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Journal articles on the topic 'Partitions'
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1
Devi, E. Anna, and J. Martin Leo Manickam. "Reconnection of Wireless Sensor Network Partitions on Multi-Agent Platform." International Journal of Business Analytics 6, no. 1 (January 2019): 43–54. http://dx.doi.org/10.4018/ijban.2019010103.
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In wireless sensor networks, repairing partitions is of high priority. Various methods have been proposed for detecting partitions in the networks. One approach for reconnecting a partitioned network is to repair partitions using mobile nodes. For reconnecting the partitions approaches like transmission range adjustment and message ferry methods have been proposed but these are based on the degree of connectivity with neighbors. In the proposed method, we consider a partition detection system where the base station knows the position of the sensor nodes and the base station communicates with the nodes at regular intervals. The failure of the base station to communicate with a group of sensor nodes located together is the proof that some partitions have occurred. There could be two or more partitions occurring at a time and so multiple mobile nodes are to be employed. The aim of the algorithm is to coordinate among the mobile nodes and the partitioned network and to reconnect the partition. Here the safety of nodes, security of the network and scalability are considered.
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Hoang, Loc, Roshan Dathathri, Gurbinder Gill, and Keshav Pingali. "CuSP." ACM SIGOPS Operating Systems Review 55, no. 1 (June 2, 2021): 47–60. http://dx.doi.org/10.1145/3469379.3469385.
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Graph analytics systems must analyze graphs with billions of vertices and edges which require several terabytes of storage. Distributed-memory clusters are often used for analyzing such large graphs since the main memory of a single machine is usually restricted to a few hundreds of gigabytes. This requires partitioning the graph among the machines in the cluster. Existing graph analytics systems use a built-in partitioner that incorporates a particular partitioning policy, but the best policy is dependent on the algorithm, input graph, and platform. Therefore, built-in partitioners are not sufficiently flexible. Stand-alone graph partitioners are available, but they too implement only a few policies. CuSP is a fast streaming edge partitioning framework which permits users to specify the desired partitioning policy at a high level of abstraction and quickly generates highquality graph partitions. For example, it can partition wdc12, the largest publicly available web-crawl graph with 4 billion vertices and 129 billion edges, in under 2 minutes for clusters with 128 machines. Our experiments show that it can produce quality partitions 6× faster on average than the state-of-theart stand-alone partitioner in the literature while supporting a wider range of partitioning policies.
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Ramdhani, Vivi, and Fathur Rahmi. "The Partition Dimension of a Path Graph." Sainstek : Jurnal Sains dan Teknologi 13, no. 2 (December 31, 2021): 66. http://dx.doi.org/10.31958/js.v13i2.4719.
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Resolving partition is part of graph theory. This article, explains about resolving partition of the path graph, with. Given a connected graph and is a subset of writen . Suppose there is , then the distance between and is denoted in the form . There is an ordered set of -partitions of, writen then the representation of with respect tois the The set of partitions ofis called a resolving partition if the representation of each to is different. The minimum cardinality of the solving-partition to is called the partition dimension of G which is denoted by . Before getting the partition dimension of a path graph, the first step is to look for resolving partition of the graph. Some resolving partitions of path graph, with , and are obtained. Then, the partition dimension of the path graph which is the minimum cardinality of resolving partition, namely pd (Pn)=2Resolving partition is part of graph theory. This article, explains about resolving partition of the path graph, with. Given a connected graph and is a subset of writen . Suppose there is , then the distance between and is denoted in the form . There is an ordered set of -partitions of, writen then the representation of with respect tois the The set of partitions ofis called a resolving partition if the representation of each to is different. The minimum cardinality of the solving-partition to is called the partition dimension of G which is denoted by . Before getting the partition dimension of a path graph, the first step is to look for resolving partition of the graph. Some resolving partitionsof path graph, with , and are obtained. Then, the partition dimension of the path graph which is the minimum cardinality of resolving partition, namely.
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CUI, SU-PING, and NANCY SHAN SHAN GU. "CONGRUENCES FOR k DOTS BRACELET PARTITION FUNCTIONS." International Journal of Number Theory 09, no. 08 (December 2013): 1885–94. http://dx.doi.org/10.1142/s1793042113500644.
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Andrews and Paule introduced broken k-diamond partitions by using MacMahon's partition analysis. Recently, Fu found a generalization which he called k dots bracelet partitions and investigated some congruences for this kind of partitions. In this paper, by finding congruence relations between the generating function for 5 dots bracelet partitions and that for 5-regular partitions, we get some new congruences modulo 2 for the 5 dots bracelet partition function. Moreover, for a given prime p, we study arithmetic properties modulo p of k dots bracelet partitions.
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Li, Yu, Jianfeng Wu, Chunfu Lu, Zhichuan Tang, and Chengmin Li. "Pillow Support Model with Partitioned Matching Based on Body Pressure Distribution Matrix." Healthcare 9, no. 5 (May 12, 2021): 571. http://dx.doi.org/10.3390/healthcare9050571.
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(1) Objective: Sleep problems have become one of the current serious public health issues. The purpose of this research was to construct an ideal pressure distribution model for head and neck support through research on the partitioned support surface of a pillow in order to guide the development of ergonomic pillows. (2) Methods: Seven typical memory foam pillows were selected as samples, and six subjects were recruited to carry out a body pressure distribution experiment. The average value of the first 10% of the samples in the comfort evaluation was calculated to obtain the relative ideal body pressure distribution matrix. Fuzzy clustering was performed on the ideal matrix to obtain the support surface partition. The ideal body pressure index of each partition was calculated, and a hierarchical analysis of each partition was then performed to determine the pressure sensitivity weight of each partition. Using these approaches, the key ergonomic node coordinates of the partitions of four different groups of people were extracted. The ergonomic node coordinates and the physical characteristics of the material were used to design a pillow prototype. Five subjects were recruited for each of the four groups to repeat the body pressure distribution experiment to evaluate the pillow prototype. (3) Results: An ideal support model with seven partitions, including three partitions in the supine position and four partitions in the lateral position, was constructed. The ideal body pressure distribution matrix and ideal body pressure indicators and pressure sensitivity weights for each partition were provided. The pillow that was designed and manufactured based on this model reproduced the ideal pressure distribution matrix evaluated by various groups of people. (4) Conclusion: The seven-partition ideal support model can effectively describe the head and neck support requirements of supine and lateral positions, which can provide strong support for the development of related products.
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Merca, Mircea, and Iulia-Ionelia Radu. "Plane Partitions as Sums over Partitions." Symmetry 15, no. 10 (September 25, 2023): 1820. http://dx.doi.org/10.3390/sym15101820.
