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Journal articles on the topic 'Backward class'

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Published: 18 May 2024

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1

Ambhore, Dr Shankar B., and Dr Pawar Ashok S. "Backward Class Disparities in higher Education in India." Indian Journal of Applied Research 1, no. 7 (October 1, 2011): 59–60. http://dx.doi.org/10.15373/2249555x/apr2012/19.

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2

He, Shengnan, Yu Huang, and Zongbin Yin. "Jℱ-Class Weighted Backward Shifts." International Journal of Bifurcation and Chaos 28, no. 06 (June 15, 2018): 1850076. http://dx.doi.org/10.1142/s0218127418500761.

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In this article [Formula: see text]-class operators are introduced and some basic properties of [Formula: see text]-vectors are given. The [Formula: see text]-class operators include the [Formula: see text]-class operators and [Formula: see text]-class operators introduced by Costakis and Manoussos in 2008. This class also includes the [Formula: see text]-class and [Formula: see text]-class operators defined by Zhang [2012]. Furthermore, for the unilateral weighted backward shifts on a Fréchet sequence space, we establish a criterion under which the shift operators belong to the [Formula: see text]-class. From the criterion it is easy to obtain the existing criteria of hypercyclic backward shifts and of the topological mixing backward shifts. The obtained criterion also reveals the characteristic of [Formula: see text]-class shift operators by the recurrence property. Meanwhile, we obtain infinite topological entropy when the shifts have stronger recurrence property, which generalizes the related results by Brian et al. in 2017.

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3

Ko, Eungil. "Trace class backward weighted shifts are quasisubscalar." Proceedings of the American Mathematical Society 124, no. 4 (1996): 1111–15. http://dx.doi.org/10.1090/s0002-9939-96-03084-5.

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4

Gao, Zhengyuan, and Christian M. Hafner. "Looking Backward and Looking Forward." Econometrics 7, no. 2 (June 14, 2019): 27. http://dx.doi.org/10.3390/econometrics7020027.

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Filtering has had a profound impact as a device of perceiving information and deriving agent expectations in dynamic economic models. For an abstract economic system, this paper shows that the foundation of applying the filtering method corresponds to the existence of a conditional expectation as an equilibrium process. Agent-based rational behavior of looking backward and looking forward is generalized to a conditional expectation process where the economic system is approximated by a class of models, which can be represented and estimated without information loss. The proposed framework elucidates the range of applications of a general filtering device and is not limited to a particular model class such as rational expectations.

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5

MARTÍNEZ-GIMÉNEZ, F., and A. PERIS. "CHAOS FOR BACKWARD SHIFT OPERATORS." International Journal of Bifurcation and Chaos 12, no. 08 (August 2002): 1703–15. http://dx.doi.org/10.1142/s0218127402005418.

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Backward shift operators provide a general class of linear dynamical systems on infinite dimensional spaces. Despite linearity, chaos is a phenomenon that occurs within this context. In this paper we give characterizations for chaos in the sense of Auslander and Yorke [1980] and in the sense of Devaney [1989] of weighted backward shift operators and perturbations of the identity by backward shifts on a wide class of sequence spaces. We cover and unify a rich variety of known examples in different branches of applied mathematics. Moreover, we give new examples of chaotic backward shift operators. In particular we prove that the differential operator I + D is Auslander–Yorke chaotic on the most usual spaces of analytic functions.

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6

PROTOPOPESCU, V., and Y. Y. AZMY. "TOPOLOGICAL CHAOS FOR A CLASS OF LINEAR MODELS." Mathematical Models and Methods in Applied Sciences 02, no. 01 (March 1992): 79–90. http://dx.doi.org/10.1142/s0218202592000065.

