Academic literature on the topic 'N-centre problem'

AbstractThe planar N-centre problem describes the motion of a particle moving in the plane under the action of the force fields of N fixed attractive centres: $$\begin{aligned} \ddot{x}(t)=\sum _{j=1}^N\nabla V_j(x(t)-c_j). \end{aligned}$$ x ¨ ( t ) = ∑ j = 1 N ∇ V j ( x ( t ) - c j ) . In this paper we prove symbolic dynamics at slightly negative energy for an N-centre problem where the potentials $$V_j$$ V j are positive, anisotropic and homogeneous of degree $$-\alpha _j$$ - α j : $$\begin{aligned} V_j(x)=|x|^{-\alpha _j}V_j\left( \frac{x}{|x|}\right) . \end{aligned}$$ V j ( x ) = | x | - α j V j x | x | . The proof is based on a broken geodesics argument and trajectories are extremals of the Maupertuis’ functional. Compared with the classical N-centre problem with Kepler potentials, a major difficulty arises from the lack of a regularization of the singularities. We will consider both the collisional dynamics and the non collision one. Symbols describe geometric and topological features of the associated trajectory.

The article presents the problem of paradoxicality of the activity of juvenile institutional education (i.e., socialisation centres operating in Lithuania). Several important variables have not been considered in the interaction of the activities of the socialisation centre, simultaneously of pedagogical and other staff and learners, their families/foster parents, and this resulted in inconsistency of the implementation of the complex resocialisation process. The article calls for the scientific discussion, actualising essential principles of resocialisation observed in socialisation centres, grounded on empirical data of children’s subjective experience (N= 97) and assessment of specialists of the child socialisation centre (N=94).

In this thesis we study periodic solutions of several N-body and N-centre systems with different potentials from a variational viewpoint. The underlying focus is on understanding the structure of various action functionals, and the relationship between this and the system's periodic orbits and their properties. In particular we: investigate the integrable central force problems with potentials Valpha(x) = - 1/|x|alpha for 1≤ alpha ≤ 2. We show that for 1 < alpha < 2 there are only finitely many homotopy classes that do not contain a prime-period, but that this number diverges as alpha →1+ or alpha → 2--. Given any non-null homotopy class of loops and any period T > 0 we list the finitely many distinct critical manifolds of collisionless orbits in that class in order of their action, and label them with their Morse indices with respect to the action functional. We investigate the 2-body/1-centre problem with Lennard-Jones potential. We find the region of energy-momentum space that supports the existence of periodic or quasiperiodic motion. We also show there exists m ∈ N such that for all q ≥ m there are periodic orbits in Op= UT>0 OpT (p ∈ Z - {0}) with q 'radial oscillations' in one period. Obtain results on which homotopy and homology classes of loops contain periodic solutions of the symmetric planar Newtonian 2-centre problem, see theorem 4.4.1. In particular we find that the integrability of the system places strong constraints on which homology classes of loops contain periodic solutions and obtain some interesting results on prime-period solutions. We also order by action 'P1 orbits' in all homotopy classes of loops that contain them and label them by their Morse indices with respect to the action functional. We investigate the 7V-body problem with identical particles interacting through a potential of Lennard-Jones (LJ) type. We consider any subset of loop space that satisfies a few basic conditions, one of which corresponds to the notion of 'tiedness' introduced by Gordon in [41]. We show that this system admits periodic solutions in every homotopy class of this subset of loop space. More precisely we show that every homotopy class contains at least two periodic solutions for sufficiently large periods. One of these solutions is a local minimum and the other is a mountain-pass critical point of the action functional. We also prove that given a homotopy class of one of these subsets there do not exist any periodic solutions in it for sufficiently small periods. The results have wide applicability. For example, one can consider the space of choreographies and prove existence results for choreographical solutions. Our existence proof relies upon an assumption that global minimizers of standard strong force potentials on suitable spaces are nondegenerate up to some symmetries. We also find periodic solutions in some classes of loops that do not satisfy any tiedness condition. In particular we use a result in [27] to construct a periodic solution of the restricted spatial (2N + 2)-body problem. o present a note on McCord, Montaldi, Roberts and Sbano's paper on relative periodic orbits in symmetric Lagrangian systems, see [54]. For the N-centre problem with a strong force potential that is bounded above we find those homotopy classes of relative loops on which the action functional is coercive. We describe the homotopy types of the homotopy classes of relative loops. Under the assumption that the action functional is an S1-invariant Morse function we describe a set of homotopy classes that contain infinitely many periodic orbits. The work can be viewed as an expansion on an example presented at the end of [54] which had N = 2; in particular we correct and generalize some assertions made regarding coercivity of the action functional and the centralizers of the g-twisted action. Some of the results are subject to numerically motivated assumptions detailed in the thesis.

This thesis is devoted to the study of several problems arising in the field of nonlinear analysis. The work is divided in two parts: the first one concerns existence of oscillating solutions, in a suitable sense, for some nonlinear ODEs and PDEs, while the second one regards the study of qualitative properties, such as monotonicity and symmetry, for solutions to some elliptic problems in unbounded domains. Although the topics faced in this work can appear far away one from the other, the techniques employed in different chapters share several common features. In the firts part, the variational structure of the considered problems plays an essential role, and in particular we obtain existence of oscillating solutions by means of non-standard versions of the Nehari's method and of the Seifert's broken geodesics argument. In the second part, classical tools of geometric analysis, such as the moving planes method and the application of Liouville-type theorems, are used to prove 1-dimensional symmetry of solutions in different situations.

No presente trabalho apresentaremos alguns aspectos do problema Newtoniano de n Corpos. Estudaremos o caso de dois corpos, que tem solução direta, embora não seja possível obter todas as variáveis como função do tempo. No caso n maior ou igual a 3 mostraremos que não existe método para integrar este problema via quadraturas. Podemos tirar apenas algumas informações sobre o caso geral, como a Identidade de Lagrange-Jacobi, o Teorema de Sundman-Weierstrass entre outros. Veremos alguns casos de soluções particulares, que serão chamadas de soluções homográficas. Nestas soluções a forma geométrica da configuração inicial dos corpos é preservada durante o movimento. Veremos condições necessárias sobre as configurações iniciais para que seja possível obter estas soluções. Mostraremos uma relação existente entre estas soluções particulares e os pontos críticos de uma aplicação, que associa a uma configuração a energia total e o momento angular total do sistema. Nestes vários casos, cairemos numa mesma equação algébrica, que será chamada de equação das configurações centrais. Mostraremos, em seguida, que as equações de configurações centrais são equivalentes a um outro conjunto de equações algébricas, que servem também para calcular as chamadas configurações centrais, porém, com estas equações as simetrias do problema ficam mais claras, às vezes. Faremos algumas aplicações diretas destas equações algébricas. Uma subclasse interessante da classe das configurações centrais são as chamadas de equações diferenciais empilhadas, nas quais um subconjunto próprio dos corpos também forma uma configuração central. Nos dois últimos capítulos veremos alguns exemplos de configurações centrais deste tipo, em especial aquelas onde podemos retirar uma massa e ainda ter uma configuração central.
In this work we present some aspects of the Newtonian n--body problem. We study the case of two bodies, which have a straightforward solution, although we can not get all the variables as functions of the time. For n greater or equal to 3 we show that there is no method to integrate this problem by quadratures. We can have just some information about the general case, as the Lagrange-Jacobi\'s Identity the Sundman-Weierstrass\'s theorem and others. We will see some cases of particular solutions, which will be called homographic solutions. In these solutions the geometric shape of initial configuration of the bodies is preserved during the movement. We will see necessary conditions on the initial positions that turn possible to obtain these solutions. We show a relation between these particular solutions and critical points of an application, that associate the total energy and total angular momentum of the system. In these several cases, we will fall in same algebraic equation, which we called of the central configurations equations. We show that the central configurations equations are equivalent to another set of algebraic equations, which are also used to compute the central configurations, but with these equations the symmetries of the problem become clearer. We will make some direct applications these algebraic equations. An interesting subclass of the class of central configurations are called stacked differential equations, in which a proper subset of the bodies form a central configuration too. In the last two chapters we will see some examples of central configurations of this kind, especially those where we can remove a mass and still have a central configuration.

