Embedding Properties Research Articles

Emulsion and hot asphalt chip seal evaluation and field correlation using sweep test

Limited number of studies relate laboratory studies to chip seal performance over several years. This paper investigate the relationship between chip seal sweep test results and field performance. The study compares between the performance of hot applied chip seals and emulsified asphalts chip seals using sweep test. Performance evaluation is based upon aggregate retention, texture depth and embedment properties. In addition, parameters such as: aggregate type, aggregate coating, seal type, and their combined interaction effect on chip seal aggregate retention properties are presented in the study. Sweep test analysis of variance (ANOVA) findings revealed that aggregate coating has resulted in a significant enhancement in aggregate retention properties. Coated crushed stone aggregates have also provided the highest embedment percentiles, regardless of the seal type being used. However, they acquired less mean texture depth when compared to uncoated stones specimens. The laboratory analysis further found out that hot applied modified asphalt PG (72-28) with pre-coated crushed stones combination have yielded the most enhanced aggregate retention properties when compared to the rest of examined combinations of aggregates and seal types. The highest embedment properties were observed in specimens with pre-coated aggregates and emulsified asphalt (CRS-2). Finally, the study found that laboratory performance trends were in alignment with field performance trends of six chip seal projects constructed with comparable asphalt materials and same source aggregates.

A generalization to Sylow permutability of pronormal subgroups of finite groups

In this note, we present a new subgroup embedding property that can be considered as an analogue of pronormality in the scope of permutability and Sylow permutability in finite groups. We prove that finite PST-groups, or groups in which Sylow permutability is a transitive relation, can be characterized in terms of this property, in a similar way as T-groups, or groups in which normality is transitive, can be characterized in terms of pronormality.

Global Well-Posedness for the Massive Maxwell–Klein–Gordon Equation with Small Critical Sobolev Data

In this paper we prove global well-posedness and modified scattering for the massive Maxwell–Klein–Gordon equation in the Coulomb gauge on $$\mathbb {R}^{1+d}$$ $$(d \ge 4)$$ for data with small critical Sobolev norm. This extends to the general case $$ m^2 > 0 $$ the results of Krieger–Sterbenz–Tataru ( $$d=4,5 $$ ) and Rodnianski–Tao ( $$ d \ge 6 $$ ), who considered the case $$ m=0$$ . We proceed by generalizing the global parametrix construction for the covariant wave operator and the functional framework from the massless case to the Klein–Gordon setting. The equation exhibits a trilinear cancelation structure identified by Machedon–Sterbenz. To treat it one needs sharp $$L^{2}$$ null form bounds, which we prove by estimating renormalized solutions in null frames spaces similar to the ones considered by Bejenaru–Herr. To overcome logarithmic divergences we rely on an embedding property of $$ \Box ^{-1} $$ in conjunction with endpoint Strichartz estimates in Lorentz spaces.

Morrey Sequence Spaces: Pitt\u2019s Theorem and Compact Embeddings

Morrey (function) spaces and, in particular, smoothness spaces of Besov–Morrey or Triebel–Lizorkin–Morrey type have enjoyed a lot of interest recently. Here we turn our attention to Morrey sequence spaces m_{u,p}=m_{u,p}(mathbb {Z}^d), 0<ple u<infty , which have yet been considered almost nowhere. They are defined as natural generalizations of the classical ell _p spaces. We consider some basic features, embedding properties, a pre-dual, a corresponding version of Pitt’s compactness theorem, and further characterize the compactness of embeddings of related finite-dimensional spaces.

Current sheets in planetary magnetospheres

In this article we aim to highlight the problems related to the structure and stability of the comparatively thin current sheets that were relatively recently discovered by space missions in the magnetospheres of the Earth and planets, as well as in the solar wind. These magnetoplasma structures are universal in collisionless cosmic plasmas and can play a key role in the processes of storage and release of energy in the space environment. The development of a self-consistent theory for these sheets in the Earth’s magnetosphere, where they were first discovered, has a long and dramatic history. Solution of the problem of the thin current sheet structure and stability become possible in the framework of a kinetic quasi-adiabatic approach required to explain their embedding and metastability properties. It was found that the structure and stability of current structures are completely determined by the nonlinear dynamics of plasma particles. Theoretical models have been developed to predict many properties of these structures and interpret many experimental observations in planetary magnetospheres and the heliosphere.

