Intersection Property Research Articles

The Intersection Property of Annihilators of Both Modules and Maximal Submodules Belonging to the Same Module

During that article T stands for a commutative ring with identity and that S stands for a unitary module over T. The intersection property of annihilatoers of a module X on a ring T and a maximal submodule W of M has been reviewed under this article where he provide several examples that explain that the property. Add to this a number of equivalent statements about the intersection property have been demonstrated as well as the direct sum of module that realize that the characteristic has studied here we proved that the modules that achieve the intersection property are closed under the direct sum with a specific condition. In addition to all this, the relationship between the modules that achieve the above characteristics with other types of modules has been given.

Experimental and numerical investigation on nonlinear flow behaviour through three dimensional fracture intersections and fracture networks

Abstract Fluid flow tests were conducted on four kinds of fracture intersections, namely straight fracture intersection, buckling fracture intersection, crossing fracture intersection and furcating fracture intersection. Corresponding numerical simulations were performed by solving the Navier-Stokes equations. The resultant flow force perpendicular to fracture walls were derived. The results show that at high hydraulic gradients the increased normal resultant force perpendicular to fracture walls will change the original flow direction and consequently cause the formation of eddies which triggers flow nonlinearity. Greater buckling angle and smaller crossing angle would result in the onset of nonlinear flow at a higher critical hydraulic gradient for the cases of buckling and crossing fracture intersections. The critical hydraulic gradient for the case of furcating fracture intersection depends on the absolute angle between furcating flow and the original flow direction. Based on the analyses, three nonlinear models for coefficient B in the Forchheimer law corresponding to three cases of fracture intersections are proposed, which are related to the fracture intersection angle and hydraulic aperture. These models are further validated using flow experimental data from a real fracture network created in a rock specimen with the corresponding fracture model constructed using the computed tomography (CT) method.

Effective bounds on ampleness of cotangent bundles

We prove that a general complete intersection of dimension $n$, codimension $c$ and type $d_1, \dots, d_c$ in $\mathbb{P}^N$ has ample cotangent bundle if $c \geq 2n-2$ and the $d_i$'s are all greater than a bound that is $O(1)$ in $N$ and quadratic in $n$. This degree bound substantially improves the currently best-known super-exponential bound in $N$ by Deng, although our result does not address the case $n \leq c < 2n-2$.

Gendered translocal connectedness: Rural–urban migration, remittances, and social resilience in Thailand

AbstractRemittances play a central role in debates on migration and development as well as migration as adaptation to climate change. We seek to contribute to the growing body of literature that addresses the role of gender relations for remittance sending and usage. Based on multisited qualitative research on rural–urban migration in Thailand, we apply the concept of translocal social resilience to expound the multilocal and intersectional dimension of remittances and their impact on social resilience. Building on typical constellations of remittance transfer and usage, the paper accentuates how gender, generational relations, and the household's socio‐economic status shape remittance practices and their effects on social resilience across space. We can thus conclude that addressing intersecting socio‐spatial levels and axes of difference enhances the understanding of remittance potentials for resilience, which also enriches research that frames migration as a means of adaptation.

On obvious strategy-proofness and single-peakedness

We characterize the set of all obviously strategy-proof and onto social choice functions on the domain of single-peaked preferences. Since obvious strategy-proofness implies strategy-proofness, and the set of strategy-proof and onto social choice functions on this domain coincides with the class of generalized median voter schemes, we focus on this class. We identify a condition on generalized median voter schemes for which the following characterization holds. A generalized median voter scheme is obviously strategy-proof if and only if it satisfies the increasing intersection property. Our proof is constructive; for each generalized median voter scheme that satisfies the increasing intersection property we define an extensive game form that implements it in obviously dominant strategies.

Complete Intersection Hom Injective Dimension

We introduce and investigate a new injective version of the complete intersection dimension of Avramov, Gasharov, and Peeva. It is like the complete intersection injective dimension of Sahandi, Sharif, and Yassemi in that it is built using quasi-deformations. Ours is different, however, in that we use a Hom functor in place of a tensor product. We show that (a) this invariant characterizes the complete intersection property for local rings, (b) it fits between the classical injective dimension and the G-injective dimension of Enochs and Jenda, (c) it provides modules with Bass numbers that are bounded by polynomials, and (d) it improves a theorem of Peskine, Szpiro, and Roberts (Bass’ conjecture).

