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Topic: Reflection positivity

In the News (Sat 28 Nov 09)

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Mickey Rourke

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Danny Boyle

Hugh Jackman

	G.W.F. Hegel -- Social and Political Thought [Internet Encyclopedia of Philosophy]
		He held public positions as a member of the Royal Examination Commission of the Province of Brandenberg and also as a councellor in the Ministry of Education.
		In the performance of duty the individual exhibits virtue when the ethical order is reflected in his or her character, and when this is done by simple conformity with one's duties it is rectitude.
		Landed gentry inherit their estates and so owe their position to birth (primogeniture) and thus are free from the exigencies and uncertainties of the life of business and state interference.
	www.iep.utm.edu /h/hegelsoc.htm (14441 words)

	Classroom Management for Middle and Secondary Schools
		Asking reflective questions is significantly more effective and longer lasting than telling someone what to do.
		Communicating in positive terms, offering choices, and honing the skill of asking reflective questions are three principles to practice.
		During inappropriate behavior, the teacher asks or suggests that the disruptive student reflect on the level of chosen behavior.
	www.marvinmarshall.com /classroommanagement.htm (2400 words)

	Positivity and analytic properties of QCD Green functions
		Such positivity violations are thus a sufficient (but not necessary) condition for confinement.
		Both lattice and recent DSE studies show evidence for positivity violation in the gluon propagator (and trivially in the (negative metric) ghost propagator).
		The situation for the quark propagator is less clear; the analytic structure of the quark propagator and the (non)positivity of solutions of the quark DSE appears to be sensitive to the presence of a scalar contribution in the quark gluon vertex (expected from gauge symmetry).
	www.phys.washington.edu /users/savage/NucTheory/annual_03/node30.html (189 words)

	Compare Prices and Read Reviews on Reflection Eternal [PA] - Talib Kweli & Hi-Tek at Epinions.com (Site not responding. Last check: 2007-10-12)
		Even though many rappers have ignored his suggestions, Talib Kweli continues to remain a positive rap influence as one of the few willing to walk through the darkness carrying a torch.
		Talib Kweli asks “where were you the day hip-hop died” on “Too Late”, a short piece reflecting on the current state of hip-hop.
		Even though Hi-Tek’s guitar driven beat is not as good as the rest of his tracks on this LP, the light-hearted presence of De La adds a lot of juice to the track.
	www.epinions.com /content_10281127556 (953 words)

	The Cognition of States of Affairs: Reinach's Theory of Judgment
		Reinach adopted a Platonistic position also however because he held - with Meinong and Marty - that in order to uphold the correspondence theory of truth in its full generality it is necessary to suppose that to each variety of judgment there is correlated an appropriate variety of truth-making states of affairs.
		Closer reflection suggests, however, that an act which might putatively be described as one of apprehension which did not immediately give rise to a conviction of the corresponding content would have all the marks of a non-standard case (compare a putative promise which did not immediately give rise to mutually correlated claim and obligation).
		This negative conviction in a positive state of affairs is to be contrasted, on Reinach's theory, with the case of positive conviction in a negative state of affairs.
	www.ontology.buffalo.edu /smith/articles/cogsvh/cogsvh.html (15315 words)

	Promoting positivity, choice and reflection: these three simple practices can make school a place where teachers and ... (Site not responding. Last check: 2007-10-12)
		Promoting positivity, choice and reflection: these three simple practices can make school a place where teachers and students want to be
		This article describes three simple practices that foster positive school climates--where both teachers and students want to be.
		The importance of understanding how positive emotions are critical to learning is reinforced every time I ask attendees in my seminars what the conversation might sound like after a child comes home from the first day at school.
	www.findarticles.com /p/articles/mi_m0HUL/is_5_34/ai_n13820034 (471 words)

