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Journal articles on the topic 'Monotonity'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Bobor, Kristóf, and György Krállics. "Study of Non-Monotonity of Forming Processes Using Finite Element Analysis." Materials Science Forum 659 (September 2010): 373–78. http://dx.doi.org/10.4028/www.scientific.net/msf.659.373.

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The method of severe plastic deformation is often used to produce bulk ultra-fine grained materials. Numerous methods exist, which are able to produce ultra fine grained materials. Investigated the mechanical schema of these procedures, we searched for such attributes, which characterize the mentioned techniques. By our previous researches can be established, that for these techniques shear deformation as well as the so-called non-monotonic deformation are characteristic. In this paper a degree of non-monotonity is presented, which is an appropriate measure to characterize the forming processes. Besides this the combined Euler – Lagrange method is showed, which is appropriate to obtain a continuous velocity field from finite element analysis. Eventually the mechanical analysis of the extrusion, conventional and asymmetric rolling is showed with respect to the non-monotonity.

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2

Fiala, Tibor. "On the monotonity of incomplete factorization." Numerische Mathematik 57, no. 1 (December 1990): 473–79. http://dx.doi.org/10.1007/bf01386424.

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Polyakov, O. V. "On one property of zeros of polynomials of the least $$$(\alpha; \beta)$$$-deviation from zero in weighted space $$$L_p$$$." Dnipro University Mathematics Bulletin 26, no. 1 (June 25, 2018): 79. http://dx.doi.org/10.15421/241810.

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Szabó, Gy, K. Sárneczky, and L. L. Kiss. "The O–C diagrams of minor planets − a new approach to modelling the rotation." International Astronomical Union Colloquium 173 (1999): 185–88. http://dx.doi.org/10.1017/s0252921100031407.

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AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

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Bobor, K., and Gy Krallics. "Characterization of metal-forming processes with respect to non-monotonity." Journal of Physics: Conference Series 240 (July 1, 2010): 012126. http://dx.doi.org/10.1088/1742-6596/240/1/012126.

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Peng, Jianwen. "System of generalised set-valued quasi-variational-like inequalities." Bulletin of the Australian Mathematical Society 68, no. 3 (December 2003): 501–15. http://dx.doi.org/10.1017/s0004972700037904.

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In this paper, we shall introduce a system of generalised set-valued quasi-variational-like inequalities, which generalises and unifies systems of generalised vector variational inequalities, systems of variational inequalities, generalised vector quasi-variational-like inequalities as well as various extensions of the classic variational inequalities in the literature. Some existence results for a solution of a system of generalized set-valued quasi-variational-like inequalities without any monotonity are obtained.

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Némethi, András, and Meral Tosun. "Invariants of open books of links of surface singularities." Studia Scientiarum Mathematicarum Hungarica 48, no. 1 (March 1, 2011): 135–44. http://dx.doi.org/10.1556/sscmath.2010.1159.

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If M is the link of a complex normal surface singularity, then it carries a canonical contact structure ξcan, which can be identified from the topology of the 3-manifold M. We assume that M is a rational homology sphere. We compute the support genus, the binding number and the norm associated with the open books which support ζcan, provided that we restrict ourselves to the case of (analytic) Milnor open books. In order to do this, we determine monotonity properties of the genus and the Milnor number of all Milnor fibrations in terms of the Lipman cone.We generalize results of [3] valid for links of rational surface singularities, and we answer some questions of Etnyre and Ozbagci [7, section 8] regarding the above invariants.

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Cai, Qian, Weiqiang Gong, Yue Deng, and Haixian Wang. "Single-Trial EEG Classification via Common Spatial Patterns with Mixed Lp- and Lq-Norms." Mathematical Problems in Engineering 2021 (June 3, 2021): 1–13. http://dx.doi.org/10.1155/2021/6645322.

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As a multichannel spatial filtering technique, common spatial patterns (CSP) have been successfully applied in brain-computer interfaces (BCI) community based on electroencephalogram (EEG). However, it is sensitive to outliers because of the employment of the L2-norm in its formulation. It is beneficial to perform robust modelling for CSP. In this paper, we propose a robust framework, called CSP-Lp/q, by formulating the variances of two EEG classes with Lp- and Lq-norms ( 0 < p and q < 2 ) separately. The method CSP-Lp/q with mixed Lp- and Lq-norms takes the class-wise difference into account in formulating the sample dispersion. We develop an iterative algorithm to optimize the objective function of CSP-Lp/q and show its monotonity theoretically. The superiority of the proposed CSP-Lp/q technique is experimentally demonstrated on three real EEG datasets of BCI competitions.

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Abbas, Rachid, Caroline Rossoni, Thomas Jaki, Xavier Paoletti, and Pavel Mozgunov. "A comparison of phase I dose-finding designs in clinical trials with monotonicity assumption violation." Clinical Trials 17, no. 5 (July 7, 2020): 522–34. http://dx.doi.org/10.1177/1740774520932130.

