On indecomposable normal matrices in spaces with indefinite scalar product

Finite dimensional linear spaces (both complex and real) with indefinite scalar product [.,.] are considered. Upper and lower bounds are given for the size of an indecomposable matrix that is normal with respect to this scalar product in terms of specific functions of v = min{v-, v+}, where v-, (v+) is the number of negative (positive) squares of the form [x,x]. All the bounds except for one are proved to be strict.Comment: 9 page

Now Hear This! Orientation and Behavioral Responses of Hatchling Loggerhead Sea Turtles, Caretta caretta, to Environmental Acoustic Cues

Although the visual and geologic orientation cues utilized by sea turtle hatchlings during seafinding, when they move from the nest to the sea after hatching, have been well studied, the potential for auditory stimuli to act as an orientation cue has not been well explored. Over the past several decades our knowledge of the auditory capacity of sea turtles has increased greatly, yet little is known about the biological significance of this sensory ability. To investigate whether hatchlings can use ocean sounds during seafinding, we measured the behavioral responses of hatchling loggerhead sea turtles (Caretta caretta) collected from nesting beaches in North Carolina to the presence of beach wave sound recorded on a nesting beach during the summer of 2015. The highest sound energy of beach waves occursHz, which overlaps with the most sensitive hearing range of loggerhead hatchlings (range of frequency detection: 50-1600 Hz, maximum sensitivity: 50-400 Hz). In our experiment, we placed turtles in a V-maze that isolated them from visual, vibratory, and chemical cues. One end of the V held a speaker producing beach wave sounds recorded from nesting beaches, while the other end held sound-reducing foam. We examined the phonotaxic behaviors of the hatchlings at two sound pressure levels (68 dB re: 20μPa and 64 dB re: 20μPa measured directly in front of the speaker). In the presence of the higher sound pressure level (68 dB re: 20μPa), hatchlings exhibited no phonotaxic response (p=1.0); yet, at the reduced sound pressure level (64 dB re: 20μPa), hatchlings exhibited a negative phonotaxic response (p=0.005). In control trials, hatchlings oriented to the two sides of the V-maze equally (p=0.701), suggesting the hatchlings in the lower volume treatment group were responding negatively to the sound. These results indicate the need for further auditory orientation experiments to better understand hatchling behavioral responses to environmental acoustic cues and to address possible impacts of anthropogenic beach sounds that have the potential to disorient hatchlings during seafinding

M-matrices satisfy Newton's inequalities

Newton's inequalities $c_n^2 \ge c_{n-1}c_{n+1}$ are shown to hold for the normalized coefficients $c_n$ of the characteristic polynomial of any $M$- or inverse $M$-matrix. They are derived by establishing first an auxiliary set of inequalities also valid for both of these classes. They are also used to derive some new necessary conditions on the eigenvalues of nonnegative matrices.Comment: 6 page

The technology utilization process - An overview

Technology utilization process, and NASA programs for transferring technology and disseminating information on product developmen