Super-Shuffle Product and Cut-Box Coproduct on (0,1)-Matrices

In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.

Duality theorem for smash coproduct over quantum groupoids

The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.

Duality theorem for L-R crossed coproducts

In this paper, the notion of L-R crossed coproduct is introduced as a unified approach for smash coproducts, crossed coproducts and L-R smash coproducts of Hopf algebras.A duality theorem for L-R crossed coproduct is proved.

The quasi-triangular structures over Hom-ω-smash coproduct Hopf algebras

Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be a Hom-bialgebra. We study the quasi-triangular structures over （Cω H, γ） and show the necessary and sufficient conditions for （Cω H, γ R） to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D（H）＊ and construct quasi-triangular structures over D（H）＊.

Constructing the Cocyclic Structures for Crossed Coproduct Coalgebras

In this paper, we construct a cocylindrical object associated to two coalgebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduet coalgebra induced from two coalgebras with a cotwisted map and the cocyclic object related to the diagonal of the cocylindrical object.

Commercial Demonstration Unit for Manufacture of Aromatics from Toluene and Methanol with Coproduction of Low-Carbon Olefins Will Be Set Up

On November 29,2013 the Shaanxi Coal Chemicals Technology Engineering Center,Ltd.(SCCTEC),the CNOOC Huizhou Refining and Chemical Company and the SINOPEC Luoyang Engineering Company,Ltd.signed an agreement on cooperation in development of

A Novel Process Using Ion Exchange Resins for the Coproduction of Ethyl and Butyl Acetates

Before proposing an innovative process for the coproduction of ethyl and butyl acetates, the individual syntheses of ethyl acetate and butyl acetate by two different routes were first studied. These syntheses involved the reaction of ethanol or n-butanol with acetic acid or acetic anhydride in the presence of ion exchange resins: Amberlyst 15, Amberlyst 16, Amberlyst 36 and Dowex 50WX8. Kinetic and thermodynamic studies were performed with all resins. The lowest activation energy (Ea) value was obtained with Dowex 50WX8, which was identified as the best-performing resin, able to be reused at least in four runs without regeneration. The presence of water-azeotropes during the synthesis of ethyl acetate makes its purification difficult. A new strategy was adopted here, involving the use of ethanol and acetic anhydride as the starting material. In order to minimize acetic acid as co-product of this reaction, a novel two-step process for the coproduction of ethyl and butyl acetates was developed. The first step involves the production of ethyl acetate and its purification. Butyl acetate was produced in the second step: n-butanol was added to the mixture of acetic acid and the resin remaining after the first-step distillation. This process yields ethyl acetate and butyl acetate at high purity and shows an environmental benefit over the independent syntheses by green metrics calculation and life cycle assessment.

Cylinder Coalgebras and Cylinder Coproducts for Quasitriangular Hopf Algebras

This paper introduces the concepts of cylinder coalgebras and cylinder coproducts for quasitriangular bialgebras, and points out that there exists an anti-coalgebra isomorphism （H,△^-）≌ （H,△^-）, where （H, △^-） is the cylinder coproduct, and （H,△^-） is the braided coproduct given by Kass. For any finite dimensional Hopf algebra H, the Drinfel＇d double （D（H）,△^-D（H）） is proved to be the cylinder coproduct. Let （H, H, R） be copaired Hopf algebras. If R ∈ Z（H×H） with inverse R-1 and skew inverse R, then the twisted coalgebra （H^R）^R-1 is constructed via twice twists, whose comultiplication is exactly the cylinder coproduct. Moreover, for any generalized Long dimodule, some solutions for Yang-Baxter equations, four braid pairs and Long equations are constructed via cylinder twists.

