The probabilistic powerdomain from a topological viewpoint

Lyu, Zhenchao; Kou, Hui

doi:10.1016/j.topol.2018.01.008

Cited by 6 publications

(7 citation statements)

References 9 publications

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“…[20] The use of toughening agent like ethylene-butylacrylate-glycidyl methacrylate in PC-PBT blends increases the VST, impact strength, and elongation at break with reduction in mechanical properties like tensile strength, flexural modulus, and flexural strength as studied by Bai et al [25] In order to improve the chemical resistance, mechanical tensile stress-strain, and impact strength, the incorporation of impact modifier like butyl acrylate and butadiene was supportive. [26] It was very interesting to observe that above 0 C, butyl acrylate as impact modifier had resulted in higher impact resistance than the butadiene rubber based impact modifier. On the other hand, below 0 C (sub zero), the butadiene rubber based impact modifier greatly improved the impact resistance strength than that of butyl acrylate-based impact modifier.…”

Section: Impact Modified Pc-pbt Blend For Usefulnessmentioning

confidence: 99%

“…Unique transesterification chemistry [2,4,5,9,6,12,20,8,11,21,35,52,[60][61][62][63][64][65][66][67][68][69][70] Mechanical and Morphology [1,4,13,21,22,36,48,56,35,68] Chemical resistance [4,5,26,44,45] Rheology and Processing [26, 43-49, 8, 46, 52, 54, 63, 66, 67] Recycling [58] Flame retardant characteristics [69] Impact modification [12,19,21,23,25,55,43,35,[60]…”

Section: Salient Features Of Pc-pbt Blendmentioning

confidence: 99%

“…In order to improve the chemical resistance, mechanical tensile stress–strain, and impact strength, the incorporation of impact modifier like butyl acrylate and butadiene was supportive. [ 26 ] It was very interesting to observe that above 0°C, butyl acrylate as impact modifier had resulted in higher impact resistance than the butadiene rubber based impact modifier. On the other hand, below 0°C (sub zero), the butadiene rubber based impact modifier greatly improved the impact resistance strength than that of butyl acrylate‐based impact modifier.…”

Section: Introductionmentioning

confidence: 99%

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Review on transesterification in polycarbonate–poly(butylene terephthalate) blend

Ganguly¹,

Channe

Jha³

et al. 2021

Polymer Engineering & Sci

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Various polycarbonate ‐ poly(butylene terephthalate) polyester (PC‐PBT) blend prepared by reactive melt blending primarily in extruder with range of temperature and time are discussed in this review article. In the melt blended PC‐PBT blend system, transesterification plays a major role in formation of PC‐PBT blend. Transesterification reactions between these two polymers have been analyzed by proper polymer sample, end‐capped or having reactive chain end group. The kinetics of mechanism is a function of temperature and PC‐PBT ratio. Trace catalyst residue present in PBT catalyzes the transesterification reaction. As the extent of transesterification is increased, it forms various composition of copolymer. Inhibition in the transesterification reaction of PC‐PBT blend has been observed when different type of alkyl, aryl, and alkyl‐aryl group of phosphite are introduced into it, otherwise there has been collateral change in the morphology, thermal, and mechanical property of blend. Therefore, this PC‐PBT blend has been an interesting topic of research in academia and industries.

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Section: Impact Modified Pc-pbt Blend For Usefulnessmentioning

confidence: 99%

Section: Salient Features Of Pc-pbt Blendmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Review on transesterification in polycarbonate–poly(butylene terephthalate) blend

Ganguly¹,

Channe

Jha³

et al. 2021

Polymer Engineering & Sci

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“…Lemma 3.16. ( [15]) Let P and Q be complete lattices, and let g : P → Q and d : Q → P be maps which preserve arbitrary sups and g • d = 1 Q .…”

Section: The Correspondent Properties Between P and γ(P )mentioning

confidence: 99%

Two topologies on the lattice of Scott closed subsets

Chen

Kou

Lyu

2021

Preprint

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For a poset P , let σ(P ) and Γ(P ) respectively denote the lattice of its Scott open subsets and Scott closed subsets ordered by inclusion, and set ΣP = (P, σ(P )). In this paper, we discuss the lower Vietoris topology and the Scott topology on Γ(P ) and give some sufficient conditions to make the two topologies equal. We built an adjunction between σ(P ) and σ(Γ(P )) and proved that ΣP is core-compact iff ΣΓ(P ) is core-compact iff ΣΓ(P ) is sober, locally compact and σ(Γ(P )) = υ(Γ(P )) (the lower Vietoris topology). This answers a question in [17]. Brecht and Kawai [2] asked whether the consonance of a topological space X implies the consonance of its lower powerspace, we give a partial answer to this question at the last part of this paper.

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“…Jones proved that if X is a domain, then the probabilistic powerdomain of X can be realized as the space of valuations, which is still a domain in her PhD thesis [16]. It has since then been studied extensively by a number of authors, such as, Plotkin [15], Graham [9], Heckmann [10,11], Goubault and Jung [7], Tix and Keimel [17,31], Lyu and Kou [20]. However, the category of domains together with Scott continuous maps is not cartesian closed.…”

Section: Introductionmentioning

confidence: 99%

The Directed Probabilistic Powerspace

Xie¹,

Kou²,

Lyu³

2022

Preprint

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Probabilistic powerdomain in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages with probabilistic choice. In this paper, we extend the notion of powerdomain to directed spaces, which is equivalent to the notion of the T 0 monotone-determined space [4]. We construct the probabilistic powerspace of the directed space, which is definded as a free directed space-cone. In addition, the relationships between our construction and classical probabilistic powerdomain are studied.

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The probabilistic powerdomain from a topological viewpoint

Cited by 6 publications

References 9 publications

Review on transesterification in polycarbonate–poly(butylene terephthalate) blend

Review on transesterification in polycarbonate–poly(butylene terephthalate) blend

Two topologies on the lattice of Scott closed subsets

The Directed Probabilistic Powerspace

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