We study corners and fundamental corners of the irreducible subquotients of reducible elementary representations of the groups G = Spin(n, 1). For even n we obtain results in a way analogous to the results in [8] for the groups SU(n, 1). Especially, we again get a bijection between the nonelementary part Gˆ0 of the unitary dual Gˆ and the unitary dual K. ˆ In the case of odd n we get a bijection between Gˆ0 and a true subset of K.
{"title":"Nonelementary irreducible representations of Spin(n, 1)","authors":"D. Kovacevic, H. Kraljevic","doi":"10.32817/ams.2.2","DOIUrl":"https://doi.org/10.32817/ams.2.2","url":null,"abstract":"We study corners and fundamental corners of the irreducible subquotients of reducible elementary representations of the groups G = Spin(n, 1). For even n we obtain results in a way analogous to the results in [8] for the groups SU(n, 1). Especially, we again get a bijection between the nonelementary part Gˆ0 of the unitary dual Gˆ and the unitary dual K. ˆ In the case of odd n we get a bijection between Gˆ0 and a true subset of K.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124061156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that general integral triangle inequality does not hold for shifted q-integrals. Furthermore, we obtain a triangle inequality for shifted qintegrals. We also give an estimate for q-integrable product and use it to refine some recently obtained Ostrowski inequalities for quantum calculus.
{"title":"Triangle inequality for quantum integral operator","authors":"A. Aglić Aljinović, I. Brnetić, Ana Žgaljić Keko","doi":"10.32817/ams.2.7","DOIUrl":"https://doi.org/10.32817/ams.2.7","url":null,"abstract":"We show that general integral triangle inequality does not hold for shifted q-integrals. Furthermore, we obtain a triangle inequality for shifted qintegrals. We also give an estimate for q-integrable product and use it to refine some recently obtained Ostrowski inequalities for quantum calculus.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122423760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study algebraic systems MΓ of free semigroup structure, where Γ is a well ordered finite alphabet, discovered in 1970s within the Theory of Electric Circuits by Miro Šare, and and finding recent recent applications in Multivalued Logic, as well as in Computational Linguistics. We provide three simple axioms (reversion axiom (5) and two compression axioms (6) and (7)), which generate the corresponding equivalence relation between words. We also introduce a class of incompressible words, as well as the quotient Šare system MΓ~. The main result is contained in Theorem 16, announced by Šare without proof, which characterizes the equivalence of two words by means of Šare sums. The proof is constructive. We describe an algorithm for compression of words, study homomorphisms between quotient Šare systems for various alphabets Γ (Theorem 38), and introduce two natural Šare categories ŠŠa(M) and ŠŠa(M~). Šare systems are not inverse semigroups.
{"title":"Šare’s algebraic systems","authors":"M. Essert, D. Zubrinic","doi":"10.32817/ams.2.1","DOIUrl":"https://doi.org/10.32817/ams.2.1","url":null,"abstract":"We study algebraic systems MΓ of free semigroup structure, where Γ is a well ordered finite alphabet, discovered in 1970s within the Theory of Electric Circuits by Miro Šare, and and finding recent recent applications in Multivalued Logic, as well as in Computational Linguistics. We provide three simple axioms (reversion axiom (5) and two compression axioms (6) and (7)), which generate the corresponding equivalence relation between words. We also introduce a class of incompressible words, as well as the quotient Šare system MΓ~. The main result is contained in Theorem 16, announced by Šare without proof, which characterizes the equivalence of two words by means of Šare sums. The proof is constructive. We describe an algorithm for compression of words, study homomorphisms between quotient Šare systems for various alphabets Γ (Theorem 38), and introduce two natural Šare categories ŠŠa(M) and ŠŠa(M~). Šare systems are not inverse semigroups.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131945218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The special properties of an abstract category morphism (for instance, being an identity, an isomorphism, an epimorphism., a monomorphism . . . ) fully depend on the category composition. Consequently, an isomorphic category to a concrete category may be not concrete, i.e., the concreteness is not a category invariant. Further, every small category is isomorphic to a small category whose objects are sets and whose morphisms are functions between those sets.