“合供”视角下职业教育现场工程师培养的合作机理与优化路径

职业教育现场工程师培养是中国特色学徒制的体现,也是职业教育产教融合协同育人的创新举措。为实现人才培养目标及能力要求,需要多元主体协同合作。“合供”理论源于公共管理学,强调政府与多元主体协同合作,以提高政策执行效率与公共服务能力。基于“合供”理论的内涵及应用,围绕“谁参与合供”“为什么合供”“怎么合供”三个问题,分析政府部门、项目企业、职业院校以及公共组织在合作培养职业教育现场工程师中的主体作用。通过阐释职业教育现场工程师合作培养的缘由及意义,来选择多元主体合作育人模式、搭建多元主体合作育人平台、实施多元主体合作育人管理等方式,优化职业教育现场工程师合作培养的实践路径,以满足数智化职业场景对高素质技能人才的现实需求。

A duality theorem of crossed coproduct for Hopf algebras

A duality theorem for Hopf crossed coproduct is proved. This theorem plays a role similar to that appearing in the work of Koppinen (which generalized the corresponding results of group grraded ring).

Nutrient profile and digestibility of tubers and agro-industrial coproducts determined using an in vitro model of swine

Exploring and evaluating alternative feed ingredients to be used in swine diet is essential due to highly variable cost and limited availability of conventional feed ingredients. Tubers and agro-industrial coproducts could provide the basis for producing affordable swine feed. However, information on the nutritional value of these potential alternative feedstuffs is necessary while considering their use in swine feeding program. Four tubers(purple sweet potato [PSP], okinawan sweet potato, taro and cassava) and 3 coproducts(okara, wheat millrun [WMR] and barley brewers grain [BBG]) were analyzed for their proximate nutrients, starch, fibers and gross energy(GE) content. Two independent in vitro studies were carried out for tubers and coproducts to determine their nutrients digestibility using a 3-step enzymatic assay(which mimics the digestion occurring in the gastrointestinal tract of swine) with 9 replicates of each sample digested in 3 batches equally. All replicate samples were used to determine in vitro dry matter digestibility(IVDDM) while 2 replicates from each batch were used to determine in vitro GE digestibility(IVDGE). Among tubers, CP content was the highest in taro(8.8%) and the lowest in cassava(3.7%), while CP content among coproducts was the highest in okara(22.7%) and the lowest in WMR(11.8%). Ether extract content among tubers ranged from 1.1% to 2.8%. The GE content among tubers, ranged from 4,134 to 4,334 kcal/kg whereas among coproducts it ranged from 4,270 to 4,794 kcal/kg. Among tubers, IVDDM for PSP was significantly higher(86.8%, P < 0.001) than taro(70.3%). Among coproducts, IVDDM of okara(74.1%) was significantly higher(P < 0.05) than BBG(61.3%). In conclusion,both tubers and coproducts can be used as a partial substitute of conventional energy feedstuffs in swine diets as these are rich in GE and other nutrients and are fairly digestible.

Cosemisimple Coextensions and Homological Dimension of Smash Coproducts

Let H be a finite dimensional cosemisimple Hopf algebra, C a left H-comodule coalgebra and let C = C/C（H^＊）^＋ be the quotient coalgebra and the smash coproduct of C and H. It is shown that if C/C is a eosemisimple coextension and C is an injective right C-comodule, then gl. dim（the smash coproduct of C and H） = gl. dim（C） = gl. dim（C）, where gl. dim（C） denotes the global dimension of coalgebra C.

THE GENERALIZED SMASH PRODUCT AND COPRODUCT

The author discusses the braiding structures of the generalized smash product bialgebra and the cobraiding structures of the generalized smash coproduct bialgebra. It is pointed out that doublecrossed product determined by a cocycle is the generalized smash product and that doublecocrossed coproduct determined by a weak R-matrix is the generalized smash coproduct.

(f,ω)-Compatible Pair (B,H) for ω-Smash Coproduct Hopf Algebras

In this paper we introduce the notion of （f,ω）-compatible pair （B,H）, by which we construct a Hopf algebra in the category HHYD of Yetter-Drinfeld H-modules by twisting the comultiplication of B. We also study the property of ω-smash coproduct Hopf algebras Bω H.

