Equivalent Characterizations Research Articles

Characterizations of vanishing Campanato classes related to Schrödinger operators via fractional semigroups on stratified groups

Let be a Schrödinger operator on stratified Lie groups, where is the sub‐Laplacian on and V belongs to the reverse Hölder class. In this paper, we introduce a new Campanato‐type space of vanishing mean oscillation associated with L. By Carleson measures related to fractional heat semigroups, we establish an equivalent characterization of . As an application, we prove that the dual of is , where is the completeness of .

Stability of heat kernel estimates for symmetric non-local Dirichlet forms

In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, we establish stability of heat kernel estimates for α \alpha -stable-like processes even with α ≥ 2 \alpha \ge 2 when the underlying spaces have walk dimensions larger than 2 2 , which has been one of the major open problems in this area.

Equivalent Characterization on Besov Space

In this paper, we give an equivalent characterization of the Besov space. This reveals the equivalent relation between the mixed derivative norm and single-variable norm. Fourier multiplier, real interpolation, and Littlewood-Paley decomposition are applied.

Handling inconsistency in partially preordered ontologies: the Elect method

Abstract We focus on the problem of handling inconsistency in lightweight ontologies. We assume that the terminological knowledge base (TBox) is specified in DL-Lite and that the set of assertional facts (ABox) is partially preordered and may be inconsistent with respect to the TBox. One of the main contributions of this paper is the provision of an efficient and safe method, called Elect, to restore the consistency of the ABox with respect to the TBox. In the case where the assertional base is flat (i.e. no priorities are associated with the ABox) or totally preordered, we show that our method collapses with the well-known intersection ABox repair semantics and the non-defeated semantics, respectively. The semantic justification of the Elect method is obtained by first viewing a partially preordered ABox as a family of totally preordered ABoxes and then applying non-defeated inference to each of the totally preordered ABoxes. We introduce the notion of elected assertions which allows us to provide an equivalent characterization of the Elect method without explicitly generating all the totally preordered ABoxes. We show that computing the set of elected assertions is done in polynomial time with respect to the size of the ABox. The second part of the paper discusses how to go beyond the Elect method. In particular, we discuss to what extent the Elect method can be generalized to description logics that are more expressive than DL-Lite.

An aggregate gradation detection method based on multi-view information fusion

In this study, the morphologies of the aggregate in multiple views were analysed during the falling of particles to calculate aggregate gradation. Four types of characterisation parameters were selected to extract the multi-view information of aggregate particles in five views. Based on the multi-view information, the aggregate particles were classified using principal component analysis and a probabilistic neural network. An aggregate equivalent volume characterisation method was formulated to calculate the aggregate mass, whereby the aggregate volume was converted into the aggregate mass by the least-squares method. The experimental results show that the proposed aggregate sieving method can effectively realise the gradation classification of aggregates. Considering the product of the maximum area and the minimum equivalent Feret ellipse minor axis as the equivalent volume, the calculated aggregate mass yielded a good correlation with the actual aggregate mass. Compared with single-view information, multi-view information can improve the accuracy and repeatability of gradation calculations. The use of multi-view information to calculate aggregate gradation can reduce manpower and improve detection efficiency, which is important for applications in the construction industry.

IMAT: The Iterative Medial Axis Transform

AbstractWe present the iterative medial axis transform (IMAT), an iterative descent method that constructs a medial axis transform (MAT) for a sparse, noisy, oriented point cloud sampled from an object's boundary. We first establish the equivalence between the traditional definition of the MAT of an object, i.e., the set of centres and corresponding radii of all balls maximally inscribed inside the object, with an alternative characterization matching the boundary enclosing the union of the balls with the object boundary. Based on this boundary equivalence characterization, a new MAT algorithm is proposed, in which an error function that reflects the difference between the two boundaries is minimized while restricting the number of balls to within some a priori specified upper limit. An iterative descent method with guaranteed local convergence is developed for the minimization that is also amenable to parallelization. Both quantitative and qualitative analyses of diverse 2D and 3D objects demonstrate the noise robustness, shape fidelity, and representation efficiency of the resulting MAT.

