Cubic Nonlinearity in Elastic Materials: Theoretical Prediction and Computer Modelling of New Wave Effects

Our object of interest is nonlinear interaction of waves in elastic materials. The new model of a material is proposed that takes into account the mechanism of simultaneous quadratic and cubic nonlinear deformations. Introduction of cubic nonlinearity into the model makes the general wave picture more complicated and creates new possibilities for the wave analysis. We present four possibilities for the evolution of profiles of plane harmonic waves. It is noted that quadratic and cubic nonlinearities emerge first of all in the second and third harmonics generation, respectively. Further, we discuss the results of computer modelling of the wave profile evolution. The influence of the progress of second and third harmonics on the wave profile evolution is studied separately. We study separately how second and third harmonics influence the evolution of the wave profile. We also investigate how the progress of harmonics depends on the initial frequency and amplitude. We find two distinct schemes of the evolution progress: the scheme (in) with four stages for the second harmonics and the scheme with three stages for the third harmonics. As a result the influence of both harmonics could be observed simultaneously, and such a case is demonstrated in the paper. Nevertheless this phenomenon is not necessarily present in every material which explains the absence of experimental observations of the third harmonics by this time.     

A Quantitative Voronovskaya Formula for Mellin Convolution Operators

Here we give a quantitative Voronovskaya formula for a class of Mellin convolution operators of type

Molecular calculations with the nonempirical ab initioMODPOT,VRDDO, and MODPOT/VRDDO procedures. XI. Theoretical study of the [C6H5OH ⃛OC6H5]− molecular complex: Ab initioMODPOT/VRDDO calculations and electrostatic molecular potential contour maps

The transport of C₆H₅O^? (or similarly charged moieties) through a lipoidal membrane may possibly be facilitated by forming complexes with the neutral compound. Thus, theoretical studies were performed on the model [C₆H₅OH ?OC₆H₅]^? molecular complex to obtain some information concerning the possible molecular and electronic structure of such complexes. Ab initio MODPOT /VRDDO SCF calculations were carried out on the neutral-anion dimer [C₆H₅OH ?OC₆H₅] to optimize the equilibrium geometry. Electrostatic molecular potential contour maps have been generated from the ab initio MODPOT /VRDDO results in the molecular plane and in the plane perpendicular to the molecular plane and intersecting the hydrogen bond O ?H? O. Difference maps have also been generated showing the change of potential on complex formation. There is a decrease of electrostatic interactions of the phenoxide anion upon complex formation with the neutral phenol. Counterpoise corrections for basis set size could not be made since calculation of the phenoxide anions in the basis set of the phenol plus the phenoxide anion led to an excited state for the phenoxide anion. This behavior is somewhat similar to that occurring in the stabilization method for excited states of negative ions as the size of the basis set is increased.     

An asymptotically exact algorithm for the high-multiplicity bin packing problem

The bin packing problem consists of finding the minimum number of bins, of given capacity D, required to pack a set of objects, each having a certain weight. We consider the high-multiplicity version of the problem, in which there are only C different weight values. We show that when C=2 the problem can be solved in time O( log D). For the general case, we give an algorithm which provides a solution requiring at most C−2 bins more than the optimal solution, i.e., an algorithm that is asymptotically exact. For fixed C, the complexity of the algorithm is O(poly( log D)), where poly(·) is a polynomial function not depending on C.     

Dynamical iteration schemes for multiscale simulation in nanoelectronics

In this paper we present the spatial discretization of the thermal element model for coupled electrothermal simulation introduced in [1] with a suitable multiscale Finite Element scheme. The structure of the local matrices for the the thermal element is presented in detail and some preliminary numerical results are reported. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non–existence of theta–shaped self–similarly shrinking networks moving by curvature

We prove that there are no networks homeomorphic to the Greek “Theta” letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees, such that under the motion by curvature they are self–similarly shrinking.

