Robinson Property Research Articles

Graph sequences sampled from Robinson graphons

The function Γ on the space of graphons, introduced in Chuangpishit et al. (2015), aims to measure the extent to which a graphon w exhibits the Robinson property: for all x<y<z, w(x,z)≤min{w(x,y),w(y,z)}. Robinson graphons form a model for graphs with a natural line embedding so that most edges are local. The function Γ is compatible with the cut-norm ‖⋅‖□, in the sense that graphons close in cut-norm have similar Γ-values. In particular, any graphon close in cut-norm to the set of all Robinson graphons has small Γ-values. Here we show the converse, by proving that every graphon w can be approximated by a Robinson graphon Rw so that ‖w−Rw‖□ is bounded in terms of Γ(w). We then use classical techniques from functional analysis to show that a converging graph sequence {Gn} converges to a Robinson graphon if and only if Γ(Gn)→0. Finally, using probabilistic techniques we show that the rate of convergence of Γ for graph sequences sampled from a Robinson graphon can differ substantially depending on how strongly w exhibits the Robinson property.

Amalgamation and Robinson property in universal algebraic logic

Abstract There is a well-established correspondence between interpolation and amalgamation for algebraizable logics that satisfy certain additional assumptions. In this paper, we introduce the Robinson property of a logic and show that a conditionally algebraizable logic without any additional assumptions has the Robinson property if and only if the corresponding class of Lindenbaum–Tarski algebras has the amalgamation property. Moreover, we give the logical characterization of the strong amalgamation property, solving an open problem of Andréka–Németi–Sain. It is also shown that given the mentioned extra assumptions the Robinson property implies the interpolation property. As conditionally algebraizable logics cover algebraizable logics as well as various quantifier logics such as classical first order logic, our results yield a generalization of some of the results concerning interpolation and amalgamation.

Performance Analysis and Optimization of a Novel Combined Cooling, Heating, and Power System‐Integrated Rankine Cycle and Brayton Cycle Utilizing the Liquified Natural Gas Cold Energy

For realizing efficient utilization of liquified natural gas cold energy and high‐temperature flue gas waste heat, herein, a combined cooling, heating, and power system using Peng–Robinson property package in Aspen HYSYS software, which includes a three‐stage parallel Rankine cycle (RC) in series with single‐stage RC and a supercritical CO2 (S‐CO2) Brayton cycle, is proposed. The system performance is evaluated using the first law of thermodynamics, second law of thermodynamics, specific energy costing method, and exergoenvironment analysis method. The influences of the pump 1 outlet pressure, turbine 3 inlet temperature, working fluid R23 mass flow rate, compressor 1 outlet pressure, CO2 liquefaction pressure, and ambient temperature on system performance are investigated. The nondominated sorting whale optimization algorithm and technique for order preference by similarity to ideal situation are applied to optimize the multiobjective system performance, and the payback periods of system before and after optimization are calculated. The analysis indicates that under the initial conditions, the thermal efficiency, exergy efficiency, total product unit cost, and sustainability index of the system are 41.68%, 48.50%, 112.293 $ GJ−1, and 1.75, respectively. After optimization, exergy efficiency increases by 2.4% and exergoeconomy decreases by 8.277 $ GJ−1.

Northcott numbers for the house and the Weil height

For an algebraic number α $\alpha$ and γ ∈ R $\gamma \in \mathbb {R}$ , let be the house, h ( α ) $h(\alpha )$ be the (logarithmic) Weil height, and h γ ( α ) = ( deg α ) γ h ( α ) $h_\gamma (\alpha )=(\deg \alpha )^\gamma h(\alpha )$ be the γ $\gamma$ -weighted (logarithmic) Weil height of α $\alpha$ . Let f : Q ¯ → [ 0 , ∞ ) $f:\overline{\mathbb {Q}}\rightarrow [0,\infty )$ be a function on the algebraic numbers Q ¯ $\overline{\mathbb {Q}}$ , and let S ⊂ Q ¯ $S\subset \overline{\mathbb {Q}}$ . The Northcott number N f ( S ) $\mathcal {N}_f(S)$ of S $S$ , with respect to f $f$ , is the infimum of all X ⩾ 0 $X\geqslant 0$ such that { α ∈ S ; f ( α ) < X } $\lbrace \alpha \in S; f(\alpha )< X\rbrace$ is infinite. This paper studies the set of Northcott numbers N f ( O ) $\mathcal {N}_f({\mathcal {O}})$ for subrings of Q ¯ $\overline{\mathbb {Q}}$ for the house, the Weil height, and the γ $\gamma$ -weighted Weil height. We show: (1) Every t ⩾ 1 $t\geqslant 1$ is the Northcott number of a ring of integers of a field w.r.t. the house . (2) For each t ⩾ 0 $t\geqslant 0$ , there exists a field with Northcott number in [ t , 2 t ] $ [t,2t]$ w.r.t. the Weil height h ( · ) $h(\cdot )$ . (3) For all 0 ⩽ γ ⩽ 1 $0\leqslant \gamma \leqslant 1$ and γ ′ < γ $\gamma ^{\prime }<\gamma$ , there exists a field K $K$ with N h γ ′ ( K ) = 0 $\mathcal {N}_{h_{\gamma ^{\prime }}}(K)=0$ and N h γ ( K ) = ∞ $\mathcal {N}_{h_\gamma }(K)=\infty$ . For (1) we provide examples that satisfy an analogue of Julia Robinson's property (JR), examples that satisfy an analogue of Vidaux and Videla's isolation property, and examples that satisfy neither of those. Item (2) concerns a question raised by Vidaux and Videla due to its direct link with decidability theory via the Julia Robinson number. Item (3) is a strong generalisation of the known fact that there are fields that satisfy the Lehmer conjecture but which are not Bogomolov in the sense of Bombieri and Zannier.

