An Improved Prediction Method of Soil-Water Characteristic Curve by Geometrical Derivation and Empirical Equation

Much attention has been paid on the soil-water characteristic curve (SWCC) during decades because it plays great roles in unsaturated soil mechanics. However, it is time-consuming and costly to obtain a series of entire saturation-suction data by experiments. The curves acquired by directly fitting empirical equations to limited experimental data are greatly different from the actual SWCC, and the relevant soil parameters obtained by inaccurate curve are also incorrect. Thus, an improved prediction method for more accurate entire SWCC was established. This novel method was based on the analysis of shape characteristics of SWCC with three critical points S , C 1 , and C 2 under the hypothesis of geometrical symmetric relation. The theoretical computation was specifically deduced under conventional Gardner, VG, and FX models, respectively, and then inferred on different soil types of 45 collected SWCC datasets. This geometrical symmetric relation exhibited well in all these three conventional empirical equations, especially in Gardner equation. Finally, a series of filer paper tests on sand, silt, and clay were also carried out to acquire entire SWCC curve for the verification and evaluation of the proposed geometrical method. Results show that this improved prediction method effectively decreases deviation resulting from directly fitting empirical equations to limited data of wide types of soils. The averaged improvement was larger under VG equation than under Gardner and FX equation. It proved that the accuracy of predicting greatly depends on the shape characteristic point of maximum curve curvature (point C 2 ), other than the number of points. This research provides a novel computation method to improve prediction accuracy even under relative less experimental data.

LAPREL: A Label-Aware Parallel Network for Relation Extraction

Relation extraction is a crucial task in natural language processing (NLP) that aims to extract all relational triples from a given sentence. Extracting overlapping relational triples from complex texts is challenging and has received extensive research attention. Most existing methods are based on cascade models and employ language models to transform the given sentence into vectorized representations. The cascaded structure can cause exposure bias issue; however, the vectorized representation of each sentence needs to be closely related to the relation extraction with pre-defined relation types. In this paper, we propose a label-aware parallel network (LAPREL) for relation extraction. To solve the exposure bias issue, we apply a parallel network, instead of the cascade framework, based on the table-filling method with a symmetric relation pair tagger. To obtain task-related sentence embedding, we embed the prior label information into the token embedding and adjust the sentence embedding for each relation type. The proposed method can also effectively deal with overlapping relational triples. Compared with 10 baselines, extensive experiments are conducted on two public datasets to verify the performance of our proposed network. The experimental results show that LAPREL outperforms the 10 baselines in extracting relational triples from complex text.

Types of Complex Fuzzy Relations with Applications in Future Commission Market

In this paper, we introduce types of relations on complex fuzzy sets such as the complex fuzzy (CF) inverse relation, complex fuzzy reflexive relation, complex fuzzy symmetric relation, complex fuzzy antisymmetric relation, complex fuzzy transitive relation, complex fuzzy irreflexive relation, complex fuzzy asymmetric relation, complex fuzzy equivalence relation, and complex fuzzy-order relation. We study some basic results and particular examples of these relations. Moreover, we discuss the applications of complex fuzzy relations in Future Commission Market (FCM). We show that the introduction of CF relations to applications of FCMs can give a significant method for describing the temporal dependence between parameters of a Future Commission Market.

Inverse scattering transform and soliton solutions of an integrable nonlocal Hirota equation

<p style='text-indent:20px;'>In this work, we study the inverse scattering transform of a nonlocal Hirota equation in detail, and obtain the corresponding soliton solutions formula. Starting from the Lax pair of this equation, we obtain the corresponding infinite number of conservation laws and some properties of scattering data. By analyzing the direct scattering problem, we get a critical symmetric relation which is different from the local equations. A novel left-right Riemann-Hilbert problem is proposed to develop the inverse scattering theory. The potentials are recovered and the pure soliton solutions formula is obtained when the reflection coefficients are zero. Based on the zero types of scattering data, nine types of soliton solutions are obtained and three typical types are described in detail. In addition, some dynamic behaviors are given to illustrate the soliton characteristics of the space symmetric nonlocal Hirota equation.</p>

