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This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. vol.4, pp.94--104.
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
In this paper we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent…
Assuming that the Generalized Riemann Hypothesis (GRH) holds, we prove an explicit formula for the number of representations of an integer as a sum of $k\geq 5$ primes. Our error terms in such a formula improve by some logarithmic factors…
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
Gives an elementary exposition of the twisted group algebra rep- resentation of simple Clifford algebras
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
In this paper we prove an exponential covering lemma implying the three dimensional case of a well-known conjecture formulated by A. Zygmund circa 1935 and solved by A. C\'ordoba in 1978. Our approach avoids a subtle argument involving the…
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
In this short note we give counterexamples to several results related to extension theorems published recently.
We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice combinatorial identities that can be directly extracted…
Many scientific investigations require that the values of a set of model parameters are estimated using recorded data. In Bayesian inference, information from both observed data and prior knowledge is combined to update model parameters…
We present a short proof of Reisner's Theorem, characterizing which simplicial complexes have a Cohen-Macaulay face ring. In some cases, we can also express some homological invariants of the face ring in terms of the reduced homology of…
Iverson (2006) proposed the law of similarity \[ \xi_{s}(\lambda x)= \gamma(\lambda, s)\xi_{\eta(\lambda, s)}(x) \] for the sensitivity functions $\xi_{s}\, (s\in S)$. Compared to the former models, the generality of this one lies in that…
We give a simple proof of some explicit formulas of periodic continuants by Chebyshev polynomials of the second kind given by Rozsa.
This is an addendum to a previous article, which aims to provide the proofs of some results in that paper (Theorem 7.5 and Proposition 9.15) which were removed from its final version. The reason for such omission is that these proofs follow…
A startlingly simple characterization of the p-norms has recently been found by Aubrun and Nechita (arXiv:1102.2618) and by Fernandez-Gonzalez, Palazuelos and Perez-Garcia. We deduce a simple characterization of the power means of order…
We provide a short proof for the twisted multiplicativity property of the operator-valued S-transform. This is my contribution to the topical collection ''Multivariable Operator Theory. The J\"org Eschmeier Memorial'' of Complex Analysis…
We give a proof of a Martingale Representation Theorem using the methods of nonstandard analysis.