Lindström theorems in graded model theory

Stemming from the works of Petr Hájek on mathematical fuzzy logic, graded model theory has been developed by several authors in the last two decades as an extension of classical model theory that studies the semantics of many-valued predicate logics. In this paper we take the first steps towards an abstract formulation of this model theory. We give a general notion of abstract logic based on many-valued models and prove six Lindström-style characterizations of maximality of first-order logics in terms of metalogical properties such as compactness, abstract completeness, the Löwenheim–Skolem property, the Tarski union property, and the Robinson property, among others. As necessary technical restrictions, we assume that the models are valued on finite MTL-chains and the language has a constant for each truth-value.

Clustering Analysis of a Dissimilarity: a Review of Algebraic and Geometric Representation

It is customary to split clustering analysis into an optimization level, then a (preferably) graphical representation level to take benefit of human vision for an effective understanding of (big) data structure. This article aspires to clarify relationships between clustering, both its process and its representation, and the underlying structural graph properties, both algebraic and geometric, starting from the mere knowledge of a dissimilarity matrix among items, possibly with missing entries. It is inspired by an analogous work on seriation problem, relating Robinson property in a dissimilarity with missing entries, with interval graph recognition using a sequence of 4 lexicographic breadth first searches.

The Robinson property and amalgamations of higher arities

In this article we discuss a version of the Robinson property studied recently by Gyenis in , and we present a solution to one of his open problems. We say that a first‐order structure satisfies the Robinson property whenever the union of two non‐trivial partial n‐types over different finite sets is realizable if and only if they are not explicitly contradictory. In his article, Gyenis showed that a universal, homogeneous structure over a language that consists of at most binary relation symbols satisfies the Robinson property if and only if its age has a generalized amalgamation property (the so called prescribed amalgamation property, PAP). We go further and define a series of new kinds of amalgamation properties, APn for any natural number n. Using these properties we can characterize all universal and homogeneous structures that satisfy the Robinson property independently from the arities of relation symbols of the language.

Optimization and control for CO2 compression and purification unit in oxy-combustion power plants

High CO2 purity products can be obtained from oxy-combustion power plants through a CO2 CPU (compression and purification unit) based on phase separation method. To ensure that CPU (with double flash separators) can be operated under optimal conditions, this paper focuses on single variable analysis, multi-variable optimization, dynamic simulation and control system design for CPU in oxy-combustion power plants. It is found that optimal operating conditions are 30 bar, 30.42 °C, −24.64 °C, and −55 °C for multi-stage CO2 compressor discharge pressure, flue gas temperature after compression, first flash separator temperature, and second flash separator temperature, respectively. The designed double temperature control structure based on a systematic top-down analysis and bottom-up design method is more suitable than the single temperature control structure under different operating scenarios (load change and flue gas composition ramp change). To bear operating disturbances, operating strategies like elevating temperature, manipulating valves and adjusting setpoints are proposed. Influence of SOx would be more obvious than that of NOx, whilst the kij mixing parameters in Peng–Robinson property method affects little on process optimization and control system design. Comprehensive dynamic model with specified control system provides possibility to integrate CPU with full-train oxy-combustion power plants.

Amalgamation and interpolation in ordered algebras

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension property, and the flat amalgamation property and the deductive interpolation property, as well as various dependencies between these properties. These relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice-ordered abelian groups and MV-algebras, and to determine important subvarieties of residuated lattices where these properties hold or fail. In particular, a full description is given of all subvarieties of commutative GMV-algebras possessing the amalgamation property.