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In this paper, we consider complete homogeneous symmetric functions and provide a new formula for the number of plane partitions of n. This formula expresses the number of plane partitions of n in terms of binomial coefficients as a sum over all the partitions of n, considering the multiplicity of the parts greater than one. We obtain similar results for the number of strict plane partition of n and the number of symmetric plane partitions of n.
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Thompson, J. M., and R. M. Butterfield. "Changes in body composition relative to weight and maturity of Australian Dorset Horn rams and wethers 4. Adipocyte volume and number in dissected fat partitions." Animal Production 46, no. 3 (June 1988): 387–93. http://dx.doi.org/10.1017/s0003356100018997.
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ABSTRACTThe effect of castration on the cellular characteristics of dissected fat partitions was examined in 20 Dorset Horn rams and 20 Dorset Horn wethers. Cellular characteristics of dissected carcass (subcutaneous and intermuscular partitions) and non-carcass (kidney fat, omental and mesenteric partitions) fat partitions were examined in 13 mature animals, and the rate of change in adipocyte volume relative to the change in chemical-fat weight in that partition, examined in 27 immature animals.Mature wethers had a greater concentration of chemical fat in the subcutaneous fat partition than mature rams (917 v. 885 g/kg, respectively). This, in combination with a greater weight of dissected subcutaneous fat, resulted in a greater weight of chemical fat in the subcutaneous partition of wethers compared with rams. Mature wethers had larger adipocytes than mature rams in all dissected fat partitions, with the largest increase in the subcutaneous and omental fat partitions. The increased adipocyte volume in the dissected fat partitions in mature wethers resulted in a smaller total estimated number of adipocytes in all carcass and non-carcass fat partitions compared with mature rams.Standardized allometric coefficients for adipocyte volume relative to chemical-fat weight in that partition showed that increases in chemical-fat weight were due to a combination of hypertrophy and hyperplasia. In the omental and kidney fat partitions, hypertrophy contributed more to the increase in chemical-fat weight in wethers compared with rams.
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Cheng, Qian, Qing Fan Gu, and Li Song Wang. "Partition Scheduling Research of Hard Real-Time and Multi-Core System." Applied Mechanics and Materials 490-491 (January 2014): 824–27. http://dx.doi.org/10.4028/www.scientific.net/amm.490-491.824.
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For and multi-core in integrated avionics system used in the challenge, will partition scheduling on a single core changed concurrently on multi-core scheduling problems, we will partition into two partitions exclusive partitions and perform part to solve scheduling resource sharing and synchronization issues. We partition as a unit, to establish a and multi-core partition scheduling model and proposed approximate minimum core and multi-core partition scheduling algorithm to ensure exclusive partitions can be scheduled in the case, you can create a mapping for and multi-core partition to partition scheduling on multi-core .
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Andrews, George E., and Cristina Ballantine. "Almost partition identities." Proceedings of the National Academy of Sciences 116, no. 12 (March 4, 2019): 5428–36. http://dx.doi.org/10.1073/pnas.1820945116.
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An almost partition identity is an identity for partition numbers that is true asymptotically100%of the time and fails infinitely often. We prove a kind of almost partition identity, namely that the number of parts in all self-conjugate partitions of n is almost always equal to the number of partitions of n in which no odd part is repeated and there is exactly one even part (possibly repeated). Not only does the identity fail infinitely often, but also, the error grows without bound. In addition, we prove several identities involving the number of parts in restricted partitions. We show that the difference in the number of parts in all self-conjugate partitions of n and the number of parts in all partitions of n into distinct odd parts equals the number of partitions of n in which no odd part is repeated, the smallest part is odd, and there is exactly one even part (possibly repeated). We provide both analytic and combinatorial proofs of this identity.
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Infante, Guillermo, Anders Jonsson, and Vicenç Gómez. "Globally Optimal Hierarchical Reinforcement Learning for Linearly-Solvable Markov Decision Processes." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 6 (June 28, 2022): 6970–77. http://dx.doi.org/10.1609/aaai.v36i6.20655.
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We present a novel approach to hierarchical reinforcement learning for linearly-solvable Markov decision processes. Our approach assumes that the state space is partitioned, and defines subtasks for moving between the partitions. We represent value functions on several levels of abstraction, and use the compositionality of subtasks to estimate the optimal values of the states in each partition. The policy is implicitly defined on these optimal value estimates, rather than being decomposed among the subtasks. As a consequence, our approach can learn the globally optimal policy, and does not suffer from non-stationarities induced by high-level decisions. If several partitions have equivalent dynamics, the subtasks of those partitions can be shared. We show that our approach is significantly more sample efficient than that of a flat learner and similar hierarchical approaches when the set of boundary states is smaller than the entire state space.
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Cao, Zhu, and Shi-Chao Chen. "On generalized Schur’s partitions." International Journal of Number Theory 13, no. 06 (December 5, 2016): 1381–91. http://dx.doi.org/10.1142/s1793042117500774.
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In 1926, I. Schur proved that the number of partitions of [Formula: see text] into parts [Formula: see text] equals the number of partitions of [Formula: see text] of the form [Formula: see text] such that [Formula: see text] with strictly inequality if [Formula: see text]. We prove that Schur’s partition function is related to a weight 3/2 Hecke eigenform modulo 2. As a consequence, we obtain some congruences for Schur’s partitions functions. Schur’s partitions theorem can be easily generalized to general moduli. We show that the generalized Schur’s partition functions satisfy beautiful transformation properties. We also find an unexpected relation between the generalized Schur’s partitions and singular overpartitions, which was introduced by G. E. Andrews recently.
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Alghamdi, Wajdi, and Muhammad Ahsan Asim. "On the Bounded Partition Dimension of Some Generalised Graph Structures." Journal of Mathematics 2022 (December 5, 2022): 1–11. http://dx.doi.org/10.1155/2022/9531182.
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Consider λ to be a connected graph with a vertex set V λ that may be partitioned into any partition set S . If each vertex in λ has a separate representation with regard to S and is an ordered k partition, then the set with S is a resolving partition of λ . . A partition dimension of λ , represented by p d , is the minimal cardinality of resolving k partitions of V λ . The partition dimension of various generalised families of graphs, such as the Harary graph, Cayley graph, and Pendent graph, is given as a sharp upper bound in this article.
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Jia, Lianyin, Chongde Zhang, Mengjuan Li, Yinong Chen, Yong Liu, and Jiaman Ding. "An Efficient Two-Level-Partitioning-Based Double Array and Its Parallelization." Applied Sciences 10, no. 15 (July 30, 2020): 5266. http://dx.doi.org/10.3390/app10155266.