	Probability Abstract Service
		For a fixed position of the rod, this lattice fluid is in equilibrium with a vertical height profile reversible for the monomers' motion.
		The exact behavior of $G_n$ in this last case depends on the positive tail of the distribution of $X_v$; we show that if it is nontrivial and has exponential moments, then $G_n \approx \log n$, with a transition from $G_n \approx n^d$ occurring in general not as predicted by large deviations estimates.
		For this model, it is proved that for every fixed value of the temperature $\beta^{-1}$, there exists a positive $m_\ast(\beta)$ such that for the values of the physcal mass of the particle $m\in(0,m_\ast(\beta))$, the set of tempered Gibbs states consits of exactly one element.
	www.math.u-psud.fr /~paserv/Letters/letter_55.html (5512 words)

	Some properties of frustrated spin systems: extensions and applications of Lieb-Schupp approach (Site not responding. Last check: 2007-10-12)
		The basic tool used was certain version of "spin-reflection positivity" method.
		It needs an assumption of reflection symmetry present in the system.
		In this paper, it is shown that analogous results hold also for other symmetries (inversion etc.).
	www.edpsciences.org /articles/epjb/abs/2005/08/b04421/b04421.html (195 words)

	Untitled Document
		Before deciding whether a North Carolina lottery for education would benefit students, Charlotte Advocates for Education, a local education fund, sought to answer whether a lottery is an effective alternative way to fund education by looking at the experiences of states with a lottery.
		This research paper seeks to examine: (1) The impact of lotteries on funding for education, both negative and positive impact; (2) Whether lotteries are a reliable, sustainable source of annual income for education; and (3) Methods that could be used to ensure lottery funding supplements education funding and does not merely supplant existing funding.
		Either way, reports Lynn Thompson, the multiple valedictorians at Garfield are reflective of a national trend of rewarding a number of high-achieving students at graduation rather than singling out one.
	www.publiceducation.org /NewsBlast/Jun05/jun25.htm (2786 words)

	Amazon.com: The Mathematics of the Bose Gas and its Condensation (Oberwolfach Seminars): Books: Elliott H. Lieb,Robert ... (Site not responding. Last check: 2007-10-12)
		SIPs: reflection positivity, condensate wave function, bulk limit, optical lattice, scattering length (more)
		Schrödinger's equation of 1926 defined a new mechanics whose Hamiltonian is based on classical mechanics.
		reflection positivity, condensate wave function, bulk limit, optical lattice, scattering length, ground state energy, scattering equation, ground state wave function, thermodynamic limit, energy expectation, momentum part, homogeneous gas
	www.amazon.com /exec/obidos/tg/detail/-/3764373369?v=glance (647 words)

	Probability Abstract Service
		We prove that whenever the associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition (which occurs near the mean-field transition temperature), provided the dimension is sufficiently large or the first-order transition in the mean-field model is sufficiently strong.
		Fitzsimmons and R. Getoor The potential kernel of a positive left additive functional (of a strong Markov process $X$) maps positive functions to strongly supermedian functions and satisfies a variant of the classical domination principle of potential theory.
		We prove that the vortex equation has a unique solution in an appropriate space and can be interpreted in a probabilistic point of view through a nonlinear reflected process with space-time random births on the boundary of the domain.
	www.math.u-psud.fr /~paserv/Letters/letter_70.shtml (3389 words)

	American Hit Network
		Most touching is âHope,â a reflective piece rich in wordplay that confronts illness and mortality with sensitivity and grace.
		Fifteen years into their career, the band still sounds vital, proving not just that they are relevant, but that they remain one of the best.
		âThe Liftingâ kicks off the proceedings on an appropriate note of positivity-laced reflection, a mood that continues on âIâve Been High,â âShe Just Wants to Be,â and ends with the closing track âBeachballâ.
	www.americanhitnetwork.com /whatshot.cfm?uid=700&view=yes (1948 words)

	Penn State Department of Statistics
		Probability Inequalities: The algebraic and analytic techniques utilized in Dr. Richards' work on multivariate statistical analysis, generalized special functions, and harmonic analysis are closely related to his research in total positivity and probability inequalities, e.g.
		new concepts of total positivity germane to the theory of finite reflection groups, and correlation inequalities of FKG type, motivated by problems in statistics, probability, and mathematical physics.
		Total positivity, finite reflection groups and a formula of Harish-Chandra.
	www.stat.psu.edu /people/faculty/richards.html (266 words)

