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Artykuły w czasopismach na temat „Bernoulli hypothesis”

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Data publikacji: 29 lipca 2024

Data aktualizacji: 19 lipca 2025

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Sampath, S., and L. Pephine Renitta. "Chance Hypotheses Testing." International Journal of Fuzzy System Applications 5, no. 3 (2016): 77–108. http://dx.doi.org/10.4018/ijfsa.2016070105.

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This paper considers the problem of testing hypotheses about hybrid distributions which are models representing situations where impreciseness (explained through fuzzy measure) and randomness (explained through probability measure) coexist. A criterion similar to the Neyman-Pearson criterion is proposed for testing a simple chance null hypothesis against a simple chance alternative hypothesis. The suggested criterion has been applied for testing hypotheses about hybrid triangular Bernoulli distribution and hybrid Poisson distribution. Optimal properties of the resulting tests have also been investigated.

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Babilua, Petre, and Elizbar Nadaraya. "On a new method of the testing hypothesis of equality of two Bernoulli regression functions for group observations." Georgian Mathematical Journal 29, no. 2 (2022): 167–77. http://dx.doi.org/10.1515/gmj-2021-2133.

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Abstract In the paper, the limiting distribution is established for an integral square deviation of estimates of Bernoulli regression functions based on two group samples. Based on these results, the new test is constructed for the hypothesis testing on the equality of two Bernoulli regression functions. The question of consistency of the constructed test is studied, and the asymptotic of the test power is investigated for some close alternatives.

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Zaikin, A. A. "Asymptotic Expansion of D-Risks for Hypothesis Testing in Bernoulli Scheme." Lobachevskii Journal of Mathematics 39, no. 3 (2018): 413–23. http://dx.doi.org/10.1134/s1995080218030204.

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Ciuonzo, D., A. De Maio, and P. Salvo Rossi. "A Systematic Framework for Composite Hypothesis Testing of Independent Bernoulli Trials." IEEE Signal Processing Letters 22, no. 9 (2015): 1249–53. http://dx.doi.org/10.1109/lsp.2015.2395811.

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Granstrom, Karl, Peter Willett, and Yaakov Bar-Shalom. "Approximate Multi-Hypothesis Multi-Bernoulli Multi-Object Filtering Made Multi-Easy." IEEE Transactions on Signal Processing 64, no. 7 (2016): 1784–97. http://dx.doi.org/10.1109/tsp.2015.2500884.

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Novikov, Andrey. "A numerical approach to sequential multi-hypothesis testing for Bernoulli model." Sequential Analysis 42, no. 3 (2023): 303–22. http://dx.doi.org/10.1080/07474946.2023.2215825.

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Karelis, Charles. "Distributive Justice and the Public Good." Economics and Philosophy 2, no. 1 (1986): 101–25. http://dx.doi.org/10.1017/s026626710000081x.

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Many philosophers and some economists value economic equality on the ground that transfers from the relatively rich to the relatively poor increase the utility of the poor more than they reduce the utility of the rich. These philosophers and economists are assuming the ethical principle that a pattern of economic distribution is justified by maximizing aggregate utility. They are also assuming the truth of an empirical generalization proposed in the eighteenth century by Daniel Bernoulli–that successive equal increments of income produce ever-diminishing increments in an individual's level of utility. In the first part of this essay I will argue against Bernoulli's hypothesis, and suggest an alternative view of the relation between income and utility.

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Zhang, Zijing, Fei Zhang, and Chuantang Ji. "Multi-robot cardinality-balanced multi-Bernoulli filter simultaneous localization and mapping method." Measurement Science and Technology 33, no. 3 (2021): 035101. http://dx.doi.org/10.1088/1361-6501/ac3784.

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Abstract In order to improve the simultaneous localization and mapping (SLAM) accuracy of mobile robots in complex indoor environments, the multi-robot cardinality-balanced multi-Bernoulli filter SLAM (MR-CBMber-SLAM) method is proposed. First of all, this method introduces a multi-Bernoulli filter based on the random finite set (RFS) theory to solve the complex data association problem. This method aims to overcome the problem that the multi-Bernoulli filter will overestimate the aspect of SLAM map feature estimation, and combines the strategy of balancing cardinality with a multi-Bernoulli filter. What is more, in order to further improve the accuracy and operating efficiency of SLAM, a multi-robot strategy and a multi-robot Gaussian information-fusion method are proposed. In the experiment, the MR-CBMber-SLAM method is compared with the multi-vehicle probability hypothesis density SLAM (MV-PHD-SLAM) method. The experimental results show that the MR-CBMber-SLAM method is better than MV-PHD-SLAM method. Therefore, it effectively verifies that the MR-CBMber-SLAM method is more adaptable to a complex indoor environment.

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Ren, Yayun, and Benlian Xu. "A Quantitative Analysis on Two RFS-Based Filtering Methods for Multicell Tracking." Mathematical Problems in Engineering 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/495765.

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Multiobject filters developed from the theory of random finite sets (RFS) have recently become well-known methods for solving multiobject tracking problem. In this paper, we present two RFS-based filtering methods, Gaussian mixture probability hypothesis density (GM-PHD) filter and multi-Bernoulli filter, to quantitatively analyze their performance on tracking multiple cells in a series of low-contrast image sequences. The GM-PHD filter, under linear Gaussian assumptions on the cell dynamics and birth process, applies the PHD recursion to propagate the posterior intensity in an analytic form, while the multi-Bernoulli filter estimates the multitarget posterior density through propagating the parameters of a multi-Bernoulli RFS that approximates the posterior density of multitarget RFS. Numerous performance comparisons between the two RFS-based methods are carried out on two real cell images sequences and demonstrate that both yield satisfactory results that are in good agreement with manual tracking method.

