Equivalent Characterizations Research Articles

Study on Stress Sensitivity of Ultra-Low Permeability Sandstone Reservoir Considering Starting Pressure Gradient

When studying the influence of nonlinear seepage on the water flooding development of ultra-low permeability reservoirs, it is difficult to accurately characterize the nonlinear seepage state of ultra-low permeability reservoirs using conventional reservoir numerical simulation methods. A large number of field development and tests in the oil fields show that there are indeed starting pressure gradients and stress sensitivity effects in ultra-low permeability sandstone reservoirs. In this study, taking the tight sandstone of the Chang 6 Member in the Yanchang Formation as an example, the rock displacement vector was utilized to equivalently characterize the stress-sensitive effect of the reservoir based on a novel numerical simulation software tNavigator. Furthermore, the starting pressure gradient and the feasibility of a new stress-sensitive equivalent characterization method were verified combining the poroelastic media physics equations. In addition, we systematically studied the impact of stress-sensitive effects on oil well productivity under the influence of starting pressure gradient and considering petrophysical properties. The results show that the existence of the starting pressure gradient can improve the stress sensitivity of the matrix reservoir. Considering the starting pressure gradient, when the rock shear modulus is 14.29 GPa, the cumulative oil production decreases by 4.1%; when the rock shear modulus is 11.36 GPa, the cumulative oil production decreases by 11.2%. Finally, a numerical simulation was conducted with Block B in the Zhouwan-Wugucheng area, and the model can accurately predict the reservoir stress sensitivity based on the starting pressure gradient. When both the starting pressure gradient and stress sensitivity are considered, the crude oil recovery degree of the target layer decreases by 11.7%; when only the starting pressure gradient is considered, the crude oil recovery degree decreases by 8.8%; and when only the stress sensitivity is considered, the crude oil recovery degree decreases by 0.5%.

Equivalent noise characterization of human lightness constancy.

A goal of visual perception is to provide stable representations of task-relevant scene properties (e.g. object reflectance) despite variation in task-irrelevant scene properties (e.g. illumination and reflectance of other nearby objects). To study such stability in the context of the perceptual representation of lightness, we introduce a threshold-based psychophysical paradigm. We measure how thresholds for discriminating the achromatic reflectance of a target object (task-relevant property) in rendered naturalistic scenes are impacted by variation in the reflectance functions of background objects (task-irrelevant property), using a two-alternative forced-choice paradigm in which the reflectance of the background objects is randomized across the two intervals of each trial. We control the amount of background reflectance variation by manipulating a statistical model of naturally occurring surface reflectances. For low background object reflectance variation, discrimination thresholds were nearly constant, indicating that observers’ internal noise determines threshold in this regime. As background object reflectance variation increases, its effects start to dominate performance. A model based on signal detection theory allows us to express the effects of task-irrelevant variation in terms of the equivalent noise, that is relative to the intrinsic precision of the task-relevant perceptual representation. The results indicate that although naturally occurring background object reflectance variation does intrude on the perceptual representation of target object lightness, the effect is modest – within a factor of two of the equivalent noise level set by internal noise.

Approximation by a class of neural network operators on scattered data

Scattered data are a class of common data in the real world. Naturally, how to efficiently process scattered data is important. This paper uses a class of feedforward neural networks with four layers as tool to fit scattered data and establishes the estimates of the approximation error. In particular, an inverse theorem of the approximation is established. Concretely, we first extend an existed result on to the case of arbitrary bounded convex set in . Secondly, we introduce a modified feedforward neural network with four layers, which is a class of quasi‐interpolation operators and can keep the smoothness of the objective function. By establishing two Bernstein‐type inequalities for the operators, we establish both the direct and converse results of the approximation by the operator, which follows the equivalence characterization theorem of the approximation.

