Journal of the Australian Mathematical Society最新文献

{"title":"COSUPPORT FOR COMPACTLY GENERATED TRIANGULATED CATEGORIES","authors":"Xiaoyan Yang","doi":"10.1017/s1446788722000222","DOIUrl":"https://doi.org/10.1017/s1446788722000222","url":null,"abstract":"\u0000 The goal of the article is to better understand cosupport in triangulated categories since it is still quite mysterious. We study boundedness of local cohomology and local homology functors using Koszul objects, give some characterizations of cosupport, and get some results that, in special cases, recover and generalize the known results about the usual cosupport. Additionally, we include some computations of cosupport and provide a comparison of support and cosupport for cohomologically finite objects. Finally, we assign to any object of the category a subset of \u0000 \u0000 \u0000 \u0000$mathrm {Spec}R$\u0000\u0000 \u0000 , called the big cosupport, and study some of its properties.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80670884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ON THE ALGEBRAS","authors":"REZA ESMAILVANDI, MEHDI NEMATI, NAGESWARAN SHRAVAN KUMAR","doi":"10.1017/s1446788722000192","DOIUrl":"https://doi.org/10.1017/s1446788722000192","url":null,"abstract":"<p>Let <span>H</span> be an ultraspherical hypergroup and let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231109001332944-0291:S1446788722000192:S1446788722000192_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$A(H)$</span></span></img></span></span> be the Fourier algebra associated with <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231109001332944-0291:S1446788722000192:S1446788722000192_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$H.$</span></span></img></span></span> In this paper, we study the dual and the double dual of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231109001332944-0291:S1446788722000192:S1446788722000192_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$A(H).$</span></span></img></span></span> We prove among other things that the subspace of all uniformly continuous functionals on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231109001332944-0291:S1446788722000192:S1446788722000192_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$A(H)$</span></span></img></span></span> forms a <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231109001332944-0291:S1446788722000192:S1446788722000192_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$C^*$</span></span></img></span></span>-algebra. We also prove that the double dual <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231109001332944-0291:S1446788722000192:S1446788722000192_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$A(H)^{ast ast }$</span></span></img></span></span> is neither commutative nor semisimple with respect to the Arens product, unless the underlying hypergroup <span>H</span> is finite. Finally, we study the unit elements of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231109001332944-0291:S1446788722000192:S1446788722000192_inline10.png\"><span data-mathjax-type=\"texmath\"><span>$A(H)^{ast ast }.$</span></span></img></span></span></p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ON POSSIBLE VALUES OF THE INTERIOR ANGLE BETWEEN INTERMEDIATE SUBALGEBRAS","authors":"V. Gupta, Deepika Sharma","doi":"10.1017/s1446788723000058","DOIUrl":"https://doi.org/10.1017/s1446788723000058","url":null,"abstract":"\u0000 We show that all values in the interval \u0000 \u0000 \u0000 \u0000$[0,{pi }/{2}]$\u0000\u0000 \u0000 can be attained as interior angles between intermediate subalgebras (as introduced by Bakshi and the first named author [‘Lattice of intermediate subalgebras’, J. Lond. Math. Soc. (2)104(2) (2021), 2082–2127]) of a certain inclusion of simple unital \u0000 \u0000 \u0000 \u0000$C^*$\u0000\u0000 \u0000 -algebras. We also calculate the interior angles between intermediate crossed product subalgebras of any inclusion of crossed product algebras corresponding to any action of a countable discrete group and its subgroups on a unital \u0000 \u0000 \u0000 \u0000$C^*$\u0000\u0000 \u0000 -algebra.