This article investigates the second overtone thickness-extensional(TE2)vibrations and associated mode-coupling behaviors in ZnO piezoelectric film bulk acoustic resonator(FBAR),utilizing its wave dispersion relation ...This article investigates the second overtone thickness-extensional(TE2)vibrations and associated mode-coupling behaviors in ZnO piezoelectric film bulk acoustic resonator(FBAR),utilizing its wave dispersion relation and the higher-order stress balance principle.By superimposing the general wave solutions of multiple eigenmodes within the frequency range of the TE2 mode,mode-coupling solutions for ZnO FBAR are constructed.The substitution of these mode-coupling solutions into the higher-order stress balance principle,as laterally weak boundary conditions,leads to the frequency spectrogram equation,determining the relationship between resonance frequency and plate length-to-thickness ratio.A modified algorithm that combines the bisection method and the complex modulus ratio method is developed to solve the dispersion equation and frequency spectrogram equation(namely a kind of 2D complex transcendental equations)accurately and efficiently.The obtained results indicate that the operational TE2 mode may couple to unwanted 3^(rd)thickness-shear,fundamental thickness-shear,and flexural modes.Moreover,the mode-coupling behaviors depend strongly on resonance frequencies and plate length-to-thickness ratio.The displacement distributions of total displacement components,alongside the main displacement com-ponents of all considered eigenmodes,clearly demonstrate the variety of coupling behaviors.According to the obtained frequency spectrograms,the desirable values of plate length-to-thickness ratio for a clean operating mode with very weak coupling intensity are determined.These findings are of vital importance for the understanding of the mode-coupling me-chanism in overtone thickness-extensional FBARs,which will facilitate the structural design and optimization of FBAR devices.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
By using the Nevanlinna value distribution theory, we will mainly investigate the form of entire solutions with finite order on a type of system of differential-difference equations and a type of differential-differen...By using the Nevanlinna value distribution theory, we will mainly investigate the form of entire solutions with finite order on a type of system of differential-difference equations and a type of differential-difference equations, two interesting results are obtained. And it extends some results concerning complex differential（difference） equations to the systems of differential-difference equations.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 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
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
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
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
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
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
In this paper, we investigate the complex oscillation of the differential equation f<sup>k</sup>+A<sub>k-1</sub>f<sup>k-1</sup>+…+A<sub>O</sub>f=F where A<sub>k-1...In this paper, we investigate the complex oscillation of the differential equation f<sup>k</sup>+A<sub>k-1</sub>f<sup>k-1</sup>+…+A<sub>O</sub>f=F where A<sub>k-1</sub>.…, A<sub>o</sub> F 0 are finite order transcendental entire functions, such that there exists an A<sub>d</sub>（0≤d≤k-1） being dominant in the sense that either it has larger order than any other A<sub>j</sub>（j=0.…. d-l. d+l.…. k-1）, or it is the only transcendental function. We obtain some precise estimates of the exponent of convergence of the zero-sequence of solutions to the above equation.展开更多
This paper considers the dynamics associated with an arbitrary semigroup of transcendental meromorphic functions. Fatou-Julia theory was used to investigate the dynamics of these semigroups. Some results of the dynami...This paper considers the dynamics associated with an arbitrary semigroup of transcendental meromorphic functions. Fatou-Julia theory was used to investigate the dynamics of these semigroups. Some results of the dynamics of a rational mapping on the Riemann sphere were extended to the case.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some re...Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some results of some authors.展开更多
Let f be a transcendental entire function with order ρ 〈 1/2 and let a be a sufficiently large constant. We prove that if there exists r0 〉 1 such that, for all r 〉 r0 and any small ε 〉0,M（r^σ,f）≥M（r,f）σ...Let f be a transcendental entire function with order ρ 〈 1/2 and let a be a sufficiently large constant. We prove that if there exists r0 〉 1 such that, for all r 〉 r0 and any small ε 〉0,M（r^σ,f）≥M（r,f）σ＋ε.then every component of the Fatou set F（f） is bounded.展开更多
