In the last four decades there has been enormous progress in Shape from Shading (SfS) with respect to both modelling and numerics. In particular approaches based on advanced model assumptions such as perspective cameras and non-Lambertian surfaces have become very popular. However, regarding the positioning of the light source, almost all recent approaches still follow the simplest geometric co...

In this note we define geometric classical r-matrices and quantum R-matrices, and show how any geometric classical r-matrix can be quantized to a geometric quantum R-matrix. This is one of the simplest nontrivial examples of quantization of solutions of the classical Yang-Baxter equation, which can be explicitly computed.

Abstract: A brief history and a mathematical description of the dynamic projection operators technique is presented. An example of the general Cauchy problem for evolution equations in 1+1 dimensions is studied in detail. A boundary regime propagation is formulated in terms of operators and illustrated by the simplest one-dimensional diffusion equation. The problem of temperature waves is discu...

TheWDVV equations of associativity arising in twodimensional topological field theory can be represented, in the simplest nontrivial case, by a single third order equation of the MongeAmpère type. By investigating its Lie point symmetries, we reduce it to various nonlinear ordinary differential equations, and we obtain several new explicit solutions.

Abstract. A white noise quantum stochastic calculus is developped using classical measure theory as mathematical tool. Wick’s and Ito’s theorems have been established. The simplest quantum stochastic differential equation has been solved, unicity and the conditions for unitarity have been proven. The Hamiltonian of the associated one parameter strongly continuous group has been calculated expli...

Complex multiplication in its simplest form is a geometric tiling property. In its advanced form it is a unifying motivation of classical mathematics from elliptic integrals to number theory; and it is still of active interest. This interrelation is explored in an introductory expository fashion with emphasis on a central historical problem, the modular equation between j(z) and j(2z).

INTRODUCTION Every lexicographer knows that the meaning of a word is time dependent, and, in favour of the argument that it is also dependent on latitude and longitude, the perverse amonst us would cite Oscar Wilde's dictum, "England and America are two countries separated by a common language". Certainly the word radical has changed its meaning for chemits who originally thought of it as part ...

We explain some essential aspects of the simplest Eisenstein series for SL2(Z) on the upper half-plane H. There are many different proofs of meromorphic continuation and functional equation of the simplest Eisenstein series for Γ = SL2(Z). We will follow [Godement 1966a] rewriting of a Poisson summation argument that appeared in [Rankin 1939], if not earlier. This argument is the most elementar...

The logic I is the sentential logic defined in the language with just implication → by the axiom of reflexivity or identity “φ→ φ” and the rule of Modus Ponens “from φ and φ→ ψ to infer ψ”. The theorems of this logic are exactly all formulas of the form φ→ φ. I argue that this is the simplest protoalgebraic logic, and that in it every set of assumptions encodes in itself not only all its conseq...