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We construct an example of linear rate equation in the Banach space of summable sequences, l1, that exhibits the three properties required as signature of topological chaos, namely: (i) topological transitivity, (ii) dense periodic orbits, and (iii) positive Lyapunov exponents. The example is based on the properties of the backward shift operator on the Banach space l1. Since linear chaos in the sense described above can occur only in an infinite-dimensional setting, possible finite-dimensional approximate manifestations are investigated. The relationship between the linear backward shift and the nonlinear Bernoulli shift is also discussed.

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7

Han, Bao Yan. "Comparison Theorems for the Multi-Dimensional Backward Doubly Stochastic Differential Equations." Applied Mechanics and Materials 166-169 (May 2012): 3210–13. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.3210.

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8

Han, Bao Yan. "Comparison Theorem for Solutions of BSDEs under Non-Lipschitzian Coefficient." Applied Mechanics and Materials 373-375 (August 2013): 1910–13. http://dx.doi.org/10.4028/www.scientific.net/amm.373-375.1910.

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9

Levitt, Steven D., John A. List, and Sally E. Sadoff. "Checkmate: Exploring Backward Induction among Chess Players." American Economic Review 101, no. 2 (April 1, 2011): 975–90. http://dx.doi.org/10.1257/aer.101.2.975.

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Although backward induction is a cornerstone of game theory, most laboratory experiments have found that agents are not able to successfully backward induct. We analyze the play of world-class chess players in the centipede game, which is ill-suited for testing backward induction, and in pure backward induction games—Race to 100 games. We find that chess players almost never play the backward induction equilibrium in the centipede game, but many properly backward induct in the Race to 100 games. We find no systematic within-subject relationship between choices in the centipede game and performance in pure backward induction games. (JEL C73)

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10

Janković, Svetlana, Jasmina Djordjević, and Miljana Jovanović. "On a class of backward doubly stochastic differential equations." Applied Mathematics and Computation 217, no. 21 (July 2011): 8754–64. http://dx.doi.org/10.1016/j.amc.2011.03.128.

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11

Djordjević, Jasmina, and Svetlana Janković. "On a class of backward stochastic Volterra integral equations." Applied Mathematics Letters 26, no. 12 (December 2013): 1192–97. http://dx.doi.org/10.1016/j.aml.2013.07.006.

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12

Zhang, Yinnan, and Weian Zheng. "Discretizing a backward stochastic differential equation." International Journal of Mathematics and Mathematical Sciences 32, no. 2 (2002): 103–16. http://dx.doi.org/10.1155/s0161171202110234.

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We show a simple method to discretize Pardoux-Peng's nonlinear backward stochastic differential equation. This discretization scheme also gives a numerical method to solve a class of semi-linear PDEs.

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13

Khuntia, Janmejoy. "A comparative analysis of economic characteristics of registered micro and small enterprises run respectively by backward and forward classes in India." Journal of Business Management and Information Systems 3, no. 2 (December 31, 2016): 47–51. http://dx.doi.org/10.48001/jbmis.2016.0302005.

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One of the major features of Indian economy is inequality in income and asset distribution. A comparative study of principal characteristics of micro and small enterprises owned by backward classes which include Scheduled Caste, Scheduled Tribe and Other Backward Class and Others belonging to forward class in India reveal this phenomenon. It is a well-known fact that small industry sector provides lively hood to large number of people across India through ownership of small business enterprise. However, with respect to their performance, they differ significantly. This paper tries to study the inequality existing in the principal characteristic among registered enterprises owned by backward classes and Others respectively.

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14

Kim, Su-Yeong, Ji-Eun Yi, and Hyeon-Suk Kang. "A Study on the Practice of Multicultural Class through Backward Design: Focusing on equitable learning and language development." Korean Association For Learner-Centered Curriculum And Instruction 22, no. 18 (September 30, 2022): 783–800. http://dx.doi.org/10.22251/jlcci.2022.22.18.783.

