Nutation electron spin echo ofE-centers in quartz

Attenuation of the signals of the nutation echo of E’-centers in crystalline and glass quartz was experimentally investigated at room temperature. The nutation echo in EPR was excited in the single-photon regime and formed by two Zeeman-field pulses with duration t₁ and t₂ (t₁<t₂) and time interval between them τ. The echo signal was recorded during the second pulse at t≈2t₁+τ. It was established that this signal attenuation, measured as t₁ increased, follows an, exponential law, its rate Γ is much less than 1/T₂ (T₂ is the transverse relaxation time), and it linearly increases with an increase in the amplitude of the exciting SHF field B₁. The parameters of the dependence of Γ on B₁ correlate with the parameters of the analogous dependence revealed previously for attenuation of nutation of E’-centers in quartz in the two-photon regime at T=4.2 K. At the same time, the value of Γ measured with different values of τ is independent of B₁ and is equal to 1/T₁, where T₁ is the longitudinal relaxation time. A. N. Sevchenko Scientific Research Institute of Applied Physical Problems, 7, Kurchatov St., Minsk, 220064, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 3, pp. 405–411, May–June, 1998.     

Small random perturbations of one-dimensional diffusion processes

In the present paper we consider the small random perturbations of one-dimensional diffusion processes. By virtue of stochastic analysis methods, we investigate the asymptotics of the mean exit times and probabilistical estimates of the exit times as the perturbations tend to zero. Partially supported by the Young Teachers Foundation of Beijing Institute of Technology     

Impact of flexible machines on automated manufacturing systems

Although the problem of scheduling dynamic job shops is well studied, setup and changeover times are often assumed to be negligibly small and therefore ignored. In cases where the product mix changes occur frequently, setup and changeover times are of critical importance. This paper applies some known results from the study of multi-class single-server queues with setup and changeover times to develop an approximation for evaluating the performance of job shops. It is found that the product mix, setup and changeover times, and scheduling rules affect the performance significantly, in particular at high levels of machine utilisation. This approach could be used to determine the required level of flexibility of machines and to choose an appropriate scheduling policy such that production rates remain within acceptable limits for foreseeable changes in the product mix.     

On the finite-source G/M/r queue

The aim of the present paper is to give the main characteristics of the finite-source $\text{G}\text{/}\text{M}\text{/r}$ queue in equilibrium. Here unit i stays in the source for a random time having general distribution function F_i(x) with density f_i(x). The service times of all units are assumed to be identically and exponentially distributed random variables with means 1/μ. It is shown that the solution to this $\text{G}\text{/}\text{M}\text{/r}$ model is similar in most important respects to that for the M/M/r model.     

Batching in single operation manufacturing systems

We introduce a new decision problem important to the efficient operation of resources in manufacturing systems. This problem of ‘batching’ is considered for single machine activities. It is shown that even for these simple models, lot splitting may occur and that these batching decisions may have a dramatic impact on the manufacturing lead time of items to be processed.     

Characterization of proton NMR relaxation times in normal and pathological tissues by correlation with other tissue parameters

To help understand which tissue parameters best account for the water proton NMR relaxation times, the longitudinal relaxation time (T₂), the transverse relaxation time (T₂), and the water content of 16 tissues from normal adult rats were measured at 10.7 MHz and 29°C. Regression analyses between the above and other tissue parameters were performed. These other tissue parameters included: the amounts of various organic and inorganic components, protein synthetic rate, oxygen consumption rate, and morphological composition. In addition, the differences in T₁, T₂, and water content values between normal liver and malignant tumor (Morris #7777 a transplantable hepatoma) were studied to help understand how a disease state can be detected and characterized by NMR spectroscopy. The results of this study and information from the literature allow the following generalizations to be made about tissue T₁ and T₂ values: (1) Each normal tissue has rather consistent and characteristic T₁ and T₂ relaxation times which are always shorter than the T₁ and T₂ of bulk water; (2) tissues with higher water content tend to have longer T₁ relaxation times; (3) tissue T₂ values are not, however, as well correlated with water content as T₁ values; (4) tissues with shorter T₁ values have higher calculated hydration fractions, greater amounts of rough endoplasmic reticulum, and a greater rate of protein synthetic activity; (5) tissues with higher lipid content, associated with intracellular non-membrane bounded lipid droplets, tend to have longer T₂ values; (6) tissues with greater overall surface area, whether in the form of cellular membranes or intracellular or extracellular fibrillar macromolecules, tend to have shorter T₂ values; (7) the differences between T₁ and T₂ values between tumor and normal tissues correlated with differences in the volume fraction (amounts) of extracellular fluid volumes and in the amounts of membrane and fibrillar surface area in the cells. The above generalizations should be useful in predicting T₁ and T₂ changes associated with specific tissue pathologies.     

Enhanced T1 differentiation between normal and dystrophic muscles

Proton spin-lattice relaxation times (T1) of pectoralis major muscles from normal (Line 412) and homozygous dystrophic (Line 413) chicks was measured by FONAR QED 80 at 1.69 MHz. The T1 values of dystrophic muscles (216.8 +/- 17.3 ms) was two-fold higher than those of normal muscles (110.2 +/- 8.1 msec). When these values were compared with the T1 values obtained at high frequencies (20 MHz and 32 MHz), the T1 differentiation between normal and dystrophic muscles was considerably enhanced at 1.69 MHz. Based on these results, we suggest that the high resolution of T1 obtained at low frequency (1.69 MHz) could be effectively used to detect the degenerative processes in muscles by the NMR techniques.     

A priori bounds for elliptic equations

In this paper we study the relationship existing between the maximum principle and the principal eigenvalue of second order elliptic operators and the expected exit times of the corresponding diffusions. A probabilistic approach is discussed that provides a good understanding of classical results established analytically. We also obtain an Alexandrov-Bakelman-Pucci type of estimate using similar methods.     

Singular differential game numerical techniques

This paper develops a numerical technique to solve a class of zero-sum differential games with singular control. By using this technique and the application of inverse systems, a near-optimal closed-loop technique is developed to generate a numerical solution to this class of problems.     

On the exact asymptotic behaviour of the distribution of ladder epochs

Let T₊ denote the first increasing ladder epoch in a random walk with a typical step-length X. It is known that for a large class of random walks with E(X)=0,E(X²)=∞, and the right-hand tail of the distribution function of X asymptotically larger than the left-hand tail, $\text{P}\text{T}{}_{\mathrm{+}}\text{?n∽n}{}^{\mathrm{<mtext>1</mtext><mtext>\beta ?1</mtext>}}\text{L}{}_{\mathrm{+}}\text{(n)}$ as n→∞, with 1<β<2 and L₊ slowly varying, if and only if$\text{P}\text{{X?x}∽ 1/{x}{}^{\mathrm{\beta }}\text{L(x)}}$ as x→+∞, with L slowly varying. In this paper it is shown how the asymptotic behaviour of L determines the asymptotic behaviour of L₊ and vice versa. As a by-product, it follows that a certain class of random walks which are in the domain of attraction of one-sided stable laws is such that the down-going ladder height distribution has finite mean.