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Journal articles on the topic 'Discrete Sequences'

Author: Grafiati

Published: 30 November 2024

Last updated: 5 July 2025

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1

Nikolov, Nikolai, and Mladen Savov. "Properties and Conjectures Regarding Discrete Renewal Sequences." Mathematics and Informatics 67, no. 2 (2024): 111–18. https://doi.org/10.53656/math2024-2-1-pro.

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In this work we review and derive some elementary properties of the discrete renewal sequences based on a positive, finite and integervalued random variable. Our results consider these sequences as dependent on the probability masses of the underlying random variable. In particular we study the minima and the maxima of these sequences and prove that they are attained for indices of the sequences smaller or equal than the support of the underlying random variable. Noting that the minimum itself is a minimum of multi-variate polynomials we conjecture that one universal polynomial envelopes the minimum from below and that it is maximal in some sense and largest in another. We prove this conjecture in a special case.

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2

Pétermann, Y. F. S., Jean-Luc Rémy, and Ilan Vardi. "Discrete Derivatives of Sequences." Advances in Applied Mathematics 27, no. 2-3 (2001): 562–84. http://dx.doi.org/10.1006/aama.2001.0750.

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3

Wang, Larry X. W., and Eve Y. Y. Yang. "Laguerre inequalities for discrete sequences." Advances in Applied Mathematics 139 (August 2022): 102357. http://dx.doi.org/10.1016/j.aam.2022.102357.

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4

Thom, Andreas. "Convergent Sequences in Discrete Groups." Canadian Mathematical Bulletin 56, no. 2 (2013): 424–33. http://dx.doi.org/10.4153/cmb-2011-155-3.

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AbstractWe prove that a finitely generated group contains a sequence of non-trivial elements that converge to the identity in every compact homomorphic image if and only if the group is not virtually abelian. As a consequence of the methods used, we show that a finitely generated group satisfies Chu duality if and only if it is virtually abelian.

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5

Ivanov, V. A., and G. I. Ivchenko. "Frequency tests for discrete sequences." Journal of Soviet Mathematics 39, no. 4 (1987): 2846–56. http://dx.doi.org/10.1007/bf01092335.

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6

He, Tian-Xiao. "A-sequences, Z-sequence, and B-sequences of Riordan matrices." Discrete Mathematics 343, no. 3 (2020): 111718. http://dx.doi.org/10.1016/j.disc.2019.111718.

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7

Xie, Pan, Qipeng Zhang, Peng Taiying, Hao Tang, Yao Du, and Zexian Li. "G2P-DDM: Generating Sign Pose Sequence from Gloss Sequence with Discrete Diffusion Model." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 6 (2024): 6234–42. http://dx.doi.org/10.1609/aaai.v38i6.28441.

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The Sign Language Production (SLP) project aims to automatically translate spoken languages into sign sequences. Our approach focuses on the transformation of sign gloss sequences into their corresponding sign pose sequences (G2P). In this paper, we present a novel solution for this task by converting the continuous pose space generation problem into a discrete sequence generation problem. We introduce the Pose-VQVAE framework, which combines Variational Autoencoders (VAEs) with vector quantization to produce a discrete latent representation for continuous pose sequences. Additionally, we propose the G2P-DDM model, a discrete denoising diffusion architecture for length-varied discrete sequence data, to model the latent prior. To further enhance the quality of pose sequence generation in the discrete space, we present the CodeUnet model to leverage spatial-temporal information. Lastly, we develop a heuristic sequential clustering method to predict variable lengths of pose sequences for corresponding gloss sequences. Our results show that our model outperforms state-of-the-art G2P models on the public SLP evaluation benchmark. For more generated results, please visit our project page: https://slpdiffusier.github.io/g2p-ddm.

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8

Gupal, N. A. "Methods of Numeration of Discrete Sequences." Cybernetics and Computer Technologies, no. 2 (June 30, 2021): 63–67. http://dx.doi.org/10.34229/2707-451x.21.2.6.

