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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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We discuss the outline of the shapes of graphs of χ 2 statistics for distributions of leading digits of irrational rotations under some conditions on mth convergent. We give some estimates of important coefficients Lk ’s, which determine the graphical shapes of χ2 statistics. This means that the denominator qm of mth convergent and the large partial quotient am +1 determine the outline of shapes of graphs, when we observe values of χ 2 statistics with step qm .

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In this note, we introduce the concept of semi-*-IFP, the involutive version of semi-IFP, which is a generalization of quasi-*-IFP and *-reducedness of *-rings. We study the basic structure and properties of *-rings having semi-*-IFP and give results for IFPs in rings with involution. Several results and counterexamples are stated to connect the involutive versions of IFP. We discuss the conditions for the involutive IFPs to be extended into *-subrings of the ring of upper triangular matrices. In *-rings with quasi-*-IFP, it is shown that Köthe’s conjecture has a strong affirmative solution. We investigate its related properties and the relationship between *-rings with quasi-*-IFP and *-Armendariz properties.

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In the present paper, we establish the convergence rates of the single logarithm and the iterated logarithm for martingale differences which give some further results for the open question in Stoica [6].

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We give a full, correct proof of the following result, earlier claimed in [1]. If the Continuum Hypothesis holds then there is a coloring of the plane with countably many colors, with no monocolored right triangle.

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The famous Hadwiger–Nelson problem asks for the minimum number of colors needed to color the points of the Euclidean plane so that no two points unit distance apart are assigned the same color. In this note we consider a variant of the problem in Minkowski metric planes, where the unit circle is a regular polygon of even and at most 22 vertices. We present a simple lattice–sublattice coloring scheme that uses 6 colors, proving that the chromatic number of the Minkowski planes above are at most 6. This result is new for regular polygons having more than 8 vertices.

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Studia Scientiarum Mathematicarum Hungarica
Andras Bezdek
Haile Gilroy
Owen Henderschedt
, and
Alason Lakhani

John Horton Conway stood out from many famous mathematicians for his love of games and puzzles. Among others, he is known for inventing the two-player topological games called Sprouts and Brussels Sprouts. These games start with n spots (n crosses resp.), have simple rules, last for finitely many moves, and the player who makes the last move wins. In the misère versions, the player who makes the last move loses. In this paper, we make Brussels Sprouts colored, preserving the aesthetic interest and balance of the game. In contrast to the original Sprouts, Colored Brussels Sprouts allows mathematical analysis without computer programming and has winning strategies for a large family of the number of spots.

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Given graphs H and F, the generalized Turán number ex(n, H, F) is the largest number of copies of H in n-vertex F-free graphs. Stability refers to the usual phenomenon that if an n-vertex F-free graph G contains almost ex(n, H, F) copies of H, then G is in some sense similar to some extremal graph. We obtain new stability results for generalized Turán problems and derive several new exact results.

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Let T be a tree. The reducible stem of T is the smallest subtree that contains all branch vertices of T. In this paper, we first use a new technique of Gould and Shull [5] to state a new short proof for a result of Kano et al. [10] on the spanning tree with a bounded number of leaves in a claw-free graph. After that, we use a similar idea to prove a sharp sufficient condition for a claw-free graph having a spanning tree whose reducible stem has few leaves.

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Let n ∈ ℕ. An element (x 1, … , xn ) ∈ En is called a norming point of T L n E if x 1 = = x n = 1 and T x 1 , , x n = T , where L n E denotes the space of all continuous symmetric n-linear forms on E. For T L n E , we define

Norm T = x 1 , , x n E n : x 1 , , x n  is a norming of  T .

Norm(T) is called the norming set of T.

Let · 2 be the plane with a certain norm such that the set of the extreme points of its unit ball ext B · 2 = ± W 1 , ± W 2 for some W 1 ± W 2 · 2 .

In this paper, we classify Norm(T) for every T L n · 2 . We also present relations between the norming sets of L n l 2 and L n l 1 2 .

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