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Journal articles on the topic 'Rational expression'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Lombardy, Sylvain, and Jacques Sakarovitch. "DERIVED TERMS WITHOUT DERIVATION A SHIFTED PERSPECTIVE ON THE DERIVED-TERM AUTOMATON." Journal of Computer Science and Cybernetics 37, no. 3 (2021): 201–21. http://dx.doi.org/10.15625/1813-9663/37/3/16263.

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We present here a construction for the derived term automaton (aka partial derivative, or Antimirov, automaton) of a rational (or regular) expression based on a sole induction on the depth of the expression and without making reference to an operation of derivation of the expression. It is particularly well-suited to the case of weighted rational expressions.

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Osborn, Eric. "Rational Faith." Pacifica: Australasian Theological Studies 6, no. 3 (1993): 297–310. http://dx.doi.org/10.1177/1030570x9300600304.

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This article explores three overlooked contemporary arguments concerning faith (raised by Iris Murdoch, Boyce Gibson, and Hans Küng). It shows how these arguments found expression at the beginning of Christian thought, and consider their weaknesses and strengths.

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3

张, 金凤. "Rational Expression in Modern Decorative Painting." Art Research Letters 10, no. 04 (2021): 93–98. http://dx.doi.org/10.12677/arl.2021.104013.

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4

Widmer, Gerhard. "Modeling the Rational Basis of Musical Expression." Computer Music Journal 19, no. 2 (1995): 76. http://dx.doi.org/10.2307/3680601.

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MORI, Kazuyoshi. "Youla–Kučera Parametrization with no Coprime Factorization—Single-Input Single-Output Case." Information 10, no. 4 (2019): 120. http://dx.doi.org/10.3390/info10040120.

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We present a generalization of the Youla—Kučera parametrization to obtain all stabilizing controllers for single-input and single-output plants. This uses three parameters and can be applied to plants that may not admit coprime factorizations. In this generalization, at most two rational expressions of plants are required, while the Youla–Kučera parametrization requires precisely one rational expression.

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Guellouma, Younes, and Hadda Cherroun. "From Tree Automata to Rational Tree Expressions." International Journal of Foundations of Computer Science 29, no. 06 (2018): 1045–62. http://dx.doi.org/10.1142/s012905411850020x.

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We propose a construction of rational tree expression from finite tree automata. First, we define rational expression equation systems and we propose a substitution based method to find the unique solution. Furthermore, we discuss the case of recursion being present in an equation system, and then show under which restrictions such systems can effectively be solved. Secondly, we show that any finite tree automaton can be associated to a rational tree equation system, and that the latter can in turn be resolved. Finally, using the previous steps, a rational tree expression equivalent to the und

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Malachivskyi, R. P., R. A. Bun, and I. P. Medynskyi. "Chebyshev approximation by the exponent from a rational expression." Mathematical Modeling and Computing 12, no. 1 (2025): 233–40. https://doi.org/10.23939/mmc2025.01.233.

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A method for constructing Chebyshev approximation with relative error of the exponential from a rational expression is proposed. It implies constructing an intermediate Chebyshev approximation with absolute error by a rational expression of the logarithm of the function being approximated. The approximation by a rational expression is calculated as the boundary mean-power approximation using an iterative scheme based on the least squares method with two variable weight functions. The presented results of solving test examples confirm the fast convergence of the method.

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8

Gordon, Russell A. "Rational arc length." Mathematical Gazette 102, no. 554 (2018): 210–25. http://dx.doi.org/10.1017/mag.2018.52.

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Finding an expression for the length of a curve is one of the simpler geometric applications of the integral. If f is a function with a continuous derivative, then the expression gives the length of the curve y = f (x) on an interval [a, b]. However, after writing out the integrand for familiar functions such as y = x2 and y = sin x, it quickly becomes apparent that, in general, finding an antiderivative is a challenge. Of course, a computer can give accurate approximations for the value of the integral for the length of a curve, but it would be nice to find the exact length rather than a deci

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Bal, Susan, Ahmet Dogan, Hani Hassoun, Sham Mailankody, Sergio A. Giralt, and Heather J. Landau. "Rational Targets in Systemic AL Amyloidosis." Blood 138, Supplement 1 (2021): 4706. http://dx.doi.org/10.1182/blood-2021-151051.

