Embeddings in the Strong Reducibilities Between 1 and npm

We consider the strongest (most restricted) forms of enumeration reducibility, those that occur between 1- and npm-reducibility inclusive. By defining two new reducibilities (which we call n1- and ni-reducibility) which are counterparts to 1- and i-reducibility, respectively, in the same way that nm- and npm-reducibility are counterparts to m- and pm-reducibility, respectively, we bring out the structure (under the natural relation on reducibilities strong with respect to') of the strong reducibilities. By further restricting n1- and nm-reducibility we are able to define infinite families of reducibilities which isomorphically embed the r. e. Turing degrees. Thus the many well-known results in the theory of the r. e. Turing degrees have counterparts in the theory of strong reducibilities. We are also able to positively answer the question of whether there exist distinct reducibilities ≤_y and ≤_a between ≤_e and ≤_m such that there exists a non-trivial ≤_y-contiguous ≤_z degree.     

Transverse mode frequency pulling in free electron lasers

We consider the spectral evolution of transverse modes in free electron lasers. While the gain maxima of the various transverse modes occur at different frequencies, coupling between the modes via the electron beam causes the modes to shift frequency such that the final laser frequency differs from what one would expect if only the TEM₀₀ mode were present. This can strongly effect the turn-on behavior in lasers with short electron pulses.     

Transient Transformation of Whispering Gallery Resonator Modes Due to Time Variations in Dielectric Permittivity

This paper considers the switching effects on whispering gallery modes in circular dielectric resonators when their material is subject to abrupt time changes in permittivity. Both the transient response and the new steady-state regime are described in detail by means of an analytical approach.     

Dynamic lot-sizing with setup cost reduction

One of the fundamental tenets of the Just-in-Time (JIT) manufacturing philosophy is that reduction or even elimination of inventory conserves valuable resources and reduces wasteful spending. In many cases, to achieve inventory reductions requires investment in reduction of setup costs. For this reason, certain proposals for incorporating means for reducing setup costs into classical production-inventory models have been offered in recent years. This article considers a dynamic lot-sizing model M where the values of the setup costs can be reduced by various amounts depending upon the level of funds R committed to this reduction. We show that for each fixed value of R, the model can be represented as a shortest path problem. By minimizing the optimal value function V(R) of the shortest path problem over R, model M can, in theory, be solved. In practice, the viability of this approach depends crucially upon the properties of the function V. Since these properties depend upon the nature of the setup cost function K used in model M, we analyze how V varies as K varies. This allows us to propose two exact, finite algorithms for solving model M, one for the case when K is a concave function, the other for the case when K is convex. Computational results for the convex case are presented. The problems solved demonstrate that, in practice, setup cost reductions chosen according to model M have the potential to significantly reduce both inventory levels and total costs.     

The synthesis and liquid crystal properties of some 4-n-nonylphenyl esters of 3-(4'-n-alkoxybiphenylyl)- and 3-(4'-n-alkoxybiphenylyl)-3-methyl-propanoic acids and their laterally fluorinated analogues

A number of 4-n-nonylphenyl esters and mono- and di-fluorinated 4-n-nonylphenyl esters derived from 3-(4'-n-alkoxybiphenylyl)propanoic acids (II) have been synthesized and their thermotropic liquid crystal properties assessed with a view to obtaining tilted smectic phases for possible use in ferroelectric display devices. Many of these compounds exhibit wide temperature range S_C and S_I/F phases, but none gave the ideal phase sequence S_C-S_A-N-I mainly because the structure of these compounds was not conducive to the formation of the nematic phase. To try to alleviate this problem a series of 4-n-nonylphenyl esters based on 3-(4'-n-alkoxybiphenylyl)-3-methylpropanoic acid was prepared, where a lateral methyl group was incorporated in the β-position of the -CH₂CH₂CO₂- linkage. Incorporation of the lateral methyl group encouraged the formation of a nematic phase at the expense of both the smectic A phase and tilted smectic phases.     

Optimal Two-Dimensional Compressed Matching

Recent proliferation of digitized data and the unprecedented growth in the volume of stored and transmitted data motivated the definition of the compressed matching paradigm. This is the problem of efficiently finding a patternPin a compressed textTwithout the need to decompress. We present the firstoptimaltwo-dimensional compressed matching algorithm. The compression under consideration is the two dimensional run-length compression, used by FAX transmission. We achieve optimal time by proving new properties of two-dimensional periodicity. This enables performing duels in which no witness is required. At the heart of the dueling idea lies the concept that two overlapping occurrences of a pattern in a text can use the content of apredetermined text positionorwitnessin the overlap to eliminate one of them. Finding witnesses is a costly operation in a compressed text, thus the importance of witness-free dueling.     

PIV analysis of in-cylinder flow structures over a range of realistic engine speeds

In-cylinder PIV measurements have been performed in a four-valve single cylinder optical gasoline direct injection engine, motored at speeds of 750, 2,000 and 3,500 rpm. Mean vector flow fields have been produced during the latter half of the intake stroke in the symmetry plane between the valve pairs. The flow fields show the development of the in-cylinder flow structures at 1.6, 2.4 and 3.2° crank angle steps for a time period of approximately 5 ms at each of the three engine speeds, respectively. Tumble ratios have been calculated for the available field of view showing a change in the flow structure between 2,000 and 3,500 rpm. This is believed to be caused by an increase in the flow of air traveling underneath the recirculation vortex at the higher engine speed. This translates the vortex position upwards and further to the right when compared to the lower engine speeds.