WKB Approximation to the Power Wall

We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply, monotonically rising potential. The models studied in detail have potentials proportional to $x^{\alpha}$ for $x>0$; the limit $\alpha\to\infty$ would reproduce a perfectly reflecting boundary, but at present we concentrate on the cases $\alpha =1$ and 2, for which exact solutions in terms of well known functions are available for comparison. We classify the classical paths in this system by their qualitative nature and calculate the contributions of the various classes to the leading-order semiclassical approximation: For each classical path we find the action $S$, the amplitude function $A$ and the Laplacian of $A$. (The Laplacian is of interest because it gives an estimate of the error in the approximation and is needed for computing higher-order approximations.) The resulting semiclassical propagator can be used to rewrite the exact problem as a Volterra integral equation, whose formal solution by iteration (Neumann series) is a semiclassical, not perturbative, expansion. We thereby test, in the context of a concrete problem, the validity of the two technical hypotheses in a previous proof of the convergence of such a Neumann series in the more abstract setting of an arbitrary smooth potential. Not surprisingly, we find that the hypotheses are violated when caustics develop in the classical dynamics; this opens up the interesting future project of extending the methods to momentum space.Comment: 30 pages, 8 figures. Minor corrections in v.

Self-Selected Journal Writing in the Kindergarten Classroom: Five Conditions that Foster Literacy Development

What can kindergarten children write? This question came from Doris, a middle school language arts teacher when she was told about Nancy\u27s kindergarten classroom. Nancy had a regularly scheduled self selected journal writing time. The children were allowed to choose their messages and forms of writing. Children scribbled, drew, wrote nonphonetic letter strings, and demonstrated phonetic and conventional spelling. These are all forms of spelling exhibited by emerging writers according to Sulzby, Teale, and Kamberelis, 1989

Operator Systems and Correlation Sets

Στην παρούσα εργασία μελετάτε η μη-τοπική Θεωρία Παιγνίων μέσα από μεθόδους της Θεωρίας Τελεστών. Αρχικά βλέπουμε πως το τανυστικό γινόμενο δύο συστημάτων τελεστών μπορεί να εφοδιαστεί με μία κατάλληλη διάταξη πινάκων ούτως ώστε να γίνει και αυτό ένα σύστημα τελεστών. Παρουσιάζουμε τρεις από αυτές τις διατάξεις πινάκων οι οποίες ορίζουν τα ακόλουθα τανυστικά γινόμενα συστημάτων τελεστών: το μεγιστικό (maximal), το ελαχιστικό (minimal) και το commuting. Έπειτα εξετάζουμε την σχέση μεταξύ των στοιχείων ορισμένων κλάσεων οι οποίες αποτελούνται από non-signalling συσχετίσεις και των καταστάσεων στα προαναφερθέντα τανυστικά γινόμενα κάποιων συστημάτων τελεστών.In the current paper we study the theory of non-local games through Operator Theory methods. We will see that the tensor product of two operator systems can be equipped with suitable matrix orderings making it an operator system. Three such matrix orderings are presented, these define the maximal, the minimal and the commuting operator system tensor products. Then we examine the connection between the states on the aforementioned tensor products of some operator systems and the elements of several classes of non-signalling correlations

Hertz Potentials and Differential Geometry

I review the construction of Hertz potentials in vector calculus starting from Maxwell's equations. From here, I lay the minimal foundations of differential geometry to construct Hertz potentials for a general (spatially compact) Lorentzian manifold with or without boundary. In this general framework, I discuss "scalar" Hertz potentials as they apply to the vector calculus situation, and I consider their possible generalization, showing which procedures used by previous authors fail to generalize and which succeed, if any. I give specific examples, including the standard at coordinate systems and an example of a non-flat metric, specifically a spherically symmetric black hole. Additionally, I generalize the introduction of gauge terms, and I present techniques for introducing gauge terms of arbitrary order. Finally, I give a treatment of one application of Hertz potentials, namely calculating electromagnetic Casimir interactions for a couple of systems

The Master and the Slave. A glance at the social life of molecules

Low energy interactions induce the formation of molecular assemblies that can display a large variety of sizes and shapes such as dimers, oligomers, colloids, gels, helices, cylinders, etc. These grouping modes mimic human relationships, as people generally flock together according to their affinities. Moreover, chemical reactions, undergone under strong energy interactions, that result in bond breaking and formation of new compounds, can also be compared to human behaviour. The fables usually involve animals but rarely molecules to play the role of human beings. In this article, we report a molecular tale where two different 9-substituted anthracene derivatives compete in a photochemical reaction, simulating the behaviour of a master and a slave, respectivel

Perceptions of Cooperation in a Longitudinal Social Dilemma

Most social dilemma studies of communication’s effects on cooperation are based on laboratory results with trivial incentives. Studies of real-life social dilemmas with nontrivial rewards are needed to extend the generality of laboratory results. Perceptions of cooperation on a group product (weekly group essay) were examined as a public goods dilemma embedded in a longitudinal study of groups using either face-to-face or computer-mediated communication. Perceptions of cooperation increased over time, whereas measures of group identity did not. No media effect on perceptions of cooperation was observed. Several predictors of late perceptions of cooperation were examined, but only early perception of cooperation was significant. Results are discussed with respect to several current hypotheses regarding communication and cooperation in social dilemmas.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

A Family of Styrylcoumarins: Synthesis, Spectroscopic, Photophysical and Photochemical Properties

A new family of 5-styrylcoumarins exhibit E–Z isomerization around the Cα[DOUBLE BOND]Cβ bond with large extinction coefficients, medium-lived excited states, and moderate fluorescence quantum yields (see picture). The alteration of these photophysical properties is also corroborated by computational studies