BackgroundThe pursuit of a cure for HIV is a high priority for researchers, funding agencies, governments and people living with HIV (PLWH). To date, over 250 biomedical studies worldwide are or have been related to discovering a safe, effective, and scalable HIV cure, most of which are early translational research and experimental medicine. As HIV cure research increases, it is critical to identify and address the ethical challenges posed by this research.MethodsWe conducted a scoping review of the growing HIV cure (...) research ethics literature, focusing on articles published in English peer-reviewed journals from 2013 to 2021. We extracted and summarized key developments in the ethics of HIV cure research. Twelve community advocates actively engaged in HIV cure research provided input on this summary and suggested areas warranting further ethical inquiry and foresight via email exchange and video conferencing.DiscussionDespite substantial scholarship related to the ethics of HIV cure research, additional attention should focus on emerging issues in six categories of ethical issues: (1) social value (ongoing and emerging biomedical research and scalability considerations); (2) scientific validity (study design issues, such as the use of analytical treatment interruptions and placebos); (3) fair selection of participants (equity and justice considerations); (4) favorable benefit/risk balance (early phase research, benefit-risk balance, risk perception, psychological risks, and pediatric research); (5) informed consent (attention to language, decision-making, informed consent processes and scientific uncertainty); and (6) respect for enrolled participants and community (perspectives of people living with HIV and affected communities and representation).ConclusionHIV cure research ethics has an unfinished agenda. Scientific research and bioethics should work in tandem to advance ethical HIV cure research. Because the science of HIV cure research will continue to rapidly advance, ethical considerations of the major themes we identified will need to be revisited and refined over time. (shrink)

In this paper we will address the problem of the existence of orbitals by analyzing the relationship between molecular chemistry and quantum mechanics. In particular, we will consider the concept of orbital in the light of the arguments that deny its referring character. On this basis, we will conclude that the claim that orbitals do not exist relies on a metaphysical reductionism which, if consistently sustained, would lead to consequences clashing with the effective practice of science in its different (...) branches. (shrink)

Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of semiclassical recurrence functions. A band-limited periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. The frequencies of the periodic orbit signal are the semiclassical eigenvalues, and are determined by either linear predictor, Padé approximant, or signal diagonalization. The second method is based upon the direct application (...) of the Padé approximant to the periodic orbit sum. The Padé approximant allows the resummation of the, typically exponentially, divergent periodic orbit terms. Both techniques do not depend on the existence of a symbolic dynamics, and can be applied to bound as well as to open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard. (shrink)

Social theorists, drawing on the study of complex dynamical systems to address global processes, tend to evoke an immanent globality devoid of a constitutive otherness or outside. However, as well as dealing with the internal dynamics of systems, complexity studies point to the mutual implication of systems and their surroundings: a concern that resonates with the interest in the convolutions of the inside–outside relationship prominent in post-structural philosophies. This article, looking at theories about the dynamical characteristics of the solar system, (...) galaxy and universe, develops the idea of an ex-orbitant globality that treats the earth as a system in active and ongoing interchange with its cosmic environment. A sense of the inevitable excess and unpredictability that attends this openness to the cosmos and to further other-than-human influences, it is suggested, has repercussions for the way we respond to environmental change injecting an element of abyssal undecidability into all our deliberations. (shrink)

Some strategies to turn any logic into a paraconsistent system are examined. In the environment of universal logic, we show how to paraconsistentize logics at the abstract level using a transformation in the class of all abstract logics called paraconsistentization by consistent sets. Moreover, by means of the notions of paradeduction and paraconsequence we go on applying the process of changing a logic converting it into a paraconsistent system. We also examine how this transformation can be performed using multideductive abstract (...) logics. To conclude, the conceptual notion paraconsistent orbit of a logic is proposed. (shrink)

In this article we establish the existence of a number of new orbits in the automorphism group of the computably enumerable sets. The degree theoretical aspects of these orbits also are examined.

The Scientific Revolution was far from the anti-Aristotelian movement traditionally pictured. Its applied mathematics pursued by new means the Aristotelian ideal of science as knowledge by insight into necessary causes. Newton’s derivation of Kepler’s elliptical planetary orbits from the inverse square law of gravity is a central example.

In this paper we show that there are "E₀ many" orbit inequivalent free actions of the free groups Fn. 2 ≤ n ≤ ∞ by measure preserving transformations on a standard Borel probability space. In particular, there are uncountably many such actions.