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Trie is one of the most common data structures for string storage and retrieval. As a fast and efficient implementation of trie, double array (DA) can effectively compress strings to reduce storage spaces. However, this method suffers from the problem of low index construction efficiency. To address this problem, we design a two-level partition (TLP) framework in this paper. We first divide the dataset is into smaller lower-level partitions, and then we merge these partitions into bigger upper-level partitions using a min-heap based greedy merging algorithm (MH-GMerge). TLP has an excellent characteristic of load balancing and can be easily parallelized. We implemented two efficient parallel partitioned DAs based on TLP. Extensive experiments were carried out, and the results showed that the proposed methods can significantly improve the construction efficiency of DA and can achieve a better trade-off between construction and retrieval performance than the existing state-of-the-art methods.
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Das, Sabuj. "PARTITION CONGRUENCES AND DYSON’S RANK." International Journal of Research -GRANTHAALAYAH 2, no. 2 (November 30, 2014): 49–60. http://dx.doi.org/10.29121/granthaalayah.v2.i2.2014.3066.
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In this article the rank of a partition of an integer is a certain integer associated with the partition. The term has first introduced by freeman Dyson in a paper published in Eureka in 1944. In 1944, F.S. Dyson discussed his conjectures related to the partitions empirically some Ramanujan’s famous partition congruences. In 1921, S. Ramanujan proved his famous partition congruences: The number of partitions of numbers 5n+4, 7n+5 and 11n +6 are divisible by 5, 7 and 11 respectively in another way. In 1944, Dyson defined the relations related to the rank of partitions. These are later proved by Atkin and Swinnerton-Dyer in 1954.
The proofs are analytic relying heavily on the properties of modular functions. This paper shows how to generate the generating functions for In this paper, we show how to prove the Dyson’s conjectures with rank of partitions.
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Martin, Paul, and Volodymyr Mazorchuk. "Partitioned Binary Relations." MATHEMATICA SCANDINAVICA 113, no. 1 (September 1, 2013): 30. http://dx.doi.org/10.7146/math.scand.a-15480.
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We define the category of partitioned binary relations and show that it contains many classical diagram categories, including categories of binary relations, maps, injective maps, partitions, (oriented) Brauer diagrams and (oriented) Temperley-Lieb diagrams. We construct a one-parameter deformation of the category of partitioned binary relations and show that it gives rise to classical one-parameter deformations of partition, Brauer and Temperley-Lieb categories. Finally, we describe a factorization of partitioned binary relations into a product of certain idempotents and pairs of usual binary relations.
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Crane, Harry, and Peter McCullagh. "Reversible Markov structures on divisible set partitions." Journal of Applied Probability 52, no. 03 (September 2015): 622–35. http://dx.doi.org/10.1017/s0021900200113336.
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We studyk-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integerk= 1, 2, …. In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, fork> 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is needed to obtain a partition structure. We describe explicit Chinese restaurant-type seating rules for generating families of exchangeablek-divisible partitions that are consistent under random deletion. We further introduce the notion ofMarkovian partition structures, which are ensembles of exchangeable Markov chains onk-divisible partitions that are consistent under a random process ofMarkovian deletion. The Markov chains we study are reversible and refine the class of Markov chains introduced in Crane (2011).
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Bérard, P., and B. Helffer. "Remarks on the boundary set of spectral equipartitions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2007 (January 28, 2014): 20120492. http://dx.doi.org/10.1098/rsta.2012.0492.
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Given a bounded open set in (or in a Riemannian manifold), and a partition of Ω by k open sets ω j , we consider the quantity , where λ ( ω j ) is the ground state energy of the Dirichlet realization of the Laplacian in ω j . We denote by ℒ k ( Ω ) the infimum of over all k -partitions. A minimal k -partition is a partition that realizes the infimum. Although the analysis of minimal k -partitions is rather standard when k =2 (we find the nodal domains of a second eigenfunction), the analysis for higher values of k becomes non-trivial and quite interesting. Minimal partitions are in particular spectral equipartitions, i.e. the ground state energies λ ( ω j ) are all equal. The purpose of this paper is to revisit various properties of nodal sets, and to explore if they are also true for minimal partitions, or more generally for spectral equipartitions. We prove a lower bound for the length of the boundary set of a partition in the two-dimensional situation. We consider estimates involving the cardinality of the partition.
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DIGBY, DAVID, WILLIAM SEFFENS, and FISSEHA ABEBE. "RUNS OF AMINO ACIDS ARE LONGER THAN EXPECTED IN PROTEINS BASED ON A GRAPH THEORY REPRESENTATION OF THE GENETIC CODE." Journal of Biological Systems 10, no. 04 (December 2002): 319–35. http://dx.doi.org/10.1142/s0218339002000718.
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An in silico study of mRNA secondary structure has found a bias within the coding sequences of genes that favors "in-frame" pairing of nucleotides. This pairing of codons, each with its reverse-complement, partitions the 20 amino acids into three subsets. The genetic code can therefore be represented by a three-component graph. The composition of proteins in terms of amino acid membership in the three subgroups has been measured, and sequence runs of members within the same subgroup have been analyzed using a runs statistic based on Z-scores. In a GENBANK database of over 416,000 protein sequences, the distribution of this runs-test statistic is negatively skewed. To assess whether this statistical bias was due to a chance grouping of the amino acids in the real genetic code, several alternate partitions of the genetic code were examined by permuting the assignment of amino acids to groups. A metric was constructed to define the difference, or "distance", between any two such partitions, and an exhaustive search was conducted among alternate partitions maximally distant from the natural partition of the genetic code, to select sets of partitions that were also maximally distant from one another. The statistical skewness of the runs statistic distribution for native protein sequences were significantly more negative under the natural partition than they were under all of the maximally different partition of codons, although for all partitions, including the natural one, the randomized sequences had quite similar skewness. Hence under the natural graph theory partition of the genetic code there is a preference for more protein sequences to contain fewer runs of amino acids, than they do under the other partitions, meaning that the average run must be longer under the natural partition. This suggests that a corresponding bias may exist in the coding sequences of the actual genes that code for these proteins.
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Crane, Harry, and Peter McCullagh. "Reversible Markov structures on divisible set partitions." Journal of Applied Probability 52, no. 3 (September 2015): 622–35. http://dx.doi.org/10.1239/jap/1445543836.