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Li, Shijie, and Humin Lei. "Measurement-Driven Multi-Target Multi-Bernoulli Filter." Mathematical Problems in Engineering 2018 (July 22, 2018): 1–9. http://dx.doi.org/10.1155/2018/6515608.

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A measurement-driven multi-target multi-Bernoulli (MeMBer) filter which modifies the MeMBer filter by the measurements information is proposed in this paper. The proposed filter refines both the legacy estimates and the data-induced estimates of the MeMBer filter. For the targets under the legacy track set, the detection probabilities derived from the measurements are employed to refine the multi-target distribution. And for the targets under the data-induced track set, the multi-target distribution is further improved by the modified existence probabilities of the legacy tracks. Unlike the cardinality balanced MeMBer (CBMeMBer) filter, the proposed filter removes the cardinality bias in the MeMBer filter by utilizing the measurements information. Simulation results show that, compared with the traditional methods, the proposed filter can improve the stability and accuracy of the estimates and does not need the high detection probability hypothesis.

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Gunel, Erdogan. "Bernoulli Trials and the Weight of Evidence in Favour of a Null Hypothesis." Biometrika 74, no. 2 (1987): 440. http://dx.doi.org/10.2307/2336162.

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GÜnel, ERDOGAN. "Bernoulli trials and the weight of evidence in favour of a null hypothesis." Biometrika 74, no. 2 (1987): 440–42. http://dx.doi.org/10.1093/biomet/74.2.440.

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Qiu, Hao, Gaoming Huang, and Jun Gao. "Centralized multi-sensor multi-target tracking with labeled random finite set." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 231, no. 4 (2016): 669–76. http://dx.doi.org/10.1177/0954410016641447.

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Tracking multiple objects with multiple sensors is widely recognized to be much more complex than the single-sensor scenario. This contribution proposes a computationally tractable multi-sensor multi-target tracker. Based on Bayes equation and multi-senor observation model, a new corrector for multi-senor is derived. To lower the complexity of update operation, a parallel track-to-measurement association strategy is applied to the corrector. Hypotheses truncation scheme along with first-moment approximation of multi-target density are also employed to improve the tracking efficiency. The tracker is applied to a couple-sensor scenario. Experiment results validate the advantages of proposed method compared to the standard single-sensor δ-generalized labeled multi-Bernoulli filter and the iterated-corrector probability hypothesis density filter.

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Chi, Luo-jia, Xin-xi Feng, and Lu Miao. "Generalized Labeled Multi-Bernoulli Extended Target Tracking Based on Gaussian Process Regression." MATEC Web of Conferences 176 (2018): 01017. http://dx.doi.org/10.1051/matecconf/201817601017.

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For the problems that Gamma Gaussian Inverse Wishart Cardinalized Probability Hypothesis Density (GGIW-CPHD) filter cannot accurately estimate the extended target shape and has a bad tracking performance under the condition of low SNR, a new generalized labeled multi-Bernoulli algorithm based on Gaussian process regression is proposed. The algorithm adopts the star convex to model the extended target, and realizes the online learning of the Gaussian process by constructing the state space model to complete the estimation of the extended target shape. At the same time, in the low SNR environment, the target motion state is tracked by the good tracking performance of the generalized label Bernoulli filter. Simulation results show that for any target with unknown shape, the proposed algorithm can well offer its extended shape and in the low SNR environment it can greatly improve the accuracy and stability of target tracking.

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RODRIGUEZ HERTZ, F., M. A. RODRIGUEZ HERTZ, A. TAHZIBI, and R. URES. "Maximizing measures for partially hyperbolic systems with compact center leaves." Ergodic Theory and Dynamical Systems 32, no. 2 (2011): 825–39. http://dx.doi.org/10.1017/s0143385711000757.

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AbstractWe obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of three-dimensional manifolds having compact center leaves: either there is a unique entropy-maximizing measure, this measure has the Bernoulli property and its center Lyapunov exponent is 0, or there are a finite number of entropy-maximizing measures, all of them with non-zero center Lyapunov exponents (at least one with a negative exponent and one with a positive exponent), that are finite extensions of a Bernoulli system. In the first case of the dichotomy, we obtain that the system is topologically conjugated to a rotation extension of a hyperbolic system. This implies that the second case of the dichotomy holds for an open and dense set of diffeomorphisms in the hypothesis of our result. As a consequence, we obtain an open set of topologically mixing diffeomorphisms having more than one entropy-maximizing measure.

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Mittou, Brahim, and Abdallah Derbal. "Method for calculating Dirichlet L-functions." Mathematica Montisnigri 54 (2022): 51–58. http://dx.doi.org/10.20948/mathmontis-2022-54-5.

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Recently, the authors gave asymptotic formulas for L(s, χ), which associated with a primitive Dirichlet character χ, in terms of the generalized Bernoulli numbers. In this paper, based on the aforementioned asymptotic formulas we describe a method for calculating Dirichlet L-functions that can be used to validate the generalized Riemann hypothesis up to a height T > 0. Our method is a refinement of the one presented by Davies and Haselgrove.

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Zozulya, V. V. "Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models." Curved and Layered Structures 4, no. 1 (2017): 104–18. http://dx.doi.org/10.1515/cls-2017-0008.

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AbstractNew models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke’s law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.

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Sutejo, Sutejo, Eka Yuli Sari Asmawati, Lakon Wahono, and Nyoto Suseno. "Project Based Learning (Pjbl) dalam Proses Pembelajaran Daring pada Materi Hukum Bernoulli Menggunakan Botol Bekas." Jurnal Pendidikan Fisika dan Teknologi 7, no. 2 (2021): 218–23. http://dx.doi.org/10.29303/jpft.v7i2.3268.