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Um esquema central em volumes finitos para a solução numérica de problemas hiperbólicos escalares bidimensionais, definido sobre domínios computacionais discretizados por malhas triangulares não estruturadas, é proposto. O método é bipartido (staggered), de modo que /e definida uma malha dual e auxiliar a malha de triângulos original para que se alternem a posição dos graus de liberdade numéricos entre duas iterações sucessivas. Neste sentido, o esquema proposto é híbrido, podendo ser encarado como um método centrado nas células triangulares da malha, a forma escolhida neste trabalho, ou centrado em seus n/os. O esquema é também conservativo, o que significa que deriva diretamente da lei de conservação da qual o problema diferencial provém, e assim está apto a aproximar satisfatoriamente soluções generalizadas. O método é inicialmente desenvolvido para lidar com leis de conservação convectivas não lineares e uniformes. Uma extensão, entretanto, é realizada para que ele seja também aplicável a problemas que envolvam a equação de transporte. São apresentadas tanto uma formulação de baixa ordem quanto Uma variação de alta resolução Essa /ultima criada a partir de reconstruções polinomiais Lineares por partes, célula a célula, limitadas geometricamente e não pelo uso de funções limitadoras. Por fim, esquemas derivados segundo o processo proposto são aplicados para solução de problemas hiperbólicos simples que possuam solução exata conhecida. A conformidade dos resultados obtidos sugere que a convergência desses esquemas não pode ser peremptoriamente refutada. Além disso, a ordem com que essa convergência é estabelecida é estimada através de testes.

We extend the concept of central configurations to the N-body problem in spaces of nonzero constant curvature. Based on the work of Florin Diacu on relative equilib- ria of the curved N-body problem and the work of Smale on general relative equilibria, we find a natural way to define the concept of central configurations with the effective potentials. We characterize the ordinary central configurations as constrained critical points of the cotangent potential, which helps us to establish the existence of ordi- nary central configurations for any given masses. After these fundamental results, we study central configurations on H2, ordinary central configurations in S3, and special central configurations in S3 in three separate chapters. For central configurations on H2, we generalize the theorem of Moulton on geodesic central configurations, the theorem of Shub on the compactness of central configurations, the theorem of Conley on the index of geodesic central configurations, and the theorem of Palmore on the lower bound for the number of central configurations. We show that all three-body central configurations that form equilateral triangles must have three equal masses. For ordinary central configurations in S3, we construct a class of S3 ordinary central configurations. We study the geodesic central configurations of two and three bodies. Three-body non-geodesic ordinary central configurations that form equilateral trian- gles must have three equal masses. We also put into the evidence some other classes of central configurations. For special central configurations, we show that for any N ≥ 3, there are masses that admit at least one special central configuration. We then consider the Dziobek special central configurations and obtain the central con- figuration equation in terms of mutual distances and volumes formed by the position vectors. We end the thesis with results concerning the stability of relative equilibria associated with 3-body special central configurations. We find that these relative equilibria are Lyapunov stable when confined to S1, and that they are linearly stable on S2 if and only if the angular momentum is bigger than a certain value determined by the configuration.
Graduate

We consider the N-body problem given by quasihomogeneous force functions of the form (C_1)/r^a + (C_2)/r^b (C_1, C_2, a, b constants and a, b positive with a less than or equal to b) and address the fundamentals of homographic solutions. Generalizing techniques of the classical N-body problem, we prove necessary and sufficient conditions for a homographic solution to be either homothetic, or relative equilibrium. We further prove an analogue of the Lagrange-Pizzetti theorem based on our techniques. We also study the central configurations for quasihomogeneous force functions and settle the classification and properties of simultaneous and extraneous central configurations. In the last part of the thesis, we combine these findings with the Lagrange-Pizzetti theorem to show the link between homographic solutions and central configurations, to prove the existence of homographic solutions and to give algorithms for their construction.
Graduate

We study topological bifurcations of critical orbits of equivariant gradient equations. We give necessary and sufficient conditions for the existence of global bifurcations of solutions of these equations. Moreover, we apply these abstract results to the study of bifurcations of new families of planar and spatial central configurations of the N-body problem. It is worth pointing out that the shapes of the bifurcating families are less symmetrical than the shapes of the considered families of planar and spatial central configurations.

Der Bericht ist ausschließlich als PDF-Dokument erschienen! Content Foreword 1 ADAS Seeing With Sound – Next-level 3D ultrasonic sensors based on echolocation 5 N. Knappstein, Toposens, Munich Ensuring the reliability, availability and safety of fully automated and autonomous transport systems through modern system architectures 11 J. Heinrich, A. Braasch, Institut für Qualitäts- und Zuverlässigkeitsmanagement GmbH, Wuppertal; F. Plinke, Institut für Qualitäts- und Zuverlässigkeitsmanagement GmbH, Hamburg ADAS/AD Systems: Efficient Testing & Validation – From data acquisition to data analytics 21 M. Kremer, M. Kreutz, M. Luxen, S. Christiaens, FEV Europe GmbH, Aachen Problems and solution spaces for driver-initiated handover from automatic to manual driving mode 31 J. Klesing, Nexteer Automotive, Auburn Hills, USA; S. Safour, Nexteer Automotive, Paris, France UX User-centred development of a display concept for fully automated driving – A methodical approach 45 L. Gaue...

