Search

Accurate flux measurement of low energy charged particles, trapped in the magnetosphere, is necessary for Space Weather characterization and to study the coupling between the lithosphere and magnetosphere, allowing the investigation of the correlations between seismic events and particle precipitation from Van Allen Belts. In this work, the project of a CubeSat space spectrometer, the Low Energy Module (LEM), is shown. The detector will be able to perform an event-based measurement of energy, arrival direction, and composition of low-energy charged particles down to 0.1 MeV. Moreover, thanks to a CdZnTe mini-calorimeter, the LEM spectrometer also allows photon detection in the sub-MeV range, joining the quest for the investigation of the nature of Gamma Ray Bursts. The particle identification of the LEM relies on the $\Delta E - E$ technique performed by thin silicon detectors. This multipurpose spectrometer will fit within a 10x10x10 $\text{cm}^3$ CubeSat frame and it will be constructed as a joining project between the University of Trento, FBK, and INFN-TIFPA. To fulfil the size and mass requirements an innovative approach, based on active particle collimation, was designed for the LEM, this avoids heavy/bulky passive collimators of previous space detectors. In this paper, we will present the LEM geometry, its detection concept, and the results from the developed GEANT4 simulation.

The nuclide $^{176}$Lu is one of the few naturally occurring isotopes that are potentially unstable with respect to electron capture (EC). Although experimental evidence for $^{176}$Lu EC decay is still missing, this isotope is instead well known to $\beta^-$ decay into $^{176}$Hf with an half-life of about 38 Gyr. The precise investigation of all $^{176}$Lu possible decay modes is interesting because the Lu/Hf ratio is adopted as an isotopic clock. Previous searches for the $^{176}$Lu EC decay were performed by using a passive Lutetium source coupled with an HP-Ge spectrometer. Our approach uses a LYSO crystal both as Lutetium source and as an active detector. Scintillation light from the LYSO crystal is acquired in coincidence with the signals from the HP-Ge detector, this allows a powerful suppression of the background sourcing from the well known $\beta^-$ decay branch. This coincidence approach led to an improvement on the $^{176}$Lu EC branching ratio limits by a factor 3 to 30, depending on the considered EC channel., Comment: 9 pages, 14 figures

The axion particle is the outcome of the proposed Peccei-Quinn mechanism for solving the strong CP problem. Axion is also a popular dark matter candidate. Thus there is an increased interest in establishing its existence. Axions couple to two photons and most experiments search for the transition of an axion into a photon, in the presence of a magnetic field. In our study we examine the coupling of the axion into a pair of entangled photons. The presence of a magnetic field changes the polarization correlations of the entagled photons, thus offering an unambiguous signature for axion existence, Comment: 4 pages

We suggest that the unusual events observed by the ANITA experiment originate from axion particles traversing the Earth. Under the influence of the geomagnetic field, the axion may oscillate into a photon and vice-versa. To amplify the axion transition into photon, we consider that the phenomenon takes place at resonance, where the effective photon mass is equal to the axion mass. This requirement fixes the axion mass at 200 eV. An axion at this mass scale reproduces the cold dark matter scenario. If our interpretation prevails, with the help of axions we can establish an axion tomography of the Earth., Comment: 8 pages

Evolution consists of distinct stages: cosmological, biological, linguistic. Since biology verges on natural sciences and linguistics, we expect that it shares structures and features from both forms of knowledge. Indeed, in DNA we encounter the biological "atoms", the four nucleotide molecules. At the same time these four nucleotides may be considered as the "letters" of an alphabet. These four "letters", through a genetic code, generate biological "words", "phrases", "sentences" (aminoacids, proteins, cells, living organisms). In this spirit we may consider equally well a DNA strand as a mathematical statement. Inspired by the work of Kurt G\"odel, we attach to each DNA strand a G\"odel's number, a product of prime numbers raised to appropriate powers. To each DNA chain corresponds a single G\"odel's number $G$, and inversely given a G\"odel's number $G$, we can specify the DNA chain it stands for. Next, considering a single DNA strand composed of $N$ bases, we study the statistical distribution of $g$, the logarithm of $G$. Our assumption is that the choice of the $m$-th term is random and with equal probability for the four possible outcomes. The "experiment", to some extent, appears as throwing $N$ times a four-faces die. Through the moment generating function we obtain the discrete and then the continuum distribution of $g$. There is an excellent agreement between our formalism and simulated data. At the end we compare our formalism to actual data, to specify the presence of traces of non-random dynamics., Comment: 11 pages, 2 figures

