An Approach Based on Multilevel Convolution for Sentence-Level Element Extraction of Legal Text

In the judicial field, with the increase of legal text data, the extraction of legal text elements plays a more and more important role. In this paper, we propose a sentence-level model of legal text element extraction based on the structure of multilabel text classification. Our proposed model contains an encoder and an improved decoder. The encoder applies multilevel convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) as feature extraction networks to extract local neighborhood and context information from legal text, and a decoder applies LSTM with multiattention and full connection layer with an improved initialization method to decode and generate label sequences. To our best knowledge, it is one of the first attempts to apply a multilabel classification algorithm for element extraction of legal text. In order to verify the effectiveness of our model, we conduct experiments not only on three real legal text datasets but also on a general multilabel text classification dataset.The experimental results demonstrate that our proposed model outperforms baseline models on legal text datasets, and our model is competitive to baseline models on the general text multilabel classification dataset, which indicates that our proposed model is useful for multilabel classification tasks of ordinary texts and legal texts with an uncertain number of characters in words and short lengths.

The lattice and semigroup structure of multipermutations

We study the algebraic properties of binary relations whose underlying digraph is smooth, that is, has no source or sink. Such objects have been studied as surjective hyper-operations (shops) on the corresponding vertex set, and as binary relations that are defined everywhere and whose inverse is also defined everywhere. In the latter formulation, they have been called multipermutations. We study the lattice structure of sets (monoids) of multipermutations over an [Formula: see text]-element domain. Through a Galois connection, these monoids form the algebraic counterparts to sets of relations closed under definability in positive first-order logic without equality. We show one side of this Galois connection, and give a simple dichotomy theorem for the evaluation problem of positive first-order logic without equality on the class of structures whose preserving multipermutations form a monoid closed under inverse. These problems turn out either to be in [Formula: see text]or to be [Formula: see text]-complete. We go on to study the monoid of all multipermutations on an [Formula: see text]-element domain, under usual composition of relations. We characterize its Green relations, regular elements and show that it does not admit a generating set that is polynomial on [Formula: see text].

How long is my SVG element?

SVG layout requires that the developer be in control of the dimensions of the objects that must be placed in the coordinate space. It is easy to specify (or compute based on other specifications) the size (bounding box height and width) of many SVG objects (e.g., rectangles, circles, lines), but identifying the bounding box for text is challenging because SVG text does not know its own length. In this report we explore two methods for working around this limitation. The first method, implemented in XSLT, consults exported font metrics to determine the length of SVG <text> elements and uses that information to make layout decisions as the SVG is created. The second method, implemented in JavaScript, determines the length of SVG <text> objects as the SVG is rendered in a browser and uses the information to control the layout at rendering time.

A criterion for the existence of nilpotent hall π-subgroups

Let [Formula: see text] be a nontrivial normal subgroup of [Formula: see text] and [Formula: see text]. In this paper, we show that if [Formula: see text] and for every [Formula: see text]-element [Formula: see text] with [Formula: see text], [Formula: see text], for some integer [Formula: see text], then [Formula: see text] has nilpotent Hall [Formula: see text]-subgroups. Further, we show that if [Formula: see text], then [Formula: see text] has abelian Hall [Formula: see text]-subgroups.

The Most Likely Object to be Seen Through a Window

We study data structures to answer window queries using stochastic input sequences. The first problem is the most likely maximal point in a query window: Let [Formula: see text] be constants, with [Formula: see text]. Let [Formula: see text] be a set of [Formula: see text] points in [Formula: see text], for some fixed [Formula: see text]. For [Formula: see text], each point in [Formula: see text] is associated with a probability [Formula: see text] of existence. A point [Formula: see text] in [Formula: see text] is on the maximal layer of [Formula: see text] if there is no other point [Formula: see text] in [Formula: see text] such that [Formula: see text]. Consider a random subset of [Formula: see text] obtained by including, for [Formula: see text], each point of [Formula: see text] independently with probability [Formula: see text]. For a query interval [Formula: see text], with [Formula: see text], we report the point in [Formula: see text] that has the highest probability to be on the maximal layer of [Formula: see text] in [Formula: see text] time using [Formula: see text] space. We solve a special problem as follows. A sequence [Formula: see text] of [Formula: see text] points in [Formula: see text] is given ([Formula: see text]), where each point [Formula: see text] has a probability [Formula: see text] of existence associated with it. Given a query interval [Formula: see text] and an integer [Formula: see text] with [Formula: see text], we report the probability of [Formula: see text] to be on the maximal layer of [Formula: see text] in [Formula: see text] time using [Formula: see text] space. The second problem we consider is the most likely common element problem. Let [Formula: see text] be the universe. Let [Formula: see text] be a sequence of random subsets of [Formula: see text] such that for [Formula: see text] and [Formula: see text], element [Formula: see text] is added to [Formula: see text] with probability [Formula: see text] (independently of other choices). Let [Formula: see text] be a fixed real number with [Formula: see text]. For query indices [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], with [Formula: see text] and [Formula: see text], we decide whether there exists an element [Formula: see text] with [Formula: see text] such that [Formula: see text] in [Formula: see text] time using [Formula: see text] space and report these elements in [Formula: see text] time, where [Formula: see text] is the size of the output.

