Linear combination of hybrid orbitals: Cyclobutane as test-case

Hybrid-based molecular orbitals are constructed for puckered cyclobutane, and used subsequently in a configurational-interaction process. The bent-bond structure, diagonal interaction and excited states of the molecule are discussed.     

Optimal paths in disordered complex networks

We study the optimal distance in networks, l(opt), defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For strong disorder, where the maximal weight along the path dominates the sum, we find that l(opt) approximately N(1/3) in both Erdos-Rényi (ER) and Watts-Strogatz (WS) networks. For scale-free (SF) networks, with degree distribution P(k) approximately k(-lambda), we find that l(opt) scales as N((lambda-3)/(lambda-1)) for 3 or =4. Thus, for these networks, the small-world nature is destroyed. For 2相似文献   

Generalized Stress Concentration Factors for Equilibrated Forces and Stresses

As a sequel to a recent work we consider the generalized stress concentration factor, a purely geometric property of a body that for the various loadings indicates the ratio between the maximum of the optimal stress and maximum of the loading fields. The optimal stress concentration factor pertains to a stress field that satisfies the principle of virtual work and for which the stress concentration factor is minimal. Unlike the previous work, we require that the external loading be equilibrated and that the stress field be a symmetric tensor field.     

On smoothly growing bodies and the eshelby tensor

A continuum mechanical theory of growing bodies is presented. It is assumed that the various parts of the body are identifiable. The growth of a body is manifested by mapping the identifiable elements of the growing body into a material manifold. Kinematics and stress theory are formulated on the basis of an infinite dimensional differentiable bundle structure for the configuration space. Stresses representing the forces associated with the growth of the body are analogous to the Eshelby tensor.

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Sommario Si propone una teoria meccanica dei corpi di massa crescente. Si postula che le varie parti del corpo siano identificabili. La crescita del corpo si manifesta mediante l'applicazione degli elementi identificabili del corpo in una varietà materiale. La cinematica e la teoria degli sforzi vengono formulati sulla base di un fibrato differenziabile a infinite dimensioni per lo spazio delle configurazioni. Gli sforzi associati alla crescita del corpo sono analoghi al tensore di Eshelby.

     

Backscattering response from periodic spatial patterns in random media

Abstract

In wave-based remote sensing or radio-location of distant objects in a random medium, a high-frequency electromagnetic wave is scattered by object discontinuities, and portions of the scattered radiation can traverse the same random inhomogeneities as the initial incident field. The statistical dependence of the forward–backward travelling events results in an anomaly in the backscattered intensity pattern that carries information about the scattering object. The quality of this information depends on the ability to resolve the fine-structure elements. In this work we investigate the resolving properties of periodic spatial objects by using the random propagators of the stochastic geometrical theory of diffraction.     

On the connection between weak and strong convergencies in Cm

In this work wome connections are pursued between weak and strong convergence in the spaces C^m (m-times continuously differentiable functions on Rⁿ). Let f_n, f?C^{m + 1}, where n = 1, 2,…, and m is a nonnegative integer. Suppose that the sequence {f_n} converges to f relative to the weak topology of C^{m + 1}. It is shown that this implies the convergence of {f_n} to f with respect to the strong topology of C^m. Several corollaries to this theorem are established; among them is a sufficient condition for uniform convergence. A stronger result is shown to exist when the sequence constitutes an output sequence of a linear weakly continuous operator.     

Overcoming intuitive interference in mathematics: insights from behavioral, brain imaging and intervention studies

It is well known that many students encounter difficulties when solving problems in mathematics. Research indicates that some of these difficulties may stem from intuitive interference with formal/logical reasoning. Our research aims at deepening the understanding of these difficulties and their underlying reasoning mechanisms to help students overcome them. For this purpose we carried out behavioral, brain imaging and intervention studies focusing on a previously demonstrated obstacle in mathematics education. The literature reports that many students believe that shapes with a larger area must have a larger perimeter. We measured the accuracy of responses, reaction time, and neural correlates (by fMRI) while participants compared the perimeters of geometrical shapes in two conditions: (1) congruent, in which correct response was in line with intuitive reasoning (larger area–larger perimeter) and (2) incongruent, in which the correct answer was counterintuitive. In the incongruent condition, accuracy dropped and reaction time for correct responses was longer than in the congruent condition. The congruent condition activated bilateral parietal brain areas, known to be involved in the comparison of quantities, while correctly answering the incongruent condition activated bilateral prefrontal areas known for their executive control over other brain regions. The intervention, during which students’ attention was drawn to the relevant variable, increased accuracy in the incongruent condition, while reaction times increased in both congruent and incongruent conditions. The findings of the three studies point to the importance of control mechanisms in overcoming intuitive interference in mathematics. Overall, it appears that adding a cognitive neuroscience perspective to mathematics education research can contribute to a better understanding of students’ difficulties and reasoning processes. Such information is important for educational research and practice.