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Covid-19 has an impact on education. In order to maintain the quality of learning, online mode learning innovation is carried out with the application of project based learning through experiments in the application of Bernoulli's Law on used bottle leaks. Online learning at SMAN 1 Metro usually uses Problem Based Learning. In this study will be used PjBl to increase the creativity of students. This research aims to explore students' ability in problem solving in dynamic fluid concepts. This type of research is quantitative with a Quasi Experimental approach, and the design used is Nonequivalent Group Design. The subject of the study was Sma N 1 Metro in class XI IPA which numbered 67 students. The analysis method uses the N-Gain Test and the different tests between the two sample groups. Results: N-Gain in experimental class by 65.74% and in control class by 25.04%. Based on hypothesis tests, it was found that the effect of applying madel project based learning in improving student learning outcomes in Bernoulli Law material. Project based learning model in online learning is also effective in developing 4Cs.

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Wang, Ping, Liang Ma, and Kai Xue. "Multitarget tracking in sensor networks via efficient information-theoretic sensor selection." International Journal of Advanced Robotic Systems 14, no. 5 (2017): 172988141772846. http://dx.doi.org/10.1177/1729881417728466.

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In networks composed of moving robots or static sensing nodes, multitarget tracking is critical and fundamental for high-level applications, such as scene analysis or event detection. However, tracking multiple targets in the sensor network is challenging for two reasons: multisensor multitarget fusion itself is difficult and dynamic sensor scheduling is necessary to balance the tracking accuracy and energy consumption of the sensor network. In this article, we present a novel information-theoretic sensor selection method for multitarget tracking via the multi-Bernoulli filter. The sensor selection is based on the multi-Bernoulli filtering and a collection of subselection problems for individual target to avoid the combinatorial optimization. A subselection problem for each target is investigated under the framework of partially observed Markov decision process, and we propose to solve it by maximizing the information gain of the probability hypothesis density. Simulation results validate the effectiveness and efficiency of our method for multitarget tracking in sensor networks.

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Sun, Chengkun, Jinqian Pan, Russell Stevens Terry, Jiang Bian, and Jie Xu. "BGDB: Bernoulli-Gaussian Decision Block with Improved Denoising Diffusion Probabilistic Models." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 19 (2025): 20681–89. https://doi.org/10.1609/aaai.v39i19.34279.

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Generative models can enhance discriminative classifiers by constructing complex feature spaces, thereby improving performance on intricate datasets. Conventional methods typically augment datasets with more detailed feature representations or increase dimensionality to make nonlinear data linearly separable. Utilizing a generative model solely for feature space processing falls short of unlocking its full potential within a classifier and typically lacks a solid theoretical foundation. We base our approach on a novel hypothesis: the probability information (logit) derived from a single model training can be used to generate the equivalent of multiple training sessions. Leveraging the central limit theorem, this synthesized probability information is anticipated to converge toward the true probability more accurately. To achieve this goal, we propose the Bernoulli-Gaussian Decision Block (BGDB), a novel module inspired by the Central Limit Theorem and the concept that the mean of multiple Bernoulli trials approximates the probability of success in a single trial. Specifically, we utilize Improved Denoising Diffusion Probabilistic Models (IDDPM) to model the probability of Bernoulli Trials. Our approach shifts the focus from reconstructing features to reconstructing logits, transforming the logit from a single iteration into logits analogous to those from multiple experiments. We provide the theoretical foundations of our approach through mathematical analysis and validate its effectiveness through experimental evaluation using various datasets for multiple imaging tasks, including both classification and segmentation.

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Shaptsev, V. A. "Introducing a Dependency into the Bernoulli Trial Scheme." Mathematical structures and modeling, no. 2 (2017): 29–35. https://doi.org/10.24147/2222-8772.2017.2.29-35.

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A new structure of analytical representation of the scheme of $n$ independent Bernoulli trials is proposed by means of ordered subsets $m$ ($m < n$) of numbers of successful and $n-m$ unsuccessful trials. In this case, the probability characteristic of the type $P_{n}(m)$ is determined by summing the binomial formula ${p^{m}(1-p)^{n-m}}$ over all such subsets, and not by simple multiplication by the number of combinations $C_{n}^{m}$. The corresponding expressions for the probability of success with two and $k > 2$ outcomes of experiments are given, for the cases of equal and different probabilities of outcomes in different trials. In this symbolism, expressions are obtained for calculating the corresponding probabilities of a given number of successful trials in the presence of a dependence of the probabilities of outcomes on some parameter changing in time (from trial to trial), regularly or randomly. Thus, a basis for applying the dependent testing scheme to assessing the probabilistic characteristics of complex stochastic systems, network architecture, in particular, characterized by some changing quality indicator, is created. In conclusion, an expression is given for the mathematical expectation of the probability of $m$ successful tests out of n in the case of a random parameter on which the probabilities of outcomes depend. A hypothesis is formulated on the possibility of using a finite-dimensional characteristic function of a random parameter in the corresponding expression with an exponential dependence of the probability of the outcome of the experiment on the random parameter.

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ALKAN, EMRE. "RAMANUJAN SUMS AND THE BURGESS ZETA FUNCTION." International Journal of Number Theory 08, no. 08 (2012): 2069–92. http://dx.doi.org/10.1142/s1793042112501187.

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The Mellin transform of a summatory function involving weighted averages of Ramanujan sums is obtained in terms of Bernoulli numbers and values of the Burgess zeta function. The possible singularity of the Burgess zeta function at s = 1 is then shown to be equivalent to the evaluation of a certain infinite series involving such weighted averages. Bounds on the size of the tail of these series are given and specific bounds are shown to be equivalent to the Riemann hypothesis.