Interpretation of experiments involving use of vacuum ultraviolet radiation to effect ionization of N 2 in terms of measurements of a molecular orbital is erroneous.

Sum rules are derived for the quantum wave functions of the Hadamard billiard in arbitrary dimensions. This billiard is a strongly chaotic (Anosov) system which consists of a point particle moving freely on a D-dimensional compact manifold (orbifold) of constant negative curvature. The sum rules express a general (two-point)correlation function of the quantum mechanical wave functions in terms of a sum over the orbits of the corresponding classical system. By taking the trace of the orbit sum rule or pre-trace formula, (...) one obtains the Selberg trace formula. The sum rules are applied in two dimensions to a compact Riemann surface of genus two, and in three dimensions to the only non-arithmetic tetrahedron existing in hyperbolic 3-space. It is shown that the quantum wave functions can be computed from classical orbits. Conversely, we demonstrate that the structure of classical orbits can be extracted from the quantum mechanical energy levels and wave functions (inverse quantum chaology). (shrink)

We investigate the orbit of a low computably enumerable set under automorphisms of the partial order of c.e. sets under inclusion. Given an arbitrary low c.e. set A and an arbitrary noncomputable c.e. set C, we use the New Extension Theorem of Soare to construct an automorphism of mapping A to a set B such that CTB. Thus, the orbit in of the low set A cannot be contained in the upper cone above C. This complements a result of Harrington, (...) who showed that the orbit of a noncomputable c.e. set cannot be contained in the lower cone below any incomplete c.e. set. (shrink)

The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...) _\alpha ^0 $ orbit (from the proof). (shrink)

The Scientific Revolution was far from the anti-Aristotelian movement traditionally pictured. Its applied mathematics pursued by new means the Aristotelian ideal of science as knowledge by insight into necessary causes. Newton’s derivation of Kepler’s elliptical planetary orbits from the inverse square law of gravity is a central example.

In 1969 Jasia Reichardt curated an exhibition at the Institute of Contemporary Art in London called Play Orbit. Although it has not achieved the landmark status of Reichardt's Cybernetic Serendipity, which was presented in London a year earlier, it caught the intellectual and artistic mood of a newly emergent constituency of (largely British) artists who had benefited from a post-war revision of art education and a de-centring of intellectual energy away from the economic capitals. It may be that Play Orbit (...) will eventually be regarded in much the same way as Cybernetic Serendipity that is, as a significant footnote in the history of contemporary art. By turning artists' attention to toys through this project, the categories of painting and sculpture dissolved and the Modernist imperative of the enduring observation that had informed the arts and letters in a centred intellectual regime was seen for what it was: a colonial anachronism. The unapologetic relativism of play and the provisional truths of games coalesced in Play Orbit as confrontations to the essentialist materialism of the prevailing orthodoxy. In this sense Play Orbit, and its extensive catalogue of images and essays, foreshadowed not only the critical style that followed the influence of Continental Theory in the mid 1970s but also anticipated the agenda of virtually all that has been written about games in the last decade. For all its apparent whimsy and reification of idiosyncrasy, Play Orbit can now be seen as, above all, a constructively political intervention levered through the arts. For example, one of the more enduring and least contested impacts of the intellectual revisions of the last thirty years that Play Orbit foreshadowed is evident in the practice of history not least the practice of history as a game to be played. This paper elaborates on these assertions and asks how games and games theory might be connected with their own political and intellectual history, and how contemporary artists who choose to benefit from the licence that play endows might situate their work within what might be called Art Ludistory: a political play on the history of play. (shrink)

The article disputes the recent claim featured in "Nature" magazine and many other science magazines to the effect that atomic orbitals have been observed for the first time. The claim is incorrect in view of the unconvincing nature of the evidence adduced and since atomic orbitals are deemed unobservable in principle by quantum mechanics. In addition, the possible educational drawbacks of this incorrect claim are discussed.

We give a proof of a theorem of Harrington that there is no orbit of the lattice of recursively enumerable sets containing elements of each nonzero recursively enumerable degree. We also establish some degree theoretical extensions.

