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61.
Farhod Abdullayev Marian Bocea Mihai Mihăilescu 《Applied Mathematics and Optimization》2014,69(3):487-503
The effective yield set of ionic polycrystals is characterized by means of variational principles in $L^\infty $ associated to supremal functionals acting on matrix-valued divergence-free fields. 相似文献
62.
In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings. 相似文献
63.
Robert J. Bellair Mihai Manitiu Esin Gulari Rangaramanujam M. Kannan 《Journal of Polymer Science.Polymer Physics》2010,48(8):823-831
Superior property enhancements in polymer–clay nanocomposites can be achieved if one can significantly enhance the nanoclay dispersion and polymer–clay interactions. Recent studies have shown that nanoclays can be dispersed in polymers using supercritical carbon dioxide (scCO2). However, there is need for a better understanding of how changing the clay modifier affects the clay dispersability by scCO2 and the resultant nanocomposite rheology. To address this, the polystyrene (PS)/clay nanocomposites with “weak” interaction (Cloisite 93A clay) and “strong” interaction (Cloisite 15A clay) have been prepared using the supercritical CO2 method in the presence of a co‐solvent. Transmission electron microscopy images and small‐angle X‐ray diffraction illustrate that composites using 15A and 93A clays show similar magnitude of reduction in the average tactoid size, and dispersion upon processing with scCO2. When PS and the clays are coprocessed in scCO2, the “dispersion” of clays appears to be independent of modifier or polymer–clay interaction. However, the low‐frequency storage modulus in the scCO2‐processed 15A nanocomposites is two orders of magnitude higher than that of 93A nanocomposites. It is postulated that below percolation (solution blended composites), the strength of polymer–clay interaction is not a significant contributor to rheological enhancement. In the scCO2‐processed nanocomposites the enhanced dispersion passes the percolation threshold and the interactions dictate the reinforcement potential of the clay–polymer–clay network. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 823–831, 2010 相似文献
64.
We study a non-homogeneous boundary value problem in a smooth bounded domain in RN. We prove the existence of at least two non-negative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma. 相似文献
65.
We construct six unitary trace invariants for 2×2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We have discovered a curious trace identity for two unit-speed one-parameter subgroups of Sp(1). A modification gives an infinite family of trace identities for quaternions as well as for 2×2 complex matrices. We were not able to locate these identities in the literature. We prove two quaternionic versions of a well known characterization of triangularizable subalgebras of matrix algebras over an algebraically closed field. Finally we consider the problem of describing the semi-algebraic set of pairs (X,Y) of quaternionic n×n matrices which are simultaneously triangularizable. Even the case n=2, which we analyze in more detail, remains unsolved. 相似文献
66.
Mihai Ciucu 《Journal of Algebraic Combinatorics》2003,17(3):335-375
In the last decade there have been many results about special families of graphs whose number of perfect matchings is given by perfect or near perfect powers (N. Elkies et al., J. Algebraic Combin.
1 (1992), 111–132; B.-Y. Yang, Ph.D. thesis, Department of Mathematics, MIT, Cambridge, MA, 1991; J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this paper we present an approach that allows proving them in a unified way. We use this approach to prove a conjecture of James Propp stating that the number of tilings of the so-called Aztec dungeon regions is a power (or twice a power) of 13. We also prove a conjecture of Matt Blum stating that the number of perfect matchings of a certain family of subgraphs of the square lattice is a power of 3 or twice a power of 3. In addition we obtain multi-parameter generalizations of previously known results, and new multi-parameter exact enumeration results. We obtain in particular a simple combinatorial proof of Bo-Yin Yang's multivariate generalization of fortresses, a result whose previously known proof was quite complicated, amounting to evaluation of the Kasteleyn matrix by explicit row reduction. We also include a new multivariate exact enumeration of Aztec diamonds, in the spirit of Stanley's multivariate version. 相似文献
67.
68.
I. Chiorean A. B. Németh C. I. Gheorghiu Mihai Putinar V. Kalashnikov 《Acta Appl Math》1994,35(3):299-302
69.
Björn Gustafsson Mihai Putinar 《Journal of Mathematical Analysis and Applications》2007,328(2):995-1006
The analytic continuation of the exponential transform of a domain in Rn is proved under some global geometric assumptions on the boundary. Two approximation schemes of the continued transform (one based on a Taylor series truncation, the other on a global eigenfunction expansion) are also discussed. 相似文献
70.