This paper is divided into two parts. The first part
traces (in details providing proofs and examples) the
history of the solutions of polynomial equations(of the
first, second, third, and fourth degree) by radicals from
Babylonian times (2000 B.C.) through 20th century. Also it
is shown that there is no...
Stable isotope analysis of human tissue can provide information about diet independent of artifactual remains. Food is broken down and used in the synthesis of body tissue, so the isotopic composition of hair keratin reflects the isotopic composition of foods consumed. Therefore, the analysis of hair can provide a window...
Directional wave spectra have been estimated in this study based
upon simultaneous subsurface measurements of current and pressure.
Two previously developed methods, the stochastic and deterministic
approaches, have been reviewed and restudied. It is demonstrated by
means of the Correlation Theorem that the stochastic and deterministic
approaches are, under certain...
Quantitative habitat models of wildlife-habitat relationships are developed to
formalize our current understanding about an ecological system. A habitat
association model is one of these models that is useful for answering questions
about how the habitat is occupied, how much growth habitat is required by the
animal, or how the...
A new second order accurate nonuniform grid spacing technique which does not
depend on supraconvergence is developed for Finite Difference Time Domain (FDTD)
simulation of general three dimensional structures. The technique is useful for FDTD
simulations of systems which require finer details in small regions of the simulation space by...
Modular arithmetic operations (i.e., inversion, multiplication and exponentiation) are used in several cryptography applications, such as decipherment operation of RSA algorithm, Diffie-Hellman key exchange algorithm, elliptic curve cryptography, and the Digital Signature Standard including the Elliptic Curve Digital Signature Algorithm. The most important of these arithmetic operations is the modular...
Modular Multiplication is a time-consuming arithmetic operation because it involves multiplication as well as division. Modular exponentiation can be performed as a sequence of modular multiplications. Speeding the modular multiplication increases the speed of modular exponentiation. Modular exponentiation and modular multiplication are heavily used in current cryptographic systems. Well-known cryptographic...