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Kurt Gödel and the logic of concepts 库尔特-哥德尔与概念逻辑
Publications de l'Institut Math?matique (Belgrade) Pub Date : 2024-06-08 DOI: 10.2298/pim2429001k
Jovana Kosti'c, Slobodan Vujovsevi'c
{"title":"Kurt Gödel and the logic of concepts","authors":"Jovana Kosti'c, Slobodan Vujovsevi'c","doi":"10.2298/pim2429001k","DOIUrl":"https://doi.org/10.2298/pim2429001k","url":null,"abstract":"The literature dealing with G?del?s legacy is largely preoccupied with\u0000 challenging his philosophical views, regarding them as outdated. We believe\u0000 that such an approach prevents us from seeing G?del?s views in the right\u0000 light and understanding their rationale. In this article, his views are\u0000 discussed in the philosophical realm in which he himself understood them. We\u0000 explore the consequences of G?del?s incompleteness theorems for the question\u0000 of the objectivity of mathematics and its epistemology. Taking set theory as\u0000 the paradigm of formal mathematical theories, we examine the relationship\u0000 between its incompleteness and extensionality. We argue, based on his\u0000 philosophical views, that G?del believed incompleteness can be overcome only\u0000 by some intensional considerations about concepts from the basis of\u0000 mathematical theories. These considerations should eventually lead to\u0000 founding the so-called logic of concepts.","PeriodicalId":319403,"journal":{"name":"Publications de l'Institut Math?matique (Belgrade)","volume":" 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141369838","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}
引用次数: 0
Evaluating the sum of convergent positive series 求收敛的正级数的和
Publications de l'Institut Math?matique (Belgrade) Pub Date : 2021-08-14 DOI: 10.2298/pim2225041a
V. Abramov
{"title":"Evaluating the sum of convergent positive series","authors":"V. Abramov","doi":"10.2298/pim2225041a","DOIUrl":"https://doi.org/10.2298/pim2225041a","url":null,"abstract":"We provide numerical procedures for possibly best evaluating the sum of\u0000 positive series under quite general setting. Our procedures are based on the\u0000 application of a generalized version of Kummer's test.","PeriodicalId":319403,"journal":{"name":"Publications de l'Institut Math?matique (Belgrade)","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124883236","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}
引用次数: 0
A new test for convergence of positive series 正级数收敛性的一个新检验
Publications de l'Institut Math?matique (Belgrade) Pub Date : 2021-04-09 DOI: 10.2298/PIM2123061A
V. Abramov, M. Cadena, E. Omey
{"title":"A new test for convergence of positive series","authors":"V. Abramov, M. Cadena, E. Omey","doi":"10.2298/PIM2123061A","DOIUrl":"https://doi.org/10.2298/PIM2123061A","url":null,"abstract":"The paper provides a new test of convergence and divergence of positive\u0000 series. In particular, it extends the known test by Margaret Martin [Bull.\u0000 Amer. Math. Soc. 47 (1941), 452-457].","PeriodicalId":319403,"journal":{"name":"Publications de l'Institut Math?matique (Belgrade)","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123142155","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}
引用次数: 1
Inverse theorem for certain directional Gowers uniformity norms 某些定向Gowers均匀性范数的逆定理
Publications de l'Institut Math?matique (Belgrade) Pub Date : 2021-03-10 DOI: 10.2298/pim2327001m
L. Milicevic
