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Journal articles on the topic 'Recurrent formula'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Wang, Yan, Muhammet Cihat Dağli, Xi-Min Liu, and Feng Qi. "Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials." Axioms 10, no. 1 (2021): 37. http://dx.doi.org/10.3390/axioms10010037.

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In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials.

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2

Bardovi-Harlig, Kathleen. "Formulas, Routines, and Conventional Expressions in Pragmatics Research." Annual Review of Applied Linguistics 32 (March 2012): 206–27. http://dx.doi.org/10.1017/s0267190512000086.

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This article reviews the recent research on formulaic language in pragmatics from three perspectives: foundational issues, recurrent research questions, and the populations studied. Examination of foundational issues, including definitions and operationalization of the concept of formula in pragmatics, shows the way in which pragmatics understands formulaic language and what it contributes to the study of formulaic language, namely, a strong sense of social contract. Recurrent themes in contemporary investigations include how formulas are used in general and in specific contexts, determining h

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Abdelli, Hafedh, and Habib Marzougui. "Invariant Sets for Monotone Local Dendrite Maps." International Journal of Bifurcation and Chaos 26, no. 09 (2016): 1650150. http://dx.doi.org/10.1142/s0218127416501509.

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Let [Formula: see text] be a local dendrite and let [Formula: see text] be a monotone map. Denote by [Formula: see text], RR[Formula: see text], UR[Formula: see text], [Formula: see text] the set of periodic (resp., regularly recurrent, uniformly recurrent, recurrent) points and [Formula: see text] the union of all [Formula: see text]-limit sets of [Formula: see text]. We show that if [Formula: see text] is nonempty, then (i) [Formula: see text]. (ii) R[Formula: see text] if and only if every cut point is a periodic point. If [Formula: see text] is empty, then (iii) [Formula: see text]. (iv) R

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Hu, Hong. "Recursion Formula of Second-Order Recurrent Sequences." Rocky Mountain Journal of Mathematics 37, no. 4 (2007): 1173–79. http://dx.doi.org/10.1216/rmjm/1187453104.

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Zhong, Hao, and Tianxin Cai. "On the Lucas property of linear recurrent sequences." International Journal of Number Theory 13, no. 06 (2016): 1617–25. http://dx.doi.org/10.1142/s1793042117500920.

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Let [Formula: see text] be an arithmetic function. [Formula: see text] has Lucas property if for any prime [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] In this paper, we discuss the Lucas property of Fibonacci sequences and Lucas numbers. Meanwhile, we find some other interesting results.

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Šíma, Jiří. "Energy Complexity of Recurrent Neural Networks." Neural Computation 26, no. 5 (2014): 953–73. http://dx.doi.org/10.1162/neco_a_00579.

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Recently a new so-called energy complexity measure has been introduced and studied for feedforward perceptron networks. This measure is inspired by the fact that biological neurons require more energy to transmit a spike than not to fire, and the activity of neurons in the brain is quite sparse, with only about 1% of neurons firing. In this letter, we investigate the energy complexity of recurrent networks, which counts the number of active neurons at any time instant of a computation. We prove that any deterministic finite automaton with m states can be simulated by a neural network of optima

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Nakasone, Ruka, Kazumichi Fujioka, Shutaro Suga, et al. "A Preterm Case of Cow’s Milk Allergy Presenting with Recurrent Ascites Treated with Donor Breast Milk." International Journal of Environmental Research and Public Health 18, no. 3 (2021): 1187. http://dx.doi.org/10.3390/ijerph18031187.

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We report a case of a preterm infant who developed cow’s milk allergy. This male infant presented with recurrent ascites and was successfully treated with donated breast milk. He was born at 24 weeks’ gestation with a birthweight of 506 g. From day 20, infant formula, soy protein-based formula, and casein-hydrolyzed formula were used due to insufficient maternal lactation. This resulted in abdominal distention, generalized edema, and recurrent ascites. We diagnosed him with cow’s milk allergy since these symptoms improved on exclusive breast milk feeding. No recurrence of symptoms occurred whe

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8

Soleiman, Amr. "Recurrent Finsler manifolds under projective change." International Journal of Geometric Methods in Modern Physics 13, no. 10 (2016): 1650126. http://dx.doi.org/10.1142/s0219887816501267.

