Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:Casazza; Peter G., Dilworth, Stephen J., Kutzarova, Denka, Motakis, Pavlos Pages: 1073 - 1083 Abstract: Motivated by Altshuler’s famous characterization of the unit vector basis of or among symmetric bases (Altshuler [1976, Israel Journal of Mathematics, 24, 39–44]), we obtain similar characterizations among democratic bases and among bidemocratic bases. We also prove a separate characterization of the unit vector basis of . PubDate: 2023-02-21 DOI: 10.4153/S0008439523000176

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Authors:Shchepin; E., Valov, V. Pages: 1084 - 1090 Abstract: We discuss the question of extending homeomorphisms between closed subsets of the Cantor cube . It is established that any homeomorphism between two closed negligible subsets of can be extended to an autohomeomorphism of . PubDate: 2023-02-28 DOI: 10.4153/S0008439523000188

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Authors:Lappo; Egor Pages: 1091 - 1108 Abstract: We define smooth notions of concordance and sliceness for spatial graphs. We prove that sliceness of a spatial graph is equivalent to a condition on a set of linking numbers together with sliceness of a link associated with the graph. This generalizes the result of Taniyama for -curves. PubDate: 2023-03-15 DOI: 10.4153/S000843952300019X

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Authors:Collari; Carlo Pages: 1109 - 1121 Abstract: A result of Corfield, Sati, and Schreiber asserts that -weight systems associated with the defining representation are quantum states. In this short note, we extend this result to all -weight systems corresponding to labeling by symmetric and exterior powers of the defining representation. PubDate: 2023-03-09 DOI: 10.4153/S0008439523000206

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Authors:Garcia; Stephan Ramon, Lagarias, Jeffrey, Lee, Ethan Simpson Pages: 1122 - 1134 Abstract: We improve upon the traditional error term in the truncated Perron formula for the logarithm of an L-function. All our constants are explicit. PubDate: 2023-03-09 DOI: 10.4153/S0008439523000218

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Authors:Čech; Martin Pages: 1135 - 1151 Abstract: We study the double character sum and its smoothly weighted counterpart. An asymptotic formula with power saving error term was obtained by Conrey, Farmer, and Soundararajan by applying the Poisson summation formula. The result is interesting because the main term involves a non-smooth function. In this paper, we apply the inverse Mellin transform twice and study the resulting double integral that involves a double Dirichlet series. This method has two advantages—it leads to a better error term, and the surprising main term naturally arises from three residues of the double Dirichlet series. PubDate: 2023-03-22 DOI: 10.4153/S000843952300022X

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Authors:Cavey; Daniel Pages: 1152 - 1163 Abstract: This papers classifies toric Fano threefolds with singular locus for building on the work of Batyrev (1981, Nauk SSSR Ser. Mat. 45, 704–717) and Watanabe–Watanabe (1982, Tokyo J. Math. 5, 37–48). This is achieved by completing an equivalent problem in the language of Fano polytopes. Furthermore, we identify birational relationships between entries of the classification. For a fixed value , there are exactly two such toric Fano threefolds linked by a blowup in a torus-invariant line. PubDate: 2023-03-29 DOI: 10.4153/S0008439523000231

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Authors:Esipova; Maria S., Yeats, Karen Pages: 1164 - 1178 Abstract: The invariant is an arithmetic graph invariant related to quantum field theory. We give a relation modulo p between the invariant at p and the invariant at by proving a relation modulo p between certain coefficients of powers of products of particularly nice polynomials. The relation at the level of the invariant provides evidence for a conjecture of Schnetz. PubDate: 2023-04-24 DOI: 10.4153/S0008439523000243

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Authors:de la Rosa-Navarro; Brenda Leticia, Frías-Medina, Juan Bosco, Lahyane, Mustapha Pages: 1179 - 1193 Abstract: This paper is devoted to determine the geometry of a class of smooth projective rational surfaces whose minimal models are the Hirzebruch ones; concretely, they are obtained as the blowup of a Hirzebruch surface at collinear points. Explicit descriptions of their effective monoids are given, and we present a decomposition for every effective class. Such decomposition is used to confirm the effectiveness of some divisor classes when the Riemann–Roch theorem does not give information about their effectiveness. Furthermore, we study the nef divisor classes on such surfaces. We provide an explicit description for their nef monoids, and, moreover, we present a decomposition for every nef class. On the other hand, we prove that these surfaces satisfy the anticanonical orthogonal property. As a consequence, the surfaces are Harbourne–Hirschowitz and their Cox rings are finitely generated. Finally, we prove that the complete linear system associated with any nef divisor is base-point-free; thus, the semi-ample and nef monoids coincide. The base field is assumed to be algebraically closed of arbitrary characteristic. PubDate: 2023-04-11 DOI: 10.4153/S0008439523000255