	Promoting Positivity, Choice And Reflection
		When reflective questions are asked, the student is prompted to think and respond.
		When attention is given to the positive, when the option of choice is recognized and when reflection is used, life is conducted more successfully and with greater pleasure.
		These three principles are the keys to establishing and maintaining positive school climates--with one stipulation: They must be practiced.
	www.marvinmarshall.com /promoting_positivity.htm (1648 words)

	Not Even Wrong » 2006 » March
		Schroer’s politics are diametrically opposite to those of Jordan, but he is highly sympathetic to Jordan’s scientific point of view, from the earliest years of quantum mechanics, that it is necessary to think about quantum systems in a way which doesn’t depend on starting with a classical Lagrangian and “quantizing”.
		This week is the second anniversary of this weblog, so perhaps a good moment for some reflections on what has been happening over the past two years.
		The two post 2000 papers that are widely cited reflect the two main topics that string theorists are still working on.
	www.math.columbia.edu /~woit/wordpress/?m=200603 (4531 words)

	Donald St. P. Richards - Mathematician of the African Diaspora
		While pubishing numerous papers, he had several positions: University of the West Indies (1979-1981); University of North Carolina (1981-1987); University of Wyoming (1983-1984).
		The research on generalized special functions has led also to generalizations of results well-known for the classical special functions; this line of work relies heavily on representation theory and harmonic analysis.
		The algebraic and analytic techniques utilized in my work on multivariate analysis and generalized special functions are closely related to my research on total positivity and probability inequalities, e.g.
	www.math.buffalo.edu /mad/PEEPS/richards_donald.html (861 words)

	Nikolay Milkov: On the Use of Philosophy in Political Theory / Labyrinth vol. 3, Winter 2001
		The author of these words, Bryan Magee, is well-experienced both in politics—he has been a Member of Parliament in the UK, as well as in philosophy—he is the author of more than ten books on the subject, and has brought philosophy into people’s lives through popular television programs for the BBC.
		On reflection, the source of his criticism of the contemporary political vocabulary is not difficult to identify: the Oxford school of analysis of ordinary language.
		The task of the theoretical philosopher is to divert, with the help of the will, the most convenient of the positions, attitudes, decisions — in everyday life, in science, in art.
	labyrinth.iaf.ac.at /2001/Milkov.html (5211 words)

	Social Memory Complex » The Law of One (Site not responding. Last check: 2007-10-12)
		It may not reflect the deep structure of the brain, which is often unconscious, but is instead the equivalent of conscious thought.
		By keeping ourselves attentive, positive, and open to innovation and the resulting creative synergies, we will continue to manifest what could be the grandest stage of our evolution as a species.
		That polarity of which I speak is the choice of negativity or positivity (more crudely explained as good and evil), the two ways one may use energy to do work in the higher densities through which spiritual evolution takes a person.
	blog.6thdensity.net /?cat=22 (5980 words)

	Time Travel Portal :: View topic - Lorentzian Quantum Gravity, Causality & Curing Sickness (Site not responding. Last check: 2007-10-12)
		The reflection positivity of the model ensures the existence of a well-defined Hamiltonian.
		They have to reflect the fact that the geometric degrees of freedom are dynamical, and that therefore also the lattice theory must be formulated in a background-independent way.
		Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant.
	timetravelportal.com /viewtopic.php?t=1748 (3521 words)

	Mark Kac Seminar, Sep 30, 2005 (Site not responding. Last check: 2007-10-12)
		Applying this expansion to the ferromagnetic case, we can prove that the model exhibits the mean-field behavior if the dimension d is greater than 4 and the coordination number N (= 2d for the nearest-neighbor model, for example) is sufficiently large.
		The main point of this approach is that we do not have to require the reflection positivity of the spin-spin coupling, which has long been an essential ingredient for the proof of the mean-field behavior.
		In the talk, I will briefly explain 1) the derivation of the lace expansion for the Ising model, 2) the implication assuming its convergence, and 3) the reason why the expansion converges when d>4 and N>>1.
	www.win.tue.nl /markkac/2005-10.htm (241 words)