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Objectives This study focuses on the difficulties of teaching-learning occurring in multicultural classrooms with diverse cultural and linguistic backgrounds of students. It was intended to seek ways to ensure learning equity and in-depth understanding of all students. In other words, the purpose is to examine the application of classes for language development in multicultural classrooms and to design classes that support language development by applying backward design. Methods To achieve the purpose of the study, literature analysis and unit design research were conducted. Through literature analysis, the study analyzed the role of language in learning equity, in-depth learning, backward design, and learning and class in multicultural instruction classroom, and revealed the foundation of class application. After that, science and unit were developed through unit design research. Results For the class reflecting culture, language and diversity in the multicultural classroom, the responsive instructional studies that understand the characteristics of multicultural students and emphasize specific practice were significant. Therefore, as a way to promote the learning and language development of the subject on the basis of the application of this class, the unit of ‘properties of matter’ in the third grade science class of elementary school was developed by applying the linguistic lens to the backward design. Conclusions Backward design applying a linguistic lens is a useful way to develop a rigorous curriculum to provide equal learning opportunities to all students in subject learning in multicultural classrooms.

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15

KLEMM, M., and P. E. BECKMANN. "THE TOPOLOGY OF BASIN BOUNDARIES IN A CLASS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS." International Journal of Bifurcation and Chaos 06, no. 01 (January 1996): 161–67. http://dx.doi.org/10.1142/s0218127496001909.

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We will develop new methods to determine the topology of the basin boundary in a class of three-dimensional dynamical systems. One approach is to approximate the basin boundary by backward integration. Unfortunately, there are dynamical systems where it is hard to approximate the basin boundary by a numerical backward integration algorithm. We will introduce topological methods which will provide new information about the structure of the basin boundary. The topological invariants which we will use can be numerically computed.

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16

Duan, Pengju. "SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions." Journal of Function Spaces 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/5916132.

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The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by constructing Cauchy sequence and fixed point theorem. Moreover, we give a probabilistic solution of stochastic partial differential integral equations by means of the solution of backward stochastic differential equations. Finally, we give an example to illustrate.

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17

Jia, Guangyan. "A class of backward stochastic differential equations with discontinuous coefficients." Statistics & Probability Letters 78, no. 3 (February 2008): 231–37. http://dx.doi.org/10.1016/j.spl.2007.05.028.

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18

Thanh, Bui Le Trong, Flavia Smarrazzo, and Alberto Tesei. "Sobolev regularization of a class of forward–backward parabolic equations." Journal of Differential Equations 257, no. 5 (September 2014): 1403–56. http://dx.doi.org/10.1016/j.jde.2014.05.004.

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19

Luo, Mei, JinRong Wang, and Donal O'Regan. "A class of conformable backward stochastic differential equations with jumps." Miskolc Mathematical Notes 23, no. 2 (2022): 811. http://dx.doi.org/10.18514/mmn.2022.3766.

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In this paper, we study conformable backward stochastic differential equations driven by a Brownian motion and a compensated random measure. We derive the conformable Ito’s ˆ formula with jumps and a priori estimates and we obtain the existence and uniqueness of solutions under some assumptions in the framework of the conformable derivative. In addition we get a predictable representation of the solution. Comparison theorems for the operator g under different conditions are given. We also establish the inverse comparison theorem for the operator g under a Lipschitz condition.

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20

Saxton, Alexander. "In Dubious Battle: Looking Backward." Pacific Historical Review 73, no. 2 (May 1, 2004): 249–62. http://dx.doi.org/10.2307/3641601.

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Revised from an address in Santa Cruz (2002) commemorating the John Steinbeck centennial, this essay focuses on Steinbeck's views on race and class as expressed in his writings on agricultural labor in California, especially In Dubious Battle and The Grapes of Wrath. Grapes of Wrath, which played an important part in rallying support for the New Deal program of Social Security, is described as a "supreme portrayal of Great Depression America" and Steinbeck's finest novel. Steinbeck's work is linked to that of his predecessor, Edward Bellamy, author of Looking Backward. Both writers are presented as belonging to a tradition of "humane and humanist radicalism" in American culture and politics that reaches back at least as far as Tom Paine and Frances Wright.