{"title":"A note on a category composition","authors":"N. Uglešić","doi":"10.32817/ams.2.3","DOIUrl":"https://doi.org/10.32817/ams.2.3","url":null,"abstract":"The special properties of an abstract category morphism (for instance, being an identity, an isomorphism, an epimorphism., a monomorphism . . . ) fully depend on the category composition. Consequently, an isomorphic category to a concrete category may be not concrete, i.e., the concreteness is not a category invariant. Further, every small category is isomorphic to a small category whose objects are sets and whose morphisms are functions between those sets.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121615391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let p be a prime number and | · |p the p-adic absolute value on Q and on the p-adic field Qp normalized such that |p|p = p −1 . Let ξ be a quadratic real number and α a quadratic p-adic number. We prove that there exist positive, effectively computable, real numbers c1 = c1(ξ), τ1 = τ1(ξ), c2 = c2(α), τ2 = τ2(α), such that |yξ − x| · |y|p ≥ c1|y| −2+τ1 , for x, y ∈ Z̸=0, and |bα − a|p ≥ c2|ab| −2+τ2 , for a, b ∈ Z̸=0. Both results improve the effective lower bounds which follow from an easy Liouville-type argument.
{"title":"On effective approximation to quadratic numbers","authors":"Y. Bugeaud","doi":"10.32817/ams.2.6","DOIUrl":"https://doi.org/10.32817/ams.2.6","url":null,"abstract":"Let p be a prime number and | · |p the p-adic absolute value on Q and on the p-adic field Qp normalized such that |p|p = p −1 . Let ξ be a quadratic real number and α a quadratic p-adic number. We prove that there exist positive, effectively computable, real numbers c1 = c1(ξ), τ1 = τ1(ξ), c2 = c2(α), τ2 = τ2(α), such that |yξ − x| · |y|p ≥ c1|y| −2+τ1 , for x, y ∈ Z̸=0, and |bα − a|p ≥ c2|ab| −2+τ2 , for a, b ∈ Z̸=0. Both results improve the effective lower bounds which follow from an easy Liouville-type argument.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127602730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Motived by the characterization of the positive elements in a C ∗–algebra and the decomposition of an operator into a sum of orthogonal projections, we introduce the notions of positive operator and K-operator frame for B(H). Also, we give some properties.
{"title":"Positive Operator Frame for Hilbert spaces","authors":"Mohamed Rossafi, Y. Aribou","doi":"10.32817/ams.2.4","DOIUrl":"https://doi.org/10.32817/ams.2.4","url":null,"abstract":"Motived by the characterization of the positive elements in a C ∗–algebra and the decomposition of an operator into a sum of orthogonal projections, we introduce the notions of positive operator and K-operator frame for B(H). Also, we give some properties.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123646942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we want to optimize a certain gain/loss function which has no analytical form and thus cannot be measured directly but only by comparison of two parameter sets. We also experimentally compare the new method with the famous SPSA method.
{"title":"Bayesian statistics approach to chess engines optimization","authors":"Ivan Ivec, Ivana Vojnovi'c","doi":"10.32817/ams.2.5","DOIUrl":"https://doi.org/10.32817/ams.2.5","url":null,"abstract":"We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we want to optimize a certain gain/loss function which has no analytical form and thus cannot be measured directly but only by comparison of two parameter sets. We also experimentally compare the new method with the famous SPSA method.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122496723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let G be a graph with edge set E(G) that admits a perfect matching M. A forcing set of M is a subset of M contained in no other perfect matchings of G. A complete forcing set of G, recently introduced by Xu et al. [Complete forcing numbers of catacondensed hexagonal systems, J. Combin. Optim. 29(4) (2015) 803-814], is a subset of E(G) on which the restriction of any perfect matching M is a forcing set of M. The minimum possible cardinality of complete forcing sets of G is the complete forcing number of G. In this article, we discuss the complete forcing number of rectangular polyominoes (or grids), i.e., the Cartesian product of two paths of various lengths, and show explicit formulae for the complete forcing numbers of rectangular polyominoes in terms of the lengths.