With a dozen influential publications,Professor Dan Zahavi has established himself as a world-leading interpreter of Husserl and a pioneering scholar working at the intersection between phenomenological philosophy and...With a dozen influential publications,Professor Dan Zahavi has established himself as a world-leading interpreter of Husserl and a pioneering scholar working at the intersection between phenomenological philosophy and empirical research such as cognitive sciences,altruistic study,and nursing study.On the one hand,with the book Husserl and Transcendental Intersubjectivity(2001),Zahavi provides an in-depth interpretation of Husserfs theory of intersubjectivity and defends his transcendental approach against the widespread Schutzian critique that takes his theory to be an unfortunate philosophical failure.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 order to take into account the computing efficiency and flexibility of calculating transcendental functions, this paper proposes one kind of reconfigurable transcendental function generator. The generator is of a r...In order to take into account the computing efficiency and flexibility of calculating transcendental functions, this paper proposes one kind of reconfigurable transcendental function generator. The generator is of a reconfigurable array structure composed of 30 processing elements （PEs）. The coordinate rotational digital computer （CORDIC） algorithm is implemented on this structure. Different functions, such as sine, cosine, inverse tangent, logarithmic, etc., can be calculated based on the structure by reconfiguring the functions of PEs. The functional simulation and field programmable gate array （FPGA） verification show that the proposed method obtains great flexibility with acceptable performance.展开更多
Let ω1,..., ωs be a set of real transcendental numbers satisfying a certain Diophantine inequality. The upper bound for the discrepancy of the Kronecker sequence （{nω1},..., {nωs}）（1 ≤ n ≤ N） is given. In pa...Let ω1,..., ωs be a set of real transcendental numbers satisfying a certain Diophantine inequality. The upper bound for the discrepancy of the Kronecker sequence （{nω1},..., {nωs}）（1 ≤ n ≤ N） is given. In particular, some low-discrepancy sequences are constructed.展开更多
A transcendental polynomial which has all its roots lying in the left half plane is called stable. In this paper, the stability of transcendental polynomials which are nearly as general as those discussed by L. S. Po...A transcendental polynomial which has all its roots lying in the left half plane is called stable. In this paper, the stability of transcendental polynomials which are nearly as general as those discussed by L. S. Pontryagin are investigated through direct analytic method.For application of the method presented in this paper, the asymptotic stability of some differential-difference equations is investigated.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12192210,12192211,12102183,12302200,and 12402192)the Natural Science Foundation of Zhejiang Province(Grant No.LD21A020001)+2 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20230873)the National Postdoctoral Program for Innovation Talents(Grant No.BX2021261)supported by the specialized research projects of Huanjiang Laboratory,Zhuji,Zhejiang Province.
文摘This article investigates the second overtone thickness-extensional(TE2)vibrations and associated mode-coupling behaviors in ZnO piezoelectric film bulk acoustic resonator(FBAR),utilizing its wave dispersion relation and the higher-order stress balance principle.By superimposing the general wave solutions of multiple eigenmodes within the frequency range of the TE2 mode,mode-coupling solutions for ZnO FBAR are constructed.The substitution of these mode-coupling solutions into the higher-order stress balance principle,as laterally weak boundary conditions,leads to the frequency spectrogram equation,determining the relationship between resonance frequency and plate length-to-thickness ratio.A modified algorithm that combines the bisection method and the complex modulus ratio method is developed to solve the dispersion equation and frequency spectrogram equation(namely a kind of 2D complex transcendental equations)accurately and efficiently.The obtained results indicate that the operational TE2 mode may couple to unwanted 3^(rd)thickness-shear,fundamental thickness-shear,and flexural modes.Moreover,the mode-coupling behaviors depend strongly on resonance frequencies and plate length-to-thickness ratio.The displacement distributions of total displacement components,alongside the main displacement com-ponents of all considered eigenmodes,clearly demonstrate the variety of coupling behaviors.According to the obtained frequency spectrograms,the desirable values of plate length-to-thickness ratio for a clean operating mode with very weak coupling intensity are determined.These findings are of vital importance for the understanding of the mode-coupling me-chanism in overtone thickness-extensional FBARs,which will facilitate the structural design and optimization of FBAR devices.