	Organizational Blogs and the Human Voice: Relational Strategies and Relational Outcomes
		Microsoft was the single largest host of corporate blogs in October 2004 according to data collected by Sifry, who mused that "that there is still a tremendous opportunity for forward-thinking companies and management to have a significant positive impact on their public perception" by way of hosting blogs (2004).
		Furthermore, as a relational maintenance strategy, voice correlated positively and significantly with all four of the key relational outcomes measured: trust, satisfaction, control mutuality, and commitment.
		Blogs are a good place to speak candidly with a conversational style (e.g., "invite people to a conversation"), and this conversational style may be an important part of the process of building and maintaining computer-mediated relationships.
	jcmc.indiana.edu /vol11/issue2/kelleher.html (6312 words)

	Public Knowledge Publications (Site not responding. Last check: 2007-10-12)
		Among the ready-and-waiting sources of under-utilized public knowledge, the social sciences seem well positioned to add to people’s understanding, to the self-determination of their lives, and to their collective action and democratic processes.
		The challenge for defenders of the public sector is to catch the wave and play on technology’s plasticity to direct the machines toward broader interests of education, reflection, and action.
		[2] Gould: “My initial burst of positivity amounted to little more than an emotional gut reaction — and would have endured for only a short time, had I not been able to bolster the feeling with a genuine reason for optimism based upon a better analysis of papers that seemed so brutally pessimistic.
	www.pkp.ubc.ca /publications/if.html (8038 words)

	Not Even Wrong » Blog Archive » Baez and Schroer
		So in superstrings, as I understand it, they assume an open or closed string, instead of a traditional point particle, associate position and momentum operators with this so-called ’string’ (I mean, is it really like a little piece of spaghetti?), and then simply assume commutation relations ‘by analogy’ with point particles.
		It was already mentioned before that whereas it is true that the extension of the classical Nambu-Goto string (whose canonically quantized version is the “mother” of the string-theoretic reformulation of Veneziano’s dual model) is really a relativistic spacetime string, this is not the case for its canonically quantized counterparts.
		The only intrinsic notion of a quantum relativistic localization is that obtained by translating this object into other positions and checking whether its commutator with the original object is nonvanishing once the second would be string shape enters the causal influence region of the first.
	www.math.columbia.edu /~woit/wordpress/?p=361 (4179 words)

	2.5 Proving reflection positivity
		In the same paper, they gave a unified treatment of Poincaré, de Sitter and conformal gravity, and showed that reflection positivity for O (4)-gravity (as well as for the two other gauge groups) holds exactly and for general functions only provided a signature factor sign
		An extension of the results of [167] to supergravity with the super-Poincaré group is also possible [62].
		One can prove reflection positivity and finds a matching gravitino doubling in the perturbative expansion.
	relativity.livingreviews.org /Articles/lrr-1998-13/node7.html (222 words)

	Rutgers Lie Group Seminar Spring 2000
		For the case in which W is the group of permutations on n symbols, this notion reduces to the classical formulation of total positivity.
		We prove a basic composition formula for this generalization of total positivity; in the case in which W is the Weyl group for a compact connected Lie group we apply an integral formula of Harish-Chandra to construct examples of totally positive functions.
		As an application of these results, we derive an FKG-type correlation inequality in the case in which W is the Weyl group of SO(5); and we derive some new positivity inequalities for the classical Bessel functions.
	www.math.rutgers.edu /~knop/seminar/Seminar_Fall00.html (1176 words)

	MA5P8 - CONFORMAL FIELD THEORY - Section 4 (Site not responding. Last check: 2007-10-12)
		This section is technically the most demanding of the module, and some of the constructions and proofs will have to remain on a sketchy level.
		I discuss the state-field correspondence and show how it is implemented in CFTs through the definition of so-called n-point functions together with a property called reflection positivity which ensures that the 2-point functions encode the scalar product on the pre-Hilbert space.
		The properties of n-point functions lead to the definition of the operator product expansion (OPE) and its representations on n-point functions.
	www.maths.warwick.ac.uk /~wendland/cft/s4.html (181 words)

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