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The main goal of this paper is to study the existence of solutions for several new classes of singular convolution integral equations containing the Cauchy operator in the normal type case. To investigate the solutions of such equations, we establish the Noethericity theory of solvability. By means of the properties of complex Fourier transforms, we transform these equations into Riemann boundary value problems with nodes. The analytic solutions and conditions of solvability are obtained via using Riemann–Hilbert approach. Moreover, we also discuss the asymptotic property of solutions near nodes. Thus, this paper generalizes the theories of complex analysis, functional analysis, integral equations and the classical Riemann boundary value problems. [ABSTRACT FROM AUTHOR]

Magnetic shape memory alloys Mn2NiGa1−xCux (x = 0–0.7) melt-spun ribbons were synthesized, and their crystal structure, martensitic transformation, and magnetic and transport properties were studied. In Mn2NiGa1−xCux, unusual composition dependences of these properties were observed: the lattice parameter increases with Cu-doping, though Cu has a smaller atomic radius compared with Ga. The martensitic transformation temperature decreases with increasing Cu content at first and reaches a minimum at x = 0.3 and then increases rapidly as Cu content increases further. The variation tendency of magnetization is just opposite. When Cu content gets higher, a semiconductor-like to metal-like crossover in electron transport properties is observed. The martensite resistivity also changes from lower than that of austenite to higher than that. First-principles calculations indicate that these unusual properties are related to the competing occupation of Cu between A and D sites. Cu-doping can also enhance the metallic bonding in Mn2NiGa1−xCux, which can reduce the intrinsic brittleness and improve their mechanical properties. All this provides a fresh idea and method for the development of NiMn-based solid-state refrigeration materials. [ABSTRACT FROM AUTHOR]