scholarly journals Cluster characters II: a multiplication formula

2011 ◽  
Vol 104 (1) ◽  
pp. 57-78 ◽  
Author(s):  
Yann Palu
Keyword(s):  
Multiplication Formula

scholarly journals On the unified family of generalized Apostol-type polynomials of higher order and multiple power sums

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 929-935 ◽  
Author(s):  
Veli Kurt
Keyword(s):  
Recurrence Relations ◽  
Higher Order ◽  
Euler Polynomials ◽  
Multiplication Formula ◽  
Power Sums ◽  
Genocchi Polynomials ◽  
Alternating Sums ◽  
Multiple Power

In last last decade, many mathematicians studied the unification of the Bernoulli and Euler polynomials. Firstly Karande B. K. and Thakare N. K. in [6] introduced and generalized the multiplication formula. Ozden et. al. in [14] defined the unified Apostol-Bernoulli, Euler and Genocchi polynomials and proved some relations. M. A. Ozarslan in [13] proved the explicit relations, symmetry identities and multiplication formula. El-Desouky et. al. in ([3], [4]) defined a new unified family of the generalized Apostol-Euler, Apostol-Bernoulli and Apostol-Genocchi polynomials and gave some relations for the unification of multiparameter Apostol-type polynomials and numbers. In this study, we give some symmetry identities and recurrence relations for the unified Apostol-type polynomials related to multiple alternating sums.

scholarly journals PROFIL KESALAHAN SISWA DALAM MENYELESAIKAN SOAL MATRIKS BERDASARKAN JENIS KELAMIN DI SMA NEGERI 7 PALU

Aksioma ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 110-124
Author(s):  
Fausan Fausan ◽  
Gandung Sugita ◽  
Sukayasa Sukayasa
Keyword(s):  
Matrix Multiplication ◽  
Male Student ◽  
Female Students ◽  
Inverse Matrix ◽  
Male Students ◽  
Research Subjects ◽  
Multiplication Formula ◽  
Interview Methods ◽  
The Matrix ◽  
Matrix Problems

Abstrak: Penelitian ini merupakan penelitian kualitatif yang bertujuan untuk memperoleh profil kesalahan yang dilakukan siswa dalam menyelesaikan soal matriks berdasarkan jenis kelamin di SMA Negeri 7 Palu. Data dikumpulkan dengan cara metode tes dan wawancara. Subjek penelitian terdiri dari satu siswa laki-laki (SH) dan satu siswa perempuan (DS). Hasil Penelitian menunjukkan bahwa kesalahan konseptual yang dilakukan siswa laki-laki (SH) yaitu : 1) kesalahan tidak memahami konsep rumus perkalian matriks, 2) kesalahan konsep perkalian matriks, 3) kesalahan tidak menerapkan rumus invers, 4) kesalahan konsep invers matriks dan 5)  kesalahan konsep adjoin. Kesalahan prosedural yang dilakukan siswa laki-laki berupa 1) kesalahan dalam melakukan perhitungan, 2) kesalahan tidak menyederhanakan dan 3) kesalahan tidak menuliskan tanda operasi pada matriks. Sedangkan kesalahan konseptual yang dilakukan siswa perempuan (DS) yaitu: 1) kesalahan tidak memahami konsep rumus perkalian matriks, 2) kesalahan konsep perkalian matriks, 3) kesalahan konsep adjoin dan 4) kesalahan konsep invers matriks. Kesalahan prosedural yang dilakukan siswa perempuan berupa 1) kesalahan dalam melakukan perhitungan. Siswa laki-laki banyak melakukan kesalahan dari pada siswa perempuan dikarenakan, siswa laki-laki tidak teliti dan terburu-buru dalam menyelesaikan soal matriks. Sedangkan siswa perempuan tidak terlalu banyak melakukan kesalahan dikarenakan cenderung lebih teliti dan cermat dalam menyelesaikan soal matriks. Kata kunci: Profil Kesalahan, Jenis Kelamin dan Matriks Abstract: This research is a qualitative research which aims to obtain a profile of errors students make in solving matrix problems based on sex in SMA 7 Palu. Data was collected by means of test and interview methods. The research subjects consisted of one male student (SH) and one female student (DS). The results showed that the conceptual errors made by male students (SH) were: 1) errors not understanding the concept of matrix multiplication formula, 2) errors in matrix multiplication concepts, 3) errors not applying inverse formulas, 4) inverse matrix concept errors and 5 ) the error of the adjoin concept. Procedural errors made by male students in the form of 1) errors in making calculations, 2) errors do not simplify and 3) errors do not write the operation mark on the matrix. Whereas the conceptual errors made by female students (DS) are: 1) errors do not understand the concept of matrix multiplication formula, 2) errors in the concept of matrix multiplication, 3) errors in adjoining concepts and 4) inverse matrix concept errors. Procedural errors made by female students in the form of 1) errors in carrying out calculations. Male students make a lot of mistakes than female students because , male students are not careful and in a hurry to solve the matrix problem. Whereas female students don't make too many mistakes becausethey tend to be more thorough and careful in solving matrix problems. Keywords: Error Profile, Gender and Matrix

