We revisit the foundational Moment Formula proved by Roger Lee fifteen years ago. show that when underlying stock price martingale admits finite log-moments E[|log (S)|^q] for some positive q, arbitrage-free growth in left wing of implied volatility smile is less constrained than Lee's bound. The result rationalised a market trading discretely monitored variance swaps wherein payoff function sq...

The analysis of time-dependent data is often guided by the question of how dominant structures develop over time. It is important to understand how patterns or structures identified for one time step evolve over time, by changing or moving in the domain. To gain insight into such evolving structural change it is crucial to effectively compare different time steps. This paper proposes a comparis...

We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a tracial sequence. We prove that such a sequence can be represented with tracial moments of matrices if its corresponding moment matrix is positive semidefini...

It is shown that the truncated multidimensional moment problem is more general than the full multidimensional moment problem.

The trajectory of a spherical object which falls freely in gravitational field is fixed by its initial position and velocity. However, an can control shape also motion: Except where forbidden symmetries their associated conservation laws, shape-changing (but rocket-free) spacecraft have complete over trajectory. We discuss general formalism allows rocket-free maneuvers to be understood without ...

This study was performed in connection with the experiment planned by researchers from three institutions (Institute of Theoretical and Experimental Physics, Joint Institute for Nuclear Research, and the All-Russia Research Institute for Experimental Physics) to look for the magnetic moment of the electron neutrino [1]. This experiment is presumed to study the spectra of energy deposited in a d...

An attempt is made to improve the currently accepted muonic value for the 197Au nuclear quadrupole moment [+0.547(16)x10(-28) m2] for the 3/2+ nuclear ground state obtained by Powers et al. [Nucl. Phys. A230, 413 (1974)]. From both measured Mossbauer electric quadrupole splittings and solid-state density-functional calculations for a large number of gold compounds a nuclear quadrupole moment of...

We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of these rules. We provide a combinatorial interpretation for partial freeness as the presence of closed paths in Hilbert space defined by particular joint moments....

We study Voiculescu’s microstate free entropy for a single non–selfadjoint random variable. The main result is that certain additional constraints on eigenvalues of microstates do not change the free entropy. Our tool is the method of random regularization of Brown measure which was studied recently by Haagerup and the author. As a simple application we present an upper bound for the free entro...