Analogues of classical combinatorial identities for elementary and homogeneous symmetric functions with coefficients in the Yangian are proved. As a corollary, similar relations are deduced for shifted Schur polynomials.
Transforming growth factor (TGF)-β is a multifunctional peptide growth factor with a wide range of potential effects on growth, differentiation, extracellular matrix deposition, and the immune response. General TGF-β signaling pathways have been described in detail over the last several years, but factors that determine the nature of the TGF-β response are poorly understood. In particular, signaling pathways that specifically mediate the matrix effects of TGF-β have received little attention, although they will be important therapeutic targets in the treatment of pathological fibrosis. This themes article focuses on TGF-β signaling and highlights potential points for generating matrix-specific responses.
In the present investigation, we define the arrowhead-Jacobsthal sequence by the arrowhead matrix defined with the help of the characteristic polynomial of the generalized order-k Jacobsthal numbers. Next, we derive various properties of the arrowhead-Jacobsthal sequence by using its generating matrix. Also, we give connections between Fibonacci, Jacobsthal, Pell and arrowhead-Jacobsthal numbers.
In the present paper, we define q-matrix polynomials in several variables
which reduces Chan-Chyan-Srivastava and Lagrange-Hermite matrix polynomials
in [6]. Then several results involving generating matrix functions for these
matrix polynomials are derived.
Electricity is an essential basic need that the South African government needs to pay special attention. A continuous or uninterrupted supply of electricity is essential for industrial production and economic growth and development. Since South Africa is overly reliant on coal fired electricity generating technologies which are environmentally damaging, the move towards green energy technologies to form part of the electricity generating matrix is highly desirable not only to reduce environmental pollution, but also to increase the supply of electricity to meet rising demand. However, the adoption and implementation of green energy projects has not been that easy and progress has been far from satisfactory. This study was therefore consummated to assess the effectiveness of installed green technology in the area of Pinetown in Kwazulu-Natal. The study also investigated the technological challenges affecting the implementation of green energy projects in SME sector in Pinetown Kwazulu-Natal. Furthermore, the study also examined as to what extent technological challenges are affecting the use of installed green technology in the selected area of Pinetown in Kwazulu-Natal. This was followed by exploring strategies that could be implemented to improve effectiveness of installed green technology in Pinetown. A quantitative research approach was adopted. Data collection for this study was performed by distributing and collecting a structured survey questionnaire to respondents. Data analysis for this research was performed using SPSS.
Various families of generating matrix functions have been established in diverse ways. The objective of the present paper is to investigate these generalized Hermite matrix polynomials, and derive some important results for them, such as, the generating matrix functions, matrix recurrence relations, an expansion of xnI, finite summation formulas, addition theorems, integral representations, fractional calculus operators, and certain other implicit summation formulae.
Generating matrix of the bi-periodic Lucas numbers