We identify a class of transcendental entire maps of finite order, of disjoint-type, satisfying the rapid derivative growth condition. Within this class, we show that there exist hyperbolic transcendental entire maps ...We identify a class of transcendental entire maps of finite order, of disjoint-type, satisfying the rapid derivative growth condition. Within this class, we show that there exist hyperbolic transcendental entire maps that generate a large class of potentials which intersect the so-called tame potentials and form a distinct class of potentials. The methods and techniques derived from the thermodynamic formalism are applied to these potentials for transcendental entire maps acting on some subset of the Julia set which is conjugated to the shift map over a code space with a countable alphabet endowed with the euclidean induced metric on the complex plane.展开更多
Let f and g be two permutable transcendental entire functions. In this paper, we first prove that J(fg)=J(f n g m) for any positive integers n and m . Then we prove that the function h(p(z))+az ∈/ B , where h(z) is...Let f and g be two permutable transcendental entire functions. In this paper, we first prove that J(fg)=J(f n g m) for any positive integers n and m . Then we prove that the function h(p(z))+az ∈/ B , where h(z) is any transcendental entire function with h′(z)=0 having infinitely many solutions, p(z) is a polynomial with deg p ≥2 and a(≠0) ∈ C .展开更多
Emily Dickinson is one of the most widely read and well-known American poets. Although there were just seven poems published during her lifetime, she was brought to many people's attention. Some people believe tha...Emily Dickinson is one of the most widely read and well-known American poets. Although there were just seven poems published during her lifetime, she was brought to many people's attention. Some people believe that Dickinson is a real romantic but others think she is a transcendentalist. However, both the factors of romanticism and transcendentalism can be seen in her character indeed. Romantic factors include individualism in her personality and her escaping from society. Transcendental factors are oversoul and mysticalness. If all the factors are taken into account, Emily Dickinson can fall into the category of both romanticism and transcendentalism.展开更多
Let fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbound...Let fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbounded positive real interval.展开更多
Suppose that f and g are two transcendental entire functions, and h is a non-constant periodic entire function. We denote the Julia set and Fatou set off by J（f） and F（f）, respectively, lffand g are semiconjugated...Suppose that f and g are two transcendental entire functions, and h is a non-constant periodic entire function. We denote the Julia set and Fatou set off by J（f） and F（f）, respectively, lffand g are semiconjugated, that is, h · f = g · h, in this paper, we will show that z ∈ J（f） if and only if h（z） ∈ J（g） （ similarly, z F（f） if and only ifh（z） ∈ F（g））, and this extends a result of Bergweiler.展开更多
Let f be a meromorphic function in C. If the order of f is greater than 2,has finitely many zeros and f takes a non-zero finite value finitely times, and then ?is unbounded.