The main milestones of the formation and development of astronomical science in Kharkiv during 1883–1945 are reconstructed on the example of the activities of the astronomical observatory of Kharkiv University. During this period, the outstanding worldview science in Kharkiv has achieved significant success: the works of Kharkiv astronomers have received world recognition; a well-known scientific planetary school has been established at the Observatory; the scientific community highly appreciated the research on the physics and chemistry of the Moon, the giant and small planets of the Solar System. The primary goal of the research is to inscribe the history of the university Observatory into the European and world context. Its purpose is to summarize the results of a comprehensive historical ad scientific study of the development of astronomical research in Kharkiv at the end of the 19th century – the first half of the 20th century and identification of ways of further scientific research. The completed research, which continues the problems of works devoted to the study of the history of astronomical science in Ukraine, focuses on expanding the well-known source base by attracting new retro-information resources. In particular, the monograph used a significant array of archival primary sources from almost twenty archival and library institutions of different countries. Most of them were introduced into scientific circulation for the first time, which allowed to determine and specify the sequence of stages of development of astronomical science in Kharkiv during the research period, to clarify and identify the little-known circumstances of the observatory life. The methodological basis of the study is the principles of historism, objectivity and a systematic approach to studying the problem. To solve specific problematic tasks in the monograph, general scientific and specially historical methods were used which allowed to study, analyze and summarize the presented factual material in a complex manner. The main sections of the monograph represent the dynamics of replenishment of the instrumental base of the university observatory, the chronology of the construction of the observatory complex of buildings at the location of the modern Scientific Research Institute of Astronomy of the V. N. Karazin Kharkiv National University. According to the author’s periodization, the stages of formation of subjects and directions of scientific work of university astronomers have been analyzed, including: seismic observations with the help of horizontal Rebeur-Paschwitz pendulums, research of the activity of the Sun, astrometric observations on the Repsold meridian circle of for the purpose of compiling a catalog of zodiac stars, studying lunar eclipses and meteor showers. The participation of university astronomers in the creation of the plan of the city of Kharkiv and its connection with the general network of precise geometric leveling of the Military Topographic Department of the General Staff; the organization of observations by an expedition of Kharkiv astronomers of the total Solar eclipse of 1914 in Henichesk; the creation of the School-workshop of precision mechanics at the Faculty of Physics and Mathematics of Kharkiv University were considered; information on the participation of Kharkiv astronomers in the events of the civil war during the Ukrainian Revolution was documented. The scientific research activity of Kharkiv astronomers during 1920-1930-s which was devoted to carrying out important astrometric works on meridian observations of star declinations by absolute methods and observations of Kopf-Rentz stars according to the programs of the International Astronomical Union; the initiation of the creation of the Catalog of faint stars; research in astrophysics aimed at studying the physical conditions on the Moon and the Sun, planets and the interstellar environment; performing long series of spectrophotometric observations of the Moon, Jupiter, Mars and Saturn under different conditions of observation; study of the kinematics of stellar systems of different order, the physical parameters and evolution of stars, the morphology of the Galaxy, the nature of the stellar subsurfaces and atmospheres, dust and gas nebulae, new stars and the variability of stars have been considered; the directions of solid works carried out in the field of celestial mechanics, devoted to the dynamics of the minor planets of the Jupiter group, the definition and improvement of the orbits of minor planets have been clarified. The development of amateur astronomy in Kharkiv, in particular, the functioning of circles and societies that directed their activities to the dissemination of astronomical knowledge, was highlighted; the participation of their representatives in astronomical observations at the Kharkiv Astronomical Observatory was emphasized. Reconstructed the development of historical events in the 1930s related to the involvement of Soviet and Western astronomers in the processes of political confrontation between the USSR and the Western world; investigated the course of circumstances that prevented the implementation of the project of creating a new modern astronomical center of national importance – the central Ukrainian observatory in Kharkiv; the participation of an expedition of Kharkiv astronomers in the observation of the «great Soviet eclipse» – the total solar eclipse of 1936 – in the North Caucasus is highlighted; established the facts of political «purges» and repressions by the People’s Commissariat for Internal Affairs ( the NKVD) in the Kharkiv Astronomical Observatory. The activity of the Kharkiv Astronomical Observatory has been documented and authentic biographical information about its representatives during the Nazi occupation of 1941–1943, the period of the German-Soviet war, has been presented; the unpopular facts of the forced collaboration of some scientists are highlighted; the process of recovery and reconstruction of the Kharkiv Astronomical Observatory after the liberation of the city is characterized. With the aim of researching the personal history of Kharkiv astronomy of the studied period, the monograph presents the results of a historical and biographical study of facts of life and scientific heritage of scientists who fully devoted themselves to Science, laid the foundations for the future development of many directions of modern astronomical research, made a significant contribution to the treasury of the national and European astronomical science, whose activities were connected with the Kharkiv Astronomical Observatory, in particular: Grigory Levytsky, Ludwig Struve, Mykola Evdokymov, Otto Struve, Mykola Barabashov, Boris Gerasimovich, Vasil Fesenkov, Oleksiy Razdolsky, Boris Ostashchenko-Kudryavtsev, Nicholas Bobrovnikov, Paraskovia Parkhomenko, Mstislav Savron, Boris Semeykin, Kostyantyn Savchenko and others (25 biographical essays are presented). A significant part of the mentioned factual material was also introduced into scientific circulation for the first time. A separate section of the monograph provides chronologically structured information that reflects the sequence of research work of the Kharkiv Astronomical Observatory employees during the period under study: from astrometric observations of stars and seismic research to spectrohelioscopic and spectroheliographic observations of the Sun and the initiation of the Kharkiv school of planetary science. It is assumed that the materials of the monograph will be used in research work devoted to the study of the process of institutionalization of astronomical research in Kharkiv at the end of the 19th century – the first half of the 20th century.

