Michael Freedman,1 Chetan Nayak,1,2 and Kirill Shtengel3,4,* 1Microsoft Research, Station Q, CNSI Building, University of California, Santa Barbara, California 93106, USA 2Department of Physics, University of California, Santa Barbara, California 93106, USA 3Department of Physics and Astronomy, University of California, Riverside, California 92521, USA 4California Institute of Technology, Pasad...

For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, of arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C logL)/L. This result can be regarded as a multi-dimensio...

In 1982 Pimsner and Voiculescu computed the K0and K1-groups of the reduced group C∗-algebra C∗ red(Fk) of the free group Fk on k generators and settled thereby a long standing conjecture: C∗ red(Fk) has no projections except for the trivial projections 0 and 1. Later simpler proofs of this conjecture were found by methods from K-theory or from non-commutative differential geometry. In this pape...

In this paper, the authors present new indices for estimating technical change, return to scale, and TFP growth, as well as its decomposition. These indices, Modified General Index (MGI), Generalized Modified General Index (GMGI), and General Time Trend index (GTTI), are generalization of General Index approaches. These approaches were used for productivity decomposition of Iran's barely produc...

This study, conducted between 2016–2021 on Southeast Asian mining companies, introduces the Modified Enterprise Risk Management (ERM) Index (MERMi) to measure implementation of ERM based COSO 2017 principles. The study found that is influenced by industry competition, company complexity, international diversification, and financial leverage. Meanwhile, size along with positively impact firm per...

The genus Tortula includes about 114 species in the world and 18 species were found in Iran. In the present paper, T. vahliana (Schultz) Mont. is reported for the first time from Iran.

In this paper, we present some new lower and upper bounds for the modified Randic index in terms of maximum, minimum degree, girth, algebraic connectivity, diameter and average distance. Also we obtained relations between this index with Harmonic and Atom-bond connectivity indices. Finally, as an application we computed this index for some classes of nano-structures and linear chains.

If a graph is connected then the largest eigenvalue (i.e., index) generally changes (decreases or increases) if some local modifications are performed. In this paper two types of modifications are considered: (i) for a fixed vertex, t edges incident with it are deleted, while s new edges incident with it are inserted; (ii) for two non-adjacent vertices, t edges incident with one vertex are dele...