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We study k-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integer k = 1, 2, …. In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, for k > 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is needed to obtain a partition structure. We describe explicit Chinese restaurant-type seating rules for generating families of exchangeable k-divisible partitions that are consistent under random deletion. We further introduce the notion of Markovian partition structures, which are ensembles of exchangeable Markov chains on k-divisible partitions that are consistent under a random process of Markovian deletion. The Markov chains we study are reversible and refine the class of Markov chains introduced in Crane (2011).
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KAAVYA, S. J. "CRANK 0 PARTITIONS AND THE PARITY OF THE PARTITION FUNCTION." International Journal of Number Theory 07, no. 03 (May 2011): 793–801. http://dx.doi.org/10.1142/s1793042111004381.
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A well-known problem regarding the integer partition function p(n) is the parity problem, how often is p(n) even or odd? Motivated by this problem, we obtain the following results: (1) A generating function for the number of crank 0 partitions of n. (2) An involution on the crank 0 partitions whose fixed points are called invariant partitions. We then derive a generating function for the number of invariant partitions. (3) A generating function for the number of self-conjugate rank 0 partitions.
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Paul, Rourab, Sreetama Sarkar, Suman Sau, Sanghamitra Roy, Koushik Chakraborty, and Amlan Chakrabarti. "Voltage Scaled Low Power DNN Accelerator Design on Reconfigurable Platform." Electronics 13, no. 8 (April 10, 2024): 1431. http://dx.doi.org/10.3390/electronics13081431.
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The exponential emergence of Field-Programmable Gate Arrays (FPGAs) has accelerated research on hardware implementation of Deep Neural Networks (DNNs). Among all DNN processors, domain-specific architectures such as Google’s Tensor Processor Unit (TPU) have outperformed conventional GPUs (Graphics Processing Units) and CPUs (Central Processing Units). However, implementing low-power TPUs in reconfigurable hardware remains a challenge in this field. Voltage scaling, a popular approach for energy savings, can be challenging in FPGAs, as it may lead to timing failures if not implemented appropriately. This work presents an ultra-low-power FPGA implementation of a TPU for edge applications. We divide the systolic array of a TPU into different FPGA partitions based on the minimum slack value of different design paths of Multiplier Accumulators (MACs). Each partition uses different near-threshold (NTC) biasing voltages to run its FPGA cores. The biasing voltage for each partition is roughly calculated by the proposed static schemes. However, further calibration of biasing voltage is performed by the proposed runtime scheme. To overcome the timing failure caused by NTC, the MACs with higher minimum slack are placed in lower-voltage partitions, while the MACs with lower minimum slack paths are placed in higher-voltage partitions. The proposed architecture is implemented in a commercial platform, namely Vivado with Xilinx Artix-7 FPGA and academic platform VTR with 22 nm, 45 nm and 130 nm FPGAs. Any timing error caused by NTC can be caught by the Razor flipflop used in each MAC. The proposed voltage-scaled, partitioned systolic array can save 3.1% to 11.6% of dynamic power in Vivado and VTR tools, respectively, depending on the FPGA technology, partition size, number of partitions and biasing voltages. The normalized performance and accuracy of benchmark models running on our low-power TPU are very competitive compared to existing literature.
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Matte, M. L. "Some Special Integer Partitions Generated by a Family of Functions." Trends in Computational and Applied Mathematics 24, no. 4 (November 27, 2023): 717–44. http://dx.doi.org/10.5540/tcam.2023.024.04.00717.
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In this work, inspired by Ramanujan’s fifth order Mock Theta function f1(q), we define acollection of functions and look at them as generating functions for partitions of some integer n containing at least m parts equal to each one of the numbers from 1 to its greatest part s, with no gaps.We set a two-line matrix representation for these partitions for any m ≥ 2 and collect the values of the sum of the entries in the second line of those matrices. These sums contain information about some parts of the partitions, which lead us to closed formulas for the number of partitions generated by our functions, and partition identities involving other simpler and well known partition functions.
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Lafta Ghashim Jassim, Sajida. "Numerical Analysis of Laminar Natural Convection in Square Enclosure with and without Partitions and Study Effect of pPartition on the Flow Pattern and Heat Transfer." Iraqi Journal of Chemical and Petroleum Engineering 13, no. 1 (March 30, 2012): 33–54. http://dx.doi.org/10.31699/ijcpe.2012.1.4.
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The problem of steady, laminar, natural convective flow in an square enclosure with and without partitions is considered for Rayleigh number (103-106) and Prandtl number (0.7). Vertical walls were maintained isothermal at different temperatures while horizontal walls and the partitions were insulated. The length of partition was taken constant. The number of partitions were placed on horizontal surface in staggered arrangement from (1– 3) and ratio of partition thickness (H/L= 0.033, 0.083, 0.124). The problem is formulated in terms of the vorticity-stream function procedure. A numerical solution based on a program in Fortran 90 with the finite difference method is obtained. Representative results illustrating the effects of the thickness and number of partitions on the contour maps of the streamlines and temperature are reported and discussed. In addition, the local Nusselt number is evaluated. Results show that the values of stream function (the strength of flow) in enclosure increases with the increasing Rayleigh number. As the number of partitions and thickness of partition increases, the strength of flow decreases. Mean Nusselt number increases with increasing Rayleigh number at different number of partitions. The numerical results are compared with available numerical results and experimental data and a good agreement is obtained.
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Staroletov, Sergey Mikhailovich. "A Formal Model of a Partitioned Real-Time Operating System in Promela." Proceedings of the Institute for System Programming of the RAS 32, no. 6 (2020): 49–66. http://dx.doi.org/10.15514/ispras-2020-32(6)-4.
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Real-time partitioned operating systems meet the current avionics standard of reliable software; they are capable of responding to events from devices with an expected speed, as well as sharing processor time and memory between isolated partitions. Model-based Checking is a formal verification technique in which a software model is developed and then it is automatically checked for the compliance with formal requirements. This method allows proving the correct operation of the model on all possible input data, all possible ways of processes switching and interactions. In this article, we describe a formalized model of an open-source partitioned operating system POK. We implement the model in Promela language for SPIN tool with the purposes of formal verification using the Model Checking method. The model is designed to describe the behavior of: partition and process schedulers, system calls through a software interrupt, kernel libraries for working with synchronization primitives and processes awaiting, user code which consists of several processes in different partitions that are synchronized through a semaphore. The described approach can be used to verify the correct synchronization, the proper operation of the scheduler algorithms, and the accurate data access from different partitions by introducing the corresponding requirements in the form of formulas of the linear-time temporal logic.
