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Journal articles on the topic 'Binary vectors'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Fei, Sheng-wei. "Fault diagnosis of bearing based on relevance vector machine classifier with improved binary bat algorithm for feature selection and parameter optimization." Advances in Mechanical Engineering 9, no. 1 (2017): 168781401668529. http://dx.doi.org/10.1177/1687814016685294.

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In this article, fault diagnosis of bearing based on relevance vector machine classifier with improved binary bat algorithm is proposed, and the improved binary bat algorithm is used to select the appropriate features and kernel parameter of relevance vector machine. In the improved binary bat algorithm, the new velocities updating method of the bats is presented in order to ensure the decreasing of the probabilities of changing their position vectors’ elements when the position vectors’ elements of the bats are equal to the current best location’s element, and the increasing of the probabilit

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2

Arai, Kenichi, and Hiroyuki Okazaki. "N-Dimensional Binary Vector Spaces." Formalized Mathematics 21, no. 2 (2013): 75–81. http://dx.doi.org/10.2478/forma-2013-0008.

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Summary The binary set {0, 1} together with modulo-2 addition and multiplication is called a binary field, which is denoted by F2. The binary field F2 is defined in [1]. A vector space over F2 is called a binary vector space. The set of all binary vectors of length n forms an n-dimensional vector space Vn over F2. Binary fields and n-dimensional binary vector spaces play an important role in practical computer science, for example, coding theory [15] and cryptology. In cryptology, binary fields and n-dimensional binary vector spaces are very important in proving the security of cryptographic s

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3

Komori, Toshiyuki, Teruyuki Imayama, Norio Kato, Yuji Ishida, Jun Ueki, and Toshihiko Komari. "Current Status of Binary Vectors and Superbinary Vectors." Plant Physiology 145, no. 4 (2007): 1155–60. http://dx.doi.org/10.1104/pp.107.105734.

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4

Tissier, Julien, Christophe Gravier, and Amaury Habrard. "Near-Lossless Binarization of Word Embeddings." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 7104–11. http://dx.doi.org/10.1609/aaai.v33i01.33017104.

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Word embeddings are commonly used as a starting point in many NLP models to achieve state-of-the-art performances. However, with a large vocabulary and many dimensions, these floating-point representations are expensive both in terms of memory and calculations which makes them unsuitable for use on low-resource devices. The method proposed in this paper transforms real-valued embeddings into binary embeddings while preserving semantic information, requiring only 128 or 256 bits for each vector. This leads to a small memory footprint and fast vector operations. The model is based on an autoenco

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5

Niederreiter, Harald, Joël Rivat, and András Sárközy. "Pseudorandom sequences of binary vectors." Acta Arithmetica 133, no. 2 (2008): 109–25. http://dx.doi.org/10.4064/aa133-2-2.

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6

Steinbach, Bernd, and Christian Posthoff. "Set-based SAT-solving." Facta universitatis - series: Electronics and Energetics 20, no. 3 (2007): 395–414. http://dx.doi.org/10.2298/fuee0703395s.

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The 3-SAT problem is one of the most important and interesting NP-complete problems with many applications in different areas. In several previous papers we showed the use of ternary vectors and set-theoretic considerations as well as binary codings and bit-parallel vector operations in order to solve this problem. Lists of orthogonal ternary vectors have been the main data structure, the intersection of ternary vectors (representing sets of binary solution candidates) was the most important set theoretic operation. The parallelism of the solution process has been established on the register l

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7

Bouyukliev, Iliya, and Valentin Bakoev. "Efficient Computing of some Vector Operations over GF(3) and GF(4)." Serdica Journal of Computing 2, no. 2 (2008): 137–44. http://dx.doi.org/10.55630/sjc.2008.2.137-144.

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The problem of efficient computing of the affine vector operations (addition of two vectors and multiplication of a vector by a scalar over GF (q)), and also the weight of a given vector, is important for many problems in coding theory, cryptography, VLSI technology etc. In this paper we propose a new way of representing vectors over GF (3) and GF (4) and we describe an efficient performance of these affine operations. Computing weights of binary vectors is also discussed.

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8

Journal, Baghdad Science. "An algorithm for binary codebook design based on the average bitmap replacement error (ABPRE)." Baghdad Science Journal 8, no. 2 (2011): 684–88. http://dx.doi.org/10.21123/bsj.8.2.684-688.