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Abstract Introduction Dysproteinemia refers to a spectrum of gammopathies in which an aberrant clone(s) of late stage B lymphoid cells or plasma cells produces monoclonal immunoglobulins and/or fragments. The spectrum includes incidentally noted benign conditions like monoclonal gammopathy of undetermined significance (MGUS) to life threatening diseases such as multiple myeloma (MM) and systemic light chain (AL) amyloidosis. Exploitation of normal plasma cell biology forms the basis of treatments used in both MM and AL amyloidosis. In recent years, immunotherapeutic strategies targeting plasma

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10

Choi, Haeng-joon. "Artistic Expression and Rational Communication in Humanities Education." Journal of Korean Philosophical Society 151 (August 31, 2019): 331–54. http://dx.doi.org/10.20293/jokps.2019.151.331.

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Rosado, Alberto López, Federico Prieto Muñoz, and Roberto Alvarez Fernández. "An Analytic Expression for the Inverse Involute." Mathematical Problems in Engineering 2019 (September 29, 2019): 1–9. http://dx.doi.org/10.1155/2019/3586012.

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This article introduces new types of rational approximations of the inverse involute function, widely used in gear engineering, allowing the processing of this function with a very low error. This approximated function is appropriate for engineering applications, with a much reduced number of operations than previous formulae in the existing literature, and a very efficient computation. The proposed expressions avoid the use of iterative methods. The theoretical foundations of the approximation theory of rational functions, the Chebyshev and Jacobi polynomials that allow these approximations t

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12

Rawlins, A. D. "A Green's function for diffraction by a rational wedge." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 1 (1989): 185–92. http://dx.doi.org/10.1017/s0305004100001523.

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AbstractIn this paper we derive an expression for the point source Green's function for the reduced wave equation, valid in an angular sector whose angle is equal to a rational multiple of π. This Green's function can be used to find new expressions for the field produced by the diffraction of a spherical wave by a wedge whose angle can be expressed as a rational multiple of π. The expressions obtained will be in the form of source terms and real integrals representing the diffracted field. The general result obtained is used to derive a new representation for the solution of the problem of di

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Malachivskyy, P. S., B. R. Montsibovych, Ya V. Pizyur, and R. P. Malachivskyi. "Chebyshev Approximation by Rational Expression Functions of Two Variables." Mathematical and computer modelling. Series: Technical sciences, no. 19 (June 20, 2019): 75–81. http://dx.doi.org/10.32626/2308-5916.2019-19.75-81.

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14

Kemming, D., U. Vogt, N. Tidow, et al. "Whole Genome Expression Analysis for Biologic Rational Pathway Modeling." Molecular Diagnosis & Therapy 10, no. 5 (2006): 271–80. http://dx.doi.org/10.1007/bf03256202.

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15

Cushman, Thomas. "Freedom of Expression versus Diversity and Inclusion." Contexts 18, no. 3 (2019): 9. http://dx.doi.org/10.1177/1536504219864949.

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Head, A. K. "Explicit Galoisian solutions in anisotropic elasticity." European Journal of Applied Mathematics 2, no. 3 (1991): 191–97. http://dx.doi.org/10.1017/s0956792500000504.

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A practical method is given that can determine whether or not it is possible for all or part of a problem in crystal elasticity to be expressed in explicit rational or radical terms when the characteristic sextic polynomial is known to be unsolvable. It involves the determination of the group to which an elastic quantity (displacement, stress, strain, energy density) belongs under permutations of the roots of the sextic polynomial. If this is not the symmetric group then a rational or radical expression is impossible. It is applied to the three-dimensional problem of a point force (the Green's

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Rusu, Marius-Mihai. "Homo Oeconomicus – Expression of the Theory of Rational Economic Choice." International conference KNOWLEDGE-BASED ORGANIZATION 30, no. 2 (2024): 1–6. http://dx.doi.org/10.2478/kbo-2024-0054.

