Correspondence between geometrical and differential definitions of the sine and cosine functions and connection with kinematics

In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms correspond to two different definitions of trigonometric functions, one geometrical using right triangles and unit circles, and the other employing differential equations. Although the two definitions must be equivalent, this equivalence is not demonstrated in textbooks. In this manuscript, the equivalence between the geometrical and the differential definition is presented assuming no a priori knowledge of the properties of sine and cosine functions. We start with the usual length projections on the unit circle and use elementary geometry and elementary calculus to arrive to harmonic differential equations. This more general and abstract treatment not only reveals the equivalence of the two definitions but also provides an instructive perspective on circular and harmonic motion as studied in kinematics. This exercise can help develop an appreciation of abstract thinking in physics.Comment: 6 pages including 1 figur

Multi-relational data mining

An important aspect of data mining algorithms and systems is that they should scale well to large databases. A consequence of this is that most data mining tools are based on machine learning algorithms that work on data in attribute-value format. Experience has proven that such 'single-table' mining algorithms indeed scale well. The downside of this format is, however, that more complex patterns are simply not expressible in this format and, thus, cannot be discovered. One way to enlarge the expressiveness is to generalize, as in ILP, from one-table mining to multiple table mining, i.e., to support mining on full relational databases. The key step in such a generalization is to ensure that the search space does not explode and that efficiency and, thus, scalability are maintained. In this paper we present a framework and an architecture that provide such a generalization. In this framework the semantic information in the database schema, e.g., foreign keys, are exploited to prune the search space and, in the architecture, database primitives are defined to ensure efficiency. Moreover, the framework induces a canonical generalization of algorithms, i.e., if the generalized algorithms are run on a single table database, they give the same results as their single-table counterparts. The framework is illustrated by the Warmr algorithm, which is a multi-relational generalization of the Apriori algorithm

Measurements of the helium propagation at 4.4 K in a 480 m long stainless steel pipe

The Relativistic Heavy Ion Collider (RHIC), with two concentric rings 3.8 km in circumference, uses superconducting magnets to focus the high energy beams. Each sextant of RHIC will have continuous cryostats up to 480 m in length housing the magnets and the cold beam pipes. For an acceptable lifetime of the stored beam, the pressure in the cold beam pipe will be < 10{sup {minus}11} Torr. The characteristics of He pressure front propagation due to He leaks will be of importance for beam lifetimes and for vacuum monitoring due to the high vapor pressure of He at 4.4 K, even with small surface coverage. The travel of the He pressure fronts along a 480 m long, 6.9 cm I.D. stainless steel beam pipe cooled to 4.4 K has recently been measured during the RHIC first sextant test. The experiment was carried out over a 12-day period by bleeding in a calibrated He leak of 3 {times} 10{sup {minus}5} Torr{center_dot}l/s (20 C) while measuring the He pressures along this 480 m cold tube at {approximately} 30 m intervals. The measured speed of the pressure fronts and the pressure profiles are summarized and compared with the calculated ones

Examining Student Responses to Concept-Oriented Reading Instruction in Nutrition Education

The concept-oriented reading instruction (CORI) framework was designed to increase student reading motivation, strategy usage, and conceptual learning. Thus far, CORI has only been studied in regards to science education. This descriptive mixed method case study examined two classes of sixth grade students' responses to CORI in nutrition education that relied heavily on inquiry, reading, and performance-based tasks which was implemented to help students develop conceptual knowledge in nutrition and improve their abilities to analyze influences on eating behaviors and habits. Each sixth grade class participated in a six-day CORI nutrition unit (N=63). Pre and post nutrition concept and skill questionnaires, pre and post student interest surveys, observations and field notes, and student artifacts were used to answer the following questions: 1) To what extent do students acquire conceptual knowledge when CORI is used to teach nutrition education?; 2) To what extent can students apply a health skill (analyzing influences) when CORI is used to teach nutrition education?; 3) In what ways does the use of CORI in nutrition education engage students?; 4) What interests students about reading informational and narrative texts provided in a CORI health class? Students in case 1 experienced significant gains in concept acquisition after a CORI nutrition unit; however concept gains in case 2 were non significant. There was no statistically significant evidence to suggest that the CORI unit affected students' skill acquisition and application. Gender and ethnicity did not have a statistically significant affect on students' concept and skill acquisition following a CORI nutrition unit. Responses to student interest surveys suggest a high level of interest in the hands-on activities and qualitative data report specific interest in the reading activities that were a part of the health education instruction. Quantitative data indicate increases in students' interest in information texts and using texts to find new information; however, quantitative data also suggest there is no change after a CORI nutrition unit in students' self-reported persistence even though a text is difficult to read. Qualitative data suggest an increase in student engagement in the CORI hands-on activities, reading assignments, cognitive processing of the material, and application in authentic tasks. Limitations of this study and implications for future research are also discussed