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In this paper, an algorithm for binary codebook design has been used in vector quantization technique, which is used to improve the acceptability of the absolute moment block truncation coding (AMBTC) method. Vector quantization (VQ) method is used to compress the bitmap (the output proposed from the first method (AMBTC)). In this paper, the binary codebook can be engender for many images depending on randomly chosen to the code vectors from a set of binary images vectors, and this codebook is then used to compress all bitmaps of these images. The chosen of the bitmap of image in order to comp

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9

Hameed, Maha A. "An algorithm for binary codebook design based on the average bitmap replacement error (ABPRE)." Baghdad Science Journal 8, no. 2 (2011): 684–88. http://dx.doi.org/10.21123/bsj.2011.8.2.684-688.

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In this paper, an algorithm for binary codebook design has been used in vector quantization technique, which is used to improve the acceptability of the absolute moment block truncation coding (AMBTC) method. Vector quantization (VQ) method is used to compress the bitmap (the output proposed from the first method (AMBTC)). In this paper, the binary codebook can be engender for many images depending on randomly chosen to the code vectors from a set of binary images vectors, and this codebook is then used to compress all bitmaps of these images. The chosen of the bitmap of image in order to comp

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10

Yeh, Wei-Chang, Guangyi Yang, and Chia-Ling Huang. "A New Node-Based Algorithm for Identifying the Complete Minimal Cut Set." Electronics 13, no. 3 (2024): 603. http://dx.doi.org/10.3390/electronics13030603.

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The binary-state network, which is fundamental to several modern systems, only operates in two states: operational or inoperable. Network reliability is crucial in its planning, design, and evaluation, with the minimal cut (MC) being a cornerstone for reliability algorithms. A recursive binary-addition-tree algorithm (BAT) excels in its capacity to promptly eliminate infeasible vectors. However, it relies on a depth-first search (DFS), a technique surpassed in efficiency by BAT. To the best of our knowledge, no exploration into a recursive MC-based BAT for MC identification has been undertaken

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11

Kozyra, Paweł Marcin. "Analysis of minimal path and cut vectors in multistate monotone systems and use it for detection of binary type multistate monotone systems." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 234, no. 5 (2020): 686–95. http://dx.doi.org/10.1177/1748006x20922083.

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Theorem specifying how all minimal cut (path) vectors to level j can be obtained from all minimal path (cut) vectors to level j in any multistate monotone system is proven. Characterizations of binary type multistate monotone systems and binary type multistate strongly coherent systems by minimal cut and path vectors and corresponding to them, binary type cut and path sets are also demonstrated.

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12

Mustafa, Adnan A. "Two Probabilistic Models for Quick Dissimilarity Detection of Big Binary Data." WSEAS TRANSACTIONS ON MATHEMATICS 20 (May 19, 2021): 244–54. http://dx.doi.org/10.37394/23206.2021.20.25.

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The task of data matching arises frequently in many aspects of science. It can become a time consuming process when the data is being matched to a huge database consisting of thousands of possible candidates, and the goal is to find the best match. It can be even more time consuming if the data are big (> 100 MB). One approach to reducing the time complexity of the matching process is to reduce the search space by introducing a pre-matching stage, where very dissimilar data are quickly removed. In this paper we focus our attention to matching big binary data. In this paper we present two pr

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13

Grošek, Otokar, and Viliam Hromada. "Rotation-Equivalence Classes of Binary Vectors." Tatra Mountains Mathematical Publications 67, no. 1 (2016): 93–98. http://dx.doi.org/10.1515/tmmp-2016-0033.

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Abstract In this paper we study equivalence classes of binary vectors with regards to their rotation by using an algebraic approach based on the theory of linear feedback shift registers. We state the necessary and sufficient condition for existence of an equivalence class with given cardinality and provide two formulas. The first represents the sharp distribution of cardinalities for given length and Hamming weight of binary vectors and the second enables us to determine the number of different classes with the same cardinality.

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14

Lee, Lan-Ying, and Stanton B. Gelvin. "T-DNA Binary Vectors and Systems." Plant Physiology 146, no. 2 (2008): 325–32. http://dx.doi.org/10.1104/pp.107.113001.

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15

Rachkovskij, D. A. "Formation of Similarity-Reflecting Binary Vectors with Random Binary Projections." Cybernetics and Systems Analysis 51, no. 2 (2015): 313–23. http://dx.doi.org/10.1007/s10559-015-9723-z.

