For subspaces, X and Y , of the space, D, of all derivatives M(X, Y ) denotes the set of all g ∈ D such that fg ∈ Y for all f ∈ X. Subspaces of D are defined depending on a parameter p ∈ [0,∞]. In Section 6, M(X, D) is determined for each of these subspaces and in Section 7, M(X, Y ) is found for X and Y any of these subspaces. In Section 3, M(X, D) is determined for other spaces of functions o...

Today, half of the world’s population lives in urban areas. By 2050, 70 percent of the population will be urban. India has been witnessing massive urbanization. Over the six decades since independence, India’s population grew three-fold from 350 million in 1947 to 1027 million in the year in 2001. During the same period, the urban population grew almost 4.6 fold as fast – from 62.4 million to 2...

Changing the internal structure of a program without changing its behavior is called restructuring. This paper presents a transformation called tuck for restructuring programs by decomposing large functions into small functions. Tuck consists of three steps: Wedge, Split, and Fold. A wedge—a subset of statements in a slice—contains computations that are related and that may create a meaningful ...

The impact-parameter representation of the spin-flip amplitude of hadron elastic scattering is examined in different unitarisation schemes, taking the Born term of the spin-flip amplitude from the Dubna Dynamical Model (DDM). It is shown that the basic properties of the unitarisation schemes are independent of the functional form used for unitarisation but heavily depend on the asymptotic value...

<p style='text-indent:20px;'>For an integer <inline-formula><tex-math id="M1">\begin{document}$ r\ge0 $\end{document}</tex-math></inline-formula>, we prove the id="M2">\begin{document}$ r^{\mathrm{th}} $\end{document}</tex-math></inline-formula> order Reshetnyak formula for ray transform of rank id="M3">\begin{document}$ m symmetric tensor fields ...

Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.