The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

Motivated by Poincar\'e's orbits going to infinity in the (restricted) three-body (see [26] and [6]), we investigate generic existence of heteroclinic-like a neighbourhood critical set $b$-contact form. This is done using singular counterpart [3] Etnyre--Ghrist's contact/Beltrami correspondence [9], genericity results concerning eigenfunctions Laplacian established Uhlenbeck [29]. Specifically,...

In this article, we present $GPW$-flatness property of acts over monoids, which is a generalization of principal weak flatness. We say that a right $S$-act $A_{S}$ is $GPW$-flat if for every $s in S$, there exists a natural number $n = n_ {(s, A_{S})} in mathbb{N}$ such that the functor $A_{S} otimes {}_{S}- $ preserves the embedding of the principal left ideal ${}_{S}(Ss^n)$ into ${}_{S}S$. We...

By the SYZ construction, a mirror pair (X,Xˇ) of complex torus X and partner Xˇ is described as special Lagrangian fibrations X→B Xˇ→B on same base space B. Then, by transform, we can construct simple projectively flat bundle from each affine multisection with unitary local system along it. However, there are ambiguities choices transition functions it, this causes difficulties when try to func...

We study the axial transition form factors $G_A^{B\to B'}(Q^2)$ as well charges $g_A^{B\to B'}$ of octet baryons in perturbative chiral quark model~(PCQM) with including both ground and excited states intermediate propagators. The PCQM results on are found good agreement existing experimental data lattice-QCD values. figures out that for all transitions behave dipolelike form, which is dominant...

We perform global fits within Standard Model Effective Field Theory (SMEFT) combining top-quark pair production processes and decay with $b\rightarrow s$ flavor changing neutral current transitions $Z \to b \bar b$ in three stages: using existing data from the LHC $B$-factories, projections for HL-LHC Belle II, studying additional new physics impact a future lepton collider. The latter is ideal...