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BÉAL, MARIE-PIERRE, FABIO BURDERI, and ANTONIO RESTIVO. "CODING PARTITIONS OF REGULAR SETS." International Journal of Algebra and Computation 19, no. 08 (December 2009): 1011–23. http://dx.doi.org/10.1142/s0218196709005457.
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A coding partition of a set of words partitions this set into classes such that whenever a sequence, of minimal length, has two distinct factorizations, the words of these factorizations belong to the same class. The canonical coding partition is the finest coding partition that partitions the set of words in at most one unambiguous class and other classes that localize the ambiguities in the factorizations of finite sequences. We prove that the canonical coding partition of a regular set contains a finite number of regular classes and we give an algorithm for computing this partition. From this we derive a canonical decomposition of a regular monoid into a free product of finitely many regular monoids.
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Stewart, Noral. "Operable partitions - a life of experiences, observations, and testing plus comments on standards." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 3 (August 1, 2021): 3448–53. http://dx.doi.org/10.3397/in-2021-2407.
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Experiences testing operable partitions since 1986 will be reviewed including typical performance and various problems observed with both the partitions and surrounding structures. ASTM standards E557 on proper building preparation for an operable partition and E336 for the measurement of field performance will be discussed, including the 2005 revision of E336 as it affects evaluation of operable partitions.
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Chandon, Jean-Louis, and Florence Dano. "Analyses typologiques confirmatoires. Evaluation d'une partition hypothétique issue d'une étude sémiotique." Recherche et Applications en Marketing (French Edition) 12, no. 2 (June 1997): 1–22. http://dx.doi.org/10.1177/076737019701200201.
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On constate qu'il est très important d'avoir des méthodes d'évaluation des partitions afin d'évaluer les résultats des analyses typologiques. Cet article développe une méthode fondée sur des critères internes et externes permettant d'estimer l'adéquation entre les partitions devant être évaluées et les données à partir desquelles elles ont été générées. La première partie présente plusieurs critères internes et externes de validation en typologie, et les solutions retenues par le logiciel Evalu-P, conçu par le premier auteur. La seconde partie illustre les étapes de validation d'une partition hypothétique en cinq classes de consommateurs, issue des résultats d'une analyse sémiotique du discours des consommateurs sur le packaging. 43 partitions pour le riz et 54 partitions pour le shampoing ont été générées en utilisant des méthodes de classification hiérarchique et de réallocation. Ces partitions empiriques ont été évaluées par rapport à la partition hypothétique en utilisant cinq critères internes et cinq critères externes de validation.
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Amurrio, A., E. Azketa, M. Aldea, and J. J. Gutiérrez. "How windows size and number can influence the schedulability of hierarchically-scheduled time-partitioned distributed real-time systems." ACM SIGAda Ada Letters 41, no. 1 (October 28, 2022): 64–68. http://dx.doi.org/10.1145/3570315.3570319.
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Partitioning techniques are implemented in the development of safety-critical applications to ensure isolation among components. An adequate scheduling of the execution of such partitions is a key challenge so that applications meet the hard deadlines imposed. In this work, we study the effect of different partition window configuration parameters, with the aim of analyzing their impact in the worst-case response times of system tasks. This is the first step in the development of an algorithm for optimizing partition windows in hierarchically-scheduled time partitioned distributed systems.
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Andrews, George E., and Peter Paule. "MacMahon's partition analysis XII: Plane partitions." Journal of the London Mathematical Society 76, no. 3 (November 14, 2007): 647–66. http://dx.doi.org/10.1112/jlms/jdm079.
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Andrews, George E., and Jim Lawrence. "Binary partitions and binary partition polytopes." Aequationes mathematicae 91, no. 5 (May 27, 2017): 859–69. http://dx.doi.org/10.1007/s00010-017-0493-8.
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Zhao, Wanying, Christopher Y. Choi, Xinyi Du, Huiyuan Guan, Hao Li, and Zhengxiang Shi. "Effects of Ventilation Fans and Type of Partitions on the Airflow Speeds of Animal Occupied Zone and Physiological Parameters of Dairy Pre-Weaned Calves Housed Individually in a Barn." Agriculture 13, no. 5 (May 1, 2023): 1002. http://dx.doi.org/10.3390/agriculture13051002.
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Calves raised in barns are usually kept in individual pens separated by either solid or mesh partitions. To quantify the effects that the two types of partition have on airflow speed in an axial-ventilated-barn, the indoor environment of a calf barn was simulated using computational fluid dynamics (CFD) with validation accomplished by means of direct measurement. To ascertain the effects that two types of partition have on the physiological parameters and health of pre-weaned calves, 24 calves (3–11-day-olds) were selected, equally divided into four groups and sequestered as follows: calves placed in pens separated by solid partitions receiving “low-speed” or “high-speed” airflow; calves separated by mesh partitions receiving “low-speed” or “high-speed” airflow. The results of the CFD simulation showed that the percentage of airflow speed that exceeded 0.5 m s−1 at a height of 0.4 m above the floor of the animal occupied zone where calves were separated by mesh partitions was 88%, while the speed was 66–70% for calves separated by solid partitions. The duration of treatment provided to the calves in the MP-LA (mesh partitions and subjected to a low-speed airflow) and MP-HA (mesh partitions and subjected to a high-speed airflow) groups, were both lower than the SP-LA (solid partitions and subjected to a low-speed airflow) and SP-HA (solid partitions and subjected to a high-speed airflow) groups. We conclude that when the fan is operating, contact between calves separated by mesh partitions produces no negative impact on the health of calves; furthermore, this arrangement can provide a higher airflow speed than that delivered to calves raised in pens separated by solid partitions, especially to those calves in pens farther from the fans.
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Saltykov, Ivan P. "Sound insulation design of the thin partitions on the base of concentrated parameters model." Vestnik MGSU, no. 3 (March 2020): 353–67. http://dx.doi.org/10.22227/1997-0935.2020.3.353-367.
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Introduction. The theoretical and practical approach on the base of the discrete parameter's method to the acoustic insulation of the thin partitions by Candidate of Science, Prof. Zakharov A.V. is given in this issue. The method allowed to develop a logically conclusive and consistent physical airborne sound insulation model for one-layered massive and light partitions either. This issue concentrates on providing of the engineer calculation technique of the sound insula-tion for the thin partitions and, also, on comparison of the technique's results with the computations by the current normative documents.
Materials and methods. The application of the same “Mass Action Law's” formula both for the normal and the oblique noise wave's incidence on the sound isolating plate, regardless the sound waves angles, is mathematically and physically approved. The essence of the concentrated parameters, such as concentrated and reduced material's mass, is revealed. The equations of momentum conservation law and kinetic energy conservation are used to obtain the coefficient of the oscillation velocity transmission. The formulas for airborne sound insulation at the diapasons before and after the sound wave's coincidence frequency are written.