Comparing the Roller and B(X) boundaries of CAT(0) cube complexes

The Roller boundary is a well-known compactification of a CAT(0) cube complex X. When X is locally finite, essential, irreducible, non-Euclidean and admits a cocompact action by a group G, Nevo—Sageev show that a subset, B(X), of the Roller boundary is the realization of the Poisson boundary and that the action of G on B(X) is minimal and strongly proximal. Additionally, these authors show B(X) satisfies many other desirable dynamical and topological properties. In this article we give several equivalent characterizations for when B(X) is equal to the entire Roller boundary. As an application we show, under mild hypotheses, that if X is also 2-dimensional then X is G-equivariantly quasi-isometric to a CAT(0) cube complex X′ whose Roller boundary is equal to B(X′). Additionally, we use our characterization to show that the usual CAT(0) cube complex for which an infinite right-angled Coxeter/Artin group acts on geometrically has Roller boundary equal to B(X), as long as the corresponding group does not decompose as a direct product.

Measure Complexity and Rigid Systems

In this paper we introduce two metrics: the max metric dn,q and the mean metric $${\bar d_{n,q}}$$ . We give an equivalent characterization of rigid measure preserving systems by the two metrics. It turns out that an invariant measure μ on a topological dynamical system (X, T) has bounded complexity with respect to dn,q if and only if μ has bounded complexity with respect to $${\bar d_{n,q}}$$ if and only if (X, $${\cal B}x$$ , μ, T) is rigid. We also obtain computation formulas of the measure-theoretic entropy of an ergodic measure preserving system (resp. the topological entropy of a topological dynamical system) by the two metrics dn,q and $${\bar d_{n,q}}$$ .

Characterizations of Product Hardy Spaces in Bessel Setting

In this paper, we work in the setting of Bessel operators and Bessel Laplace equations studied by Weinstein, Huber, and the harmonic function theory in this setting introduced by Muckenhoupt–Stein, especially the generalised Cauchy–Riemann equations and the conjugate harmonic functions. We provide the equivalent characterizations of product Hardy spaces associated with Bessel operators in terms of the Bessel Riesz transforms, non-tangential and radial maximal functions defined via Poisson and heat semigroups, based on the atomic decomposition, the generalised Cauchy–Riemann equations, the extension of Merryfield’s result which connects the product non-tangential maximal function and area function, and on the grand maximal function technique which connects the product non-tangential and radial maximal function. We then obtain directly the decomposition of the product BMO space associated with Bessel operators.

Snow Ensemble Uncertainty Project (SEUP): quantification of snow water equivalent uncertainty across North America via ensemble land surface modeling

Abstract. The Snow Ensemble Uncertainty Project (SEUP) is an effort to establish a baseline characterization of snow water equivalent (SWE) uncertainty across North America with the goal of informing global snow observational needs. An ensemble-based modeling approach, encompassing a suite of current operational models is used to assess the uncertainty in SWE and total snow storage (SWS) estimation over North America during the 2009–2017 period. The highest modeled SWE uncertainty is observed in mountainous regions, likely due to the relatively deep snow, forcing uncertainties, and variability between the different models in resolving the snow processes over complex terrain. This highlights a need for high-resolution observations in mountains to capture the high spatial SWE variability. The greatest SWS is found in Tundra regions where, even though the spatiotemporal variability in modeled SWE is low, there is considerable uncertainty in the SWS estimates due to the large areal extent over which those estimates are spread. This highlights the need for high accuracy in snow estimations across the Tundra. In midlatitude boreal forests, large uncertainties in both SWE and SWS indicate that vegetation–snow impacts are a critical area where focused improvements to modeled snow estimation efforts need to be made. Finally, the SEUP results indicate that SWE uncertainty is driving runoff uncertainty, and measurements may be beneficial in reducing uncertainty in SWE and runoff, during the melt season at high latitudes (e.g., Tundra and Taiga regions) and in the western mountain regions, whereas observations at (or near) peak SWE accumulation are more helpful over the midlatitudes.

Perfect codes in Euclidean lattices

In the present paper, we investigate the existence of lattice perfect codes when considered as sublattices of other lattices under the Euclidean metric. We discuss the connection between a discrete tiling of a lattice and a continuous tilling of the n-dimensional space and equivalent characterizations of discrete tilings. We generalize bounds on the radius of perfect codes in a generic lattice, which were previously known for the cubic lattice, and we provide some new bounds. The new bounds are based on the packing and the covering densities and on the covering radius of the ambient lattice. An algorithm is presented for the search of perfect codes which is used to derive all perfect codes for a collection of ambient lattices in dimensions two and three. In contrast to the cubic lattice, these case studies show that by considering general ambient lattices one can find rich sets of perfect codes.