Nationalism: Past as Prologue began as a single volume being compiled by Ad Akande, a scholar from South Africa, who proposed it to me as co-author about two years ago. The original idea was to examine how the damaging roots of nationalism have been corroding political systems around the world, and creating dangerous obstacles for necessary international cooperation. Since I (Bruce E. Johansen) has written profusely about climate change (global warming, a.k.a. infrared forcing), I suggested a concerted effort in that direction. This is a worldwide existential threat that affects every living thing on Earth. It often compounds upon itself, so delays in reducing emissions of fossil fuels are shortening the amount of time remaining to eliminate the use of fossil fuels to preserve a livable planet. Nationalism often impedes solutions to this problem (among many others), as nations place their singular needs above the common good. Our initial proposal got around, and abstracts on many subjects arrived. Within a few weeks, we had enough good material for a 100,000-word book. The book then fattened to two moderate volumes and then to four two very hefty tomes. We tried several different titles as good submissions swelled. We also discovered that our best contributors were experts in their fields, which ranged the world. We settled on three stand-alone books:” 1/ nationalism and racial justice. Our first volume grew as the growth of Black Lives Matter following the brutal killing of George Floyd ignited protests over police brutality and other issues during 2020, following the police assassination of Floyd in Minneapolis. It is estimated that more people took part in protests of police brutality during the summer of 2020 than any other series of marches in United States history. This includes upheavals during the 1960s over racial issues and against the war in Southeast Asia (notably Vietnam). We choose a volume on racism because it is one of nationalism’s main motive forces. This volume provides a worldwide array of work on nationalism’s growth in various countries, usually by authors residing in them, or in the United States with ethnic ties to the nation being examined, often recent immigrants to the United States from them. Our roster of contributors comprises a small United Nations of insightful, well-written research and commentary from Indonesia, New Zealand, Australia, China, India, South Africa, France, Portugal, Estonia, Hungary, Russia, Poland, Kazakhstan, Georgia, and the United States. Volume 2 (this one) describes and analyzes nationalism, by country, around the world, except for the United States; and 3/material directly related to President Donald Trump, and the United States. The first volume is under consideration at the Texas A & M University Press. The other two are under contract to Nova Science Publishers (which includes social sciences). These three volumes may be used individually or as a set. Environmental material is taken up in appropriate places in each of the three books. * * * * * What became the United States of America has been strongly nationalist since the English of present-day Massachusetts and Jamestown first hit North America’s eastern shores. The country propelled itself across North America with the self-serving ideology of “manifest destiny” for four centuries before Donald Trump came along. Anyone who believes that a Trumpian affection for deportation of “illegals” is a new thing ought to take a look at immigration and deportation statistics in Adam Goodman’s The Deportation Machine: America’s Long History of Deporting Immigrants (Princeton University Press, 2020). Between 1920 and 2018, the United States deported 56.3 million people, compared with 51.7 million who were granted legal immigration status during the same dates. Nearly nine of ten deportees were Mexican (Nolan, 2020, 83). This kind of nationalism, has become an assassin of democracy as well as an impediment to solving global problems. Paul Krugman wrote in the New York Times (2019:A-25): that “In their 2018 book, How Democracies Die, the political scientists Steven Levitsky and Daniel Ziblatt documented how this process has played out in many countries, from Vladimir Putin’s Russia, to Recep Erdogan’s Turkey, to Viktor Orban’s Hungary. Add to these India’s Narendra Modi, China’s Xi Jinping, and the United States’ Donald Trump, among others. Bit by bit, the guardrails of democracy have been torn down, as institutions meant to serve the public became tools of ruling parties and self-serving ideologies, weaponized to punish and intimidate opposition parties’ opponents. On paper, these countries are still democracies; in practice, they have become one-party regimes….And it’s happening here [the United States] as we speak. If you are not worried about the future of American democracy, you aren’t paying attention” (Krugmam, 2019, A-25). We are reminded continuously that the late Carl Sagan, one of our most insightful scientific public intellectuals, had an interesting theory about highly developed civilizations. Given the number of stars and planets that must exist in the vast reaches of the universe, he said, there must be other highly developed and organized forms of life. Distance may keep us from making physical contact, but Sagan said that another reason we may never be on speaking terms with another intelligent race is (judging from our own example) could be their penchant for destroying themselves in relatively short order after reaching technological complexity. This book’s chapters, introduction, and conclusion examine the worldwide rise of partisan nationalism and the damage it has wrought on the worldwide pursuit of solutions for issues requiring worldwide scope, such scientific co-operation public health and others, mixing analysis of both. We use both historical description and analysis. This analysis concludes with a description of why we must avoid the isolating nature of nationalism that isolates people and encourages separation if we are to deal with issues of world-wide concern, and to maintain a sustainable, survivable Earth, placing the dominant political movement of our time against the Earth’s existential crises. Our contributors, all experts in their fields, each have assumed responsibility for a country, or two if they are related. This work entwines themes of worldwide concern with the political growth of nationalism because leaders with such a worldview are disinclined to co-operate internationally at a time when nations must find ways to solve common problems, such as the climate crisis. Inability to cooperate at this stage may doom everyone, eventually, to an overheated, stormy future plagued by droughts and deluges portending shortages of food and other essential commodities, meanwhile destroying large coastal urban areas because of rising sea levels. Future historians may look back at our time and wonder why as well as how our world succumbed to isolating nationalism at a time when time was so short for cooperative intervention which is crucial for survival of a sustainable earth. Pride in language and culture is salubrious to individuals’ sense of history and identity. Excess nationalism that prevents international co-operation on harmful worldwide maladies is quite another. As Pope Francis has pointed out: For all of our connectivity due to expansion of social media, ability to communicate can breed contempt as well as mutual trust. “For all our hyper-connectivity,” said Francis, “We witnessed a fragmentation that made it more difficult to resolve problems that affect us all” (Horowitz, 2020, A-12). The pope’s encyclical, titled “Brothers All,” also said: “The forces of myopic, extremist, resentful, and aggressive nationalism are on the rise.” The pope’s document also advocates support for migrants, as well as resistance to nationalist and tribal populism. Francis broadened his critique to the role of market capitalism, as well as nationalism has failed the peoples of the world when they need co-operation and solidarity in the face of the world-wide corona virus pandemic. Humankind needs to unite into “a new sense of the human family [Fratelli Tutti, “Brothers All”], that rejects war at all costs” (Pope, 2020, 6-A). Our journey takes us first to Russia, with the able eye and honed expertise of Richard D. Anderson, Jr. who teaches as UCLA and publishes on the subject of his chapter: “Putin, Russian identity, and Russia’s conduct at home and abroad.” Readers should find Dr. Anderson’s analysis fascinating because Vladimir Putin, the singular leader of Russian foreign and domestic policy these days (and perhaps for the rest of his life, given how malleable Russia’s Constitution has become) may be a short man physically, but has high ambitions. One of these involves restoring the old Russian (and Soviet) empire, which would involve re-subjugating a number of nations that broke off as the old order dissolved about 30 years ago. President (shall we say czar?) Putin also has international ambitions, notably by destabilizing the United States, where election meddling has become a specialty. The sight of Putin and U.S. president Donald Trump, two very rich men (Putin $70-$200 billion; Trump $2.5 billion), nuzzling in friendship would probably set Thomas Jefferson and Vladimir Lenin spinning in their graves. The road of history can take some unanticipated twists and turns. Consider Poland, from which we have an expert native analysis in chapter 2, Bartosz Hlebowicz, who is a Polish anthropologist and journalist. His piece is titled “Lawless and Unjust: How to Quickly Make Your Own Country a Puppet State Run by a Group of Hoodlums – the Hopeless Case of Poland (2015–2020).” When I visited Poland to teach and lecture twice between 2006 and 2008, most people seemed to be walking on air induced by freedom to conduct their own affairs to an unusual degree for a state usually squeezed between nationalists in Germany and Russia. What did the Poles then do in a couple of decades? Read Hlebowicz’ chapter and decide. It certainly isn’t soft-bellied liberalism. In Chapter 3, with Bruce E. Johansen, we visit China’s western provinces, the lands of Tibet as well as the Uighurs and other Muslims in the Xinjiang region, who would most assuredly resent being characterized as being possessed by the Chinese of the Han to the east. As a student of Native American history, I had never before thought of the Tibetans and Uighurs as Native peoples struggling against the Independence-minded peoples of a land that is called an adjunct of China on most of our maps. The random act of sitting next to a young woman on an Air India flight out of Hyderabad, bound for New Delhi taught me that the Tibetans had something to share with the Lakota, the Iroquois, and hundreds of other Native American states and nations in North America. Active resistance to Chinese rule lasted into the mid-nineteenth century, and continues today in a subversive manner, even in song, as I learned in 2018 when I acted as a foreign adjudicator on a Ph.D. dissertation by a Tibetan student at the University of Madras (in what is now in a city called Chennai), in southwestern India on resistance in song during Tibet’s recent history. Tibet is one of very few places on Earth where a young dissident can get shot to death for singing a song that troubles China’s Quest for Lebensraum. The situation in Xinjiang region, where close to a million Muslims have been interned in “reeducation” camps surrounded with brick walls and barbed wire. They sing, too. Come with us and hear the music. Back to Europe now, in Chapter 4, to Portugal and Spain, we find a break in the general pattern of nationalism. Portugal has been more progressive governmentally than most. Spain varies from a liberal majority to military coups, a pattern which has been exported to Latin America. A situation such as this can make use of the term “populism” problematic, because general usage in our time usually ties the word into a right-wing connotative straightjacket. “Populism” can be used to describe progressive (left-wing) insurgencies as well. José Pinto, who is native to Portugal and also researches and writes in Spanish as well as English, in “Populism in Portugal and Spain: a Real Neighbourhood?” provides insight into these historical paradoxes. Hungary shares some historical inclinations with Poland (above). Both emerged from Soviet dominance in an air of developing freedom and multicultural diversity after the Berlin Wall fell and the Soviet Union collapsed. Then, gradually at first, right wing-forces began to tighten up, stripping structures supporting popular freedom, from the courts, mass media, and other institutions. In Chapter 5, Bernard Tamas, in “From Youth Movement to Right-Liberal Wing Authoritarianism: The Rise of Fidesz and the Decline of Hungarian Democracy” puts the renewed growth of political and social repression into a context of worldwide nationalism. Tamas, an associate professor of political science at Valdosta State University, has been a postdoctoral fellow at Harvard University and a Fulbright scholar at the Central European University in Budapest, Hungary. His books include From Dissident to Party Politics: The Struggle for Democracy in Post-Communist Hungary (2007). Bear in mind that not everyone shares Orbán’s vision of what will make this nation great, again. On graffiti-covered walls in Budapest, Runes (traditional Hungarian script) has been found that read “Orbán is a motherfucker” (Mikanowski, 2019, 58). Also in Europe, in Chapter 6, Professor Ronan Le Coadic, of the University of Rennes, Rennes, France, in “Is There a Revival of French Nationalism?” Stating this title in the form of a question is quite appropriate because France’s nationalistic shift has built and ebbed several times during the last few decades. For a time after 2000, it came close to assuming the role of a substantial minority, only to ebb after that. In 2017, the candidate of the National Front reached the second round of the French presidential election. This was the second time this nationalist party reached the second round of the presidential election in the history of the Fifth Republic. In 2002, however, Jean-Marie Le Pen had only obtained 17.79% of the votes, while fifteen years later his daughter, Marine Le Pen, almost doubled her father's record, reaching 33.90% of the votes cast. Moreover, in the 2019 European elections, re-named Rassemblement National obtained the largest number of votes of all French political formations and can therefore boast of being "the leading party in France.” The brutality of oppressive nationalism may be expressed in personal relationships, such as child abuse. While Indonesia and Aotearoa [the Maoris’ name for New Zealand] hold very different ranks in the United Nations Human Development Programme assessments, where Indonesia is classified as a medium development country and Aotearoa New Zealand as a very high development country. In Chapter 7, “Domestic Violence Against Women in Indonesia and Aotearoa New Zealand: Making Sense of Differences and Similarities” co-authors, in Chapter 8, Mandy Morgan and Dr. Elli N. Hayati, from New Zealand and Indonesia respectively, found that despite their socio-economic differences, one in three women in each country experience physical or sexual intimate partner violence over their lifetime. In this chapter ther authors aim to deepen understandings of domestic violence through discussion of the socio-economic and demographic characteristics of theit countries to address domestic violence alongside studies of women’s attitudes to gender norms and experiences of intimate partner violence. One of the most surprising and upsetting scholarly journeys that a North American student may take involves Adolf Hitler’s comments on oppression of American Indians and Blacks as he imagined the construction of the Nazi state, a genesis of nationalism that is all but unknown in the United States of America, traced in this volume (Chapter 8) by co-editor Johansen. Beginning in Mein Kampf, during the 1920s, Hitler explicitly used the westward expansion of the United States across North America as a model and justification for Nazi conquest and anticipated colonization by Germans of what the Nazis called the “wild East” – the Slavic nations of Poland, the Baltic states, Ukraine, and Russia, most of which were under control of the Soviet Union. The Volga River (in Russia) was styled by Hitler as the Germans’ Mississippi, and covered wagons were readied for the German “manifest destiny” of imprisoning, eradicating, and replacing peoples the Nazis deemed inferior, all with direct references to events in North America during the previous century. At the same time, with no sense of contradiction, the Nazis partook of a long-standing German romanticism of Native Americans. One of Goebbels’ less propitious schemes was to confer honorary Aryan status on Native American tribes, in the hope that they would rise up against their oppressors. U.S. racial attitudes were “evidence [to the Nazis] that America was evolving in the right direction, despite its specious rhetoric about equality.” Ming Xie, originally from Beijing, in the People’s Republic of China, in Chapter 9, “News Coverage and Public Perceptions of the Social Credit System in China,” writes that The State Council of China in 2014 announced “that a nationwide social credit system would be established” in China. “Under this system, individuals, private companies, social organizations, and governmental agencies are assigned a score which will be calculated based on their trustworthiness and daily actions such as transaction history, professional conduct, obedience to law, corruption, tax evasion, and academic plagiarism.” The “nationalism” in this case is that of the state over the individual. China has 1.4 billion people; this system takes their measure for the purpose of state control. Once fully operational, control will be more subtle. People who are subject to it, through modern technology (most often smart phones) will prompt many people to self-censor. Orwell, modernized, might write: “Your smart phone is watching you.” Ming Xie holds two Ph.Ds, one in Public Administration from University of Nebraska at Omaha and another in Cultural Anthropology from the Chinese Academy of Social Sciences, Beijing, where she also worked for more than 10 years at a national think tank in the same institution. While there she summarized news from non-Chinese sources for senior members of the Chinese Communist Party. Ming is presently an assistant professor at the Department of Political Science and Criminal Justice, West Texas A&M University. In Chapter 10, analyzing native peoples and nationhood, Barbara Alice Mann, Professor of Honours at the University of Toledo, in “Divide, et Impera: The Self-Genocide Game” details ways in which European-American invaders deprive the conquered of their sense of nationhood as part of a subjugation system that amounts to genocide, rubbing out their languages and cultures -- and ultimately forcing the native peoples to assimilate on their own, for survival in a culture that is foreign to them. Mann is one of Native American Studies’ most acute critics of conquests’ contradictions, and an author who retrieves Native history with a powerful sense of voice and purpose, having authored roughly a dozen books and numerous book chapters, among many other works, who has traveled around the world lecturing and publishing on many subjects. Nalanda Roy and S. Mae Pedron in Chapter 11, “Understanding the Face of Humanity: The Rohingya Genocide.” describe one of the largest forced migrations in the history of the human race, the removal of 700,000 to 800,000 Muslims from Buddhist Myanmar to Bangladesh, which itself is already one of the most crowded and impoverished nations on Earth. With about 150 million people packed into an area the size of Nebraska and Iowa (population less than a tenth that of Bangladesh, a country that is losing land steadily to rising sea levels and erosion of the Ganges river delta. The Rohingyas’ refugee camp has been squeezed onto a gigantic, eroding, muddy slope that contains nearly no vegetation. However, Bangladesh is majority Muslim, so while the Rohingya may starve, they won’t be shot to death by marauding armies. Both authors of this exquisite (and excruciating) account teach at Georgia Southern University in Savannah, Georgia, Roy as an associate professor of International Studies and Asian politics, and Pedron as a graduate student; Roy originally hails from very eastern India, close to both Myanmar and Bangladesh, so he has special insight into the context of one of the most brutal genocides of our time, or any other. This is our case describing the problems that nationalism has and will pose for the sustainability of the Earth as our little blue-and-green orb becomes more crowded over time. The old ways, in which national arguments often end in devastating wars, are obsolete, given that the Earth and all the people, plants, and other animals that it sustains are faced with the existential threat of a climate crisis that within two centuries, more or less, will flood large parts of coastal cities, and endanger many species of plants and animals. To survive, we must listen to the Earth, and observe her travails, because they are increasingly our own.

