b→sγb \rightarrow s \gamma and ϵb\epsilon_b Constraints on Two Higgs Doublet Model

We perform a combined analysis of two stringent constraints on the 2 Higgs doublet model, one coming from the recently announced CLEO II bound on $B(b \rightarrow s \gamma)$ and the other from the recent LEP data on $\epsilon_b$. We have included one-loop vertex corrections to $Z \rightarrow b \overline b$ through $\epsilon_b$ in the model. We find that the new $\epsilon_b$ constraint excludes most of the less appealing window \tan\beta\lsim 1 at $90\%$C.~L. for m_t=150\GeV. We also find that although $b \rightarrow s \gamma$ constraint is stronger for $\tan\beta>1$, $\epsilon_b$ constraint is stronger for \tan\beta\lsim 1, and therefore these two are the strongest and complimentary constraints present in the charged Higgs sector of the model.Comment: LATEX, 9 Pages+1 Figure, the Figure available upon request as a Postscript file, CTP-TAMU-69/9

Inclusion of Z->b b-bar vertex corrections in Precision Electroweak Tests on the Sp(6)_L X U(1)_Y Model

We extend our previous work on the precision electroweak tests in the Sp(6)_L X U(1)_Y family model to include for the first time the important Z->b b-bar vertex corrections encoded in a new variable epsilon_b, utilizing all the latest LEP data. We include in our analysis the one loop EW radiative corrections due to the new bosons in terms of epsilon_1, epsilon_b and $\Delta\Gamma_Z$. We find that the correlation between epsilon_1 and epsilon_b makes the combined constraint much stronger than the individual ones. The model is consistent with the recent CDF result of m_t=174\pm 10^{+13}_{-12}\GeV, but it can not accomodate m_t\gsim 195\GeV.Comment: Latex, 16 pages+4 figures(not included but available as uuencoded or PS files from [email protected]), PURD-TH-94-08, SNUTP-94-4

Precision Electroweak Tests on the Sp(6)L×U(1)YSp(6)_L \times U(1)_Y Model

We perform precision electroweak tests on the $Sp(6)_L \times U(1)_Y$ model. The purpose of the analysis is to delineate the model parameters such as the mixing angles of the extra gauge bosons present in this model. We find that the model is already constrained considerably by the present LEP data.Comment: 14 pages+2 figures(not included), PURD-TH-93-13, to appear in Phys. Rev. D(figures available upon request by regular mail

Pre-service Teachers’ Conceptions of Mathematical Argumentation

Drawing on a situated perspective on learning, we analyzed written, open-ended journals of 52 pre-service teachers (PSTs) concurrently enrolled in mathematics and pedagogy with field experience courses for elementary education majors. Our study provides insights into PSTs’ conceptualizations of mathematical argumentation in terms of its meanings. The data reveals how PSTs perceive teacher actions, teaching strategies, classroom expectations, mathematics content, and tasks that facilitate student engagement in mathematical argumentation. It also shows what instructional benefits of enacting mathematical argumentation in the elementary mathematics classroom they perceive

A general method for determining the masses of semi-invisibly decaying particles at hadron colliders

We present a general solution to the long standing problem of determining the masses of pair-produced, semi-invisibly decaying particles at hadron colliders. We define two new transverse kinematic variables, $M_{CT_\perp}$ and $M_{CT_\parallel}$, which are suitable one-dimensional projections of the contransverse mass $M_{CT}$. We derive analytical formulas for the boundaries of the kinematically allowed regions in the $(M_{CT_\perp},M_{CT_\parallel})$ and $(M_{CT_\perp},M_{CT})$ parameter planes, and introduce suitable variables $D_{CT_\parallel}$ and $D_{CT}$ to measure the distance to those boundaries on an event per event basis. We show that the masses can be reliably extracted from the endpoint measurements of $M_{CT_\perp}^{max}$ and $D_{CT}^{min}$ (or $D_{CT_\parallel}^{min}$). We illustrate our method with dilepton $t\bar{t}$ events at the LHC.Comment: thoroughly revised; all new figures; new results on pages 3 and 4; new illustrative example; includes detector simulation. 4 pages, 6 figures, uses revtex and axodra