Gorenstein Projective Coresolutions and Co-Tate Homology Functors

For a local commutative Gorenstein ring [Formula: see text], Enochs et al. in [Gorenstein projective resolvents, Comm. Algebra 44 (2016) 3989–4000] defined a functor [Formula: see text] and showed that this functor can be computed by taking a totally acyclic complex arising from a projective coresolution of the first component or a totally acyclic complex arising from a projective resolution of the second component. In order to define the functor [Formula: see text] over general rings, we introduce the right Gorenstein projective dimension of an [Formula: see text]-module [Formula: see text], [Formula: see text], via Gorenstein projective coresolutions, and give some equivalent characterizations for the finiteness of [Formula: see text]. Then over a general ring [Formula: see text] we define a co-Tate homology group [Formula: see text] for [Formula: see text]-modules [Formula: see text] and [Formula: see text] with [Formula: see text] and [Formula: see text], and prove that [Formula: see text] can be computed by complete projective coresolutions of the first variable or by complete projective resolutions of the second variable.

Affine equivalences of surfaces of translation and minimal surfaces, and applications to symmetry detection and design

We introduce a characterization for affine equivalence of two surfaces of translation defined by either rational or meromorphic generators. In turn, this induces a similar characterization for minimal surfaces. In the rational case, our results provide algorithms for detecting affine equivalence of these surfaces, and therefore, in particular, the symmetries of a surface of translation or a minimal surface of the considered types. Additionally, we apply our results to designing surfaces of translation and minimal surfaces with symmetries, and to computing the symmetries of the higher-order Enneper surfaces.

Parameterized combinatorial curvatures and parameterized combinatorial curvature flows for discrete conformal structures on polyhedral surfaces

Discrete conformal structure on polyhedral surfaces is a discrete analogue of the smooth conformal structure on surfaces that assigns discrete metrics by scalar functions defined on vertices. It unifies and generalizes tangential circle packing, Thurston's circle packing, inversive distance circle packing and the vertex scaling described by Luo [29] and others. In this paper, we introduce combinatorial α-curvature for discrete conformal structures on polyhedral surfaces, which is a parameterized generalization of the classical combinatorial curvature. Then we prove the local and global rigidity of combinatorial α-curvature with respect to discrete conformal structures on polyhedral surfaces, which confirms parameterized Glickenstein rigidity conjecture in [22]. To study the Yamabe problem for combinatorial α-curvature, we introduce combinatorial α-Ricci flow for discrete conformal structures on polyhedral surfaces, which is a generalization of Chow-Luo's combinatorial Ricci flow for Thurston's circle packings [4] and Luo's combinatorial Yamabe flow for vertex scaling [29] on polyhedral surfaces. To handle the potential singularities of the combinatorial α-Ricci flow, we extend the flow through the singularities by extending the inner angles in triangles by constants. Under the existence of a discrete conformal structure with prescribed combinatorial curvature, the solution of extended combinatorial α-Ricci flow is proved to exist for all time and converge exponentially fast for any initial value. This confirms a parameterized generalization of another conjecture of Glickenstein in [22] on the convergence of combinatorial Ricci flow, gives an almost equivalent characterization of the solvability of Yamabe problem for combinatorial α-curvature in terms of combinatorial α-Ricci flow and provides an effective algorithm for finding discrete conformal structures with prescribed combinatorial α-curvatures.

Further properties of fractional stochastic dominance

AbstractA continuum of stochastic dominance rules, also referred to as fractional stochastic dominance (SD), was introduced by Müller, Scarsini, Tsetlin, and Winkler (2017) to cover preferences from first- to second-order SD. Fractional SD can be used to explain many individual behaviors in economics. In this paper we introduce the concept of fractional pure SD, a special case of fractional SD. We investigate further properties of fractional SD, for example the generating processes of fractional pure SD via $\gamma$ -transfers of probability, Yaari’s dual characterization by utilizing the special class of distortion functions, the separation theorem in terms of first-order SD and fractional pure SD, Strassen’s representation, and bivariate characterization. We also establish several closure properties of fractional SD under quantile truncation, under comonotonic sums, and under distortion, as well as its equivalence characterization. Examples of distributions ordered in the sense of fractional SD are provided.