The M-intersection graph of ideals of a commutative ring

2018 ◽  
Vol 10 (03) ◽  
pp. 1850038 ◽  
Author(s):  
F. Heydari
Keyword(s):  
Commutative Ring ◽  
Clique Number ◽  
Intersection Graph ◽  
Sufficient Condition ◽  
Semilocal Ring ◽  
Multiplication Formula ◽  
Vertex Set

Let [Formula: see text] be a commutative ring and [Formula: see text] be an [Formula: see text]-module, and let [Formula: see text] be the set of all nontrivial ideals of [Formula: see text]. The [Formula: see text]-intersection graph of ideals of [Formula: see text], denoted by [Formula: see text], is a graph with the vertex set [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. For every multiplication [Formula: see text]-module [Formula: see text], the diameter and the girth of [Formula: see text] are determined. Among other results, we prove that if [Formula: see text] is a faithful [Formula: see text]-module and the clique number of [Formula: see text] is finite, then [Formula: see text] is a semilocal ring. We denote the [Formula: see text]-intersection graph of ideals of the ring [Formula: see text] by [Formula: see text], where [Formula: see text] are integers and [Formula: see text] is a [Formula: see text]-module. We determine the values of [Formula: see text] and [Formula: see text] for which [Formula: see text] is perfect. Furthermore, we derive a sufficient condition for [Formula: see text] to be weakly perfect.

The derivative and tangent operators of a motion in Lorentzian space

2017 ◽  
Vol 14 (04) ◽  
pp. 1750058 ◽  
Author(s):  
Olgun Durmaz ◽  
Buşra Aktaş ◽  
Hali̇t Gündoğan
Keyword(s):  
Matrix Multiplication ◽  
Spatial Motion ◽  
Lorentzian Space ◽  
Matrix Groups ◽  
Multiplication Formula ◽  
Tangent Operator ◽  
Special Matrix ◽  
Lorentzian Matrix Multiplication

In this paper, by using Lorentzian matrix multiplication, [Formula: see text]-Tangent operator is obtained in Lorentzian space. The [Formula: see text]-Tangent operators related with planar, spherical and spatial motion are computed via special matrix groups. [Formula: see text]-Tangent operators are related to vectors. Some illustrative examples for applications of [Formula: see text]-Tangent operators are also presented.

scholarly journals Applications of the multiplication formula for the gamma function to E-function series

1960 ◽  
Vol 4 (3) ◽  
pp. 114-118 ◽  
Author(s):  
T. M. Macrobert
Keyword(s):  
Infinite Series ◽  
Gamma Function ◽  
Multiplication Formula ◽  
Function Series

In two recent papers [1, 2] the Barnes integral for the E-functions was employed to sum a number of infinite series of E-functions. In §2 of this paper, by making use of the multiplication formula for the gamma function, the method is extended to series of E-functions of a different type.

scholarly journals On Multiple Generalizedw-Genocchi Polynomials and Their Applications

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
Lee-Chae Jang
Keyword(s):  
Integral Representation ◽  
Explicit Formula ◽  
Recurrence Formula ◽  
Multiplication Formula ◽  
Type Formula ◽  
Genocchi Polynomials ◽  
Invariant Integrals

We define the multiple generalizedw-Genocchi polynomials. By using fermionicp-adic invariant integrals, we derive some identities on these generalizedw-Genocchi polynomials, for example, fermionicp-adic integral representation, Witt's type formula, explicit formula, multiplication formula, and recurrence formula for thesew-Genocchi polynomials.

NON-SPLITTABLE EXTENSIONS OF THE VIRASORO AND SUPERCONFORMAL ALGEBRAS VIA PSEUDODIFFERENTIAL OPERATORS

1991 ◽  
Vol 06 (28) ◽  
pp. 2639-2648
Author(s):  
E. S. FRADKIN ◽  
V. YA. LINETSKY
Keyword(s):  
Pseudodifferential Operators ◽  
Kdv Equation ◽  
Quantum Corrections ◽  
Poisson Brackets ◽  
Multiplication Formula ◽  
The Kdv Equation ◽  
Abelian Kernel

Applying the Weyl symbols techniques to the algebra of pseudodifferential operators on a circle and its extensions, a number of non-splittable Abelian, as well as infinite tower of non-Abelian, kernel extensions of the Virasoro and superconformal algebras have been explicitly constructed. The corresponding non-trivial cocycles appear as quantum corrections to the Poisson brackets when developing the Weyl multiplication formula. As an application, this construction may yield interesting generalizations of the KdV equation.

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