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101.
It has recently been pointed out that the existence of massless chiral edge excitations has important strong coupling consequences for the topological concept of an instanton vacuum. In the first part of this paper we elaborate on the effective action for “edge excitations” in the Grassmannian U (m + n)/U (m) × U (n) non-linear sigma model in the presence of the θ term. This effective action contains complete information on the low energy dynamics of the system and defines the renormalization of the theory in an unambiguous manner. In the second part of this paper we revisit the instanton methodology and embark on the non-perturbative aspects of the renormalization group including the anomalous dimension of mass terms. The non-perturbative corrections to both the β and γ functions are obtained while avoiding the technical difficulties associated with the idea of constrained instantons. In the final part of this paper we present the detailed consequences of our computations for the quantum critical behavior at θ = π. In the range 0 ? m, n ? 1 we find quantum critical behavior with exponents that vary continuously with varying values of m and n. Our results display a smooth interpolation between the physically very different theories with m = n = 0 (disordered electron gas, quantum Hall effect) and m = n = 1 (O (3) non-linear sigma model, quantum spin chains) respectively, in which cases the critical indices are known from other sources. We conclude that instantons provide not only a qualitative assessment of the singularity structure of the theory as a whole, but also remarkably accurate numerical estimates of the quantum critical details (critical indices) at θ = π for varying values of m and n. 相似文献
102.
Precoloring extension on unit interval graphs 总被引:1,自引:0,他引:1
Dániel Marx 《Discrete Applied Mathematics》2006,154(6):995-1002
In the precoloring extension problem a graph is given with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper k-coloring of the graph. Answering an open question of Hujter and Tuza [Precoloring extension. III. Classes of perfect graphs, Combin. Probab. Comput. 5 (1) (1996) 35-56], we show that the precoloring extension problem is NP-complete on unit interval graphs. 相似文献
103.
D. S. L. Pontes E. Longo F. M. Pontes M. S. Galhiane L. S. Santos Marcelo A. Pereira-da-Silva J. H. D. da Silva A. J. Chiquito P. S. Pizani 《Applied Physics A: Materials Science & Processing》2009,96(3):731-740
Ferroelectric Pb1−x−y
Ca
x
Sr
y
TiO3 thin films (denoted by PCST90, PCST70, and PCST30) were deposited on the Pt/Ti/SiO2/Si substrates by a chemical solution deposition method. Their properties were investigated from the viewpoint of crystal
structure, microstructure, dielectric, and ferroelectric properties. X-ray diffraction patterns revealed the formation of
PCST90, PCST70, and PCST30 thin films without any secondary phases. Infrared and Raman spectroscopy results show that a gradual
phase transition from tetragonal to pseudocubic or cubic perovskite structure may occur in PCST thin films with the simultaneous
increase of Ca2+ and Sr2+ contents. Both substitution of isovalent Ca2+ and Sr2+ at Pb2+-site enhanced the dielectric constant and reduced the remnant polarization. In addition, ferroelectric test analyses show
that the PCST thin films undergo a ferroelectric-to-paraelectric phase transformation with an amount of Pb2+, Ca2+, and Sr2+ at 30%, 35%, and 35% mol, respectively. Hence, the absence of ferroelectric property may be attributed to a decreasing of
the octahedron distortion in the perovskite structure accompanied by a weakening of long-range ferroelectric order. 相似文献
104.
Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem
In this paper, we first give an interesting operator identity. Furthermore, using the q-exponential operator technique to the multiple q-binomial theorem and q-Gauss summation theorem, we obtain some transformation formulae and summation theorems of multiple basic hypergeometric series. 相似文献
105.
In this note we study the property (w), a variant of Weyl's theorem introduced by Rako?evi?, by means of the localized single-valued extension property (SVEP). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (w) holds. We also relate this property with Weyl's theorem and with another variant of it, a-Weyl's theorem. We show that Weyl's theorem, a-Weyl's theorem and property (w) for T (respectively T*) coincide whenever T* (respectively T) satisfies SVEP. As a consequence of these results, we obtain that several classes of commonly considered operators have property (w). 相似文献
106.
Cornel Pasnicu 《Journal of Mathematical Analysis and Applications》2006,323(2):1213-1224
Let A be the C∗-algebra associated to an arbitrary continuous field of C∗-algebras. We give a necessary and sufficient condition for A to have the ideal property and, if moreover A is separable, we give a necessary and sufficient condition for A to have the projection property. Some applications of these results are given. We also prove that “many” crossed products of commutative C∗-algebras by discrete, amenable groups have the projection property, generalizing some of our previous results. 相似文献
107.
Carlos Lizama 《Journal of Mathematical Analysis and Applications》2006,324(2):921-933
In this paper we characterize the existence and uniqueness of periodic solutions of inhomogeneous abstract delay equations and establish maximal regularity results for strong solutions. The conditions are obtained in terms of R-boundedness of linear operators determined by the equations and Lp- Fourier multipliers. Periodic mild solutions are also studied and characterized. 相似文献
108.
N. G. Karpova 《Mathematical Notes》1998,64(1):55-62
LetG be a domain in
n
,n2, letA be a connected complex (n–1)-dimensional submanifold ofG, and let be a plurisubharmonic function inGA. We obtain conditions on the growth of that guarantee the local boundedness of at a point a A G and the existence of a plurisubharmonic extension of toG.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 64–72, July, 1998.The author wishes to express her gratitude to Professor E. M. Chirka for numerous useful discussions and for his assistance in writing the present text. 相似文献
109.
Matthew Elder 《Discrete Mathematics》2008,308(16):3479-3490
A path bundle is a set of 2a paths in an n-cube, denoted Qn, such that every path has the same length, the paths partition the vertices of Qn, the endpoints of the paths induce two subcubes of Qn, and the endpoints of each path are complements. This paper shows that a path bundle exists if and only if n>0 is odd and 0?a?n-⌈log2(n+1)⌉. 相似文献
110.
The representation of dual spaces of EM(μ,X), owing to its extensive application, is given in this paper. Using the representation, we get the sufficient and necessary conditions of LM(μ,X) possessing drop property, and extend the result of Hudzik and Wang [H. Hudzik, B. Wang, Approximative compactness in Orlicz spaces, J. Approx. Theory 95 (1998) 82-89]. Simultaneously, under some conditions, the weak∗ drop property in LM(μ,X∗) and LM∗(μ,X) is discussed. 相似文献