In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by...In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.展开更多
Related to the basic features of Emerson＇s theories of Transcendentalism, the exploration of the novel in this thesis goes on three aspects. First, Bellow＇s concept of nature adopted in this novel is an expression ...Related to the basic features of Emerson＇s theories of Transcendentalism, the exploration of the novel in this thesis goes on three aspects. First, Bellow＇s concept of nature adopted in this novel is an expression of transcendental notion of nature. Secondly, in Henderson the Rain King Bellow also inherits the legacy of American transcendentalism as the emphasis of spirit or the oversoul. Thirdly, Bellow values individuality as highly as his literary predecessor Emerson did, however, in this novel he discards individualism. As Bellow＇s first mature novel, Henderson the Rain King reflects Bellow＇s attitude toward the tradition of American Transcendentalism： acceptance and surpass.展开更多
Transcendentalism is the most significant movement in American literature.In Little Women,"self-reliance"plays an important role in forming the theme of this novel,which is a major idea in Emerson’s Transce...Transcendentalism is the most significant movement in American literature.In Little Women,"self-reliance"plays an important role in forming the theme of this novel,which is a major idea in Emerson’s Transcendentalism.This paper intends to analyze the spirit of the March family in the view of self-reliance and gives the public a sense of love and unity,and it will make people get a better understanding of the theme.展开更多
As an outstanding poet in America,Emily Dickinson had crafted dozens of great works. The essay focuses on the influence of Transcendentalism on her poems with the following three aspects:the unity of the world and God...As an outstanding poet in America,Emily Dickinson had crafted dozens of great works. The essay focuses on the influence of Transcendentalism on her poems with the following three aspects:the unity of the world and God,the delight in nature and the pursuit of immorality and the soul.展开更多
The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial...The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial series and the factorial system is that the factorial series does not set an upper bound at a given place after the radix point, while in the factorial system (i – 1) is the maximal possible value for r<sub>i</sub> after the radix point. I give an extended definition of periodic numbers, and show the relationship between periodic and irrational numbers. I prove the transcendence of e by means of the factorial series and the factorial number system.展开更多
Liberty is a common wish of all people,a luxury that little has really attained in life.The emphasis will be placed on the philosophical meaning in different values in this essay,and a contrastive research of liberty ...Liberty is a common wish of all people,a luxury that little has really attained in life.The emphasis will be placed on the philosophical meaning in different values in this essay,and a contrastive research of liberty will be rendered in transcendentalism and Taoism in terms of Berlin 's two concepts of liberty,namely negative liberty and positive liberty.展开更多
Transcendental functions are important functions in various high performance computing applications.Because these functions are time-consuming and the vector units on modern processors become wider and more scalable,t...Transcendental functions are important functions in various high performance computing applications.Because these functions are time-consuming and the vector units on modern processors become wider and more scalable,there is an increasing demand for developing and using vector transcendental functions in such performance-hungry applications.However,the performance of vector transcendental functions as well as their accuracy remain largely unexplored.To address this issue,we perform a comprehensive evaluation of two Single Instruction Multiple Data(SIMD)intrinsics based vector math libraries on two ARMv8 compatible processors.We first design dedicated microbenchmarks that help us understand the performance behavior of vector transcendental functions.Then,we propose a piecewise,quantitative evaluation method with a set of meaningful metrics to quantify their performance and accuracy.By analyzing the experimental results,we find that vector transcendental functions achieve good performance speedups thanks to the vectorization and algorithm optimization.Moreover,vector math libraries can replace scalar math libraries in many cases because of improved performance and satisfactory accuracy.Despite this,the implementations of vector math libraries are still immature,which means further optimization is needed,and our evaluation reveals feasible optimization solutions for future vector math libraries.展开更多
In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The prop...In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.展开更多
文摘We identify a class of transcendental entire maps of finite order, of disjoint-type, satisfying the rapid derivative growth condition. Within this class, we show that there exist hyperbolic transcendental entire maps that generate a large class of potentials which intersect the so-called tame potentials and form a distinct class of potentials. The methods and techniques derived from the thermodynamic formalism are applied to these potentials for transcendental entire maps acting on some subset of the Julia set which is conjugated to the shift map over a code space with a countable alphabet endowed with the euclidean induced metric on the complex plane.
文摘Let f and g be two permutable transcendental entire functions. In this paper, we first prove that J(fg)=J(f n g m) for any positive integers n and m . Then we prove that the function h(p(z))+az ∈/ B , where h(z) is any transcendental entire function with h′(z)=0 having infinitely many solutions, p(z) is a polynomial with deg p ≥2 and a(≠0) ∈ C .
文摘Emily Dickinson is one of the most widely read and well-known American poets. Although there were just seven poems published during her lifetime, she was brought to many people's attention. Some people believe that Dickinson is a real romantic but others think she is a transcendentalist. However, both the factors of romanticism and transcendentalism can be seen in her character indeed. Romantic factors include individualism in her personality and her escaping from society. Transcendental factors are oversoul and mysticalness. If all the factors are taken into account, Emily Dickinson can fall into the category of both romanticism and transcendentalism.
