相关论文: On proof and progress in mathematics

This note discusses recent new approaches to studying flopping curves on 3-folds. In a joint paper, the author and Michael Wemyss introduced a 3-fold invariant, the contraction algebra, which may be associated to such curves. It…

Some properties of non-orientable 3-manifolds are shown. The semi-group of cobordism of immersions of surfaces in such manifolds is computed and proven actually to be a group. Explicit invariants are provided.

We explore the rational, formal and non-formal criteria of consistency, non-triviality and redundancy in the mathematical research now a days. We develop a paradigmatic discussion by analysing the different conceptions of those criteria,…

I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.

This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…

Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…

Comment on Classifier Technology and the Illusion of Progress [math.ST/0606441]

Comment on Classifier Technology and the Illusion of Progress [math.ST/0606441]

The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…

In this Book we argue that the fruitful interaction of computer vision and belief calculus is capable of stimulating significant advances in both fields. From a methodological point of view, novel theoretical results concerning the…

We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of right veering. We use these to construct…

We survey the progress (or lack thereof!) that has been made on some questions about the p-adic slopes of modular forms that were raised by the first author in [Buz05], discuss strategies for making further progress, and examine other…

This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…

Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…

The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.

It is shown that the kinematic system describing planar non-steady motions of ideal fibre-reinforced fluids may be reduced to a single two-dimensional third-order partial differential equation in which time enters parametrically. A…

Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…

It is shown that mathematical physics differential equations have properties that allow describing processes such as the structures emergence, discrete transitions, quantum jumps. The peculiarity is that such properties are hidden. They do…

The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…