scholarly journals Linear Transformations Preserving the Strong $q$-log-convexity of Polynomials

10.37236/5168 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Bao-Xuan Zhu ◽  
Hua Sun
Keyword(s):  
Linear Transformation ◽  
Sufficient Condition ◽  
Linear Transformations

In this paper, we give a sufficient condition for the linear transformation preserving the strong $q$-log-convexity. As applications, we get some linear transformations (for instance, Morgan-Voyce transformation, binomial transformation, Narayana transformations of two kinds) preserving the strong $q$-log-convexity. In addition, our results not only extend some known results, but also imply the strong $q$-log-convexities of some sequences of polynomials.

scholarly journals Recurrence Relations for the Linear Transformation Preserving the Strong $q$-Log-Convexity

10.37236/5913 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Lily Li Liu ◽  
Ya-Nan Li
Keyword(s):  
Recurrence Relation ◽  
Linear Transformation ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Binomial Coefficients ◽  
Sufficient Condition ◽  
Linear Transformations ◽  
Whitney Numbers ◽  
Three Term Recurrence Relation

Let $[T(n,k)]_{n,k\geqslant0}$ be a triangle of positive numbers satisfying the three-term recurrence relation\[T(n,k)=(a_1n+a_2k+a_3)T(n-1,k)+(b_1n+b_2k+b_3)T(n-1,k-1).\]In this paper, we give a new sufficient condition for linear transformations\[Z_n(q)=\sum_{k=0}^{n}T(n,k)X_k(q)\]that preserves the strong $q$-log-convexity of polynomials sequences. As applications, we show linear transformations, given by matrices of the binomial coefficients, the Stirling numbers of the first kind and second kind, the Whitney numbers of the first kind and second kind, preserving the strong $q$-log-convexity in a unified manner.

scholarly journals Interconversion of Plasma Free Thyroxine Values from Assay Platforms with Different Reference Intervals Using Linear Transformation Methods

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 45
Author(s):  
Fanwen Meng ◽  
Jacqueline Jonklaas ◽  
Melvin Khee-Shing Leow
Keyword(s):  
Linear Transformation ◽  
Piecewise Linear ◽  
Equilibrium Dialysis ◽  
Accurate Method ◽  
Reference Intervals ◽  
Thyroid Stimulating Hormone ◽  
Free Thyroxine ◽  
Thyroid Function Tests ◽  
Linear Transformations ◽  
Transformation Methods

Clinicians often encounter thyroid function tests (TFT) comprising serum/plasma free thyroxine (FT4) and thyroid stimulating hormone (TSH) measured using different assay platforms during the course of follow-up evaluations which complicates reliable comparison and interpretation of TFT changes. Although interconversion between concentration units is straightforward, the validity of interconversion of FT4/TSH values from one assay platform to another with different reference intervals remains questionable. This study aims to establish an accurate and reliable methodology of interconverting FT4 by any laboratory to an equivalent FT4 value scaled to a reference range of interest via linear transformation methods. As a proof-of-concept, FT4 was simultaneously assayed by direct analog immunoassay, tandem mass spectrometry and equilibrium dialysis. Both linear and piecewise linear transformations proved relatively accurate for FT4 inter-scale conversion. Linear transformation performs better when FT4 are converted from a more accurate to a less accurate assay platform. The converse is true, whereby piecewise linear transformation is superior to linear transformation when converting values from a less accurate method to a more robust assay platform. Such transformations can potentially apply to other biochemical analytes scale conversions, including TSH. This aids interpretation of TFT trends while monitoring the treatment of patients with thyroid disorders.

scholarly journals On the eigenvalues of some class of pseudo-linear transformations

2007 ◽  
pp. 79-83
Author(s):  
Milica Andjelic
Keyword(s):  
Linear Transformation ◽  
Closed Field ◽  
Linear Transformations ◽  
Algebraically Closed Field ◽  
New Criterion

We develop a connection between the eigenvalues of a class of pseudo-linear transformation over a field K and the eigenvalues of a certain linear transformation. We give a new criterion for this class to be diagonalizable over algebraically closed field.

Research on the Sufficient Condition for the Existence of Periodic Solution of FGM Subjected to Aero-Thermal Load

2012 ◽  
Vol 249-250 ◽  
pp. 326-331
Author(s):  
Jing Li ◽  
Xiao Na Yin ◽  
Xiao Dong Jin
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Linear Transformation ◽  
Thermal Load ◽  
Nonlinear Dynamical System ◽  
Sufficient Condition ◽  
Nonlinear Dynamical ◽  
Multi Scale ◽  
Approach Method ◽  
Nonsingular Linear Transformation

In this paper, the average equations are given through using the multi-scale approach method. By using the Melinkov function, the nonsingular linear transformation and the Poincaré map, the sufficient condition for existence of periodic solution of the nonlinear dynamical system about the FGM subjected to aero-thermal load is derived.