文摘Let fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbounded positive real interval.
文摘Suppose that f and g are two transcendental entire functions, and h is a non-constant periodic entire function. We denote the Julia set and Fatou set off by J（f） and F（f）, respectively, lffand g are semiconjugated, that is, h · f = g · h, in this paper, we will show that z ∈ J（f） if and only if h（z） ∈ J（g） （ similarly, z F（f） if and only ifh（z） ∈ F（g））, and this extends a result of Bergweiler.
文摘Let f be a meromorphic function in C. If the order of f is greater than 2,has finitely many zeros and f takes a non-zero finite value finitely times, and then ?is unbounded.
文摘In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.
文摘Related to the basic features of Emerson＇s theories of Transcendentalism, the exploration of the novel in this thesis goes on three aspects. First, Bellow＇s concept of nature adopted in this novel is an expression of transcendental notion of nature. Secondly, in Henderson the Rain King Bellow also inherits the legacy of American transcendentalism as the emphasis of spirit or the oversoul. Thirdly, Bellow values individuality as highly as his literary predecessor Emerson did, however, in this novel he discards individualism. As Bellow＇s first mature novel, Henderson the Rain King reflects Bellow＇s attitude toward the tradition of American Transcendentalism： acceptance and surpass.
文摘Transcendentalism is the most significant movement in American literature.In Little Women,"self-reliance"plays an important role in forming the theme of this novel,which is a major idea in Emerson’s Transcendentalism.This paper intends to analyze the spirit of the March family in the view of self-reliance and gives the public a sense of love and unity,and it will make people get a better understanding of the theme.
文摘As an outstanding poet in America,Emily Dickinson had crafted dozens of great works. The essay focuses on the influence of Transcendentalism on her poems with the following three aspects:the unity of the world and God,the delight in nature and the pursuit of immorality and the soul.
文摘The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial series and the factorial system is that the factorial series does not set an upper bound at a given place after the radix point, while in the factorial system (i – 1) is the maximal possible value for r<sub>i</sub> after the radix point. I give an extended definition of periodic numbers, and show the relationship between periodic and irrational numbers. I prove the transcendence of e by means of the factorial series and the factorial number system.
文摘Liberty is a common wish of all people,a luxury that little has really attained in life.The emphasis will be placed on the philosophical meaning in different values in this essay,and a contrastive research of liberty will be rendered in transcendentalism and Taoism in terms of Berlin 's two concepts of liberty,namely negative liberty and positive liberty.
基金supported by the National Key Research and Development Program of China under Grant No.2020YFA0709803the National Natural Science Foundation of China under Grant Nos.61902407 and 61802416.
文摘Transcendental functions are important functions in various high performance computing applications.Because these functions are time-consuming and the vector units on modern processors become wider and more scalable,there is an increasing demand for developing and using vector transcendental functions in such performance-hungry applications.However,the performance of vector transcendental functions as well as their accuracy remain largely unexplored.To address this issue,we perform a comprehensive evaluation of two Single Instruction Multiple Data(SIMD)intrinsics based vector math libraries on two ARMv8 compatible processors.We first design dedicated microbenchmarks that help us understand the performance behavior of vector transcendental functions.Then,we propose a piecewise,quantitative evaluation method with a set of meaningful metrics to quantify their performance and accuracy.By analyzing the experimental results,we find that vector transcendental functions achieve good performance speedups thanks to the vectorization and algorithm optimization.Moreover,vector math libraries can replace scalar math libraries in many cases because of improved performance and satisfactory accuracy.Despite this,the implementations of vector math libraries are still immature,which means further optimization is needed,and our evaluation reveals feasible optimization solutions for future vector math libraries.
基金supported partly by the National Natural Science Foundation of China(11926201,12171050)the National Science Foundation of Guangdong Province(2018A030313508)。
文摘In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.