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By using the Nevanlinna value distribution theory, we will mainly investigate the form of entire solutions with finite order on a type of system of differential-difference equations and a type of differential-difference equations, two interesting results are obtained. And it extends some results concerning complex differential（difference） equations to the systems of differential-difference equations.
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 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.
基金Project supported by the National Natural Science Foundation of China
文摘In this paper, we investigate the complex oscillation of the differential equation f<sup>k</sup>+A<sub>k-1</sub>f<sup>k-1</sup>+…+A<sub>O</sub>f=F where A<sub>k-1</sub>.…, A<sub>o</sub> F 0 are finite order transcendental entire functions, such that there exists an A<sub>d</sub>（0≤d≤k-1） being dominant in the sense that either it has larger order than any other A<sub>j</sub>（j=0.…. d-l. d+l.…. k-1）, or it is the only transcendental function. We obtain some precise estimates of the exponent of convergence of the zero-sequence of solutions to the above equation.
文摘This paper considers the dynamics associated with an arbitrary semigroup of transcendental meromorphic functions. Fatou-Julia theory was used to investigate the dynamics of these semigroups. Some results of the dynamics of a rational mapping on the Riemann sphere were extended to the case.
基金Supported by the National Natural Science Foundation of China (Grant No.10471065)the Natural Science Foundation of Guangdong Province (Grant No.04010474)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some results of some authors.
基金Supported by National Natural Science Foundation of China(Grant Nos.11261002 and 11261069)Natural Science Foundation of Yunnan Province of China(Grant No.2012FZ167)Educational Commission of Yunnan Province of China(Grant No.2012Z121)
文摘Let f be a transcendental entire function with order ρ 〈 1/2 and let a be a sufficiently large constant. We prove that if there exists r0 〉 1 such that, for all r 〉 r0 and any small ε 〉0,M（r^σ,f）≥M（r,f）σ＋ε.then every component of the Fatou set F（f） is bounded.
文摘With a dozen influential publications,Professor Dan Zahavi has established himself as a world-leading interpreter of Husserl and a pioneering scholar working at the intersection between phenomenological philosophy and empirical research such as cognitive sciences,altruistic study,and nursing study.On the one hand,with the book Husserl and Transcendental Intersubjectivity(2001),Zahavi provides an in-depth interpretation of Husserfs theory of intersubjectivity and defends his transcendental approach against the widespread Schutzian critique that takes his theory to be an unfortunate philosophical failure.
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 by the National Natural Science Foundation of China(61272120,61602377,61634004)the Natural Science Foundation of Shaanxi Province of China(2015JM6326)+1 种基金Shaanxi Provincial Co-ordination Innovation Project of Science and Technology(2016KTZDGY02-04-02)the Project of Education Department of Shaanxi Provincial Government(15JK1683)
文摘In order to take into account the computing efficiency and flexibility of calculating transcendental functions, this paper proposes one kind of reconfigurable transcendental function generator. The generator is of a reconfigurable array structure composed of 30 processing elements （PEs）. The coordinate rotational digital computer （CORDIC） algorithm is implemented on this structure. Different functions, such as sine, cosine, inverse tangent, logarithmic, etc., can be calculated based on the structure by reconfiguring the functions of PEs. The functional simulation and field programmable gate array （FPGA） verification show that the proposed method obtains great flexibility with acceptable performance.
基金Project supported by National Natural Science Foundation of China(No.10571180)
文摘Let ω1,..., ωs be a set of real transcendental numbers satisfying a certain Diophantine inequality. The upper bound for the discrepancy of the Kronecker sequence （{nω1},..., {nωs}）（1 ≤ n ≤ N） is given. In particular, some low-discrepancy sequences are constructed.
文摘A transcendental polynomial which has all its roots lying in the left half plane is called stable. In this paper, the stability of transcendental polynomials which are nearly as general as those discussed by L. S. Pontryagin are investigated through direct analytic method.For application of the method presented in this paper, the asymptotic stability of some differential-difference equations is investigated.
