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Global burden and trends in ovarian cancer attributable to environmental risks and occupational risks in females aged 20-49 from 1990 to 2021, with projections to 2050: a cross-sectional study. [PDF]
BMC Public HealthZhang R +6 more
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Physics informed neural networks for fluid flow analysis with repetitive parameter initialization. [PDF]
Sci RepLee J +7 more
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Optimizing genomic prediction for complex traits via investigating multiple factors in switchgrass. [PDF]
Plant PhysiolWang P +5 more
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Enhancing energy predictions in multi-atom systems with multiscale topological learning.
J Mater Chem A MaterChen D, Wang R, Wei GW, Pan F.
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Complex Modular Numbers: Complex Numbers Need not be Complex
The Mathematics Teacher, 1976Most students are faced with the task of solving the equation x2 + 1 = 0 over the real numbers at some time in their algebra classes. After they substitute values for x unsuccessfully, they usually attempt to solve the equivalent equation x2 = -1. They soon realize that it is impossible to square a real number and obtain a negative number.
Susan J. Grant, Ward R. Stewart
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Concurrency: Practice and Experience, 1999
Efficient and elegant complex numbers are one of the preconditions for the use of Java in scientific computing. This paper introduces a preprocessor and its translation rules that map a new basic type complex and its operations to pure Java. For the mapping is insufficient to just replace one complex-variable with two double-variables.
Michael Philippsen, Edwin Günthner
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Efficient and elegant complex numbers are one of the preconditions for the use of Java in scientific computing. This paper introduces a preprocessor and its translation rules that map a new basic type complex and its operations to pure Java. For the mapping is insufficient to just replace one complex-variable with two double-variables.
Michael Philippsen, Edwin Günthner
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1973
Publisher Summary This chapter provides an overview on complex numbers. Each complex number α = a + bi is completely determined by the ordered pair (a, b) of real numbers where a the real part of α and b the imaginary part of α. For each complex number α = a + bi, the complex conjugate α is defined by α = a − bi = a + (−b)i. The conjugate of a − bi is
Harley Flanders, Justin J. Price
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Publisher Summary This chapter provides an overview on complex numbers. Each complex number α = a + bi is completely determined by the ordered pair (a, b) of real numbers where a the real part of α and b the imaginary part of α. For each complex number α = a + bi, the complex conjugate α is defined by α = a − bi = a + (−b)i. The conjugate of a − bi is
Harley Flanders, Justin J. Price
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, 2017 The motivation for this chapter concerns the solvability of equations of degree larger than one which is only partly possible in the domain of real numbers. For example, no negative real number has a real square root. By postulating that the number -1 obtains a square root, we are led to the field of complex numbers.
Jürg Kramer, Anna-Maria von Pippich
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