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Introduction. Numeration, or code, discrete sequences act fundamental part in the theory of recognition and estimation. By the code get codes or indexes of the programs and calculated functions. It is set that the universal programs are that programs which will realize all other programs. This one of basic results in the theory of estimation. On the basis of numeration of discrete sequences of Godel proved a famous theorem about incompleteness of arithmetic. Purpose of the article. To develop synonymous numerations by the natural numbers of eventual discrete sequences programs and calculable functions mutually. Results. On the basis of numerations of eventual discrete sequences numerations are built for four commands of machine with unlimited registers (MUR) in the natural numbers of type of 4u, 4u +1, 4u+2, 4u+3 accordingly. Every program consists of complete list of commands. On the basis of bijection for four commands of MUR certainly mutually synonymous numerations for all programs of MUR. Thus, on the basis of the set program it is possible effectively to find its code number, and vice versa, on the basis of the set number it is possible effectively to find the program. Conclusions. Synonymous numerations by the natural numbers of complete discrete sequences are developed mutually, programs for MUR and calculable functions. Leaning against numeration of the programs it is set in the theory of calculable functions, that the universal programs are, that programs which will realize all other programs. By application of the calculated functions and s-m-n theorem are got to operation on the calculated functions: combination φx and φy, giving work φxφy, operation of conversion of functions, effective operation of recursion. Thus, the index of function φxφy is on the indexes of x and y [2]. Keywords: numeration, Godel code number, diagonal method.

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9

Belov, Yurii, Tesfa Y. Mengestie, and Kristian Seip. "Discrete Hilbert transforms on sparse sequences." Proceedings of the London Mathematical Society 103, no. 1 (2011): 73–105. http://dx.doi.org/10.1112/plms/pdq053.

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10

Pereira, J. S., and H. J. A. da Silva. "Orthogonal perfect discrete Fourier transform sequences." IET Signal Processing 6, no. 2 (2012): 107. http://dx.doi.org/10.1049/iet-spr.2010.0195.

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11

Weigand, Hans-Georg. "Sequences—Basic elements for discrete mathematics." Zentralblatt für Didaktik der Mathematik 36, no. 3 (2004): 91–97. http://dx.doi.org/10.1007/bf02652776.

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12

MacCluer, Barbara D. "Uniformly discrete sequences in the ball." Journal of Mathematical Analysis and Applications 318, no. 1 (2006): 37–42. http://dx.doi.org/10.1016/j.jmaa.2005.05.029.

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13

Osikiewicz, Jeffrey A. "Equivalence results for discrete Abel means." International Journal of Mathematics and Mathematical Sciences 30, no. 12 (2002): 727–31. http://dx.doi.org/10.1155/s0161171202109264.

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14

Petrovich Pashintsev, Vladimir, Igor Anatolyevich Kalmykov, Aleksandr Pavlovich Zhuk, Dmitrii Viktorovich Orel, and Elena Pavlovna Zhuk. "Formation Algorithms and Properties of Binary Quasi-Orthogonal Code Sequence of Modern Satellite Systems." International Journal of Engineering & Technology 7, no. 4.38 (2018): 1205. http://dx.doi.org/10.14419/ijet.v7i4.38.27763.

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Increased number of threats to user interface of navigation signals, mainly in the form of suppression of navigation signals by jamming as well as navigation signal spoofing by false signals, assumes development of counter measures including improvement of structure security of navigation signals on the basis of stochastic use of code sequences which are ranging codes. This article proves the required number of unique discrete code sequences which can improve structure security of navigation signal in global navigation satellite system upon their stochastic use. Properties of discrete quasi-orthogonal code sequences are estimated which are used and proposed for use in global navigation satellite systems with channel code division, they are compared with optimum values of code balancing, number of element series and lower bounds of maximum lateral peaks of aperiodic auto-correlation function and maximum peaks of aperiodic mutual-correlation function. The experimental results show that the minimum values of the considered correlation functions of discrete quasi-orthogonal code sequences of known global navigation satellite systems exceed the lower bound by 3–6 times. The performances of code balancing and element series of discrete quasi-orthogonal code sequences of the known global navigation satellite systems satisfy in average the allowable intervals. The number of source lines of discrete quasi-orthogonal code sequences of the known global navigation satellite systems is significantly lower than their umber required for improvement of structure security of navigation signal based on their stochastic use. On the basis of the revealed drawbacks of the known discrete quasi-orthogonal code sequences, the necessity to develop new methods is substantiated allowing to obtain their required number together with statistic properties comparable with the best values of discrete quasi-orthogonal code sequences applied as navigation signals in global navigation satellite systems.