Analysis of a degenerated reaction–diffusion cholera model with spatial heterogeneity and stabilized total humans

In this paper, we perform a complete analysis on a degenerated reaction–diffusion cholera model with stabilizing total humans and non-mobility of cholera bacteria in a spatially heterogeneous bounded domain. The existence of a global attractor is established through introducing the Kuratowski measure of non-compactness. The basic reproduction number and its equivalent characterizations have been used to analyze the threshold-type results, where the persistence and extinction of cholera can also be characterized by the dispersal rate of infected humans. In the homogeneous case, the global attractivity of the unique positive equilibrium is achieved by the Lyapunov function. Moreover, we compare the basic reproduction numbers for the models without and with considering the mobility of cholera bacteria. Our results suggest that: the basic reproduction numbers attain different values as the dispersal rates of infected humans and cholera approach to infinity, while they attain the same value as the dispersal rates of infected humans and cholera approach to zero. Numerical simulations support our analytical results and discuss the impact of the dispersal rate of infected humans on the transmission of cholera.

Multiplicities and mixed multiplicities of arbitrary filtrations

We develop a theory of multiplicities and mixed multiplicities of filtrations, extending the theory for filtrations of m-primary ideals to arbitrary (not necessarily Noetherian) filtrations. The mixed multiplicities of r filtrations on an analytically unramified local ring R come from the coefficients of a suitable homogeneous polynomial in r variables of degree equal to the dimension of the ring, analogously to the classical case of the mixed multiplicities of m-primary ideals in a local ring. We prove that the Minkowski inequalities hold for arbitrary filtrations. The characterization of equality in the Minkowski inequality for m-primary ideals in a local ring by Teissier, Rees and Sharp and Katz does not extend to arbitrary filtrations, but we show that they are true in a large and important subcategory of filtrations. We define divisorial and bounded filtrations. The filtration of powers of a fixed ideal is a bounded filtration, as is a divisorial filtration. We show that in an excellent local domain, the characterization of equality in the Minkowski equality is characterized by the condition that the integral closures of suitable Rees like algebras are the same, strictly generalizing the theorem of Teissier, Rees and Sharp and Katz. We also prove that a theorem of Rees characterizing the inclusion of ideals with the same multiplicity generalizes to bounded filtrations in excellent local domains. We give a number of other applications, extending classical theorems for ideals.

On weak G-completeness for fuzzy metric spaces

In this paper, we provide equivalent characterizations of weak G-complete fuzzy metric spaces. Since such spaces are complete, we also characterize fuzzy metric spaces that have weak G-complete fuzzy metric completions. Moreover, we establish analogous results for classical metric spaces.

Stochastic integration with respect to fractional processes in Banach spaces

In the article, integration of temporal functions in (possibly non-UMD) Banach spaces with respect to (possibly non-Gaussian) fractional processes from a finite sum of Wiener chaoses is treated. The family of fractional processes that is considered includes, for example, fractional Brownian motions of any Hurst parameter or, more generally, fractionally filtered generalized Hermite processes. The class of Banach spaces that is considered includes a large variety of the most commonly used function spaces such as the Lebesgue spaces, Sobolev spaces, or, more generally, the Besov and Lizorkin-Triebel spaces. In the article, a characterization of the domains of the Wiener integrals on both bounded and unbounded intervals is given for both scalar and cylindrical fractional processes. In general, the integrand takes values in the space of γ-radonifying operators from a certain homogeneous Sobolev-Slobodeckii space into the considered Banach space. Moreover, an equivalent characterization in terms of a pointwise kernel of the integrand is also given if the considered Banach space is isomorphic with a subspace of a cartesian product of mixed Lebesgue spaces. The results are subsequently applied to stochastic convolution for which both necessary and sufficient conditions for measurability and sufficient conditions for continuity are found. As an application, space-time continuity of the solution to a parabolic equation of order 2m with distributed noise of low time regularity is shown as well as measurability of the solution to the heat equation with Neumann boundary noise of higher regularity.