GPS, an excellent tool for geodesy, may serve also particle physics. In the presence of Earth's magnetic field, a GPS photon may be transformed into an axion. The proposed experimental setup involves the transmission of a GPS signal from a satellite to another satellite, both in low orbit around the Earth. To increase the accuracy of the experiment, we evaluate the influence of Earth's gravitational field on the whole quantum phenomenon. There is a significant advantage in our proposal. While geomagnetic field B is low, the magnetized length L is very large, resulting into a scale (BL)^2 orders of magnitude higher than existing or proposed reaches. The transformation of the GPS photons into axion particles will result in a dimming of the photons and even to a "light shining through the Earth" phenomenon., Comment: 9 pages

A manifestly covariant equation is derived to describe the second order perturbations in topological defects and membranes on arbitrary curved background spacetimes. This, on one hand, generalizes work on macroscopic strings in Minkowski spacetime and introduces a framework for studing in a precise manner membranes behavior near the black hole horizon and on the other hand, introduces a more general framework for examining the stability of topological defects in curved spacetimes., Comment: 8 pages. arXiv admin note: text overlap with arXiv:gr-qc/9411060 by other authors

The phenomenon of neutrino oscillations is studied usually as a mixing between the flavor neutrinos and the neutrinos having a definite mass. The mixing angles and the mass eigenvalues are treated independently in order to accommodate the experimental data. We suggest that neutrino oscillations are connected to the structure of spacetime. We expand on a recently proposed model, where two "mirror" branes coexist. One brane hosts left-handed particles (our brane), while the other brane hosts right-handed particles. Majorana-type couplings mixes neutrinos in an individual brane, while Dirac-type couplings mixes neutrinos across the brares. We first focus our attention in a single brane. The mass matrix, determined by the Majorana mass, leads to mass eigenstates and further to mixing angles identical to the mixing angles proposed by the tri-bimaximal mixing. When we include the Dirac-type coupling, connecting the two branes, we obtain a definite prediction for the transition to a sterile neutrino (right-handed neutrino). With m_L (m_R) the Majorana mass for the left (right) brane, we are able to explain the solar and the atmospheric neutrino data with m_L = 2m_R and m_R = 10**(-2) eV.

We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics., Comment: arXiv admin note: text overlap with arXiv:0804.3080, arXiv:0812.1946

It has been suggested that relational logic, a form of logic developed by C. S. Peirce, is the common inner syntax of quantum mechanics and string theory. A relation may be represented by a spinor and the Cartan-Penrose connection of spinor to geometry, allows to abstract geometry from a calculus of relations-spinors, reviving Wheeler\textquoteright{}s pregeometry. With a single spinor related to the null cone of Minkowski space-time, we search for the geometry emerging when we entangle a left-handed spinor and a right-handed spinor. We find that the quantum entanglement generates an extra dimension and the distance in the extra dimension is measured by the amount of entanglement. The emerging geometry corresponds to a Milne space-time, with two branes coexisting in the extra dimension. One brane hosts left-handed particles (our brane), while the other brane hosts right-handed particles. A distinct phenomenology accompanies our proposal. During the brane collision all points are causally connected, making less pressing the inflationary scenario. The left-right symmetry is achieved with having two "mirror" branes and the neutrino appears as the ideal mediator between the branes. We may revisit also the dark matter, dark energy issues, with everything on the other brane and in the bulk appearing "dark" to us. If biohomochirality is due to parity violation, we anticipate that the life-forms in the other brane demonstrate opposite chiralities. Our scheme brings closer logic - quantum theory - string theory -- geometry -- cosmology, while space-time, rather than an abstract and a apriori construction, appears as the outcome of a quantum logical act., Comment: 13 pages

Solar, atmospheric and reactor neutrino experiments established that neutrinos are massive. It is quite natural then to consider neutrinos as candidate particles for explaining the dark matter in halos around galaxies. We study the gravitational clustering of these neutrinos within a model of a massive core and a surrounding spherical neutrino halo. The neutrinos form a degenerate Fermi gas and a loaded polytropic equation is established. We solve the equation and we obtain the neutrino density in a galaxy, the size of the galaxy and the galactic rotational curves. The available data favor a neutrino with a mass around 10eV. The consequent cosmological implications are examined., Comment: 5 pages, 2 figures