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15

Studenikin, A. V., and A. P. Zhuk. "MODELING OF DISCRETE ORTHOGONAL CODE SEQUENCES FOR INFORMATION TRANSMISSION SYSTEMS." H&ES Research 13, no. 1 (2021): 36–43. http://dx.doi.org/10.36724/2409-5419-2021-13-1-36-43.

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The development of wireless information transmission systems with code division of channels, taking into account the specifics of their functioning, is associated with the generation and processing of complex signals with a wide frequency band of the spectrum and the required correlation characteristics, as well as with the use of special algorithms for information exchange. The problem of synthesizing ensembles of discrete orthogonal code sequences with minimal side peaks of correlation functions and having minimal dis placement of the amplitude-frequency spectra is relevant. Successful solution of this problem affects the quality of output information, noise immunity, and signal-to-noise level of the information trans mission system. The aim of the article is to synthesize an ensemble of discrete orthogonal code sequences for a wireless information transmission system with code division of channels, taking into account restrictions on energy, spectral and correlation characteristics. A variant of solving the problem of synthesizing ensembles of discrete orthogonal code sequences with minimal side peaks of correlation functions having minimal displacement of the amplitude-frequency spectra is to use the modeling method based on eigenvectors of diagonal symmetric matrices. The article presents a synthesized ensemble of discrete orthogonal phase-manipulated sequences with a volume of N = 16. The use of a synthesized ensemble of discrete orthogonal sequences as modulating sequences in wireless information transmission systems with code division of channels provides a gain in noise immunity in the case of narrow-band interference of fixed power. From the above, it can be seen that the resulting ensemble of discrete orthogonal code sequences exceeds the characteristics of the known systems of orthogonal code sequences and meets the requirements. The use of the proposed method for modeling ensembles of discrete orthogonal code sequences with improved autocorrelation and spectral properties for wireless information transmission systems with code separation of channels makes it possible to increase the noise immunity and efficiency of using the frequency range of these systems.

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16

Niederreiter, Harald, and Ashot Yu Shahverdian. "DISCREPANCY ESTIMATES FOR ROTATION SEQUENCES AND OSCILLATION SEQUENCES." Asian-European Journal of Mathematics 05, no. 02 (2012): 1250020. http://dx.doi.org/10.1142/s1793557112500209.

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Two kinds of sequences, which are of interest in problems of uniform distribution and dynamical systems, are considered. The rotation sequences (or Kronecker sequences) (KS) are closely related to the orbits of the rotation map and the oscillation sequences (OS) are a discrete-time form of orbits of the simplest oscillators. The discrepancy of these sequences, which is a measure of deviation of the empirical distribution of a sequence from the ideal uniform distribution, is studied.

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17

Qi, Yuchan, and Huaning Liu. "Binary sequences and lattices constructed by discrete logarithms." AIMS Mathematics 7, no. 3 (2022): 4655–71. http://dx.doi.org/10.3934/math.2022259.

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<abstract><p>In 1997, Mauduit and Sárközy first introduced the measures of pseudorandomness for binary sequences. Since then, many pseudorandom binary sequences have been constructed and studied. In particular, Gyarmati presented a large family of pseudorandom binary sequences using the discrete logarithms. Ten years later, to satisfy the requirement from many applications in cryptography (e.g., in encrypting "bit-maps'' and watermarking), the definition of binary sequences is extended from one dimension to several dimensions by Hubert, Mauduit and Sárközy. They introduced the measure of pseudorandomness for this kind of several-dimension binary sequence which is called binary lattices. In this paper, large families of pseudorandom binary sequences and binary lattices are constructed by both discrete logarithms and multiplicative inverse modulo $ p $. The upper estimates of their pseudorandom measures are based on estimates of either character sums or mixed exponential sums.</p></abstract>

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18

Boza, Santiago. "Factorization of sequences in discrete Hardy spaces." Studia Mathematica 209, no. 1 (2012): 53–69. http://dx.doi.org/10.4064/sm209-1-5.

