Connectedness Result Research Articles

Who are the influencers in the commodity markets during COVID-19?

Price volatility caused by the pandemic has caused serious concern in global commodity markets. The quantile connectedness method is used to investigate the net receiving/transmitting role of energy, shipping, metals and commodity markets. The results show dynamic quantile connectedness in the short run in the pre-pandemic. The net directional connectedness result explores that oil prices and commodity markets roles change between transmitting to receiving in the medium to upper quantiles. However, the receiving role is found for both the shipping industry and metals markets in upper quantiles. Similarly, the results of the dynamic connectedness during the COVID-19 display strong connectedness for higher volatility. The net directional connectedness outcomes show that oil prices, shipping and commodity markets have a transmitting/receiving role in the higher quantiles. The net transmitting period is seen more actively than the receiving one during the COVID-19. The policymakers are in need of planning policies while considering the heterogeneous impact of the international oil market on these commodity markets.

Connectedness of Kisin varieties associated to absolutely irreducible Galois representations

AbstractWe consider the Kisin variety associated to ann-dimensional absolutely irreducible modpGalois representationρ¯{\bar{\rho}}of ap-adic fieldKtogether with a cocharacter μ. Kisin conjectured that the Kisin variety is connected in this case. We show that Kisin’s conjecture holds ifKis totally ramified withn=3{n=3}or μ is of a very particular form. As an application, we get a connectedness result for the deformation ring associated toρ¯{\bar{\rho}}of given Hodge–Tate weights. We also give counterexamples to show Kisin’s conjecture does not hold in general.

A note on the ADHM description of Quot schemes of points on affine spaces

We give an Atiyah–Drinfel’d–Hitchin–Manin (ADHM) description of the Quot scheme of points [Formula: see text] of length [Formula: see text] and rank [Formula: see text] on affine spaces [Formula: see text] which naturally extends both Baranovsky’s representation of the punctual Quot scheme on a smooth surface and the Hilbert scheme of points on affine spaces [Formula: see text] described by the first author and M. Jardim. Using results on the variety of commuting matrices, and combining them with our construction, we prove new properties concerning irreducibility and reducedness of [Formula: see text] and its punctual version [Formula: see text] where [Formula: see text] is a fixed point on a smooth affine variety [Formula: see text]. In this last case, we also study a connectedness result, for some special cases of higher [Formula: see text] and [Formula: see text].

On the basis pair graphs of signed-graphic matroids

There is a long-standing conjecture being open for decades regarding the connectedness of the basis pair graphs of matroids. In this work we provide results for the class of signed-graphic matroids and their duals. Specifically, signed-graphic matroids having no particular matroids as minors are proven to have connected basis pair graphs. The main obstacles in proving the aforementioned connectedness result for the whole class of signed-graphic matroids have been identified and approaches on overcoming them are proposed.

Risk Connectedness Heterogeneity in the Cryptocurrency Markets

This paper examines the risk connectedness across the seven cryptocurrencies, Bitcoin, Ethereum, Ripple, Litecoin, Stellar, Monero and Dash, who admit large capitalizations in the cryptocurrency market. The data sample is from August 7, 2015 to February 15, 2020. We apply the CAViaR model to measure the return risks of the cryptocurrencies, showing their similar risk tendencies with volatility clusterings during the beginning of 2017 and the end of 2018. The net pairwise spillover index developed by Diebold and Yilmaz (2012) is use as the measure for the risk connectedness among the cryptocurrencies. We find that the risk spillover directions are highly correlative with the capitalizations of the cryptocurrencies. The cryptocurrencies with small capitalizations transmit risks to those with large cryptocurrencies. In the risk downward tendency, the risk spillover levels among the cryptocurrencies are stronger than that in the risk upward tendency, while the spillover directions keep the same in both risk tendencies, except the cryptocurrency Monero, which may be due to the trading volume difference from the others. We use the generalized forecast error variance decomposition for the spillover index and explore the risk connectedness across the cryptocurrencies in differen time frequencies, including the short term (0-4 days), medium term (4-30 days) and long term (30-300 days) frequency. The risk spillovers in the short term frequency can be neglected, which implies the delay effects of risk spillovers. The risk spillovers in medium term frequency are mostly stronger than that in long term frequency. The dynamic connectedness result shows the risk spillover mean in the long term frequency is larger than that in the medium term frequency. An inverse result holds for the risk spillover range. The risk spillover fluctuations in the long and medium term frequency admit the coincident comparison for spillover levels in these two frequencies. The findings in this paper provide suggestions for regulators controlling the market stability and investors generating investment strategies.

Generalization of a connectedness result to cohomologically complete intersections

It is a well-known result from Hartshorne that, in projective space over a field, every set-theoretical complete intersection of positive dimension is connected in codimension one. Another important connectedness result (also from Hartshorne) is that a local ring with disconnected punctured spectrum has depth at most 1 1 . The two results are related; Hartshorne calls the latter “the keystone to the proof” of the former. In this short note we show how the latter result generalizes smoothly from set-theoretical to cohomologically complete intersections, i.e., to ideals for which there is in terms of local cohomology no obstruction to be a complete intersection. The proof is based on the fact that for cohomologically complete intersections over a complete local ring, the endomorphism ring of the (only) local cohomology module is the ring itself and hence is indecomposable as a module.