The Idempotency of Convolution Operations on Fuzzy Truth Values

Recently, convolution operations on fuzzy truth values (FTVs, that is, functions from [0, 1] to [0, 1]) and their basic properties have become a hot research area, such as type-2 t-norms, type-2 aggregation operations, type-2 implications, etc., and the closure, monotonicity, distributivity, etc. However, the idempotency of convolution operations has not been studied so far. In this article, we give the equivalent characterization of the idempotency of convolution operations on FTVs.

Adic semidualizing complexes

We introduce and study a class of objects that encompasses Christensen and Foxby’s semidualizing modules and complexes and Kubik’s quasi-dualizing modules: the class of [Formula: see text]-adic semidualizing modules and complexes. We give examples and equivalent characterizations of these objects, including a characterization in terms of the more familiar semidualizing property. As an application, we give a proof of the existence of dualizing complexes over complete local rings that does not use the Cohen Structure Theorem.

Quadri Partitioned Neutrosophic Soft Set

The aim of this paper is to introduce the new concept of quadri partitioned neutrosophic soft set and discussed some of its properties.And the focus of this paper is to propose a new notion of quadri partitioned neutrosophic soft set and to study some basic operations and results in quadri partitioned neutrosophic soft set. Further we develop a systematic study on quadri partitioned neutrosophic soft set and obtain various properties induced by them. Some equivalent characterization and inter-relations among them are discussed with counter example.

GORENSTEIN SILTING COMPLEXES

AbstractWe introduce and study the notion of Gorenstein silting complexes, which is a generalization of Gorenstein tilting modules in Gorenstein-derived categories. We give the equivalent characterization of Gorenstein silting complexes. We give a sufficient condition for a partial Gorenstein silting complex to have a complement.

Equivalent Characterizations and Pointwise Multipliers of Normal Weight Dirichlet Space on the Unit Ball

Let $$\mu $$ be a normal function on [0, 1) and $$p>0$$ . In this paper, the authors give several equivalent characterizations of the functions in the normal weight Dirichlet type space $$D_{\mu }^{p}(B)$$ on the unit ball B in $$\mathbf{C}^{n}$$ . At the same time, the authors describe the boundedness of a class of integral operator T from the normal weight Lebesgue space $$L_{\mu }^{p}(B)$$ to the abstract measure Lebesgue space $$L_{\mu ,\psi }^{p}(B)$$ . As an application of the previous results, the authors discuss the pointwise multipliers on $$D_{\mu }^{p}(B)$$ or from $$D_{\mu }^{p}(B)$$ to $${\mathcal {B}}_{\nu _{p}}(B)$$ .

Tight K-frames and weaving of K-frames

In this paper we find that a result of an equivalent characterization of tight K-g-frames obtained by Huang and Shi is incorrect, and we give a sufficient condition for a given Bessel sequence to be a tight K-frame. We also characterize the weaving of K-frames in Hilbert spaces. We give several kinds of sufficient conditions such that the type $$\{T_{1} f_{i}\}_{i\in I}$$ and $$\{T_{2} g_{i}\}_{i\in I}$$ are K-woven (resp. woven) on $$\mathcal {H}$$ or its subspace R(K), given that $$\{f_{i}\}_{i\in I}$$ and $$\{g_{i}\}_{i\in I}$$ are K-frames (resp. frames) on $$\mathcal {H}$$ and $$T_{1}, T_{2}$$ are surjective operators on $$\mathcal {H}$$ . Finally we discuss that we can plus two different Bessel sequences to a K-woven pair such that the new obtained pair are K-woven on $$\mathcal {H}$$ .

On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

Analytical Meir–Keeler type contraction mappings and equivalent characterizations

Analytical Meir–Keeler type contraction mappings and equivalent characterizations

Ideal theory on EQ-algebras

<abstract><p>In this article, we introduce ideals and other special ideals on EQ-algebras, such as implicative ideals, primary ideals, prime ideals and maximal ideals. At first, we give the notion of ideal and its related properties on EQ-algebras, and give its equivalent characterizations. We discuss the relations between ideals and filters, and study the generating formula of ideals on EQ-algebras. Moreover, we study the properties of implicative ideals, primary ideals, prime ideals and maximal ideals and their relations. For example, we prove that every maximal ideal is prime and if prime ideals are implicative, then they are maximal in the EQ-algebra with the condition $ (DNP) $. Finally, we introduce the topological properties of prime ideals. We get that the set of all prime ideals is a compact $ T_{0} $ topological space. Also, we transferred the spectrum of EQ-algebras to bounded distributive lattices and given the ideal reticulation of EQ-algebras.</p></abstract>