The aim of this paper is to study in details the regular holonomic $$D-$$ module introduced Barlet (Math Z 302 $$n^03$$ : 1627–1655, 2022 arXiv:1911.09347 [math]) whose local solutions outside polar hyper-surface $$\{\Delta (\sigma ).\sigma _k = 0 \}$$ are given by system generated power $$\lambda $$ branches multivalued function which root universal degree k equation $$z^k + \sum _{h=1}^k (-1)...

six sigma methodology is one of the most famous effective problem solving approaches that helps organizations to achieve their goals. despite the variety of its positive advantage, most companies have failed to implement six sigma successfully. the reason for this includes lack of the organizations attention to success or failure factors when implement six sigma projects. hence, while performin...

An ideal I on a cardinal κ is called rigid if all automorphisms of P (κ)/I are trivial. An ideal is called μ-minimal if whenever G ⊆ P (κ)/I is generic and X ∈ P (μ)V [G] \ V , it follows that V [X] = V [G]. We prove that the existence of a rigid saturated μ-minimal ideal on μ+, where μ is a regular cardinal, is consistent relative to the existence of large cardinals. The existence of such an i...

we investigate the problem of the existence of a frame forright ideals of a c*-algebra a, without the use of the kasparov stabilizationtheorem. we show that this property can not characterize a as a c*-algebraof compact operators.

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

We show that the category of finite-length generalized modules for singlet vertex algebra M(p), p∈Z>1, is equal to OM(p) C1-cofinite M(p)-modules, and this admits algebraic braided tensor structure Huang-Lepowsky-Zhang. Since includes uncountably many typical which are simple M(p)-module structures on Heisenberg Fock modules, our results substantially extend previous work categories atypical M(...

We prove that in a 2-Calabi-Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen-Macaulay modules is 3-CalabiYau. We deduce in particular that cluster-tilted algebras are Gorenstein of dimension at most one, and hereditary if they are of finite globa...

In this paper we present a new type of simple, pneumatically actuated, soft modular robotic system that can reproduce fundamental cell behaviors observed during morphogenesis; the initial shaping stage of the living embryo. The fabrication method uses soft lithography for producing composite elastomeric hollow cubes and permanent magnets as passive docking mechanism. Actuation is achieved by co...

Amyloid curli fibers and cellulose are extracellular matrix components produced in the stationary phase top layer of E. coli macrocolonies, which confer physical protection, strong cohesion, elasticity, and wrinkled morphology to these biofilms. Curli and cellulose synthesis is controlled by a three-level transcription factor (TF) cascade with the RpoS sigma subunit of RNA polymerase at the top...