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Background/Aims In oncology, new combined treatments make it difficult to order dose levels according to monotonically increasing toxicity. New flexible dose-finding designs that take into account uncertainty in dose levels ordering were compared with classical designs through simulations in the setting of the monotonicity assumption violation. We give recommendations for the choice of dose-finding design. Methods Motivated by a clinical trial for patients with high-risk neuroblastoma, we considered designs that require a monotonicity assumption, the Bayesian Continual Reassessment Method, the modified Toxicity Probability Interval, the Bayesian Optimal Interval design, and designs that relax monotonicity assumption, the Bayesian Partial Ordering Continual Reassessment Method and the No Monotonicity Assumption design. We considered 15 scenarios including monotonic and non-monotonic dose–toxicity relationships among six dose levels. Results The No Monotonicity Assumption and Partial Ordering Continual Reassessment Method designs were robust to the violation of the monotonicity assumption. Under non-monotonic scenarios, the No Monotonicity Assumption design selected the correct dose level more often than alternative methods on average. Under the majority of monotonic scenarios, the Partial Ordering Continual Reassessment Method selected the correct dose level more often than the No Monotonicity Assumption design. Other designs were impacted by the violation of the monotonicity assumption with a proportion of correct selections below 20% in most scenarios. Under monotonic scenarios, the highest proportions of correct selections were achieved using the Continual Reassessment Method and the Bayesian Optimal Interval design (between 52.8% and 73.1%). The costs of relaxing the monotonicity assumption by the No Monotonicity Assumption design and Partial Ordering Continual Reassessment Method were decreases in the proportions of correct selections under monotonic scenarios ranging from 5.3% to 20.7% and from 1.4% to 16.1%, respectively, compared with the best performing design and were higher proportions of patients allocated to toxic dose levels during the trial. Conclusions Innovative oncology treatments may no longer follow monotonic dose levels ordering which makes standard phase I methods fail. In such a setting, appropriate designs, as the No Monotonicity Assumption or Partial Ordering Continual Reassessment Method designs, should be used to safely determine recommended for phase II dose.

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Wei, Chun-Fu, and Bai-Ni Guo. "Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/851213.

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Some complete monotonicity results that the functions±1/e±t-1are logarithmically completely monotonic, and that differences between consecutive derivatives of these two functions are completely monotonic, and that the ratios between consecutive derivatives of these two functions are decreasing on0, ∞are discovered. As applications of these newly discovered results, some complete monotonicity results concerning the polylogarithm are found. Finally a conjecture on the complete monotonicity of the above-mentioned ratios is posed.

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Carbajal, Juan Carlos, and Rudolf Müller. "Monotonicity and revenue equivalence domains by monotonic transformations in differences." Journal of Mathematical Economics 70 (May 2017): 29–35. http://dx.doi.org/10.1016/j.jmateco.2016.12.008.

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Magiera, Krzysztof, and Piotr Faliszewski. "Recognizing Top-Monotonic Preference Profiles in Polynomial Time." Journal of Artificial Intelligence Research 66 (September 4, 2019): 57–84. http://dx.doi.org/10.1613/jair.1.11331.

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We provide the first polynomial-time algorithm for recognizing if a profile of (possibly weak) preference orders is top-monotonic. Top-monotonicity is a generalization of the notions of single-peakedness and single-crossingness, defined by Barbera and Moreno. Top-monotonic profiles always have weak Condorcet winners and satisfy a variant of the median voter theorem. Our algorithm proceeds by reducing the recognition problem to the SAT-2CNF problem.

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Korelstein, Leonid. "Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations." E3S Web of Conferences 102 (2019): 01004. http://dx.doi.org/10.1051/e3sconf/201910201004.

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Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations was proved. The closure relation can have very general form, restricted only by continuity and monotonicity conditions necessary for providing existence, uniqueness and continuity of flow distribution problem for each branch. It is shown that network as a whole “inherits” monotonicity and continuity of its branches behavior, and this provides existence and uniqueness of solution.

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Abe, Takaaki, and Satoshi Nakada. "Monotonic Redistribution: Reconciling Performance-Based Allocation and Weighted Division." International Game Theory Review 19, no. 04 (December 2017): 1750022. http://dx.doi.org/10.1142/s0219198917500220.

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We show that a proportional taxation redistribution rule regarding heterogeneity among members of a society is implied by four axioms: efficiency, total wealth monotonicity, contribution monotonicity and additivity. Moreover, we offer another axiomatization with dropping additivity. Our rule is an extension of [Casajus, A. [2015] Monotonic distribution of performance-based allocations: A case for proportional taxation, Theor. Econ. 10, 887–892]’s redistribution rule in which each member of a society is identified only with his/her income.

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15

Austen-Smith, David, and Jeffrey Banks. "Monotonicity in Electoral Systems." American Political Science Review 85, no. 2 (June 1991): 531–37. http://dx.doi.org/10.2307/1963173.

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Much of the literature concerning the relative merits of alternative electoral rules is centered around the extent to which particular rules select “representative” legislatures. And an important concern in evaluating the “representativeness” of an electoral rule is whether or not the rule responds positively to changes in individuals' preferences, that is, whether or not the rule is monotonic. By explicitly considering electoral rules in the context of a complete electoral system—voting, selection of legislature, and legislative choice of policy—we argue that monotonicity in electoral systems is a nonissue: depending on the behavioral model governing individual decision making, either everything is monotonic or nothing is monotonic.

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16

Qi, Feng. "A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums." ANZIAM Journal 48, no. 4 (April 2007): 523–32. http://dx.doi.org/10.1017/s1446181100003199.

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AbstractIn this paper, a function involving the divided difference of the psi function is proved to be completely monotonic, a class of inequalities involving sums is found, and an equivalent relation between complete monotonicity and one of the class of inequalities is established.

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17

Trepczyński, Marcin. "ZASADA PRAWDY FORMALNEJ W POLSKIM CYWILNYM PRAWIE PROCESOWYM A ROZUMOWANIA NIEMONOTONICZNE." Zeszyty Prawnicze 16, no. 2 (December 9, 2016): 37. http://dx.doi.org/10.21697/zp.2016.16.2.02.

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The Principle of Formal Truth in the Polish Civil Procedural Law and Non-monotonic ReasoningSummary This paper analyses the implementation of the formal truth principle in the Polish civil procedural code in the light of non-monotonic reasoning. The author starts by presenting the concept and applications of non-monotonic reasoning, and the formal truth principle and its place in Polish civil procedure. Next he examines the conditions in which non-monotonicity is admissible in civil court reasoning. While legal reasoning may generally be regarded as non-monotonic due to the assumptions it employs and treats as defensible, the author’s observations on the basis of selected civil law cases lead him to the conclusion that the use of the formal truth principle as a viable instrument in law simply forces courts to make non-monotonic inferences. In other words, adopting this principle means accepting non-monotonic reasoning, or even more: if the court keeps to the formal truth principle it is using one of the types of non-monotonic logic.