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Behdinan, K., M. C. Stylianou, and B. Tabarrok. "STATIC AND DYNAMIC ANALYSIS OF FLEXIBLE BEAMS: A CONSISTENT UPDATED LAGRANGIAN FORMULATION." Transactions of the Canadian Society for Mechanical Engineering 21, no. 2 (1997): 141–77. http://dx.doi.org/10.1139/tcsme-1997-0010.

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A study of static and dynamic analysis of slender beams undergoing large deflections is undertaken here. the Euler-Bernoulli hypothesis is employed and the beam deforms with large rotations but small strains. Initially the static analysis, using the consistent updated Lagrangian techniques which accounts for full non-linearity of the beam is undertaken and is then extended to dynamic analysis. Several examples illustrating the implementation and the performance of the proposed formulation are included and a comparison with results obtained by the co-rotational method is provided.

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Baksa, Attila, and István Ecsedi. "Bending of Curved Composite Beam with Interlayer Slip." Multidiszciplináris Tudományok 14, no. 2 (2024): 104–19. http://dx.doi.org/10.35925/j.multi.2024.2.10.

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Elastic two-layer curved composite beam with partial shear interaction is considered. It is assumed that each curved layer separately follows the Euler-Bernoulli hypothesis and the load slip relation for the flexible shear connection is a linear relationship. The curved composite beam is subjected to uniform bending. The paper presents solutions for stresses, radial displacement, and slip. The end cross sections of the layered curved beam are loaded by zero moment force couples, as a result of which each cross section of the beam is loaded by zero moment force couple resultant.

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CIELIEBAK, K., and E. VOLKOV. "A note on the stationary Euler equations of hydrodynamics." Ergodic Theory and Dynamical Systems 37, no. 2 (2015): 454–80. http://dx.doi.org/10.1017/etds.2015.50.

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This note concerns stationary solutions of the Euler equations for an ideal fluid on a closed 3-manifold. We prove that if the velocity field of such a solution has no zeroes and real analytic Bernoulli function, then it can be rescaled to the Reeb vector field of a stable Hamiltonian structure. In particular, such a vector field has a periodic orbit unless the 3-manifold is a torus bundle over the circle. We provide a counterexample showing that the correspondence breaks down without the real analyticity hypothesis.

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Xu, Wenjie, Huaguo Zhang, Gaiyou Li, and Wanchun Li. "Vardiational Bayesian Hybrid Multi-Bernoulli and CPHD Filters for Superpositional Sensors." Electronics 12, no. 9 (2023): 2083. http://dx.doi.org/10.3390/electronics12092083.

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This paper addresses the problem of multi-target tracking with superpositional sensors, while the covariance matrices of measurement noise are not known. The proposed method is based on the hybrid multi-Bernoulli cardinalized probability hypothesis density (HMB-CPHD) filter, which has been developed for superpositional sensors-based multi-target tracking with known measurement noises. Specifically, we firstly propose the Gaussian mixture (GM) implementation of the HMB-CPHD filter, and then the covariance matrices of measurement noises are augmented into the target state vector, resulting in the Gaussian and inverse Wishart mixture (GIWM) representation of the augmented state. Then the variational Bayesian (VB) method is exploited to approximate the posterior distribution so that it maintains the same form as the prior distribution. A remarkable feature of the proposed method is that it can jointly perform multi-target tracking and measurement noise covariance estimation. The performance of the proposed algorithm is demonstrated via simulations.

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Zozulya, V. V. "Nonlocal theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models." Curved and Layered Structures 4, no. 1 (2017): 221–36. http://dx.doi.org/10.1515/cls-2017-0015.

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Abstract New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.

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Tsarev, O. Yu, and Yu A. Tsarev. "Validation of Reliability Indices during Experimental Development of a Complex Technical Series System." Advanced Engineering Research 23, no. 1 (2023): 26–33. http://dx.doi.org/10.23947/2687-1653-2023-23-1-26-33.

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Introduction. The article studies the problem of validating the specified levels of reliability during experimental development of a complex technical series system. Such tasks arise when it is required to make a decision on testing the system as part of a larger one or on the completion of experimental development and the start of series production. The study is aimed at validating the reduction of the experimental development time. The task is to determine whether the hypothesis Но is accepted or rejected.Materials and Methods. To implement the research objective and task, a critical area described by the inequality was constructed based on the test results. The formulation of the requirements validation task was based on well-known approaches to testing statistical hypotheses. The conceptual apparatus of information theory, probability, and statistics was involved. The theoretical and applied literature on mathematical methods in reliability theory was studied. The particular tasks of the work were solved by known ways. Thus, the probability of obtaining the exact number of successful outcomes in a certain number of experiments was determined by the Bernoulli scheme. The exact confidence interval based on the binomial distribution was derived from the Clopper-Pearson relation. The theorem of A.D. Solovyov and R. A. Mirny made it possible to assess the system reliability based on the test results of its components.Results. Control rules adequate to the stage of experimental development (with insufficient data on the technical system) and the stage of series production were mathematically defined. The probability of a successful outcome when testing technical systems was represented by:– the probability of event for a system element;– confidence value;– required scope of tests.In these terms, the null and alternative hypotheses and the corresponding reliability control procedures were investigated. Two provisions were considered. The first one provided using the null confidence hypothesis Но = {Р ≥ РТ} and an alternative Н = { Р < РТ} to confirm the requirements (РТ, γ) for the reliability indicator of one parameter for any (РТ, γ). In this case, one trouble-free test was enough. The second provision considered a sequential technical system with independent elements that were tested separately from the system according to the Bernoulli scheme for one parameter. We considered the requirements for the system in the form of a set of values (РТ, γ) and the requirements for any of its elements (РТi, γ). They coincided when the planned outcome of the tests corresponded to the cases when the ratio Р= lim 1≤i≤N : Р i = Р m was fulfilled, and the null alternative hypothesis was selected from the theory of statistical hypothesis testing.Discussion and Conclusions. The experimental development strategy should be implemented in two stages: the search and validation of the reliability of the elements through a series of fail-safe tests. In this case, the planned scope of tests of each element is determined taking into account the confidence probability, the lower limit of the confidence interval, and the requirements for reliability indices of one parameter of the technical system. If the use of the null confidence hypothesis is acceptable, one fail-safe test is sufficient to confirm the requirements for the reliability index.

