This paper is designed to introduce the reader to Gröbner bases as well as demonstrate how they may applied in developing algorithms that“solve” solvable polynomials. Specifically, I will use these bases along with some basic invariant theory in order to derive a general formula for the roots of a cubic polynomial with rational coefficients and describe how to compute the exact roots of a quint...

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We find a sufficient condition to establish that certain abelian groups are not CI-groups with respect to ternary relational structures, and then show that the groups Z3×Z2, Z7×Z2, and Z5 ×Z2 satisfy this condition. Then we completely determine which groups Z2 ×Zp, p a prime, are CI-groups with respect to color binary and ternary relational structures. Finally, we show that Z2 is not a CI-group...

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In this paper, we give an algorithm to list and classify generalized Hadamard matrices of a given order over an arbitrary elementary Abelian group. Generalized Hadamard matrices of order less than or equal to 16 over Abelian groups Z3; Z4, Z2 Z2 and Z5 have been classi…ed up to equivalence. We have shown that generalized Hadamard matrices of order 4; 8, and 12 over EA(4) are unique up to equiva...

We report the discovery of a compact group galaxies, CGG-z5, at z ∼ 5.2 in EGS field covered by JWST/CEERS survey. CGG-z5 was selected as highest overdensity galaxies > 2 recent JWST public surveys and it consists six candidate members lying within projected area 1.5″ × 3″ (10×20 kpc ). All are HST/F435W HST/F606W dropouts while securely detected JWST/NIRCam bands, yielding narrow range robu...

During acute hypertension, Na(+)/H(+) exchangers (NHE3) retract from top to base of proximal tubule microvilli (MV) and Na(+) reabsorption decreases in proximal tubule. This study aimed to determine whether the actin-based motor myosin VI coordinately retracts with NHE3 in response to acute hypertension. BP was raised approximately 50 mmHg in rats for 20 to 30 min or sham treated, and kidneys w...

This study aims to elucidate the change in pulmonary function in stage 0 COPD patients. A total of 48 stage 0 COPD patients and 46 healthy adults were included in the study. The status of their pulmonary function was determined by an impulse oscillometry (IOS) system, and the spirometric indexes such as forced vital capacity, maximum expiratory flow-volume (MEFV) curve, total respiratory impeda...

Seven isoforms of Broad-Complex (PhBR-C), in which the sequence of the zinc finger domain differed (referred to as Z1, Z2, Z3, Z2/Z3, Z4, Z5/Z6, and Z6, respectively), were cloned from the yellow-spotted longicorn beetle Psacothea hilaris. The Z1-Z4 sequences were highly conserved among insect species. The Z5/Z6 isoform was aberrant in that it contained a premature stop codon. Z6 had previously...

This is the first in a series of papers [Z3, Z4, Z5, Z6, Z7] on inverse spectral/resonance problems for analytic plane domains Ω. In this paper, we present a rigorous version of the Balian-Bloch trace formula [BB1, BB2]. It is an asymptotic formula for the trace TrRρ(k + iτ) of the regularized resolvent of the Dirichlet Laplacian of Ω as k → ∞ with τ > 0 held fixed. When the support of ρ̂ contai...