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A new class of languages, called multi-push-down (mpd), that generalize the classical context-free (cf, or Chomsky type 2) ones is introduced. These languages preserve some important properties of cf languages: a generalization of the Chomsky-Schützenberger homomorphic characterization theorem, the Parikh theorem and a “pumping lemma” are proved. Multi-push-down languages are an AFL. Their recognizers are automata equipped with a multi-push-down tape. Multi-push-down languages form a hierarchy based on the number of push-down tapes.

Given a category fibered in groupoids over schemes with a log structure, one produces a category fibered in groupoids over log schemes. We classify the groupoid fibrations over log schemes that arise in this manner in terms of a categorical notion of "minimal" objects. The classification is actually a purely category-theoretic result about groupoid fibrations over fibered categories, though most of the known applications occur in the setting of log geometry, where our categorical framework encompasses many notions of "minimality" previously extant in the literature.

We establish natural criteria under which normally iterable premice are iterable for stacks of normal trees. Let $\mathrm{\Omega }$ be a regular uncountable cardinal. Let $m<\omega$ and $M$ be an $m$-sound premouse and $\mathrm{\Sigma }$ be an $(m,\mathrm{\Omega }+1)$-iteration strategy for $M$ (roughly, a normal $(\mathrm{\Omega }+1)$-strategy). We define a natural condensation property for iteration strategies, inflation condensation. We show that if $\mathrm{\Sigma }$ has inflation condensation then $M$ is ${(m,\mathrm{\Omega },\mathrm{\Omega }+1)}^{\ast }$-iterable (roughly, $M$ is iterable for length $\le \mathrm{\Omega }$ stacks of normal trees each of length $<\mathrm{\Omega }$), and moreover, we define a specific such strategy ${\mathrm{\Sigma }}^{\mathrm{\text{st}}}$ and a reduction of stacks via ${\mathrm{\Sigma }}^{\mathrm{\text{st}}}$ to normal trees via $\mathrm{\Sigma }$. If $\mathrm{\Sigma }$ has the Dodd-Jensen property and $\mathrm{\text{card}}(M)<\mathrm{\Omega }$ then $\mathrm{\Sigma }$ has inflation condensation. We also apply some of the techniques developed to prove that if $\mathrm{\Sigma }$ has strong hull condensation (introduced independently by John Steel), and $G$ is $V$-generic for an $\mathrm{\Omega }$-cc forcing, then $\mathrm{\Sigma }$ extends to an $(m,\mathrm{\Omega }+1)$-strategy ${\mathrm{\Sigma }}^{+}$ for $M$ with strong hull condensation, in the sense of $V[G]$. Moreover, this extension is unique. We deduce that if $G$ is $V$-generic for a ccc forcing then $V$ and $V[G]$ have the same $\omega$-sound, $(\omega ,\mathrm{\Omega }+1)$-iterable premice which project to $\omega$.

We consider the number of passes a permutation needs to take through a stack if we only pop the appropriate output values and start over with the remaining entries in their original order. We define a permutation $\pi$ to be $k$-pass sortable if $\pi$ is sortable using $k$ passes through the stack. Permutations that are $1$-pass sortable are simply the stack sortable permutations as defined by Knuth. We define the permutation class of $2$-pass sortable permutations in terms of their basis. We also show all $k$-pass sortable classes have finite bases by giving bounds on the length of a basis element of the permutation class for any positive integer $k$. Finally, we define the notion of tier of a permutation $\pi$ to be the minimum number of passes after the first pass required to sort $\pi$. We then give a bijection between the class of permutations of tier $t$ and a collection of integer sequences studied by Parker [The combinatorics of functional composition and inversion, PhD thesis, Brandeis University (1993)]. This gives an exact enumeration of tier $t$ permutations of a given length and thus an exact enumeration for the class of $(t+1)$-pass sortable permutations. Finally, we give a new derivation for the generating function in [S. Parker, The combinatorics of functional composition and inversion, PhD thesis, Brandeis University (1993)] and an explicit formula for the coefficients.

This paper deals with the design and analysis of a quarter-wavelength, 10 W capacity, thermoacoustic refrigerator using short stack boundary layer approximation assumptions. The effect of operating frequency on the performance of the refrigerator is studied using dimensional normalization technique. The variation of stack diameter with average gas pressure and cooling power is discussed. The resonator optimization is discussed and the calculation results show a 9% improvement in the coefficient of performance and 201% improvement in power density for the optimized quarter-wavelength resonator compared to published optimization studies. The optimized resonator design is tested with DeltaEC software and the results show better performance compared to past established resonator designs.

Thermoacoustic refrigerators are environmentally friendly cooling systems that use no refrigerants. Optimization of the performance of any cooling system is crucial for an efficient energy management. Most of the optimization techniques in thermoacoustic systems utilized to date involved experimental and numerical parametric studies which are generally limited to the variations of the parameters to be optimized at discrete values. This study reports on the optimization of a thermoacoustic refrigerator using multi-objective genetic algorithm (MOGA). The study introduces the ability of MOGA to optimize four different variables which are length of stack, center position of stack, blockage ratio and drive ratio simultaneously. The four variables are optimized to achieve the two objectives; a maximum cooling and minimum acoustic power required at the stack and provide the optimum coefficient of performance, COP. The results show that the optimum COP = 1.35 with a cooling power of Q_c = 6.57 W, acoustic power of W_n = 4.86 W and with the resonator diameter of D = 3.8 cm.