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21

Casserini, Matteo, and Gechun Liang. "Fully coupled forward–backward stochastic dynamics and functional differential systems." Stochastics and Dynamics 15, no. 02 (April 6, 2015): 1550006. http://dx.doi.org/10.1142/s0219493715500069.

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This paper introduces and solves a general class of fully coupled forward–backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different types of forward–backward stochastic differential equations (FBSDEs) that do not fit in the classical setting. In our approach, the equations are running in the same time direction rather than in a forward and backward way, and the conflicting nature of the structure of FBSDEs is therefore avoided.

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22

Zhu, Jinghao, Shangrui Zhao, and Guohua Liu. "Solution to Singular Optimal Control by Backward Differential Flow." Journal of Control Science and Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/678679.

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This paper presents a backward differential flow for solving singular optimal control problems. By using Krotov equivalent transformation, the cost functional is converted to a class of global optimization problems. Some properties of the flow are given to reveal the significant relationship between the dynamic of the flow and the geometry of the feasible set. The proposed method is also used in solving a class of variational problems. Some examples are illustrated.

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23

Nguyen, Tung, Lucia Cevidanes, Beatriz Paniagua, Hongtu Zhu, Leonardo Koerich, and Hugo De Clerck. "Use of shape correspondence analysis to quantify skeletal changes associated with bone-anchored Class III correction." Angle Orthodontist 84, no. 2 (July 25, 2013): 329–36. http://dx.doi.org/10.2319/041513-288.1.

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ABSTRACT Objective: To evaluate the three-dimensional (3D) skeletal changes in the mandibles of Class III patients treated with bone-anchored maxillary protraction using shape correspondence analysis. Material and Method: Twenty-five consecutive patients with skeletal Class III who were between the ages of 9 and 13 years (mean age, 11.10 ± 1.1 years) were treated using Class III intermaxillary elastics and bilateral miniplates (two in the infrazygomatic crests of the maxilla and two in the anterior mandible). Cone-beam computed tomography (CBCT) was performed for each patient before initial loading (T1) and at 1 year out (T2). From the CBCT scans, 3D models were generated, registered on the anterior cranial base, and analyzed using 3D linear distances and vectors between corresponding point-based surfaces. Results: Bone-anchored traction produced anteroposterior and vertical skeletal changes in the mandible. The novel application of Shape correspondence analysis showed vectors of mean (± standard deviation) distal displacement of the posterior ramus of 3.6 ± 1.4 mm, while the chin displaced backward by 0.5 ± 3.92 mm. The lower border of the mandible at the menton region was displaced downward by 2.6 ± 1.2 mm, and the lower border at the gonial region moved downward by 3.6 ± 1.4 mm. There was a downward and backward displacement around the gonial region with a mean closure of the gonial angle by 2.1°. The condyles were displaced distally by a mean of 2.6 ± 1.5 mm, and there were three distinct patterns for displacement: 44% backward, 40% backward and downward, and 16% backward and upward. Conclusion: This treatment approach induces favorable control of the mandibular growth pattern and can be used to treat patients with components of mandibular prognathism.

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24

BEKAKOS, M. P., and O. B. EFREMIDES. "A CLASS OF SYSTOLIC TRIDIAGONAL LINEAR SOLVERS." Parallel Processing Letters 06, no. 03 (September 1996): 355–64. http://dx.doi.org/10.1142/s0129626496000340.

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Herein, the Concurrent Backward and Forward (B&F) complete solution approach and the Main Diagonal Redirection (MDR) technique are studied, on a comparative basis, for the solution of tridiagonal linear systems on VLSI systolic processor arrays. The architectural design investigated consists of modified <2-in-1> systolic cells. The paper concludes with the generalization of both approaches for multiple pipes arrangement on a 3D Mesh(d) topology.

