Search results for "Trigonometri"
showing 10 items of 38 documents
A fast approximate method for the calculation of the infrared radiation balance within city street cavities
1983
The approximate calculation method for diffuse solar irradiances in street cavities presented in an earlier paper is extended to include infrared flux densities. By expanding the infrared sky radiance as a truncated trigonometric series, it becomes possible to solve the integrals representing the obstruction of the sky analytically. An example is worked out to demonstrate the numerically very efficient calculation procedure.
Ultrarelativistic (Cauchy) spectral problem in the infinite well
2016
We analyze spectral properties of the ultrarelativistic (Cauchy) operator $|\Delta |^{1/2}$, provided its action is constrained exclusively to the interior of the interval $[-1,1] \subset R$. To this end both analytic and numerical methods are employed. New high-accuracy spectral data are obtained. A direct analytic proof is given that trigonometric functions $\cos(n\pi x/2)$ and $\sin(n\pi x)$, for integer $n$ are {\it not} the eigenfunctions of $|\Delta |_D^{1/2}$, $D=(-1,1)$. This clearly demonstrates that the traditional Fourier multiplier representation of $|\Delta |^{1/2}$ becomes defective, while passing from $R$ to a bounded spatial domain $D\subset R$.
Geometric efficiency for a parallel-surface source and detector system with at least one axisymmetric surface
2007
Abstract An exact and numerically friendly method is given to calculate the geometric efficiency G of a planar radiation source and cosine detector system. Either the source or the detector, but not necessarily both, must have axial symmetry. For two non-coaxial disks the results are in exact agreement with a recent generalization of Ruby's formula for G. Detailed formulas and sample numerical results are given for a disk combined with rectangles and triangles. A disk and a general polygon can be solved by dividing the polygon into triangles. The method can also be applied to electrical inductance calculations and a solution recently given for the inductance of circular and elliptic loops c…
A geometrical constructive approach to infinitesimal analysis: epistemological potential and boundaries of tractional motion
2014
Recent foundational approaches to Infinitesimal Analysis are essentially algebraic or computational, whereas the first approaches to such problems were geometrical. From this perspective, we may recall the seventeenth-century investigations of the “inverse tangent problem.” Suggested solutions to this problem involved certain machines, intended as both theoretical and actual instruments, which could construct transcendental curves through so-called tractional motion. The main idea of this work is to further develop tractional motion to investigate if and how, at a very first analysis, these ideal machines (like the ancient straightedge and compass) can constitute the basis of a purely geome…
Shifting of wrapped phase maps in the frequency domain using a rational number
2016
The number of phase wraps in an image can be either reduced, or completely eliminated, by transforming the image into the frequency domain using a Fourier transform, and then shifting the spectrum towards the origin. After this, the spectrum is transformed back to the spatial domain using the inverse Fourier transform and finally the phase is extracted using the arctangent function. However, it is a common concern that the spectrum can be shifted only by an integer number, meaning that the phase wrap reduction is often not optimal. In this paper we propose an algorithm than enables the spectrum to be frequency shifted by a rational number. The principle of the proposed method is confirmed b…
A Novel Multidimensional Scaling Technique for Mapping Word-Of-Mouth Discussions
2009
The techniques which utilize Multidimensional Scaling (MDS) as a fundamental statistical tool have been well developed since the late 1970’s. In this paper we show how anMDS scheme can be enhanced by incorporating into it a Stochastic Point Location (SPL) strategy (one which optimizes the former’s gradient descent learning phase) and a new Stress function. The enhanced method, referred to as MDS SPL, has been used in conjunction with a combination of the TF-IDF and Cosine Similarities on a very noisy Word-Of-Mouth (WoM) discussion set consisting of postings concerning mobile phones, yielding extremely satisfying results.
Comparison of the P-integral with Burkill's integrals and some applications to trigonometric series
2023
It is proved that the $P_r$-integral [9] which recovers a function from its derivative defined in the space $L^r$, 1 ≤r<∞, is properly included in Burkill’s trigonometric CP-and SCP-integrals. As an application to harmonic analysis, a de La Vallée-Poussin-type theorem for the $P_r$-integral is obtained: convergence nearly everywhere of a trigonometric series to a $P_r$-integrable function f implies that this series is the Pr-Fourier series of f.
First-Order Calculus on Metric Measure Spaces
2020
In this chapter we develop a first-order differential structure on general metric measure spaces. First of all, the key notion of cotangent module is obtained by combining the Sobolev calculus (discussed in Chap. 2) with the theory of normed modules (described in Chap. 3). The elements of the cotangent module L2(T∗X), which are defined and studied in Sect. 4.1, provide a convenient abstraction of the concept of ‘1-form on a Riemannian manifold’.
Critical analysis of thermal inertia approaches for surface soil water content retrieval
2013
The “thermal inertia” method to retrieve surface soil water content maps on bare or sparsely-vegetated soils is analysed. The study area is a small experimental watershed, where optical and thermal images (in day and night time) and in situ data were simultaneously acquired. The sensitivity of thermal inertia to the phase difference between incoming radiation and soil temperature is demonstrated. Thus, to obtain an accurate value of the phase difference, the temporal distance between thermographs using a three-temperature approach is evaluated. We highlight when a cosine correction of the temperature needs to be applied, depending on whether the thermal inertia formulation includes two gene…
VizieR Online Data Catalog: 46 open clusters GaiaDR2 HR diagrams (Gaia Collaboration, 2018)
2018
We have determined the membership of 46 open clusters. For the nine clusters within 250pc we determined optimised parallaxes based on the combined information extracted from the measured parallax and proper motion values. These clusters are : in Tables A1a & A3: alphaPer, Blanco1, ComaBer, Hyades, IC2391, IC2602, NGC2451A, Pleiades, Praesepe. The remaining 37 clusters are in Table A1b & A4: Coll140, IC4651, IC4665, IC4725, IC4756, NGC0188, NGC0752, NGC0869, NGC0884, NGC1039, NGC1901, NGC2158, NGC2168, NGC2232, NGC2323, NGC2360, NGC2422, NGC2423, NGC2437, NGC2447, NGC2516, NGC2547, NGC2548, NGC2682, NGC3228, NGC3532, NGC6025, NGC6281, NGC6405, NGC6475, NGC6633, NGC6774, NGC6793, NGC7092, Sto…