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Zozulya, V. V. "Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models." Curved and Layered Structures 4, no. 1 (2017): 119–33. http://dx.doi.org/10.1515/cls-2017-0009.

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AbstractNew models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby, all equations of elasticity including Hooke’s law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

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Khan, Yasir, and Mehdi Akbarzade. "Dynamic Analysis of Nonlinear Oscillator Equation Arising in Double-Sided Driven Clamped Microbeam-Based Electromechanical Resonator." Zeitschrift für Naturforschung A 67, no. 8-9 (2012): 435–40. http://dx.doi.org/10.5560/zna.2012-0043.

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In this paper, three different analytical methods have been successfully used to study a nonlinear oscillator equation arising in the microbeam-based electromechanical resonator. These methods are: variational approach, Hamiltonian approach, and amplitude-frequency formulation. The governing equation is based on the Euler-Bernoulli hypothesis and the partial differential equation (PDE) is simplified into an ordinary differential equartion (ODE) by using the Galerkin method. A frequency analysis is carried out, and the relationship between the angular frequency and the initial amplitude is obtained in closed analytical form. A comparison of the present solutions is made with the existing solutions and excellent agreement is noted.

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Safronov, Oleksandr, Bohdan Semon, Oleksandr Nedilko, and Yurii Bodryk. "Mathematical Models of Transonic Flatter of Aerody-namic Control Surfaces of Supersonic Aircraft." Advances in Military Technology 17, no. 2 (2022): 195–209. http://dx.doi.org/10.3849/aimt.01543.

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In the article, the joint analysis of the Bernoulli equations for compressed gas, variations of the supersonic flow parameters of the Prandtl-Meyer expansion fan and the hypothesis of aerofoil dynamic curvature were used to develop a linear and a nonlinear mathematical models describing the occurrence of transonic flutter of aerodynamic control surfaces of supersonic aircraft. The analysis of the obtained mathematical models confirms a theoretical possibility of the occurrence of transonic flutter of aerodynamic control surfaces of supersonic aircraft that is due to the peculiarities of the interaction of shock waves with the angular velocity of elastic bending oscillations of aerodynamic control surfaces.

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Zhang, Yichi, and Bingen Yang. "Medium-Frequency Vibration Analysis of Timoshenko Beam Structures." International Journal of Structural Stability and Dynamics 20, no. 13 (2020): 2041009. http://dx.doi.org/10.1142/s0219455420410096.

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Medium-frequency (mid-frequency) vibration analysis of complex structures plays an important role in automotive, aerospace, mechanical, and civil engineering. Flexible beam structures modeled by the classical Euler–Bernoulli beam theory have been widely used in various engineering problems. A kinematic hypothesis made in the Euler–Bernoulli beam theory is that the plane sections of a beam normal to its neutral axis remain planes after the beam experiences bending deformation, which neglects shear deformation. However, previous investigations found out that the shear deformation of a beam (even with a large slenderness ratio) becomes noticeable in high-frequency vibrations. The Timoshenko beam theory, which describes both bending deformation and shear deformation, would naturally be more suitable for medium-frequency vibration analysis. Nevertheless, vibrations of Timoshenko beam structures in a medium frequency region have not been well studied in the literature. This paper presents a new method for mid-frequency vibration analysis of two-dimensional Timoshenko beam structures. The proposed method, which is called the augmented Distributed Transfer Function Method (DTFM), models a Timoshenko beam structure by a spatial state-space formulation in the [Formula: see text]-domain. The augmented DTFM determines the frequency response of a beam structure in an exact and analytical form, in any frequency region covering low, middle, or high frequencies. Meanwhile, the proposed method provides the local information of a beam structure, such as displacement, shear deformation, bending moment and shear force at any location, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated in numerical examples, where the efficiency and accuracy of the proposed method is demonstrated. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are examined through comparison of the Timoshenko beam and Euler–Bernoulli beam theories.

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Diochnos, Dimitrios. "On the Evolvability of Monotone Conjunctions with an Evolutionary Mutation Mechanism." Journal of Artificial Intelligence Research 70 (March 5, 2021): 891–921. http://dx.doi.org/10.1613/jair.1.12050.

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A Bernoulli(p)n distribution Bn,p over {0, 1}n is a product distribution where each variable is satisfied with the same constant probability p. Diochnos (2016) showed that Valiant's swapping algorithm for monotone conjunctions converges efficiently under Bn,p distributions over {0, 1}n for any 0 < p < 1. We continue the study of monotone conjunctions in Valiant's framework of evolvability. In particular, we prove that given a Bn,p distribution characterized by some p ∈ (0, 1/3] ∪ {1/2}, then an evolutionary mechanism that relies on the basic mutation mechanism of a (1+1) evolutionary algorithm converges efficiently, with high probability, to an ε-optimal hypothesis. Furthermore, for 0 < α ≤ 3/13, a slight modification of the algorithm, with a uniform setup this time, evolves with high probability an ε-optimal hypothesis, for every Bn,p distribution such that p ∈ [α, 1/3 - 4α/9] ∪ {1/3} ∪ {1/2}.

