Monopoly, syndicate, and shapley value: About some conjectures

Some Conjectures About Cyclotomic Integers

Some Conjectures about Integral Means Of

1. The problems. In this note we shall discuss some conjectural integral inequalities which are related to quasiconformal mappings, singular integrals, martingales and the calculus of variations.

Some Conjectures About Invariant Theory and their Applications

It turns out that various algebraic computations can be reduced to the same type of computations: one has to study the series of integrals ∫ K f(k)g(k) dk, where f, g are complex valued K-finite functions on a compact Lie group K. So it is tempting to state a general conjecture about the behavior of such integrals, and to investigate the consequences of the conjecture. Main conjecture: Let K be...

SOME CONJECTURES ABOUT INTEGRAL MEANS OF ∂f AND ∂f

Here we denote by Ẇ (C,C) denotes the “homogeneous” Sobolev space of complex valued locally integrable functions in the plane whose distributional first derivatives are in L on the plane. Integrals without specified variables are understood to be with respect to Lebesgue measure. Since ∂(f) = ∂f, Conjecture 1 is true if and only if (1.1) always holds when L(∂f, ∂f) in the integral is replaced b...

On Some Conjectures about Arithmetic Partial Differential Equations

In this paper, we study the arithmetic partial differential equations x′p = ax n and x ′ p = a. We solve a conjecture of Haukkanen, Merikoski, and Tossavainen (HMT, in short) about the number of solutions (conjectured to be finite) of the equation x ′ p = ax n and improve a theorem of HMT about finding the solutions of the same equation. Furthermore, we also improve another theorem of HMT about...