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Authors:Lecouturier; Emmanuel, Wang, Jun Pages: 1194 - 1212 Abstract: Romyar Sharifi has constructed a map from the first homology of the modular curve to the K-group , where is a primitive Mth root of unity. Sharifi conjectured that is annihilated by a certain Eisenstein ideal. Fukaya and Kato proved this conjecture after tensoring with for a prime dividing M. More recently, Sharifi and Venkatesh proved the conjecture for Hecke operators away from M. In this note, we prove two main results. First, we give a relation between and when . Our method relies on the techniques developed by Sharifi and Venkatesh. We then use this result in combination with results of Fukaya and Kato in order to get the Eisenstein property of for Hecke operators of index dividing M. PubDate: 2023-04-11 DOI: 10.4153/S0008439523000267

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Authors:Bourass; Marouane, Marrhich, Ibrahim, Mkadmi, Fouzia Pages: 1213 - 1230 Abstract: We characterize the membership in the Schatten ideals , , of composition operators acting on weighted Dirichlet spaces. Our results concern a large class of weights. In particular, we examine the case of perturbed superharmonic weights. Characterization of composition operators acting on weighted Bergman spaces to be in is also given. PubDate: 2023-04-17 DOI: 10.4153/S0008439523000292

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Authors:Ilten; Nathan, Lautsch, Oscar Pages: 1231 - 1236 Abstract: We show that a sufficiently general hypersurface of degree d in admits a toric Gröbner degeneration after linear change of coordinates if and only if . PubDate: 2023-04-20 DOI: 10.4153/S0008439523000309

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Authors:Brendle; Jörg Pages: 1237 - 1243 Abstract: A classical theorem of Balcar, Pelant, and Simon says that there is a base matrix of height , where is the distributivity number of . We show that if the continuum is regular, then there is a base matrix of height , and that there are base matrices of any regular uncountable height in the Cohen and random models. This answers questions of Fischer, Koelbing, and Wohofsky. PubDate: 2023-04-20 DOI: 10.4153/S0008439523000310

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Authors:Ray; Samya Kumar, Sarkar, Srijan Pages: 1244 - 1254 Abstract: In this article, we study the following question asked by Michael Hartz in a recent paper (Every complete Pick space satisfies the column-row property, to appear in Acta Mathematica): which operator spaces satisfy the column–row property' We provide a complete classification of the column–row property (CRP) for noncommutative -spaces over semifinite von Neumann algebras. We study other relevant properties of operator spaces that are related to the CRP and discuss their existence and nonexistence for various natural examples of operator spaces. PubDate: 2023-04-24 DOI: 10.4153/S0008439523000322

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Authors:Schopieray; Andrew Pages: 1255 - 1268 Abstract: We classify braided generalized near-group fusion categories whose global dimension is not an integer; there are exactly two up to Grothendieck equivalence and taking products with braided pointed fusion categories. PubDate: 2023-04-27 DOI: 10.4153/S0008439523000334

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Authors:Bhowmik; Bappaditya, Sen, Sambhunath Pages: 1269 - 1273 Abstract: Let be the open unit disk, and let be the class of functions f that are holomorphic in with a simple pole at , and . In this article, we significantly improve lower bounds of the Bloch and the Landau constants for functions in which were obtained in Bhowmik and Sen (2023, Monatshefte für Mathematik, 201, 359–373) and conjecture on the exact values of such constants. PubDate: 2023-04-28 DOI: 10.4153/S0008439523000346

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Authors:Forghani; Behrang, Nguyen, May Pages: 1274 - 1279 Abstract: We prove that for a vast class of random walks on a compactly generated group, the exponential growth of convolutions of a probability density function along almost every sample path is bounded by the growth of the group. As an application, we show that the almost sure and convergences of the Shannon–McMillan–Breiman theorem hold for compactly supported random walks on compactly generated groups with subexponential growth. PubDate: 2023-05-05 DOI: 10.4153/S0008439523000358

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Authors:Mohammadi; Ali, Pham, Thang, Wang, Yiting Pages: 1280 - 1295 Abstract: Given , we prove that there exist disjoint subsets such that and their additive and multiplicative energies satisfying where We also study some related questions on moderate expanders over matrix rings, namely, for , we have whenever . These improve earlier results due to Karabulut, Koh, Pham, Shen, and Vinh ([2019], Expanding phenomena over matrix rings, , 31, 951–970). PubDate: 2023-05-15 DOI: 10.4153/S000843952300036X

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Authors:Asipchuk; Oleg, Drezels, Vladyslav Pages: 1296 - 1312 Abstract: In this paper, we construct explicit exponential bases of unions of segments of total measure one. Our construction applies to finite or infinite unions of segments, with some conditions on the gaps between them. We also construct exponential bases on finite or infinite unions of cubes in and prove a stability result for unions of segments that generalize Kadec’s -theorem. PubDate: 2023-05-15 DOI: 10.4153/S0008439523000371

