The structure of students' emotions experienced during a mathematical achievement test

Several models have been developed in order to categorize the numerous expressions that people use in order to describe their emotional experiences. The focus of the present study is on one of these theoretical classifications proposed by Pekrun (1992) specifically concerning emotions which are directly related to learning and achievement in mathematics. In his model, emotions are classified according to their valence (positive vs. negative) and their level of activation. In testing the assumptions of this model, we investigated students' enjoyment, anxiety, anger and boredom experienced before, during, and after the completion of a math test. Correspondence analyses which were used to generate a graphical illustration of structural interrelationships between these emotions provide empirical support for the theoretical classification.     

Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.     

Synthesis of 5‐phenyl‐5,6,7,8‐tetrahydro‐1,6‐naphthyridines and 5‐phenyl‐6,7,8,9‐tetrahydro‐5H‐pyrido[3,2‐c]azepines as potential D1 receptor ligands

A new access to 5‐phenyl‐5,6,7,8‐tetrahydro‐1,6‐naphthyridines 25a‐28a (n=1) and 5‐phenyl‐6,7,8,9‐tetrahydro‐5H‐pyrido[3,2‐c]azepines 25b‐28b (n=2) has been developed by first preparing the functional pyridine moiety followed by intramolecular cyclization forming the partially reduced ring.     

The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.     

A note on the reflection principle for the biharmonic equation and the Stokes system

In this note, we discuss the reflection principle of the Stokes system in a half space for the threedimensional case, and of the biharmonic equation. Admitting different boundary conditions, we use the reflection principle to prove uniqueness of solutions of the Stokes system or the biharmonic equation in weightedLq-spaces