Glue Operators Research Articles

On p-Frobenius of Affine Semigroups

This paper studies the p-Frobenius vector of affine semigroups S⊂Nq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S\\subset \\mathbb {N}^q$$\\end{document}. Defined with respect to a graded monomial order, the p-Frobenius vector represents the maximum element with at most p factorizations within S. We develop efficient algorithms for computing these vectors and analyze their behavior under the gluing operations with Nq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {N}^q$$\\end{document}.

Proton momentum and angular momentum decompositions with overlap fermions

We present a calculation of the proton momentum and angular momentum decompositions using overlap fermions on a $2+1$-flavor RBC/UKQCD domain-wall lattice at 0.143 fm with a pion mass of 171 MeV which is close to the physical one. A complete determination of the momentum and angular momentum fractions carried by up, down, strange, and glue inside the proton has been done with valence pion masses varying from 171 to 391 MeV. We have utilized fast Fourier transform on the stochastic-sandwich method for connected-insertion parts and the cluster-decomposition error reduction technique technique for disconnected-insertion parts has been used to reduce statistical errors. The full nonperturbative renormalization and mixing between the quark and glue operators are carried out. The final results are normalized with the momentum and angular momentum sum rules and reported at the physical valence pion mass at $\overline{\mathrm{MS}}(\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV})$. The renormalized momentum fractions for the quarks and glue are $⟨x{⟩}^{q}=0.491(20)(23)$ and $⟨x{⟩}^{g}=0.509(20)(23)$, respectively, and the renormalized total angular momentum fractions for quarks and glue are $2{J}^{q}=0.539(22)(44)$ and $2{J}^{g}=0.461(22)(44)$, respectively. The quark spin fraction is $\mathrm{\ensuremath{\Sigma}}=0.405(25)(37)$ from our previous work and the quark orbital angular momentum fraction is deduced from $2{L}^{q}=2{J}^{q}\ensuremath{-}\mathrm{\ensuremath{\Sigma}}$ to be 0.134(22)(44).

Ratio of strange to u/d momentum fraction in disconnected insertions

The ratio of the strange quark momentum fraction $\langle x\rangle_{s+\bar{s}}$ to that of light quark $u$ or $d$ in disconnected insertions (DI) is calculated on the lattice with overlap fermions on four domain wall fermion ensembles. These ensembles cover three lattice spacings, three volumes and several pion masses including the physical one, from which a global fitting is carried out. A complete nonperturbative renormalization and the mixing between the quark and glue operators are taken into account. We find the ratio to be $\langle x\rangle_{s+\bar{s}}/\langle x\rangle_{u+\bar{u}} ({\rm DI})=0.795(79)(77)$ at $\mu = 2$ GeV in the $\overline{{\rm MS}}$ scheme. This ratio can be used as a constraint to better determine the strange parton distribution especially in the small $x$ region in the global fittings of PDFs when the connected and disconnected sea are fitted and evolved separately, demonstrating a new way that connects lattice calculations with global analyses.

Offer semantics: Achieving compositionality, flattening and full expressiveness for the glue operators in BIP

Based on a concise but comprehensive overview of some fundamental properties required from component-based frameworks, namely compositionality, incrementality, flattening, modularity and expressiveness, we review three modifications of the semantics of glue operators in the Behaviour–Interaction–Priority (BIP) framework. We provide theoretical results and examples illustrating the degree to which the three semantics meet these requirements. In particular, we show that the most recent semantics, based on the offer predicate is the only one that satisfies all of them.The classical and offer semantics are not comparable: there are systems that can be assembled in the classical semantics, but not in the offer one. We present a strict characterisation of the behaviour hierarchy determining the conditions, under which systems in the classical semantics can be transposed into the offer semantics: directly, with minor modifications, by introducing a new type of synchronisation or cannot be transposed at all.The offer semantics allows us to extend the algebras, which are used to model glue operators in BIP, to encompass priorities. This extension uses the Algebra of Causal Interaction Trees, T(P), as a pivot: existing transformations automatically provide the extensions for the Algebra of Connectors. We then extend the axiomatisation of T(P), since the equivalence induced by the new operational semantics is weaker than that induced by the interaction semantics. This extension leads to canonical normal forms for all structures and to a simplification of the algorithm for the synthesis of connectors from Boolean coordination constraints.