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18

Deng, Guannan, Lianlian Song, Yanli Jiang, and Jingchao Fu. "Monotonic Similarity Measures of Interval-Valued Fuzzy Sets and Their Applications." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 25, no. 04 (July 14, 2017): 515–44. http://dx.doi.org/10.1142/s0218488517500222.

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A similarity measure is a measure that indicates the degree of similarity between two objects. The purpose of this work is to investigate the monotonicity properties and applications of similarity measures on interval-valued fuzzy sets. Through analyzing the intuitions of similarities, three kinds of monotonic similarity measures are defined. Furthermore, their properties and relationships with entropy and inclusion measure are investigated and discussed. Finally, some applications of the proposed monotonic similarity measures, such as pattern recognition, medical recognition, and medical diagnosis are presented.

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Mughal, Aqeel Ahmad, Hassan Almusawa, Absar Ul Haq, and Imran Abbas Baloch. "Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions." Journal of Mathematics 2021 (August 9, 2021): 1–13. http://dx.doi.org/10.1155/2021/5561611.

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Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as Jensen-type inequality for harmonic h -convex functions. In this paper, we aim to establish the functional form of inequalities presented by Baloch et al. and prove the superadditivity and monotonicity properties of these functionals. Furthermore, we derive the bound for these functionals under certain conditions. Furthermore, we define more generalized functionals involving monotonic nondecreasing concave function as well as evince superadditivity and monotonicity properties of these generalized functionals.

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20

Kaas, Eigil, and Joakim R. Nielsen. "A Mass-Conserving Quasi-Monotonic Filter for Use in Semi-Lagrangian Models." Monthly Weather Review 138, no. 5 (May 1, 2010): 1858–76. http://dx.doi.org/10.1175/2009mwr3173.1.

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Abstract A new mass-conserving and quasi-monotonic antidiffusive filter has been designed for application in semi-Lagrangian-type models. The filter redistributes local mass such that the resulting values are brought closer to target values. The target values, in turn, are specified from a nonlinear antidiffusion of the original nonfiltered forecast. To achieve quasi-monotonicity, the target values are constrained to a certain interval, defined by the minimum and maximum value of the upstream grid cells surrounding the semi-Lagrangian departure point. Allowing a less local reorganization of mass the filter can be made fully monotonic and positive definite. The filter has been applied to the recently developed locally mass-conserving semi-Lagrangian (LMCSL) scheme. A number of idealized test simulations in one and two dimensions demonstrates that the combined scheme is stable and quasi monotonic. Furthermore, the accuracy is enhanced considerably as compared to the original LMCSL scheme, particularly near sharp changes in gradients. When tested in the geophysical flow environment of a shallow-water model, the proposed filter, in practice, ensures monotonicity and positive definiteness without generation of spurious features. In its present implementation the computational cost of the combined scheme is approximately twice the cost of the LMCSL scheme.

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Roerdink, J. B. T. M. "A Markov chain identity and monotonicity of the diffusion constants for a random walk in a heterogeneous environment." Mathematical Proceedings of the Cambridge Philosophical Society 108, no. 1 (July 1990): 111–26. http://dx.doi.org/10.1017/s0305004100069000.

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AbstractWe consider a 2-dimensional square lattice which is partitioned into a periodic array of rectangular cells, on which a nearest neighbour random walk with symmetric increments is defined whose transition probabilities only depend on the relative position within a cell. On the basis of a determinantal identity proved in this paper, we obtain a result for finite Markov chains which shows that the diffusion constants for the random walk are monotonic functions of the individual transition probabilities. We point out the similarity of this monotonicity property to Rayleigh's Monotonicity Law for electric networks or, equivalently, reversible random walks.

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HSU, CHENG-HSIUNG, CHUN-HSIEN LI, and SUH-YUH YANG. "DIVERSITY OF TRAVELING WAVE SOLUTIONS IN DELAYED CELLULAR NEURAL NETWORKS." International Journal of Bifurcation and Chaos 18, no. 12 (December 2008): 3515–50. http://dx.doi.org/10.1142/s0218127408022561.

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This work investigates the diversity of traveling wave solutions for a class of delayed cellular neural networks on the one-dimensional integer lattice ℤ1. The dynamics of a given cell is characterized by instantaneous self-feedback and neighborhood interaction with distributed delay due to, for example, finite switching speed and finite velocity of signal transmission. Applying the monotone iteration scheme, we can deduce the existence of monotonic traveling wave solutions provided the templates satisfy the so-called quasi-monotonicity condition. We then consider two special cases of the delayed cellular neural network in which each cell interacts only with either the nearest m left neighbors or the nearest m right neighbors. For the former case, we can directly figure out the analytic solution in an explicit form by the method of step with the help of the characteristic function and then prove that, in addition to the existence of monotonic traveling wave solutions, for certain templates there exist nonmonotonic traveling wave solutions such as camel-like waves with many critical points. For the latter case, employing the comparison arguments repeatedly, we can clarify the deformation of traveling wave solutions with respect to the wave speed. More specifically, we can describe the transition of profiles from monotonicity, damped oscillation, periodicity, unboundedness and back to monotonicity as the wave speed is varied. Some numerical results are also given to demonstrate the theoretical analysis.

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Türker, Uraz Cengiz, and Hüsnü Yenigün. "Complexities of Some Problems Related to Synchronizing, Non-Synchronizing and Monotonic Automata." International Journal of Foundations of Computer Science 26, no. 01 (January 2015): 99–121. http://dx.doi.org/10.1142/s0129054115500057.