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The aim of the present paper is to provide an intrinsic investigation of some important special Finsler spaces. These spaces are related to the Berwald [Formula: see text]-curvature tensor of transformed manifold, the Douglas tensor and the projective deviation tensor of projective change. Three spaces are studied and called symmetric, [Formula: see text]-recurrent and [Formula: see text]-recurrent manifolds.

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Haddad, Roudy El. "Repeated integration and explicit formula for the \(n\)-th integral of \(x^m(\ln x)^{m'}\)." Open Journal of Mathematical Sciences 6, no. 1 (2022): 51–75. http://dx.doi.org/10.30538/oms2022.0178.

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Repeated integration is a major topic of integral calculus. In this article, we study repeated integration. In particular, we study repeated integrals and recurrent integrals. For each of these integrals, we develop reduction formulae for both the definite as well as indefinite form. These reduction formulae express these repetitive integrals in terms of single integrals. We also derive a generalization of the fundamental theorem of calculus that expresses a definite integral in terms of an indefinite integral for repeated and recurrent integrals. From the recurrent integral formulae, we deriv

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10

Galyautdinov, I. G., and L. I. Galeeva. "GALOIS GROUPS FOR ONE CLASS OF EQUATIONS." Asian-European Journal of Mathematics 04, no. 03 (2011): 427–36. http://dx.doi.org/10.1142/s1793557111000344.

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We find recurrent formulas for obtaining minimal polynomials pn(x) ∈ ℤ[x] of numbers of the form [Formula: see text], where n ∈ ℕ. We demonstrate that Galois groups of these polynomials are commutative. By the same token we give examples of equations of arbitrarily high degrees solvable in radicals.

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Casteigts, Arnaud, Paola Flocchini, Bernard Mans, and Nicola Santoro. "Shortest, Fastest, and Foremost Broadcast in Dynamic Networks." International Journal of Foundations of Computer Science 26, no. 04 (2015): 499–522. http://dx.doi.org/10.1142/s0129054115500288.

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Highly dynamic networks rarely offer end-to-end connectivity at a given time. Yet, connectivity in these networks can be established over time and space, based on temporal analogues of multi-hop paths (also called journeys). Attempting to optimize the selection of the journeys in these networks naturally leads to the study of three cases: shortest (minimum hop), fastest (minimum duration), and foremost (earliest arrival) journeys. Efficient centralized algorithms exists to compute all cases, when the full knowledge of the network evolution is given. In this paper, we study the distributed coun

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Pire, Reinaldo, and Georgina Vargas-Simón. "Recurrent inconsistencies in publications that involve Maguire’s germination rate formula." Forest Systems 28, no. 1 (2019): eSC02. http://dx.doi.org/10.5424/fs/2019281-14063.

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Aim of study: The objective of this study was to present statistical information pertaining to recurrent inconsistencies found in the literature of the last 25 years that involve calculation of the GR and the errors that this may entail when interpreting the seed vigor of different botanical materials.Materiales y métodos: After filtering articles that did not present numerical results or in which the application of Maguire's formula was not clearly indicated, a total of 124 papers were ultimately used in this study.Main results: Germination rate (GR) represents the potential of seeds to germi

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Nüllen, H., and T. Noppeney. "REVAT (Recurrent Varices After Treatment)." Phlebologie 38, no. 06 (2009): 271–74. http://dx.doi.org/10.1055/s-0037-1622280.

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SummaryThe term “recurrent varicose veins” covers various entities. In the first instance, recurrent varicose veins may be the progression of the underlying disease, as there is a hereditary disposition to the condition, but we also find the phenomenon of neovascularisation, and lastly we repeatedly see recurrent varices as a result of technical or strategic surgical errors and the failure of endovenous procedures. No differentiation between these different types of recurrent varicose veins has previously been made in the literature, so that the numbers given vary between 6% and 60%. Up to the

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Mantica, Carlo Alberto, and Luca Guido Molinari. "On conformally recurrent manifolds of dimension greater than 4." International Journal of Geometric Methods in Modern Physics 13, no. 05 (2016): 1650053. http://dx.doi.org/10.1142/s0219887816500535.