The nucleon spin problem raises experimental and theoretical questions regarding the contribution of the orbital angular momentum of the quarks to the total spin of the nucleon. In this article we examine the commutation relationships of various operators that contribute to the total angular momentum of the nucleon. We find that the sum of the orbital plus gluon field angular momenta should satisfy the angular momentum commutators, at least up to the one-loop level. This, requirement on the sum (...) of these operators imposes a non-trivial restriction on the form of the color electric and magnetic fields. This is similar to the magnetic monopole/electric charge system where it is only the sum of the orbital plus field angular momentum that satisfies the correct commutation relationships. (shrink)

The main focus of the book is the presentation of the 'inertial' view of population growth. This view provides a rather simple model for complex population dynamics, and is achieved at the level of the single species without invoking species interactions. An important part of this account is the maternal effect. Investment of mothers in the quality of their daughters makes the rate of reproduction of the current generation depend not only on the current environment, but also on the environment (...) experienced by the previous generation. (shrink)

The present work is a comment of a recent paper by Fortin and coauthors in which the authors propose the introduction of Bohmian mechanics in the philosophy of chemistry and the use of standard quantum mechanics as a mere instrument of prediction. This way would allow overcoming the obstacles found in linking molecular chemistry and quantum mechanics. Starting from some remarks on the orbital concept, we highlight and discuss some general issues that need to be taken into account when (...) two scientific theories coexist within the same investigation field, i.e. SQM and BM. (shrink)

Like other forms of debris in terrestrial and marine environments, space debris prompts questions about how we can live with the material remains of technological endeavors past and yet to come. Although techno-societies fundamentally rely on space infrastructures, they so far have failed to address the infrastructural challenge of debris. Only very recently has the awareness of space debris as a severe risk to both space and Earth infrastructures increased within the space community. One reason for this is the renewed (...) momentum of interplanetary space exploration, including the colonization of the Moon and Mars, which is part of transhumanist and commercially driven dreams of the so-called New Space age. Understanding space infrastructures as inherently linked to earthly infrastructure, we attend to the ways in which space debris, a once accepted by-product of scientific-technological progress, economic interests, and geopolitics, increasingly becomes a matter of concern. Drawing on qualitative interviews with European space sector representatives and work in Science and Technology Studies on infrastructures, we argue that their discursive efforts and visual representation strategies coproduce space debris as a boundary infrastructure. We suggest considering this boundary infrastructure as relating orbital environments and the planet through enacting sustainability and responsibility for beyond-planetary environments. (shrink)

An equation proposed by Levy, Perdew and Sahni (Phys. Rev. A 30:2745, 1984) is an orbital-free formulation of density functional theory. However, this equation describes a bosonic system. Here, we analyze on a very fundamental level, how this equation could be extended to yield a formulation for a general fermionic distribution of charge and spin. This analysis starts at the level of single electrons and with the question, how spin actually comes into a charge distribution in a non-relativistic model. (...) To this end we present a space-time model of extended electrons, which is formulated in terms of geometric algebra. Wave properties of the electron are referred to mass density oscillations. We provide a comprehensive and non-statistical interpretation of wavefunctions, referring them to mass density components and internal field components. It is shown that these wavefunctions comply with the Schrödinger equation, for the free electron as well as for the electron in electrostatic and vector potentials. Spin-properties of the electron are referred to intrinsic field components and it is established that a measurement of spin in an external field yields exactly two possible results. However, it is also established that the spin of free electrons is isotropic, and that spin-dynamics of single electrons can be described by a modified Landau-Lifshitz equation. The model agrees with the results of standard theory concerning the hydrogen atom. Finally, we analyze many-electron systems and derive a set of coupled equations suitable to characterize the system without any reference to single electron states. The model is expected to have the greatest impact in condensed matter theory, where it allows to describe an N-electron system by a many-electron wavefunction Ψ of four, instead of 3N variables. The many-body aspect of a system is in this case encoded in a bivector potential. (shrink)

The many constraints of outer space experience challenge the human ability to coexist. Paradoxically, astronauts assert that on the international space station there are no conflicts or, at least, that they are able to manage their differences, behavioral as well as cognitive, in full respect of human rights and the imperatives of cooperative living. The question is: Why? Why in those difficult, a-terrestrial, and therefore almost unnatural conditions do human beings seem to be able to peacefully and collaboratively live together? (...) What is there beyond terrestrial boundary conditions that allows for such a result? And what can we learn from the astronauts’ experience about the effectiveness of human rights on Earth? My proposal is that the a-terrestrial dimension deeply alters the mind/body indexical framework and, in this way, disentangles the human inclination to semiosis from the cognitive and behavioral habits of categorization and territorialization inherent in the experience on Earth. If analyzed through the spectrum of an interdisciplinary approach involving anthropology, semiology, law, and human geography, I think that outer space enterprises can offer many insights into the cognitive and ethical/political hindrances to the effectiveness of human rights and their intercultural uses. Meanwhile the compulsive greed for a possessive territorialization of outer space and celestial bodies is growing by leaps and bounds. It haunts and imbues both astropolitics and space law. The astronauts’ semio-anthropological experience of human rights and cooperative coexistence seems to have been left in orbit. The future requires awareness and action by anthropologists, semioticians, cognitive scientists, geographers and lawyers, working all together in an interdisciplinary effort to move beyond approaching the experiential with a territorial mindset. The hope is that the “dark dream” of human exploitation/colonization of outer space will not turn from a political and legal speculation into a future reality. (shrink)