It has been proposed that quantum mechanics and string theory share a common inner syntax, the relational logic of C. S. Peirce. Along this line of thought we consider the relations represented by spinors. Spinor composition leads to the emergence of Minkowski spacetime. Inversely the Minkowski spacetime is istantiated by the Weyl spinors, while the merge of two Weyl spinors gives rise to a Dirac spinor. Our analysis is applied also to the string geometry. The string constraints are represented by real spinors, which create a parametrization of the string worldsheet identical to the Enneper-Weierstass representation of minimal surfaces. Further, a spinorial study of the AdS3 spacetime reveals a Hopf fibration AdS3 \rightarrow AdS2. The conformal symmetry inherent in AdS3 is pointed out. Our work indicates the hidden ties between logic-quantum mechanics-string theory-geometry and vindicates the Wheeler's proposal of pregeometry as a large network of logical propositions.

Theories with large extra dimensions may be tested using sterile neutrinos living in the bulk. A bulk neutrino can mix with a flavor neutrino localized in the brane leading to unconventional patterns of neutrino oscillations. A resonance phenomenon, strong mixing between the flavor and the sterile neutrino, allows to determine the radius of the large extra dimension. If our brane is curved, then the sterile neutrino can take a shortcut through the bulk, leading to an apparent superluminal neutrino speed. The amount of "superluminality" is directly connected to parameters determining the shape of the brane. On the experimental side, we suggest that a long baseline neutrino beam from CERN to NESTOR neutrino telescope will help to clarify these important issues., Comment: To appear in Mod. Phys. Lett. A 2012

We study the photon axion mixing in the presence of large extra dimensions. The eigenvalues and eigenstates of the mixing matrix are analyzed and we establish the resonance condition for the total conversion of a high energy photon into a Kaluza-Klein (KK) axion state. This resonant transition, a photon transformed into a KK axion travelling freely through the bulk and converting back into a photon, may provide a plausible explanation for the transparency of the universe to energetic photons. If the brane we live in is curved, then there are shortcuts through the bulk, which the axion can take. Within our model, the photons having the appropriate resonance energy are using the axionic shortcut and arrive earlier compared to the photons which follow the geodesic on the brane. We suggest that such axionic shortcuts are at the root of the dispersion of time arrival of photons observed by the MAGIC telescope. We indicate also the cosmological significance of the existence of axionic shortcuts for the photon., Comment: 7 pages

Since language is tied to cognition, we expect the linguistic structures to reflect patterns we encounter in nature and analyzed by physics. Within this realm we investigate the process of protolanguage acquisition, using analytical and tractable methods developed within physics. A protolanguage is a mapping between sounds and objects (or concepts) of the perceived world. This mapping is represented by a matrix and the linguistic interaction among individuals is described by a random matrix model. There are two essential parameters in our approach. The strength of the linguistic interaction $\beta$, which following Chomsky's tradition, we consider as a genetically determined ability, and the number $N$ of employed sounds (the lexicon size). Our model of linguistic interaction is analytically studied using methods of statistical physics and simulated by Monte Carlo techniques. The analysis reveals an intricate relationship between the innate propensity for language acquisition $\beta$ and the lexicon size $N$, $N \sim \exp(\beta)$. Thus a small increase of the genetically determined $\beta$ may lead to an incredible lexical explosion. Our approximate scheme offers an explanation for the biological affinity of different species and their simultaneous linguistic disparity., Comment: 16 pages, 4 figures. Submitted to JSTAT

The unification of Quantum Mechanics and General Relativity remains the primary goal of Theoretical Physics, with string theory appearing as the only plausible unifying scheme. In the present work, in a search of the conceptual foundations of string theory, we analyze the relational logic developed by C. S. Peirce in the late nineteenth century. The Peircean logic has the mathematical structure of a category with the relation $R_{ij}$ among two individual terms $S_i$ and $S_j$, serving as an arrow (or morphism). We introduce a realization of the corresponding categorical algebra of compositions, which naturally gives rise to the fundamental quantum laws, thus indicating category theory as the foundation of Quantum Mechanics. The same relational algebra generates a number of group structures, among them $W_{\infty}$. The group $W_{\infty}$ is embodied and realized by the matrix models, themselves closely linked with string theory. It is suggested that relational logic and in general category theory may provide a new paradigm, within which to develop modern physical theories., Comment: To appear in International Journal of Modern Physics A