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In this study, we first introduce several problems related to finding reset words for deterministic finite automata, and present motivations for these problems for practical applications in areas such as robotics and bio-engineering. We then analyse computational complexities of these problems. Second, we consider monotonic and partially specified automata. Monotonicity is known to be a feature simplyfing the synchronizability problems. On the other hand for partially specified automata, synchronizability problems are known to be harder than the completely specified automata. We investigate the complexity of some synchronizability problems for automata that are both monotonic and partially specified. We show that checking the existence, computing one, and computing a shortest reset word for a monotonic partially specified automaton is NP-hard. We also show that finding a reset word that synchronizes 𝓚 number of states (or maximum number of states) of a given monotonic non-synchronizable automaton to a given set of states is NP-hard.

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24

Li, Junfang. "Evolution of Eigenvalues along Rescaled Ricci Flow." Canadian Mathematical Bulletin 56, no. 1 (March 1, 2013): 127–35. http://dx.doi.org/10.4153/cmb-2011-162-6.

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AbstractIn this paper, we discuss monotonicity formulae of various entropy functionals under various rescaled versions of Ricci flow. As an application, we prove that the lowest eigenvalue of a family of geometric operators -4Δ+kR is monotonic along the normalized Ricci flow for all k≥1 provided the initial manifold has nonpositive total scalar curvature.

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Nguyen, A. T., and V. Yu Tsviatkou. "Division of images into areas of local extrema with a monotonic change in pixel brightness." Doklady BGUIR 19, no. 4 (July 1, 2021): 61–69. http://dx.doi.org/10.35596/1729-7648-2021-19-4-61-69.

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In this paper, the problem of segmentation of halftone images is considered, in which areas of local maxima and minima (extrema) are distinguished with a monotonic change in the brightness of pixels from local extrema to the boundaries of areas. To solve this problem, a mathematical model is proposed and a segmentation algorithm is developed on the basis of counter-wave growing of local extremum regions. The developed algorithm differs from the known segmentation algorithms by using a set of brightness thresholds (by the number of regions), varying by one in each cycle, starting from the values of local extrema, taking into account the increase or decrease in brightness to select adjacent pixels that are attached to the regions formed from these local extrema. The algorithm provides a greater deviation of pixel brightness from the average value within the region compared to known segmentation algorithms. This does not allow evaluating its efficiency using known indicators based on the variance of the brightness within the region. In this regard, estimates of the monotonicity of changes in the brightness of regions are proposed based on a) the shortest distances from each pixel of the region to the corresponding local extremum along the routes determined by the maximum increase (for the region of the local maximum) or decrease (for the region of the local minimum) the brightness of pixels and b) taking into account the number pixels that break the monotony of the segment brightness change. Using these estimates, it is shown that the proposed algorithm provides segmentation of artificial and natural grayscale images with a monotonic change in the brightness of pixels in the areas of local extrema. These properties allow us to consider the developed algorithm as a basis for the selection of texels, spots, low-contrast objects in images.

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Hou, Xiaojie. "Analysis of a Model Arising from Invasion by Precursor and Differentiated Cells." International Journal of Differential Equations 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/341473.

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We study the wave solutions for a degenerated reaction diffusion system arising from the invasion of cells. We show that there exists a family of waves for the wave speed larger than or equal a certain number and below which there are no monotonic wave solutions. We also investigate the monotonicity, uniqueness, and asymptotics of the waves.

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Gupta, Ramesh C. "MEAN RESIDUAL LIFE FUNCTION FOR ADDITIVE AND MULTIPLICATIVE HAZARD RATE MODELS." Probability in the Engineering and Informational Sciences 30, no. 2 (December 15, 2015): 281–97. http://dx.doi.org/10.1017/s0269964815000388.

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This paper deals with the mean residual life function (MRLF) and its monotonicity in the case of additive and multiplicative hazard rate models. It is shown that additive (multiplicative) hazard rate does not imply reduced (proportional) MRLF and vice versa. Necessary and sufficient conditions are obtained for the two models to hold simultaneously. In the case of non-monotonic failure rates, the location of the turning points of the MRLF is investigated in both the cases. The case of random additive and multiplicative hazard rate is also studied. The monotonicity of the mean residual life is studied along with the location of the turning points. Examples are provided to illustrate the results.

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PEDERSEN, HENRIK L. "COMPLETELY MONOTONIC FUNCTIONS RELATED TO LOGARITHMIC DERIVATIVES OF ENTIRE FUNCTIONS." Analysis and Applications 09, no. 04 (October 2011): 409–19. http://dx.doi.org/10.1142/s0219530511001911.

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The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)p(xml(x))(m+p) is a completely monotonic function for all m ≥ 0. This generalizes earlier results on complete monotonicity of functions related to Euler's psi-function. Applications to Barnes' multiple gamma functions are given.

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Amat, Sergio, Sonia Busquier, and Antonio Escudero. "On the nonexistence of strictly monotonic Hölder continuous functions." Computing Letters 2, no. 1-2 (March 6, 2006): 89–91. http://dx.doi.org/10.1163/157404006777491918.

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This note is devoted to the study of the monotony of the Hölder continuous functions. We prove the nonexistence of a strictly monotonic (increasing or decreasing) hölder continuous function with exponent s ϵ (0, 1) such that it does not belongs for anypoint in a Hölder space with exponent s + ε ε > 0. We use simple analysis’ tools.

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Zhu, Bao-Xuan. "The Monotonicity and Log-Behaviour of Some Functions Related to the Euler Gamma Function." Proceedings of the Edinburgh Mathematical Society 60, no. 2 (November 9, 2016): 527–43. http://dx.doi.org/10.1017/s001309151600016x.

