Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law

We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to 1 /| x | 2 . The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius R. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if R is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.

A study of the time complexity of an Elitist Genetic Algorithm used for associating optical observations of MEO and GEO Space Debris

Currently several thousands of objects are being tracked in the MEO and GEO regions through optical means. The problem faced in this framework is that of Multiple Target Tracking (MTT). In this context both the correct associations among the observations, and the orbits of the objects have to be determined. The complexity of the MTT problem is defined by its dimension S. Where S stands for the number of ’fences’ used in the problem, each fence consists of a set of observations that all originate from dierent targets. For a dimension of S ˃ the MTT problem becomes NP-hard. As of now no algorithm exists that can solve an NP-hard problem in an optimal manner within a reasonable (polynomial) computation time. However, there are algorithms that can approximate the solution with a realistic computational e ort. To this end an Elitist Genetic Algorithm is implemented to approximately solve the S ˃ MTT problem in an e cient manner. Its complexity is studied and it is found that an approximate solution can be obtained in a polynomial time. With the advent of improved sensors and a heightened interest in the problem of space debris, it is expected that the number of tracked objects will grow by an order of magnitude in the near future. This research aims to provide a method that can treat the correlation and orbit determination problems simultaneously, and is able to e ciently process large data sets with minimal manual intervention.

Space requirement of a prefabricated bar on two interforaminal implants: a prospective clinical study

OBJECTIVES This clinical study measured the dimensional changes of existing lower complete dentures due to the integration of a prefabricated implant bar. Additionally, the impact of this dimensional change on patient satisfaction and oral function was analyzed. METHODS Twenty edentulous patients (10 men/10 women; aged 65.9 ± 11.8 years) received two interforaminal implants. Subsequent to surgery, a chair side adapted, prefabricated bar (SFI Bar(®), C+M, Biel, Switzerland) was inserted, and the matrix was polymerized into the existing lower denture. The change of the denture's lingual dimension was recorded by means of a bicolored, silicone denture duplicate that was sectioned in the oro-vestibular direction in the regions of the symphysis (S) and the implants (I-left, I-right). On the sections, the dimensional increase was measured using a light microscope. Six months after bar insertion, patients answered a standardized questionnaire. RESULTS All dentures exhibited increased lingual volume, more extensively at S than at I (P = 0.001). At S, the median diagonal size of the denture was doubled (+4.33 mm), and at I, the median increase was 50% (I-left/-right = +2.66/+2.62 mm). The original denture size influenced the volume increase (P = 0.024): smaller dentures led to a larger increase. The amount of denture increase did not have negative impact on either self-perceived oral function or patient satisfaction. Approximately, 95% of the patients were satisfied with the treatment results. CONCLUSIONS The lingual size of a lower denture was enlarged by the integration of a prefabricated bar without any negative side effects. Thus, this attachment system is suitable to convert an existing full denture into an implant-supported overdenture.

Mapping Emotion Terms into Affective Space: Further Evidence for a Four-Dimensional Structure

Recent empirical work on the semantics of emotion terms across many different cultures and languages, using a theoretical componential approach, suggested that four dimensions are needed to parsimoniously describe the semantic space of the emotion domain as reflected in emotion terms (Fontaine, Scherer, Roesch, & Ellsworth, 2007; Fontaine, Scherer, & Soriano, 2013). In addition to valence, power, and arousal, a novelty dimension was discovered that mostly differentiated surprise from other emotions. Here, we further explore the existence and nature of the fourth dimension in semantic emotion space using a much larger and much more representative set of emotion terms. A group of 156 participants each rated 10 out of a set of 80 French emotion terms with respect to semantic meaning. The meaning of an emotion term was evaluated with respect to 68 emotion features representing the appraisal, action tendency, bodily reaction, expression, and feeling components of the emotion process. A principal component analysis confirmed the four-dimensional valence, power, arousal, and novelty structure. Moreover, this larger and much more representative set of emotion terms revealed that the novelty dimension not only differentiates surprise terms from other emotion terms, but also identifies substantial variation within the fear and joy emotion families.