Plasmonic Cloaking of Cylinders: Finite Length, Oblique Illumination and Cross-Polarization Coupling

Metamaterial cloaking has been proposed and studied in recent years following several interesting approaches. One of them, the scattering-cancellation technique, or plasmonic cloaking, exploits the plasmonic effects of suitably designed thin homogeneous metamaterial covers to drastically suppress the scattering of moderately sized objects within specific frequency ranges of interest. Besides its inherent simplicity, this technique also holds the promise of isotropic response and weak polarization dependence. Its theory has been applied extensively to symmetrical geometries and canonical 3D shapes, but its application to elongated objects has not been explored with the same level of detail. We derive here closed-form theoretical formulas for infinite cylinders under arbitrary wave incidence, and validate their performance with full-wave numerical simulations, also considering the effects of finite lengths and truncation effects in cylindrical objects. In particular, we find that a single isotropic (idealized) cloaking layer may successfully suppress the dominant scattering coefficients of moderately thin elongated objects, even for finite lengths comparable with the incident wavelength, providing a weak dependence on the incidence angle. These results may pave the way for application of plasmonic cloaking in a variety of practical scenarios of interest.Comment: 17 pages, 11 figures, 2 table

Walking in the Limits

Walking in the limits is a homogenic artistic work made of sound, words and space, dealing with the understanding of space and time in a very existential sense: it reflects upon perception and illumines the structures of individual memory.â : Isabell Hemmel, Walking in the limits, in: Tagesanzeiger Zurich, 17-8-2006 The stage space was based on a two year investigation into the supersymmetric string theory. In the case of string theory, consistency requires spacetime to have 10 (3+1+6) dimensions. The conflict between observation and theory is resolved by making the unobserved dimensions compactified. By simulating a biographical event staged over 24 hours in a hotel room in Berlin on the night that the wall fell on the 9 November 1989 and viewing these events in terms of the string theory we propose an 'observable' ten-dimensional simulation of the proposed reality offered by the string theory. Working closely with researchers at CERN in Geneva and the composer Heinz Reber the works seeks to make the invisible, visible and allow us to simulate the incomprehensible. The research goes further than illustrating a theory by proposing a new perspective on quantum physics through the disciplines of literature (Borges) Art (Wallen) and Music (Reber) by creating a fluid space in perpetual movement and ten differentiated space-time layers

Genomics reveals historic and contemporary transmission dynamics of a bacterial disease among wildlife and livestock

Whole-genome sequencing has provided fundamental insights into infectious disease epidemiology, but has rarely been used for examining transmission dynamics of a bacterial pathogen in wildlife. In the Greater Yellowstone Ecosystem (GYE), outbreaks of brucellosis have increased in cattle along with rising seroprevalence in elk. Here we use a genomic approach to examine Brucella abortus evolution, cross-species transmission and spatial spread in the GYE. We find that brucellosis was introduced into wildlife in this region at least five times. The diffusion rate varies among Brucella lineages (∼3 to 8 km per year) and over time. We also estimate 12 host transitions from bison to elk, and 5 from elk to bison. Our results support the notion that free-ranging elk are currently a self-sustaining brucellosis reservoir and the source of livestock infections, and that control measures in bison are unlikely to affect the dynamics of unrelated strains circulating in nearby elk populations