Method for measuring the resistances produced on parallel and perpendicular veneers in plywood under nail embedment loading

The resistance of wooden materials against embedment loading is an important property that governs the performance of timber joints with dowel-type fasteners including nails. When plywood is used as a sheet material in a nailed joint, veneers with different grain directions are simultaneously embedded. The resistance produced on individual veneers has to be measured to elucidate the embedment properties of plywood. This study proposes a method for measuring resistance on individual veneers. Embedment behavior was modeled using springs arranged in parallel, and the equations for calculating resistance on individual veneers were derived. Embedment tests were conducted using structural plywood composed of sugi or karamatsu. Mechanical behaviors of individual veneers were revealed as followings. In the initial range of deformation, the slope of the resistance–deformation relationship of the veneer with grain parallel to the load direction is higher than that of the resistance–deformation relationship of the veneer with grain perpendicular to the load direction. The parallel veneer began to yield under a low range of deformation, and the resistance of the perpendicular veneer under a high range of deformation became almost equal to that of the parallel veneer.

AMALGAMABLE DIAGRAM SHAPES

AbstractA category has the amalgamation property (AP) if every pushout diagram has a cocone, and the joint embedding property (JEP) if every finite coproduct diagram has a cocone. We show that for a finitely generated category I, the following are equivalent: (i) every I-shaped diagram in a category with the AP and the JEP has a cocone; (ii) every I-shaped diagram in the category of sets and injections has a cocone; (iii) a certain canonically defined category ${\cal L}\left( {\bf{I}} \right)$ of “paths” in I has only idempotent endomorphisms. When I is a finite poset, these are further equivalent to: (iv) every upward-closed subset of I is simply-connected; (v) I can be built inductively via some simple rules. Our proof also shows that these conditions are decidable for finite I.

Harmonic functions on mated-CRT maps

A mated-CRT map is a random planar map obtained as a discretized mating of correlated continuum random trees. Mated-CRT maps provide a coarse-grained approximation of many other natural random planar map models (e.g., uniform triangulations and spanning tree-weighted maps), and are closely related to $\gamma $-Liouville quantum gravity (LQG) for $\gamma \in (0,2)$ if we take the correlation to be $-\cos (\pi \gamma ^{2}/4)$. We prove estimates for the Dirichlet energy and the modulus of continuity of a large class of discrete harmonic functions on mated-CRT maps, which provide a general toolbox for the study of the quantitative properties of random walk and discrete conformal embeddings for these maps. For example, our results give an independent proof that the simple random walk on the mated-CRT map is recurrent, and a polynomial upper bound for the maximum length of the edges of the mated-CRT map under a version of the Tutte embedding. Our results are also used in other work by the first two authors which shows that for a class of random planar maps — including mated-CRT maps and the UIPT — the spectral dimension is two (i.e., the return probability of the simple random walk to its starting point after $n$ steps is $n^{-1+o_{n}(1)}$) and the typical exit time of the walk from a graph-distance ball is bounded below by the volume of the ball, up to a polylogarithmic factor.

Finite groups with the pp-embedding property

A subset X of a finite group G is called g\nbdash independent if there is no proper subset Y of X such that \langle Y,\Phi(G) \rangle = \langle X,\Phi(G) \rangle. The group G has the embedding property if every g\nbdash independent subset of G can be embedded in a minimal generating set of G .If X is a set of prime power order elements, then we say that G has the pp-embedding property. In this note we classify all finite solvable groups with the pp-embedding property. Moreover we prove that this class is equal to the class of finite solvable groups with the embedding property.

Scl in free products

We study stable commutator length (scl) in free products via surface maps into a wedge of spaces. We prove that scl is piecewise rational linear if it vanishes on each factor of the free product, generalizing the main result in Danny Calegari's paper "Scl, sails and surgery". We further prove that the property of isometric embedding with respect to scl is preserved under taking free products. The method of proof gives a way to compute scl in free products which lets us generalize and derive in a new way several well-known formulas. Finally we show independently and in a new approach that scl in free products of cyclic groups behaves in a piecewise quasi-rational way when the word is fixed but the orders of factors vary, previously proved by Timothy Susse, settling a conjecture of Alden Walker.