Properties of sets of subspaces with constant intersection dimension

<p style='text-indent:20px;'>A <inline-formula><tex-math id="M1">\begin{document}$ (k,k-t) $\end{document}</tex-math></inline-formula>-SCID (set of Subspaces with Constant Intersection Dimension) is a set of <inline-formula><tex-math id="M2">\begin{document}$ k $\end{document}</tex-math></inline-formula>-dimensional vector spaces that have pairwise intersections of dimension <inline-formula><tex-math id="M3">\begin{document}$ k-t $\end{document}</tex-math></inline-formula>. Let <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{C} = \{\pi_1,\ldots,\pi_n\} $\end{document}</tex-math></inline-formula> be a <inline-formula><tex-math id="M5">\begin{document}$ (k,k-t) $\end{document}</tex-math></inline-formula>-SCID. Define <inline-formula><tex-math id="M6">\begin{document}$ S: = \langle \pi_1, \ldots, \pi_n \rangle $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M7">\begin{document}$ I: = \langle \pi_i \cap \pi_j \mid 1 \leq i &lt; j \leq n \rangle $\end{document}</tex-math></inline-formula>. We establish several upper bounds for <inline-formula><tex-math id="M8">\begin{document}$ \dim S + \dim I $\end{document}</tex-math></inline-formula> in different situations. We give a spectrum result under certain conditions for <inline-formula><tex-math id="M9">\begin{document}$ n $\end{document}</tex-math></inline-formula>, giving examples of <inline-formula><tex-math id="M10">\begin{document}$ (k,k-t) $\end{document}</tex-math></inline-formula>-SCIDs reaching a large interval of values for <inline-formula><tex-math id="M11">\begin{document}$ \dim S + \dim I $\end{document}</tex-math></inline-formula>.

An intersection property gluing on weak outwardly hyperconvex spaces

In this paper we have generalizeda certain and adequate circumstance nether which gluings of H- metric spaces on weak outwardly hyperconvex subsets are hyperconvex. Our results are the extension of the results obtained by B. Miesch and M. Pavon (J. Topo. Anal., volume 9, issue 3, September 2017), to the case of intersection property for gluing on weak outwardly hyperconvex subsets gives rise to H- spaces

Classification theorem for strong triangle blocking arrangements

A strong triangle blocking arrangement is a geometric arrangement of some line segments in a triangle with certain intersection properties. It turns out that they are closely related to blocking sets. We prove a classification theorem for strong triangle blocking arrangements. As an application, we obtain a new proof of the result of Ackerman, Buchin, Knauer, Pinchasi and Rote which says that n points in general position cannot be blocked by n ? 1 points, unless n = 2, 4. We also conjecture an extremal variant of the blocking points problem.

Intersections of Projections and Slicing Theorems for the Isotropic Grassmannian and the Heisenberg group

AbstractThis paper studies the Hausdorff dimension of the intersection of isotropic projections of subsets of ℝ2n, as well as dimension of intersections of sets with isotropic planes. It is shown that ifAandBare Borel subsets of ℝ2nof dimension greater than m, then for a positive measure set of isotropic m-planes, the intersection of the images ofAandBunder orthogonal projections onto these planes have positive Hausdorffm-measure. In addition, ifAis a measurable set of Hausdorff dimension greater thanm, then there is a setB⊂ ℝ2nwith dimB⩽msuch that for allx∈ ℝ2n\Bthere is a positive measure set of isotropic m-planes for which the translate byxof the orthogonal complement of each such plane, intersectsAon a set of dimension dimA – m. These results are then applied to obtain analogous results on thenthHeisenberg group.

Lagrange multiplier characterizations of constrained best approximation with nonsmooth nonconvex constraints

In this paper, we consider the constraint set K := {x ? Rn : gj(x)? 0,? j = 1,2,...,m} of inequalities with nonsmooth nonconvex constraint functions gj : Rn ? R (j = 1,2,...,m).We show that under Abadie?s constraint qualification the ?perturbation property? of the best approximation to any x in Rn from a convex set ?K := C ? K is characterized by the strong conical hull intersection property (strong CHIP) of C and K, where C is an arbitrary non-empty closed convex subset of Rn: By using the idea of tangential subdifferential and a non-smooth version of Abadie?s constraint qualification, we do this by first proving a dual cone characterization of the constraint set K. Moreover, we present sufficient conditions for which the strong CHIP property holds. In particular, when the set ?K is closed and convex, we show that the Lagrange multiplier characterizations of constrained best approximation holds under a non-smooth version of Abadie?s constraint qualification. The obtained results extend many corresponding results in the context of constrained best approximation. Several examples are provided to clarify the results.

Numerical semigroup algebras

We study a numerical semigroup ring as an algebra over another numerical semigroup ring. The construction of numerical semigroup rings by gluings finds its place in the relative setting. Cohen-Macaulay, Gorenstein and complete intersection properties of the algebra are interpreted explicitly in terms of Apéry monomials to emphasize the computational aspect.

