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Through this introductory paper we announce to the worldwide mathematics community a new type of integral transform, which we call the Upadhyaya Integral Transform or, the Upadhyaya transform (UT), in short. The new transform whic...
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Through this introductory paper we announce to the worldwide mathematics community a new type of integral transform, which we call the Upadhyaya Integral Transform or, the Upadhyaya transform (UT), in short. The new transform which we propose to proclaim through this paper, is, in fact a generalized form of the celebrated Laplace transform. The power of this generalization is that this most general form of the Laplace transform generalizes and unifies, besides the classical Laplace transform and the Laplace-Carson transform, most of the very recently introduced integral transforms of this category like, the Sumudu transform, the Elzaki transform, the Kashuri and Fundo transform, the Mahgoub transform, the ZZtransform,the Sadik transform, the Kamal transform, the Natural transform, the Mohand transform, the Aboodh transform, the Ramadan Group transform, the Shehu transform, the Sawi transform, the Tarig transform, the Yang transform, etc. We develop the general theory of the Upadhyaya transform in a way which exactly parallels the existing theory of the classical Laplace transform and also provide a number of possible generalizations of this transform and thus we prepare a firm ground for future researches in this field by employing this most generalized, versatile and robust form of the classical Laplace transform - the Upadhyaya transform - in almost all the areas wherever, the classical Laplace transform and its various aforementioned variants are currently being employed for solving the vast multitude of problems arising in the areas of applied mathematics, mathematical physics and engineering sciences and other possible fields of study inside and outside the realm of mathematics.
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An essential generalization of the Lebedev index transform with the square of the Macdonald function is investigated. Namely, we consider a family of integral operators with the positive kernel vertical bar K(ir+alpha)/2(x)vertica...
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An essential generalization of the Lebedev index transform with the square of the Macdonald function is investigated. Namely, we consider a family of integral operators with the positive kernel vertical bar K(ir+alpha)/2(x)vertical bar(2), alpha is an element of R, x > 0, T E R, where K-mu(z) is the Macdonald function and i is the imaginary unit. Mapping properties such as the boundedness, compactness, invertibility are investigated for these operators and their adjoints in weighted L-p spaces. Inversion theorems are proved. Important particular cases are exhibited. As an interesting application, a solution of the initial value problem for the second order differential difference equation, involving the Laplacian, is obtained. (C) 2015 Elsevier Inc. All rights reserved.
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We present the theory and design of an adaptive lapped biorthogonal transform for image coding the proposed transform consists of basis functions overlapping across adjacent blocks and non-overlapping basis functions, where the ba...
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We present the theory and design of an adaptive lapped biorthogonal transform for image coding the proposed transform consists of basis functions overlapping across adjacent blocks and non-overlapping basis functions, where the basis functions' centers of symmetry are aligned. Because of the alignment, we can use the symmetric extension method at image boundaries when we transform an input image. Next, we show that the optimal non-overlapping basis functions in the minimal mean square error sense can be found by solving an eigenvalue problem without numerical search when the feasible overlapping basis functions are given.
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Image processing covers a wide range of processing techniques. Image Fusion is one of those technique which plays a vital role with medical images since different imaging methods provide different set of clinical information for d...
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Image processing covers a wide range of processing techniques. Image Fusion is one of those technique which plays a vital role with medical images since different imaging methods provide different set of clinical information for diagnosis. Advances in technology provide us with plenty of imaging modalities. Image fusion is essential for a joint analysis of these multimodality images since each of these modalities provide unique and complementary characterization of the underlying anatomy and tissue microstructure. This paper analyzes the image fusion methods based on multiscale transforms and implements using wavelet, contourlet, curvelet, and shearlet transform. The results are compared.
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Despite growing interest in transformative tourism and its benefits, there is not yet a precise understanding of tourist transformation. This study contributes to fill this research gap by reviewing the contexts where transformati...
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Despite growing interest in transformative tourism and its benefits, there is not yet a precise understanding of tourist transformation. This study contributes to fill this research gap by reviewing the contexts where transformative tourism research has emerged, and the main theories employed. Through a mull-disciplinary approach, the paper discusses key dimensions of transformative tourism experiences. The discussion suggests that liminality, cultural shock and challenges faced at the destination initiate transformation by provoking peak episodes, dilemmas and new performances. Contextual stimuli can lead tourists to reflectively interpret the experience and acquire skills, values and knowledge, with consequences on attitude, habits, and behaviour. A tourist transformation model is created, which provides a conceptual foundation for future research, and is relevant for designing and marketing transformative tourism experiences.
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Seven-parameter conformal coordinate transformations, also known as Helmert transformations, can be constructed in more than one way. Two possible orderings of the rotations are in common use, giving rise to Helmert versions 1 and...
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Seven-parameter conformal coordinate transformations, also known as Helmert transformations, can be constructed in more than one way. Two possible orderings of the rotations are in common use, giving rise to Helmert versions 1 and 2. It is demonstrated how the rotation parameters of either version can be converted into the rotation parameters of the other. This is useful when software is designed for the other version. It also enables computation of the same-formula inverse transformation by changing the sign of the equivalent 'other version' parameters. These results were primarily intended for conformal transformations between geodetic datums. They can, however, be extended to coordinate transformations in disciplines such as photogrammetry where rotations sometimes exceed 90 degrees.
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Unit transformer is usually connected directly to synchronous generator. Transformer windings are subject to all perturbations, coming from both generator and power grid. The paper lists different types of possible perturbations a...
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Unit transformer is usually connected directly to synchronous generator. Transformer windings are subject to all perturbations, coming from both generator and power grid. The paper lists different types of possible perturbations and presents example of unit transformer failure which occurred in one of thermal power stations.
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The integral transforms have many mathematical and physical applications; their uses are still predominant in advanced study and research. In present paper, we obtained several integral transforms viz. Fourier transform, Hankel tr...
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The integral transforms have many mathematical and physical applications; their uses are still predominant in advanced study and research. In present paper, we obtained several integral transforms viz. Fourier transform, Hankel transform, Hermite transfor
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Based on the form-invariance of Maxwell's equations under coordinate transformations, mathematically smooth deformation of space can be physically equivalent to inhomogeneous and anisotropic electromagnetic (EM) medium (called a t...
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Based on the form-invariance of Maxwell's equations under coordinate transformations, mathematically smooth deformation of space can be physically equivalent to inhomogeneous and anisotropic electromagnetic (EM) medium (called a transformation medium). It provides a geometric recipe to control EM waves at will. A series of examples of achieving transformation media by artificially structured units from conventional materials is summarized here. Such concepts are firstly implemented for EM waves, and then extended to other wave dynamics, such as elastic waves, acoustic waves, surface water waves, and even stationary fields. These shall be cataloged as transformation metamaterials. In addition, it might be conceptually attractive and practically useful to control diverse waves for multi-physics designs.
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