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Conformally recurrent pseudo-Riemannian manifolds of dimension [Formula: see text] are investigated. The Weyl tensor is represented as a Kulkarni–Nomizu product. If the square of the Weyl tensor is non-zero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak’s theorem, the explicit expression of the traceless part of the Ricci tensor is obtained, up to a scalar function. The Ricci tensor has at most two distinct eigenvalues, and the recurrence vector is an eigenvector. Lorentzian conformally recurrent manifolds are then considered. If

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Liu, Peng, Zhigang Zeng, and Jun Wang. "Multistability of Delayed Recurrent Neural Networks with Mexican Hat Activation Functions." Neural Computation 29, no. 2 (2017): 423–57. http://dx.doi.org/10.1162/neco_a_00922.

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This letter studies the multistability analysis of delayed recurrent neural networks with Mexican hat activation function. Some sufficient conditions are obtained to ensure that an [Formula: see text]-dimensional recurrent neural network can have [Formula: see text] equilibrium points with [Formula: see text], and [Formula: see text] of them are locally exponentially stable. Furthermore, the attraction basins of these stable equilibrium points are estimated. We show that the attraction basins of these stable equilibrium points can be larger than their originally partitioned subsets. The result

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PELANTOVÁ, EDITA, and ŠTÉPÁN STAROSTA. "ALMOST RICH WORDS AS MORPHIC IMAGES OF RICH WORDS." International Journal of Foundations of Computer Science 23, no. 05 (2012): 1067–83. http://dx.doi.org/10.1142/s012905411240045x.

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We focus on Θ-rich and almost Θ-rich words over a finite alphabet [Formula: see text], where Θ is an involutive antimorphism over [Formula: see text]. We show that any recurrent almost Θ-rich word u is an image of a recurrent Θ′-rich word under a suitable morphism, where Θ′ is also an involutive antimorphism. Moreover, if the word u is uniformly recurrent, we show that Θ′ can be set to the reversal mapping. We also treat one special case of almost Θ-rich words: we show that every Θ-standard word with seed is an image of an Arnoux-Rauzy word.

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17

Nishimura, Reiki, Yasuaki Sagara, Reiko Mitsueda, et al. "Abstract P5-08-19: A novel formula to improve the accuracy of predicting survival time after recurrent breast cancer." Clinical Cancer Research 31, no. 12_Supplement (2025): P5–08–19—P5–08–19. https://doi.org/10.1158/1557-3265.sabcs24-p5-08-19.

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Abstract Background: Recurrent breast cancer (BC) has a poor prognosis and is difficult to cure. The prognosis of each recurrent case also affects the social background and subsequent life plan of each patient. Recent studies have shown that advances in treatment have improved the prognosis after recurrence. To ascertain the survival time after recurrence (STR) is necessary for maintaining and improving QOL and selecting appropriate treatment. We investigated whether certain biomarkers would influence and improve the prognosis, and whether the STR can be predicted using the disease-free interv

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Sun, Hong-zhou, Qi-shi Han, Mei Zhang, and Gui-lu Long. "A Recurrent Formula for Fractional Parentage Coefficients of Identical Fermions." Communications in Theoretical Physics 11, no. 4 (1989): 441–47. http://dx.doi.org/10.1088/0253-6102/11/4/441.

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Sun, Min, Maoying Tian, and Yiju Wang. "Discrete-Time Zhang Neural Networks for Time-Varying Nonlinear Optimization." Discrete Dynamics in Nature and Society 2019 (April 8, 2019): 1–14. http://dx.doi.org/10.1155/2019/4745759.

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As a special kind of recurrent neural networks, Zhang neural network (ZNN) has been successfully applied to various time-variant problems solving. In this paper, we present three Zhang et al. discretization (ZeaD) formulas, including a special two-step ZeaD formula, a general two-step ZeaD formula, and a general five-step ZeaD formula, and prove that the special and general two-step ZeaD formulas are convergent while the general five-step ZeaD formula is not zero-stable and thus is divergent. Then, to solve the time-varying nonlinear optimization (TVNO) in real time, based on the Taylor series

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Pliushch, Oleksandr, Yurii Kravchenko, and Oleksandr Trush. "Recurrent algorithm of telecommunication systems and networks design." Advanced Information Technology, no. 1 (2) (2023): 64–72. http://dx.doi.org/10.17721/ait.2023.1.10.

