Search results for "Trigonometric functions"
showing 6 items of 16 documents
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.
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…
Frequency Regulation of Hybrid Power System by Optimized Adaptive Fuzzy PID Controller
2020
In this study, an adaptive fuzzy PID (AFPID) regulator has been proposed for frequency control of hybrid power system. For controller parameter optimization, an upgraded Whale Optimization Algorithm (WOA) has been employed. In the proposed Upgraded WOA (UWOA) technique, a cosine function is incorporated in the original WOA for determining control parameter to manage the position of whales throughout optimization procedure. Furthermore, scaling factors are employed in original WOA to adjust the travel of whales in search procedure. Proposed UWOA technique is employed to design an AFPID controller for frequency regulation of a hybrid power system It is demonstrated that UWOA technique out per…
Differential of metric valued Sobolev maps
2020
We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove that our notion is consistent with Kirchheim's metric differential when the source is a Euclidean space, and with the abstract differential provided by the first author when the target is $\mathbb{R}$.
Functional inequalities for generalized inverse trigonometric and hyperbolic functions
2014
Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse trigonometric and hyperbolic functions are given, as well as some Gr\"unbaum inequalities with the aid of the classical Bernoulli inequality. Moreover, by means of certain already derived bounds, bilateral bounding inequalities are obtained for the generalized hypergeometric ${}_3F_2$ Clausen function.