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Hsia, Hower J.

doi:10.1111/j.1460-2466.1968.tb00084.x

Cited by 2 publications

(3 citation statements)

References 17 publications

(11 reference statements)

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“…The similarity to Watson transformations [16] also becomes apparent, although a Watson transformation is a well-defined mapping on equivalence classes of forms, and a Watson transformation does not send a form with some odd prime p ∆ to a form with ∆ = 0 (mod p). The closest parallel we know involving a Watson transformation is the descent of a form (probably regular) with ∆ = 2592 = 32 · 81 to one with ∆ = 32 that is regular, in that λ 9 ( 5,9,17,6,5, 3 ) = 1, 3, 3, 1, 0, 1 .…”

Section: Tornaria's Constructionsmentioning

confidence: 99%

“…By Theorem 3.2, we know that g 1 corresponds with at least one of the three forms in the genus of f 0 . However, if 1,4,9,4, 0, 0 should represent n 2 g 1 , it would follow that 1, 4, 9, 4, 0, 0 represented the integer n 2 p 2 2 , which is of the form 2m 2 . It follows that g 0 represents either n 2 · 1, 1, 32, 0, 0, 0 or n 2 · 2, 2, 9, 2, 2, 0 .…”

Section: Proofmentioning

confidence: 99%

“…J. S. Hsia [9] confirmed for the author that, for both odd and even squarefree n = u 2 + v 2 , the genus of 1, 1, 16n, 0, 0, 0 has exactly two spinor genera, and that n itself is a spinor exceptional integer (a number not represented by one of the spinor genera). He mentioned that the methods were in [7].…”

Section: Introductionmentioning

confidence: 95%

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Integral Positive Ternary Quadratic Forms

Jagy

2013

Quadratic and Higher Degree Forms

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We discuss some families of integral positive ternary quadratic forms. Our main example is f (x, y, z) = x 2 + y 2 + 16nz 2 , where n is positive, squarefree, and n = u 2 + v 2 with u, v ∈ Z. NotationAs in [4], [13], and section 7 of [15], we let the integer sextuple a, b, c, r, s, t refer to the quadratic form f (x, y, z) = ax 2 + by 2 + cz 2 + ryz + szx + txy.The Gram matrix for the form is the matrix of second partial derivatives:So our Gram matrix is symmetric, positive definite, and has integer entries. We define our discriminant ∆ as half the determinant of the matrix above, so ∆ = 4abc + rst − ar 2 − bs 2 − ct 2 .All our forms are positive and primitive ( gcd(a, b, c, r, s, t) = 1). Note that we do allow some of r, s, t to be odd at times. When r, s, t are all even, we refer to the form as classically integral.0 ADDRESS: Math.Sci.Res.Inst.,

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Section: Tornaria's Constructionsmentioning

confidence: 99%

Section: Proofmentioning

confidence: 99%

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Integral Positive Ternary Quadratic Forms

Jagy

2013

Quadratic and Higher Degree Forms

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Multiple Resource Theory I

Basil¹

1994

Communication Research

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Comprehending television is a complex process. Multiple resource theory proposes that the necessary resources are limited. Limitations, however, depend on four separate factors. First, resources are used by three different tasks—attention, meaning-level processing, and memory. Demands arise from individual tasks and combinations. The consequences of reaching limitations are different for each task. Second, television's auditory and visual modalities use different symbol systems. Audio information might be more difficult to process and requires more resources. Third, television stimuli might contain the meaningful information in either the auditory or visual modality. Meaningful information might require more processing and resources and should result in resource shifts. Fourth, television programs use varying levels of redundancy. Whereas processing two modalities generally requires additional resources, actual demands depend on the level and nature of the redundancy. As a result of these four factors, resource limitations can inhibit one process, modality, or attribute. Systematic study of these outcomes is necessary.

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Rejoinder

Cited by 2 publications

References 17 publications

Integral Positive Ternary Quadratic Forms

Integral Positive Ternary Quadratic Forms

Multiple Resource Theory I

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