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16

Gui, Hairen, Ke Tang, Zheng Shan, et al. "AAPFE: Aligned Assembly Pre-Training Function Embedding for Malware Analysis." Electronics 11, no. 6 (2022): 940. http://dx.doi.org/10.3390/electronics11060940.

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The use of natural language processing to analyze binary data is a popular research topic in malware analysis. Embedding binary code into a vector is an important basis for building a binary analysis neural network model. Current solutions focus on embedding instructions or basic block sequences into vectors with recurrent neural network models or utilizing a graph algorithm on control flow graphs or annotated control flow graphs to generate binary representation vectors. In malware analysis, most of these studies only focus on the single structural information of the binary and rely on one co

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17

Lu, Hui-Juan, Xue-Rong Zhou, Zhu-Xun Gong, and Narayana M. Upadhyaya. "Generation of selectable marker-free transgenic rice using double right-border (DRB) binary vectors." Functional Plant Biology 28, no. 3 (2001): 241. http://dx.doi.org/10.1071/pp00129.

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Currently employed transformation systems require selectable marker genes encoding antibiotic or herbicide resistance, along with the gene of interest (GOI), to select transformed cells from among a large population of untransformed cells. The continued presence of these selectable markers, especially in food crops such as rice (Oryza sativa L.), is of increasing public concern. Techniques based on DNA recombination and Agrobacterium-mediated co-transformation with two binary vectors in a single or two different Agrobacterium strains, or with super-binary vectors carrying two sets of T-DNA bor

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18

Bai, Xue Liang, Dan Wang, Ning Ning Liu, et al. "Construction of Two Vectors for a Bypass of Monocotyledon Plants Photorespiration." Advanced Materials Research 340 (September 2011): 351–56. http://dx.doi.org/10.4028/www.scientific.net/amr.340.351.

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In order to modify the photorespiration of monocotyledonous crops, we aimed to construct vectors that will be used to introduce a bypass to the native photorespiration pathway. Firstly, we cloned the encoding sequences of glyoxylate carboligase (GCL) and tartronic semialdehyde reductase (TSR) fromE. coli, glycolate dehydrogenase (GDH) fromArabidopsis thalianaand chloroplast transit peptide (cTP) from rice. Then we constructed a universal vector pEXP harboring the encoding sequence of cTP for targeting a protein into chloroplast. By insertion of these three encoding sequences into the universal

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19

Skliarova, Iouliia, and Valeri Skliarov. "Hardware accelerators for processing clusters in binary vectors." ITM Web of Conferences 60 (2024): 00010. http://dx.doi.org/10.1051/itmconf/20246000010.

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The paper suggests fast hardware accelerators for discovering clusters of zeros and/or ones in binary vectors. Any cluster is composed of successive bits with the same value (either 1 or 0). Search for such segments is required in many practical problems, for example, coding, data, and image processing. The proposed solutions enable, for a given vector, answering such questions as how many one/zero clusters can be found; what is the largest number of consecutive ones/zeros; what is the number of clusters having k consecutive ones/zeros; is the vector only composed of segments with exactly k co

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20

CALKIN, NEIL J. "Dependent Sets of Constant Weight Binary Vectors." Combinatorics, Probability and Computing 6, no. 3 (1997): 263–71. http://dx.doi.org/10.1017/s0963548397003040.

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21

Upadhyaya, Narayana M., Brian Surin, Kerrie Ramm, et al. "Agrobacterium-mediated transformation of Australian rice cultivars Jarrah and Amaroo using modified promoters and selectable markers." Functional Plant Biology 27, no. 3 (2000): 201. http://dx.doi.org/10.1071/pp99078.

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We report the first successfulAgrobacterium-mediated transformation of Australian elite rice cultivars, Jarrah and Amaroo, using binary vectors with our improved promoters and selectable markers. Calli derived from mature embryos were used as target tissues. The binary vectors contained hph(encoding hygromycin resistance) or bar (encoding herbicide resistance) as the selectable marker gene and uidA (gus) or sgfpS65T as the reporter gene driven by different promoters. Use of Agrobacterium strain AGL1 carrying derivatives of an improved binary vector pWBVec8, wherein the CaMV35S driven hph gene

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22

Tran, Van Tuan, Thi Binh Xuan Loc Do, Thi Khanh Linh Bui, et al. "Evaluation of the effectiveness of RNA silencing in the filamentous fungus Aspergillus niger using a binary vector integrated with Gateway recombination cloning technology." Ministry of Science and Technology, Vietnam 65, no. 6 (2023): 20–25. http://dx.doi.org/10.31276/vjst.65(6).20-25.

