scholarly journals Rational function and time transformation of caloric morphism on semi-euclidean spaces

2021 ◽  
Vol 53 (0) ◽  
pp. 35-42
Author(s):  
Katsunori Shimomura
Keyword(s):  
Rational Function ◽  
Time Transformation ◽  
Euclidean Spaces

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

scholarly journals The differential Galois group of the rational function field

2021 ◽  
Vol 381 ◽  
pp. 107605
Author(s):  
Annette Bachmayr ◽  
David Harbater ◽  
Julia Hartmann ◽  
Michael Wibmer
Keyword(s):  
Galois Group ◽  
Rational Function ◽  
Function Field ◽  
Differential Galois Group ◽  
Rational Function Field

scholarly journals The bifurcation set of a rational function via Newton polytopes

2021 ◽  
Author(s):  
Tat Thang Nguyen ◽  
Takahiro Saito ◽  
Kiyoshi Takeuchi
Keyword(s):  
Rational Function ◽  
Newton Polytopes ◽  
Bifurcation Set

scholarly journals Ancient solutions for Andrews’ hypersurface flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Peng Lu ◽  
Jiuru Zhou
Keyword(s):  
Ricci Flow ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Euclidean Spaces ◽  
Round Cylinder ◽  
Ancient Solutions ◽  
Singular Time

AbstractWe construct the ancient solutions of the hypersurface flows in Euclidean spaces studied by B. Andrews in 1994.As time {t\rightarrow 0^{-}} the solutions collapse to a round point where 0 is the singular time. But as {t\rightarrow-\infty} the solutions become more and more oval. Near the center the appropriately-rescaled pointed Cheeger–Gromov limits are round cylinder solutions {S^{J}\times\mathbb{R}^{n-J}}, {1\leq J\leq n-1}. These results are the analog of the corresponding results in Ricci flow ({J=n-1}) and mean curvature flow.

scholarly journals Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1510
Author(s):  
Alaa H. Abdel-Hamid ◽  
Atef F. Hashem
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Censored Data ◽  
Sufficient Conditions ◽  
Transformation Function ◽  
Point Estimation ◽  
Estimation Methods ◽  
Time Transformation ◽  
Monte Carlo Simulation Study ◽  
Accelerated Life

In this article, the tampered failure rate model is used in partially accelerated life testing. A non-decreasing time function, often called a ‘‘time transformation function", is proposed to tamper the failure rate under design conditions. Different types of the proposed function, which have sufficient conditions in order to be accelerating functions, are investigated. A baseline failure rate of the exponential distribution is considered. Some point estimation methods, as well as approximate confidence intervals, for the parameters involved are discussed based on generalized progressively hybrid censored data. The determination of the optimal stress change time is discussed under two different criteria of optimality. A real dataset is employed to explain the theoretical outcomes discussed in this article. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

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