In enterohemorrhagic Escherichia coli, Shiga toxin is produced by lysogenic prophages. We have isolated the prophage VT2-Sa that is responsible for production of Shiga toxin type 2 protein, and determined the complete nucleotide sequence of this phage DNA. The entire DNA sequence consisted of 60,942 bp, exhibiting marked similarity to the 933W phage genome. However, several differences were observed in the immunity and replication regions, where cI, cII, cIII, N, cro, O, and P genes were present: Predicted amino acid sequences of N, cI, cro, O and P in the VT2-Sa genome did not show significant similarity to the counterparts of the 933W genome; however its cI showed higher similarity to lambda. Furthermore, O and P closely resembled those of phage HK022. These observations suggest that the various degrees of homology observed in the immunity and replication regions of VT2-Sa could have resulted from frequent recombination events among the lambdoid phages, and that these regions play a key role as a functional unit for phage propagation in competition with other lambdoid phages.

The new type of the design method proposed in this paper is similar to the one using phase lead-lag compensator and has two particular characteristics. First, the approximate system described real order lag element with a dead time element is specially adopted to identify the controlled object. The principle of the identification derived from the frequency characteristics is presented. Secondly, the compensator is composed by an integral element and phase lead-lag elements having multiple zeros and multiple poles. The order of phase lead-lag elements is, in general, an integer but in this design it will be treated as a real number. In order to use practically the compensator, the impulse response function of the compensator is obtained in the form of a series expansion of a gamma function and it can be performed by the convolution method between the impulse response function of the compensator and a deviation error signal.The compensator parameters are determined by a rule of trial and error in order to obtain a quick response using manipulating variable under the maximum value assigned in advance. Since the order of the compensator can be adjusted finely through numerical treatment as to a real, the quick response by a relatively small manipulating variable has been performed. Then, the selection of the sampling time in the case of practical digital control is considered in detail. The effectiveness of this control design method is shown by examples.

This paper proposes a design method for the real order phase lead-lag compensator to control the controlled object having a higher order lag element and a dead time. In this method, a reference model of very simple open-loop transfer function is introduced. A close relation between the resonance peak Mp of frequency response and the overshoot of the response to unit step input is shown in this model. The desgin procedure which makes the frequency characteristics of the objected open-loop system close as precisely as possible to one of the reference model is presented. The frequency chracteristics of objected system are designed to satisfy the specifid quantities such as phase margin, value of Mp and gain margin. The condition that the gain-phase plot of the open-loop system is tangent to the constant M locus in the Nichols chart is treated especially. By this method, the overshoot of the step response to reference input is able to consider to be the specification in stead of the resonance peak Mp. Finally, the effectiveness of the design method is approved by examples.

We study the ferromagnetic Ising model on the Sierpinski gasket (SG), where the spin-spin interactions depends on the direction. Using the renormalization group method, we show that the ratios of the correlation lengths restore the isotropy of the lattice as the temperature approaches zero. This restoration is either partial or perfect, depending on the interactions. In case of partial restoration, we also evaluate the leading-order singular behavior of the correlation lengths.Comment: 17 pages, 10 figures. References added in v.2 and 3. Small improvements in v.4, 5. This version will appear in Prog. Theor. Phy

The control system design method for the controlled object having such a higher order lag element and a dead time element as used in general for the process control system is treated in this paper. Two types of the transfer function with the real order element are used in the control system design method. One is the transfer function of the controlled object approximated the real order lag element and a dead time system to a higher order controlled object. The other is the transfer function of the compensator with the real order phase lead-lag element proposed previously to control this controlled object. The principle of the design for the system composed of these elements is based on frequency characteristics.In this design, parameters of the compensator for a given phase margin, a gain margin and a peak gain in Nichols chart are intended to decide. The derivation of parameters of the compensator to satisfy specifications of these frequency characteristics is described, and then the property of the control system is confirmed by the transient responses.From results of the unit step response and the consideration to specifications of the system design, a suitable range of the parameter of the compensator is researched in detail. And then a suitable combination of the peak gain and the phase margin is obtained for a given specification of the frequency characteristics. The usability of this control system design method is appreciated through some examples. Moreover, the application of the principle of this controll system design method to the control system using the most general PID compensator has shown.

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