In 1947 E. Post [28] and A. A. Markov [18] independently proved the undecidability of the word problem (or the problem of deducibility of relations) for semigroups. In 1968 V. L. Murskil [23] proved the undecidability of the identity problem (or the problem of deducibility of identities) in semigroups.If we slightly generalize the statement of these results we can state many related results in the literature and state our new results proved here. Let V denote either a (Birkhoff) variety of semigroups or groups or a pseudovariety of finite semigroups. By a very well-known theorem a (Birkhoff) variety is defined by equations or equivalently closed under substructure, surmorphisms and all products; see [7]. It is also well known that V is a pseudovariety of finite semigroups iff V is closed under substructure, surmorphism and finite products, or, equivalently, determined eventually by equations w1 = w1′, w2 = w2′, w3 = w3′,… (where the finite semigroup S eventually satisfies these equations iff there exists an n, depending on S, such that S satisfies Wj = Wj′ for j ≥ n). See [8] and [29]. All semigroups form a variety while all finite semigroups form a pseudovariety.We now consider a table (see the next page). In it, for example, the box denoting the “word” (identity) problem for the psuedovariety V” means, given a finite set of relations (identities) E and a relation (identity) u = ν, the problem of whether it is decidable that E implies u = ν inside V.
This study investigates the possible use of unstandardized bite-wing radiographs to determine the rate of alveolar bone loss over long periods of time. A total of 100 pairs of bite-wing radiographs obtained from patients of two general dental practitioners were read on a 3M Reader, normally used for reading microfilm. For the purpose of measurement, two reference points were selected on the teeth; the highest point on the occlusal surface of the crown, the mesial and distal points of the cemento-enamel junction. Both vertical and horizontal bone loss was measured. Initially bone levels on 20 full mouth bite-wing radiographs on all posterior teeth were measured, then in the next 80 cases, an abbreviated index was used. The bone heights were first examined at the beginning and then at the end of a 10-year time span. The percentages of measurable distances were 28% and 57%. From the Occlusal measurement point and the C E J measurement points, reasons for unreadability were also recorded. The annual rate of horizontal bone loss was 0.06 mm and 0.04 mm from the Occlusal reference point and the CEJ reference point. The rates for the vertical bone loss was 0.05 and 0.03 mm. In order to study whether there was a constant loss over a period of time, bone levels were measured in 10 successive years. The findings suggest that the bone loss rat per year fluctuated. The study suggests that the bite-wing radiographs can be used in longitudinal studies of periodontal disease and can provide important information on the natural history of the disease.
3-D chip packaging and optoelectronic array interconnect technologies can be combined to realize ultra-compact hardware solution to systems requiring fast processing and handling of large data arrays. Thermal management is becoming a key issue if the active volume is minimized. The use of CVD diamond layers as a thermal management tool for the implementation of 3D stacks has been demonstrated to allow up to 80 W power dissipation in densely packed stacks of less than 1 cm3. IntroductionWhen manipulation and processing of large data arrays is required in image processing and recognition applications, existing planar silicon packaging based system implementations appear to be inadequate. As the size of the data arrays increase, it becomes difficult to pack the required processing units and sufficient memory within one single chip to carry out the required computation at high speeds due to the low yield for large silicon areas. On the other hand, the use of parallel hardware with many chips is not promising due to large areas resulting &om conventional packaging techniques which increases delay and power required to support the communication between chips. New hardware solutions capable of performing at high speeds are critically needed for the implementation of real time and adaptive signal processing systems. For example, if such image processing operations were performed on 1024x1024 data arrays with 32 bit accuracy at video rates, significant improvements could be obtained in electronic warfwe and industrial control applications.One way of packing more silicon circuits into a smaller volume is to use 3-D packaging techniques by stacking electronic chips. This packaging approach has the potential to significantly reduce the interconnection length of the intrachip connections within parallel processing groups. Since inter-chip distance is minimized, delay and power performance of the assembly is increased due to reduced system area (or volume). However, the reduction in system volume comes at the expense of heat extraction from the 3-D stacks. New thermal management approaches are needed to dissipate large amount of power in small volumes.
The use of CYD dirrmond rclyers as a thermal management tool for the implemenfation of 3D slacks will &w up to IO0 Wpower &sipation in 30-MCM applications.
Since the trend for electronic systems now requires more functional density not only per unit area, hut also per unit volume, and as electronic systems become smaller and thinner, the next logical step is to thin the integrated circuit (IC). This paper looks at the mechanical and morphological effects of the thinning process on the IC, and discusses thermal management schemes used to operate the t h i i e d IC at higher power levels. The methods used for thinning the chips in this study are plasma etching and mechanical polishmg. The chips were thinned to a thickness of approximately 50 -80 microns. This paper compares the effects of these two thinning processes on the chip's surface morphology and mechanical properties. In addition to the physical analysis of the chip, different thermal management schemes are also investigated in order to help increase the chip's operating power in both the flip chip and wire bond configurations. Polyimide is a desirable substrate for conformal circuitry because of its mechanical flexibility, yet it is a poor conductor of heat. Therefore, the thermal management schemes must be inteegrated into the polyimide substrate in order to increase the flow of heat away from the chips. The investigated schemes are thermal vias and micro heat channels. Finite element analysis was used to model these thermal management schemes.
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