Peptide synthesis through segment ligation of unprotected peptides (total synthesis) and peptides to proteins (semi-synthesis) in aqueous solution is appealingly simple and efficient because protection and activation steps are not required. In addition, this method offers the potential to access a diverse group of macromolecules such as circular proteins, branched peptides, and protein conjugates which are difficult to obtain through conventional approaches using protecting group strategies. Furthermore, the use of unprotected peptide segments overcomes the problem of solubility encountered in the conventional approach to the synthesis of large peptides or proteins in solution. Conceptually, ligation can be approached two ways. In the first approach, a non-amide bond is formed between two peptide segments through a pair of mutually reactive functional groups. Typical methods of non-amide ligation include oxime, hydrazone, and thiazolidine as the coupling linkages. This type of reaction is traditionally referred to as chemoselective ligation. Non-amide ligation is characteristically flexible in joining two segments that result in amino-to-amino end, carboxyl-to-amine or end-to- side chain structures. This flexibility permits synthesis of protein mimetics and branched peptide dendrimers. In the second approach, an amide bond is formed through a two-step reaction sequence involving four functional moieties, two nucleophiles and two electrophiles in the reaction centre. This reaction is usually used for end-to-end coupling between the Cα-moiety of one peptide segment and the Nα-terminus of another peptide segment resulting in a peptide-backbone product. Similar to the non-amide chemoselective ligation, the first step in orthogonal ligation is a capture reaction by a pair of mutually reactive groups. In general, two nucleophiles, a weak-base nucleophile on the side chain and an α-amino, are located at the N-terminus as an N-terminal nucleophile 5 (NTN). The two electrophiles, usually an O-glycol-aldehyde or an S-ester 4, are located at the C-terminus of the another peptide segment. The initial non-amide capture of two segments through the side chain NTN with the O- or S-ester to form a covalent intermediate 6 enables the spontaneous proximity-driven intramolecular acyl transfer to occur. This intramolecular acyl migration achieves orthogonality in amide bond formation 7 between a specific α-amine in the presence of other free α- and ɛ-amines.

