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1.
Xue Pan 《中国物理C(英文版)》2022,46(2):024104-024104-10
High-order cumulants and factorial cumulants of conserved charges are suggested for the study of the critical dynamics in heavy-ion collision experiments. In this paper, using the parametric representation of the three-dimensional Ising model which is believed to belong to the same universality class as quantum chromo-dynamics, the temperature dependence of the second- to fourth-order (factorial) cumulants of the order parameter is studied. It is found that the values of the normalized cumulants are independent of the external magnetic field at the critical temperature, which results in a fixed point in the temperature dependence of the normalized cumulants. In finite-size systems simulated using the Monte Carlo method, this fixed point behavior still exists at temperatures near the critical. This fixed point behavior has also appeared in the temperature dependence of normalized factorial cumulants from at least the fourth order. With a mapping from the Ising model to QCD, the fixed point behavior is also found in the energy dependence of the normalized cumulants (or fourth-order factorial cumulants) along different freeze-out curves.  相似文献   
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In this text, we study factorizations of polynomials over the tropical hyperfield and the sign hyperfield, which we call tropical polynomials and sign polynomials, respectively. We classify all irreducible polynomials in either case. We show that tropical polynomials factor uniquely into irreducible factors, but that unique factorization fails for sign polynomials. We describe division algorithms for tropical and sign polynomials by linear terms that correspond to roots of the polynomials.  相似文献   
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An iterative formula for the Green polynomial is given using the vertex operator realization of the Hall-Littlewood function. Based on this, (1) a general combinatorial formula of the Green polynomial is given; (2) several compact formulas are given for Green's polynomials associated with upper partitions of length ≤3 and the diagonal lengths ≤3; (3) a Murnaghan-Nakayama type formula for the Green polynomial is obtained; and (4) an iterative formula is derived for the bitrace of the finite general linear group G and the Iwahori-Hecke algebra of type A on the permutation module of G by its Borel subgroup.  相似文献   
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利用多项式因式分解的逆变换,结合循环矩阵和切比雪夫多项式的特殊结构,首先研究第三类和第四类切比雪夫多项式的通项公式,并给出第三类、第四类切比雪夫多项式的关于行首加r尾r右循环矩阵和行尾加r首r左循环矩阵的行列式的显式表达式,最后给出算法实施步骤.  相似文献   
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Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential sums of rotation symmetric Boolean functions satisfy homogeneous linear recurrences with integer coefficients. In this work, a generalization of this result is proved over any Galois field. That is, exponential sums over Galois fields of some rotation symmetric polynomials satisfy linear recurrences with integer coefficients. In the particular case of F2, an elementary method is used to obtain explicit recurrences for exponential sums of some of these functions. The concept of trapezoid Boolean function is also introduced and it is showed that the linear recurrences that exponential sums of trapezoid Boolean functions satisfy are the same as the ones satisfied by exponential sums of the corresponding rotations symmetric Boolean functions. Finally, it is proved that exponential sums of trapezoid and symmetric polynomials also satisfy linear recurrences with integer coefficients over any Galois field Fq. Moreover, the Discrete Fourier Transform matrix and some Complex Hadamard matrices appear as examples in some of our explicit formulas of these recurrences.  相似文献   
7.
This paper studies the Hankel determinants generated by a discontinuous Gaussian weight with one and two jumps. It is an extension in a previous study, in which they studied the discontinuous Gaussian weight with a single jump. By using the ladder operator approach, we obtain a series of difference and differential equations to describe the Hankel determinant for the single jump case. These equations include the Chazy II equation, continuous and discrete Painlevé IV. In addition, we consider the large n behavior of the corresponding orthogonal polynomials and prove that they satisfy the biconfluent Heun equation. We also consider the jump at the edge under a double scaling, from which a Painlevé XXXIV appeared. Furthermore, we study the Gaussian weight with two jumps and show that a quantity related to the Hankel determinant satisfies a two variables' generalization of the Jimbo‐Miwa‐Okamoto σ‐form of the Painlevé IV.  相似文献   
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We consider the irreducibility of polynomial Ln(α)(x) where α is a negative integer. We observe that the constant term of Ln(α)(x) vanishes if and only if n|α|=?α. Therefore we assume that α=?n?s?1 where s is a non-negative integer. Let g(x)=(?1)nLn(?n?s?1)(x)=j=0najxjj! and more general polynomial, let G(x)=j=0najbjxjj! where bj with 0jn are integers such that |b0|=|bn|=1. Schur was the first to prove the irreducibility of g(x) for s=0. It has been proved that g(x) is irreducible for 0s60. In this paper, by a different method, we prove: Apart from finitely many explicitly given possibilities, either G(x) is irreducible or G(x) is linear factor times irreducible polynomial. This is a consequence of the estimate s>1.9k whenever G(x) has a factor of degree k2 and (n,k,s)(10,5,4). This sharpens earlier estimates of Shorey and Tijdeman and Nair and Shorey.  相似文献   
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