Given a Laurent polynomial over flat $$\mathbf {Z}$$ -algebra, Vlasenko defines formal group law. We identify this law with coordinate system of functor. When the “Hasse–Witt matrix” is invertible, matrix by taking certain $$p$$ -adic limit. show that Frobenius Dieudonné module modulo .

Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...

Traffic travel mode identification and classification are crucial for the development of intelligent transportation systems (ITSs). At present, scholars have investigated motorized nonmotorized traffic in various road environments; however, walking bicycle modes has been largely ignored. Therefore, this paper, we investigate propose a new low-cost system, known as Wi-Fi (Wi-CL) system that uses...

We introduce a dense and dilute loop model on causal dynamical triangulations. Both models are characterised by geometric coupling constant $g$ parameter $\alpha$ in such way that the purely triangulation is recovered for $\alpha=1$. show can be mapped to solvable planar tree model, whose partition function we compute explicitly use determine critical behaviour of model. The likewise model; how...

In this paper, we principally explore flat modules over a commutative ring with identity. We do this in relation to projective and injective modules with the help of derived functors like Tor and Ext. We also consider an extension of the property of flatness and induce analogies with the “special cases” occurring in flat modules. We obtain some results on flatness in the context of a noetherian...

Under the assumption that a residually finite-dimensional Hopf algebra H has an Artinian ring of fractions, it is proved flat module over any right coideal subalgebra satisfying polynomial identity and faithfully subalgebra. As consequence we find large class algebras which are all subalgebras subalgebras.

When G is a complex reductive algebraic group and G/K is a reductive symmetric space, the decomposition of C[G/K] as a K-module was obtained (in a non-constructive way) by R. Richardson, generalizing the celebrated result of Kostant-Rallis for the linearized problem (the harmonic decomposition of the isotropy representation). To obtain a constructive version of Richardson’s results, this paper ...