1,925 research outputs found
Fixed-point elimination in the intuitionistic propositional calculus
It is a consequence of existing literature that least and greatest
fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic
models of the Intuitionistic Propositional Calculus-always exist, even when
these algebras are not complete as lattices. The reason is that these extremal
fixed-points are definable by formulas of the IPC. Consequently, the
-calculus based on intuitionistic logic is trivial, every -formula
being equivalent to a fixed-point free formula. We give in this paper an
axiomatization of least and greatest fixed-points of formulas, and an algorithm
to compute a fixed-point free formula equivalent to a given -formula. The
axiomatization of the greatest fixed-point is simple. The axiomatization of the
least fixed-point is more complex, in particular every monotone formula
converges to its least fixed-point by Kleene's iteration in a finite number of
steps, but there is no uniform upper bound on the number of iterations. We
extract, out of the algorithm, upper bounds for such n, depending on the size
of the formula. For some formulas, we show that these upper bounds are
polynomial and optimal
The central region of the test bench cyclotron for the IsoDAR experiment
The IsoDAR experiment proposes the construction of a cyclotron to accelerate a 5 mA H+2 beam up to 60 A MeV to investigate the existence of sterile neutrinos. Due to the high beam current and the serious space charge effects,
the beam injection and the central region are challenging items for this cyclotron. For this reason, a 1 A MeV test bench cyclotron will be built. In this paper, the
simulation study for the spiral inflector and early turns of beam acceleration in the central region of the test bench cyclotron will be presented
Isotopic composition of fragments in multifragmentation of very large nuclear systems: effects of the chemical equilibrium
Studies on the isospin of fragments resulting from the disassembly of highly
excited large thermal-like nuclear emitting sources, formed in the ^{197}Au +
^{197}Au reaction at 35 MeV/nucleon beam energy, are presented. Two different
decay systems (the quasiprojectile formed in midperipheral reactions and the
unique source coming from the incomplete fusion of projectile and target in the
most central collisions) were considered; these emitting sources have the same
initial N/Z ratio and excitation energy (E^* ~= 5--6 MeV/nucleon), but
different size. Their charge yields and isotopic content of the fragments show
different distributions. It is observed that the neutron content of
intermediate mass fragments increases with the size of the source. These
evidences are consistent with chemical equilibrium reached in the systems. This
fact is confirmed by the analysis with the statistical multifragmentation
model.Comment: 9 pages, 4 ps figure
Representational task formats and problem solving strategies in kinematics and work
Previous studies have reported that students employed different problem solving approaches when presented with the same task structured with different representations. In this study, we explored and compared students’ strategies as they attempted tasks from two topical areas, kinematics and work. Our participants were 19 engineering students taking a calculus-based physics course. The tasks were presented in linguistic, graphical, and symbolic forms and requested either a qualitative solution or a value. The analysis was both qualitative and quantitative in nature focusing principally on the characteristics
of the strategies employed as well as the underlying reasoning for their applications. A comparison was also made for the same student’s approach with the same kind of representation across the two topics.
Additionally, the participants’ overall strategies across the different tasks, in each topic, were considered. On the whole, we found that the students prefer manipulating equations irrespective of the representational format of the task. They rarely recognized the applicability of a ‘‘qualitative’’ approach to solve the
problem although they were aware of the concepts involved. Even when the students included visual representations in their solutions, they seldom used these representations in conjunction with the
mathematical part of the problem. Additionally, the students were not consistent in their approach for interpreting and solving problems with the same kind of representation across the two topical areas. The representational format, level of prior knowledge, and familiarity with a topic appeared to influence their
strategies, their written responses, and their ability to recognize qualitative ways to attempt a problem. The nature of the solution does not seem to impact the strategies employed to handle the problem
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