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Background. The Erlang B-formula that establishes a relationship between probability of dropped calls, call intensity in a certain link and available communication channels in this link is widely used in telecommunication networks’ design and calculations. In a great number of applications, a problem emerges of finding required number of channels in a link for set call intensity to satisfy required probability of dropped calls. Methods. Methods of computer simulation as well as complex systems analysis. Results. With account of the fact that the number of channels enters Erlang B-formula, firs

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Luk, Abbie Sheung-Wan, Jason Cheuk-Sing Yam, Henry Hing-Wai Lau, Wilson Wai-Kuen Yip, and Alvin Lerrmann Young. "Surgical Outcome of Medial Rectus Resection in Recurrent Exotropia: A Novel Surgical Formula." Journal of Ophthalmology 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/758463.

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Purpose. To evaluate the surgical outcomes of unilateral or bilateral medial rectus (MR) muscle resection for recurrent exotropia after bilateral lateral rectus (BLR) muscle recession based on a novel surgical formula.Methods. Forty-one consecutive patients with unilateral or bilateral MR muscle resection for recurrent exotropia after BLR muscle recession were included in this retrospective study. All surgeries were performed according to the formula: 1.0 mm MR muscle resection for every 5 prism dioptres (PD) of exotropia, with an addition of 0.5 mm to each MR muscle operated on.Results. The m

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Liu, Yingyu, Xiaoyan Chen, Ruiman Li, Tin Chiu Li, and Yuanfang Zhu. "#192 : Comparison of Cytokine Profiles and Th1/Th2 Ratios in the Peri-Implantation Endometrium in Recurrent Reproductive Failure Women with and Without Chronic Endometritis." Fertility & Reproduction 05, no. 04 (2023): 498. http://dx.doi.org/10.1142/s2661318223742650.

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Background and Aims: Aberrant local endometrial microenvironment in chronic endometritis (CE) may be involved in reduced endometrial receptivity and recurrent reproductive failure. Previous studies have observed some discrepancies between different types of cytokines, without showing the predominance of a specific immune response between women with miscarriage and normal pregnancy. However, exactly how CE alters the endometrial function and interferes with the process of implantation is still uncertain. Method: It was an observational retrospective study. A total of 39 women with unexplained r

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Hakl, Robert, and Sulkhan Mukhigulashvili. "On One Estimate for Periodic Functions." gmj 12, no. 1 (2005): 97–114. http://dx.doi.org/10.1515/gmj.2005.97.

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Kravtsiv, V. V. "Analogues of the Newton formulas for the block-symmetric polynomials on $\ell_p(\mathbb{C}^s)$." Carpathian Mathematical Publications 12, no. 1 (2020): 17–22. http://dx.doi.org/10.15330/cmp.12.1.17-22.

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The classical Newton formulas gives recurrent relations between algebraic bases of symmetric polynomials. They are true, of course, for symmetric polynomials on infinite-dimensional sequences Banach space. In this paper we consider block-symmetric polynomials (or MacMahon symmetric polynomials) on Banach spaces $\ell_p(\mathbb{C}^s),$ $1\le p\le \infty.$ We prove an analogue of the Newton formula for the block-symmetric polynomials for the case $p=1.$ In the case $1< p$ we have no classical elementary block-symmetric polynomials. However, we extend the obtained Newton type formula for $\ell

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Velimirović, Ljubica, Pradip Majhi, and Uday Chand De. "Almost pseudo-Q-symmetric semi-Riemannian manifolds." International Journal of Geometric Methods in Modern Physics 15, no. 07 (2018): 1850117. http://dx.doi.org/10.1142/s0219887818501177.