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The filamentous fungus Aspergillus niger is widely employed in the production of citric acid and some industrial enzymes such as phytase, glucoamylase, and glucose oxidase. Currently, several genetic modification tools have been developed and applied to this fungal species. However, the RNA silencing technique is less used for A. niger. In the present study, an RNA silencing binary vector integrated with the Gateway recombination cloning technology was evaluated in A. niger. The integration of Gateway recombination cloning technology in binary vectors for rapid generation of hairpin RNA struct

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23

Piestrak, S. J. "Efficient Hamming weight comparators of binary vectors." Electronics Letters 43, no. 11 (2007): 611. http://dx.doi.org/10.1049/el:20070141.

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24

Horn, D. "Frustrated spin Hamiltonians with binary input vectors." Physical Review A 33, no. 4 (1986): 2595–601. http://dx.doi.org/10.1103/physreva.33.2595.

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25

Quiroz Mercado, Job Isaias, Ricardo Barrón Fernández, and Marco Antonio Ramírez Salinas. "Exploring Storing Capacity of Hyperdimensional Binary Vectors." Research in Computing Science 148, no. 10 (2019): 375–82. http://dx.doi.org/10.13053/rcs-148-10-31.

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26

Kung, Joseph P. S. "Minimal blocks of binary even-weight vectors." Linear Algebra and its Applications 416, no. 2-3 (2006): 288–97. http://dx.doi.org/10.1016/j.laa.2005.11.014.

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27

Kushilevitz, Eyal, Nathan Linial, Yuri Rabinovich, and Michael Saks. "Witness sets for families of binary vectors." Journal of Combinatorial Theory, Series A 73, no. 2 (1996): 376–80. http://dx.doi.org/10.1016/s0097-3165(96)80015-x.

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28

Lee, Sichul, Jong Seong Jeon, Ki Hong Jung, and Gynheung An. "Binary vectors for efficient transformation of rice." Journal of Plant Biology 42, no. 4 (1999): 310–16. http://dx.doi.org/10.1007/bf03030346.

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29

Gyllenberg, Mats, Timo Koski, and Martin Verlaan. "Classification of Binary Vectors by Stochastic Complexity." Journal of Multivariate Analysis 63, no. 1 (1997): 47–72. http://dx.doi.org/10.1006/jmva.1997.1687.

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30

Dor, Avner. "The Greedy Search Algorithm on Binary Vectors." Journal of Algorithms 27, no. 1 (1998): 42–60. http://dx.doi.org/10.1006/jagm.1997.0893.

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31

Watson, Eleanor, Minh Nguyen, Sarah Pan, and Shujun Zhang. "Choice Vectors: Streamlining Personal AI Alignment Through Binary Selection." Multimodal Technologies and Interaction 9, no. 3 (2025): 22. https://doi.org/10.3390/mti9030022.

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Value alignment for AI is not “one-size-fits-all”: even polite and friendly models can still fail to represent individual user contexts and preferences, and local cultural norms. This paper presents a modular workflow for personal fine-tuning, synthesizing four core components from our previous research: (1) robust vectorization of user values and preferences, (2) a binary choice user interface (UI) approach to capturing those preferences with minimal cognitive load, (3) contrastive activation methods for steering large language models (LLMs) via difference vectors, and (4) knowledge graph int

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32

Nguyen, Duc Manh, and Sunghwan Kim. "A novel construction for quantum stabilizer codes based on binary formalism." International Journal of Modern Physics B 34, no. 08 (2020): 2050059. http://dx.doi.org/10.1142/s0217979220500599.

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In this research, we propose a novel construction of quantum stabilizer code based on a binary formalism. First, from any binary vector of even length, we generate the parity-check matrix of the quantum code from a set composed of elements from this vector and its relations by shifts via subtraction and addition. We prove that the proposed matrices satisfy the condition constraint for the construction of quantum codes. Finally, we consider some constraint vectors which give us quantum stabilizer codes with various dimensions and a large minimum distance with code length from six to twelve digi

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33

Rohde, Douglas L. T. "Methods for Binary Multidimensional Scaling." Neural Computation 14, no. 5 (2002): 1195–232. http://dx.doi.org/10.1162/089976602753633457.

