Spectral function

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  • In this work, we study the one-dimensional Dirac system on a whole line with impulsive conditions. We construct a spectral function of this system. Using the spectral function, we establish a Parseval equality and spectral expansion formula for such a system.

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  • (bq) part 1 book "functional analysis, sobolev spaces and partial differential equations" has contents: the hahn–banach theorems - introduction to the theory of conjugate convex functions; the uniform boundedness principle and the closed graph theorem; compact operators - spectral decomposition of self adjoint compact operators,...and other contents.

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  • This paper deals with the above mentioned problem. The main idea of this work is the use of an analytical simulation of random excitation given by its spectral density function and afterward application of the well known procedure of the asymptotic method to obtain an asymptotic expression of the response spectral density function.

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  • In this paper, we investigate analytical and asymptotic properties of the Jost solution and Jost function of the impulsive discrete Dirac equations. We also study eigenvalues and spectral singularities of these equations. Then we obtain characteristic properties of the scattering function of the impulsive discrete Dirac systems.

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  • The final chapter of the book presents an innovative method for fluid mechanical design in which an object within the flow field is build element-by-element. Each element is introduced into the flow, and its effect on a cost function is minimized with respect to the object’s position. An element may represent added material or a removed part of the existing structure. This chapter presents a strong degree of mathematical formality.

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  • In fact, since the MEM estimate may have very sharp spectral features, one wants to be able to evaluate it on a very fine mesh near to those features, but perhaps only more coarsely farther away from them. Here is a function which

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  • We have defined the convolution of two functions for the continuous case in equation (12.0.8), and have given the convolution theorem as equation (12.0.9). The theorem says that the Fourier transform of the convolution of two functions is equal to the product of their individual Fourier transforms.

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  • Consider the inverse eigenvalue problem of the Schr¨dinger operator deo fined on a finite interval. We give optimal and almost optimal conditions for a set of eigenvalues to determine the Schr¨dinger operator. These conditions are o simple closedness properties of the exponential system corresponding to the known eigenvalues. The statements contain nearly all former results of this topic. We give also conditions for recovering the Weyl-Titchmarsh m-function from its values m(λn ).

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  • Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Pseudo-thường xuyên phổ chức năng trong không gian Krein...

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  • V an isometry, as in the theorem of Plancherel, is not just a weighted L2-norm on some measure space. This is due to the fact that the back transformation Z has a different expression on each branch, and this is caused by the ramification of the domain. It is not clear to us how one could find a family of generalized eigenfunctions leading to a spectral representation of A.

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Design of Ultraspherical Window Functions with Prescribed Spectral Characteristics

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  • A small part of the absorbed light energy in the photosynthesis process is lost during the migration from the pigment antenna to the reaction centers and are dissipated by a number of non-photochemical processes, including heat, and re-emission of a small but easily detectable amount (2-5% in vivo) of the absorbed radiation. This re-emission occurs at longer wavelengths in the red and far-red spectral regions and is termed as Chlorophyll Fluorescence (ChlF) (Shreiber, 1983; Backer & Bradbury, 1981)....

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  • Previous work from this laboratory has shown that the spectral and functional properties of a prokaryotic xanthine dehydrogenase fromComamonas acidovoransshow some similarities to those of the well-characterized eukaryotic enzymes isolated from bovine milk and from chicken liver [Xiang, Q. & Edmondson, D.E. (1996) Biochemistry35, 5441–5450]. Therefore, this system was chosen to study the factors involved in the expression of functional recombinant enzyme in Escherichia colito provide insights into the assembly of the functional Mo-pyranopterin center....

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  • Study differences in experimental design, including choice of spectral bands, brain regions, brain states (activated or resting) and type of analysis, as well as small sample sizes, differences in sample age ranges, diversityofseverityofimpairment, lack of replication tests and disparity of results make difficult a meaningful summary of spectral coherence findings in ASD. Furthermore, few studies considered the reality of ASD group-specific EEG artifacts, including eye blink and muscle movement, and their potential spurious effects upon coherence.

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  • In this article we generalized some properties of Banach algebras, to a new class of topological algebras namely fundamental and fundamental locally multiplicative topological algebras (abbreviated by F LM ). Also the new notion of sub-multiplicatively metrizable topological algebra is given and some well known spectral properties of Banach algebras are generalized to such kind of algebras.

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  • In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl’s limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular.

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  • In this paper, we investigate the spectral properties of the maximal dissipative extension of the minimal symmetric differential operator generated by a second order differential expression and dissipative and eigenparameter dependent boundary conditions. For this purpose we use the characteristic function of the maximal dissipative operator and inverse operator.

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  • In this paper we consider the Sturm-Liouville equations on a finite interval which is fractional-linear in the spectral parameter. The inverse spectral problem consisting of the recovering of the operator from the two spectra is investigated and a uniqueness theorem for solution of the inverse problem is proved.

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  • The fundamental frequency of the electric cabinet is sensitive because of many attached devices. To bypass this complex problem, the average spectral acceleration ðSaÞ in the range of period that cover the first mode period is chosen as an intensity measure on the fragility function. The nonlinear time history analyses for cabinet are conducted using a suite of 40 ground motions. The obtained curves with different approaches are compared, and the variability of risk assessment is evaluated for restrained and anchored models.

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  • Tín hiệu năng lượng: – Energy spectral density (ESD): • Tín hiệu công suất: – Power spectral density (PSD): • Quá trình ngẫu nhiên: – Power spectral density (PSD): Facuty of Electronics & Telecommunications 31 .3. Một số khái niệm Nhiễu trong hệ thống truyền thông Nhiễu nhiệt n(t) được diễn tả bởi một quá trình ngẫu nhiên Gaussian có trị trung bình bằng 0. PSD của nhiễu nhiệt thì phẳng vì vậy gọi là nhiễu trắng. [w/Hz] Power spectral density Autocorrelation function Probability density function Facuty of Electronics & Telecommunications 32 .3.

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