revisionism.Palavras-chave Cinema histórico, legitimação, mitos nacionais Mots-clés Cinéma historique, légitimation, mythes nationauxKeywords Historical cinema, legitimization, national myths 


Author(s):  
TALAT KILIC ◽  
Sebnem Kilic ◽  
Nurcan Kirici Berber ◽  
Ayten Gunduz ◽  
Yasemin Ersoy

Objectives: Studies have shown that severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is primarily transmitted from person to person via airborne droplets. It is unclear whether it can be shed into human milk and transmitted to a child via breastfeeding.We investigated the presence of SARS-CoV-2 RNA in human milk samples of 15 mothers with coronavirus disease 19(COVID-19) and in the throat swab samples of their infants. Methods: This is a prospective observational study in which breast milk samples were collected from 15 mothers with COVID-19. The presence of SARS-CoV-2 RNA in the whole human milk samples of the patients was investigated using RT-qPCR. All of the infants underwent a clinical follow-up during their 14-day isolation and their throat swab samples were tested for SARS-CoV-2 RNA. Results: Of 15 mothers with COVID-19, SARS-CoV-2 RNA was detected in milk samples from 4 mothers. The throat swab samples from these mothers’ infants were found to be positive for SARS-CoV-2 RNA. Three of the four mothers were breastfeeding. In addition, during the 14-day isolation, all but three of the mothers breastfed their infants. Of the 12 breastfed infants, while the test for SARS-CoV-2 RNA in throat swab samples was negative in six of the infants, the other six infants, who had mild COVID-19 symptoms, tested positive for SARS-CoV-2 RNA.Clinical outcomes of all mothers and infants were uneventful. Conclusion: To our knowledge, this is the first case series with the largest number of cases with SARS-CoV-2 RNA positivity in human milk samples of mothers with COVID-19. However, we believe that the benefits of breastfeeding may outweigh the risk of SARS-CoV-2 infection in infants


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