We consider the following question within both Newtonian physics and relativity theory. "Given two point particles X and Y, if Y is rotating relative to X, does it follow that X is rotating relative to Y?" As it stands the question is ambiguous. We discuss one way to make it precise and show that, on that reading at least, the answers given by the two theories are radically different. The relation of relative orbital rotation turns out to be symmetric (...) in Newtonian physics, but not in relativity theory. (shrink)

Carl F. H. Henry serves as a fruitful resource for the integration of faith and learning. The central issue in Christian scholarship is to properly associate the revelation of God with the knowledge of God’s world across all academic disciplines. The particular effort of this article is to demonstrate the clarity Henry provides as it relates to general revelation, special revelation, and knowledge explored in a comprehensive university setting. Building on Henry’s clarity, an orientation of knowledge to Jesus Christ, a (...) proposal for the resulting vision for Christian scholarship, and habits of Christian educational institutions follows. (shrink)

Being in the contextual orbit boldly affirms young people are the rolling waves of positive change in the world. They are indeed the rolling stream of life and its creative melody, but most important they are indefatigable explorers of the meaning of human existence. Let them roll forward with their 'will to win' attitude not just to live but to live well for them, but also for the sake of generations to follow in the future.

continent. 1.2 (2011): 125-128. What is the nature of sound? What is the nature of volume? William James, in attempting to address these simple questions wrote, “ The voluminousness of the feeling seems to bear very little relation to the size of the ocean that yields it . The ear and eye are comparatively minute organs, yet they give us feelings of great volume” (203-­4, itals. original). This subtle extensivity of sensation finds its peer in the subtle yet significant influence (...) of habituated action upon our lives. This expansive quality of habit­making is what Craig Dongoski's bodies of work enable us to appreciate. Nearly ten years ago Dongoski had a habit of turning on his audio recorder every day at three o'clock for three minutes. No matter what the setting, what the activity, Dongoski recorded the ambient sounds in his environment at that moment. As it happened, one day he was teaching a drawing class and he recorded the sounds of their pencils scratching across their respective surfaces. This was a critical moment for him. Later he would place a contact mic onto a drawing surface and record the sound of his signature. Signatures change over time, they respond to the conditions in which they are performed. Signatures speak volumes about the author, but a practice of attunement is required for the volume to be audible. To hear all that a signature can tell about its author, the listener must tune into the frequency at which this information is being broadcast. Dongoski's drawings and video works draw­out the peculiar artifact that habit makes of living: habits establish a tempo of living and it seems that one's habitus is the signature of habitual living. I sat down with Craig in an attempt to sound­out some of the depths of thought in his practice. What follows is selected from our conversation. Paul Boshears (PB): Clearly your work is dealing with time: from the painstaking action of rendering the drawing to the free­form approach of launching a microphone into a body of water and waiting to see what's recorded. Craig Dongoski (CD): Are we talking about the films or the drawings? PB: Well, it's a bit of both in my mind. I know the drawings on first glance seem to be these flows of lines without concern but I realize that there is this painstaking action involved. CD: I'm interested in time because I'm interested in forms outside of control, outside of politics, and outside of economics. I think that art, when it's alive, does go beyond those. I'm interested in duality and paradox—a stream of contradiction, I suppose. For instance, scale and size. There is a tendency to think that these are the same thing. But really you can have something small that has a lot of scale—look at Goya's drawings, Los Caprichos , they're very small but they have a lot of scale. Likewise things that are spontaneous don't necessarily mean that they take only two or three seconds to do. This latter distinction is what I'm most interested in. Having that appearance of spontaneity. The image has rhythm, you can latch onto it; but the reality is that it took many hours—and many months in some cases—to arrive at. And this is in keeping with geological time. I like to insert this series of thoughts into my work sometimes as an attempt to make some of this stuff comprehensible. There are all these distractions inundating us throughout our days now. Time gets tweaked by all these technologies that we interact with daily. There's more than just digital time or the mechanical time of your watch. There's biological time, that time in which you're growing. PB: I'm reminded of McLuhan here: he made his career by making that strong claim that the humans of today are not the same humans of three generations ago because technology has fundamentally changed us. Are we not the same human beings as a hundred years ago? CD: I mean, I don't think we're the same human beings that we were when he was around! It's my understanding that before painting a flower, monks would meditate for hours on that flower and then they would complete the painting of that flower in less than a minute. That's what I want to point out about our world today, we have all this information, but how much of it are we metabolizing? PB: Is there a message you're looking for? Or that you're trying to share? CD: These drawings set­up the circumstances for me to continue them forever. I'm only about six years into it, but with more time, things can unfold. You know? If you take this cup of coffee and vow to restrict your work to only this material and medium for seven years—you'll make interesting work. The problem is that most people can't hold on to things or they give up or they get distracted. They don't trust that anything is possible; anything is potential material. Staying with this cup of coffee example, we can get enveloped in the history