The unification of Quantum Mechanics and General Relativity remains the primary goal of Theoretical Physics, with string theory appearing as the only plausible unifying scheme. In the present work, in a search of the conceptual foundations of string theory, we analyze the relational logic developed by C. S. Peirce in the late nineteenth century. The Peircean logic has the mathematical structure of a category with the relation $R_{ij}$ among two individual terms $S_i$ and $S_j$, serving as an arrow (or morphism). We introduce a realization of the corresponding categorical algebra of compositions, which naturally gives rise to the fundamental quantum laws, thus underscoring the relational character of Quantum Mechanic. The same relational algebra generates a number of group structures, among them $W_{\infty}$. The group $W_{\infty}$ is embodied and realized by the matrix models, themselves closely linked with string theory. It is suggested that relational logic and in general category theory may provide a new paradigm, within which to develop modern physical theories., Comment: typographical mistakes corrected, 10 pages, 3 figures

Silicon-based CMOS technologies are predicted to reach their ultimate limits by the middle of the next decade. Research on nanotechnologies is actively conducted, in a world-wide effort to develop new technologies able to maintain the Moore's law. They promise revolutionizing the computing systems by integrating tremendous numbers of devices at low cost. These trends will have a profound impact on the architectures of computing systems and will require a new paradigm of CAD. The paper presents a work in progress on this direction. It is aimed at fitting requirements and constraints of nanotechnologies, in an effort to achieve efficient use of the huge computing power promised by them. To achieve this goal we are developing CAD tools able to exploit efficiently these huge computing capabilities promised by nanotechnologies in the domain of simulation of complex systems composed by huge numbers of relatively simple elements., Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions)

In TeV scale unification models, gravity propagates in 4+d dimensions while gauge and matter fields are confined to a four dimensional brane, with gravity becoming strong at the TeV scale. For a such scenario, we study strong gravitational interactions in a effective Schwarzschild geometry. Two regimes appear. For large impact parameters, the ratio rho=(Rs/ro)1+d, (with Rs the Schwarzschild radius and ro the closest approach to the black hole), is small and the deflection angle is proportional to rho (like Rutherford-type scattering).For small impact parameters, the deflection angle develops a logarithmic singularity and becomes infinite for rho=rho crit= 2/(3+d). This singularity is reflected into a strong enhancement of the backward scattering (like a glory-type effect). We suggest a distinctive signature of black hole formation in particle collisions at TeV energies, the observation of the backward scattering events and its associated diffractive effects., Comment: Expanded version, references added, 8 pages, no figures

We have proposed that the cosmic ray spectrum "knee", the steepening of the cosmic ray spectrum at energy $E \gsim 10^{15.5}$ eV, is due to "new physics", namely new interactions at TeV cm energies which produce particles undetected by the experimental apparatus. In this letter we examine specifically the possibility that this interaction is low scale gravity. We consider that the graviton propagates, besides the usual four dimensions, into an additional $\delta$, compactified, large dimensions and we estimate the graviton production in $p p$ collisions in the high energy approximation where graviton emission is factorized. We find that the cross section for graviton production rises as fast as $(\sqrt{s}/M_f)^{2+\delta}$, where $M_f$ is the fundamental scale of gravity in $4+\delta$ dimensions, and that the distribution of radiating a fraction $y$ of the initial particle's energy into gravitational energy (which goes undetected) behaves as $\delta y^{\delta -1}$. The missing energy leads to an underestimate of the true energy and generates a break in the {\sl inferred} cosmic ray spectrum (the "kne"). By fitting the cosmic ray spectrum data we deduce that the favorite values for the parameters of the theory are $M_f \sim 8$ TeV and $\delta =4$., Comment: 8 pages, 1 figure

Theories with large extra dimensions provide the possibility that a flavor neutrino, localized in a 3+1 brane, can mix with a singlet neutrino living in the bulk. This mixing leads to unconventional patterns of neutrino matter oscillations and we examine in details how these oscillations depend upon two parameters: the brane-bulk coupling $\xi$ and the effective mass $\mu$ of the flavor neutrino inside matter. We find that high energy $(E \ge 50$ GeV) $\nu_\mu$ neutrinos, to be detected by neutrino telescopes, can give signals of extra dimensions. With a 1 k$m^{3}$ neutrino telescope extra dimensions with radius down to $1\mu m$ can be tested directly, while for smaller radius an indirect evidence can be established., Comment: 14 pages, 5 figures, added conclusions

