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Mathematics and statistics journals publish papers on the theory and application of mathematics, statistics, and probability. Most mathematics journals have a broad scope that encompasses most mathematical fields. These commonly include logic and foundations, algebra and number theory, analysis (including differential equations, functional analysis and operator theory), geometry, topology, combinatorics, probability and statistics, numerical analysis and computation theory, mathematical physics, etc.

Mathematics and Statistics

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Let X be a smooth projective K3 surface over the complex numbers and let C be an ample curve on X. In this paper we will study the semistability of the Lazarsfeld-Mukai bundle EC,A associated to a line bundle A on C such that |A| is a pencil on C and computes the Clifford index of C. We give a necessary and sufficient condition for EC,A to be semistable.

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We prove criteria for a graph to be the Reeb graph of a function of a given class on a closed manifold: Morse–Bott, round, and in general smooth functions whose critical set consists of a finite number of submanifolds. The criteria are given in terms of whether the graph admits an orientation, which we call S-good orientation, with certain conditions on the degree of sources and sinks, similar to the known notion of good orientation in the context of Morse functions. We also study when such a function is the height function associated with an immersion of the manifold. The condition for a graph to admit an S-good orientation can be expressed in terms of the leaf blocks of the graph.

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For each Montesinos knot K, we propose an efficient method to explicitly determine the irreducible SL(2, )-character variety, and show that it can be decomposed as χ0(K)⊔χ1(K)⊔χ2(K)⊔χ'(K), where χ0(K) consists of trace-free characters χ1(K) consists of characters of “unions” of representations of rational knots (or rational link, which appears at most once), χ2(K) is an algebraic curve, and χ'(K) consists of finitely many points when K satisfies a generic condition.

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We offer new properties of the special Gini mean S(a, b) = aa /( a + b )bb /( a + b ), in connections with other special means of two arguments.

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Mathematica Pannonica
Authors:
Allan Frendrup
,
Zsolt Tuza
, and
Preben Dahl Vestergaard

We treat a variation of graph domination which involves a partition (V 1, V 2,..., Vk ) of the vertex set of a graph G and domination of each partition class V i over distance d where all vertices and edges of G may be used in the domination process. Strict upper bounds and extremal graphs are presented; the results are collected in three handy tables. Further, we compare a high number of partition classes and the number of dominators needed.

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Proctor and Scoppetta conjectured that

  • (1) there exists an infinite locally finite poset that satisfies their conditions VT and NTC but not SIS;

  • (2) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MF but not both VT and FT; and

  • (3) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MD but not NCC.

In this note, the conjecture of Proctor and Scoppetta, which is related to d-complete posets, is proven.

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In this paper we introduce the concept of the Hamilton triangle of a given triangle in an isotropic plane and investigate a number of important properties of this concept. We prove that the Hamilton triangle is homological with the observed triangle and with its contact and complementary triangles. We also consider some interesting statements about the relationships between the Hamilton triangle and some other significant elements of the triangle, like e.g. the Euler and the Feuerbach line, the Steiner ellipse and the tangential triangle.

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We prove certain Menon-type identities associated with the subsets of the set {1, 2,..., n} and related to the functions f, fk , Ф and Ф k , defined and investigated by Nathanson.

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Generalizing results of Schatte [11] and Atlagh and Weber [2], in this paper we give conditions for a sequence of random variables to satisfy the almost sure central limit theorem along a given sequence of integers.

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In the 1980’s the author proved lower bounds for the mean value of the modulus of the error term of the prime number theorem and other important number theoretic functions whose oscillation is in connection with the zeros of the Riemann zeta function. In the present work a general theorem is shown in a simple way which gives a lower bound for the mentioned mean value as a function of a hypothetical pole of the Mellin transform of the function. The conditions are amply satisfied for the Riemann zeta function. In such a way the results recover the earlier ones (even in a slightly sharper form). The obtained estimates are often optimal apart from a constant factor, at least under reasonable conditions as the Riemann Hypothesis. This is the case, in particular, for the error term of the prime number theorem.

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