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25

Zhu, Lei, and Weiwei Xu. "Backward Error Analysis for an Eigenproblem Involving Two Classes of Matrices." East Asian Journal on Applied Mathematics 4, no. 4 (November 2014): 329–44. http://dx.doi.org/10.4208/eajam.090614.031014a.

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AbstractWe consider backward errors for an eigenproblem of a class of symmetric generalised centrosymmetric matrices and skew-symmetric generalised skew-centrosymmetric matrices, which are extensions of symmetric centrosymmetric and skew-symmetric skew-centrosymmetric matrices. Explicit formulae are presented for the computable backward errors for approximate eigenpairs of these two kinds of structured matrices. Numerical examples illustrate our results.

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26

LI, HUAIBIN. "ON SUMMABILITY CONDITIONS FOR INTERVAL MAPS." Bulletin of the Australian Mathematical Society 89, no. 2 (June 13, 2013): 308–15. http://dx.doi.org/10.1017/s0004972713000464.

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AbstractConsider a map of class ${C}^{3} $ with nonflat critical points and with all periodic points hyperbolic repelling. We show that the ‘backward contracting condition’ implies the summability condition. This result is the converse of Theorem 3 of Bruin et al. [‘Large derivatives, backward contraction and invariant densities for interval maps’, Invent. Math. 172 (2008), 509–533].

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27

Gröchenig, Karlheinz, and Andrew Haas. "Backward Continued Fractions and their Invariant Measures." Canadian Mathematical Bulletin 39, no. 2 (June 1, 1996): 186–98. http://dx.doi.org/10.4153/cmb-1996-023-8.

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AbstractThis paper continues our investigation of backward continued fractions, associated with the generalized Renyi maps on [0,1). We first show that the dynamics of the shift map on a specific class of shift invariant spaces of nonnegative integer sequences exactly models the maps Tu for u € (0,4). In the second part we construct a new family of explicit invariant measures for certain values of the parameter u.

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28

Zhu, Bo, and Baoyan Han. "Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/582645.

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We give a sufficient condition on the coefficients of a class of infinite horizon BDSDEs, under which the infinite horizon BDSDEs have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations. A probabilistic interpretation for solutions to a class of stochastic partial differential equations is given.

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29

CONFORTOLA, FULVIA. "DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 09, no. 01 (March 2006): 155–68. http://dx.doi.org/10.1142/s0219025706002287.

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We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

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30

REN, YONG, and XILIANG FAN. "REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A LÉVY PROCESS." ANZIAM Journal 50, no. 4 (April 2009): 486–500. http://dx.doi.org/10.1017/s1446181109000303.

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AbstractIn this paper, we deal with a class of reflected backward stochastic differential equations (RBSDEs) corresponding to the subdifferential operator of a lower semi-continuous convex function, driven by Teugels martingales associated with a Lévy process. We show the existence and uniqueness of the solution for RBSDEs by means of the penalization method. As an application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions.

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31

Negrea, Romeo, and Ciprian Preda. "Fixed point technique for a class of backward stochastic differential equations." Journal of Nonlinear Sciences and Applications 06, no. 01 (February 8, 2013): 41–50. http://dx.doi.org/10.22436/jnsa.006.01.07.

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32

Choi, Yun-Kyoung, and Hyeon-Suk Kang. "A Study on an Application of Backward Design for Music Class." Journal of Curriculum and Evaluation 11, no. 2 (November 2008): 211–30. http://dx.doi.org/10.29221/jce.2008.11.2.211.

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33

Singh, Gurjinder, V. Kanwar, and Saurabh Bhatia. "A class of the backward Euler's method for initial value problems." Research Journal of Engineering and Technology 6, no. 1 (2015): 207. http://dx.doi.org/10.5958/2321-581x.2015.00031.8.

