I outline some nonperturbative relativistic effects that arise from gravitational corrections to the Boltzmann equations. These may be important for the study of CMB temperature anisotropies, particularly their interpretation. These terms are not included in the canonical treatment as they arise from the exact equations. Here a weakly nonlinear investigation of these effects is defined and inve...

The notion of the sub-exact sequence is generalization exact in algebra especially on a module. A module over ring R vector space field F. Refers to special F when we have complete inner product space, it called Hilbert space. if every Cauchy converges. Now, introduce which can later be useful statistics. This paper aims investigate properties and their relation direct summand As result, get tw...

The first collection of a macrofungal agaric species, with morphological features similar to already described Anamika species, has been found in association with animal bones in north Queensland, Australia. This species also shares features with several, commonly occurring and previously described Australian Hebeloma species. An integrated morphological and molecular study has resulted in the ...

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...

We associate two modules, the \(G\)-parking critical module and toppling module, to an undirected connected graph \(G\). The are canonical modules (with suitable twists) of quotient rings well-studied function ideal ideal, respectively. For each we establish a Tutte-like short exact sequence relating associated \(G\), edge contraction \(G/e\) deletion \(G \setminus e\) (\(e\) is non-bridge). ob...