With the emergence of parallel computing, the notion of prefix computation has gained considerable attention in the literature and it plays a central role in parallel algorithm design. This introductory chapter begins with the definition of the prefix problem. The ubiquitous nature of this problem is then illustrated using a host of examples drawn from a variety of application areas. Readers unfamiliar with a particular application area may choose to consult the appropriate references given in Section 1.4, Notes and References. After gaining sufficient familiarity with the remainder of this book, the reader will profit by revisiting Chapter 1 to apply the parallel prefix algorithms to several of the problems introduced here. In fact, many interesting class projects can be developed by cleverly mixing the problems and the algorithms. Let A be a set and o be a binary operation defined over the elements of A. It is assumed that Cl. A is closed under the binary operation o, that is, if a and b are in A, then so is a o b, and C2. the operation o is associative, that is, if a, b, and c are in A, Then . . . (a o b) o c = a o (b o c) = a o b o c. . . . The system (A, o) satisfying conditions Cl and C2 is called a semi-group (Birkhoff and Bartee [1970]). Examples include, (a) A is the set of integers (or real or complex numbers) and o denotes either the addition or the multiplication operation, and (b) A is a set of finite alphabet and o denotes the concatenation. To render our exposition self-contained, in Appendix A we discuss various properties of semigroups of interest to us in this book. Let d = ( d 1 , d2, • • • , 4N)', where di ∈ A, for 1≤ i ≤ N. Consider the problem of computing . . . xi =xi-1 o di. . . . for 2 ≤ i ≤ N, given that x1 = d1.

This chapter is dedicated to the Gaussian approximation of a reversible Markov chain. Regarding this problem, the coefficients of dependence for reversible Markov chains are actually the covariances between the variables. We present here the traditional form of the martingale approximation including forward and backward martingale approximations. Special attention is given to maximal inequalities which are building blocks for the functional limit theorems. When the covariances are summable we present the functional central limit theorem under the standard normalization √n. When the variance of the partial sums are regularly varying with n, we present the functional CLT using as normalization the standard deviation of partial sums. Applications are given to the Metropolis–Hastings algorithm.

O PRESENTE TRABALHO FOI DESENVOLVIDO BASEADO NAS EXPERI?NCIAS VIVENCIADAS NA DISCIPLINA DE BIOLOGIA EM DUAS TURMAS DO 1? ANO, DURANTE O EST?GIO SUPERVISIONADO NO ENSINO M?DIO, EM UMA ESCOLA P?BLICA CENTRO NO MUNIC?PIO DE VIT?RIA DA CONQUISTA ? BA, E BUSCA RETRATAR O PROBLEMA DA DESMOTIVA??O E DESINTERESSE DOS ALUNOS, CONSTATADO DURANTE O PER?ODO DE REG?NCIA DAS ESTAGIARIAS NA ESCOLA. A FALTA DE MOTIVA??O ?, ATUALMENTE, UM DOS PRINCIPAIS PROBLEMAS ENFRENTADOS PELOS PROFESSORES EM SALA DE AULA, O QUE RESULTA EM UMA APRENDIZAGEM MENOS SATISFAT?RIA POR PARTES DOS ALUNOS, SENDO NECESS?RIO A PARTICIPA??O M?TUA DE PROFESSORES E ALUNOS PARA A REALIZA??O EFETIVA DO ENSINO-APRENDIZAGEM. CONTUDO ? POSS?VEL RESSALTAR QUE A APRENDIZAGEM DE BIOLOGIA N?O ? F?CIL, POIS APRESENTA CONTE?DOS ABSTRATOS E DE DIF?CIL COMPREENS?O. DIANTE DISSO ? FUNDAMENTAL QUE OS DOCENTES ESTEJAM CONSTANTEMENTE BUSCANDO MANEIRAS ADEQUADAS PARA MELHORAR A QUALIDADE DO PROCESSO DE ENSINO E APRENDIZAGEM.

This chapter discusses the progress made towards problems originating from Stein's seminal paper, “Some problems in harmonic analysis.” It is by now well-known that the mapping properties of Fourier restriction operators to hypersurfaces in R ⁿ and their variable coefficient generalizations are intimately related to questions of a combinatorial nature. Over recent years there has been quite a bit of research around these underlying issues. In some way, it became interdisciplinary with connections towards geometric measure theory, the theory of finite fields, incidence geometry, and mathematical computer science. While the central original problems remain unsolved, this line of research has produced many new results of independent interest, though the chapter focuses primarily on developments around the theory of oscillatory integrals.

The falling birth rate in 1948 became a political problem, and all demographic data were made secret thereafter. V. N. Starovskii, the head of the Central Statistical Administration, suggested that the rising number of illegal abortions was the primary cause of the declining birth rate. Saddled with this allegation, the medical and legal professions undertook comprehensive study of both legal and illegal abortion, including a survey of illegal abortion, compiled through interviews with hundreds of women hospitalized after botched abortions. The results led to a shift in reformist focus from prosecution to prevention, and a new understanding of the causes underlying Soviet women’s reproductive decisions.

This chapter introduces basic concepts of modern finance theory and demonstrates how to apply them in complex real-world problems. Financial deals and investment decisions are typically determined under uncertainty.Therefore, although this chapter is self-contained, we have to expect some theoretical background in individual decisionmaking and optimal investment under uncertainty. We organize our discussion into four central sections. The starting point is a portfolio choice problem, where an investor has to choose between different assets with specific risk and return characteristics. We then move on to some option pricing applications. We first derive analytical formulas and then evaluate numerical procedures for pricing European and American options as well as more exotic option products. The third section elaborates on credit risk measurement and management using a corporate bond portfolio as example. In the last section we discuss mortality risk and the optimal portfolio structure of a life insurance company. This section provides different numerical approaches to find an optimal portfolio structure with many risky assets. It begins with simple measures of risk and return of a single asset and then develops decision rules to choose optimal portfolios that maximize expected utility of wealth in worlds without and with riskless borrowing and lending opportunities. The purpose of this section is to optimize a portfolio of equity shares and a risk-free investment opportunity. The investor faces the most basic two-period investment choice problem: He buys assets in the first period and these assets pay off in the next period. The problem of the investor is to choose from i = 1, . . . ,N risky assets which may be shares, bonds, real estate, etc. The gross return of each asset i is denoted by rit = qit/qit−1 − 1, where qit−1 is the first-period market price and qit − qit−1 the second-period payoff.

Several important hormones such as oxytocin, secretin, and LHRH are known to be peptidyl amides. In addition to these, other peptidyl amides such as indolicidin and the protegrins have been shown to exhibit potent antimicrobial activity. The in vivo production of such compounds is via endogenous enzymatic cleavage of propeptides, making their synthesis by genetic engineering notoriously difficult. Furthermore, to facilitate the survival of synthetic peptidyl amides in vivo, an obvious defence against the action of carboxypeptidases is the N-alkylation of the carboxylic amide terminus. Such secondary amides would be expected to exhibit vastly different solubility and transport properties to primary amides, thus their chemical synthesis is of immense importance. The solid phase synthesis of peptidyl amides and peptidyl N-alkyl amides is centred around two main strategies: 1. Ammonolysis/aminolysis of resin-bound esters. 2. Use of resin-bound primary amines, which may in turn be chemically modified to generate novel secondary amine functionalized linkers for the synthesis of peptidyl N-alkyl amides. Early examples of the use of resin-bound amines for the solid synthesis of peptidyl amides involve the use of linkers such as benzhydrylamine or benzylamine. Following peptide assembly, these linkers require highly acidic (e.g. HF) mediated cleavage, and hence simultaneous removal of acid-labile sidechain protection groups occurs and may cause problems. Systematic modifications of these linker-resins by substitution with electron-donating substituents have resulted in the generation of numerous linker-resins with increased acid sensitivity. Notably, the 4-(2',4'-dimethoxyphenylaminomethyl) phenoxy derivatized (Rink) resin 1, which is cleavable by 95% v/v TFA, and the 5-(2-fluorenylmethoxycarbonylaminornethyl-3,5-dimethoxy)- phenoxyvaleric acid (PAL) linker 2 acidolysed by 75% v/v TFA. Greater acid lability has been achieved using the xanthenyl derivatized resin, 9-(fluorenylmethoxycarbonylamino)xanthen-3-yloxymethyl polystyrene (Sieber amide) resin 3, which besides being cleavable by 1% v/v TFA, holds the added advantage of readily undergoing reductive N-alkylation to afford resin-bound secondary amines for the synthesis of peptidyl N-alkyl amides. In addition to the method detailed below, a number of alternative approaches have recently been reported.