Some Implications of Noncoaxiality in Finite Deformations

1973 ◽  
Vol 95 (2) ◽  
pp. 87-93
Author(s):  
T. C. Hsu
Keyword(s):  
Rigid Body ◽  
Linear Transformation ◽  
Metal Forming ◽  
Principal Axis ◽  
Pure Shear ◽  
Finite Deformations ◽  
Two Dimensional ◽  
Body Rotation ◽  
Linear Transformations ◽  
Rectangular Grids

Two-dimensional finite deformations are analyzed by factoring and multiplying the matrices of the linear transformations representing them. A general linear transformation consists of a pure shear, a uniform dilation, and a rigid-body rotation. Coaxiality is defined for finite deformations and its effect on the resultant distortion discussed. Tests for coaxiality are devised for use on rectangular grids which are often employed in metal forming research. Formulas are derived for the initial and final directions of the resultant major principal axis in both equal and unequal noncoaxial pure shears and, in particular, conditions are found for the constancy of distortion in the second deformation.

Sign Variation of Vectors and TN Linear Transformations

2011 ◽  
Author(s):  
Shaun M. Fallat ◽  
Charles R. Johnson
Keyword(s):  
Continuous Function ◽  
Linear Transformation ◽  
Approximation Theory ◽  
Linear Transformations ◽  
Shape Preserving ◽  
Sign Changes

This chapter develops an array of results about TP/TN matrices and sign variation diminution, along with appropriate converses. If the entries of a vector represent a sampling of consecutive function values, then a change in the sign of consecutive vector entries corresponds to the important event of the (continuous) function passing through zero. It has been known that as a linear transformation, a TP matrix cannot increase the number of sign changes in a vector. The transformations that never increase the number of sign variations are of interest in a variety of applications, including approximation theory and shape preserving transforms, and are of mathematical interest as well.

On the Convergence of Mean Values Over Lattices

1958 ◽  
Vol 10 ◽  
pp. 103-110 ◽  
Author(s):  
Wolfgang Schmidt
Keyword(s):  
Linear Transformation ◽  
Measurable Function ◽  
Dimensional Space ◽  
Fundamental Region ◽  
Geometry Of Numbers ◽  
Linear Transformations ◽  
Mean Values ◽  
Unimodular Transformations

Recently C. A.Rogers (2, Theorem 4) proved the following theorem which applies to many problems in geometry of numbers: Let f(X1,X2, … , Xk) be a non-negative B or el-measurable function in the nk-dimensional space of points (X1,X2. Further, let Λo be the fundamental lattice, Ω a linear transformation of determinant 1, F a fundamental region in the space of linear transformations of determinant 1, defined with respect to the subgroup of unimodular transformations and μ(Ω) the invariant measure1 on the space of linear transformations of determinant 1 in Rn.

scholarly journals Linear Transformations on Algebras of Matrices

1959 ◽  
Vol 11 ◽  
pp. 61-66 ◽  
Author(s):  
Marvin Marcus ◽  
B. N. Moyls
Keyword(s):  
Linear Transformation ◽  
Complex Numbers ◽  
List Type ◽  
Hermitian Matrices ◽  
Linear Transformations ◽  
Unimodular Group

Let Mn denote the algebra of n-square matrices over the complex numbers; and let Un, Hn, and Rk denote respectively the unimodular group, the set of Hermitian matrices, and the set of matrices of rank k, in Mn. Let ev(A) be the set of n eigenvalues of A counting multiplicities. We consider the problem of determining the structure of any linear transformation (l.t.) T of Mn into Mn having one or more of the following properties:(a)T(Rk) ⊆ for k = 1, …, n.(b)T(Un) ⊆ Un(c)det T(A) = det A for all A ∈ Hn.(d)ev(T(A)) = ev(A) for all A ∈ Hn.We remark that we are not in general assuming that T is a multiplicative homomorphism; more precisely, T is a mapping of Mn into itself, satisfyingT(aA + bB) = aT(A) + bT(B)for all A, B in Mn and all complex numbers a, b.

scholarly journals Sums of Linear Transformations in Higher Dimensions

2019 ◽  
Vol 70 (3) ◽  
pp. 965-984 ◽  
Author(s):  
Akshat Mudgal
Keyword(s):  
Natural Number ◽  
Linear Transformation ◽  
Finite Subset ◽  
Absolute Constant ◽  
Higher Dimensions ◽  
Dimensional Subspace ◽  
Main Term ◽  
Linear Transformations ◽  
One Dimensional

AbstractIn this paper, we prove the following two results. Let d be a natural number and q, s be co-prime integers such that 1<qs<|q|. Then there exists a constant δ>0 depending only on q, s and d such that for any finite subset A of ℝd that is not contained in a translate of a hyperplane, we have |q⋅A+s⋅A|≥(|q|+|s|+2d−2)|A|−Oq,s,d(|A|1−δ).The main term in this bound is sharp and improves upon an earlier result of Balog and Shakan. Secondly, let L∈GL2(ℝ) be a linear transformation such that L does not have any invariant one-dimensional subspace of ℝ2. Then, for all finite subsets A of ℝ2, we have |A+L(A)|≥4|A|−O(|A|1−δ), for some absolute constant δ>0. The main term in this result is sharp as well.

scholarly journals On the Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Mohammad Abobala
Keyword(s):  
Linear Transformation ◽  
Vector Spaces ◽  
Linear Transformations

The objective of this paper is to study the representation of neutrosophic matrices defined over a neutrosophic field by neutrosophic linear transformations between neutrosophic vector spaces, where it proves that every neutrosophic matrix can be represented uniquely by a neutrosophic linear transformation. Also, this work proves that every neutrosophic linear transformation must be an AH-linear transformation; i.e., it can be represented by classical linear transformations.

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