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19

Lafuente, Miguel, Raúl Gouet, F. Javier López, and Gerardo Sanz. "Near-Record Values in Discrete Random Sequences." Mathematics 10, no. 14 (2022): 2442. http://dx.doi.org/10.3390/math10142442.

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Given a sequence (Xn) of random variables, Xn is said to be a near-record if Xn∈(Mn−1−a,Mn−1], where Mn=max{X1, …, Xn} and a>0 is a parameter. We investigate the point process η on [0,∞) of near-record values from an integer-valued, independent and identically distributed sequence, showing that it is a Bernoulli cluster process. We derive the probability generating functional of η and formulas for the expectation, variance and covariance of the counting variables η(A),A⊂[0,∞). We also derive the strong convergence and asymptotic normality of η([0,n]), as n→∞, under mild regularity conditions on the distribution of the observations. For heavy-tailed distributions, with square-summable hazard rates, we prove that η([0,n]) grows to a finite random limit and compute its probability generating function. We present examples of the application of our results to particular distributions, covering a wide range of behaviours in terms of their right tails.

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20

Chandola, V., A. Banerjee, and V. Kumar. "Anomaly Detection for Discrete Sequences: A Survey." IEEE Transactions on Knowledge and Data Engineering 24, no. 5 (2012): 823–39. http://dx.doi.org/10.1109/tkde.2010.235.

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21

Modarresi, N., and S. Rezakhah. "Characterization of discrete scale invariant Markov sequences." Communications in Statistics - Theory and Methods 45, no. 18 (2015): 5263–78. http://dx.doi.org/10.1080/03610926.2014.942427.

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22

Barreira, Luis, and Claudia Valls. "Robustness of Discrete Dynamics via Lyapunov Sequences." Communications in Mathematical Physics 290, no. 1 (2009): 219–38. http://dx.doi.org/10.1007/s00220-009-0762-z.

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23

Ramayyan, A. "ON NONOSCILLATORY SEQUENCES OVER DISCRETE HARDY FIELDS." Acta Mathematica Scientia 14, no. 1 (1994): 100–106. http://dx.doi.org/10.1016/s0252-9602(18)30096-1.

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24

UGOWSKI, Henryk, and Andrzej DYKA. "ON THE CONVOLUTION INVERSE OF DISCRETE SEQUENCES." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 10, no. 2 (1991): 65–82. http://dx.doi.org/10.1108/eb010081.

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25

UGOWSKI, Henryk, and Andrzej DYKA. "ON THE CONVOLUTION INVERSE OF DISCRETE SEQUENCES." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 10, no. 2 (1991): 83–90. http://dx.doi.org/10.1108/eb010082.

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26

Rodríguez-Horta, Edwin, Alejandro Lage-Castellanos, and Roberto Mulet. "Ancestral sequence reconstruction for co-evolutionary models." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (2022): 013502. http://dx.doi.org/10.1088/1742-5468/ac3d93.

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Abstract The ancestral sequence reconstruction problem is the inference, back in time, of the properties of common sequence ancestors from the measured properties of contemporary populations. Standard algorithms for this problem assume independent (factorized) evolution of the characters of the sequences, which is generally wrong (e.g. proteins and genome sequences). In this work, we have studied this problem for sequences described by global co-evolutionary models, which reproduce the global pattern of cooperative interactions between the elements that compose it. For this, we first modeled the temporal evolution of correlated real valued characters by a multivariate Ornstein–Uhlenbeck process on a finite tree. This represents sequences as Gaussian vectors evolving in a quadratic potential, who describe the selection forces acting on the evolving entities. Under a Bayesian framework, we developed a reconstruction algorithm for these sequences and obtained an analytical expression to quantify the quality of our estimation. We extend this formalism to discrete valued sequences by applying our method to a Potts model. We showed that for both continuous and discrete configurations, there is a wide range of parameters where, to properly reconstruct the ancestral sequences, intra-species correlations must be taken into account. We also demonstrated that, for sequences with discrete elements, our reconstruction algorithm outperforms traditional schemes based on independent site approximations.

