Purpose: The Pythagorean Comma refers to an ancient Greek musical, mathematical tuning method that defines an integer ratio of exponential coupling constant harmonic law of two frequencies and a virtual frequency. A C...Purpose: The Pythagorean Comma refers to an ancient Greek musical, mathematical tuning method that defines an integer ratio of exponential coupling constant harmonic law of two frequencies and a virtual frequency. A Comma represents a physical harmonic system that is readily observable and can be mathematically simulated. The virtual harmonic is essential and indirectly measurable. The Pythagorean Comma relates to two discrete frequencies but can be generalized to any including infinite harmonics of a fundamental frequency, vF. These power laws encode the physical and mathematical properties of their coupling constant ratio, natural resonance, the maximal resonance of the powers of the frequencies, wave interference, and the beat. The hypothesis is that the Pythagorean power fractions of a fundamental frequency, vF are structured by the same harmonic fraction system seen with standing waves. Methods: The Pythagorean Comma refers to the ratio of (3/2)12 and 27 that is nearly equal to 1. A Comma is related to the physical setting of the maximum resonance of the powers of two frequencies. The powers and the virtual frequency are derived simulating the physical environment utilizing the Buckingham Π theorem, array analysis, and dimensional analysis. The powers and the virtual frequency can be generalized to any two frequencies. The maximum resonance occurs when their dimensionless ratio closest to 1 and the virtual harmonic closest to 1 Hz. The Pythagorean possible power arrays for a vF system or any two different frequencies are evaluated. Results: The generalized Pythagorean harmonic power law for any two different frequencies coupling constant are derived with a form of an infinite number of powers defining a constant power ratio and a single virtual harmonic frequency. This power system has periodic and fractal properties. The Pythagorean power law also encodes the ratio of logs of the frequencies. These must equal or nearly equal the power ratio. When all of the harmonics are powers of a vF the Pythagorean powers are defined by a consecutive integer series structured in the identical form as standard harmonic fractions. The ratio of the powers is rational, and all of the virtual harmonics are 1 Hz. Conclusion: The Pythagorean Comma power law method can be generalized. This is a new isomorphic wave perspective that encompasses all harmonic systems, but with an infinite number of possible powers. It is important since there is new information: powers, power ratio, and a virtual frequency. The Pythagorean relationships are different, yet an isomorphic perspective where the powers demonstrate harmonic patterns. The coupling constants of a vF Pythagorean power law system are related to the vFs raised to the harmonic fraction series which accounts for the parallel organization to the standing wave system. This new perspective accurately defines an alternate valid physical harmonic system.展开更多
Let T be a right exact functor from an abelian category B into another abelian category A.Then there exists a functor p from the product category A×B to the comma category(T↓A).In this paper,we study the propert...Let T be a right exact functor from an abelian category B into another abelian category A.Then there exists a functor p from the product category A×B to the comma category(T↓A).In this paper,we study the property of the extension closure of some classes of objects in(T↓A),the exactness of the functor p and the detailed description of orthogonal classes of a given class p(X,Y)in(T↓A).Moreover,we characterize when special precovering classes in abelian categories A and B can induce special precovering classes in(T↓A).As an application,we prove that under suitable conditions,the class of Gorenstein projective leftΛ-modules over a triangular matrix ringΛ=(R M 0 S)is special precovering if and only if both the classes of Gorenstein projective left R-modules and left S-modules are special precovering.Consequently,we produce a large variety of examples of rings such that the class of Gorenstein projective modules is special precovering over them.展开更多
Jose Garcia Villa’s "comma poem,"in which he introduces“a new,special and poetic use”for the comma,is arguably the poet's most contentious innovation.Starting from an appropriation of Leonard Caspar’...Jose Garcia Villa’s "comma poem,"in which he introduces“a new,special and poetic use”for the comma,is arguably the poet's most contentious innovation.Starting from an appropriation of Leonard Caspar’s description of the comma poems as "demonstrably malfunctional as a dragging foot,"this essay argues that the comma poem was a visual performance whereby Villa dis-oriented and de-naturalized poetic“flows”through a quccr/crip aesthetic of hesitation and brokenness.Read as footsteps and/or footnotes,the comma’s minor mark interrupts and dis-ablcs normative flow,forcing the reader to adopt a nonnormative“gait.”Utilizing Sara Ahmed’s phenomenological theory of "queer orientation,"I examine how the comma poems’specific incongruity extends beyond modem grammars:anticipating readings of his“foreignness”and"insensitivity"to the English language.Villa performs the essentiality of the“minor mark”through linguistic experimentation.In doing so,he queers not only the“direction”of modem poetry and its canonicity,but also a contemporary politics of recuperation.展开更多
It was a Monday morning.As a teacher walked into the ___1___,he heard a low voice(说话声):"here is the teacher.I am___2___this boring fellow(烦人的家伙)is going to talk about putting in commas(逗号).”It was___3_...It was a Monday morning.As a teacher walked into the ___1___,he heard a low voice(说话声):"here is the teacher.I am___2___this boring fellow(烦人的家伙)is going to talk about putting in commas(逗号).”It was___3___voice.His name was Bill.He was talking__4__the boy next to him.展开更多