Toward a General Direct Product Testing Theorem

The direct product encoding of a string a ∈ { 0,1} n on an underlying domain V ⊆ ( k [ n ] ) is a function DP V ( a ) that gets as input a set S ∈ V and outputs a restricted to S . In the direct product testing problem, we are given a function F : V → { 0,1} k , and our goal is to test whether F is close to a direct product encoding—that is, whether there exists some a ∈ { 0,1} n such that on most sets S , we have F ( S )=DP V ( a )( S ). A natural test is as follows: select a pair ( S , S ′)∈ V according to some underlying distribution over V × V , query F on this pair, and check for consistency on their intersection. Note that the preceding distribution may be viewed as a weighted graph over the vertex set V and is referred to as a test graph. The testability of direct products was studied over various domains and test graphs: Dinur and Steurer (CCC’14) analyzed it when V equals the k -th slice of the Boolean hypercube and the test graph is a member of the Johnson graph family. Dinur and Kaufman (FOCS’17) analyzed it for the case where V is the set of faces of a Ramanujan complex, where in this case ∣ V ∣= O k ( n ). In this article, we study the testability of direct products in a general setting, addressing the question: what properties of the domain and the test graph allow one to prove a direct product testing theorem? Towards this goal, we introduce the notion of coordinate expansion of a test graph. Roughly speaking, a test graph is a coordinate expander if it has global and local expansion, and has certain nice intersection properties on sampling. We show that whenever the test graph has coordinate expansion, it admits a direct product testing theorem. Additionally, for every k and n , we provide a direct product domain V ⊆ ( k n ) of size n , called the sliding window domain , for which we prove direct product testability.

Amenable and Locally Amenable Algebraic Frames

We say a prime element of an algebraic frame is amenable if it comparable to every compact element. If every prime element of an algebraic frame L is amenable, we say L is an amenable frame. If the localization of L at every prime element is amenable, we say L is locally amenable. These concepts are motivated by notions of divided and locally divided commutative rings. We show that an algebraic frame is (i) amenable precisely when its prime elements form a chain, and (ii) locally amenable precisely when its prime elements form a tree. Given any prime element p of L, we construct a certain pullback in the category of algebraic frames with the finite intersection property on compact elements, and characterize (in terms of the localization Lp and the quotient ↑p of L) when this pullback is amenable and when it is locally amenable.

Existence of periodically invariant tori on resonant surfaces for twist mappings

In this paper we will prove the existence of periodically invariant tori of twist mappings on resonant surfaces under the low dimensional intersection property.

On one-point intersection property for self-similar fractals

This was a long-standing question since 90s whether one-point intersection property for a self-similar set implies open set condition (OSC). We answer this question negatively. We give an example of a totally disconnected self-similar set which does not have OSC and has minimal overlap of its pieces, that is, all intersections of its pieces are empty except only one, which is a single point.

Complete Intersection Monomial Curves and the Cohen—Macaulayness of Their Tangent Cones

Let C(n) be a complete intersection monomial curve in the 4-dimensional affine space. In this paper we study the complete intersection property of the monomial curve C(n + wv), where w &gt; 0 is an integer and v ∈ ℕ4. In addition, we investigate the Cohen–Macaulayness of the tangent cone of C(n + wv).

Results on fuzzy supra soft topological spaces

The concept of fuzzy supra soft topological spaces was presented by Abd El-latif [2]. He derived their fundamental properties in detail. In this paper, we investigated more properties to the concept of fss-compact spaces based on the finite intersection property and the fuzzy supra irresolute open soft functions and got some new important results. The concept of fssalmost compact spaces is introduced as a generalization to that’s in [2]. Furthermore, many of its interested properties are provided. We introduced the notion of fss-generalized closed sets and use it to introduce another type of compactness, named fss-generalized compactness. Also, we introduced some fundamental definitions and theorems of these concepts.

Bowditch’s Q-conditions and Minsky’s primitive stability

For the action of the outer automorphism group of the rank two free group on the corresponding variety of P S L ( 2 , C ) \mathsf {PSL}(2,\mathbb {C}) characters, two domains of discontinuity have been known to exist that are strictly larger than the set of Schottky characters. One was introduced by Bowditch in 1998 (followed by Tan, Wong, and Zhang in 2008) and the other by Minsky in 2013. We prove that these two domains are equal. We then show that they are contained in the set of characters having what we call the bounded intersection property.

Generalized SSP-modules

We say an R-module M has the generalized summand sum property (GSSP), if the sum of any two direct summands is isomorphic to a direct summand of M. This is dual notion to the generalized summand intersection property of modules, and also the class of modules having the GSSP is a proper generalization of the class of modules having the SSP. In this note, the characterization of this property over rings and modules is investigated.