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27

�okovi?, Dragomir ? "Base sequences, complementary ternary sequences, and orthogonal designs." Journal of Combinatorial Designs 4, no. 5 (1996): 339–51. http://dx.doi.org/10.1002/(sici)1520-6610(1996)4:5<339::aid-jcd3>3.0.co;2-g.

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28

Qi, Yu-Chan, and Hua-Ning Liu. "On uniformly distributed $[0,1)$ sequences and binary sequences constructed by discrete logarithms." Publicationes Mathematicae Debrecen 100, no. 1-2 (2022): 69–86. http://dx.doi.org/10.5486/pmd.2022.9012.

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29

Wang, Tao, Jiang-hua Huang, Lin Lin, and Chang'an A. Zhan. "Continuous- and Discrete-Time Stimulus Sequences for High Stimulus Rate Paradigm in Evoked Potential Studies." Computational and Mathematical Methods in Medicine 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/396034.

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To obtain reliable transient auditory evoked potentials (AEPs) from EEGs recorded using high stimulus rate (HSR) paradigm, it is critical to design the stimulus sequences of appropriate frequency properties. Traditionally, the individual stimulus events in a stimulus sequence occur only at discrete time points dependent on the sampling frequency of the recording system and the duration of stimulus sequence. This dependency likely causes the implementation of suboptimal stimulus sequences, sacrificing the reliability of resulting AEPs. In this paper, we explicate the use of continuous-time stimulus sequence for HSR paradigm, which is independent of the discrete electroencephalogram (EEG) recording system. We employ simulation studies to examine the applicability of the continuous-time stimulus sequences and the impacts of sampling frequency on AEPs in traditional studies using discrete-time design. Results from these studies show that the continuous-time sequences can offer better frequency properties and improve the reliability of recovered AEPs. Furthermore, we find that the errors in the recovered AEPs depend critically on the sampling frequencies of experimental systems, and their relationship can be fitted using a reciprocal function. As such, our study contributes to the literature by demonstrating the applicability and advantages of continuous-time stimulus sequences for HSR paradigm and by revealing the relationship between the reliability of AEPs and sampling frequencies of the experimental systems when discrete-time stimulus sequences are used in traditional manner for the HSR paradigm.

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30

Anashin, Vladimir. "Discreteness causes waves." Facta universitatis - series: Physics, Chemistry and Technology 14, no. 3 (2016): 143–96. http://dx.doi.org/10.2298/fupct1603143a.

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In the paper, we show that matter waves can be derived from discreteness and causality. Namely we show that matter waves can naturally be ascribed to finite discrete causal systems, the Mealy automata having binary input/output which are bit sequences. If assign real numerical values (?measured quantities?) to bit sequences, the waves arise as a correspondence between the numerical values of input sequences (?impacts?) and output sequences (?system-evoked responses?). We show that among all discrete causal systems with arbitrary (not necessarily binary) inputs/outputs, only the ones with binary input/output can be ascribed to matter waves ?(x,t) = ei(kx??t).

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31

Driess, Danny, Jung-Su Ha, and Marc Toussaint. "Learning to solve sequential physical reasoning problems from a scene image." International Journal of Robotics Research 40, no. 12-14 (2021): 1435–66. http://dx.doi.org/10.1177/02783649211056967.

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In this article, we propose deep visual reasoning, which is a convolutional recurrent neural network that predicts discrete action sequences from an initial scene image for sequential manipulation problems that arise, for example, in task and motion planning (TAMP). Typical TAMP problems are formalized by combining reasoning on a symbolic, discrete level (e.g., first-order logic) with continuous motion planning such as nonlinear trajectory optimization. The action sequences represent the discrete decisions on a symbolic level, which, in turn, parameterize a nonlinear trajectory optimization problem. Owing to the great combinatorial complexity of possible discrete action sequences, a large number of optimization/motion planning problems have to be solved to find a solution, which limits the scalability of these approaches. To circumvent this combinatorial complexity, we introduce deep visual reasoning: based on a segmented initial image of the scene, a neural network directly predicts promising discrete action sequences such that ideally only one motion planning problem has to be solved to find a solution to the overall TAMP problem. Our method generalizes to scenes with many and varying numbers of objects, although being trained on only two objects at a time. This is possible by encoding the objects of the scene and the goal in (segmented) images as input to the neural network, instead of a fixed feature vector. We show that the framework can not only handle kinematic problems such as pick-and-place (as typical in TAMP), but also tool-use scenarios for planar pushing under quasi-static dynamic models. Here, the image-based representation enables generalization to other shapes than during training. Results show runtime improvements of several orders of magnitudes by, in many cases, removing the need to search over the discrete action sequences.