{"title":"Inverse theorem for certain directional Gowers uniformity norms","authors":"L. Milicevic","doi":"10.2298/pim2327001m","DOIUrl":"https://doi.org/10.2298/pim2327001m","url":null,"abstract":"Let G be a finite-dimensional vector space over a prime field Fp with some\u0000 subspaces H1,...,Hk. Let f : G ? C be a function. Generalizing the\u0000 notion of Gowers uniformity norms, Austin introduced directional Gowers\u0000 uniformity norms of f over (H1,...,Hk) as ||f||2kU(H1,...,Hk) = E\u0000 x?G,h1?H1,...,hk?Hk ? ?h1... ??hk f(x) where ??uf(x) : = f(x + u)?f(x) is\u0000 the discrete multiplicative derivative. Suppose that G is a direct sum of\u0000 subspaces G = U1 ? U2 ?...? Uk. In this paper we prove the inverse\u0000 theorem for the norm ||?||U(U1,...,Uk,G,...,G), with ? copies of G in the\u0000 subscript, which is the simplest interesting unknown case of the inverse\u0000 problem for the directional Gowers uniformity norms. Namely, writing ||? ||U\u0000 for the norm above, we show that if f : G ? C is a function bounded by 1\u0000 in magnitude and obeying ||f||U ? c, provided ? < p, one can find a polynomial\u0000 ?: G ? Fp of degree at most k + ? ? 1 and functions gi : ?j?[k]{i} Uj ? {z\u0000 ? C: |z| ? 1} for i ? [k] such that |Ex?G f(x)??(x) ? i? [k] gi(x1,... ,xi?1, xi+1,..., xk)| ? (exp(Op,k,?(1))(Op,k,?(c?1)))?1. The proof\u0000 relies on an approximation theorem for the cuboid-counting function that is\u0000 proved using the inverse theorem for Freiman multi-homomorphisms.","PeriodicalId":319403,"journal":{"name":"Publications de l'Institut Math?matique (Belgrade)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116508569","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}
引用次数: 2
Linear combinations of polynomials with three-term recurrence 三项递归多项式的线性组合
Publications de l'Institut Math?matique (Belgrade) Pub Date : 2019-07-31 DOI: 10.2298/pim2124029t
Khang Tran, M. Zhang
{"title":"Linear combinations of polynomials with three-term recurrence","authors":"Khang Tran, M. Zhang","doi":"10.2298/pim2124029t","DOIUrl":"https://doi.org/10.2298/pim2124029t","url":null,"abstract":"We study the zero distribution of the sum of the first n polynomials\u0000 satisfying a three-term recurrence whose coefficients are linear\u0000 polynomials. We also extend this sum to a linear combination, whose\u0000 coefficients are powers of az + b for a, b ? R, of Chebyshev polynomials. In\u0000 particular, we find necessary and sufficient conditions on a, b such that\u0000 this linear combination is hyperbolic.","PeriodicalId":319403,"journal":{"name":"Publications de l'Institut Math?matique (Belgrade)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121288122","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}
引用次数: 1
The Boole Polynomials Associated with the p-adic Gamma Function 与 p-adic Gamma 函数相关的布尔多项式
Publications de l'Institut Math?matique (Belgrade) Pub Date : 2019-05-16 DOI: 10.20944/PREPRINTS201905.0216.V1
U. Duran, M. Acikgoz
{"title":"The Boole Polynomials Associated with the p-adic Gamma Function","authors":"U. Duran, M. Acikgoz","doi":"10.20944/PREPRINTS201905.0216.V1","DOIUrl":"https://doi.org/10.20944/PREPRINTS201905.0216.V1","url":null,"abstract":"The main aim of this paper is to set some correlations between Boole polynomials and p-adic gamma function in conjunction with p-adic Euler contant. We develop diverse formulas for p-adic gamma function by means of their Mahler expansion and fermionic p-adic integral on ℤ_{p}. Also, we acquire two fermionic p-adic integrals of p-adic gamma function in terms of Boole numbers and polynomials. We then provide fermionic p-adic integral of the derivative of p-adic gamma function and a representation for the p-adic Euler constant by means of the Boole polynomials. Furthermore, we investigate an explicit representation for the aforesaid constant covering Stirling numbers of the first kind.","PeriodicalId":319403,"journal":{"name":"Publications de l'Institut Math?matique (Belgrade)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126560281","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}
引用次数: 0
On estimates of deviation of conjugate functions from matrix operators of their Fourier series by some expressions with r-differences of the entries 共轭函数与傅里叶级数的矩阵算子的偏差估计用一些项有r差的表达式
Publications de l'Institut Math?matique (Belgrade) Pub Date : 2019-04-05 DOI: 10.2298/PIM2123109L
W. Lenski, B. Szal