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AbstractThe aim of this paper is to develop analytic techniques to deal with the monotonicity of certain combinatorial sequences. On the one hand, a criterion for the monotonicity of the function is given, which is a continuous analogue of a result of Wang and Zhu. On the other hand, the log-behaviour of the functionsis considered, where ζ(x) and Γ(x) are the Riemann zeta function and the Euler Gamma function, respectively. Consequently, the strict log-concavities of the function θ(x) (a conjecture of Chen et al.) and for some combinatorial sequences (including the Bernoulli numbers, the tangent numbers, the Catalan numbers, the Fuss–Catalan numbers, and the binomial coefficients are demonstrated. In particular, this contains some results of Chen et al., and Luca and Stănică. Finally, by researching the logarithmically complete monotonicity of some functions, the infinite log-monotonicity of the sequenceis proved. This generalizes two results of Chen et al. that both the Catalan numbers and the central binomial coefficients are infinitely log-monotonic, and strengthens one result of Su and Wang that is log-convex in n for positive integers d > δ. In addition, the asymptotically infinite log-monotonicity of derangement numbers is showed. In order to research the stronger properties of the above functions θ(x) and F(x), the logarithmically complete monotonicity of functionsis also obtained, which generalizes the results of Lee and Tepedelenlioǧlu, and Qi and Li.

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Rebrus, Péter, and Miklós Törkenczy. "Monotonicity and the typology of front/back harmony." Theoretical Linguistics 41, no. 1-2 (January 1, 2015): 1–61. http://dx.doi.org/10.1515/tl-2015-0001.

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AbstractIn this paper, we analyse the surface patterns of suffix harmony in front/back harmony systems as the harmonic values front and back being assigned to harmonic contexts consisting of strings of syllables combining front, back and neutral nuclei. We claim that the harmonic contexts can be arranged in a fixed (universal) scale, the frontness/backness scale, with reference to which the possible (i.e. attested) front/back harmony systems can be characterised in a simple way: only those systems are possible where the assignment of values to the harmonic contexts is monotonic, which makes sure that only contiguous (non-interrupted) sequences of harmonic values are assigned to the harmonic contexts. We give formal definitions of monotonicity in terms of ordering and similarity and discuss predictions about possible harmony systems that follow from monotonicity (which we claim are borne out). These predictions are typological: harmony systems can show disharmonic behaviour, but in a principled way: only those systems exist (at least in front/back harmony) that exhibit a monotonic pattern. In the second half of the paper, we discuss variation in harmony and analyse in detail variation in anti-harmony and transparency in Hungarian, which is thus an example of a variable harmony pattern. We argue that variable front/back harmony patterns assign a “variable” value to some harmonic contexts in addition to the front and back values and can be shown to be constrained by monotonicity, whose definition is naturally extendable to patterns with variation. We discuss both the ordering-based and the similarity-based definitions and the predictions about possible variable harmony systems that follow from the definitions. One of the main predictions of the paper is a consequence of monotonicity: the locus of the variation in a pattern occurs only “in between” non-variable subpatterns. We explore a possible way of quantification in which we identify the harmonic values with the relative token frequency of the forms where the number associated with a variable value is

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32

Buzyakova, Raushan. "On monotonic bijections on subgroups of R." Applied General Topology 17, no. 2 (October 3, 2016): 83. http://dx.doi.org/10.4995/agt.2016.4116.

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We show that for any continuous monotonic bijection $f$ on a $\sigma$-compact subgroup $G\subset \mathbb R$ there exists a binary operation $+_f$ such that $\langle G, +_f\rangle$ is a topological group topologically isomorphic to $\langle G, +\rangle$ and $f$ is a shift with respect to $+_f$. We then show that monotonicity cannot be replaced by a periodic-point free continuous bijections. We explore a few routes leading to generalizations and counterexamples

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González, Sergio, Francisco Herrera, and Salvador García. "Monotonic Random Forest with an Ensemble Pruning Mechanism based on the Degree of Monotonicity." New Generation Computing 33, no. 4 (July 2015): 367–88. http://dx.doi.org/10.1007/s00354-015-0402-4.

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González, Sergio, Salvador García, Sheng-Tun Li, Robert John, and Francisco Herrera. "Fuzzy k-nearest neighbors with monotonicity constraints: Moving towards the robustness of monotonic noise." Neurocomputing 439 (June 2021): 106–21. http://dx.doi.org/10.1016/j.neucom.2019.12.152.

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Morita, Takashi. "Scalar implicatures in non-monotonic environments." Semantics and Linguistic Theory 26 (October 15, 2016): 205. http://dx.doi.org/10.3765/salt.v26i0.3799.

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Scalar implicatures (SIs) have been traditionally analyzed as pragmatic inferences that arise after semantic computation. Recent studies, however, have presented various challenges to this classic analysis; for instance, it has been claimed that SIs can be interpreted within the scope of various semantic operators. These observations motivate a grammatical analysis of SIs: SIs are derived during or before semantic computation. Among various kinds of evidence for the grammati- cal approach to SIs, especially convincing one is SIs embedded in non-monotonic (NM) environments, which post-semantic analyses have difficulty deriving. This paper introduces a new example of NM operators that allow the SI-embedding in their scope, and I thereby provide further empirical support for the grammatical analysis. On the other hand, I will also show that not all NM operators behave in the same way with respect to SI-embedding. It will turn out that Strawson non- monotonicity is required to embed SIs in the negative component of NM envi- ronments; i.e. SI-embedding is unavailable if the NMity can be decomposed into monotonic assertion and monotonic presupposition.

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Chand, A. K. B., and N. Vijender. "Monotonicity Preserving Rational Quadratic Fractal Interpolation Functions." Advances in Numerical Analysis 2014 (January 30, 2014): 1–17. http://dx.doi.org/10.1155/2014/504825.

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Fractal interpolation is an advanced technique for analysis and synthesis of scientific and engineering data. We introduce the 𝒞1-rational quadratic fractal interpolation functions (FIFs) through a suitable rational quadratic iterated function system (IFS). The novel notion of shape preserving fractal interpolation without any shape parameter is introduced through the rational fractal interpolation model in the literature for the first time. For a prescribed set of monotonic data, we derive the sufficient conditions by restricting the scaling factors for shape preserving 𝒞1-rational quadratic FIFs. A local modification pertaining to any subinterval is possible in this model if the scaling factors are chosen appropriately. We establish the convergence results of a monotonic rational quadratic FIF to the original function in 𝒞4. For given data with derivatives at grids, our approach generates several monotonicity preserving rational quadratic FIFs, whereas this flexibility is not available in the classical approach. Finally, numerical experiments support the importance of the developed rational quadratic IFS scheme through construction of visually pleasing monotonic rational fractal curves including the classical one.