Results. The damping air property's influence on the thin partition's sound insulation is considered, and it's formulas are represented. The formulas for taking into account the reduction of sound insulation at the resonances in sound protective slab or in a partition are also given. The general equation for the thin partition's sound insulation by the method of localized (discrete) parameters are derived. The example of detailed calculation of the sound isolation of the thin asbestos-cement partition is demonstrated. The comparison between the medial three octave deviations of the sound isolation values and the experimental results in case of the SP (Russian normative document) method and in case of the introduced author's method for the different construction materials is represented.
Conclusions. The proposedsound insulation calculation method for the thin light partitions, which is based on the concentrated parameters model, gives very close to experiments results. So, it enables to find the insulation figures across the entire standard frequency range, according to the initial physical and technical materials' and constructions' features.
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Thompson, J. M., R. M. Butterfield, and K. J. Reddacliff. "Food intake, growth and body composition in Australian Merino sheep selected for high and low weaning weight 5. Adipocyte volume and number in the dissected fat partitions." Animal Production 46, no. 3 (June 1988): 395–402. http://dx.doi.org/10.1017/s0003356100019000.
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ABSTRACTThe cellular characteristics of dissected carcass (subcutaneous and intermuscular fat) and non-carcass (kidney fat, omental and mesenteric fat) fat partitions were examined at maturity in a total of 34 rams and ewes from flocks of Peppin Merino sheep selected for high (weight-plus) or low (weight-minus) weaning weight and from a randomly bred control flock. Strain and sex effects on the rate of change in adipocyte volume in each fat partition relative to the change in chemical-fat weight in that partition, were examined in 60 immature animals.Selection for high or low weaning weight had no effect on adipocyte volume in the mature animals, with the increased weight of fat in the weight-plus animals due to an increased number of adipocytes in the dissected fat partitions. Consequently, hyperplasia had a greater contribution to increases in chemical-fat weight in the weight-plus, compared with the weight-minus animals.Mature ewes had larger and fewer adipocytes in the subcutaneous and intermuscular partitions than the mature rams, whereas there was no difference between the sexes in adipocyte volume in the kidney, omental and mesenteric fat partitions. Mature ewes had fewer adipocytes than the mature rams in the subcutaneous, intermuscular, omental and mesenteric fat partitions. With the exception of the kidney fat partition, there was no sex effect on the relative contribution of hypertrophy to increases in chemical-fat weight of the dissected carcass and non-carcass fat partitions.
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HEDEN, OLOF. "A SURVEY OF THE DIFFERENT TYPES OF VECTOR SPACE PARTITIONS." Discrete Mathematics, Algorithms and Applications 04, no. 01 (March 2012): 1250001. http://dx.doi.org/10.1142/s1793830912500012.
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A vector space partition is here a collection [Formula: see text] of subspaces of a finite vector space V(n, q), of dimension n over a finite field with q elements, with the property that every non-zero vector is contained in a unique member of [Formula: see text]. Vector space partitions relate to finite projective planes, design theory and error correcting codes. In the first part of the paper I will discuss some relations between vector space partitions and other branches of mathematics. The other part of the paper contains a survey of known results on the type of a vector space partition, more precisely: the theorem of Beutelspacher and Heden on T-partitions, rather recent results of El-Zanati et al. on the different types that appear in the spaces V(n, 2), for n ≤ 8, a result of Heden and Lehmann on vector space partitions and maximal partial spreads including their new necessary condition for the existence of a vector space partition, and furthermore, I will give a theorem of Heden on the length of the tail of a vector space partition. Finally, I will also give a few historical remarks.
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Tutaş, Nesrin. "On Partitions and Arf Semigroups." Open Mathematics 17, no. 1 (May 11, 2019): 343–55. http://dx.doi.org/10.1515/math-2019-0025.
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Abstract In this study we examine some combinatorial properties of the Arf semigroup. In previous work, the author and Karakaş, Gümüşbaş defined an Arf partition of a positive integer n. Here, we continue this work and give new results on Arf partitions. In particular, we analyze the relation among an Arf partition, its Young dual diagram, and the corresponding rational Young diagram. Additionally, this study contains some results that present the relations between partitions and Arf semigroup polynomials.
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Scholtz, Clarke, Armanda Bastos, and Catherine Sole. "Do individual and combined data analyses of molecules and morphology reveal the generic status of 'Pachysoma' MacLeay (Coleoptera: Scarabaeidae)?" Insect Systematics & Evolution 38, no. 3 (2007): 311–30. http://dx.doi.org/10.1163/187631207788754411.
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AbstractScarabaeus (Pachysoma) comprises 13 flightless dung beetle species endemic to the west coast of southern Africa that are biologically unique and have a variable taxonomic history at the generic level. Initially considered a valid genus Pachysoma was subsequently synonymised with the genus Scarabaeus and later assigned sub-generic status within this genus. In an attempt to resolve past taxonomic inconsistencies, morphological and molecular data partitions, and combinations thereof, were analysed and compared across different phylogenetic inference methods. Trees obtained from the individual datasets which comprised 64 morphological characters and 1197 nucleotide sites of the mitochondrial Cytochrome Oxidase I (COI) gene, were less well-resolved than those obtained from analyses in which the data partitions were combined whilst Bayesian inference generally out-performed parsimony. However, both the individual and combined data partitions, irrespective of the method of analysis, confirmed the monophyly of the Pachysoma lineage. The relative contribution of each data partition to individual nodes as assessed by positive partitioned Bremer support values was 6:5:4 for the molecular:combined:morphological data partitions. However, in terms of contribution to the resolution of terminal versus internal nodes, the morphological dataset made proportionally the greatest contribution and was crucial for recovering a sister relationship of Pachysoma to Scarabaeus, i.e. a generic level, rather than a sub-generic one. This together with the monophyly of the Pachysoma lineage across all methods of analysis and data partitions as well as the unique morphology and biology of its constituent species warrants reinstatement of Pachysoma to its former full generic status.
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Desfontaines, Damien, James Voss, Bryant Gipson, and Chinmoy Mandayam. "Differentially private partition selection." Proceedings on Privacy Enhancing Technologies 2022, no. 1 (November 20, 2021): 339–52. http://dx.doi.org/10.2478/popets-2022-0017.