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Multidimensional scaling (MDS) is the process of transforming a set of points in a high-dimensional space to a lower-dimensional one while preserving the relative distances between pairs of points. Although effective methods have been developed for solving a variety of MDS problems, they mainly depend on the vectors in the lower-dimensional space having real-valued components. For some applications, the training of neural networks in particular, it is preferable or necessary to obtain vectors in a discrete, binary space. Unfortunately, MDS into a low-dimensional discrete space appears to be a

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34

HEUBERGER, CLEMENS, and SARA KROPF. "Analysis of the Binary Asymmetric Joint Sparse Form." Combinatorics, Probability and Computing 23, no. 6 (2014): 1087–113. http://dx.doi.org/10.1017/s0963548314000352.

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We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight,i.e., the number of non-zero digit vectors. This leads to efficient linear combination algorithms in abelian groups, which are used in elliptic curve cryptography, for instance.If the digit set is a set of contiguous integers containing zero, a special syntactical condition is known to minimize the weight. We analyse the optimal weight of all non-negative integer vectors with maximum entry less thanN. The expectation and the variance are given with a main term and a p

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35

Chen, Chunxian, Qifa Zheng, Xu Xiang, et al. "Development of pGreen-derived GFP Binary Vectors for Citrus Transformation." HortScience 42, no. 1 (2007): 7–10. http://dx.doi.org/10.21273/hortsci.42.1.7.

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Eight new green fluorescent protein (GFP) binary vectors were developed by inserting gfp reporter gene cassettes into pGreen vectors. We chose one of them, pG52KF, with the nptII selection and gfp reporter gene and one recombinant construct, pG52KFp, for a preliminary evaluation in citrus using Agrobacterium-mediated transformation. High-transformation efficiency was observed, whereas green fluorescence greatly facilitated the early in vivo screening and categorizing of the transformants. These pGreen-derived GFP binary vectors, freely available on request, provide more and flexible options fo

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36

CHEN, RONG-CHANG, TUNG-SHOU CHEN, and CHIH-CHIANG LIN. "A NEW BINARY SUPPORT VECTOR SYSTEM FOR INCREASING DETECTION RATE OF CREDIT CARD FRAUD." International Journal of Pattern Recognition and Artificial Intelligence 20, no. 02 (2006): 227–39. http://dx.doi.org/10.1142/s0218001406004624.

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Recently, a new personalized model has been developed to prevent credit card fraud. This model is promising; however, there remains some problems. Existing approaches cannot identify well credit card frauds from few data with skewed distributions. This paper proposes to address the problem using a binary support vector system (BSVS). The proposed BSVS is based on the support vectors in the support vector machines (SVM) and the genetic algorithm (GA) is employed to select support vectors. To obtain a high true negative rate, self-organizing mapping (SOM) is first employed to estimate the distri

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37

Ren, Bo Yan, Zheng Qin, and Feng Fei Zhao. "Optional Feature Vector Generation for Linear Value Function Approximation with Binary Features." Advanced Materials Research 756-759 (September 2013): 3967–71. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.3967.

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Linear value function approximation with binary features is important in the research of Reinforcement Learning (RL). When updating the value function, it is necessary to generate a feature vector which contains the features that should be updated. In high dimensional domains, the generation process will take lot more time, which reduces the performance of algorithm a lot. Hence, this paper introduces Optional Feature Vector Generation (OFVG) algorithm as an improved method to generate feature vectors that can be combined with any online, value-based RL method that uses and expands binary feat

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38

Iwaszkiewicz, Jan, Adam Muc, and Agata Bielecka. "Polar Voltage Space Vectors of the Six-Phase Two-Level VSI." Energies 15, no. 8 (2022): 2763. http://dx.doi.org/10.3390/en15082763.