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34

Bertsch, Michiel, Flavia Smarrazzo, and Alberto Tesei. "On a Class of Forward-Backward Parabolic Equations: Properties of Solutions." SIAM Journal on Mathematical Analysis 49, no. 3 (January 2017): 2037–60. http://dx.doi.org/10.1137/16m1067378.

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35

He, Ping, Yong Ren, and Defei Zhang. "A Study on a New Class of Backward Stochastic Differential Equation." Mathematical Problems in Engineering 2020 (May 21, 2020): 1–9. http://dx.doi.org/10.1155/2020/1518723.

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The existence and uniqueness for a new type of backward stochastic differential equation when the generator includes the values of solutions of the past, the present, and the future are obtained in this paper. An important comparison theorem for this sort of BSDEs is also proved.

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36

Yin, Jingxue, and Chunpeng Wang. "Young measure solutions of a class of forward–backward diffusion equations." Journal of Mathematical Analysis and Applications 279, no. 2 (March 2003): 659–83. http://dx.doi.org/10.1016/s0022-247x(03)00054-4.

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37

Bertsch, Michiel, Flavia Smarrazzo, and Alberto Tesei. "Nonuniqueness of solutions for a class of forward–backward parabolic equations." Nonlinear Analysis 137 (May 2016): 190–212. http://dx.doi.org/10.1016/j.na.2015.12.028.

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38

Bertsch, Michiel, Flavia Smarrazzo, and Alberto Tesei. "On a class of forward–backward parabolic equations: Existence of solutions." Nonlinear Analysis 177 (December 2018): 46–87. http://dx.doi.org/10.1016/j.na.2017.09.011.

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39

Zhu, Qing-feng, and Yu-feng Shi. "A class of backward doubly stochastic differential equations with discontinuous coefficients." Acta Mathematicae Applicatae Sinica, English Series 30, no. 4 (November 23, 2011): 965–76. http://dx.doi.org/10.1007/s10255-011-0136-0.

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40

Ji, Yuan, Hiroki Takanari, Muge Qile, Lukas Nalos, Marien J. C. Houtman, Fee L. Romunde, Raimond Heukers, Paul M. P. van Bergen en Henegouwen, Marc A. Vos, and Marcel A. G. van der Heyden. "Class III antiarrhythmic drugs amiodarone and dronedarone impair KIR2.1 backward trafficking." Journal of Cellular and Molecular Medicine 21, no. 10 (April 19, 2017): 2514–23. http://dx.doi.org/10.1111/jcmm.13172.

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41

Kicsiny, R., Z. Varga, and A. Scarelli. "Backward induction algorithm for a class of closed-loop Stackelberg games." European Journal of Operational Research 237, no. 3 (September 2014): 1021–36. http://dx.doi.org/10.1016/j.ejor.2014.02.057.

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42

Bertsch, M., F. Smarrazzo, and A. Tesei. "On a class of forward-backward parabolic equations: Formation of singularities." Journal of Differential Equations 269, no. 9 (October 2020): 6656–98. http://dx.doi.org/10.1016/j.jde.2020.05.007.

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43

Djordjevic, Jasmina. "Lp - estimates of solutions of backward doubly stochastic differential equations." Filomat 31, no. 8 (2017): 2365–79. http://dx.doi.org/10.2298/fil1708365d.

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This paper deals with a large class of nonhomogeneous backward doubly stochastic differential equations which have a more general form of the forward It? integrals. Terms under which the solutions of these equations are bounded in the Lp-sense, p ? 2, under both the Lipschitz and non-Lipschitz conditions, are given, i.e. Lp - stability for this general type of backward doubly stochastic differential equations is established.

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44

정현서 and 이의재. "Impact of Physical Education Class Applying Backward Educational Model on Class Satisfaction of Middle School Students." Asian Journal of Physical Education and Sport Science 6, no. 3 (December 2018): 27–40. http://dx.doi.org/10.24007/ajpess.2018.6.3.003.