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Jiang, Defu, Ming Liu, Yiyue Gao, Yang Gao, Wei Fu, and Yan Han. "Time-Matching Random Finite Set-Based Filter for Radar Multi-Target Tracking." Sensors 18, no. 12 (2018): 4416. http://dx.doi.org/10.3390/s18124416.

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The random finite set (RFS) approach provides an elegant Bayesian formulation of the multi-target tracking (MTT) problem without the requirement of explicit data association. In order to improve the performance of the RFS-based filter in radar MTT applications, this paper proposes a time-matching Bayesian filtering framework to deal with the problem caused by the diversity of target sampling times. Based on this framework, we develop a time-matching joint generalized labeled multi-Bernoulli filter and a time-matching probability hypothesis density filter. Simulations are performed by their Gaussian mixture implementations. The results show that the proposed approach can improve the accuracy of target state estimation, as well as the robustness.

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Číhal, Michal, Jaromír Kabeláč, Michael Konečný, and Lukáš Juříček. "Serviceability Limit State Evaluation in Discontinuity Regions." Solid State Phenomena 292 (June 2019): 203–9. http://dx.doi.org/10.4028/www.scientific.net/ssp.292.203.

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Discontinuity Region Design method was recently extended to allow assessment of serviceability limit states (SLS) for regions of concrete structural members where the Bernoulli-Navier hypothesis does not hold, such as dapped ends, openings, frame corners, etc. The method uses material models which consider the impact of short- and long-term loading effects (creep) as well as the influence of tension stiffening, which are calculated from reinforcement ratios. The method can be used to perform assessment of stress limitation SLS as well as to calculate crack widths. Crack width calculations for both stabilized and non-stabilized cracks have been compared with real-world experiments. Calculations regarding deflection and strain in concrete and concrete rebars are compared with analytical calculations.

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Daniel, Popescu. "VIBRATION ANALYSIS OF THE TOOL BEARING SPINDLE IN CASE OF SUPERFINISHING TECHNOLOGIAL PROCESSES ESTABLISHMENT OF THE GENERAL MOVEMENT EQUATIONS." International Journal of Research -GRANTHAALAYAH 8, no. 5 (2020): 339–47. https://doi.org/10.29121/granthaalayah.v8.i5.2020.222.

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The paper presents a mathematical model for determining the general movement equations that describe the vibration movement of the tool bearer spindle at superfinishing operations. There are presented the specific problems and the work schematics. The mathematical model uses the axioms of kinetic impulse and moment derivatives. At superfinishing, the spindle is eccentric and its working position is vertical. A series of simplifying assumptions are used, such as: Bernoulli’s hypothesis, the movement is without shocks, there are no remnant tensions, the strains are of elastic nature only. There are emphasized the components of the movement equations under restricted matrix form. The effect of transversal contraction and the torsion vibrations are neglected.

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Abraham, Rosmi, Faheem Khan, Syed A. Bukhari, et al. "Effect of Surface and Interfacial Tension on the Resonance Frequency of Microfluidic Channel Cantilever." Sensors 20, no. 22 (2020): 6459. http://dx.doi.org/10.3390/s20226459.

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The bending resonance of micro-sized resonators has been utilized to study adsorption of analyte molecules in complex fluids of picogram quantity. Traditionally, the analysis to characterize the resonance frequency has focused solely on the mass change, whereas the effect of interfacial tension of the fluid has been largely neglected. By observing forced vibrations of a microfluidic cantilever filled with a series of alkanes using a laser Doppler vibrometer (LDV), we studied the effect of surface and interfacial tension on the resonance frequency. Here, we incorporated the Young–Laplace equation into the Euler–Bernoulli beam theory to consider extra stress that surface and interface tension exerts on the vibration of the cantilever. Based on the hypothesis that the near-surface region of a continuum is subject to the extra stress, thin surface and interface layers are introduced to our model. The thin layer is subject to an axial force exerted by the extra stress, which in turn affects the transverse vibration of the cantilever. We tested the analytical model by varying the interfacial tension between the silicon nitride microchannel cantilever and the filled alkanes, whose interfacial tension varies with chain length. Compared with the conventional Euler–Bernoulli model, our enhanced model provides a better agreement to the experimental results, shedding light on precision measurements using micro-sized cantilever resonators.

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Pereira, Carlos, Eduardo Nakano, Victor Fossaluza, Luís Esteves, Mark Gannon, and Adriano Polpo. "Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions." Entropy 19, no. 12 (2017): 696. http://dx.doi.org/10.3390/e19120696.

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Sebbar, Ahmed. "Harmonic numbers, harmonic series and zeta function." Moroccan Journal of Pure and Applied Analysis 4, no. 2 (2018): 122–57. http://dx.doi.org/10.1515/mjpaa-2018-0012.

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AbstractThis paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. Robin, as formulated by J. Lagarias. The other parts are devoted to the series $\mathcal{M}{i_s}(z) = \sum\limits_{n = 1}^\infty {{{\mu (n)} \over {{n^s}}}{z^n}} $. A significant result is that the real part f of$$\sum {{{\mu (n)} \over n}{e^{2in\pi \theta }}}$$is an example of a non-trivial real-valued continuous function f on the real line which is 1-periodic, is not odd and has the property $\sum\nolimits_{h = 1}^n {f(h/k) = 0}$ for every positive integer k.

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Al-Labadi, Luai, Yifan Cheng, Forough Fazeli-Asl, Kyuson Lim, and Yanqing Weng. "A Bayesian One-Sample Test for Proportion." Stats 5, no. 4 (2022): 1242–53. http://dx.doi.org/10.3390/stats5040075.