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RAITH, PETER. "Discontinuities of the pressure for piecewise monotonic interval maps." Ergodic Theory and Dynamical Systems 21, no. 1 (February 2001): 197–232. http://dx.doi.org/10.1017/s0143385701001122.

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For a piecewise monotonic map T:X\to{\Bbb R}, where X is a finite union of closed intervals, define R(T)= \bigcap_{n=0}^{\infty}\overline{T^{-n}X}. The influence of small perturbations of T on the dynamical system (R(T),T) is investigated. If P is a finite and T-invariant subset of R(T), and if f_0:P\to{\Bbb R} is a non-negative continuous function, then it is proved that the infimum of the topological pressure p(R(T),T,f) over all non-negative continuous functions f:X\to{\Bbb R} with f|_P=f_0 equals the maximum of h_{\text{\rm top}}(R(T),T) and p(P,T,f_0). This result is used to obtain stability conditions, which are equivalent to the upper semi-continuity of the topological pressure for every continuous function f:X\to{\Bbb R}. In the case of a continuous piecewise monotonic map T:X\to{\Bbb R} one of these stability conditions is: there exists no endpoint of an interval of monotonicity of T which is periodic and contained in the interior of X. Furthermore, these results are applied to monotonic mod one transformations, another special case of piecewise monotonic maps.

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Michelena, N. F., and A. M. Agogino. "Formal Solution of N-Type Robust Parameter Design Problems with Stochastic Noise Factors." Journal of Mechanical Design 116, no. 2 (June 1, 1994): 501–7. http://dx.doi.org/10.1115/1.2919407.

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The Taguchi method of product design is a statistical experimental technique aimed at reducing the variance of a product performance characteristic due to uncontrollable factors. The goal of this paper is to provide a monotonicity analysis based methodology to facilitate the solution of N-type parameter design problems. The design obtained is robust in that the sensitivity to variations of uncontrollable factors (noise) has been minimized. The performance characteristic is unbiased in the sense that its expected value equals a target or specification. The proposed loss function is based on the absolute deviation of the characteristic with respect to the target, instead of the common square error approach. Conditions, like those imposed by monotonicity analysis, on the monotonic characteristics of the performance function are proven even for problems where the objective function is not monotonic and contains stochastic parameters. These conditions allow the qualitative analysis of the problem to identify the activity of some constraints. Identification of active sets of constraints allows a problem reduction strategy to be used, where the solution to the original problem is obtained by solving a set of problems with fewer degrees of freedom. Results for the case of one uncontrollable factor are independent of the probability measure on the factor. However, conclusions for the multiparametric case must take into account the characteristics of the probability space on which the random parameters are defined.

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Guo, Hongpeng, and Zhiming Guo. "Traveling Waves Solutions for Delayed Temporally Discrete Non-Local Reaction-Diffusion Equation." Mathematics 9, no. 16 (August 20, 2021): 1999. http://dx.doi.org/10.3390/math9161999.

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This paper deals with the existence of traveling wave solutions to a delayed temporally discrete non-local reaction diffusion equation model, which has been derived recently for a single species with age structure. When the birth function satisfies monotonic condition, we obtained the traveling wavefront by using upper and lower solution methods together with monotonic iteration techniques. Otherwise, without the monotonicity assumption for birth function, we constructed two auxiliary equations. By means of the traveling wavefronts of the auxiliary equations, using the Schauder’ fixed point theorem, we proved the existence of a traveling wave solution to the equation under consideration with speed c>c*, where c*>0 is some constant. We found that the delayed temporally discrete non-local reaction diffusion equation possesses the dynamical consistency with its time continuous counterpart at least in the sense of the existence of traveling wave solutions.

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Gao, Liang, Senbin Yu, Menghui Li, Zhesi Shen, and Ziyou Gao. "Weighted h-index for Identifying Influential Spreaders." Symmetry 11, no. 10 (October 10, 2019): 1263. http://dx.doi.org/10.3390/sym11101263.

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In this paper, we propose weighted h-index h w and h-index strength s h to measure spreading capability and identify the most influential spreaders. Experimental results on twelve real networks reveal that s h was more accurate and more monotonic than h w and four previous measures in ranking the spreading influence of a node evaluated by the single seed SIR spreading model. We point out that the questions of how to improve monotonicity and how to determine a proper neighborhood range are two interesting future directions.

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Yin, Hong. "Forward–backward stochastic partial differential equations with non-monotonic coefficients." Stochastics and Dynamics 16, no. 06 (November 6, 2016): 1650025. http://dx.doi.org/10.1142/s0219493716500258.

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In this paper we study the solvability of a class of fully-coupled forward–backward stochastic partial differential equations (FBSPDEs) with non-monotonic coefficients. These FBSPDEs cannot be put into the framework of stochastic evolution equations in general, and the usual decoupling methods for the Markovian forward–backward SDEs are difficult to apply. We prove the well-posedness of such FBSPDEs by using the method of continuation. Contrary to the common belief, we show that the usual monotonicity assumption can be removed by a change of the diffusion term.

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Giuggioli, L., J. R. Potts, and S. Harris. "Predicting oscillatory dynamics in the movement of territorial animals." Journal of The Royal Society Interface 9, no. 72 (January 18, 2012): 1529–43. http://dx.doi.org/10.1098/rsif.2011.0797.

