We give an integrability criterion for a projective limit of Banach distributions on Fr\'echet manifold which is manifolds. This leads to result involutive bundles sequence can be seen as version Frobenius Theorem in setting. As consequence, we obtain the third Lie theorem Fr\'echet-Lie group submersive groups. also application prolongations algebroid.

 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. ‎$R$...

We address the problem of the continuum limit for a system of Hausdorff lattices (namely lattices of isolated points) approximating a topological space M . The correct framework is that of projective systems. The projective limit is a universal space from which M can be recovered as a quotient. We dualize the construction to approximate the algebra C(M) of continuous functions onM . In a compan...

Two types of tests are available for studying personality. These are the paper-pencil tests and the projective tests. Projective techniques which reveal the subject's personality through his treatment of the test material are generally more valid and more revealing than the paper-pencil tests which require the underlining of words or the answering of "Yes" or "No" to a list of questions. This i...

We deene a new invariant for symbolic Z 2-actions, the projective fundamental group. This invariant is the limit of an inverse system of groups, each of which is the fundamental group of a space associated with the Z 2-action. The limit group measures a kind of long-distance order that is manifested along loops in the plane, and roughly speaking bears the same relation to the mixing properties ...

A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spaces, describing the basic process by which one homogeneous geometry may transf...

Let V be a crystalline p-adic representation of the absolute Galois group GK of an finite unramified extension K of Qp and T a lattice of V stable by GK . We prove the following result : Let FilV be the maximal sub-representation of V with Hodge-Tate weights strictly positive and FilT = T ∩ FilV . Then, the projective limit of the H g (K(μpn), T ) is equal up to torsion to the projective limit ...

The effects of parental divorce on the levels of aggression, hostility, and anxiety in children, as measured by the Rorschach test, together with the type and direction of aggression, as measured by the Rosenzweig Picture-Frustration (P-F) Study, were studied. The Rorschach and the Rosenzweig P-F study were administered to a nonclinical sample of 108 Swedish children ranging in age from 10 to 1...

‎Let $C$ be a semidualizing module‎. ‎We first investigate the properties of‎ ‎finitely generated $G_C$-projective modules‎. ‎Then‎, ‎relative to $C$‎, ‎we introduce and study the rings over which‎ ‎every submodule of a projective (flat) module is $G_C$-projective (flat)‎, ‎which we call $C$-Gorenstein (semi)hereditary rings‎. ‎It is proved that every $C$-Gorenstein hereditary ring is both cohe...