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The paper recommends polar voltage space vectors of the six-phase and two-level inverter as a useful mathematical tool for vector control of the inverter. The inverter model is described using three mathematical tools: analytic expressions, voltage state, and space vectors. The analytic formulas allow for the determination of elementary physical inverter quantities: current and voltage. The state voltage vectors make it easy to define phase voltage distribution in every possible state of the inverter and voltage space vectors are the most important tool used for inverters’ control. The space v

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39

Jen-Chun Chang, Rong-Jaye Chen, T. Klove, and Shi-Chun Tsai. "Distance-preserving mappings from binary vectors to permutations." IEEE Transactions on Information Theory 49, no. 4 (2003): 1054–59. http://dx.doi.org/10.1109/tit.2003.809507.

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40

Jen-Chun Chang. "Distance-increasing mappings from binary vectors to permutations." IEEE Transactions on Information Theory 51, no. 1 (2005): 359–63. http://dx.doi.org/10.1109/tit.2004.839527.

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41

GRITSENKO, Volodymyr, A. RACHKOVSKIJ, A. FROLOV, R. GAYLER, D. KLEYKO, and E. OSIPOV. "Neural Autoassociative Memories for Binary Vectors: A Survey." Kibernetika i vyčislitelʹnaâ tehnika 2017, no. 2(188) (2017): 5–35. http://dx.doi.org/10.15407/kvt188.02.005.

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42

Copelli, Mauro, and Christian Van den Broeck. "Unsupervised learning of binary vectors: A Gaussian scenario." Physical Review E 61, no. 6 (2000): 6971–80. http://dx.doi.org/10.1103/physreve.61.6971.

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43

Hellens, Roger, Philip Mullineaux, and Harry Klee. "Technical Focus:A guide to Agrobacterium binary Ti vectors." Trends in Plant Science 5, no. 10 (2000): 446–51. http://dx.doi.org/10.1016/s1360-1385(00)01740-4.

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44

Apostol, Tom M. "Binary vectors with prescribed subsets of consecutive ones." Journal of Combinatorial Theory, Series A 47, no. 2 (1988): 176–90. http://dx.doi.org/10.1016/0097-3165(88)90017-9.

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45

Aharoni, R., G. T. Herman, and A. Kuba. "Binary vectors partially determined by linear equation systems." Discrete Mathematics 171, no. 1-3 (1997): 1–16. http://dx.doi.org/10.1016/s0012-365x(96)00068-4.

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46

Rachkovskij, D. A. "Binary Vectors for Fast Distance and Similarity Estimation." Cybernetics and Systems Analysis 53, no. 1 (2017): 138–56. http://dx.doi.org/10.1007/s10559-017-9914-x.

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47

Lin, W. "Manipulating general vectors on synchronous binary n-cube." IEEE Transactions on Computers 42, no. 7 (1993): 863–71. http://dx.doi.org/10.1109/12.237726.

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48

McBride, Kevin E., and Kristin R. Summerfelt. "Improved binary vectors for Agrobacterium-mediated plant transformation." Plant Molecular Biology 14, no. 2 (1990): 269–76. http://dx.doi.org/10.1007/bf00018567.

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49

Xu, Qingyang. "Minimal Structural ART Neural Network and Fault Diagnosis Application of Gas Turbine." Open Mechanical Engineering Journal 10, no. 1 (2016): 13–22. http://dx.doi.org/10.2174/1874155x01610010013.

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Adaptive Resonance Theory (ART) model is a special neural network based on unsupervised learning which simulates the cognitive process of human. However, ART1 can be only used for binary input, and ART2 can be used for binary and analog vectors which have complex structures and complicated calculations. In order to improve the real-time performance of the network, a minimal structural ART is proposed which combines the merits of the two models by subsuming the bottom-up and top-down weight. The vector similarity test is used instead of vigilance test. Therefore, this algorithm has a simple str

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LACOLLE, B., N. SZAFRAN, and P. VALENTIN. "GEOMETRIC MODELLING AND ALGORITHMS FOR BINARY MIXTURES." International Journal of Computational Geometry & Applications 04, no. 03 (1994): 243–60. http://dx.doi.org/10.1142/s021819599400015x.

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We present some computational methods in a particular case of mixing and separation theory, as an application of classical results in the field of computational geometry. Our aim is the production of some given mixtures by mixing parts of basic products. In the geometrical approach we use, products or mixtures are characterized by vectors and the mixing process by vector sums, in the vector space of physico-chemical species. The feasibility of a mixture is viewed as a point-inclusion in the convex set of mixtures which is a zonotope associated with basic mixtures. This paper is concerned with

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