Uncountably many non-commensurable pro-p groups of homological type FPk but not FPk+1

We show that there are uncountably many non-commensurable metabelian pro-[Formula: see text] groups of homological type [Formula: see text] but not of type [Formula: see text], generated by [Formula: see text] element, where [Formula: see text] and [Formula: see text]. In particular there are uncountably many non-commensurable finitely presented metabelian pro-[Formula: see text] groups that are not of type [Formula: see text]. We show furthermore that there are uncountably many non-isomorphic one related 2-generated pro-[Formula: see text] groups.

A Stabilized Finite Volume Element Method for Stationary Stokes–Darcy Equations Using the Lowest Order

We present a stabilized finite volume element method for the coupled Stokes–Darcy problem with the lowest order [Formula: see text] element for the Stokes region and [Formula: see text] element for the Darcy region. Based on adding a jump term of discrete pressure to the approximation equation, a discrete inf-sup condition is established for the proposed method. The optimal error estimates in the [Formula: see text]-norm for the velocity and piezometric head and in the [Formula: see text]-norm for the pressure are proved. And they are also verified through some numerical experiments. Two figures are given to show the full comparison for the local mass conservation between the proposed method and the stabilized finite element method. And this method can also be computed directly in the irregular domain according to the last experiment.

Investigation of the synthesis of the unknown superheavy nuclei 309,312126

In this paper, we applied the method developed by Santhosh and Safoora in [Phys. Rev. C 94 (2016) 024623; 95 (2017) 064611] to theoretically investigate the fusion, evaporation-residue (ER) and fission cross-sections of the synthesis of the unknown superheavy [Formula: see text]126 nuclei produced by using the [Formula: see text]Ni + [Formula: see text]Cf and [Formula: see text]Zn + [Formula: see text]Cm combinations. The charge asymmetry, mass asymmetry and fissility of the DiNuclear System (DNS) in the synthesis of the mentioned combinations are also estimated. The calculated results show that the ER cross-sections for the synthesis of the [Formula: see text]126 nuclei are predicted to be much less than 1.0[Formula: see text]fb. In particular, it has been found that there may exist a valley of the ER cross-sections in the synthesis of a superheavy [Formula: see text] element, which produces the [Formula: see text]126 isotope. Subsequently, a model for the mass dependence of the ER cross-section in the synthesis of the [Formula: see text]126 isotopes has been proposed for the first time. On the other hand, the quasi-fission process strongly dominates over the fusion in the two concerned interacting systems. The present results, together with those reported in the previous studies, indicate that the investigated projectile–target combinations are not capable for the synthesis of the [Formula: see text]126 isotopes due to tiny fusion cross-sections (about 2–3[Formula: see text]zb), which go beyond the limitations of available facilities. Further studies are thus recommended to search for alternative interacting systems. In conclusion, this work provides useful information for the synthesis of the gap isotopes [Formula: see text]126, which have not been well studied up to date.

Nuclear structure and α-decay study of Og isotopes

We have examined the binding energy, root-mean-square radii and two neutrons separation energies for the recently accepted super-heavy element [Formula: see text] established as Og using the axially deformed relativistic mean field (RMF) model with NL3 force parameter set. The calculation is extended to various isotopes of [Formula: see text] element, starting from [Formula: see text] till [Formula: see text]. The most stable isotope is found to be at [Formula: see text]. Also, the [Formula: see text]-decay energy [Formula: see text] and hence the half-lives [Formula: see text] is carried out by taking three different empirical formulae for the [Formula: see text]-decay chains of [Formula: see text] supporting the possible shell closure at daughter nuclei [Formula: see text] and/ or 184 and at parent nucleus of [Formula: see text] with [Formula: see text].

3He(α,γ)7Be and 3H(α,γ)7Li reaction rates and implication for Big Bang nucleosynthesis in the potential model

The reaction rates of the direct astrophysical capture processes [Formula: see text] and [Formula: see text], as well as the abundance of the [Formula: see text] element are estimated in the framework of a two-body potential model. The estimated [Formula: see text] abundance ratio of [Formula: see text] is in a very good agreement with the recent measurement [Formula: see text] of the LUNA collaboration.