On Waring's problem: two squares and three biquadrates

We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam Conjecture, we show that all large natural numbers n with 8 not dividing n, n not congruent to 2 modulo 3, and n not congruent to 14 modulo 16, are the sum of 2 squares and 3 biquadrates.Comment: to appear in Mathematik

A land mobile satellite data system

The Telesat Mobile Incorporated (TMI) Mobile Data System (MDS) was developed to apply satellite technology to the transportation industry's requirement for a fleet management system. It will provide two-way messaging and automatic position reporting capabilities between dispatch centers and customers' fleets of trucks. The design was based on the Inmarsat L-Band space segment with system link parameters and margins adjusted to meet the land mobile satellite channel characteristics. The system interfaces with the Teleglobe Des Laurentides earth station at Weir, Quebec. The signaling protocols were derived from the Inmarsat Standard C packet signalling system with unique trucking requirements incorporated where necessary

Plethodon petraeus

Number of Pages: 2Integrative BiologyGeological Science

M2 growth in 1995: a return to normalcy?

A discussion of M2's demise as a reliable indicator of financial conditions in the economy, and a look at recent evidence suggesting that even though the aggregate has been behaving more normally over the past year or so, it is unlikely to regain its status as a key policy guide any time soon.Economic indicators ; Money supply

Hearing and Echolocation in the Australian Grey Swiftlet, Collocalia Spodiopygia

The frequency sensitivity of hearing in the grey swiftlet, Collocalia spodiopygia, was determined by neuronal recordings from the auditory midbrain (MLD). The most sensitive best frequency response thresholds occurred between 0.8 and 4.7 kHz, with the upper frequency limit near 6 kHz. Spectral analysis of echolocation click pairs revealed energy peaks between 3.0 and 8.0kHz for the foreclick, compared to 4.0-6.0 kHz for the principal click. The relationship between good hearing sensitivity and click energy peaks in the swiftlet extends about an octave higher than it does in the oilbird (Steatornis caripensis)

The Distributional Impact of Social Security

In the first part of the paper we report estimated transfers in the Social Security system for the Retirement History Survey sample.We define transfers to be the difference between the expected presentvalue of benefits less the present value of taxes paid in, where the latter is adjusted for the probability of living to reach retirement age.Unlike previous researchers we, therefore, account for the taxes paid by people who died before retirement, and it turns out this adjustment is important for some groups. The Retirement History Survey cohort will receive large transfers: roughly benefits will be about four times taxes,and the real internal rate of return will be about eight percent. We study how transfers vary by a comprehensive measure of wealth. People in the highest wealth quartile have the largest absolute transfers, and their internal rate of return is as high as that of any wealth quartile.In the second part of the paper we study transfers forsix synthetic cohorts, the heads of which are age 65 in the ten-year intervals 1970 through 2020. Within each cohort 12 families are defined according to earnings levels.We find that transfers are positive and large for the 1970 cohort, and that they decline steadily until they are negative for most groups in the 2020 cohort. Although high earners initially have the largest transfers in the 1970 cohort, they have the largest negative transfers in the 2020 cohort.

Financial Structure: An International Persepective

macroeconomics, financial structure