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The object of the present paper is to study almost pseudo-[Formula: see text]-symmetric manifolds [Formula: see text]. Some geometric properties have been studied which recover some known results of pseudo [Formula: see text]-symmetric manifolds. We obtain a necessary and sufficient condition for the [Formula: see text]-curvature tensor to be recurrent in [Formula: see text]. Also, we provide several interesting results. Among others, we prove that a Ricci symmetric [Formula: see text] is an Einstein manifold under certain condition. Moreover we deal with [Formula: see text]-flat perfect fluid

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Bhaskar, Anand, John A. Kamm, and Yun S. Song. "Approximate Sampling Formulae for General Finite-Alleles Models of Mutation." Advances in Applied Probability 44, no. 2 (2012): 408–28. http://dx.doi.org/10.1239/aap/1339878718.

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Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation, such as the infinite-alleles model or the finite-alleles parent-independent mutation model, closed-form sampling distributions under the coalescent have been known for many decades. However, no exact formula is currently known for more general models of mutation that are of biological interest. In this paper, models with finitely-many alleles are considered, and an urn

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Bhaskar, Anand, John A. Kamm, and Yun S. Song. "Approximate Sampling Formulae for General Finite-Alleles Models of Mutation." Advances in Applied Probability 44, no. 02 (2012): 408–28. http://dx.doi.org/10.1017/s0001867800005668.

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Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation, such as the infinite-alleles model or the finite-alleles parent-independent mutation model, closed-form sampling distributions under the coalescent have been known for many decades. However, no exact formula is currently known for more general models of mutation that are of biological interest. In this paper, models with finitely-many alleles are considered, and an urn

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Mileva, M., D. Pencheva, No author No author, R. Bryaskova, and P. Kantardjiev. "Experimental treatment of recurrent otitis externa." Open Veterinary Journal 5, no. 2 (2015): 38. http://dx.doi.org/10.5455/ovj.2015.v5.i1.p38.

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The aim of this research is to determine the effect of the hybrid material based on polyvinyl alcohol and silver nanoparticles (PVA/AgNps) in the treatment of the otitis externa as an additional component in the commercial product “Betazon Trio”. It was established that the experimental creamy formula with silver concentration 600 mg/L is suitable for recovery of the microbial homeostasis when it is administrated once daily in dose 1 ml over a period of 14 days.

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Abdirasulova, Zhainagul, Singh Manvendra, Damira Begmatova, Makhabat Bugubaeva, and Romanbek Kalmatov. "RECURRENT URINARY TRACT INFECTION IN WOMEN (OBSERVATIONAL STUDY BETWEEN KYRGYZSTAN AND INDIA)." Вестник Ошского государственного университета. Медицина, no. 1(1) (June 16, 2023): 49–60. http://dx.doi.org/10.52754/16948831_2023_1(1)_7.

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When it comes to recurrent urinary tract infection, India and Kyrgyzstan have very different approaches. In India, this infection is usually treated with antibiotics and preventive measures such as drinking plenty of fluids and maintaining good hygiene. However, in Kyrgyzstan, this condition is treated with antibiotics and traditional medicine – a combination of herbal products that includes tarragon, oregano, and St John’s wart. This herbal formula has been proven effective against recurrent urinary tract infections. What's more, traditional medicine has fewer side effects than antibiotics. T

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Knoblauch, Andreas, and Günther Palm. "Iterative Retrieval and Block Coding in Autoassociative and Heteroassociative Memory." Neural Computation 32, no. 1 (2020): 205–60. http://dx.doi.org/10.1162/neco_a_01247.

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Neural associative memories (NAM) are perceptron-like single-layer networks with fast synaptic learning typically storing discrete associations between pairs of neural activity patterns. Gripon and Berrou ( 2011 ) investigated NAM employing block coding, a particular sparse coding method, and reported a significant increase in storage capacity. Here we verify and extend their results for both heteroassociative and recurrent autoassociative networks. For this we provide a new analysis of iterative retrieval in finite autoassociative and heteroassociative networks that allows estimating storage

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BALIBREA, FRANCISCO, FRANCISCO ESQUEMBRE, and ANTONIO LINERO. "SMOOTH TRIANGULAR MAPS OF TYPE 2∞ WITH POSITIVE TOPOLOGICAL ENTROPY." International Journal of Bifurcation and Chaos 05, no. 05 (1995): 1319–24. http://dx.doi.org/10.1142/s0218127495000983.