{"title":"Complete forcing numbers of rectangular polynominoes","authors":"Hong Chang, Yongqi Feng, H. Bian, Shoujun Xu","doi":"10.32817/AMS.1.1.7","DOIUrl":"https://doi.org/10.32817/AMS.1.1.7","url":null,"abstract":"Let G be a graph with edge set E(G) that admits a perfect matching M. A forcing set of M is a subset of M contained in no other perfect matchings of G. A complete forcing set of G, recently introduced by Xu et al. [Complete forcing numbers of catacondensed hexagonal systems, J. Combin. Optim. 29(4) (2015) 803-814], is a subset of E(G) on which the restriction of any perfect matching M is a forcing set of M. The minimum possible cardinality of complete forcing sets of G is the complete forcing number of G. In this article, we discuss the complete forcing number of rectangular polyominoes (or grids), i.e., the Cartesian product of two paths of various lengths, and show explicit formulae for the complete forcing numbers of rectangular polyominoes in terms of the lengths.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115006643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let A^n be the completion by the degree of a differential operator of the n-th Weyl algebra with generators x1,…,xn,∂1,…,∂n. Consider n elements X1,…,Xn in A^n of the formXi=xi+∑K=1∞∑l=1n∑j=1nxlpijK−1,l(∂)∂j,where pijK−1,l(∂) is a degree (K−1) homogeneous polynomial in ∂1,…,∂n, antisymmetric in subscripts i,j. Then for any natural k and any function i:{1,…,k}→{1,…,n} we prove∑σ∈Σ(k)Xiσ(1)⋯Xiσ(k)▹1=k!xi1⋯xik,where Σ(k) is the symmetric group on k letters and ▹ denotes the Fock action of the A^n on the space of (commutative) polynomials.
{"title":"A note on symmetric orderings","authors":"Zoran vSkoda","doi":"10.32817/AMS.1.1.5","DOIUrl":"https://doi.org/10.32817/AMS.1.1.5","url":null,"abstract":"Let A^n be the completion by the degree of a differential operator of the n-th Weyl algebra with generators x1,…,xn,∂1,…,∂n. Consider n elements X1,…,Xn in A^n of the formXi=xi+∑K=1∞∑l=1n∑j=1nxlpijK−1,l(∂)∂j,where pijK−1,l(∂) is a degree (K−1) homogeneous polynomial in ∂1,…,∂n, antisymmetric in subscripts i,j. Then for any natural k and any function i:{1,…,k}→{1,…,n} we prove∑σ∈Σ(k)Xiσ(1)⋯Xiσ(k)▹1=k!xi1⋯xik,where Σ(k) is the symmetric group on k letters and ▹ denotes the Fock action of the A^n on the space of (commutative) polynomials.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123393961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The argument shift method is a well-known method for generating commutative families of functions in Poisson algebras from central elements and a vector field, verifying a special condition with respect to the Poisson bracket. In this notice we give an analogous construction, which gives one a way to create commutative subalgebras of a deformed algebra from its center (which is as it is well known describable in the terms of the center of the Poisson algebra) and an L∞-differentiation of the algebra of Hochschild cochains, verifying some additional conditions with respect to the Poisson structure.
{"title":"L∞ - derivations and the argument shift method for deformation quantization algebras","authors":"G. Sharygin","doi":"10.32817/AMS.1.1.6","DOIUrl":"https://doi.org/10.32817/AMS.1.1.6","url":null,"abstract":"The argument shift method is a well-known method for generating commutative families of functions in Poisson algebras from central elements and a vector field, verifying a special condition with respect to the Poisson bracket. In this notice we give an analogous construction, which gives one a way to create commutative subalgebras of a deformed algebra from its center (which is as it is well known describable in the terms of the center of the Poisson algebra) and an L∞-differentiation of the algebra of Hochschild cochains, verifying some additional conditions with respect to the Poisson structure.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131645989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：