Related papers: Vector variational principle

New direct proofs of variational principles for $t$-entropy, spectral radius of weighted shift operators, and entropy statistic theorem are given. The equivalence of these statements is obtained.

We show that on a generic curve, a bundle obtained by successive extensions is stable. We compute the dimension of the set of such extensions. We use degeneration methods specializing the curve to a chain of elliptic components

We give a counting based proof of the Graham Pollak Theorem

A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual…

We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.

In this article we describe vector bundles over projectivoid line and show how it is similar to (and different) from Gorthendieck's classification of vector bundles over projective line.

We prove a local version of the Mazur-Ulam theorem.

We prove some variational analysis of regularity and weak convergence of nonlocal variational principle.

We extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, `vector-valued' means `taking values in a function…

This paper studies robustness of multivariable systems with parametric uncertainties, and establishes a multivariable version of Edge Theorem. An illustrative example is presented.

A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…

A new construction, with more visible canonical features, of a qKdV equation in a q-Virasoro context is exhibited.

A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that incremental stability may be verified by separation of Scaled…

Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…

New cases of the multiplicity conjecture are considered.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…

The paper gives a unified and simple proof of both theorems and Cousin's theorem.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

The paper proves the intermediate value theorem for polynomials and power series over a valued field with divisible valuation group and infinite residue field. Some further results on the behaviour of the valuation are obtained using…