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We explicitly construct for any k in ℕ a [Formula: see text]-differentiable triangular map in the square I2 with the following properties: (a) it has periodic orbits of period 2n for any n and no other periodic orbits, (b) the topological entropy is positive, and (c) the set of recurrent points contains properly the set of uniformly recurrent points.

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Kuzovatov, V. I., А. А. Kytmanov, and Е. К. Myshkina. "On calculating partial sums of multiple numerical series by methods of Computer Algebra." Программирование, no. 2 (April 15, 2024): 74–78. http://dx.doi.org/10.31857/s0132347424020094.

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A method to calculate partial sums of some multiple numerical series arising when searching for the resultant of a polynomial and an entire function is proposed. One can apply a symbolic algorithm that uses recurrent Newton formulas to find power sums of roots included in this formula without finding the very roots of the system. The algorithm that implements the proposed approach to calculate partial sums of multiple numerical series is implemented in Maple. Examples of using this algorithm to find partial sums of some classes of multiple numerical series are given.

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Kulikovsky, A. A. "Рекуррентная формула для вычисления импеданса катодного каталитического слоя в топливном элементе с полимерным электролитом". Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), № 2 (5 квітня 2023): 127–31. http://dx.doi.org/10.26089/nummet.v24r209.

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A recurrent formula for estimating an impedance of the cathode catalyst layer with fast oxygen transport in a polymer electrolyte fuel cell is derived. The catalyst layer is divided into N sub-layers and application of the charge conservation law enables to obtain the nonlinear recurrent relation Zn = f(Zn−1), where Zn is the accumulated impedance of all sub-layers up to the n-th one. Numerical solution of this relation gives the total impedance of the catalyst layer with taking into account variation of the static overpotential of the oxygen reduction reaction along the depth of this layer. T

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Eteudo, Samuel, and Henry Ufomba. "The Search for a Symphony: A Discourse on the Issue of Derivation, Revenue Allocation, and Fiscal Federalism in Nigeria." Pacha. Revista de Estudios Contemporáneos del Sur Global 3, no. 8 (2022): e21097. http://dx.doi.org/10.46652/pacha.v3i8.97.

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This paper joins the debate on the fiscal policy of the Nigerian government in terms of the revenue allocation formula of the federating units which has been a recurring theme in the country’s political existence. A review of revenue allocation formulas shows that the tools used as a measure to allocate and distribute revenue had been more of political gerrymandering, with each regime choosing which formula suits them without minding how the federating units react (Adedokun, 2002). An introspective analysis of the various Decrees enacted by the military regimes and the Acts between 1979 and 19

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Bernacchia, Alberto, and Xiao-Jing Wang. "Decorrelation by Recurrent Inhibition in Heterogeneous Neural Circuits." Neural Computation 25, no. 7 (2013): 1732–67. http://dx.doi.org/10.1162/neco_a_00451.

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The activity of neurons is correlated, and this correlation affects how the brain processes information. We study the neural circuit mechanisms of correlations by analyzing a network model characterized by strong and heterogeneous interactions: excitatory input drives the fluctuations of neural activity, which are counterbalanced by inhibitory feedback. In particular, excitatory input tends to correlate neurons, while inhibitory feedback reduces correlations. We demonstrate that heterogeneity of synaptic connections is necessary for this inhibition of correlations. We calculate statistical ave

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Zhang, Guanmao, and Xiaoping Zhang. "Rapid numerical difference recurrent formula of nonlinear Schrödinger equation and its application." Optics Communications 270, no. 2 (2007): 379–83. http://dx.doi.org/10.1016/j.optcom.2006.08.047.

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Tango, Toshiro. "Sample size formula for randomized controlled trials with counts of recurrent events." Statistics & Probability Letters 79, no. 4 (2009): 466–72. http://dx.doi.org/10.1016/j.spl.2008.09.016.

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Kimura, Fuminori. "Chronic Infection in Recurrent Pregnancy Loss." Fertility & Reproduction 05, no. 04 (2023): 241. http://dx.doi.org/10.1142/s2661318223740559.