Information Design of Dynamic Mechanisms

Two dynamic game forms are said to be behaviorally equivalent if they share the "same" profiles of structurally reduced strategies (Battigalli et al., 2020). In the context of dynamic implementation, behaviorally equivalent game forms are interchangeable under a wide range of solution concepts for the purpose of implementing a social choice function. A gradual mechanism (Chew and Wang, 2022), which designs a procedure of information transmission mediated by a central administrator, enables a formal definition of information flow. We provide a characterization of behavioral equivalence between gradual mechanisms in terms of their informational equivalence -- each agent is designed the "same" information flow. Information flow also helps in defining an intuitive notion of immediacy for gradual mechanisms which is equivalent to their game structures being minimal. Given that the class of gradual mechanisms serves as a revelation principle for dynamic implementation (Li, 2017; Akbarpour and Li, 2020; Mackenzie, 2020; Chew and Wang, 2022), the class of immediate gradual mechanisms provides a refined revelation principle.

High-Temperature Deformation Behavior of Sintered Nanocu Paste Used in Power Electronics Packaging: A Constitutive Modeling and Stochastically Equivalent Finite Element Characterization

High-Temperature Deformation Behavior of Sintered Nanocu Paste Used in Power Electronics Packaging: A Constitutive Modeling and Stochastically Equivalent Finite Element Characterization

Smooth Output-to-State Stability for multistable systems on compact manifolds

Output-to-State Stability (OSS) is a notion of detectability for nonlinear systems that is formulated in the ISS framework. We generalize the notion of OSS for systems which possess a decomposable invariant set and evolve on compact manifolds. Building upon a recent extension of the ISS theory for this very class of [systems [D. Angeli and D. Efimov, IEEE Trans. Autom. Control 60 (2015) 3242–3256.], the paper provides equivalent characterizations of the OSS property in terms of asymptotic estimates of the state trajectories and, in particular, in terms of existence of smooth Lyapunov-like functions.

A Generalized Definition of Fuzzy Subrings

In this study, under the condition that L is a completely distributive lattice, a generalized definition of fuzzy subrings is introduced. By means of four kinds of cut sets of fuzzy subset, the equivalent characterization of L‐fuzzy subring measures are presented. The properties of L‐fuzzy subring measures under these two kinds of product operations are further studied. In addition, an L‐fuzzy convexity is directly induced by L‐fuzzy subring measure, and it is pointed out that ring homomorphism can be regarded as L‐fuzzy convex preserving mapping and L‐fuzzy convex‐to‐convex mapping. Next, we give the definition and related properties of the measure of L‐fuzzy quotient ring and give a new characterization of L‐fuzzy quotient ring when the measure of L‐fuzzy quotient ring is 1.

Equivalent characterizations of harmonic Teichmüller mappings

<abstract><p>In this paper, three equivalent conditions of $ \rho $-harmonic Teichmüller mapping are given firstly. As an application, we investigate the relationship between a $ \rho $-harmonic Teichmüller mapping and its associated holomorphic quadratic differential and obtain a relatively simple method to prove Theorem 2.1 in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>. Furthermore, the representation theorem of $ 1/|\omega|^{2} $-harmonic Teichmüller mappings is given as a by-product. Our results extend the corresponding researches of harmonic Teichmüller mappings.</p></abstract>

Study on the effect of multiple non-breathable gangue occurrence on gas migration in coal seams

Abstract As the mining environment gradually moves toward deep, the form and occurrence mode of gangue are more complex. The occurrence of non-breathable gangue seriously worsens gas migration conditions, which greatly reduces the gas extraction efficiency and increases the possibility of coal and gas outburst. Therefore, in order to explore the effect of multiple non-breathable gangue occurrence on gas migration in coal seams, the self-developed the constant pressure coal and rock mass gas seepage test system is used to systematically study the characteristics of coal seam gas migration under different layers of gangue and the differentiated occurrence of multiple gangue. The equivalent characterization of coal seam gas migration under the condition of multiple inclusions is proposed through theoretical analysis and numerical simulation. Research shows: the permeability factor of the whole coal sample, sample containing a single layer gangue and sample containing double layers gangue exhibits a “V-shaped variation law with the increase of the gas adsorption equilibrium pressure. There is a critical gas pressure point when the permeability factor is the lowest, and with the increase in the number of gangue layers, the greater the pressure value of the critical gas pressure point. According to the characteristics of gas pressure distribution, the sample containing gangue can be roughly divided into four influence areas: gas expansion affected area, gas stable seepage area and upper and lower effective seepage area. The more the number of gangue layers and the larger the area of gangue layers, the upper and lower effective seepage area is smaller, the closer the positions of gangue are to the gas source, gas expansion affected area is smaller, both of them will cause more difficult in gas migration and the lower of the sample permeability factor. When different sizes of gangue are used at two positions of the gangue in the samples, with the increase of gas adsorption equilibrium pressure, the attenuation rate of permeability factor in the early stage of the sample is significantly higher than that of the sample with the same size of gangues in the front and at the back. The results of the paper have certain actual guiding significance for improving gas extraction efficiency and preventing mine gas disasters.