Validated bounds on embedding constants for Sobolev space Banach algebras

Sobolev spaces and their embedding properties have long been of central importance in the study of partial differential equations, particularly for the classical theoretical analysis of both linear and nonlinear problems. In recent years, computer‐assisted proof techniques have been developed for obtaining existence and uniqueness proofs of solutions to a variety of nonlinear partial differential equations that arise in applications, and they have led to a number of new results that currently lie beyond the reach of classical analytical approaches. The use of computer‐assisted methods, however, frequently relies on the explicit knowledge of a variety of embedding constants for Sobolev spaces. In the present paper, we show that in the context of certain Sobolev space Banach algebras, these constants themselves can be bounded rigorously and precisely using validated computations based on interval arithmetic, combined with analytical error estimates.

Representation learning over multiple knowledge graphs for knowledge graphs alignment

Abstract The goal of representation learning of knowledge graph is to encode both entities and relations into a low-dimensional embedding spaces. Mostly current works have demonstrated the benefits of knowledge graph embedding in single knowledge graph completion, such as relation extraction. The most significant distinction between multiple knowledge graphs embedding and single knowledge graph embedding is that the former must consider the alignments between multiple knowledge graphs which is very helpful to some applications built on multiple KGs, such as KB-QA and KG integration. In this paper, we proposed a new automatic representation learning model over Multiple Knowledge Graphs (MGTransE) by adopting a bootstrapping method. More specifically, MGTransE consists of three core components: Structure Model, Semantically Smooth Embedding Model and Iterative Smoothness Model. The experiment results on two real-world datasets show that our method achieves better performance on two new multiple KGs tasks compared with state-of-the-art KG embedding models and also preserves the key properties of knowledge graph embedding on traditional single KG tasks as compared to those methods learned from single KG.

A note on the embedding properties of p-subgroups in finite groups

In this note, we prove that a finite group $G$ is $p$-supersolvable if and only if there exists a power $d$ of $p$ with $p^2 \leq d d$ if there exists a power $d$ of $p$ with $1 \leq d < |P|$ such that $H\cap O^p(G^*_{p^2})$ is normal in $O^p(G)$ for all non-meta-cyclic normal subgroups $H$ of $P$ with $|H| = d$.

Excluding subdivisions of bounded degree graphs

Let H be a fixed graph. What can be said about graphs G that have no subgraph isomorphic to a subdivision of H? Grohe and Marx proved that such graphs G satisfy a certain structure theorem that is not satisfied by graphs that contain a subdivision of a (larger) graph H1. Dvořák found a clever strengthening—his structure is not satisfied by graphs that contain a subdivision of a graph H2, where H2 has “similar embedding properties” as H. Building upon Dvořák's theorem, we prove that said graphs G satisfy a similar structure theorem. Our structure is not satisfied by graphs that contain a subdivision of a graph H3 that has similar embedding properties as H and has the same maximum degree as H. This will be important in a forthcoming application to well-quasi-ordering.

Long-time behavior of almost periodically forced parabolic equations on the circle

We study the long-time behavior of the skew-product semiflow generated by scalar reaction-diffusion equation on the circle with almost periodic forcing:ut=uxx+f(t,u,ux),t>0,x∈S1=R/2πZ, where f(t,u,ux) is uniformly almost-periodic in t. Almost periodic environmental forcing exhibits the external effects which are roughly but not exactly periodic.Contrary to the time-periodic cases (for which any ω-limit set Ω can be embedded into a periodically forced circle flow), we show that, for almost-periodic forcing, the problem that whether Ω can be embedded into an almost-periodically forced circle flow is strongly related to the dimension of the center space Vc(Ω) associated with Ω. On the one hand, if dimVc(Ω)≤1 then Ω is either spatially-inhomogeneous or spatially-homogeneous; and moreover, any spatially-inhomogeneous Ω can be embedded into an almost periodically-forced circle flow. On the other hand, when dimVc(Ω)>1, it is shown that the above embedding property cannot hold anymore. These reveal that for such system there are essential differences between time periodic forcing and non-periodic forcing.

