A new method (by Kersten, Krasil'shchik and Verbovetsky), based on the theory of differential coverings, allows to relate a system PDEs with operator in such way that maps conserved quantities into symmetries PDEs. When applied quasilinear first-order Dubrovin–Novikov homogeneous Hamiltonian yields conditions have interesting projective geometric interpretations.

We introduce a kind of partial observability to the projective simulation (PS) learning method. It is done by adding belief projection operator and an parameter original framework efficiency PS model. I provide theoretical formulations, network representations, situated scenarios derived from invasion toy problem as starting point for some multi-agent models.

We consider a spin coherent states description of a general quantum spin system. It is shown that it is possible to use the spin-1/2 representation to study the general spin-J case. We identify the 1/2 spinor components as the homogeneous coordinates of the projective space associated to the complex variable that labels the coherent states and establish a relation between the two-component spin...

We consider the (projective) representations of the group of holomorphic automorphisms of a symmetric tube domain V ⊕ iΩ that are obtained by analytic continuation of the holomorphic discrete series. For a representation corresponding to a discrete point in the Wallach set, we find the decomposition under restriction to the identity component of GL(Ω). Using Riesz distributions, an explicit int...

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

While the question “how many CNOT gates are needed to simulate an arbitrary twoqubit operator” has been conclusively answered – three are necessary and sufficient – previous work on this topic assumes that one wants to simulate a given unitary operator up to global phase. However, in many practical cases additional degrees of freedom are allowed. For example, if the computation is to be followe...

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

In the 1960’s, Dwork developed a p-adic cohomology theory of de Rham type for varieties over finite fields, based on a trace formula for the action of a Frobenius operator on certain spaces of p-analytic functions. One can consider a purely algebraic analogue of Dwork’s theory for varieties over a field of characteristic zero and ask what is the connection between this theory and ordinary de Rh...

In this paper, we extend the definition of the Nathanson height from points in projective spaces over Fp to points in projective spaces over arbitrary finite fields. If [a0 : . . . : an] ∈ P(Fp), then the Nathanson height is hp([a0 : a1 : . . . : ad]) = min b∈Fp d ∑ i=0 H(bai) where H(ai) = |N(ai)|+p(deg(ai)−1) with N the field norm and |N(ai)| the element of {0, 1, . . . , p− 1} congruent to N...