Tracing the origin of the single-spin asymmetries observed in inclusive hadron production processes at high energies

It is pointed out that the existing models for the left-right asymmetries observed in single-spin inclusive hadron production processes can be differentiated experimentally. Several such experiments are proposed with which the basic assumptions of these models can be tested individually.Comment: 12 pages, one figur

Game saturation of intersecting families

We consider the following combinatorial game: two players, Fast and Slow, claim $k$-element subsets of $[n]=\{1,2,...,n\}$ alternately, one at each turn, such that both players are allowed to pick sets that intersect all previously claimed subsets. The game ends when there does not exist any unclaimed $k$-subset that meets all already claimed sets. The score of the game is the number of sets claimed by the two players, the aim of Fast is to keep the score as low as possible, while the aim of Slow is to postpone the game's end as long as possible. The game saturation number is the score of the game when both players play according to an optimal strategy. To be precise we have to distinguish two cases depending on which player takes the first move. Let $gsat_F(\mathbb{I}_{n,k})$ and $gsat_S(\mathbb{I}_{n,k})$ denote the score of the saturation game when both players play according to an optimal strategy and the game starts with Fast's or Slow's move, respectively. We prove that $\Omega_k(n^{k/3-5}) \le gsat_F(\mathbb{I}_{n,k}),gsat_S(\mathbb{I}_{n,k}) \le O_k(n^{k-\sqrt{k}/2})$ holds

How Much Is Winning a Matter of Luck? A Comparison of 3 × 3 and 5v5 Basketball

Background: The comparison of team sports based on luck has a long tradition and remains unsolved. A contrast between the new Olympic format three-on-three (3 × 3) and five-on-five (5v5) forms of basketball has never been analyzed and provides a comparison within the same form of sports. Methods: We developed a new method to calculate performance indicators for each team and invented the Relative Score Difference Index, a new competitive balance indicator that allows the comparison of luck in the two basketball forms for both men and women. We collected game-level data about 3 × 3 and 5v5 from the World Cups held between 2010 and 2019 (N = 666). Luck was defined as the difference between the expected and the actual outcomes of games. Using the basketball World Cup data, we applied the Surprise Index, ran probit regression models, and compared the basketball forms on the goodness-of-fit of the models. Results: As we predicted, there are differential effects of luck between game formats and sex, such that the 3 × 3 form depends more on luck and women’s games are less influenced by luck when compared to men’s games. Conclusion: Coaches may better understand the differences between the two forms and sexes regarding luck if they are aware that the 3 × 3 and men’s competitions are usually more influenced by luck. The findings provide a leverage point for testing new performances and competition balance indicators and will acknowledge the number of games we enjoy watching

Experimental data on the single spin asymmetry and their interpretations by the chromo-magnetic string model

An attempt is made to interpret the various existing experimental data on the single spin asymmetries in inclusive pion production by the polarized proton and antiproton beams. As the basis of analysis the chromo-magnetic string model is used. A whole measured kinematic region is covered. The successes and fails of such approach are outlined. The possible improvements of model are discussed.Comment: 17 pages, 3 figure

Algebraic conditions for additive functions over the reals and over finite fields

Let $C$ be an affine plane curve. We consider additive functions $f: K\rightarrow K$ for which $f(x)f(y)=0$, whenever $(x,y)\in C$. We show that if $K=\mathbb{R}$ and $C$ is the hyperbola with defining equation $xy=1$, then there exist nonzero additive functions with this property. Moreover, we show that such a nonzero $f$ exists for a field $K$ if and only if $K$ is transcendental over $\mathbb{Q}$ or over $\mathbb{F}_p$, the finite field with $p$ elements. We also consider the general question when $K$ is a finite field. We show that if the degree of the curve $C$ is large enough compared to the characteristic of $K$, then $f$ must be identically zero.Comment: 11 page