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Understanding ecological processes relies upon the knowledge of the dynamics of each individual component. In the context of animal population ecology, the way animals move and interact is of fundamental importance in explaining a variety of observed patterns. Here, we present a theoretical investigation on the movement dynamics of interacting scent-marking animals. We study how the movement statistics of territorial animals is responsible for the appearance of damped oscillations in the mean square displacement (MSD) of the animals. This non-monotonicity is shown to depend on one dimensionless parameter, given by the ratio of the correlation distance between successive steps to the size of the territory. As that parameter increases, the time dependence of the animal's MSD displays a transition from monotonic, characteristic of Brownian walks, to non-monotonic, characteristic of highly correlated walks. The results presented here represent a novel way of determining the degree of persistence in animal movement processes within confined regions.

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TAY, KAI MENG, and CHEE PENG LIM. "ON MONOTONIC SUFFICIENT CONDITIONS OF FUZZY INFERENCE SYSTEMS AND THEIR APPLICATIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 19, no. 05 (October 2011): 731–57. http://dx.doi.org/10.1142/s0218488511007210.

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An important and difficult issue in designing a Fuzzy Inference System (FIS) is the specification of fuzzy sets and fuzzy rules. In this paper, two useful qualitative properties of the FIS model, i.e., the monotonicity and sub-additivity properties, are studied. The monotonic sufficient conditions of the FIS model with Gaussian membership functions are further analyzed. The aim is to incorporate the sufficient conditions into the FIS modeling process, which serves as a simple (which can be easily understood by domain users), easy-to-use (which can be easily applied to or can be a part of the FIS model), and yet reliable (which has a sound mathematical foundation) method to preserve the monotonicity property of the FIS model. Another aim of this paper is to demonstrate how these additional qualitative information can be exploited and extended to be part of the FIS designing procedure (i.e., for fuzzy sets and fuzzy rules design) via the sufficient conditions (which act as a set of useful governing equations for designing the FIS model). The proposed approach is able to avoid the "trial and error" procedure in obtaining a monotonic FIS model. To assess the applicability of the proposed approach, two practical problems are examined. The first is an FIS-based model for water level control, while the second is an FIS-based Risk Priority Number (RPN) model in Failure Mode and Effect Analysis (FMEA). To further illustrate the importance of the sufficient conditions as the governing equations, an analysis on the consequences of violating the sufficient conditions of the FIS-based RPN model is presented.

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Fantuzzi, Giovanni, Anton Pershin, and Andrew Wynn. "Bounds on heat transfer for Bénard–Marangoni convection at infinite Prandtl number." Journal of Fluid Mechanics 837 (January 5, 2018): 562–96. http://dx.doi.org/10.1017/jfm.2017.858.

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The vertical heat transfer in Bénard–Marangoni convection of a fluid layer with infinite Prandtl number is studied by means of upper bounds on the Nusselt number $Nu$ as a function of the Marangoni number $Ma$. Using the background method for the temperature field, it has recently been proved by Hagstrom & Doering (Phys. Rev. E, vol. 81, 2010, art. 047301) that $Nu\leqslant 0.838Ma^{2/7}$. In this work we extend previous background method analysis to include balance parameters and derive a variational principle for the bound on $Nu$, expressed in terms of a scaled background field, that yields a better bound than Hagstrom & Doering’s formulation at a given $Ma$. Using a piecewise-linear, monotonically decreasing profile we then show that $Nu\leqslant 0.803Ma^{2/7}$, lowering the previous prefactor by 4.2 %. However, we also demonstrate that optimisation of the balance parameters does not affect the asymptotic scaling of the optimal bound achievable with Hagstrom & Doering’s original formulation. We subsequently utilise convex optimisation to optimise the bound on $Nu$ over all admissible background fields, as well as over two smaller families of profiles constrained by monotonicity and convexity. The results show that $Nu\leqslant O(Ma^{2/7}(\ln Ma)^{-1/2})$ when the background field has a non-monotonic boundary layer near the surface, while a power-law bound with exponent $2/7$ is optimal within the class of monotonic background fields. Further analysis of our upper-bounding principle reveals the role of non-monotonicity, and how it may be exploited in a rigorous mathematical argument.

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Lazaropoulos, Athanasios G. "Best L1 Piecewise Monotonic Data Approximation in Overhead and Underground Medium-Voltage and Low-Voltage Broadband over Power Lines Networks: Theoretical and Practical Transfer Function Determination." Journal of Computational Engineering 2016 (September 6, 2016): 1–24. http://dx.doi.org/10.1155/2016/6762390.

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This paper investigates the efficiency and accuracy of the best L1 piecewise monotonic data approximation (best L1PMA) in order either to approximate the transfer functions of distribution BPL networks or to reveal the aforementioned transfer functions when various faults occur during their determination. The contribution of this paper is quadruple. First, based on the inherent piecewise monotonicity of distribution BPL transfer functions, a piecewise monotonic data approximation is first applied in BPL networks; best L1PMA is outlined and applied during the determination of distribution BPL transfer functions. Second, suitable performance metrics such as the percent error sum (PES) and fault PES are reported and applied so as to assess the efficiency and accuracy of the best L1PMA during the determination of distribution BPL transfer functions. Third, the factors of distribution BPL networks that influence the performance of best L1PMA are identified. Fourth, the accuracy of the best L1PMA is assessed with respect to its inherent properties, namely, the assumed number of monotonic sections and the nature of faults, that is, faults that follow either continuous uniform distribution (CUD) or normal distribution (ND), during the determination of distribution BPL transfer functions. Finally, best L1PMA may operate as the necessary intermediate antifault method for the theoretical and practical transfer function determination of distribution BPL networks.

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Uhler, Caroline, and Donald Richards. "Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables." Journal of Algebraic Statistics 10, no. 1 (April 10, 2019): 1–12. http://dx.doi.org/10.18409/jas.v10i1.71.

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We consider the lattice, $\mathcal{L}$, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and supermodularity for the marginalization function, $n(\cdot)$, on $\mathcal{L}$. We derive from the supermodularity of $n(\cdot)$ some generalized Fr\'echet inequalities complementing and extending inequalities of Dobra and Fienberg. Further, we construct new monotonic and supermodular functions from $n(\cdot)$, and we remark on the connection between supermodularity and some correlation inequalities for probability distributions on lattices. We also apply an inequality of Ky Fan to derive a new approach to Fr\'echet inequalities for multidimensional contingency tables.