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In the present study, the effects of chronic endometritis (CE) on implantation and pregnancy outcomes, the effects of CE on endometrial function, and the effects of progesterone as a treatment for CE were examined. It was found that the pregnancy rate and live birth rate were significantly lower in CE patients in a prospective study. When patients were diagnosed with CE, not only were the pregnancy rate and live birth rate significantly lower, but the miscarriage rate was higher in a retrospective study. Next, the presence of chronic deciduitis (CD) in the miscarriage specimen was determined i

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YANG, YAPING, and ZURONG YU. "q-TENSOR METHOD OF DETERMINING IRREDUCIBLE REPRESENTATION OF QUANTUM ALGEBRA SUq(3)." Modern Physics Letters A 08, no. 32 (1993): 3025–30. http://dx.doi.org/10.1142/s0217732393001987.

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In this paper, we construct irreducible q-tensor operators of rank [Formula: see text] of quantum algebra SU q(2) using the generators of quantum algebra SU q(3). By means of property of q-tensor operator, we can easily obtain irreducible representation (IR) of SU q(3). A recurrent formula to calculate reduced coefficients of SU q(3) is obtained and the multiplicity of reduced coefficients is discussed.

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AHN, CHOON KI. "${\mathcal H}_{\infty}$ WEIGHT LEARNING ALGORITHM OF RECURRENT NEURAL NETWORKS WITH TIME-DELAY." Modern Physics Letters B 24, no. 12 (2010): 1217–27. http://dx.doi.org/10.1142/s0217984910023244.

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In this letter, we propose a new weight learning algorithm, called an [Formula: see text] learning law (HLL), for recurrent neural networks with time-delay. Based on the Lyapunov–Krasovskii stability theory, the HLL is presented to not only guarantee asymptotical stability but also reduce the effect of external disturbance to an [Formula: see text] norm constraint. An existence condition for the HLL is represented in terms of linear matrix inequality (LMI). An illustrative example is given to demonstrate the effectiveness of the proposed HLL.

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Dai, Changxi, Meifeng Dai, Tingting Ju, Xiangmei Song, Yu Sun, and Weiyi Su. "Eigentime identity of the weighted (m,n)-flower networks." International Journal of Modern Physics B 34, no. 18 (2020): 2050159. http://dx.doi.org/10.1142/s0217979220501593.

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The eigentime identity for random walks on the weighted networks is the expected time for a walker going from a node to another node. Eigentime identity can be studied by the sum of reciprocals of all nonzero Laplacian eigenvalues on the weighted networks. In this paper, we study the weighted [Formula: see text]-flower networks with the weight factor [Formula: see text]. We divide the set of the nonzero Laplacian eigenvalues into three subsets according to the obtained characteristic polynomial. Then we obtain the analytic expression of the eigentime identity [Formula: see text] of the weighte

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Villegas-Ch, William, Joselin García-Ortiz, and Angel Jaramillo-Alcazar. "An Approach Based on Recurrent Neural Networks and Interactive Visualization to Improve Explainability in AI Systems." Big Data and Cognitive Computing 7, no. 3 (2023): 136. http://dx.doi.org/10.3390/bdcc7030136.

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This paper investigated the importance of explainability in artificial intelligence models and its application in the context of prediction in Formula (1). A step-by-step analysis was carried out, including collecting and preparing data from previous races, training an AI model to make predictions, and applying explainability techniques in the said model. Two approaches were used: the attention technique, which allowed visualizing the most relevant parts of the input data using heat maps, and the permutation importance technique, which evaluated the relative importance of features. The results

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Wu, Xiaoying, Yuanlong Chen, Jing Tian, and Liangliang Li. "Chaotic Dynamics of Discrete Multiple-Time Delayed Neural Networks of Ring Architecture Evoked by External Inputs." International Journal of Bifurcation and Chaos 26, no. 11 (2016): 1650179. http://dx.doi.org/10.1142/s0218127416501790.

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In this paper, we consider a general class of discrete multiple-time delayed recurrent neural networks with external inputs. By applying a new transformation, we transform an m-neuron network model into a parameterized map from [Formula: see text] to [Formula: see text]. A chaotic invariant set of the neural networks system is obtained by using a family of projections from [Formula: see text] onto [Formula: see text]. Furthermore, we prove that the dynamics of this neural networks system restricted to the chaotic invariant set is topologically conjugate to the dynamics of the full shift map wi

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Gerhart, Kimberly D., Debra A. Stern, Stefano Guerra, Wayne J. Morgan, Fernando D. Martinez, and Anne L. Wright. "Protective effect of breastfeeding on recurrent cough in adulthood." Thorax 73, no. 9 (2018): 833–39. http://dx.doi.org/10.1136/thoraxjnl-2017-210841.