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Abstract Many data analysis operations can be expressed as a GROUP BY query on an unbounded set of partitions, followed by a per-partition aggregation. To make such a query differentially private, adding noise to each aggregation is not enough: we also need to make sure that the set of partitions released is also differentially private. This problem is not new, and it was recently formally introduced as differentially private set union [14]. In this work, we continue this area of study, and focus on the common setting where each user is associated with a single partition. In this setting, we propose a simple, optimal differentially private mechanism that maximizes the number of released partitions. We discuss implementation considerations, as well as the possible extension of this approach to the setting where each user contributes to a fixed, small number of partitions.
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Sankhavara, C. D., and H. J. Shukla. "Influence of Partition Length on Natural Convection in Partially Divided Square Enclosure." Journal of Heat Transfer 129, no. 11 (April 19, 2007): 1592–99. http://dx.doi.org/10.1115/1.2764087.
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Numerical investigation is carried out for natural convection in square enclosures consisting of partitions protruding from the end walls with different thermal boundary conditions at the end walls and partitions. The vertical walls were maintained isothermal at different temperatures. The Rayleigh number varies from 104 to 106 and the Prandtl number is 0.71. The thickness of the partition is fixed and is equal to one-tenth of the width of the enclosure. Their nondimensional length (l∕H) varies from 0 (a nonpartitioned enclosure) to 0.5 (two separate enclosures). A good agreement was found between the results in the present study and those published previously. The partitions were found to significantly influence the convective heat transfer. The average Nusselt number is less in the presence of partitions, and it decreases with increasing partition length (l∕H) from 0 to 0.5.
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Bakir, Ilke, Natashia Boland, Brian Dandurand, and Alan Erera. "Sampling Scenario Set Partition Dual Bounds for Multistage Stochastic Programs." INFORMS Journal on Computing 32, no. 1 (January 2020): 145–63. http://dx.doi.org/10.1287/ijoc.2018.0885.
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We consider multistage stochastic programming problems in which the random parameters have finite support, leading to optimization over a finite scenario set. There has been recent interest in dual bounds for such problems, of two types. One, known as expected group subproblem objective (EGSO) bounds, require solution of a group subproblem, which optimizes over a subset of the scenarios, for all subsets of the scenario set that have a given cardinality. Increasing the subset cardinality in the group subproblem improves bound quality, (EGSO bounds form a hierarchy), but the number of group subproblems required to compute the bound increases very rapidly. Another is based on partitions of the scenario set into subsets. Combining the values of the group subproblems for all subsets in a partition yields a partition bound. In this paper, we consider partitions into subsets of (nearly) equal cardinality. We show that the expected value of the partition bound over all such partitions also forms a hierarchy. To make use of these bounds in practice, we propose random sampling of partitions and suggest two enhancements to the approach: sampling partitions that align with the multistage scenario tree structure and use of an auxiliary optimization problem to discover new best bounds based on the values of group subproblems already computed. We establish the effectiveness of these ideas with computational experiments on benchmark problems. Finally, we give a heuristic to save computational effort by ceasing computation of a partition partway through if it appears unpromising.
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Jakimczuk, Rafael. "Restricted partitions." International Journal of Mathematics and Mathematical Sciences 2004, no. 36 (2004): 1893–96. http://dx.doi.org/10.1155/s0161171204306502.
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We prove a known partitions theorem by Bell in an elementary and constructive way. Our proof yields a simple recursive method to compute the corresponding Sylvester polynomials for the partition. The previous known methods to obtain these polynomials are in general not elementary.
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Pąk, Karol. "Euler’s Partition Theorem." Formalized Mathematics 23, no. 2 (June 1, 2015): 93–99. http://dx.doi.org/10.1515/forma-2015-0009.
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Abstract In this article we prove the Euler’s Partition Theorem which states that the number of integer partitions with odd parts equals the number of partitions with distinct parts. The formalization follows H.S. Wilf’s lecture notes [28] (see also [1]). Euler’s Partition Theorem is listed as item #45 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/ [27].
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Hoshikawa, Kyosuke, Takuma Yuri, Hugo Giambini, and Yoshiro Kiyoshige. "Shoulder scaption is dependent on the behavior of the different partitions of the infraspinatus muscle." Surgical and Radiologic Anatomy 43, no. 5 (January 19, 2021): 653–59. http://dx.doi.org/10.1007/s00276-020-02674-6.
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Abstract Purpose The purpose of this study was to investigate if the three partitions (superior, middle, and inferior partitions) of the infraspinatus muscle previously described in anatomical studies will present different behavior during scapular plane abduction (scaption) as described using shear-wave elastography, especially during initial range of motion. Methods Eight volunteers held their arm against gravity 15° intervals from 30° to 150° in scaption. Shear-wave elastography was implemented at each position to measure shear modulus at rest and during muscle contraction, as a surrogate for muscle stiffness, of each partition. Muscle activity was defined as the difference in stiffness values between the resting positions and those during muscle contraction (ΔE = stiffness at contraction—stiffness at rest). Results The activity value for the middle partition was 25.1 ± 10.8 kPa at 30° and increased up to 105° (52.2 ± 10.8 kPa), with a subsequent decrease at larger angle positions (p < .001). The superior partition showed a flatter and constant behavior with smaller activity values except at higher angles (p < .001). Peak activity values for the superior partition were observed at 135° (23.0 ± 12.0 kPa). Increase activity for inferior partition began at 60° and showed a peak at 135° (p < .001; 32.9 ± 13.8 kPa). Conclusion Stiffness measured using shear-wave elastography in each partition of the infraspinatus muscle demonstrated different behavior between these partitions during scaption. The middle partition generated force throughout scaption, while the superior and inferior partitions exerted force at end range.
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Wang, Lei, Bo Yu, Fang Chen, Congrong Li, Bin Li, and Ning Wang. "A Cluster-Based Partition Method of Remote Sensing Data for Efficient Distributed Image Processing." Remote Sensing 14, no. 19 (October 5, 2022): 4964. http://dx.doi.org/10.3390/rs14194964.
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Data stream partitioning is a fundamental and important mechanism for distributed systems. However, use of an inappropriate partition scheme may generate a data skew problem, which can influence the execution efficiency of many application tasks. Processing of skewed partitions usually takes a longer time, need more computational resources to complete the task and can even become a performance bottleneck. To solve such data skew issues, this paper proposes a novel partition method to divide on demand the image tiles uniformly into partitions. The partitioning problem is then transformed into a uniform and compact clustering problem whereby the image tiles are regarded as image pixels without spectrum and texture information. First, the equal area conversion principle was used to select the seed points of the partitions and then the image tiles were aggregated in an image layout, thus achieving an initial partition scheme. Second, the image tiles of the initial partition were finely adjusted in the vertical and horizontal directions in separate steps to achieve a uniform distribution among the partitions. Two traditional partition methods were adopted to evaluate the efficiency of the proposed method in terms of the image segmentation testing, data shuffle testing, and image clipping testing. The results demonstrated that the proposed partition method solved the data skew problem observed in the hash partition method. In addition, this method is designed specifically for processing of image tiles and makes the related processing operations for large-scale images faster and more efficient.