{"title":"On estimates of deviation of conjugate functions from matrix operators of their Fourier series by some expressions with r-differences of the entries","authors":"W. Lenski, B. Szal","doi":"10.2298/PIM2123109L","DOIUrl":"https://doi.org/10.2298/PIM2123109L","url":null,"abstract":"We extend the results of the authors from [Abstract and Applied Analysis,\u0000 Volume 2016, Article ID 9712878] to the case conjugate Fourier series.","PeriodicalId":319403,"journal":{"name":"Publications de l'Institut Math?matique (Belgrade)","volume":"302 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132795072","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}
引用次数: 0
Integer points enumerator of hypergraphic polytopes 超图形多面体的整数点枚举器
Publications de l'Institut Math?matique (Belgrade) Pub Date : 2018-12-23 DOI: 10.2298/PIM200205001P
M. Pešović
{"title":"Integer points enumerator of hypergraphic polytopes","authors":"M. Pešović","doi":"10.2298/PIM200205001P","DOIUrl":"https://doi.org/10.2298/PIM200205001P","url":null,"abstract":"For a hypergraphic polytope there is a weighted quasisymmetric function which\u0000 enumerates positive integer points in its normal fan and determines its\u0000 f-polynomial. This quasisymmetric function invariant of hypergraphs extends\u0000 the Stanley chromatic symmetric function of simple graphs. We consider a\u0000 certain combinatorial Hopf algebra of hypergraphs and show that universal\u0000 morphism to quasisymmetric functions coincides with this enumerator function.\u0000 We calculate the f-polynomial of uniform hypergraphic polytopes.","PeriodicalId":319403,"journal":{"name":"Publications de l'Institut Math?matique (Belgrade)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131127321","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}
引用次数: 1
Improving a constant in high-dimensional discrepancy estimates 改进高维差异估计中的常数
Publications de l'Institut Math?matique (Belgrade) Pub Date : 2018-10-26 DOI: 10.2298/pim2021067p
Hendrik Pasing, Christian Weiss
{"title":"Improving a constant in high-dimensional discrepancy estimates","authors":"Hendrik Pasing, Christian Weiss","doi":"10.2298/pim2021067p","DOIUrl":"https://doi.org/10.2298/pim2021067p","url":null,"abstract":"For all s ? 1 and N ? 1 there exist sequences (z1,..., zN) in [0, 1]s\u0000 such that the star-discrepancy of these points can be bounded by D* N(z1,..., zN) ? c ?s/?N . In practice it is desirable to obtain low values of c.\u0000 The best known value for the constant is c = 10 as has been calculated by\u0000 Aistleitner. In this paper we improve the bound to c = 9.","PeriodicalId":319403,"journal":{"name":"Publications de l'Institut Math?matique (Belgrade)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125465498","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}
引用次数: 3
Classification theorem for strong triangle blocking arrangements 强三角形阻塞排列的分类定理
Publications de l'Institut Math?matique (Belgrade) Pub Date : 2018-09-23 DOI: 10.2298/pim2021001m
L. Milicevic
{"title":"Classification theorem for strong triangle blocking arrangements","authors":"L. Milicevic","doi":"10.2298/pim2021001m","DOIUrl":"https://doi.org/10.2298/pim2021001m","url":null,"abstract":"A strong triangle blocking arrangement is a geometric arrangement of some\u0000 line segments in a triangle with certain intersection properties. It turns\u0000 out that they are closely related to blocking sets. We prove a\u0000 classification theorem for strong triangle blocking arrangements. As an\u0000 application, we obtain a new proof of the result of Ackerman, Buchin,\u0000 Knauer, Pinchasi and Rote which says that n points in general position\u0000 cannot be blocked by n ? 1 points, unless n = 2, 4. We also conjecture an\u0000 extremal variant of the blocking points problem.","PeriodicalId":319403,"journal":{"name":"Publications de l'Institut Math?matique (Belgrade)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115280291","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}
引用次数: 4
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