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32

Pau, Jordi, and Pascal J. Thomas. "DECREASE OF BOUNDED HOLOMORPHIC FUNCTIONS ALONG DISCRETE SETS." Proceedings of the Edinburgh Mathematical Society 46, no. 3 (2003): 703–18. http://dx.doi.org/10.1017/s001309150200086x.

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AbstractWe provide uniqueness results for holomorphic functions in the Nevanlinna class which bridge those previously obtained by Hayman and by Lyubarskii and Seip. In particular, we propose certain classes of hyperbolically separated sequences in the disc, in terms of the rate of non-tangential accumulation to the boundary (the outer limits of this spectrum of classes being, respectively, the sequences with a non-tangential cluster set of positive measure, and the sequences satisfying the Blaschke condition). For each of those classes, we give a critical condition of radial decrease on the modulus which will force a Nevanlinna class function to vanish identically.AMS 2000 Mathematics subject classification: Primary 30D50; 30D55

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33

Sultanova, V. "BOUNDARY-VALUE PROBLEM FOR A TWO-DIMENSIONAL SECOND ORDER-TYPE EQUATION WITH DISCRETE ADDITIVE AND MULTIPLICATIVE DERIVATIVES." East European Scientific Journal 1, no. 4(68) (2021): 61–63. http://dx.doi.org/10.31618/essa.2782-1994.2021.1.68.16.

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The present paper is concerned with the study of solutions to the boundary-value problem for a two-dimensional second order-type differential equation with a discrete additive derivative for one argument and a discrete multiplicative derivative for another argument. We will determine the general solution of the considered equation, containing some derived sequences. Further, these unknown sequences are determined using an assigned boundary condition.

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Tian, Chuanjun. "Continuous Sequences with Frequency Independence Generated by Discrete Spatiotemporal Systems." International Journal of Bifurcation and Chaos 30, no. 03 (2020): 2050050. http://dx.doi.org/10.1142/s0218127420500509.

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This paper is concerned with the frequency independent continuous sequences generated by the following discrete spatiotemporal system: [Formula: see text] where [Formula: see text] is a function and [Formula: see text] is a bounded subset of [Formula: see text]. Based on frequency measurement theory, a series of continuous sequences with frequency independence generated by a special case of this discrete spatiotemporal system is constructed.

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35

Vorontsov, Oleg, and Iryna Vorontsova. "THE ONE-DIMENSIONAL GEOMETRIC IMAGES FORMATION BY SUPERPOSITIONS OF POINT SETS UNDER THE GIVEN BOUNDARY CONDITIONS AND FINITE DIFFERENCE." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 104 (February 3, 2025): 59–79. https://doi.org/10.32347/0131-579x.2023.104.59-79.