Makeup Interpolation Based on Color and Shape Parametrization

In this paper, we address the problem of synthesizing continuous variations with the appearance of makeup by taking a linear combination of the examples. Makeup usually shows a vague boundary and does not form a clear shape, which makes this problem unique from the existing image interpolation problems. We approach this problem as an interpolation between semi-transparent image layers and tackle this by presenting new parametrization schemes for the color and for the shape separately in order to achieve an effective interpolation. For the color parametrization, our main idea is based on the observation of the symmetric relation between the color and transparency of the makeup; we provide an optimization framework for extracting a representative palette of colors associated with the transparent values, which enables us to easily set up the color correspondence among the multiple makeup samples. For the shape parametrization, we exploit a polar coordinate system, that creates the in-between shapes effectively, without ghosting artifacts.

On applications for Mahler expansion associated with p-adic q-integrals

In this paper, we primarily consider a generalization of the fermionic [Formula: see text]-adic [Formula: see text]-integral on [Formula: see text] including the parameters [Formula: see text] and [Formula: see text] and investigate its some basic properties. By means of the foregoing integral, we introduce two generalizations of [Formula: see text]-Changhee polynomials and numbers as [Formula: see text]-Changhee polynomials and numbers with weight [Formula: see text] and [Formula: see text]-Changhee polynomials and numbers of second kind with weight [Formula: see text]. For the mentioned polynomials, we obtain new and interesting relationships and identities including symmetric relation, recurrence relations and correlations associated with the weighted [Formula: see text]-Euler polynomials, [Formula: see text]-Stirling numbers of the second kind and Stirling numbers of first and second kinds. Then, we discover multifarious relationships among the two types of weighted [Formula: see text]-Changhee polynomials and [Formula: see text]-adic gamma function. Also, we compute the weighted fermionic [Formula: see text]-adic [Formula: see text]-integral of the derivative of [Formula: see text]-adic gamma function. Moreover, we give a novel representation for the [Formula: see text]-adic Euler constant by means of the weighted [Formula: see text]-Changhee polynomials and numbers. We finally provide a quirky explicit formula for [Formula: see text]-adic Euler constant.

Symmetry

Chapter 5 determines the semantic typology of patterns III and VI, sometimes termed the vowel-lengthening patterns. It asserts that verbs formed in these patterns are symmetrical predicates, denoting relations consisting of two complementary forces. It shows that the difference between the two patterns results from the interplay between an underlying symmetric relation and a figure–ground orientation in which one of the participant roles involved is made more prominent than the other. The chapter divides verbs formed in pattern III into verbs of resistance, risk, competition, interaction, and co-action, and those formed in pattern VI into reciprocal verbs, feigning verbs, chaining verbs, and verbs of progressive change. It argues that an account based on a common symmetric structure is able to unite this diverse range of verbs within one analysis, and it offers data from other languages to support this claim.

Ontological Separation in Aristotle’s Metaphysics

Ontological separation plays a key role in Aristotle’s metaphysical project: substances alone are ontologically χωριστόν. The standard view identifies Aristotelian ontological separation with ontological independence, so that ontological separation is a non-symmetric relation. I argue that there is strong textual evidence that Aristotle employs an asymmetric notion of separation in theMetaphysics—one that involves the dependence of other entities on the independent entity. I argue that this notion allows Aristotle to prevent the proliferation of substance-kinds and thus to secure the unity of his metaphysical system.

Does weak discernibility determine metaphysics?

Two entities are weakly discernible when an irreflexive and symmetric relation holds between them. That weak discernibility holds in quantum mechanics is fairly uncontroversial nowadays. The ontological consequences of weak discernibility, however, are far from clear. Part of the literature seems to imply that weak discernibility points to a definite metaphysics to quantum mechanics. In this paper we shall discuss the metaphysical contribution of weak discernibility to quantum mechanics and argue that, contrary to part of current literature, it does not provide for a fully naturalistic determination of metaphysics. Underdetermination of the metaphysics still plagues the way of the naturalist.