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HIAI, FUMIO, MILÁN MOSONYI, DÉNES PETZ, and CÉDRIC BÉNY. "QUANTUM f-DIVERGENCES AND ERROR CORRECTION." Reviews in Mathematical Physics 23, no. 07 (August 2011): 691–747. http://dx.doi.org/10.1142/s0129055x11004412.

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Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well-known distinguishability measures of quantum states are given by, or derived from, f-divergences. Special examples include the quantum relative entropy, the Rényi relative entropies, and the Chernoff and Hoeffding measures. Here we show that the quantum f-divergences are monotonic under substochastic maps whenever the defining function is operator convex. This extends and unifies all previously known monotonicity results for this class of distinguishability measures. We also analyze the case where the monotonicity inequality holds with equality, and extend Petz' reversibility theorem for a large class of f-divergences and other distinguishability measures. We apply our findings to the problem of quantum error correction, and show that if a stochastic map preserves the pairwise distinguishability on a set of states, as measured by a suitable f-divergence, then its action can be reversed on that set by another stochastic map that can be constructed from the original one in a canonical way. We also provide an integral representation for operator convex functions on the positive half-line, which is the main ingredient in extending previously known results on the monotonicity inequality and the case of equality. We also consider some special cases where the convexity of f is sufficient for the monotonicity, and obtain the inverse Hölder inequality for operators as an application. The presentation is completely self-contained and requires only standard knowledge of matrix analysis.

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Kampik, Timotheus, and Juan Carlos Nieves. "Abstract argumentation and the rational man." Journal of Logic and Computation 31, no. 2 (February 4, 2021): 654–99. http://dx.doi.org/10.1093/logcom/exab003.

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Abstract Abstract argumentation has emerged as a method for non-monotonic reasoning that has gained popularity in the symbolic artificial intelligence community. In the literature, the different approaches to abstract argumentation that were refined over the years are typically evaluated from a formal logics perspective; an analysis that is based on models of economically rational decision-making does not exist. In this paper, we work towards addressing this issue by analysing abstract argumentation from the perspective of the rational man paradigm in microeconomic theory. To assess under which conditions abstract argumentation-based decision-making can be considered economically rational, we derive reference independence as a non-monotonic inference property from a formal model of economic rationality and create a new argumentation principle that ensures compliance with this property. We then compare the reference independence principle with other reasoning principles, in particular with cautious monotony and rational monotony. We show that the argumentation semantics as proposed in Dung’s seminal paper, as well as other semantics we evaluate, with the exception of naive semantics and the SCC-recursive CF2 semantics, violate the reference independence principle. Consequently, we investigate how structural properties of argumentation frameworks impact the reference independence principle and identify cyclic expansions (both even and odd cycles) as the root of the problem. Finally, we put reference independence into the context of preference-based argumentation and show that for this argumentation variant, which explicitly models preferences, reference independence cannot be ensured in a straight-forward manner.

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Górska, Katarzyna, Andrzej Horzela, and Roberto Garrappa. "Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type." Fractional Calculus and Applied Analysis 22, no. 5 (October 25, 2019): 1284–306. http://dx.doi.org/10.1515/fca-2019-0068.

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Abstract The paper [5] by R. Garrappa, S. Rogosin, and F. Mainardi, entitled “On a generalized three-parameter Wright function of the Le Roy type” and published in Fract. Calc. Appl. Anal. 20 (2017), 1196–1215, ends up leaving the open question concerning the range of the parameters α, β and γ for which Mittag-Leffler functions of Le Roy type $\begin{array}{} F_{\alpha, \beta}^{(\gamma)} \end{array}$ are completely monotonic. Inspired by the 1948 seminal H. Pollard’s paper which provides the proof of the complete monotonicity of the one-parameter Mittag-Leffler function, the Pollard approach is used to find the Laplace transform representation of $\begin{array}{} F_{\alpha, \beta}^{(\gamma)} \end{array}$ for integer γ = n and rational 0 < α ≤ 1/n. In this way it is possible to show that the Mittag-Leffler functions of Le Roy type are completely monotone for α = 1/n and β ≥ (n + 1)/(2n) as well as for rational 0 < α ≤ 1/2, β = 1 and n = 2. For further integer values of n the complete monotonicity is tested numerically for rational 0 < α < 1/n and various choices of β. The obtained results suggest that for the complete monotonicity the condition β ≥ (n + 1)/(2n) holds for any value of n.

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Wang, Hua Dong, Si Cong Guo, Seyed Mojtaba Hosseini Bamakan, and Yong Shi. "Homeomorphism Problems of Fuzzy Real Number Space and The Space of Bounded Functions with Same Monotonicity on [-1,1]." International Journal of Computers Communications & Control 10, no. 6 (October 3, 2015): 129. http://dx.doi.org/10.15837/ijccc.2015.6.2079.

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<p>In this paper, based on the fuzzy structured element, we prove that there is a bijection function between the fuzzy number space ε1 and the space B[−1, 1], which defined as a set of standard monotonic bounded functions with monotonicity on interval [−1, 1]. Furthermore, a new approach based upon the monotonic bounded functions has been proposed to create fuzzy numbers and represent them by suing fuzzy structured element. In order to make two different metrics based space in B[−1, 1], Hausdorff metric and Lp metric, which both are classical functional metrics, are adopted and their topological properties are discussed. In addition, by the means of introducing fuzzy functional to space B[−1, 1], we present two new fuzzy number’s metrics. Finally, according to the proof of homeomorphism between fuzzy number space ε1 and the space B[−1, 1], it’s argued that not only does it give a new way to study the fuzzy analysis theory, but also makes the study of fuzzy number space easier.</p>

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