Extended Connectors: Structuring Glue Operators in BIP

Based on a variation of the BIP operational semantics using the offer predicate introduced in our previous work, we extend the algebras used to model glue operators in BIP to encompass priorities. This extension uses the Algebra of Causal Interaction Trees, T(P), as a pivot: existing transformations automatically provide the extensions for the Algebra of Connectors. We then extend the axiomatisation of T(P), since the equivalence induced by the new operational semantics is weaker than that induced by the interaction semantics. This extension leads to canonical normal forms for all structures and to a simplification of the algorithm for the synthesis of connectors from Boolean coordination constraints.

A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in

The integral representations of the solution around the vertices of the interior reentered angles (on the “singular” parts) are approximated by the composite midpoint rule when the boundary functions are from These approximations are connected with the 9-point approximation of Laplace's equation on each rectangular grid on the “nonsingular” part of the polygon by the fourth-order gluing operator. It is proved that the uniform error is of order where and is the mesh step. For the -order derivatives () of the difference between the approximate and the exact solutions, in each “ singular” part order is obtained; here is the distance from the current point to the vertex in question and is the value of the interior angle of the th vertex. Numerical results are given in the last section to support the theoretical results.

Towards a Theory of Glue

We propose and study the notions of behaviour type and composition operator making a first step towards the definition of a formal framework for studying behaviour composition in a setting sufficiently general to provide insight into how the component-based systems should be modelled and compared. We illustrate the proposed notions on classical examples (Traces, Labelled Transition Systems and Coalgebras). Finally, the definition of memoryless glue operators, takes us one step closer to a formal understanding of the separation of concerns principle stipulating that computational aspects of a system should be localised within its atomic components, whereas coordination layer responsible for managing concurrency should be realised by memoryless glue operators.

Methylene chloride exposures in two gluing operations.

Methylene chloride exposures in two gluing operations.

An Apparatus for Gluing Split Panels

A WOOD panel painting which has split into two often warps in such a way that each part shows a different deformation. This happens particularly when the boards of the panel have a complicated grain structure. The purpose of the apparatus described below is to allow the panels to be rejoined without flattening them even along the line of the join. The apparatus is adaptable enough to be useful for many other gluing operations. The author designed this apparatus in 1947 and it was made in the precision workshops of the Wawel in I950. The frame is in two parts (Fig. I). The main frame consists of two horizontal beams (A) carried by posts at either end. On either side of the posts, to left and right in Fig. I, can be seen two trestles, carrying lighter horizontal beams (B). The trestles with their beams (B) are quite independent of the main frame. Running between beams B are two boxsection metal beams. These are shown best in Figs. 2 and 3. Fig. 2 also shows the horizontal and vertical clamping devices. The vertical clamps are adjustable for length, and carry a pad at the end which bears on the picture. The other end bears on one of the beams A, above or below. The horizontal clamps are attached at intervals to a metal strip which can be locked in a suitable position on the metal beams. The joining of a panel is carried out as follows: The two pieces of the panel are placed on the metal beams, with padding, so that the crack runs parallel to beams A. Both pieces are then clamped vertically and horizontally, warp being corrected by gently adjusting the vertical clamps, until the edges to be joined match perfectly. Raking light (see Fig. 2) makes any slight difference in height detectable. One panel must now be removed for application of the glue, but can be quickly replaced in position and further adjustments made before the glue sets. For gluing operations requiring pressure on to a plain surface a table can be placed on the lower of the two main beams (Fig. 4). Thus the apparatus can be used to attach cradling. Other uses of the apparatus are for gluing cleaved plywood, mosaics, marquetries, parts of sculptures, etc. Special modifications allow the joining of warped panels (Fig. 5). RUDOLF KOZIOWSKI