scholarly journals On Symmetric Identities of Carlitz’s Type q-Daehee Polynomials

2019 ◽  
Vol 2019 ◽  
pp. 1-5 ◽  
Author(s):  
Won Joo Kim ◽  
Lee-Chae Jang ◽  
Byung Moon Kim
Keyword(s):  
Symmetry Group ◽  
Symmetric Identities

In this paper, we study Carlitz’s type q-Daehee polynomials and investigate the symmetric identities for them by using the p-adic q-integral on Zp under the symmetry group of degree n.

scholarly journals Symmetric Properties of Carlitz’s Type q-Changhee Polynomials

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 634 ◽  
Author(s):  
Yunjae Kim ◽  
Byung Kim ◽  
Jin-Woo Park
Keyword(s):  
Symmetry Group ◽  
Symmetric Identities ◽  
Changhee Polynomials ◽  
Symmetric Properties

Changhee polynomials were introduced by Kim, and the generalizations of these polynomials have been characterized. In our paper, we investigate various interesting symmetric identities for Carlitz’s type q-Changhee polynomials under the symmetry group of order n arising from the fermionic p-adic q-integral on Z p .

scholarly journals Some symmetric identities for the higher-order q-Euler polynomials related to symmetry group S3 arising from p-adic q-fermionic integrals on Zp

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1717-1721 ◽  
Author(s):  
Dae Kim ◽  
Taekyun Kim
Keyword(s):  
Symmetry Group ◽  
Higher Order ◽  
Euler Polynomials ◽  
Symmetric Identities

The purpose of this paper is to give some new symmetric identities for the higher-order q-Euler polynomials of the first kind related to symmetry group S3 arising from p-adic q-fermionic integrals on Zp.

scholarly journals Deformation classes in generalized Kähler geometry

2020 ◽  
Vol 7 (1) ◽  
pp. 241-256
Author(s):  
Matthew Gibson ◽  
Jeffrey Streets
Keyword(s):  
Symmetry Group ◽  
Ricci Flow ◽  
Kahler Geometry ◽  
Poisson Tensor ◽  
Natural Extensions ◽  
Generalized Kähler Geometry ◽  
Kähler Structures

AbstractWe describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

Block-diagonalization of the variational nodal response matrix using the symmetry group theory

2017 ◽  
Vol 351 ◽  
pp. 230-253 ◽  
Author(s):  
Zhipeng Li ◽  
Hongchun Wu ◽  
Yunzhao Li ◽  
Liangzhi Cao
Keyword(s):  
Group Theory ◽  
Symmetry Group ◽  
Response Matrix ◽  
Block Diagonalization

Local material symmetry group for first- and second-order strain gradient fluids

2021 ◽  
pp. 108128652110216
Author(s):  
Victor A. Eremeyev
Keyword(s):  
Symmetry Group ◽  
Strain Gradient ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Mass Density ◽  
Material Model ◽  
Second Order ◽  
Material Symmetry ◽  
Local Material ◽  
Current Mass

Using an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients. Both models found applications to modeling of materials with complex inner structure such as beam-lattice metamaterials and fluids at small scales. The local material symmetry group is formed through such transformations of a reference placement which cannot be experimentally detected within the considered material model. We show that considering maximal symmetry group, i.e. material with strain energy that is independent of the choice of a reference placement, one comes to the constitutive equations of gradient fluids introduced independently on general strain gradient continua.

scholarly journals Three-dimensional assessment of the anterior and inferior loop of the inferior alveolar nerve using computed tomography images in patients with and without mandibular asymmetry

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Jae-Young Kim ◽  
Michael D. Han ◽  
Kug Jin Jeon ◽  
Jong-Ki Huh ◽  
Kwang-Ho Park
Keyword(s):  
Computed Tomography ◽  
Symmetry Group ◽  
Three Dimensional ◽  
Inferior Alveolar Nerve ◽  
Mental Foramen ◽  
3D Analysis ◽  
Mandibular Asymmetry ◽  
Computed Tomography Images ◽  
Significant Difference ◽  
Mandibular Body

Abstract Background The purpose of this study was to investigate the differences in configuration and dimensions of the anterior loop of the inferior alveolar nerve (ALIAN) in patients with and without mandibular asymmetry. Method Preoperative computed tomography images of patients who had undergone orthognathic surgery from January 2016 to December 2018 at a single institution were analyzed. Subjects were classified into two groups as “Asymmetry group” and “Symmetry group”. The distance from the most anterior and most inferior points of the ALIAN (IANant and IANinf) to the vertical and horizontal reference planes were measured (dAnt and dInf). The distance from IANant and IANinf to the mental foramen were also calculated (dAnt_MF and dInf_MF). The length of the mandibular body and symphysis area were measured. All measurements were analyzed using 3D analysis software. Results There were 57 total eligible subjects. In the Asymmetry group, dAnt and dAnt_MF on the non-deviated side were significantly longer than the deviated side (p < 0.001). dInf_MF on the non-deviated side was also significantly longer than the deviated side (p = 0.001). Mandibular body length was significantly longer on the non-deviated side (p < 0.001). There was no significant difference in length in the symphysis area (p = 0.623). In the Symmetry group, there was no difference between the left and right sides for all variables. Conclusion In asymmetric patients, there is a difference tendency in the ALIAN between the deviated and non-deviated sides. In patients with mandibular asymmetry, this should be considered during surgery in the anterior mandible.

scholarly journals Construction and Characterization of Representations of SU(7) for GUT Model Builders

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1044
Author(s):  
Daniel Jones ◽  
Jeffery A. Secrest
Keyword(s):  
Gauge Symmetry ◽  
Symmetry Group ◽  
Lie Group ◽  
Cartan Subalgebra ◽  
Natural Extension ◽  
Grand Unification ◽  
Raising And Lowering Operators ◽  
Higher Dimensional ◽  
Lowering Operators

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

scholarly journals Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character χ

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 675 ◽  
Author(s):  
Serkan Araci ◽  
Waseem Khan ◽  
Kottakkaran Nisar
Keyword(s):  
Bernoulli Polynomials ◽  
Dirichlet Character ◽  
Bernoulli Numbers ◽  
Complex Order ◽  
Arbitrary Complex ◽  
Symmetric Identities

We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character χ and investigate certain symmetric identities involving the polynomials, by mainly using the theory of p-adic integral on Z p . The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities.

scholarly journals Some Symmetric Identities Involving Fubini Polynomials and Euler Numbers

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 303 ◽  
Author(s):  
Zhao Jianhong ◽  
Chen Zhuoyu
Keyword(s):  
Calculation Method ◽  
Computational Formula ◽  
Euler Numbers ◽  
Special Sequence ◽  
Computational Problem ◽  
Elementary Methods ◽  
Symmetric Identities ◽  
Recursive Calculation

The aim of this paper is to use elementary methods and the recursive properties of a special sequence to study the computational problem of one kind symmetric sums involving Fubini polynomials and Euler numbers, and give an interesting computational formula for it. At the same time, we also give a recursive calculation method for the general case.

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