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This paper deals with a new Bayesian approach to the one-sample test for proportion. More specifically, let x=(x1,…,xn) be an independent random sample of size n from a Bernoulli distribution with an unknown parameter θ. For a fixed value θ0, the goal is to test the null hypothesis H0:θ=θ0 against all possible alternatives. The proposed approach is based on using the well-known formula of the Kullback–Leibler divergence between two binomial distributions chosen in a certain way. Then, the difference of the distance from a priori to a posteriori is compared through the relative belief ratio (a measure of evidence). Some theoretical properties of the method are developed. Examples and simulation results are included.

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Kim, Steven B., and Jeffrey O. Wand. "A Paradox in Bland-Altman Analysis and a Binary Approach." International Journal of Statistics and Probability 9, no. 3 (2020): 1. http://dx.doi.org/10.5539/ijsp.v9n3p1.

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A reliable method of measurement is important in various scientific areas. When a new method of measurement is developed, it should be tested against a standard method that is currently in use. Bland and Altman proposed limits of agreement (LOA) to compare two methods of measurement under the normality assumption. Recently, a sample size formula has been proposed for hypothesis testing to compare two methods of measurement. In the hypothesis testing, the null hypothesis states that the two methods do not satisfy a pre-specified acceptable degree of agreement. Carefully considering the interpretation of the LOA, we argue that there are cases of an acceptable degree of agreement inside the null parameter space. We refer to this subset as the paradoxical parameter space in this article. To address this paradox, we apply a Bernoulli approach to modify the null parameter space and to relax the normality assumption on the data. Using simulations, we demonstrate that the change in statistical power is not negligible when the true parameter values are inside or near the paradoxical parameter space. In addition, we demonstrate an application of the sequential probability ratio test to allow researchers to draw a conclusion with a smaller sample size and to reduce the study time.

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Kwon, Young-Doo, and Jin-Sik Han. "New realistic hypothesis on corner stiffness of right-angle frames for increased analysis accuracy." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 9 (2015): 1738–48. http://dx.doi.org/10.1177/0954406215622499.

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Structural elements like bars, trusses, beams, frames, plates, and shells have long been used in structures and machines because of their large stiffness-to-weight ratios. The Euler–Bernoulli theory for beam elements is currently used in a wide range of engineering fields. Frames may essentially be considered to be a type of general beam with axial loads. In the analysis of a right-angle frame, the stiffness of a corner has been assumed to be infinite, which is allowable only when the frame is sufficiently slender. However, a comparison of the results of a finite element analysis showed that the assumption of rigid corner stiffness is unacceptable for most cases because of the considerable errors that result. To resolve this problem, we assumed that the stiffness of a corner in a right-angle frame was finite, which is mostly the case, and solved the problem of a right-angle frame with round corners under internal pressure. Using the derived formula based on the assumption of finite corner stiffness and the formula for the round corner stiffness, we analyzed the entire right-angle frame structure and compared the results to finite element analysis results. As a final attempt, the quasi-optimal dimension of the corner was found to exhibit the lowest von Mises equivalent stress. This proposed approach could be applied to many problems involving frames with various boundary conditions to improve the accuracy.

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La Malfa Ribolla, Emma, Milan Jirásek, and Martin Horák. "BEAM ELEMENT UNDER FINITE ROTATIONS." Acta Polytechnica CTU Proceedings 30 (April 22, 2021): 87–92. http://dx.doi.org/10.14311/app.2021.30.0087.

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The present work focuses on the 2-D formulation of a nonlinear beam model for slender structures that can exhibit large rotations of the cross sections while remaining in the small-strain regime. Bernoulli-Euler hypothesis that plane sections remain plane and perpendicular to the deformed beam centerline is combined with a linear elastic stress-strain law.The formulation is based on the integrated form of equilibrium equations and leads to a set of three first-order differential equations for the displacements and rotation, which are numerically integrated using a special version of the shooting method. The element has been implemented into an open-source finite element code to ease computations involving more complex structures. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions.

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Coffey, Mark W. "New results concerning power series expansions of the Riemann xi function and the Li/Keiper constants." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2091 (2008): 711–31. http://dx.doi.org/10.1098/rspa.2007.0212.

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The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. A new representation of λ k is developed in terms of the Stieltjes constants γ j and the subcomponent sums are discussed and analysed. Accompanying this decomposition, we find a new representation of the constants η j entering the Laurent expansion of the logarithmic derivative of the Riemann zeta function about s =1. We also demonstrate that the η j coefficients are expressible in terms of the Bernoulli numbers and certain other constants. We determine new properties of η j and σ j , where are the sums of reciprocal powers of the non-trivial zeros of the Riemann zeta function.

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Yu, Benru, Hong Gu, and Weimin Su. "A Robust Interacting Multi-Model Multi-Bernoulli Mixture Filter for Maneuvering Multitarget Tracking under Glint Noise." Sensors 24, no. 9 (2024): 2720. http://dx.doi.org/10.3390/s24092720.

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In practical radar systems, changes in the target aspect toward the radar will result in glint noise disturbances in the measurement data. The glint noise has heavy-tailed characteristics and cannot be perfectly modeled by the Gaussian distribution widely used in conventional tracking algorithms. In this article, we investigate the challenging problem of tracking a time-varying number of maneuvering targets in the context of glint noise with unknown statistics. By assuming a set of models for the possible motion modes of each single-target hypothesis and leveraging the multivariate Laplace distribution to model measurement noise, we propose a robust interacting multi-model multi-Bernoulli mixture filter based on the variational Bayesian method. Within this filter, the unknown noise statistics are adaptively learned while filtering and the predictive likelihood is approximately calculated by means of the variational lower bound. The effectiveness and superiority of our proposed filter is verified via computer simulations.