We propose that the knee in the cosmic ray spectrum at energies E ~ 10^{15.5} eV is due to "new physics", namely to a channel in the high energy (~ TeV in the CM) proton interactions hitherto unaccounted for in estimating the energies of the air shower cosmic rays. The new interaction transfers part of the primary particle's energy to modes which do not trigger the experimental arragement (neutrinos, lightest supersymmetric particle, gravitons) thus underestimating its true energy. We show that this underestimate leads naturally to the observed break (the "knee") in the inferred cosmic ray spectrum. The suggestion we advance fits nicely to current theoretical extensions of the Standard Model (supersymmetry, technicolor, low scale gravity) where new physics at the TeV scale manifests with the distinct signature of missing energy. We present a simple model where the new physics proceeds via gluon fusion and assuming a single power law for the galactic (E ~ 10^{18.5} eV) cosmic ray spectrum, we produce a good fit to the data in the 10^{14}-10^{18.5} eV range. Our proposal should be testable in laboratory experiments (LHC) in the near future and, should it be proven correct, it would signal besides the presence of new physics in high energy interactions, a drastically different interpretation of the sources and acceleration of cosmic rays., Comment: 8 pages, 1 figure

Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessaary for a consistent computation of the energy. We also quantize the perturbations and derive the mass-formula up to second order in perturbations for an observer using world-sheet time $\tau $. The high frequency modes give the standard Minkowski result while, interestingly enough, the Hamiltonian turns out to be non-diagonal in oscillators for low-frequency modes. Using an alternative definition of the vacuum, it is possible to diagonalize the Hamiltonian, and the standard string mass-spectrum appears for all frequencies. We finally discuss how our results are also relevant for the problems concerning string-spreading near a black hole horizon, as originally discussed by Susskind., Comment: New discussion about the quantum mass-spectrum in chapter 4

The dispersion relation of energetic (few TeV) neutrinos traversing a medium is studied. We use the real time formalism of thermal field theory and we include the effects from the propagator of the W gauge boson. We consider then the MSW oscillations for cosmic neutrinos traversing the Earth, adopting for the neutrino parameters values suggested by the LSND results. It is found that the $\nu_\mu$ flux, for neutrinos passing through the center of the Earth, will appear reduced by 15% for energies around 10 TeV., Comment: 12 pages, latex, 2 figures

The phenomenon of string spreading on the black hole horizon, as originally discussed by Susskind, is considered in the {\it exact} curved Schwarzschild background. We consider an oscillating string encircling the black hole and contracting towards the horizon. We then compute the angular and radial spreading of the string, as seen by a static observer at spatial infinity using fixed finite resolution time. Within our case study we find that there is indeed a spreading of the string in the angular direction, such that the string eventually covers the whole horizon. However, regarding the radial direction, we find that Lorentz-contraction suppresses the radial string spreading., Comment: 14 pages, Latex. No figures

We suggest that dark matter is made up of massive quark objects that have survived from the Big Bang, representing the ground state of ``baryonic'' matter. Hence, there was no overall phase transition of the original quark matter, but only a split-up into smaller objects. We speculate that normal hadronic matter comes about through enforced phase transitions when such objects merge or collide, which also gives rise to the cosmic gamma-ray bursts., Comment: 8 pages Latex, no figures; to be published in the Proceedings of Dark '98, Heidelberg, July 1998

We present a new scenario for the development of the Universe after the Big Bang, built on the conjecture that a vast majority of the primordial quark matter did not undergo a phase transition to normal nuclear matter, but rather split up into massive quark objects that remained stable. Hence, such primordial quark matter would make up the so-called dark matter. We discuss, mostly in qualitative terms, the consequences for galaxy formation, the origin of normal matter, the occurrence of massive black-holes in galactic centres and the cosmic gamma-ray bursts., Comment: 32 pages Latex, 3 postscipt figures

We investigate the possibility that gamma-ray bursts originate in a concentric spherical shell with a given average redshift and find that this is indeed compatible with the data from the third BATSE (3B) catalog. It is also shown that there is enough freedom in the choice of unknown burst properties to allow even for extremely large distances to the majority of bursts. Therefore, we speculate about an early, and very energetic, origin of bursts, and suggest that they come from phase transitions in massive objects of pure quark matter, left over from the Big Bang., Comment: 11 pages, Latex, 3 postscript figures, to be publ in the Proc of the Joint Meeting of the Networks 'The Fundamental Structure of Matter' and 'Tests of the Electroweak Symmetry Breaking', Ouranoupolis, Greece, May 1997