Although thermoacoustic devices comprise simple components, the design of these machines is very challenging. In order to predict the behavior and optimize the performance of a thermoacoustic refrigerator driven by a standing-wave thermoacoustic engine, considering the changes in geometrical parameters, two analogies have been presented in this paper. The first analogy is based on CFD analysis where a 2D model is implemented to investigate the influence of stack parameters on the refrigerator performance, to analyze the time variation of the temperature gradient across the stack, and to examine the refrigerator performance in terms of refrigeration temperature. The second analogy is based on the use of an optimization algorithm based on the simplified linear thermoacoustic theory applied for designing thermoacoustic refrigerators with different stack parameters and operating conditions. Simulation results show that the engine produced a high-powered acoustic wave with a pressure amplitude of 23kPa and a frequency of 584Hz and this wave applies a temperature difference across the refrigeration stack with a cooling temperature of 292.8K when the stacks are positioned next to the pressure antinode. The results from the algorithm give the ability to design any thermoacoustic refrigerator with high performance by picking the appropriate parameters.

This paper presents the application of the Pareto-based multicriteria optimization technique to problems of increasing the efficiency of piezoelectric generators (PEGs). The optimization problem was solved for two types of generators: cantilever and stack. For the cantilever generator, the task was to optimize the design in such a way as to obtain the maximum output power for a given mechanical excitation. The optimization process was divided into several stages, which significantly reduced the amount of calculations. The task of optimizing the stack type for a given form of mechanical loading consisted in finding the geometric parameters of the generator at which the output voltage and power would be maximum. In the result of solving both problems, sets of geometric design parameters of PEGs were obtained, on the basis of which efficient transducers can be developed for specific operating conditions. It turned out that this technique is more suitable for optimizing the design of cantilever generators than for stack ones in given constraints. The solution of both problems was realized using the finite element method.

Environmental regulations have turned their focus on controlling and mitigating air emissions that contribute to abundant air pollution. The primary pollutants found in air emissions from stack discharges are NO_x, SO_x, particulates and smog. With continued federal action by the EPA, coupled with action from state and local regulatory agencies, mitigation of air pollution containing harmful pollutants can be achieved to a certain scale. This chapter will focus on the harmful effects of sulfur dioxide (SO₂), considered the most harmful intentionally discharged air pollutant to the environment. Due to its impact in the form of acid rain and, on a larger scale, ozone depletion, SO₂ mitigation is a high priority. Additionally, methods and equipment used as well as being developed for use will be discussed for their ability to effectively treat stack discharges and mitigate SO₂ pollution.

We developed anode supported flat tube SOFC to improve the power density of the cylindrical tube cell and studied basic technology of key components in anode supported flat tube SOFC such as electrode, electrolyte, ceramic interconnect materials, and metallic bipolar plate materials for making the cell stack. Performance of the flat tube cell showed 300 mW/cm² (0.6V, 500 mA/cm²) at 800°C. Fe-16Cr (SUS 430) alloy as metallic bipolar plate was coated with LSM (La_0.85Sr_0.15)_0.9MnO₃) and LCC (La_0.75Ca_0.27CrO₃) and their electrical conductivity and microstructure were examined. The Fe-16Cr alloy with LSM coating layer was sustained for 2600hrs with 70mΩcm² without increasing it's value and the alloy with LCC layer showed lower resistance. These results indicated that these metallic bipolar plates could be used effectively for making anode supported flat tube cell stack. As ceramic interconnect of flat tube cell, several kinds of materials with compositions of La_1-xCa_xCrO₃ were synthesized by Pechini method and coated onto one side of the anode flat tube in the form of band by plasma spray and vacuum slurry coating method. Through these experiments, we obtained basic technology of the anode-supported flat tube cell and established the proprietary concept of the anode-supported flat tube cell stack.

In the present paper, we introduce spin groupoids associated with the degree two Stiefel-Whitney classes, and we also introduce spinor torsors equipped with certain connections compatible with an action of spin groupoid. Using the connection, we propose a Dirac-like operator acting on the space of smooth sections of the spinor torsor. We can show that its Dirac-Laplacian admits a heat kernel in a formal sense.

In all of the routing protocols of Ad hoc networks, GPSR based on geographical information is a robust protocol with broad prospects. GPSR is composed of greedy algorithm and perimeter forwarding algorithm. While there are many packets need to be perimeter forwarded, it may produce lots of hops. This paper analyses perimeter forwarding firstly; and then puts forward an improving approach plus a stack in the memory of each forwarding node. The detailed steps are described in this paper to present the improved algorithm as well. Based on the theory demonstrations, we concluded that the improved algorithm can reduce routing hops and time complexity obviously. Furthermore, it can be implemented easily to improve routing performance. The innovation of this paper is that the time complexity is reduced by adding the space complexity.