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A variation of the external load distribution function between nodes of a discrete grid in the static-geometric method allows discretely modeling curves of different shapes and solving problems of discrete interpolation on the area. The form of the continuous analogue of the discretely presented curve directly depends on the nature of the functions specified control load, which forms the discretely presented curve (DPC). There are known studies of the aspects of the relationship between the static geometric method of forming the DPC and the analytical description of a continuous curve through the synthesis of the static geometric method of forming discrete curves and the method of modeling them with numerical sequences. Separate issues of determining the correspondence of the equations of the continuous surface to the discrete function of the distribution of the external load are also investigated. This article examines the patterns of changes in the values of the superposition coefficients of two arbitrarily specified, both adjacent and non-adjacent nodal points, under the condition of a known distribution law of the magnitude of the finite difference, which in some cases will be a prototype of the external load between the nodes of the frame, which is a discrete model of a defined geometric image. If we change the uniformly distributed value of the finite difference or the value of the distribution function of the value of the finite difference, or the ordinates of one or two (marginal) nodal points at fixed values of the superposition coefficients, we can control the shape of the curve, discretely represented by the nodal points of its numerical sequence. The research data determine a general approach to obtaining similar patterns of changes in the values of the superposition coefficients of two arbitrarily specified, both adjacent and non-adjacent nodal points for determining the coordinates of points of modeling any one-dimensional functional dependencies and arbitrary one-dimensional sets of points. The results of the study of the regularities of changes in the values of the superposition coefficients given by two nodal points of different elementary functions, under the condition of a known distribution law of the magnitude of the finite difference, will allow solving the problems of continuous discrete interpolation and extrapolation by numerical sequences of any one-dimensional functional dependencies (determine the ordinates of the sought points of discrete curves) without time-consuming operations of assembling and solving large systems of linear equations

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36

Zhu, Huaiyu, and Wolfgang Kinzel. "Antipredictable Sequences: Harder to Predict Than Random Sequences." Neural Computation 10, no. 8 (1998): 2219–30. http://dx.doi.org/10.1162/089976698300017043.

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For any discrete-state sequence prediction algorithm A, it is always possible, using an algorithm B no more complicated than A, to generate a sequence for which A's prediction is always wrong. For any prediction algorithm A and sequence x, there exists a sequence y no more complicated than x, such that if A performs better than random on x, then it will perform worse than random on y by the same margin. An example of a simple neural network predicting a bit sequence is used to illustrate this very general but not widely recognized phenomenon. This implies that any predictor with good performance must rely on some (usually implicitly) assumed prior distributions of the problem.

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37

Sharma, Vinod. "Approximations of general discrete time queues by discrete time queues with arrivals modulated by finite chains." Advances in Applied Probability 29, no. 4 (1997): 1039–59. http://dx.doi.org/10.2307/1427853.

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Recently, Asmussen and Koole (Journal of Applied Probability30, pp. 365–372) showed that any discrete or continuous time marked point process can be approximated by a sequence of arrival streams modulated by finite state continuous time Markov chains. If the original process is customer (time) stationary then so are the approximating processes. Also, the moments in the stationary case converge. For discrete marked point processes we construct a sequence of discrete processes modulated by discrete time finite state Markov chains. All the above features of approximating sequences of Asmussen and Koole continue to hold. For discrete arrival sequences (to a queue) which are modulated by a countable state Markov chain we form a different sequence of approximating arrival streams by which, unlike in the Asmussen and Koole case, even the stationary moments of waiting times can be approximated. Explicit constructions for the output process of a queue and the total input process of a discrete time Jackson network with these characteristics are obtained.

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38

Sharma, Vinod. "Approximations of general discrete time queues by discrete time queues with arrivals modulated by finite chains." Advances in Applied Probability 29, no. 04 (1997): 1039–59. http://dx.doi.org/10.1017/s0001867800048011.

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Recently, Asmussen and Koole (Journal of Applied Probability 30, pp. 365–372) showed that any discrete or continuous time marked point process can be approximated by a sequence of arrival streams modulated by finite state continuous time Markov chains. If the original process is customer (time) stationary then so are the approximating processes. Also, the moments in the stationary case converge. For discrete marked point processes we construct a sequence of discrete processes modulated by discrete time finite state Markov chains. All the above features of approximating sequences of Asmussen and Koole continue to hold. For discrete arrival sequences (to a queue) which are modulated by a countable state Markov chain we form a different sequence of approximating arrival streams by which, unlike in the Asmussen and Koole case, even the stationary moments of waiting times can be approximated. Explicit constructions for the output process of a queue and the total input process of a discrete time Jackson network with these characteristics are obtained.

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Huang, Xiao Hui, Wei Zhi Huang, Ke Yuan, and Kun He. "A Fast Algorithm Based on Discrete Cosine Transform(DCT)." Applied Mechanics and Materials 644-650 (September 2014): 1488–93. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.1488.