The purpose of punctuaion is to make the reading of the sentences easier and to make the meaning of the writing clear for readers. But how to use it correctly and what is the real function of it are still problems for...The purpose of punctuaion is to make the reading of the sentences easier and to make the meaning of the writing clear for readers. But how to use it correctly and what is the real function of it are still problems for writers. The following article is that how the punctuation style shows up in liters- ature and how the tiny mark-comma is used in writing.展开更多
文摘Purpose: The Pythagorean Comma refers to an ancient Greek musical, mathematical tuning method that defines an integer ratio of exponential coupling constant harmonic law of two frequencies and a virtual frequency. A Comma represents a physical harmonic system that is readily observable and can be mathematically simulated. The virtual harmonic is essential and indirectly measurable. The Pythagorean Comma relates to two discrete frequencies but can be generalized to any including infinite harmonics of a fundamental frequency, vF. These power laws encode the physical and mathematical properties of their coupling constant ratio, natural resonance, the maximal resonance of the powers of the frequencies, wave interference, and the beat. The hypothesis is that the Pythagorean power fractions of a fundamental frequency, vF are structured by the same harmonic fraction system seen with standing waves. Methods: The Pythagorean Comma refers to the ratio of (3/2)12 and 27 that is nearly equal to 1. A Comma is related to the physical setting of the maximum resonance of the powers of two frequencies. The powers and the virtual frequency are derived simulating the physical environment utilizing the Buckingham Π theorem, array analysis, and dimensional analysis. The powers and the virtual frequency can be generalized to any two frequencies. The maximum resonance occurs when their dimensionless ratio closest to 1 and the virtual harmonic closest to 1 Hz. The Pythagorean possible power arrays for a vF system or any two different frequencies are evaluated. Results: The generalized Pythagorean harmonic power law for any two different frequencies coupling constant are derived with a form of an infinite number of powers defining a constant power ratio and a single virtual harmonic frequency. This power system has periodic and fractal properties. The Pythagorean power law also encodes the ratio of logs of the frequencies. These must equal or nearly equal the power ratio. When all of the harmonics are powers of a vF the Pythagorean powers are defined by a consecutive integer series structured in the identical form as standard harmonic fractions. The ratio of the powers is rational, and all of the virtual harmonics are 1 Hz. Conclusion: The Pythagorean Comma power law method can be generalized. This is a new isomorphic wave perspective that encompasses all harmonic systems, but with an infinite number of possible powers. It is important since there is new information: powers, power ratio, and a virtual frequency. The Pythagorean relationships are different, yet an isomorphic perspective where the powers demonstrate harmonic patterns. The coupling constants of a vF Pythagorean power law system are related to the vFs raised to the harmonic fraction series which accounts for the parallel organization to the standing wave system. This new perspective accurately defines an alternate valid physical harmonic system.
基金supported by National Natural Science Foundation of China (Grant Nos. 11671069 and 11771212)Zhejiang Provincial Natural Science Foundation of China (Grant No. LY18A010032)+1 种基金Qing Lan Project of Jiangsu Province and Jiangsu Government Scholarship for Overseas Studies (Grant No. JS2019-328)during a visit of the first author to Charles University in Prague with the support by Jiangsu Government Scholarship
文摘Let T be a right exact functor from an abelian category B into another abelian category A.Then there exists a functor p from the product category A×B to the comma category(T↓A).In this paper,we study the property of the extension closure of some classes of objects in(T↓A),the exactness of the functor p and the detailed description of orthogonal classes of a given class p(X,Y)in(T↓A).Moreover,we characterize when special precovering classes in abelian categories A and B can induce special precovering classes in(T↓A).As an application,we prove that under suitable conditions,the class of Gorenstein projective leftΛ-modules over a triangular matrix ringΛ=(R M 0 S)is special precovering if and only if both the classes of Gorenstein projective left R-modules and left S-modules are special precovering.Consequently,we produce a large variety of examples of rings such that the class of Gorenstein projective modules is special precovering over them.
文摘Jose Garcia Villa’s "comma poem,"in which he introduces“a new,special and poetic use”for the comma,is arguably the poet's most contentious innovation.Starting from an appropriation of Leonard Caspar’s description of the comma poems as "demonstrably malfunctional as a dragging foot,"this essay argues that the comma poem was a visual performance whereby Villa dis-oriented and de-naturalized poetic“flows”through a quccr/crip aesthetic of hesitation and brokenness.Read as footsteps and/or footnotes,the comma’s minor mark interrupts and dis-ablcs normative flow,forcing the reader to adopt a nonnormative“gait.”Utilizing Sara Ahmed’s phenomenological theory of "queer orientation,"I examine how the comma poems’specific incongruity extends beyond modem grammars:anticipating readings of his“foreignness”and"insensitivity"to the English language.Villa performs the essentiality of the“minor mark”through linguistic experimentation.In doing so,he queers not only the“direction”of modem poetry and its canonicity,but also a contemporary politics of recuperation.
文摘It was a Monday morning.As a teacher walked into the ___1___,he heard a low voice(说话声):"here is the teacher.I am___2___this boring fellow(烦人的家伙)is going to talk about putting in commas(逗号).”It was___3___voice.His name was Bill.He was talking__4__the boy next to him.
文摘The purpose of punctuaion is to make the reading of the sentences easier and to make the meaning of the writing clear for readers. But how to use it correctly and what is the real function of it are still problems for writers. The following article is that how the punctuation style shows up in liters- ature and how the tiny mark-comma is used in writing.