知识共生产框架下科技伦理治理主体的基础性功能与其对应的实现方式

发达的经济不仅为科技创新带来了肥沃的土壤,同时也带来了科技伦理方面的隐患。在面对越来越严峻的科技伦理治理挑战时,政府、专家和公众等主体如何达成合作来共同打开科技伦理治理的“黑箱”,是学界关注的重点。选择科技伦理治理中政府、专家和公众这3类具有代表性的重要主体,基于科技伦理治理的内容,对“知识共生产”的概念进行总结,在此基础上,进一步建构科技伦理治理主体的知识共生产研究框架,分析科技伦理治理主体的基础性功能与其对应的实现方式。研究认为,政府(治理知识型生产者)、专家(专业知识型生产者)和公众(助力知识型生产者)共同参与到科技伦理风险问题的治理过程,分别具有政策架构支持、知识储备运用和外在助力推动的基础性功能,并分别通过政策支持实现方式与宏观架构治理方式、知识储备作用方式与知识实践运用方式、现实动因推动方式与外在助力参与方式来发挥政府知识的治理作用、专家知识的专业作用和公众知识的辅助作用,从而实现知识共生产,进而推动科技伦理风险问题的有效解决。进一步提出,未来相关研究可以从框架、视角和理念三方面深入展开。

流化床煅烧菱镁矿联产CO_(2)与气氛对产物活性的影响

CO_(2)的大量排放会导致气候变化,威胁人类生存。如何遏制与中和碳排放,高效实现碳捕捉,已经是科研工作者最关心的话题之一。利用流化床颗粒采样器,通过改变升温速率、流化气氛,研究菱镁矿非等温条件下的反应特性与N_(2)、CO_(2)条件下对产物活性的影响,利用TG、BET、XRD、SEM对轻烧产物的活性及微观结构进行表征。结果表明:CO_(2)气氛抑制菱镁矿分解,当原料分解完全后,温度继续升高,晶粒尺寸逐渐变大,比表面积变小,柠檬酸法显色时间变长,活性降低;改变升温速率,升温速率变化越快,菱镁矿内外受热温度越不均,内外分解差异越大,菱镁矿分解率越低,柠檬酸显色时间越长;相同条件下,与N_(2)气氛相比,CO_(2)气氛的柠檬酸法显色时间用时更久,即产物的活性由微观结构与分解率决定。

The Global Dimensions of Crossed Products and Crossed Coproducts

In this paper, we show that if H is a finite-dimensional Hopf algebra such that H and H^＊ are semisimple, then gl.dim（A#σH）=gl.dim（A）, where a is a convolution invertible cocycle. We also discuss the relationship of global dimensions between the crossed product A^#σH and the algebra A, where A is coacted by H. Dually, we give a sufficient condition for a finite dimensional coalgebra C and a finite dimensional semisimple Hopf algebra H such that gl.dim（C α H）=gl.dim（C）.

Some Results on Cohomology of Twisted Smash Coproduct

With the main motivation to present some alternatives to the cosemisimplicity of twisted Smash coproduct,this paper first gives some basic constructions which make sense to consider the derived functors of some left exact functors from the category of comodules to vector spaces.Then,the Hochschild–Serre spectral sequence for twisted Smash coproduct coalgebras is obtained,which extends some results on homological properties given in the category of comodules over Smash coproduct in the literature.

Maschke-Type Theorems for Weak Smash Coproducts

In this paper we mainly give Maschke-type theorems for weak smash coproduct coalgebras which simultaneously show how to deal with the complicated computations of weak smash coproduct coalgebras.

PRODUCTS AND COPRODUCTS IN CATEGORY OF COMPLETELY DISTRIBUTIVE LATTICES AND THEIR STRUCTURES

Taking completely distributive lattices for objects and complete lattice homomorphisms for morphisms, we get a category Lat (see Refs. [1—3]). There is a primary question about Lat: Does every family of objects have product and coproduct in Lat? We prove that Lat has products and coproducts, and describe the intrinsic relation between