Metric and topo-geometric properties of urban street networks: some convergences, divergences, and new results

The theory of cities, which has grown out of the use of space syntax techniques in urban studies, proposes a curious mathematical duality: that urban space is locally metric but globally topo-geometric. Evidence for local metricity comes from such generic phenomena as grid intensification to reduce mean trip lengths in live centres, the fall of movement from attractors with metric distance, and the commonly observed decay of shopping with metric distance from an intersection. Evidence for global topo-geometry come from the fact that we need to utilise both the geometry and connectedness of the larger scale space network to arrive at configurational measures which optimally approximate movement patterns in the urban network. It might be conjectured that there is some threshold above which human being use some geometrical and topological representation of the urban grid rather than the sense of bodily distance to making movement decisions, but this is unknown. The discarding of metric properties in the large scale urban grid has, however, been controversial. Here we cast a new light on this duality. We show first some phenomena in which metric and topo-geometric measures of urban space converge and diverge, and in doing so clarify the relation between the metric and topo-geometric properties of urban spatial networks. We then show how metric measures can be used to create a new urban phenomenon: the partitioning of the background network of urban space into a network of semi-discrete patches by applying metric universal distance measures at different metric radii, suggesting a natural spatial area-isation of the city at all scales. On this basis we suggest a key clarification of the generic structure of cities: that metric universal distance captures exactly the formally and functionally local patchwork properties of the network, most notably the spatial differentiation of areas, while the top-geometric measures identifying the structure which overcomes locality and links the urban patchwork into a whole at different scales

Higgs Boson Mass Bounds in the Standard and Minimal Supersymmetric Standard Model with Four Generations

We study the question of distinguishability of the Higgs sector between the standard model with four generations(SM4) and the minimal supersymmetric standard model with four generations (MSSM4). We find that a gap exists between the SM4 and MSSM4 Higgs boson masses for a range of the fourth generation fermion mass considered in the analysis at a fixed top quark mass. We also compare the Higgs boson mass bounds in these models with those in the standard and the minimal supersymmetric standard models.Comment: 11 pages, Revtex, 3 postscript figures, accepted for publication in Mod. Phys. Lett.

Metric and topo-geometric properties of urban street networks: some convergences, divergences and new results

The theory of cities, which has grown out of the use of space syntax techniques in urban studies, proposes a curious mathematical duality: that urban space is locally metric but globally topo-geometric. Evidence for local metricity comes from such generic phenomena as grid intensification to reduce mean trip lengths in live centres, the fall of movement from attractors with metric distance, and the commonly observed decay of shopping with metric distance from an intersection. Evidence for global topo-geometry come from the fact that we need to utilise both the geometry and connectedness of the larger scale space network to arrive at configurational measures which optimally approximate movement patterns in the urban network. It might be conjectured that there is some threshold above which human being use some geometrical and topological representation of the urban grid rather than the sense of bodily distance to making movement decisions, but this is unknown. The discarding of metric properties in the large scale urban grid has, however, been controversial. Here we cast a new light on this duality. We show first some phenomena in which metric and topo-geometric measures of urban space converge and diverge, and in doing so clarify the relation between the metric and topo-geometric properties of urban spatial networks. We then show how metric measures can be used to create a new urban phenomenon: the partitioning of the background network of urban space into a network of semi-discrete patches by applying metric universal distance measures at different metric radii, suggesting a natural spatial area-isation of the city at all scales. On this basis we suggest a key clarification of the generic structure of cities: that metric universal distance captures exactly the formally and functionally local patchwork properties of the network, most notably the spatial differentiation of areas, while the top-geometric measures identifying the structure which overcomes locality and links the urban patchwork into a whole at different scales