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Traditional fast algorithms for DCT are aimed at sequences with 2N length and it is math-intensive for sequences which contain odd numbers of elements. This paper analyzes the redundant calculation of cosine transform of non-2N-point sequences and put forward a fast algorithm for one-dimensional DCT with odd length. Also, according to the separability of two-dimensional DCT, we can generalize the fast algorithm for one-dimensional DCT to two-dimensional DCT to implement and complete the fast algorithm. The simulation suggests that this algorithm improves the speed of calculation.

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Charlier, Émilie, Célia Cisternino, and Manon Stipulanti. "Regular sequences and synchronized sequences in abstract numeration systems." European Journal of Combinatorics 101 (March 2022): 103475. http://dx.doi.org/10.1016/j.ejc.2021.103475.

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41

Saker, Samir, and Ravi Agarwal. "Discrete Rubio De Francia extrapolation theorems in the theory of Bp−discrete weights." Filomat 38, no. 1 (2024): 147–69. http://dx.doi.org/10.2298/fil2401147s.

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In this paper, we will prove some discrete Rubio De Francia extrapolation theorems for nonincreasing sequences in the setting of the discrete Bp-weights. We also present some extensions to the discrete B?-weights. The proof of the results based on the boundedness of the discrete Hardy operator and the self-improving property of the discrete Bp weights. To the best of the authors? knowledge the discrete extrapolation theorems in connection with Bp?weights are essentially new.

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42

González, Santos, Llorenç Huguet, Consuelo Martínez, and Hugo Villafañe. "Discrete logarithm like problems and linear recurring sequences." Advances in Mathematics of Communications 7, no. 2 (2013): 187–95. http://dx.doi.org/10.3934/amc.2013.7.187.

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Mahillo, Alejandro, and Pedro J. Miana. "Caputo Fractional Evolution Equations in Discrete Sequences Spaces." Foundations 2, no. 4 (2022): 872–84. http://dx.doi.org/10.3390/foundations2040059.

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In this paper, we treat some fractional differential equations on the sequence Lebesgue spaces ℓp(N0) with p≥1. The Caputo fractional calculus extends the usual derivation. The operator, associated to the Cauchy problem, is defined by a convolution with a sequence of compact support and belongs to the Banach algebra ℓ1(Z). We treat in detail some of these compact support sequences. We use techniques from Banach algebras and a Functional Analysis to explicity check the solution of the problem.

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44

Guédon, Yann. "Estimating Hidden Semi-Markov Chains From Discrete Sequences." Journal of Computational and Graphical Statistics 12, no. 3 (2003): 604–39. http://dx.doi.org/10.1198/1061860032030.

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Mazel, D. S., and M. H. Hayes. "Using iterated function systems to model discrete sequences." IEEE Transactions on Signal Processing 40, no. 7 (1992): 1724–34. http://dx.doi.org/10.1109/78.143444.

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Masjed-Jamei, Mohammad, and Wolfram Koepf. "Two finite hypergeometric sequences of discrete orthogonal polynomials." Journal of Difference Equations and Applications 24, no. 9 (2018): 1429–43. http://dx.doi.org/10.1080/10236198.2018.1494166.

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Ming-Yue, Zhai, Heidi Kuzuma, and James W. Rector. "A new fractal algorithm to model discrete sequences." Chinese Physics B 19, no. 9 (2010): 090509. http://dx.doi.org/10.1088/1674-1056/19/9/090509.

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Devinck, Vincent. "Jamison sequences in countably infinite discrete Abelian groups." Acta Scientiarum Mathematicarum 82, no. 34 (2016): 481–508. http://dx.doi.org/10.14232/actasm-015-020-3.

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Svalbe, Imants, and Andrew Kingston. "Farey Sequences and Discrete Radon Transform Projection Angles." Electronic Notes in Discrete Mathematics 12 (March 2003): 154–65. http://dx.doi.org/10.1016/s1571-0653(04)00482-2.

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Keyantuo, Valentin, and Yevhen Zelenyuk. "Discrete subsets and convergent sequences in topological groups." Topology and its Applications 191 (August 2015): 137–42. http://dx.doi.org/10.1016/j.topol.2015.05.089.

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