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85952665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"JAZ volume 113 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s1446788721000367","DOIUrl":"https://doi.org/10.1017/s1446788721000367","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78475879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"INDEX","authors":"","doi":"10.1017/s1446788721000379","DOIUrl":"https://doi.org/10.1017/s1446788721000379","url":null,"abstract":"Acetylsalicylic acid, for tension-type headache, 287 Acupuncture, for tension-type headache, 289 Age, of headache onset, 188–189 Amitriptyline, for tension-type headache, 288 Amoxapine, for tension-type headache, 288 Anemia, in giant cell arteritis, 333 Aneurysms, cavernous sinus, 304 Anisocoria, 205–209 Antibiotics for conjunctivitis, 298–299 for corneal injury, 298 for otitis media, 316 for styes, 296 Anticoagulation, bleeding due to, 249–250 Antidepressants, for tension-type headache, 288–289 Antispasticitiy agents, for tension-type headache, 286–287 Arteriovenous malformations, 247 Arteritis, temporal (giant cell), 221–222, 254, 329–335 Atlanto-axial joint, disorders of, 271 Atlanto-occipital joint, disorders of, 270–271 Auditory canal, pain in, 313–315 Aurae, 190 Auricle, pain in, 311–313 Autoimmune diseases, headache in, 232 Autonomic symptoms, in short-lasting unilateral neuralgiform headache attacks with cranial autonomic symptoms, 323–326","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76591367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"JAZ volume 113 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s1446788721000355","DOIUrl":"https://doi.org/10.1017/s1446788721000355","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91192987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"JAZ volume 113 issue 2 Cover and Front matter","authors":"","doi":"10.1017/S1446788721000331","DOIUrl":"https://doi.org/10.1017/S1446788721000331","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87050710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"JAZ volume 113 issue 2 Cover and Back matter","authors":"","doi":"10.1017/S1446788721000343","DOIUrl":"https://doi.org/10.1017/S1446788721000343","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81681192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BOUNDARY BLOW-UP SOLUTIONS TO EQUATIONS INVOLVING THE INFINITY LAPLACIAN","authors":"Cuicui Li, Fang Liu, P. Zhao","doi":"10.1017/S1446788722000131","DOIUrl":"https://doi.org/10.1017/S1446788722000131","url":null,"abstract":"Abstract In this paper, we study the boundary blow-up problem related to the infinity Laplacian \u0000$$ begin{align*}begin{cases} Delta_{infty}^h u=u^q &mathrm{in}; Omega, u=infty &mathrm{on} ;partialOmega, end{cases} end{align*} $$\u0000 where \u0000$Delta _{infty }^h u=|Du|^{h-3} langle D^2uDu,Du rangle $\u0000 is the highly degenerate and h-homogeneous operator associated with the infinity Laplacian arising from the stochastic game named Tug-of-War. When \u0000$q>h>1$\u0000 , we establish the existence of the boundary blow-up viscosity solution. Moreover, when the domain satisfies some regular condition, we establish the asymptotic estimate of the blow-up solution near the boundary. As an application of the asymptotic estimate and the comparison principle, we obtain the uniqueness result of the large solution. We also give the nonexistence of the large solution for the case \u0000$q leq h.$","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91267317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"CONDITIONAL FLATNESS, FIBERWISE LOCALIZATIONS, AND ADMISSIBLE REFLECTIONS","authors":"M. Gran, J. Scherer","doi":"10.1017/s1446788723000046","DOIUrl":"https://doi.org/10.1017/s1446788723000046","url":null,"abstract":"\u0000 We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localization, analogous results to those obtained in the category of groups hold, and we provide existence theorems for certain localization functors in specific semi-abelian categories. We prove that a Birkhoff subcategory of an ideal determined category yields a conditionally flat localization, and explain how conditional flatness corresponds to the property of admissibility of an adjunction from the point of view of categorical Galois theory. Under the assumption of fiberwise localization, we give a simple criterion to determine when a (normal epi)-reflection is a torsion-free reflection. This is shown to apply, in particular, to nullification functors in any semi-abelian variety of universal algebras. We also relate semi-left-exactness for a localization functor L with what is called right properness for the L-local model structure.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84761063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}