of the recycling logo, or the process for harvesting coffee and so on. The same is true for my work as it has lead me into places like graphical music scores. I had, of course, known about John Cage's notations and I'd always been interested in sound itself, but this drawing practice made it feasible to explore the intersections in a meaningful way. I think that if you trust your instincts and your curiosities and your abilities, then the bus drives itself. Look at Roman Opalka, he's kind of the patron saint of time painting. The claim is that no one can count to a billion in a lifetime so he's set­out to paint to seven sevens (7,777,777). He began with white numbers on a black field but over the years he has gradually reduced the black field to ever­lightening grays. His plan is to paint these seven sevens on what ostensibly will be white on white. PB: It occurs to me that I've never thought of the actual, literal, meaning of “microphone” in relation to “microscope.” The mic has made everything loud, the world's not allowed to be quiet anymore. Maybe we should call them “macrophones” since telephone's already taken... CD: Well, a microscope is a lens. What got me interested in sound was that a microphone acts like a lens. There are wide angle lenses, or a lens that gets your eye up close to something far away, or at a tiny level. The same is true of the microphone. You can use a parabolic mic to hear what the coach is saying on a sports field or a mic that picks­up the sound from the entire cathedral. There's this whole gamut... I'm kind of playing with the words here. I'm into the minuteness of the sound, but I'm interested in the minuteness of the mark itself. PB: I guess it's a Deluezean, generative, statement, then? It's not a metaphor, it's an actual thing with which we can work. CD : That's right. PB: While doing some background work on you I found myself at interesting places on the internet. For example, Konstantin Raudive and a brief jog into Electronic Voice Phenomena (EVP); perhaps this was just synchronicity. But, it's a happy coincidence nonetheless because the them of this issue of continent. is “the moraine” and one of the nuances of this term is “what remains.” Is there a metaphysical or epistemological problem that you're sorting­out here? CD: Think about fossils: fossils are the first recording device, you know? It's the first, natural, recording device. It's in this way that I think my works are fossilized time. Artifacts of that process. Van Gogh is a strong source for me in this regard: it's not what he's painting it's how. You're seeing his nervous system at work. The what is so incidental, the chairs, the flowers, etc. It's funny: when I first started doing this, before I started drawing voices, I was doing these things in cemeteries. I was doing automatic drawings. And when I took this experiment to its maximum I was taking hydrophones and burying them in abandoned graves. I was thinking about the mic rig as the south coordinate and I'd use a shortwave radio as the north coordinate. Usually it was just white noise, but on the east and west I'd station a writer and a drawer. So I'd have these things going on simultaneously and I'd be mixing them at the same time. PB: How'd it come out? CD: Well, just like you'd expect. It was a lot of white noise. But I think that Raudive was on to something. Burroughs used to say something similar when he'd talk about being in a foreign country where he didn't know the language and then he'd start to hear things. At the base, what I'm doing is pattern recognition. I do have a writing component to the drawings. I haven't exploited it in a while but... I use a vocoder, which was developed to encrypt spy signals during one of the World Wars. The mechanism takes two channels, one being the spy's signal combined with noise and then the other channel is a sine wave so that the intended recipient can pick out the words. So I did something like this with Beowulf. I tried combining the spoken word with other television and radio sources, but that didn't work because a book on tape is usually read in a very steady clip and the result was too garbled. So the second try, instead of drawing I was writing, trying to articulate the sounds that I could hear in this garbled transmission of Beowulf. You start to think you hear something, so you start to write what you think you're hearing. But what you're hearing is just being triggered by this articulating action. When the sound of the drawing lines up with the sound of the word you get something. But it's not ever what you're really hearing. You start writing and you're trying to keep up with what you think you're hearing and it is truly, in the most true sense of the phrase, automatic writing. You can contrive and go into a “spirit trance” or whatever, but... PB: It's uninteresting to you? CD: Well, it's unbelievable. It's just listening to sounds and following along. The magic is out there, there are no tricks or anything. You do this exercise with twenty people and you will get twenty totally different writings. But, you're creating the sound and you're creating the writing as an interpretation. That's the thing with EVP, it's homophonic translation. PB: Do you trust a straight line? I know you start with these meticulous lines at the beginning of the drawings but they do change over time. CD: I'm trying to show that there are these imperfections in structures and that over the reiterations of these structures these imperfections become amplified. But you can see them in tree formation as well. The rings alter their shape as the trees grow. PB: Is that your transmission then? You're not just receiving these sounds but you're broadcasting this message as well? CD: Things exist because of their opposites. These drawings are really about nothing. It's the first body of work I've had where people project so much of stuff onto the works. So there you go, things existing because of their opposites. It's kind of like with Mike Kelley: the work was about a critique of commodity culture and commodifying emotions. Using toys this was a critique of production. But then suddenly people were saying it was about abuse and the abuse that Mike Kelley had suffered. And it wasn't but he heard that and said, “I'll go with it,” and so he did. I think that's the nature of communication: I send this but you receive that instead and this makes me think about what I sent in a different way. (shrink)

