58 research outputs found
The Efficacy of Restorative Practices on Reducing and Preventing Problem Behaviors in Adolescents
For decades, schools and juvenile detention systems in the United States and abroad have used punitive disciplinary practices such as detention, suspension, expulsion, and jail sentences to address adolescent misbehavior. These practices are considered to be retributive in that they serve as repayment to society in the case of detention and to act as “desertion” of society in the cases of suspension or incarceration” (Flanders, 2014, p. 328). Zero tolerance practices, touted by both educational and juvenile justice systems, have escalated the use of such practices. However, little evidence exists to support that these retributive practices have reduced the number of disruptions, fights, and other violent misbehaviors within schools (Lewis, 2009).
The need for a different approach to discipline within schools and juvenile justice systems has led many schools and juvenile justice programs to consider alternatives such as Restorative Justice. Also referred to as restorative practices, they are designed not only to change behavior, but also to “restore the environment and relationships damaged by the behavior” (Beale, 2003, p. 418). Some practitioners contend this approach results in lower rates of misbehavior and recidivism (Bradshaw & Roseborough, 2005; Lewis, 2009). The purpose of this paper was to demonstrate the efficacy of restorative justice and other restorative practices on reducing adolescent misbehavior
One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula
In \cite{Mul} one-parameter planar motion was first introduced and the
relations between absolute, relative, sliding velocities (and accelerations) in
the Euclidean plane were obtained. Moreover, the relations
between the Complex velocities one-parameter motion in the Complex plane were
provided by \cite{Mul}. One-parameter planar homothetic motion was defined in
the Complex plane, \cite{Kur}. In this paper, analogous to homothetic motion in
the Complex plane given by \cite{Kur}, one-parameter planar homothetic motion
is defined in the Hyperbolic plane. Some characteristic properties about the
velocity vectors, the acceleration vectors and the pole curves are given.
Moreover, in the case of homothetic scale identically equal to 1, the
results given in \cite{Yuc} are obtained as a special case. In addition, three
hyperbolic planes, of which two are moving and the other one is fixed, are
taken into consideration and a canonical relative system for one-parameter
planar hyperbolic homothetic motion is defined. Euler-Savary formula, which
gives the relationship between the curvatures of trajectory curves, is obtained
with the help of this relative system
The conic-gearing image of a complex number and a spinor-born surface geometry
Quaternion (Q-) mathematics formally contains many fragments of physical
laws; in particular, the Hamiltonian for the Pauli equation automatically
emerges in a space with Q-metric. The eigenfunction method shows that any
Q-unit has an interior structure consisting of spinor functions; this helps us
to represent any complex number in an orthogonal form associated with a novel
geometric image (the conic-gearing picture). Fundamental Q-unit-spinor
relations are found, revealing the geometric meaning of spinors as Lam\'e
coefficients (dyads) locally coupling the base and tangent surfaces.Comment: 7 pages, 1 figur
Topological defects for the free boson CFT
Two different conformal field theories can be joined together along a defect
line. We study such defects for the case where the conformal field theories on
either side are single free bosons compactified on a circle. We concentrate on
topological defects for which the left- and right-moving Virasoro algebras are
separately preserved, but not necessarily any additional symmetries. For the
case where both radii are rational multiples of the self-dual radius we
classify these topological defects. We also show that the isomorphism between
two T-dual free boson conformal field theories can be described by the action
of a topological defect, and hence that T-duality can be understood as a
special type of order-disorder duality.Comment: 43 pages, 4 figure
New symmetries of the chiral Potts model
In this paper a hithertho unknown symmetry of the three-state chiral Potts
model is found consisting of two coupled Temperley-Lieb algebras. From these we
can construct new superintegrable models. One realisation is in terms of a
staggered isotropic XY spin chain. Further we investigate the importance of the
algebra for the existence of mutually commuting charges. This leads us to a
natural generalisation of the boost-operator, which generates the charges.Comment: 19 pages, improved notation, made the text easier to read, corrected
some typo
From boundary to bulk in logarithmic CFT
The analogue of the charge-conjugation modular invariant for rational
logarithmic conformal field theories is constructed. This is done by
reconstructing the bulk spectrum from a simple boundary condition (the analogue
of the Cardy `identity brane'). We apply the general method to the c_1,p
triplet models and reproduce the previously known bulk theory for p=2 at c=-2.
For general p we verify that the resulting partition functions are modular
invariant. We also construct the complete set of 2p boundary states, and
confirm that the identity brane from which we started indeed exists. As a
by-product we obtain a logarithmic version of the Verlinde formula for the
c_1,p triplet models.Comment: 35 pages, 2 figures; v2: minor corrections, version to appear in
J.Phys.
Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model
We generalize the string functions C_{n,r}(tau) associated with the coset
^sl(2)_k/u(1) to higher string functions A_{n,r}(tau) and B_{n,r}(tau)
associated with the coset W(k)/u(1) of the W-algebra of the logarithmically
extended ^sl(2)_k conformal field model with positive integer k. The higher
string functions occur in decomposing W(k) characters with respect to level-k
theta and Appell functions and their derivatives (the characters are neither
quasiperiodic nor holomorphic, and therefore cannot decompose with respect to
only theta-functions). The decomposition coefficients, to be considered
``logarithmic parafermionic characters,'' are given by A_{n,r}(tau),
B_{n,r}(tau), C_{n,r}(tau), and by the triplet \mathscr{W}(p)-algebra
characters of the (p=k+2,1) logarithmic model. We study the properties of
A_{n,r} and B_{n,r}, which nontrivially generalize those of the classic string
functions C_{n,r}, and evaluate the modular group representation generated from
A_{n,r}(tau) and B_{n,r}(tau); its structure inherits some features of modular
transformations of the higher-level Appell functions and the associated
transcendental function Phi.Comment: 34 pages, amsart++, times. V2: references added; minor changes; some
nonsense in B.3.3. correcte
The fusion algebra of bimodule categories
We establish an algebra-isomorphism between the complexified Grothendieck
ring F of certain bimodule categories over a modular tensor category and the
endomorphism algebra of appropriate morphism spaces of those bimodule
categories. This provides a purely categorical proof of a conjecture by Ostrik
concerning the structure of F.
As a by-product we obtain a concrete expression for the structure constants
of the Grothendieck ring of the bimodule category in terms of endomorphisms of
the tensor unit of the underlying modular tensor category.Comment: 16 page
Open-closed field algebras
We introduce the notions of open-closed field algebra and open-closed field
algebra over a vertex operator algebra V. In the case that V satisfies certain
finiteness and reductivity conditions, we show that an open-closed field
algebra over V canonically gives an algebra over a \C-extension of the
Swiss-cheese partial operad. We also give a tensor categorical formulation and
categorical constructions of open-closed field algebras over V.Comment: 55 pages, largely revised, an old subsection is deleted, a few
references are adde
The logarithmic triplet theory with boundary
The boundary theory for the c=-2 triplet model is investigated in detail. In
particular, we show that there are four different boundary conditions that
preserve the triplet algebra, and check the consistency of the corresponding
boundary operators by constructing their OPE coefficients explicitly. We also
compute the correlation functions of two bulk fields in the presence of a
boundary, and verify that they are consistent with factorisation.Comment: 43 pages, LaTeX; v2: references added, typos corrected, footnote 4
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