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MERCA, MIRCEA. "Distinct partitions and overpartitions." Carpathian Journal of Mathematics 38, no. 1 (November 15, 2021): 149–58. http://dx.doi.org/10.37193/cjm.2022.01.12.
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In 1963, Peter Hagis, Jr. provided a Hardy-Ramanujan-Rademacher-type convergent series that can be used to compute an isolated value of the partition function $Q(n)$ which counts partitions of $n$ into distinct parts. Computing $Q(n)$ by this method requires arithmetic with very high-precision approximate real numbers and it is complicated. In this paper, we investigate new connections between partitions into distinct parts and overpartitions and obtain a surprising recurrence relation for the number of partitions of $n$ into distinct parts. By particularization of this relation, we derive two different linear recurrence relations for the partition function $Q(n)$. One of them involves the thrice square numbers and the other involves the generalized octagonal numbers. The recurrence relation involving the thrice square numbers provide a simple and fast computation of the value of $Q(n)$. This method uses only (large) integer arithmetic and it is simpler to program. Infinite families of linear inequalities involving partitions into distinct parts and overpartitions are introduced in this context.
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MULZER, WOLFGANG, and YANNIK STEIN. "ALGORITHMS FOR TOLERANT TVERBERG PARTITIONS." International Journal of Computational Geometry & Applications 24, no. 04 (December 2014): 261–73. http://dx.doi.org/10.1142/s0218195914600073.
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Let P be a d-dimensional n-point set. A partition [Formula: see text] of P is called a Tverberg partition if the convex hulls of all sets in [Formula: see text] intersect in at least one point. We say that [Formula: see text] is t-tolerant if it remains a Tverberg partition after deleting any t points from P. Soberón and Strausz proved that there is always a t-tolerant Tverberg partition with ⌈n/(d + 1)(t + 1)⌉ sets. However, no nontrivial algorithms for computing or approximating such partitions have been presented so far. For d ≤ 2, we show that the Soberón-Strausz bound can be improved, and we show how the corresponding partitions can be found in polynomial time. For d ≥ 3, we give the first polynomial-time approximation algorithm by presenting a reduction to the regular Tverberg problem (with no tolerance). Finally, we show that it is coNP-complete to determine whether a given Tverberg partition is t-tolerant.
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Gentil-Nunes, Pauxy. "Reading Textural Functions, Instrumental Techniques, and Space Through Partition Complexes." MusMat: Brazilian Journal of Music and Mathematics IV, no. 2 (December 28, 2020): 80–97. http://dx.doi.org/10.46926/musmat.2020v4n2.80-97.
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Partitional complexes are sets of discrete textural configurations (called shortly of partitions in Partition Analysis) that successfully interact to construct a global textural structure. This textural mode is called the Textural Proposal of a piece, where referential partitions (those that represent the main features of textural configurations in the excerpt) stand out. This conceptual environment, developed in musical texture formalization through observation and musical repertoire analysis, is now applied to musical practice. In the present work, we highlight three of these situations. The first one deals with the creative flow (compositional process) and its relation with textural planning. The second observes how these same textural functions condition the body's physical coupling to the instrument (fingers, hands, pedals, instrumentation). Finally, just as an introduction, we envisage some spatial relations, involving instrument distribution on stage, emphasizing historical concert music.
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Gordon, A. D. "Partitions of Partitions." Journal of Classification 15, no. 2 (February 1, 1998): 265–85. http://dx.doi.org/10.1007/s003579900034.
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Salenger, Kristin. "Study of various wood stud partitions with various gypsum board and proprietary acoustical sound insulation products." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 1 (August 1, 2021): 5838–46. http://dx.doi.org/10.3397/in-2021-3307.
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Wood stud construction is common in residential and hospitality buildings in some parts of the U.S.; however, there is a deficiency of field-tested sound insulation performance of partitions constructed with wood studs that are spaced closer than 16" on center. This study presents the sound isolation measurement results of a set of fifteen partitions within an existing facility that has been experiencing repeated complaints of poor acoustic privacy between horizontally adjacent spaces. The tested partition types varied between single stud, double stud, and single studs with resilient channel constructions. The walls had four materials of varying combinations applied, including 19/32" OSB, Type X gypsum board, proprietary enhanced gypsum board, and proprietary mass loaded vinyl. It was shown that the partition with enhanced gypsum board performed better than the same partition with Type X, the double stud partition performed lower than expected, and the addition of mass loaded vinyl to both double and single stud partitions did not affect the ASTC rating, among other findings.
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Lambkin, Christine L. "Partitioned Bremer support localises significant conflict in bee flies (Diptera : Bombyliidae : Anthracinae)." Invertebrate Systematics 18, no. 4 (2004): 351. http://dx.doi.org/10.1071/is04004.
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Partitioned Bremer support examination of combined cladistic analyses indicates nodes at which the support from the partitions differs, and also identifies the location of character disagreement generated by the combination of data matrices. Significant character incongruence was found between mtDNA sequence data and adult morphological characters from three tribes of bee flies (Diptera : Bombyliidae : Anthracinae : Villini, Anthracini, Exoprosopini). Partitioned Bremer support quantitatively reveals the location of significant conflict between characters from the different partitions. Examination of several partitioned support measures show which characters contributed to the disagreement at that node. A very high value of increased support at another node occurred upon combination of the data partitions and was also examined using these support measures.
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FU, SHISHUO. "COMBINATORIAL PROOF OF ONE CONGRUENCE FOR THE BROKEN 1-DIAMOND PARTITION AND A GENERALIZATION." International Journal of Number Theory 07, no. 01 (February 2011): 133–44. http://dx.doi.org/10.1142/s1793042111004022.
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In one of their recent collaborative papers, Andrews and Paule continue their study of partition functions via MacMahon's Partition Analysis by considering partition functions associated with directed graphs which consist of chains of diamond shape. They prove a congruence related to one of these partition functions and conjecture a number of similar congruence results. In this note, we reprove this congruence by constructing an explicit way to group partitions. Then we keep the essence of the method and manage to apply it to a different kind of plane partitions to get more general results and several other congruences.