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RationaleBreastfeeding protects from respiratory infections in early life but its relationship to recurrent cough and other respiratory outcomes in adult life is not well established.MethodsInfant feeding practices were assessed prospectively in the Tucson Children’s Respiratory Study, a non-selected birth cohort and categorised into formula from birth or introduced <1 month, formula introduced ≥1 to <4 months and exclusive breastfeeding for ≥4 months. Infant feeding was assessed as an ordinal variable representing an increasing dose of breastmilk across the three categories. Recurrent c

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Bulanov, A. P. "Decomposition of Sum in Recurrent Formula for Exponents of the Inverse Chain Exponential." Lobachevskii Journal of Mathematics 39, no. 6 (2018): 747–54. http://dx.doi.org/10.1134/s1995080218060045.

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Ivanov, Rossen I. "Extended Camassa-Holm Hierarchy and Conserved Quantities." Zeitschrift für Naturforschung A 61, no. 3-4 (2006): 133–38. http://dx.doi.org/10.1515/zna-2006-3-404.

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An extension of the Camassa-Holm hierarchy is constructed in this paper. The conserved quantities of the hierarchy are studied and a recurrent formula for the integrals of motion is derived. - PACS numbers: 02.30.Ik; 05.45.Yv; 45.20.Jj; 02.30.Jr.

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Lasserre, J. B. "A new policy iteration scheme for Markov decision processes using Schweitzer's formula." Journal of Applied Probability 31, no. 1 (1994): 268–73. http://dx.doi.org/10.2307/3215254.

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Given a family of Markov chains with a single recurrent class, we present a potential application of Schweitzer's exact formula relating the steady-state probability and fundamental matrices of any two chains in the family. We propose a new policy iteration scheme for Markov decision processes where in contrast to policy iteration, the new criterion for selecting an action ensures the maximal one-step average cost improvement. Its computational complexity and storage requirement are analysed.

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Lasserre, J. B. "A new policy iteration scheme for Markov decision processes using Schweitzer's formula." Journal of Applied Probability 31, no. 01 (1994): 268–73. http://dx.doi.org/10.1017/s0021900200107521.

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Given a family of Markov chains with a single recurrent class, we present a potential application of Schweitzer's exact formula relating the steady-state probability and fundamental matrices of any two chains in the family. We propose a new policy iteration scheme for Markov decision processes where in contrast to policy iteration, the new criterion for selecting an action ensures the maximal one-step average cost improvement. Its computational complexity and storage requirement are analysed.

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Murru, Nadir. "On the periodic writing of cubic irrationals and a generalization of Rédei functions." International Journal of Number Theory 11, no. 03 (2015): 779–99. http://dx.doi.org/10.1142/s1793042115500438.

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In this paper, we provide a periodic representation (by means of periodic rational or integer sequences) for any cubic irrationality. In particular, for a root α of a cubic polynomial with rational coefficients, we study the Cerruti polynomials [Formula: see text], and [Formula: see text], which are defined via [Formula: see text] Using these polynomials, we show how any cubic irrational can be written periodically as a ternary continued fraction. A periodic multidimensional continued fraction (with pre-period of length 2 and period of length 3) is proved convergent to a given cubic irrational

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Schmieder, Johannes F., Till von Wachter, and Stefan Bender. "The Long-Term Effects of UI Extensions on Employment." American Economic Review 102, no. 3 (2012): 514–19. http://dx.doi.org/10.1257/aer.102.3.514.

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The majority of papers analyzing the employment effects of unemployment insurance (UI) benefit durations focus on the duration of the first unemployment spell. In this paper, we make two contributions. First, we use a regression discontinuity design to analyze the long-term effects of extensions in UI durations. These estimates differ from standard estimates in that they incorporate differences in UI benefit receipt and employment due to recurrent unemployment spells. Second, we derive a welfare formula of UI extensions that incorporates recurrent nonemployment spells.

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