The Rees product of posets

We determine how the flag f-vector of any graded poset changes under the Rees product with the chain, and more generally, any t-ary tree. As a corollary, the M\"obius function of the Rees product of any graded poset with the chain, and more generally, the t-ary tree, is exactly the same as the Rees product of its dual with the chain, respectively, t-ary chain. We then study enumerative and homological properties of the Rees product of the cubical lattice with the chain. We give a bijective proof that the M\"obius function of this poset can be expressed as n times a signed derangement number. From this we derive a new bijective proof of Jonsson's result that the M\"obius function of the Rees product of the Boolean algebra with the chain is given by a derangement number. Using poset homology techniques we find an explicit basis for the reduced homology and determine a representation for the reduced homology of the order complex of the Rees product of the cubical lattice with the chain over the symmetric group.Comment: 21 pages, 1 figur

Stabilized gas laser oscillators Final report, 24 Jun. 1964 - 21 Jun. 1966

Phase-locking scheme for frequency-stabilized gas laser oscillator

Nuclear Arms Treaties: Their National Security Impact on America

Abstract This paper attempts to historically analyze arms treaties and arms limitation agreements between the United States and Russia. The impact of limiting and reducing strategic nuclear weapons on both countries and the ability to prevent endless proliferation is discussed. Additionally, the lack of limiting and reduction agreements on China and on tactical nuclear weapons is analyzed into projections for what the future of arms agreements or races may look like. Lastly, the extending or allowing the New START agreement and its impact on U.S. national security is assessed

Recessions and Older Workers

With the economy sliding ever deeper into recession, questions arise about how older workers are faring and how their fate relative to younger workers compares to the past. The answer to these questions turns out to be a little complicated. Two forces are at work. On the one hand, labor force participation among older workers has been rising since the early 1990s, a reversal of the long-standing trend toward ever-earlier retirement. Participation rates among older workers have even continued to rise during both of the recessions in this decade – a dramatic change from previous experience. On the other hand, the edge that older workers used to have relative to younger workers when it comes to layoffs seems to have disappeared, so the rise in the unemployment rate for older workers in recessions now looks similar to that for younger workers. Of the two forces, the trend growth in labor force participation appears to dominate, which has helped keep the employment rate of older workers from falling during the current recession. This pattern contrasts sharply with the far more typical decline in employment rates for workers under age 55. This brief is organized as follows. The first section discusses the upward trend in the labor force participation of older men. The second section explores why older men may have lost some of their edge with regard to job security. The third section looks at how these two developments – the secular upward trend in labor force participation and the heightened vulnerability to layoffs relative to younger workers – have affected the employment rates of older men in this recession compared to earlier ones. The fourth section concludes.

Biotechnology and the Environment: A Regulatory Proposal

The human race now holds the ability to alter the hereditary characteristics of all life forms through the use of biotechnology. Although the benefits seem limitless, there is a great deal of uncertainty about the risks this technology poses to human health and the environment. In Canada, the biotechnology industry is largely unregulated. The authors explore the potential and associated risks, and propose some suggestions for its regulation

Southeast Asian Refugees in Western Massachusetts: Seen but Not Heard

The United States has a long and valued tradition of receiving people from other lands as a result of social and political turmoil. This policy has been reaffirmed frequently in the last quarter century with the arrival of refugees from such geographically diverse locations as Eastern Europe, Cuba, Southeast Asia, and Central America. Perhaps, Southeast Asians have experienced greater national and personal tragedy than any other group of refugees arriving in this country in recent memory. It is specifically this population and their resettlement and adjustment to life in Western Massachusetts which is the subject of this report. These issues are discussed in six separate sections. The introduction provides a general background for Southeast Asian refugee resettlement and the goals and methods of the IRNA project; Section II presents a brief outline of refugee resettlement at the national, state and local levels with more specific details on the geographic and demographic aspects of this population in Western Massachusetts. An assessment of refugee adjustment and needs is profiled in Section III followed by evaluations of these general issues from the perspective of service providers and community-level refugee resettlement organizations in Section IV. Policy and Program Implications and concluding remarks are provided in the final section

Comparison of Pressurized and Gravity Distribution Systems for Wastewater Treatment

Pressurized distribution of domestic wastewater over a sand filter surface achieves better treatment than gravity distribution. The pressurized distribution system caused the filter to better remove organics (BOD₅) and suspended solids. Pressurized distribution also caused the sand filter to achieve more complete nitrification than the filter having gravity distribution. Two slow sand filters 15.2 cm wide, 3.1 m long and 15.2 cm deep were built and loaded with domestic septic tank effluent for 250 days at a rate of 5.1 cm per day. Influent and effluent samples were collected and analyzed for five-day Biochemical Oxygen Demand (BOD₅), suspended solids, ammonia- nitrogen, and nitrate-nitrogen. One filter received septic tank effluent through a 10 cm nominal diameter PVC perforated pipe viaa distribution box dosed by a pump with gravity flow from the distribution box to the pipe. The other filter received water through a 2.5 cm nominal diameter PVC pipe having 0.4 cm diameter holes drilled 76.2 cm on center. The gravity distribution filter system achieved mean effluent values of 36.4 mg// BOD₅ , 19.8 mg// suspended solids, 37.6 mg// ammonia-nitrogen, and 46.6 mg// nitrate-nitrogen. The pressurized distribution system achieved 19.1 mg// BOD₅\u3e 12.2 mg// suspended solids, 25.3 mg// ammonia-nitrogen, and 64.03 mg// nitrate-nitrogen. Influent to the filters averaged 132.1 mg// , 90.3 mg//, 70.3 mg// , and 3.6 mg// BOD₅ , suspended solids, ammonia-nitrogen, and nitrate- nitrogen, respectively

Coherent imaging of extended objects

When used with coherent light, optical imaging systems, even diffraction-limited, are inherently unable to reproduce both the amplitude and the phase of a two-dimensional field distribution because their impulse response function varies slowly from point to point (a property known as non-isoplanatism). For sufficiently small objects, this usually results in a phase distortion and has no impact on the measured intensity. Here, we show that the intensity distribution can also be dramatically distorted when objects of large extension or of special shapes are imaged. We illustrate the problem using two simple examples: the pinhole camera and the aberration-free thin lens. The effects predicted by our theorical analysis are also confirmed by experimental observations.Comment: 10 pages, 9 figures, submitted to Optics Communication

Control and Manipulation of Cold Atoms in Optical Tweezers

Neutral atoms trapped by laser light are amongst the most promising candidates for storing and processing information in a quantum computer or simulator. The application certainly calls for a scalable and flexible scheme for addressing and manipulating the atoms. We have now made this a reality by implementing a fast and versatile method to dynamically control the position of neutral atoms trapped in optical tweezers. The tweezers result from a spatial light modulator (SLM) controlling and shaping a large number of optical dipole-force traps. Trapped atoms adapt to any change in the potential landscape, such that one can re-arrange and randomly access individual sites within atom-trap arrays.Comment: 6 pages, 4 figure

The Rees product of the cubical lattice with the chain

We study enumerative and homological properties of the Rees product of the cubical lattice with the chain. We give several explicit formulas for the Möbius function. The last formula is expressed in terms of the permanent of a matrix and is given by a bijective proof