Polynomial-time Classification of Skew-symmetrizable Matrices with a Positive Definite Quasi-Cartan Companion

Skew-symmetrizable matrices play an essential role in the classification of cluster algebras. We prove that the problem of assigning a positive definite quasi-Cartan companion to a skew-symmetrizable matrix is in polynomial class P. We also present an algorithm to determine the finite type Δ ∈ {𝔸n; 𝔻n; 𝔹n; ℂn; 𝔼6; 𝔼7; 𝔼8; 𝔽4; 𝔾2} of a cluster algebra associated to the mutation-equivalence class of a connected skew-symmetrizable matrix B, if it has one.

New Biparametric Families of Apostol-Frobenius-Euler Polynomials level-m

We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level-$m$. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized $\lambda$-Stirling type numbers of the second kind, the generalized Apostol--Bernoulli polynomials, the generalized Apostol--Genocchi polynomials, the generalized Apostol--Euler polynomials and Jacobi polynomials. Finally, we will show the differential properties of this new family of polynomials.

Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functions

Motivated by a recent study on certain families of the incomplete H-functions (Srivastava et al. in Russ. J. Math. Phys. 25(1):116–138, 2018), we aim to investigate and develop several interesting properties related to product of a more general polynomial class together with incomplete Fox–Wright hypergeometric functions ${}_{p}\Psi _{q}^{(\gamma )}(\mathfrak{t})$ Ψ q ( γ ) p ( t ) and ${}_{p}\Psi _{q}^{(\Gamma )}(\mathfrak{t})$ Ψ q ( Γ ) p ( t ) including Marichev–Saigo–Maeda (M–S–M) fractional integral and differential operators, which contain Saigo hypergeometric, Riemann–Liouville, and Erdélyi–Kober fractional operators as particular cases regarding different parameter selection. Furthermore, we derive several integral transforms such as Jacobi, Gegenbauer (or ultraspherical), Legendre, Laplace, Mellin, Hankel, and Euler’s beta transforms.

New results on the q-generalized Bernoulli polynomials of level m

This paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials B_n^{[m - 1]}(x;q) of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of level m, as well as the q-gamma function, and the q-Stirling numbers of the second kind and the q-Bernstein polynomials.

Certain Results for the Twice-Iterated 2D q-Appell Polynomials

In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated 2D q-Appell polynomials is also derived. Further, certain twice-iterated 2D q-Appell and mixed type special q-polynomials are considered as members of this polynomial class. The determinant expressions and some other properties of these associated members are also obtained. The graphs and surface plots of some twice-iterated 2D q-Appell and mixed type 2D q-Appell polynomials are presented for different values of indices by using Matlab. Moreover, some areas of potential applications of the subject matter of, and the results derived in, this paper are indicated.

A class of finite-dimensional numerically solvable McKean-Vlasov control problems

We address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be reduced by suitable Markov embedding to finite-dimensional stochastic control problems, and provide a discussion and comparison of three probabilistic numerical methods for solving the reduced control problem: quantization, regression by control randomization, and regress-later methods. Our numerical results are illustrated on various examples from portfolio selection and liquidation under drift uncertainty, and a model of interbank systemic risk with partial observation.

Pengaruh Penggabungan Metode Outdoor Dengan Indoor Learning Menggunakan Sistem Sepur Selam

Abstrak: Penelitian ini bertujuan untuk mengetahui pengaruh penggabungan metode Outdoor dengan Indoor Learning menggunakan sistem sepekan di luar sepekan di dalam (SEPUR SELAM) terhadap prestasi belajar siswa pada pokok bahasan Polinomial kelas XI IPA SMA Negeri 1 Tawangsari tahun pelajaran 2017/2018. Jenis penelitian yang digunakan adalah penelitian eksperimen semu. Data dikumpulkan menggunakan tes, dokumentasi, angket, observasi, dan wawancara. Sampel dalam penelitian ini adalah siswa kelas XI IPA 3 sebagai kelas kontrol dan XI IPA 5 sebagai kelas eksperimen. Hasil analisis uji-t menunjukkan bahwa thitung = 6,098 > ttabel = 2,288 maka H0 ditolak. Disimpulkan bahwa terdapat pengaruh penggunaan penggabungan metode Outdoor dengan Indoor Learning menggunakan Sistem Sepekan di Luar Sepekan di Dalam (SEPUR SELAM) terdahap prestasi belajar siswa pada pokok bahasan Polinomial. Sedangkan angket respon siswa menyatakan 100% siswa tertarik dan mengalami kondisi pembelajaran yang berbeda dengan penggabungan metode Outdoor dengan Indoor Learning, sedangkan 97,4% siswa termotivasi dan tidak mengalami kejenuhan. Kata kunci: Outdoor Learning;Indoor Learning;hasil belajar matematika Abstract: His research aims to determine the effect of combining Outdoor methods with Indoor Learning using a week-long system within a week in (SEPUR SELAM) on student achievement on the subject of Polynomial class XI Science at SMA Negeri 1 Tawangsari in the academic year 2017/2018. The type of research used is experimental research. Data were collected using tests, documentation, questionnaires, observations, and interviews. The sample in this study were students of class XI IPA 3 as the control class and XI IPA 5 as the experimental class. The result of the t-test analysis shows that t count = 6.098> t table = 2.288 then H0 is rejected. It was concluded that there was an effect of using the combination of Outdoor methods with Indoor Learning using the Sepekan System outside the Week in (SEPUR SELAM) at the level of students' learning achievement on the subject of Polynomial. While the student response questionnaire stated 100% of students were interested and experienced different learning conditions with the incorporation of Outdoor methods with Indoor Learning, while 97.4% of students were motivated and did not experience saturation. Keyword: Outdoor Learning;Indoor Learning; learning outcomes of mathematics

A polynomial class of u(2) algebras

A r-parameter u{κ1,κ2,…,κr}(2) algebra is introduced. Finite unitary representations are investigated. This polynomial algebra reduces via a contraction procedure to the generalized Weyl–Heisenberg algebra 𝒜{κ1,κ2,…,κr} [M. Daoud and M. Kibler, J. Phys. A: Math. Theor.45 (2012) 244036]. A pair of nonlinear (quadratic) bosons of type 𝒜κ ≡ 𝒜{κ1=κ,κ2=0,…,κr=0} is used to construct, à la Schwinger, a one parameter family of (cubic) uκ(2) algebra. The corresponding Hilbert space is constructed. The analytical Bargmann representation is also presented.