Partially ample subvarieties of projective varieties

The goal of this article is to define partially ample subvarieties of projective varieties, generalizing Ottem’s work on ample subvarieties, and also to show their ubiquity. As an application, we obtain a connectedness result for pre-images of subvarieties by morphisms, reminiscent to a problem posed by Fulton–Hansen in the late 1970s. Similar criteria are not available in the literature.

Algebraic monodromy groups of vector bundles on p-adic curves

C. Deninger and A. Werner (2005, 2007) developed a partial p-adic analogue of the classical Narasimhan-Seshadri correspondence between vector bundles and representations of the fundamental group. We use this theory to prove a connectedness result for the algebraic monodromy groups of vector bundles on a smooth projective curve. We apply this result to the restriction of certain stable vector bundles on the projective space and compute the Tannaka dual groups in this case.

A connectedness result for commuting diffeomorphisms of the interval

AbstractLet 𝒟r+[0,1], r≥1, denote the group of orientation-preserving 𝒞r diffeomorphisms of [0,1]. We show that any two representations of ℤ2 in 𝒟r+[0,1], r≥2, are connected by a continuous path of representations of ℤ2 in 𝒟1+[0,1] . We derive this result from the classical works by G. Szekeres and N. Kopell on the 𝒞1 centralizers of the diffeomorphisms of [0,1) that are at least 𝒞2 and fix only 0 .

A Connectedness Theorem for Products of Weighted Projective Spaces

We prove a connectedness result for products of weighted projective spaces.

A connectedness result in positive characteristic

Let (R,m) be a complete local ring of dimension at least two, which contains a separably closed coefficient field of positive characteristic. Using a vanishing theorem of Peskine-Szpiro, Lyubeznik proved that the local cohomology module H 1 m (R) is Frobenius-torsion if and only if the punctured spectrum of R is connected in the Zariski topology. We give a simple proof of this theorem and, more generally, a formula for the number of connected components in terms of the Frobenius action on H 1 m (R).

Existence of Solutions to u″ + u + g(t, u, u′) = p(t), u(0) = u(π) = 0

Existence and multiplicity results for the boundary value problem[formula]are presented. The proofs are based on the alternative method, a connectedness result, the contraction mapping principle, and a detailed analysis of the bifurcation equation utilizing, e.g., a generalization of the mean value theorem for integrals. We shall obtain results with g bounded or unbounded, having finite limits at ±∞ or without limits, thus extending some recent results in the literature. The proofs offer a constructive way to find the bounds for p̄ and to find numerically the number of solutions and the approximative solutions.

Coherent Sheaves on P1: their Families and their Deformations Related to a Behavioral Approach to Singular Systems

Recently, Lomadze, Ravi, Rosenthal and Schumacher gave a natural and geometrically meaningful one-to-one correspondence between abstract linar behaviors and coherent sheaves on P1. Motivated by their result, here we give a complete picture of the deformation theory of coherent sheaves on P1. We use our results to study deformations over the field R obtaining a connectedness result for the real locus of the algebraic parameter spaces.

Contractibility and Connectedness of Efficient Point Sets

Using the technique of space theory and set-valued analysis, we establish contractibility results for efficient point sets in a locally convex space and a path connectedness result for a positive proper efficient point set in a reflexive space. We also prove a connectedness result for a positive proper efficient point set in a locally convex space; as an application, we give a connectedness result for an efficient solution set in a locally convex space.

Connectedness of efficient solutions in multiple criteria combinatorial optimization

In multiple criteria optimization an important research topic is the topological structure of the set X e of efficient solutions. Of major interest is the connectedness of X e , since it would allow the determination of Xe without considering non-efficient solutions in the process. We review general results on the subject, including the connectedness result for efficient solutions in multiple criteria linear programming. This result can be used to derive a definition of connectedness for discrete optimization problems. We present a counterexample to a previously stated result in this area, namely that the set of efficient solutions of the shortest path problem is connected. We will also show that connectedness does not hold for another important problem in discrete multiple criteria optimization: the spanning tree problem.

The connectedness of symmetric and skew-symmetric degeneracy loci: even ranks

A degeneracy locus is the set of points where a vector-bundle map has rank at most a given integer. Such a set is symmetric or skew-symmetric according as whether the vector-bundle map is symmetric or skew-symmetric. We prove a connectedness result, first conjectured by Fulton and Lazarsfeld, for skew-symmetric degeneracy loci and for symmetric degeneracy loci of even ranks.

Properly efficient and efficient solutions for vector maximization problems in euclidean space

Recently Benson proposed a definition for extending Geoffrion's concept of proper efficiency to the vector maximization problem in which the domination cone K is any nontrivial, closed convex cone. We give an equivalent definition of his notion of proper efficiency. Our definition, by means of perturbation of the cone K, seems to offer another justification of Benson's choice above Borwein's extension of Geoffrion's concept. Our result enables one to prove some other theorems concerning properly efficient and efficient points. Among these is a connectedness result.

A Kneser theorem for Volterra integral equations

A connectedness result is obtained for the space of solutions of any one of a class of Volterra integral equations.