The history of Tuolumne County during the gold rush

Back in the foothills of the Sierra Nevada, in the heart of the Mother Lode, lies Tuolumne County, whose history is rich with memories of the days of forty-nine. It was in this country of yesterdays, during those frenzied days of gold, that men fought and toiled and died for that precious metal. Miners in search of this precious substance penetrated into its forests, prospected up and down its canyons, and climbed its steep and rugged mountains. Towns sprang up overnight and disappeared almost as quickly. The miners were forever moving on to richer diggings in search of the “El Dorado.” The gold rush days found Tuolumne a wild and rough country, with the most varied population of any country in the whole region. Yankees, Mexicans, Englishmen, “Sidney Ducks”, Frenchmen, Germans, Spaniards, Chinese, Negroes, Irishmen, and Chileans rubbed elbows and occasionally fists with each other. The region was full of gamblers, drunkards, fast women and lumps of gold. Before the great rush for gold, California was a quiet, peaceful, sparsely settled land. In 1842, the population was about 5,000, not including the Indians. There were about 4,000 native Californians, 90 Mexicans, 80 Spaniards, 80 Frenchmen, 360 Scotchment, Irishmen and Englishmen, 90 Germans, Italians, and Portuguese. There was little immigration, and by 1847 the population had increased to only 7,000 or 8,000. The pueblos of Monterey, San Jose and Yorba Buena were the principal centers of trade. San Diego, Los Angeles, Sonoma and New Helvetia (now Sacramento) also contained a small population. Then came the discovery of gold. It took a little while for the news to travel, and at first people thought the reports were exaggerated, but as more and more reports were carried back to the pueblos, the excitement increased. On the first of April, 1848, the California Star printed “We are happy to be able to say that California continues to be perfectly quiet…. For more than a year no disorders have occurred, -the native Californians are beginning to mingle with our people, and are gradually turning their attention to agriculture. No further difficulties are apprehended.” Little did the writer of this article dream what was to take place before very long. BY the end of May only about 300 men were in the gold fields. So rapidly did the gold-fever take hold, however, that by the tenth of June, the same newspaper was fearing that every town would be depopulated. It reported that “every seaport south to San Diego and every interior town is drained of human beings.” As yet, of course, the news had not had time to reach the Atlantic states, so the gold rush was purely local, and there were relatively few digging for gold. The Star estimated that there were “1,000 souls washing gold”, and that about $100,000 had been taken from the mines since the first of May from an area about 100 miles in length and 200 miles wide

The Bourgain-Tzafriri conjecture and concrete constructions of non-pavable projections

It is known that the Kadison-Singer Problem (KS) and the Paving Conjecture (PC) are equivalent to the Bourgain-Tzafriri Conjecture (BT). Also, it is known that (PC) fails for $2$-paving projections with constant diagonal $1/2$. But the proofs of this fact are existence proofs. We will use variations of the discrete Fourier Transform matrices to construct concrete examples of these projections and projections with constant diagonal $1/r$ which are not $r$-pavable in a very strong sense. In 1989, Bourgain and Tzafriri showed that the class of zero diagonal matrices with small entries (on the order of $\le 1/log^{1+\epsilon}n$, for an $n$-dimensional Hilbert space) are {\em pavable}. It has always been assumed that this result also holds for the BT-Conjecture - although no one formally checked it. We will show that this is not the case. We will show that if the BT-Conjecture is true for vectors with small coefficients (on the order of $\le C/\sqrt{n}$) then the BT-Conjecture is true and hence KS and PC are true

A 4.8 kbps code-excited linear predictive coder

A secure voice system STU-3 capable of providing end-to-end secure voice communications (1984) was developed. The terminal for the new system will be built around the standard LPC-10 voice processor algorithm. The performance of the present STU-3 processor is considered to be good, its response to nonspeech sounds such as whistles, coughs and impulse-like noises may not be completely acceptable. Speech in noisy environments also causes problems with the LPC-10 voice algorithm. In addition, there is always a demand for something better. It is hoped that LPC-10's 2.4 kbps voice performance will be complemented with a very high quality speech coder operating at a higher data rate. This new coder is one of a number of candidate algorithms being considered for an upgraded version of the STU-3 in late 1989. The problems of designing a code-excited linear predictive (CELP) coder to provide very high quality speech at a 4.8 kbps data rate that can be implemented on today's hardware are considered