Regularly spaced subsums of integer partitions

For integer partitions $\lambda :n=a_1+...+a_k$, where $a_1\ge a_2\ge >...\ge a_k\ge 1$, we study the sum $a_1+a_3+...$ of the parts of odd index. We show that the average of this sum, over all partitions $\lambda$ of $n$, is of the form $n/2+(\sqrt{6}/(8\pi))\sqrt{n}\log{n}+c_{2,1}\sqrt{n}+O(\log{n}).$ More generally, we study the sum $a_i+a_{m+i}+a_{2m+i}+...$ of the parts whose indices lie in a given arithmetic progression and we show that the average of this sum, over all partitions of $n$, is of the form $n/m+b_{m,i}\sqrt{n}\log{n}+c_{m,i}\sqrt{n}+O(\log{n})$, with explicitly given constants $b_{m,i},c_{m,i}$. Interestingly, for $m$ odd and $i=(m+1)/2$ we have $b_{m,i}=0$, so in this case the error term is of lower order. The methods used involve asymptotic formulas for the behavior of Lambert series and the Zeta function of Hurwitz. We also show that if $f(n,j)$ is the number of partitions of $n$ the sum of whose parts of even index is $j$, then for every $n$, $f(n,j)$ agrees with a certain universal sequence, Sloane's sequence \texttt{#A000712}, for $j\le n/3$ but not for any larger $j$

Studies of the life histories of grass feeding Jassidae

In various papers published in these Bulletins during the past five years attention has been called to the injuries caused in grass land and pastures by the numerous species of Jassidae which swarm, often by millions to the acre, upon various species of grass. In these papers it has been shown that the loss, though seldom noticed, must be really enormous and that by the use of the tar-pan or “hopper-dozer” the insects may be to a great extent destroyed. Further than this, however, our knowledge has been too meager to furnish a certain basis for remedial measures. It is true studies were made of a few species and some facts learned as to their life-history which warranted the belief that burning, mowing or other methods more satisfactory than the tar-pan might be of service but still so much remained unknown regarding the most common species that there seemed a necessity for a more extensive study. At the beginning of the present season a study was planned, the essential features of which were: 1st, the determination of the life histories of as many as possible of the species known to feed upon grasses; 2nd, the determination of the range of food plants for each species especially in the larval stages and 3rd, the collection of all species occurring on grasses and their careful identification with a close study of the specific limits of each as a basis for further life-history studies

Information sciences experiment system

The rapid expansion of remote sensing capability over the last two decades will take another major leap forward with the advent of the Earth Observing System (Eos). An approach is presented that will permit experiments and demonstrations in onboard information extraction. The approach is a non-intrusive, eavesdropping mode in which a small amount of spacecraft real estate is allocated to an onboard computation resource. How such an approach allows the evaluation of advanced technology in the space environment, advanced techniques in information extraction for both Earth science and information science studies, direct to user data products, and real-time response to events, all without affecting other on-board instrumentation is discussed

A New Design of Flicker Photometer for Laboratory Colored Light Photometry

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Contributions to the Hemipterous Fauna of Iowa

In various papers published during the past five years the senior author has called attention to the injuries caused in grass lands and pastures by the numerous species of Jassidae, which swarm, often by millions to the acre, upon various species of grasses

Signal processing in local neuronal circuits based on activity-dependent noise and competition

We study the characteristics of weak signal detection by a recurrent neuronal network with plastic synaptic coupling. It is shown that in the presence of an asynchronous component in synaptic transmission, the network acquires selectivity with respect to the frequency of weak periodic stimuli. For non-periodic frequency-modulated stimuli, the response is quantified by the mutual information between input (signal) and output (network's activity), and is optimized by synaptic depression. Introducing correlations in signal structure resulted in the decrease of input-output mutual information. Our results suggest that in neural systems with plastic connectivity, information is not merely carried passively by the signal; rather, the information content of the signal itself might determine the mode of its processing by a local neuronal circuit.Comment: 15 pages, 4 pages, in press for "Chaos

Cycling of dissolved organic phosphorus compounds in natural waters

U.S. Department of the InteriorU.S. Geological SurveyOpe

Head-on collision of ultrarelativistic charges

We consider the head-on collision of two opposite-charged point particles moving at the speed of light. Starting from the field of a single charge we derive in a first step the field generated by uniformly accelerated charge in the limit of infinite acceleration. From this we then calculate explicitly the burst of radiation emitted from the head-on collision of two charges and discuss its distributional structure. The motivation for our investigation comes from the corresponding gravitational situation where the head-on collision of two ultrarelativistic particles (black holes) has recently aroused renewed interest.Comment: 4 figures, uses the AMSmat