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Krysko, V. A., J. Awrejcewicz, I. V. Papkova, O. A. Saltykova, and A. V. Krysko. "Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 3-4 (2019): 373–86. http://dx.doi.org/10.1515/ijnsns-2018-0132.

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AbstractDifferent kinematic mathematical models of nonlinear dynamics of a contact interaction of two microbeams are derived and studied. Dynamics of one of the microbeams is governed by kinematic hypotheses of the first, second, and third approximation orders. The second beam is excited through a contact interaction with the first beam and is described by the kinematic hypothesis of the second-order approximation in both geometric linear and nonlinear frameworks. The derived nonlinear partial differential equations (PDEs) are transformed to the counterpart system of nonlinear ordinary differential equations (ODEs) by the finite difference method. Nonlinear contact interaction dynamics of the microbeam structure is analyzed with the help of time series (signals), Fourier spectra, and wavelet spectra based on various mother wavelets, Morlet wavelet spectra employed to study synchronization phenomena, Poincaré maps, phase portraits, and the Lyapunov exponents estimated with the Wolf, Kantz, and Rosenstein algorithms. We have illustrated that neglecting the shear function (Euler–Bernoulli model) yields erroneous numerical results. We have shown that the geometric nonlinearity cannot be neglected in the analysis even for small two-layer microbeam deflection. In addition, we have detected that the contact between two microbeams takes place in the vicinity of x \approx 0.2 and x \approx 0.8 instead of the beams central points.

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Angelini, Pierpaolo, and Angela De Sanctis. "On a Geometric Extension of the Notion of Exchangeability Referring to Random Events." International Journal of Statistics and Probability 7, no. 2 (2018): 50. http://dx.doi.org/10.5539/ijsp.v7n2p50.

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The notion of exchangeability referring to random events is investigated by using a geometric scheme of representation of possible alternatives. When we distribute among them our sensations of probability, we point out the multilinear essence of exchangeability by means of this scheme. Since we observe a natural one-to-one correspondence between multilinear maps and linear maps, we are able to underline that linearity concept is the most meaningful mathematical concept of probability theory. Exchangeability hypothesis is maintained for mixtures of Bernoulli processes in the same way. We are the first in the world to do this kind of work and for this reason we believe that it is inevitable that our references limit themselves only to those pioneering works which do not keep the real and deep meaning of probability concept a secret, unlike the current ones.

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Keshmiri, Alireza, Nan Wu, and Quan Wang. "Free Vibration Analysis of a Nonlinearly Tapered Cone Beam by Adomian Decomposition Method." International Journal of Structural Stability and Dynamics 18, no. 07 (2018): 1850101. http://dx.doi.org/10.1142/s0219455418501018.

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In this paper, the free vibration of a nonlinearly tapered cone beam is analyzed based on the Euler–Bernoulli hypothesis. The characteristic/eigenvalue equation and mode shape functions of the nonlinearly tapered cone beam are derived by the Adomian decomposition method for the first time. Using a modified mathematical procedure, the natural frequencies and mode shape functions of a general nonuniform beam are analytically derived. Several numerical examples for the vibration of uniform and linearly tapered cantilever beams are presented and compared with previous results to validate the accuracy and fast convergence of the present approach. The natural frequencies and mode shapes of vibration of exponentially and trigonometrically tapered cone beams with different taper ratios are presented. The present approach enables engineers to analytically analyze tapered beams of nonuniform configurations used as various structural components in a mathematically efficient way.

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ElAlaoui, Rabie, Hamid Mounirv, Boudi El Mostapha, and Abdellatif El Marjani. "Theoretical study to calculate the vibration modes of a wind turbine blade with a new composite material." World Journal of Environmental Research 8, no. 1 (2018): 17–25. http://dx.doi.org/10.18844/wjer.v8i1.3946.

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A precise understanding of the dynamics of a blade is essential for its design, especially in the development of new structures and the resolution of noise and vibration problems. This understanding involves the study of experimental and/or theoretical modal analysis. These latter present effective tools for describing, understanding and modelling the dynamic aspect of each structure, in the present work, we are going to establish the Eigen-mode of a wind turbine blade made by a new composite material ‘hemp fibre’ using theoretical calculation for flap-wise, edge-wise and torsional mode using the finite element method applied to a structure consisting of a beam embedded at one end, based on the Euler-Bernoulli hypothesis and the equation of beam’s motion. Furthermore; we compare the obtained results with those of composite material made by fibreglass.  Keywords: Blade, Eigen-mode, hemp fibre, flap-wise, edge-wise, torsional, fibreglass.

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Moaaz, Osama, Ahmed E. Abouelregal, and Fahad Alsharari. "Lateral vibration of an axially moving thermoelastic nanobeam subjected to an external transverse excitation." AIMS Mathematics 8, no. 1 (2022): 2272–95. http://dx.doi.org/10.3934/math.2023118.

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<abstract> <p>This paper gives a mathematical formulation for the transverse resonance of thermoelastic nanobeams that are simply supported and compressed with an initial axial force. The nonlocal elasticity concept is used to analyze the influence of length scale with the dual-phase-lag (DPL) heat transfer theory. The nanobeam is due to a changing thermal load and moves in one direction at a constant speed. The governing motion equation for the nonlocal Euler-Bernoulli (EB) beam hypothesis can also be derived with the help of Hamilton's principle and then solved by means of the Laplace transform technique. The impacts of nonlocal nanoscale and axial velocity on the different responses of the moving beam are investigated. The results reveal that phase delays, as well as the nonlocal parameter and external excitation load, have a substantial impact on the system's behavior.</p> </abstract>

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