Embedding, simulation and consistency of [formula omitted]-symmetric quantum theory

A physical requirement on the Hamiltonian operator in quantum mechanics is that it must generate real energy spectrum and unitary time evolution. While the Hamiltonians are Dirac Hermitian in conventional quantum mechanics, they observe PT-symmetry in PT-symmetric quantum theory. The embedding property was first studied by Günther and Samsonov [1] to visualise the evolution of unbroken PT-symmetric Hamiltonians on C2 by Hermitian Hamiltonians on C4. This paper investigates the properties of PT-symmetric quantum systems including the embedding property. We provide a full characterization of the embedding property in the general case and show that only unbroken PT-symmetric quantum systems admit this property in a finite dimensional space. Furthermore, utilizing this property, we establish a physically realizable simulation process of the unbroken PT-symmetric Hamiltonians. An observation that the unbroken PT-symmetric quantum systems can be viewed as open systems in the conventional quantum mechanics accounts for the consistency of PT-symmetric quantum theory.

The metanorm, a characteristic subgroup: Embedding properties

Abstract The norm of a group was introduced by R. Baer as the intersection of all normalizers of subgroups, and it was later proved that the norm is always contained in the second term of the upper central series of the group. The aim of this paper is to study embedding properties of the metanorm of a group, defined as the intersection of all normalizers of non-abelian subgroups. The metanorm is related to the so-called metahamiltonian groups, i.e. groups in which all non-abelian subgroups are normal, and it is known that every locally graded metahamiltonian group is finite over its second centre. Among other results, it is proved here that if G is a locally graded group whose metanorm M is not nilpotent, then M ′ / M ′′ {M^{\prime}/M^{\prime\prime}} is a small eccentric chief factor and it is the only obstruction to a strong hypercentral embedding of M in G.

Some characterisations of groups in which normality is a transitive relation by means of subgroup embedding properties

The research of the first author has been supported by the research grant MTM2014-54707-C3-1-P by the Ministerio de Economia y Competitividad (Spain) and FEDER (European Union).

Fraïssé classes of graded relational structures

We study classes of graded structures satisfying the properties of amalgamation, joint embedding and hereditariness. Given appropriate conditions, we can build a graded analogue of the Fraïssé limit. Some examples such as the class of all finite weighted graphs or the class of all finite fuzzy orders (evaluated on a particular countable algebra) will be examined.

On the structure of holomorphic isometric embeddings of complex unit balls into bounded symmetric domains

We study general properties of holomorphic isometric embeddings of complex unit balls $\mathbb B^n$ into bounded symmetric domains of rank $\ge 2$. In the first part, we study holomorphic isometries from $(\mathbb B^n,kg_{\mathbb B^n})$ to $(\Omega,g_\Omega)$ with non-minimal isometric constants $k$ for any irreducible bounded symmetric domain $\Omega$ of rank $\ge 2$, where $g_D$ denotes the canonical K\"ahler-Einstein metric on any irreducible bounded symmetric domain $D$ normalized so that minimal disks of $D$ are of constant Gaussian curvature $-2$. In particular, results concerning the upper bound of the dimension of isometrically embedded $\mathbb B^n$ in $\Omega$ and the structure of the images of such holomorphic isometries were obtained. In the second part, we study holomorphic isometries from $(\mathbb B^n,g_{\mathbb B^n})$ to $(\Omega,g_\Omega)$ for any irreducible bounded symmetric domains $\Omega\Subset \mathbb C^N$ of rank equal to $2$ with $2N>N'+1$, where $N'$ is an integer such that $\iota:X_c\hookrightarrow \mathbb P^{N'}$ is the minimal embedding (i.e., the first canonical embedding) of the compact dual Hermitian symmetric space $X_c$ of $\Omega$. We completely classify images of all holomorphic isometries from $(\mathbb B^n,g_{\mathbb B^n})$ to $(\Omega,g_\Omega)$ for $1\le n \le n_0(\Omega)$, where $n_0(\Omega):=2N-N'>1$. In particular, for $1\le n \le n_0(\Omega)-1$ we prove that any holomorphic isometry from $(\mathbb B^n,g_{\mathbb B^n})$ to $(\Omega,g_\Omega)$ extends to some holomorphic isometry from $(\mathbb B^{n_0(\Omega)},g_{\mathbb B^{n_0(\Omega)}})$ to $(\Omega,g_\Omega)$.