The treatment of chronic pain is a chronic problem for many specialities. It is generally based on an approach with antidepressants, anti-epileptics and opioids as drugs of first choice. It has been worked by many different protocols. Ketamine, which is known as a good anaesthetic, has been used for chronic pain. When the pain has a neuropathic component, ketamine is a promising treatment for pain management. Ketamine: by inhibiting the N-methyl-D-aspartate receptor and having some other effects like enhancement of descending inhibition and anti-inflammatory effects at central sites, takes part in chronic pain management. Besides having analgesic effects, there are some concerns about the side effects of ketamine. Some psychedelic symptoms as hallucinations, memory defects, panic attacks, nausea and vomiting, somnolence, cardiovascular stimulation and sometimes hepatoxicity may be seen in patients. Ketamine is generally well-tolerated in clinical settings. Close monitoring of patients receiving ketamine should be mandatory in order to be aware of central nervous system, haemodynamic, renal and hepatic symptoms as well as abuse.

This paper investigates on the problem of functionally graded (FG) shallow conical shells subjected to low-velocity impact by a solid spherical mass at the centre. Turbomachinery blades with low aspect ratio could be idealized as twisted rotating cantilever FG shallow conical shells. An analytic solution method is developed to solve and predict the impact response in terms of contact force, impactor displacement, initial velocity of impactor, target displacement and indentation of the FG conical shells with different sigmoidal power law exponent. A modified Hertzian contact law considering permanent indentation is used to calculate the contact force along with other impact response parameters. Using the Newmark’s time integration scheme the time dependent equations are solved. An eight noded isoparametric shell element is considered for the present finite element model. Parametric studies are performed to study the effects of triggering parameters like initial velocity of impactor (VOI), mass of the impactor (M0) and twist angle (Ψ) considering different sigmoidal power law exponent (N) for Ni (Nickel)-ZrO2 (Zirconia) and Ti (Titanium alloy-Ti–6Al–4V)-ZrO2 (Zirconia) functionally graded conical shell subjected to low velocity impact.

Railway rolling noise is nowadays a major source of acoustic pollution in urban areas, with nearly up to 12 million people daily affected in Europe by this phenomenon [1]. Hence, the search for ways of decreasing such noise radiation has become a highly active and significant research field. Following this approach, a Genetic Algorithms-based shape optimization of the railway wheel [2] is developed with the aim of minimizing rolling noise. Different approaches are considered to address the problem, such as directly minimizing radiated Sound poWer Level (SWL) or using the maximization of the natural frequencies if computational efficiency is especially critical. A parametric Finite Element model is implemented for the wheel based on the most relevant geometric parameters in rolling noise radiation. For the acoustic calculation, the sound radiation models used in the TWINS software [3] are adopted, which also accounts for the whole dynamics of the wheel/rail system. Furthermore, for every candidate wheel proposed, a structural analysis is computed in order to check design feasibility in accordance with the corresponding standard [4]. In all cases, new geometries for the wheel cross section are achieved that reduce the radiated rolling noise. REFERENCES [1] WHO European Centre for Environment and Health, “Burden of disease from environmental noise”, WHO, Tech. Rep., 2011 [2] X. Garcia-Andrés, J. Gutiérrez-Gil, J. Martínez-Casas and F. D. Denia, “Wheel shape optimization approaches to reduce railway rolling noise”, Struct. Multidiscipl. Optim., Vol. 62, pp. 2555-2570, (2020). [3] D. J. Thompson, B. Hemsworth and N. Vincent, “Experimental validation of the TWINS prediction program for rolling noise, part 1: Description of the model and method”, J. Sound Vib., Vol. 193 (1), pp. 123–135, (1996). [4] UNE, “Railway applications. Wheelsets and bogies. Monobloc wheels. Technical approval procedure. Part 1: Forged and rolled wheels. UNE-EN-13979-1:2006”, Asociación Española de Normalización (UNE), Technical Standard, 2011.

Abstract The Double Circular-arc gear (W-N gear) transmission is well-known as the high contact strength, good wear resisting property and well distributed wears. As developing of its applications in recent years, the contact deformation of W-N gear become more important. In this paper, under basic assumption, the equations for calculating contact deformation of Double Circular-arc gear tooth were derived by using theory of elasticity of general contact problem between arbitrary elastic bodies in three dimensions. The equations were proved by industrial gear applications (one of the example: transmission power N = 3000KW, circumferential speed V = 120 m / s, load fact K = 188 N / cm2, the hardness of tooth surface Hv &gt; 600, surface roughness of tooth Ra &lt; 0.32μm). The relationship between contact deformation of Double Circular-arc gear and helical angle (β), ratio of tooth numbers (u) and central distance (c) was also discussed in this paper. The result of this study provides an inportant reference for tooth stiffness and tooth correction calculation of Double Circular-arc gears.

We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations. We prove that under the randomised exponential-time hypothesis it is not possible to find c > 1 such that a CSP over an arbitrary finite equality language is solvable in O(c^n) time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of 2^o(n log n) time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each c > 1 there exists an NP-hard equality CSP solvable in O(c^n) time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in O(c^n) time for a fixed c.

The Markov Decision Problem (MDP) plays a central role in AI as an abstraction of sequential decision making. We contribute to the theoretical analysis of MDP PLANNING, which is the problem of computing an optimal policy for a given MDP. Specifically, we furnish improved STRONG WORST-CASE upper bounds on the running time of MDP planning. Strong bounds are those that depend only on the number of states n and the number of actions k in the specified MDP; they have no dependence on affiliated variables such as the discount factor and the number of bits needed to represent the MDP. Worst-case bounds apply to EVERY run of an algorithm; randomised algorithms can typically yield faster EXPECTED running times. While the special case of 2-action MDPs (that is, k = 2) has recently received some attention, bounds for general k have remained to be improved for several decades. Our contributions are to this general case. For k >= 3, the tightest strong upper bound shown to date for MDP planning belongs to a family of algorithms called Policy Iteration. This bound is only a polynomial improvement over a trivial bound of poly(n, k) k^{n} [Mansour and Singh, 1999]. In this paper, we generalise a contrasting algorithm called the Fibonacci Seesaw, and derive a bound of poly(n, k) k^{0.6834n}. The key construct we use is a template to map algorithms for the 2-action setting to the general setting. Interestingly, this idea can also be used to design Policy Iteration algorithms with a running time upper bound of poly(n, k) k^{0.7207n}. Both our results improve upon bounds that have stood for several decades.

Introdução: As intervenções farmacêuticas são caracterizadas como condutas planejadas, documentadas e realizadas juntamente ao paciente e profissionais de saúde, visando solucionar ou prevenir problemas relacionados a medicamentos na farmacoterapia. A nível de atendimento individualizado ao paciente, cabe ao farmacêutico à obtenção de dados sobre o histórico medicamentoso, avaliação da conduta terapêutica adotada, fornecimento de informações baseadas em evidências à equipe multidisciplinar e acompanhamento dos exames laboratoriais. Objetivo: Este estudo tem o objetivo de descrever as intervenções farmacêuticas realizadas pelo Serviço de Farmácia Clínica de um hospital privado do Rio de Janeiro. Materiais e métodos: Trata-se de um estudo retrospectivo de intervenções farmacêuticas realizadas através do acompanhamento farmacoterapêutico de 72 pacientes atendidos pelo Serviço de Farmácia Clínica, no período de dezembro de 2021 a janeiro de 2022, na Clínica Médica, Clínica Cirúrgica e no Centro de Terapia Intensiva. Resultados: Foram realizadas 100 intervenções farmacêuticas classificadas em categorias: 49% (n=49) relacionadas à ausência da informação de alergia, 8% (n=8) dose abaixo do recomendado, 5% (n=5) substituição de medicamento e aprazamento inadequado, 4% (n=4) inclusão de medicamento, 3 % (n=3) substituição de via de administração, suspensão do medicamento, substituição de medicamento não padrão, descrição da dose incorreta, ausência de prescrição e duração de tratamento antimicrobiano, 2% (n=2) substituição de forma farmacêutica, melhora de aprazamento, facilidade de administração, e apenas 1% (n=1) dose acima do recomendado, interação medicamento x medicamento, ajuste por disfunção renal, prescrição realizada para paciente alérgico e incompatibilidade de administração. Destas, 82% (n=82) das intervenções foram aceitas pela equipe multidisciplinar. Conclusão: As intervenções farmacêuticas realizadas a partir da análise da farmacoterapia aplicada aos pacientes demonstram a relevância na promoção da conduta terapêutica adequada, segurança e qualidade na prestação do serviço de saúde.