All self-adjoint extensions of the magnetic Laplacian in nonsmooth domains and gauge transformations

We use boundary triples to find a parametrization of all self-adjoint extensions of the magnetic Schrodinger operator, in a quasi-convex domain~$\Omega$ with compact boundary, and magnetic potentials with components in $\textrm{W}^{1}_{\infty}(\overline{\Omega})$. This gives also a new characterization of all self-adjoint extensions of the Laplacian in nonregular domains. Then we discuss gauge transformations for such self-adjoint extensions and generalize a characterization of the gauge equivalence of the Dirichlet magnetic operator for the Dirichlet Laplacian; the relation to the Aharonov-Bohm effect, including irregular solenoids, is also discussed. In particular, in case of (bounded) quasi-convex domains it is shown that if some extension is unitarily equivalent (through the multiplication by a smooth unit function) to a realization with zero magnetic potential, then the same occurs for all self-adjoint realizations.

Three-hierarchical three-way decision models for conflict analysis: A qualitative improvement and a quantitative extension

Conflict analysis facilitates cause revelation and action treatments for widespread conflicts. Relevant three-way decisions on agreement, disagreement, and neutrality attitude subsets are valuable, but the initial model has a complex definition and ambiguous semantics. This paper conducts in-depth three-way decision modeling on attitude subsets by using rough sets and three-way decisions, and it establishes both an improved qualitative model and an extended quantitative model. The two novel models are formed by an intuitionistic attitude function and a complete three-way structure, so they acquire effective connotations, optimal calculations, and thorough mechanisms. Aiming at the attitude subsets of conflict analysis, first, a qualitative three-way decision model is proposed by remedying the limitations of the existing model, and the qualitative model obtains the perfect semantics, computational algorithm, qualitative monotonicity, and equivalent characterization. Then, a quantitative three-way decision model is constructed by considering probability measures and tolerance thresholds, and the quantitative model achieves the statistical measurement, computational algorithm, and quantitative nonmonotonicity. Finally, all results are effectively verified by conflict examples and data experiments. For conflict analysis, the initial, qualitative, and quantitative three-way models constitute the three levels of attitude subsets, and the latter two offer improvements and extensions. The obtained results uncover rough set interpretations and enrich three-way decision making, mainly in terms of certainty and uncertainty.

Rank axiom of modular supermatroids: A connection with directional DR submodular functions

A matroid has been one of the most important combinatorial structures since it was introduced by Whitney as an abstraction of linear independence. As an important property of a matroid, it can be characterized by several different (but equivalent) axioms, such as the augmentation, the base exchange, or the rank axiom.A supermatroid is a generalization of a matroid defined on lattices. Here, the central question is whether a supermatroid can be characterized by several equivalent axioms similar to a matroid. Barnabei, Nicoletti, and Pezzoli characterized supermatroids on distributive lattices, and Fujishige, Koshevoy, and Sano generalized the results for cg-matroids (supermatroids on lower locally distributive lattices).In this study, we focus on modular lattices, which are an important superclass of distributive lattices, and provide equivalent characterizations of supermatroids on modular lattices. We characterize supermatroids on modular lattices using the rank axiom in which the rank function is a directional DR-submodular function, which is a generalization of a submodular function introduced by the authors. Using a characterization based on rank functions, we further prove the strong exchange property of a supermatroid, which has application in optimization.We also reveal the relation between the axioms of a supermatroid on lower semimodular lattices, which is a common superclass of a lower locally distributive lattice and a modular lattice.