Optimization of CO2 compression and purification units (CO2CPU) for CCS power plants

Oxy-fuel power plants are among the currently known major carbon capture and storage (CCS) technologies those which produce the lowest carbon dioxide (CO2) purity CO2-stream. As a consequence, the oxy-fuel technology has the highest requirement towards CO2 purification. In the current paper two different purification processes are modeled in Aspen Plus™ based on a Peng–Robinson property method with kij mixing coefficients. Both separation processes are based on phase separation technique. The first one is equipped with two flash columns and the second one includes a distillation column. Both plants require a dehydration plant for water removal. For each process the impact of main design parameters on performance features such as specific power requirement, specific cooling duty, separation efficiency and CO2 purity are analyzed, including variations in flue gas composition, plant load and kij mixing parameters. The results were compared to a conventional 5-stage CO2 compressor.

On Robinsonian dissimilarities, the consecutive ones property and latent variable models

A dissimilarity measure on a set of objects is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when moving away from the main diagonal along any row or column. The Robinson property of a dissimilarity reflects an order of the objects. If a dissimilarity is not observed directly, it must be obtained from the data. Given that an ordinal structure is assumed to underlie the data, the dissimilarity function of choice may or may not recover the order correctly. For four dissimilarity measures for binary data it is investigated what ordinal data structure of 0s and 1s is correctly recovered. We derive sufficient conditions for the dissimilarity functions to be Robinsonian. The sufficient conditions differ with the dissimilarity measures. The paper concludes with some limitations of the study.

Seriation in the Presence of Errors: A Factor 16 Approximation Algorithm for l ∞-Fitting Robinson Structures to Distances

The classical seriation problem consists in finding a permutation of the rows and the columns of the distance (or, more generally, dissimilarity) matrix d on a finite set X so that small values should be concentrated around the main diagonal as close as possible, whereas large values should fall as far from it as possible. This goal is best achieved by considering the Robinson property: a distance d R on X is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when moving away from the main diagonal along any row or column. If the distance d fails to satisfy the Robinson property, then we are lead to the problem of finding a reordering of d which is as close as possible to a Robinsonian distance. In this paper, we present a factor 16 approximation algorithm for the following NP-hard fitting problem: given a finite set X and a dissimilarity d on X, we wish to find a Robinsonian dissimilarity d R on X minimizing the l ∞-error ‖d−d R ‖∞=max x,y∈X {|d(x,y)−d R (x,y)|} between d and d R .

U.S. Court of Appeals, Fifth Circuit: Reddin v. Robinson Property Group d/b/a Horseshoe Casino &amp; Hotel

U.S. Court of Appeals, Fifth Circuit: <i>Reddin v. Robinson Property Group d/b/a Horseshoe Casino &amp; Hotel</i>

Land Reform, Income Redistribution, and Agricultural Production in Korea

Jeon, Yoong-Deok; Kim, Young-Yong.January, 2000.Land reform, income redistribution, and agricultural production in Korea,Articles,[Chicago, U.S.]University of Chicago,18

Interpolation and compactness in categories of pre-institutions

An analysis of relationships between Craig-style interpolation, compactness, and other related model-theoretic properties is carried out in the softer framework of categories of pre-institutions. While the equivalence between sentence interpolation and the Robinson property under compactness and Boolean closure is well known, a similar result under different assumptions (not involving compactness) is newly established for presentation interpolation. The standard concept of naturality of model transformation is enriched by a new property, termed restriction adequacy, which proves useful for the reduction of interpolation along pre-institution transformations. A distinct reduction theorem for the Robinson property is presented as well. A variant of the ultraproduct concept is further introduced, and the related closure property for pre-institutions is shown to be equivalent to compactness

Interpolation and the Robinson property for logics not closed under the Boolean operations

A variant of the Robinson property (ROB*) is introduced. The property ROB* is equivalent to the usual Robinson property and hence is equivalent also to the interpolation property, in any compact logic closed under the Boolean operations. On the other hand, it will be shown that ROB* is not always equal to the interpolation property, if a logic is not closed under them. Next, we will study ROB* and various interpolation properties for equational logics, which are typical examples of compact logics not closed under the Boolean operations. It will be shown that an equational logic has ROB* if and only if it has the amalgamation property for isomorphic embeddings.

On linear operators on ordered banach spaces

The order structure of the space of all continuous linear operators on an ordered Banach space is studied. The main topic is the Robinson property, that is, the norm of a positive linear operator is attained on the positive unit cone.

An algebraic result about soft model theoretical equivalence relations with an application to H. Friedman's fourth problem

AbstractWe prove the following algebraic characterization of elementary equivalence: ≡ restricted to countable structures of finite type is minimal among the equivalence relations, other than isomorphism, which are preserved under reduct and renaming and which have the Robinson property; the latter is a faithful adaptation for equivalence relations of the familiar model theoretical notion. We apply this result to Friedman's fourth problem by proving that if is an (ω1, ω)-compact logic satisfying both the Robinson consistency theorem on countable structures of finite type and the Löwenheim-Skolem theorem for some λ &lt; ωω for theories having ω1 many sentences, then ≡L = ≡ on such structures.