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Authors:Amelotte; Steven, Briggs, Benjamin Pages: 1313 - 1325 Abstract: A simple polytope P is called B-rigid if its combinatorial type is determined by the cohomology ring of the moment-angle manifold over P. We show that any tensor product decomposition of this cohomology ring is geometrically realized by a product decomposition of the moment-angle manifold up to equivariant diffeomorphism. As an application, we find that B-rigid polytopes are closed under products, generalizing some recent results in the toric topology literature. Algebraically, our proof establishes that the Koszul homology of a Gorenstein Stanley–Reisner ring admits a nontrivial tensor product decomposition if and only if the underlying simplicial complex decomposes as a join of full subcomplexes. PubDate: 2023-05-15 DOI: 10.4153/S0008439523000383

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Authors:Lin; Ying-Fen, Oi, Shiho Pages: 1326 - 1340 Abstract: In this article, we give a representation of bounded complex linear operators that preserve idempotent elements on the Fourier algebra of a locally compact group. When such an operator is, moreover, positive or contractive, we show that the operator is induced by either a continuous group homomorphism or a continuous group antihomomorphism. If the groups are totally disconnected, bounded homomorphisms on the Fourier algebra can be realized by the idempotent preserving operators. PubDate: 2023-05-17 DOI: 10.4153/S0008439523000395

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Authors:Lu; Xin Yang, Wei, Jun-cheng Pages: 1341 - 1353 Abstract: We study a 3D ternary system which combines an interface energy with a long-range interaction term. Several such systems were derived as a sharp-interface limit of the Nakazawa–Ohta density functional theory of triblock copolymers. Both the binary case in 2D and 3D, and the ternary case in 2D, are quite well understood, whereas very little is known about the ternary case in 3D. In particular, it is even unclear whether minimizers are made of finitely many components. In this paper, we provide a positive answer to this, by proving that the number of components in a minimizer is bounded from above by a computable quantity depending only on the total masses and the interaction coefficients. There are two key difficulties, namely, the impossibility to decouple the long-range interaction from the perimeter term, and the absence of a quantitative isoperimetric inequality with two mass constraints in 3D. Therefore, the actual shape of minimizers is unknown, even for small masses, making the construction of suitable competing configurations significantly more delicate. PubDate: 2023-05-24 DOI: 10.4153/S0008439523000401

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Authors:Baars; Jan Pages: 1354 - 1367 Abstract: Let be a prime component, and let and be metric spaces. In [8], it was shown that if and are linearly homeomorphic, then the scattered heights and of and satisfy if and only if . We will prove that this also holds if and are linearly homeomorphic and that these results do not hold for arbitrary Tychonov spaces. We will also prove that if PubDate: 2023-05-29 DOI: 10.4153/S0008439523000413

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Authors:Bordellès; Olivier Pages: 1368 - 1375 Abstract: In this article, we provide an explicit upper bound for which depends on an effective constant in the error term of the Ideal Theorem. PubDate: 2023-05-26 DOI: 10.4153/S0008439523000425

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Authors:Charpentier; Stéphane, Fouchet, Karine, Zarouf, Rachid Pages: 1376 - 1390 Abstract: In 2005, N. Nikolski proved among other things that for any and any , the condition number of any invertible n-dimensional complex Banach space operators T satisfying the Kreiss condition, with spectrum contained in , satisfies the inequality where denotes the Kreiss constant of T and is an absolute constant. He also proved that for the latter bound is asymptotically sharp as . In this note, we prove that this bound is actually achieved by a family of explicit Toeplitz matrices with arbitrary singleton spectrum and uniformly bounded Kreiss constant. Independently, we exhibit a sequence of Jordan blocks with Kreiss constants tending to showing that Nikolski’s inequality is still asymptotically sharp as K and n go to PubDate: 2023-05-29 DOI: 10.4153/S0008439523000437

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Authors:Brzostowski; Szymon, Krasiński, Tadeusz, Oleksik, Grzegorz Pages: 1391 - 1410 Abstract: Let f be an isolated singularity at the origin of . One of many invariants that can be associated with f is its Łojasiewicz exponent , which measures, to some extent, the topology of f. We give, for generic surface singularities f, an effective formula for in terms of the Newton polyhedron of f. This is a realization of one of Arnold’s postulates. PubDate: 2023-06-26 DOI: 10.4153/S0008439523000528

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Authors:Allu; Vasudevarao, Halder, Himadri Pages: 1411 - 1422 Abstract: In this article, we study the Bohr operator for the operator-valued subordination class consisting of holomorphic functions subordinate to f in the unit disk , where is holomorphic and is the algebra of bounded linear operators on a complex Hilbert space . We establish several subordination results, which can be viewed as the analogs of a couple of interesting subordination results from scalar-valued settings. We also obtain a von Neumann-type inequality for the class of analytic self-mappings of the unit disk which fix the origin. Furthermore, we extensively study Bohr inequalities for operator-valued polyanalytic functions in certain proper simply connected domains in . We obtain Bohr radius for the operator-valued polyanalytic functions of the form , where is subordinate to an operator-valued convex biholomorphic function, and operator-valued starlike biholomorphic function in the unit disk . PubDate: 2023-06-26 DOI: 10.4153/S0008439523000541