This fact completes the classification of the self–similarly shrinking networks in the plane with at most two triple junctions, see [5 Chen, X., Guo, J.-S. (2007). Self-similar solutions of a 2-D multiple-phase curvature flow. Phys. D. 229(1):22–34.[Crossref], [Web of Science ®] , [Google Scholar], 10 Hättenschweiler, J. (2007). Mean curvature flow of networks with triple junctions in the plane. Master’s thesis. ETH Zürich. [Google Scholar], 25 Schnürer, O. C., Azouani, A., Georgi, M., Hell, J., Nihar, J., Koeller, A., Marxen, T., Ritthaler, S., Sáez, M., Schulze, F., Smith, B. (2011). Evolution of convex lens–shaped networks under the curve shortening flow. Trans. Am. Math. Soc. 363(5):2265–2294.[Crossref], [Web of Science ®] , [Google Scholar], 2 Baldi, P., Haus, E., Mantegazza, C. (2016). Networks self-similarly moving by curvature with two triple junctions. Networks self-similarly moving by curvature with two triple junctions. 28(2017):323–338. [Google Scholar]].     

Optimal strategies for mitigating the HIV/AIDS epidemic in the Philippines

The human immunodeficiency virus (HIV) impairs a person's immune system against many infections and some types of cancer, leading to acquired immunodeficiency syndrome (AIDS), which is characterized by severe illnesses. The number of HIV infections in the Philippines has increased, more than doubled, within the last decade. This alarming HIV crisis in the country requires urgent actions. In this study, a mathematical model is developed to describe the disease transmission in the Philippines. Disease-free and endemic equilibria are obtained, stability analysis is performed, and the basic reproduction number is computed. Sensitivity analyses and subset selection are performed to identify influential parameters and to determine an identifiable parameter set given measurements, respectively. Available data on the number of asymptomatic aware infectious, those who are in the AIDS stage, and those under treatment are utilized to estimate key epidemiological parameters such as transmission, treatment, and screening rates. Uncertainty of these parameter estimates is quantified through bootstrapping method. Furthermore, intervention strategies are investigated in the framework of optimal control theory. Control measures include precaution, HIV screening, antiretroviral treatment, and pre-exposure prophylaxis (PrEP) treatment. These various control efforts are compared with regard to cost efficiency and effectiveness in reducing the number of infected individuals. Given limited available control measures, the PrEP-only scenario is shown to be the most cost-effective, followed by other scenarios that combine PrEP with other controls.     

L'opération d'élagage

Résumé On introduit une opération d'élagage plus faible que celle introduite dans [1]; on montre cependant la validité des mêmes théorèmes de caractérisation dans la famille des entropies additives et subadditives.

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Riassunto Si introduce un'operazione di pruning più generale di quella introdotta in [1]; si mostra tuttavia che valgono gli stessi teoremi di caratterizzazione nella famiglia delle entropie additive e subadditive.

     

Improved Schemes for Visual Cryptography

A (k,n)-threshold visual cryptography scheme ((k,n)-threshold VCS, for short) is a method to encode a secret image SI into n shadow images called shares such that any k or more shares enable the visual recovery of the secret image, but by inspecting less than k shares one cannot gain any information on the secret image. The visual recovery consists of xeroxing the shares onto transparencies, and then stacking them. Any k shares will reveal the secret image without any cryptographic computation.In this paper we analyze visual cryptography schemes in which the reconstruction of black pixels is perfect, that is, all the subpixels associated to a black pixel are black. For any value of k and n, where 2 k n, we give a construction for (k,n)-threshold VCS which improves on the best previously known constructions with respect to the pixel expansion (i.e., the number of subpixels each pixel of the original image is encoded into). We also provide a construction for coloured (2,n)-threshold VCS and for coloured (n,n)-threshold VCS. Both constructions improve on the best previously known constructions with respect to the pixel expansion.     

The stable set problem and the thinness of a graph

We introduce a poly-time algorithm for the maximum weighted stable set problem, when a certain representation is given for a graph. The algorithm generalizes the algorithm for interval graphs and that for graphs with bounded pathwidth. By a suitable application to the frequency assignment problem, we improved several solutions to relevant benchmark instances.