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Abstract The theory of rational choice involves several aspects, which I chose to present especially in highlighting the impact it has on economic agents. The issue I have chosen to address in this paper concerns how rational decisions that impact on available resources should be made at a given time. Man from the perspective of the economic agent expresses economic rationality in situations of all kinds of constraints, in other words, he realizes the importance of some resources when economic imbalances manifest negatively on the economic agent. The notion of homo oeconomicus has evolved over

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Badmaeva, Lyubov D. "Expression of rational and irrational understanding in the Buryat language." Sibirskiy filologicheskiy zhurnal, no. 1 (2022): 221–38. http://dx.doi.org/10.17223/18137083/78/16.

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We consider the vocabulary of the Buryat language, expressing a rational and irrational understanding of a man. The actual material semantically close to the understanding model in the Buryat language is a lexical group covering more than 20 units identified from the dictionary, corpus, and contextual data. The participation of sensory perception through vision, hearing, and smell is determined to express rational understanding. Different types of expressions of irrational understanding are revealed: 1) through premonition, 2) through direct clairvoyance, 3) by clairvoyance through dream, 4) t

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Malachivskyy, P. S., L. S. Melnychok, and Y. V. Pizyur. "CHEBYSHEV APPROXIMATION MULTIVARIABLE FUNCTIONS BY THE RATIONAL EXPRESSION WITH THE INTERPOLATION." Journal of Numerical and Applied Mathematics, no. 2 (2022): 76–82. http://dx.doi.org/10.17721/2706-9699.2022.2.09.

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A method for constructing the Chebyshev approximation by the rational expression of the multivariable functions with the interpolation is proposed. The method is based on the construction of the ultimate mean-power approximation by a rational expression with the interpolation condition in the norm of space $L_p$ at $p \to \infty$. To construct such an approximation, an iterative scheme based on the least squares method with two variable weight functions was used.

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20

Popović, Branislav Z., Muhammad Shoaib, and Muhammad Sarwar. "Fixed Point Results Satisfying Rational Type Contraction inG-Metric Spaces." Journal of Function Spaces 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/9536765.

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A unique fixed point theorem for three self-maps under rational type contractive condition is established. In addition, a unique fixed point result for six continuous self-mappings through rational type expression is also discussed.

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21

Malachivskyy, P. S., and L. S. Melnychok. "The Chebyshev Approximation by the Logarithm of a Rational Expression." Cybernetics and Systems Analysis 61, no. 1 (2025): 77–85. https://doi.org/10.1007/s10559-025-00745-3.

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22

Cross, Ben. "Intolerance and Argument Expression." Social Theory and Practice 45, no. 3 (2019): 329–52. http://dx.doi.org/10.5840/soctheorpract201991762.

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Most philosophers seem to think that argument expression is not normally a form of intolerance. Call this the ‘argument-friendly view’ of intolerance. In this article, I argue that the case for the argument-friendly view is much weaker than commonly thought. I consider three possible arguments for the argument-friendly view and conclude that all three fail. This leaves us with a choice: either reject the argument-friendly view, or accept it as a feature of the concept of tolerance which has no rational basis apart from our everyday usage of the term.

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Cai, Yao-Min, Kalyani Kallam, Henry Tidd, Giovanni Gendarini, Amanda Salzman, and Nicola J. Patron. "Rational design of minimal synthetic promoters for plants." Nucleic Acids Research 48, no. 21 (2020): 11845–56. http://dx.doi.org/10.1093/nar/gkaa682.

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Abstract Promoters serve a critical role in establishing baseline transcriptional capacity through the recruitment of proteins, including transcription factors. Previously, a paucity of data for cis-regulatory elements in plants meant that it was challenging to determine which sequence elements in plant promoter sequences contributed to transcriptional function. In this study, we have identified functional elements in the promoters of plant genes and plant pathogens that utilize plant transcriptional machinery for gene expression. We have established a quantitative experimental system to inves

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24

PETROV, George Daniel. "THE RATIONAL EXPRESSION OF THE SUPREME BEING IN KANTIAN THEORETICAL PHILOSOPHY VERSUS THE EXPERIENCE OF THE PERSONAL GOD IN THEOLOGY." International Journal of Theology, Philosophy and Science 7, no. 12 (2023): 85–94. http://dx.doi.org/10.26520/ijtps.2023.7.12.85-94.

