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viAcknowledgments, vAppendices, 51AppendixTable of Minimum Weights, 52Bibliography, 56Dedication, iv

In concert hall acoustics, the reflection characteristics of the ceiling and the walls are important for minimizing the interaural cross correlation. Many design methods have been presented so far in order to design highly diffusing surfaces. This paper presents a two-dimensional digital waveguide mesh having a highly diffusing boundary using quadratic residue sequences, and illustrates its ref...

Simultaneous visualization of tissue and surgical instruments is necessary during ultrasound-guided medical procedures. Standard minimally invasive instruments are typically metallic and act as strong specular scatterers. As a result, such instruments saturate the image or disappear according to the angle of incidence, obscuring nearby tissue and making it difficult to determine the instrument'...

<span>This paper shows electromagnetic field uniformity in an compatibility (EMC) chamber that is used as a test facility for measuring interference and radiated immunity of 6G communication systems. While not defined yet, radio frequency will work the wavelength ranges above 95 GHz. With this reason, designed schroeder-type quadratic residue diffuser GHz to generate uniform EMC studied c...

Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.

Let A„{a, b) = {ban+(a-l)/b)2+4an with n > 1 and ¿>|a-l . If W is a finite set of primes such that for each n > 1 there exists some q £W for which the Legendre symbol {A„{a, b)/q) ^ -1 , we call <£ a quadratic residue cover (QRC) for the quadratic fields K„{a, b) = Q{^jA„{a, b)). It is shown how the existence of a QRC for any a, b can be used to determine lower bounds on the class number of K„{...

Plots of quadratic residues display some visual features that are analyzed mathematically in this paper. The graphical patterns of quadratic residues modulo m depend only on the residues of m modulo the lowest positive integers.

The projective special linear group PSL2(n) is 2-transitive for all primes n and 3-homogeneous for n≡ 3 (mod 4) on the set {0,1, · · · ,n−1,∞}. It is known that the extended odd-like quadratic residue codes are invariant under PSL2(n). Hence, the extended quadratic residue codes hold an infinite family of 2-designs for primes n≡ 1 (mod 4), an infinite family of 3-designs for primes n≡ 3 (mod 4)...

(here b and a run over the quadratic nonresidues and quadratic residues, respectively, that lie between 0 and p) is a unit of the real quadratic field R(y/p), and that 77> 1. The fact that -n > 1 is usually deduced from the theory of the classnumber of quadratic fields. We present a short proof independent of the theory of the class-number. As in the paper of Chowla and Mordell [Note on the non...