The origin of the string conformal anomaly is studied in detail. We use a reformulated string Lagrangian which allows to consider the string tension $T_{0}$ as a small perturbation. The expansion parameter is the worldsheet speed of light c, which is proportional to $T_{0}$ . We examine carefully the interplay between a null (tensionless) string and a tensionful string which includes orders $ c^{2} $ and higher. The conformal algebra generated by the constraints is considered. At the quantum level the normal ordering provides a central charge proportional to $ c^{2} $. Thus it is clear that quantum null strings respect conformal invariance and it is the string tension which generates the conformal anomaly., Comment: More references are included. Final version, to appear in Phys.Rev.D. 6 pages, LaTex, no figures

Active Galactic Nuclei are considered as sources of neutrinos, with neutrino energies extending up to 10^{18} eV. It is expected that these highly energetic cosmic neutrinos will be detected by the neutrino telescopes, presently under construction. The detection process is very sensitive to the total muon neutrino cross-section. We examine how the total cross section changes at high energies, by the single production of excited fermions (excited muon and muon-neutrino). For parameters (masses, couplings) of the excited fermions allowed by the experimental constraints, we find that for energies of the incoming muon-neutrino above 100 TeV the cross-section for single production of (excited muon and muon-neutrino) supersedes the standard total cross-section., Comment: 12 pages and 2 figures; typset using revtex; postscript files for the figures provided

The rise with energy of the neutrino--nucleon cross section implies that at energies above few TeV the Earth is becoming opaque to cosmic neutrinos. The neutrinos interact with the nucleons through the weak charged current, resulting into absorption, and the weak neutral current, which provides a redistribution of the neutrino energy. We Mellin transform the neutrino transport equation and find its exact solution in the moment space. A simple analytical formula is provided, which describes accurately the neutrino spectrum, after the neutrinos have traversed the Earth. The effect of the weak neutral current is most prominent for an initial flat neutrino spectrum and we find that at low energies (around 1 TeV) the neutrino intensity is even enhanced., Comment: gziped, tar file of LaTeX paper plus 2 postscript figures, 13 pages

We study quantum strings in strong gravitational fields. The relevant small parameter is $g=R_c{\sqrt T_0}$, where $R_c$ is the curvature of the spacetime and $T_0$ is the string tension. Within our systematic expansion we obtain to zeroth order the null string (string with zero tension), while the first order correction incorporates the string dynamics. We apply our formalism to quantum null strings in de Sitter spacetime. After a reparametrization of the world-sheet coordinates, the equations of motion are simplified. The quantum algebra generated by the constraints is considered, ordering the momentum operators to the right of the coordinate operators. No critical dimension appears. It is anticipated however that the conformal anomaly will appear when the first order corrections proportional to $T_0$, are introduced., Comment: 6 pages, plain Tex, no figures

The major goal of Project SPEED (at Fort Hamilton High School, Brooklyn, New York) was dropout prevention. In its first year of operation, 1982-83, the project provided English as a Second Language (ESL) instruction, bilingual instruction in basic skills required for graduation, and guidance services to approximately 300 limited English proficient (LEP) students in grades 9-12 who were regarded as high risks for dropping out. The students, mostly recent immigrants, were 65 percent Spanish speaking, 20 percent Chinese speaking, and 15 percent Arabic speaking. The project's individualized approach was based on three models, each having a specific goal and curricular emphasis: Model 1 aimed at dropout prevention, particularly for 9th and 10th graders; Model II aimed at truants whose likelihood of staying in school is minimal; and Model III aimed at retaining LEP students older than 18. Evaluation of the project, however, showed that it was impossible to examine these models as such because the counseling, educational, and vocational guidance components that were to differentiate them had not been formally implemented. In terms of student achievement, quantitative analysis indicated the following: (1) attainment of English language objectives was mixed; (2) objectives in content area courses were attained overall; (3) 75 percent of students taking the High School Equivalency Exam passed; and (4) the program attendance rate was significantly greater than the general attendance rate. In addition, curricular materials were being developed and adapted in the three native languages, and staff participated in meetings, workshops, and university courses. Finally, parent participation was minimal. (CMG)