A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let ε denote the structure of the computably enumerable sets under inclusion, $\varepsilon = (\{W_e\}_{e\in \omega}, \subseteq)$ . We previously exhibited a first order ε-definable property Q(X) such that Q(X) guarantees that X is not Turing complete (i.e., does not code complete information about c.e. sets). Here we show first that Q(X) implies that X has (...) a certain "slowness" property whereby the elements must enter X slowly (under a certain precise complexity measure of speed of computation) even though X may have high information content. Second we prove that every X with this slowness property is computable in some member of any nontrivial orbit, namely for any noncomputable A ∈ ε there exists B in the orbit of A such that X ≤ T B under relative Turing computability (≤ T ). We produce B using the Δ 0 3 -automorphism method we introduced earlier. (shrink)

It will be shown that in the lattice of recursively enumerable sets all lattices $\underline{L}(X)$ are elementarily definable with parameters, where X is Σ 0 3 and $\underline{L}^3(X)$ consists of all Σ 0 3 sets containing X.

The long-standing problem of the effect of correlations on the ferromagnetism of transition metals is apparently nearing solution. The ferromagnetism of transition metal compounds, for instance doped manganites, poses a new question: is there some kind of orbital order coexisting with itinerant ferromagnetism? The ideas and techniques introduced by Gutzwiller should be of use again.

A common reducible representation space of the Lie algebras su and su is equipped with two different types of scalar products. The representation bases are labeled by the azimuthal and magnetic quantum numbers. The generators of su are the x-, y- and z-components of the orbital angular momentum operator. The representation of each of these Lie algebras is unitary with respect to only one of the scalar products. To each positive magnetic quantum number a family of the su-Barut–Girardello coherent (...) states is associated. The normalization and resolution of the identity condition for the coherent states are realized in two different approaches, i.e. the unitary and the non-unitary approaches. For the coherent states of the non-unitary case we calculate the uncertainty relation for the Hermitian x- and y-components of the angular momentum operator. While the unitary case leads to the known uncertainty relation for the Hermitian x- and y-components of su Lie algebra. (shrink)

To describe and analyze the unstable periodic orbits of the Rucklidge system, a so-called symbolic encoding method is introduced, which has been proven to be an efficient tool to explore the topological properties concealed in these periodic orbits. In this work, the unstable periodic orbits up to a certain topological length in the Rucklidge system are systematically investigated via a proposed variational method. The dynamics in the Rucklidge system are explored by using phase portrait analysis, Lyapunov exponents, and Poincaré first (...) return maps. Symbolic encodings of the periodic orbits with two and four letters based on the trajectory topology in the phase space are implemented under two sets of parameter values. Meanwhile, the bifurcations of the periodic orbits are explored, significantly improving the understanding of the dynamics of the Rucklidge system. The multiple-letter symbolic encoding method could also be applicable to other nonlinear dynamical systems. (shrink)