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45

Wang, Tie, and Jiaxin Yu. "Anticipated Generalized Backward Doubly Stochastic Differential Equations." Symmetry 14, no. 1 (January 9, 2022): 114. http://dx.doi.org/10.3390/sym14010114.

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In this paper, we explore a new class of stochastic differential equations called anticipated generalized backward doubly stochastic differential equations (AGBDSDEs), which not only involve two symmetric integrals related to two independent Brownian motions and an integral driven by a continuous increasing process but also include generators depending on the anticipated terms of the solution (Y, Z). Firstly, we prove the existence and uniqueness theorem for AGBDSDEs. Further, two comparison theorems are obtained after finding a new comparison theorem for GBDSDEs.

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46

Gashi, Bujar, and Jiajie Li. "Backward stochastic differential equations with unbounded generators." Stochastics and Dynamics 19, no. 01 (January 27, 2019): 1950008. http://dx.doi.org/10.1142/s0219493719500084.

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In this paper, we consider two classes of backward stochastic differential equations (BSDEs). First, under a Lipschitz-type condition on the generator of the equation, which can also be unbounded, we give sufficient conditions for the existence of a unique solution pair. The method of proof is that of Picard iterations and the resulting conditions are new. We also prove a comparison theorem. Second, under the linear growth and continuity assumptions on the possibly unbounded generator, we prove the existence of the solution pair. This class of equations is more general than the existing ones.

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47

Kaminski, Marek Mikolaj. "Generalized Backward Induction: Justification for a Folk Algorithm." Games 10, no. 3 (August 30, 2019): 34. http://dx.doi.org/10.3390/g10030034.

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I introduce axiomatically infinite sequential games that extend Kuhn’s classical framework. Infinite games allow for (a) imperfect information, (b) an infinite horizon, and (c) infinite action sets. A generalized backward induction (GBI) procedure is defined for all such games over the roots of subgames. A strategy profile that survives backward pruning is called a backward induction solution (BIS). The main result of this paper finds that, similar to finite games of perfect information, the sets of BIS and subgame perfect equilibria (SPE) coincide for both pure strategies and for behavioral strategies that satisfy the conditions of finite support and finite crossing. Additionally, I discuss five examples of well-known games and political economy models that can be solved with GBI but not classic backward induction (BI). The contributions of this paper include (a) the axiomatization of a class of infinite games, (b) the extension of backward induction to infinite games, and (c) the proof that BIS and SPEs are identical for infinite games.

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48

Alwasm, Asma. "Backward doubly stochastic differential equations (BDSDEs): Existence and Uniqueness." JOURNAL OF ADVANCES IN MATHEMATICS 21 (March 24, 2022): 58–65. http://dx.doi.org/10.24297/jam.v21i.9211.

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In this paper, we present a class of stochastic differential equations with terminal condition, called backward doubly stochastic differential equations (BDSDEs). Precisely, we will prove the existence and uniqueness of the solutions of FBDSDEs but under weaker conditions

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Guatteri, Giuseppina. "On a Class of Forward-Backward Stochastic Differential Systems in Infinite Dimensions." Journal of Applied Mathematics and Stochastic Analysis 2007 (May 30, 2007): 1–33. http://dx.doi.org/10.1155/2007/42640.

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We prove that a class of fully coupled forward-backward systems in infinite dimensions has a local unique solution. After studying the regularity property of the solution, we prove that for a peculiar class of systems arising in the theory of stochastic optimal control, the solution exists in arbitrary large time interval. Finally, we investigate the connection between the solution to the systems and a stochastic optimal control problem.

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A. Krushnamma, A. Krushnamma, and D. Chenna Reddy. "Empowerment of Women Through Panchayat Raj Institutions: A Study of Backward Class Women in Anantapuramu District of Andhra Pradesh." Indian Journal of Applied Research 4, no. 6 (October 1, 2011): 504–7. http://dx.doi.org/10.15373/2249555x/june2014/158.

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