Development of spectroscopic and electrostatic probe techniques for the quantitative characterisation of low temperature laser ablated plasma plumes are described. The titanium plasma plume is formed by KrF irradiation, incident on a rotating target at laser fluences of 2-6 Jem−2 with a spot size 1.4 mm x 1.4 mm. A collimated, short pulsed, tunable dye laser at a set delay time, between 500ns - 2µs, is used to spatially and temporally probe the plasma plume in a direction parallel to the target surface (i.e. in x-z plane). For a plasma under-going self-similar expansion, the observed absorbance values A(ΔλS, z) are related to the corresponding absorber number densities N(x, z) within the (x-z) plane by (1) where f is the absorption oscillator strength, t is the probe delay time and ΔλS is the dye laser detuning from line centre wavelength λ0 of the transition.

Set up and operation of a mid to large size gas turbine requires a significant investment in the engine and the test cell. The continuing cost of operation and maintenance is also substantial. Both the capital and operating costs are well outside the budget of many educational institutions, and small research centres. Micro-turbines, in particular engines used for model aircraft, are a viable alternative. Their capital costs are low and existing facilities can often be modified to support them. Micro-turbines are complete turbojets often utilizing a centrifugal compressor from a turbo-charger and an axial turbine. This work utilized a micro-jet engine commonly used to propel remote control aircraft. The engine has been set up for research into component degradation and as a laboratory for an upper year engineering course in turbomachinery. It is rated by the manufacturer to produce 150 N of thrust at 132,000 RPM. This paper examines some of the problems encountered in installing small total pressure and temperature probes in a micro engine. The entire test rig, including measurement of thrust and mass flow is presented. As well, the addition of a PC based control system is discussed. Operating data is presented and compared to larger engines to demonstrate the viability of this engine as a test bed. Some problems encountered in using an engine such as this beyond its normal operating envelope, along with some solutions, are presented.

Considerable interest centres at the present time on the problem of approximating the dynamical motion of solitons by an underlying discrete dynamical system. It has recently been demonstrated that the dynamics of N-solitons of the Nonlinear Schrodinger Equation (NSE) is quite well approximated by Complex Toda Lattice Equations (CTLE) in the limit of large separation of almost identical solitons with arbitrary phases [1-4]. The Lagrangian method proposed in [1, 2] is a direct reduction procedure which does not depend on the integrability of the original equations, and is applicable in principle to any Hamiltonian system having sufficiently well behaved solitary waves. Here it is shown that a Lagrangian theory similar to that of Gorshkov-Ostrowski [5] reduces a large class of nonintegrable Hamiltonian wave systems to a double Toda lattice in the limit of large separations of identical solitary pulses, generalising the results of [1-4] quite considerably.

Abstract Orienting the workpiece in such a way as to minimize the number of setups in a 4-axis or a 5-axis Numerical Control (NC) machine is formulated as follows: Given a set of spherical polygons (that are representations of curved surfaces visible to a 3-axis NC machine), find a great circle (the 4th axis) or a band (the 4th and the 5th axes) containing a great circle that intersects the polygons maximally. While there are potentially infinitely many solutions to this problem, a sphere is partitioned into O(N2) regions based on the N polygons. Within each of these regions, it is shown that it requires O(NlogN) time to determine maximum intersections and all the solutions are congruent. Central projection mapping is employed so as to present the algorithms in the plane.

The research problem: Pseudomonas syringae pv. tomato (Pst) and Xanthomonas campestrispv. vesicatoria (Xcv) are the causal agents of tomato bacterial speck and spot diseases, respectively. These pathogens colonize the aerial parts of the plant and cause economically important losses to tomato yield worldwide. Control of speck and spot diseases by cultural practices or chemicals is not effective and genetic sources of resistance are very limited. In previous research supported by BARD, by gene expression profiling we identified signaling components involved in resistance to Xcvstrains. Follow up experiments revealed that a tomato gene encoding a MAP kinase kinase kinase (MAPKKKe) is required for resistance to Xcvand Pststrains. Goals: Central goal of this research was to investigate the molecular mechanisms by which MAPKKKεand associated MAP kinase cascades regulate host resistance. Specific objectives were to: 1. Determine whether MAPKKKεplays a broad role in defense signaling in plants; 2. Identify components of MAP kinase cascades acting downstream of MAPKKKε; 3. Determine the role of phosphorylation-related events in the function of MAPKKKε; 4. Isolate proteins directly activated by MAPKKKε-associatedMAPK modules. Our main achievements during this research program are in the following major areas: 1. Characterization of MAPKKKεas a positive regulator of cell death and dissection of downstream MAP kinase cascades (Melech-Bonfil et al., 2010; Melech-Bonfil and Sessa, 2011). The MAPKKKεgene was found to be required for tomato resistance to Xcvand Pstbacterial strains and for hypersensitive response cell death triggered by different R gene/effector gene pairs. In addition, overexpression analysis demonstrated that MAPKKKεis a positive regulator of cell death, whose activity depends on an intact kinase catalytic domain. Epistatic experiments delineated a signaling cascade downstream of MAPKKKεand identified SIPKK as a negative regulator of MAPKKKε-mediated cell death. Finally, genes encoding MAP kinase components downstream of MAPKKKεwere shown to contribute to tomato resistance to Xcv. 2. Identification of tomato proteins that interact with MAPKKKεand play a role in plant immunity (Oh et al., 2011). We identified proteins that interact with MAPKKKε. Among them, the 14-3-3 protein TFT7 was required for cell death mediated by several R proteins. In addition, TFT7 interacted with the MAPKK SlMKK2 and formed homodimersin vivo. Thus, TFT7 is proposed to recruit SlMKK2 and MAPKKK client proteins for efficient signal transfer. 3. Development of a chemical genetic approach to identify substrates of MAPKKKε-activated MAP kinase cascades (Salomon et al., 2009, 2011). This approach is based on engineering the kinase of interest to accept unnatural ATP analogs. For its implementation to identify substrates of MAPKKKε-activated MAP kinase modules, we sensitized the tomato MAP kinase SlMPK3 to ATP analogs and verified its ability to use them as phosphodonors. By using the sensitized SlMPK3 and radiolabeled N6(benzyl)ATP it should be possible to tag direct substrates of this kinase. 4. Development of methods to study immunity triggered by pathogen-associated molecular patterns (PAMPs) in tomato and N. benthamiana plants (Kim et al., 2009; Nguyen et al. 2010). We developed protocols for measuring various PTI-associatedphenotypes, including bacterial populations after pretreatment of leaves with PAMPs, induction of reporter genes, callose deposition at the cell wall, activation of MAP kinases, and a luciferase-based reporter system for use in protoplasts. Scientific and agricultural significance: Our research activities discovered and characterized a signal transduction pathway mediating plant immunity to bacterial pathogens. Increased understanding of molecular mechanisms of immunity will allow them to be manipulated by both molecular breeding and genetic engineering to produce plants with enhanced natural defense against disease. In addition, we successfully developed new biochemical and molecular methods that can be implemented in the study of plant immunity and other aspects of plant biology.