154 research outputs found
Shifted convolution and the Titchmarsh divisor problem over F_q[t]
In this paper we solve a function field analogue of classical problems in
analytic number theory, concerning the auto-correlations of divisor functions,
in the limit of a large finite field.Comment: 22 pages, updated versio
The Stern-Gerlach Experiment Revisited
The Stern-Gerlach-Experiment (SGE) of 1922 is a seminal benchmark experiment
of quantum physics providing evidence for several fundamental properties of
quantum systems. Based on today's knowledge we illustrate the different
benchmark results of the SGE for the development of modern quantum physics and
chemistry.
The SGE provided the first direct experimental evidence for angular momentum
quantization in the quantum world and thus also for the existence of
directional quantization of all angular momenta in the process of measurement.
It measured for the first time a ground state property of an atom, it produced
for the first time a `spin-polarized' atomic beam, it almost revealed the
electron spin. The SGE was the first fully successful molecular beam experiment
with high momentum-resolution by beam measurements in vacuum. This technique
provided a new kinematic microscope with which inner atomic or nuclear
properties could be investigated.
The original SGE is described together with early attempts by Einstein,
Ehrenfest, Heisenberg, and others to understand directional quantization in the
SGE. Heisenberg's and Einstein's proposals of an improved multi-stage SGE are
presented. The first realization of these proposals by Stern, Phipps, Frisch
and Segr\`e is described. The set-up suggested by Einstein can be considered an
anticipation of a Rabi-apparatus. Recent theoretical work is mentioned in which
the directional quantization process and possible interference effects of the
two different spin states are investigated.
In full agreement with the results of the new quantum theory directional
quantization appears as a general and universal feature of quantum
measurements. One experimental example for such directional quantization in
scattering processes is shown. Last not least, the early history of the
`almost' discovery of the electron spin in the SGE is revisited.Comment: 50pp, 17 fig
Electromagnetic properties of non-Dirac particles with rest spin 1/2
We resolve a number of questions related to an analytic description of
electromagnetic form factors of non-Dirac particles with the rest spin 1/2. We
find the general structure of a matrix antisymmetric tensor operator. We obtain
two recurrence relations for matrix elements of finite transformations of the
proper Lorentz group and explicit formulas for a certain set of such elements.
Within the theory of fields with double symmetry, we discuss writing the
components of wave vectors of particles in the form of infinite continued
fractions. We show that for (GeV/c), where is
the transferred momentum squared, electromagnetic form factors that decrease as
increases and are close to those experimentally observed in the proton
can be obtained without explicitly introducing an internal particle structure.Comment: 18 pages, 2 figure
On the asymptotic formula for Goldbach numbers in short intervals
Let
, \Sing(k) = 2
\prod\limits_{p>2}\left(1-\frac{1}{(p-1)^2}\right) \prod\limits_{\substack{
p\mid k\\ p>2 }} \left(\frac{p-1}{p-2}\right) if is even and \Sing(k)
=0 if is odd. It is known that R(k) \sim k\Sing(k) as
for almost all and that \sum_{k\in [n,n+H)}R(k) \sim
\sum_{k\in [n,n+H)} k\Sing(k) \quad\hbox{for} \quad n\to \infty \eqno{(1)}
uniformly for . Here we prove, assuming
and , that (1) holds for
almost all
Trust and the Governance of Higher Education: The Introduction of Chancellor System in Hungarian Higher Education
Trust plays a vital role in the cooperation of social actors. While researching trust becomes important in public management, the impact of trust on higher education policy and management has drawn less attention. This chapter analyses the introduction of the chancellor system in Hungarian higher education from the perspective of trust. In this new governance model, chancellors, who are appointed by the government, became responsible for the administration and budgets of higher institutions (HEIs), while rectors kept their prerogatives only on academic issues. The success of an institution now depends on the cooperation of its two interdependent leaders. Trust plays an especially critical role in such leadership constellation. The study is based on empirical data collected through two surveys conducted in 2015 and 2016 among academic leaders of Hungarian higher education institutions and uses Hurley’s decision-to-trust-model (Hurley 2012) as an analytic framework
Social interaction patterns, therapist responsiveness, and outcome in treatments for borderline personality disorder.
Inflexible social interaction patterns are defining features of borderline personality disorder (BPD). Specific beliefs about the self and others may be activated across interaction situations, often leading to instable relationships. It may be pivotal to address these difficulties in early treatment phases, through appropriate therapist responsiveness, which means an adaptation of therapist's activity to their client's behaviours using emerging information in the process (Stiles, 2009, Clinical Psychology: Science and Practice, 16, 86).
In this process-outcome study, responsiveness is operationalized by the motive-oriented therapeutic relationship (Caspar, 2007, Handbook of psychotherapeutic case formulations, 2nd ed., 251-289, Guilford), based on the Plan analysis case formulation. The present study assesses the interplay between social interaction problems and therapist responsiveness, explaining symptoms at discharge and the therapeutic alliance.
In total, N = 50 clients with BPD entered the study, and standard and responsive treatments were compared. Social interaction patterns were assessed by the newly developed Borderline Interaction Patterns Scale (BIPS), applied to recorded material of three sessions per therapy. Outcome was measured by general symptoms (OQ-45), borderline symptoms (BSL-23), interpersonal problems (IIP), and the therapeutic alliance (WAI).
Results suggest that in standard treatment, social interaction patterns are neither related to outcome nor the therapeutic alliance. In responsive treatment, more activation of social interaction patterns predicted better outcome on IIP and lower therapist ratings of the alliance.
The conclusions seem promising for specific effectiveness of responsive treatments in particular in the interpersonal problem area of BPD. Identifying social interaction patterns early in treatment may be a crucial pathway to change for BPD.
Responsive therapy activating social interaction patterns may be crucial for better outcome. Future research should focus on mechanisms of change in early treatment phases for BPD. New scale for assessing social interaction patterns specific to borderline personality disorder
Supersymmetric QCD corrections to and the Bernstein-Tkachov method of loop integration
The discovery of charged Higgs bosons is of particular importance, since
their existence is predicted by supersymmetry and they are absent in the
Standard Model (SM). If the charged Higgs bosons are too heavy to be produced
in pairs at future linear colliders, single production associated with a top
and a bottom quark is enhanced in parts of the parameter space. We present the
next-to-leading-order calculation in supersymmetric QCD within the minimal
supersymmetric SM (MSSM), completing a previous calculation of the SM-QCD
corrections. In addition to the usual approach to perform the loop integration
analytically, we apply a numerical approach based on the Bernstein-Tkachov
theorem. In this framework, we avoid some of the generic problems connected
with the analytical method.Comment: 14 pages, 6 figures, accepted for publication in Phys. Rev.
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