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the science of sciences, has tried, starting from what could be expressed rationally, to explain the existence or the possibility of man's knowledge of the existence of the Supreme Being, as designated by Immanuel Kant. The questions that can be raised are: can human reason grasp the transcendental meanings of the Supreme Being? Can philosophical reason be overcome by theological knowledge, as a result of experiencing the Personal God? The answer to these questions can only be expressed through an analysis of Kant's rational arguments alongside the mode of knowledge proposed by theology

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BAKSHI, GURMEET K., RAVINDRA S. KULKARNI, and INDER BIR S. PASSI. "THE RATIONAL GROUP ALGEBRA OF A FINITE GROUP." Journal of Algebra and Its Applications 12, no. 03 (2012): 1250168. http://dx.doi.org/10.1142/s021949881250168x.

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An explicit expression for the primitive central idempotent of the rational group algebra ℚ[G] of a finite group G associated with any complex irreducible character of G is obtained. A complete set of primitive central idempotents and the Wedderburn decomposition of the rational group algebra of a finite metabelian group is also computed.

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26

Melnychok, Lev. "Chebyshev approximation of functions of two variables by a rational expression with interpolation." Physico-mathematical modelling and informational technologies, no. 33 (September 3, 2021): 33–39. http://dx.doi.org/10.15407/fmmit2021.33.033.

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A method for constructing a Chebyshev approximation by a rational expression with interpolation for functions of two variables is proposed The idea of the method is based on the construction of the ultimate mean-power approximation in the norm of space Lp at p¬∞ . An iterative scheme based on the least squares method with two variable weight functions was used to construct such a Chebyshev approximation. The results of test examples confirm the effectiveness of the proposed method for constructing the Chebyshev approximation by a rational expression with interpolation.

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Malachivskyi, Roman, Rostyslav Bun, Jacek Majewski, and Ihor Medynskyi. "MINIMAX APPROXIMATION OF THE RESISTANCE-TEMPERATURE THERMISTOR’S DEPENDENCE." Measuring Equipment and Metrology 85, no. 4 (2024): 20–24. https://doi.org/10.23939/istcmtm2024.04.020.

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The evidence to support feasibility of using minimax approximation to calculate the parameters of thermistors’ thermometric characteristic models has been provided. Minimax approximation ensures the achievement of the minimum possible calibration error, while the least squares method minimizes the sum of squared errors. A rational expression has been proposed to describe the dependence of temperature on thermistor’s resistance. The effectiveness of the model in the form of a rational expression is illustrated with actual calibration results. This model provides higher accuracy in reproducing t

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AL-FAGIH, LULUWAH. "THE BRITISH KNOCK-OUT PUT OPTION." International Journal of Theoretical and Applied Finance 18, no. 02 (2015): 1550008. http://dx.doi.org/10.1142/s0219024915500089.

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Following the economic rationale introduced by Peskir & Samee (2011, 2013) we present a new class of barrier options within the British payoff mechanism where the holder enjoys the early exercise feature of American type options whereupon his payoff (deliverable immediately) is the best prediction of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Should the option holder believe the true drift of the stock price to be unfavorable (based upon the observed price movements) he can substitute the true drift with the contract drift and m

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Arya, M. C., N. Chandra та Mahesh C. Joshi. "Common fixed point results for a generalized ( ψ, φ )-rational contraction". Applied General Topology 24, № 1 (2023): 129–44. http://dx.doi.org/10.4995/agt.2023.18320.

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In this paper, we obtain two common fixed point results for mappings satisfying the generalized (ψ,φ)-contractive type conditions given by a rational expression on a complete metric space. Our results generalize several well known theorems of the literature in the context of (ψ,φ)-rational contraction. In addition, there is an example for obtained results.

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Juven-Gershon, Tamar, Susan Cheng, and James T. Kadonaga. "Rational design of a super core promoter that enhances gene expression." Nature Methods 3, no. 11 (2006): 917–22. http://dx.doi.org/10.1038/nmeth937.

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31

Zargar, Amin, David N. Quan, Milad Emamian, et al. "Rational design of ‘controller cells’ to manipulate protein and phenotype expression." Metabolic Engineering 30 (July 2015): 61–68. http://dx.doi.org/10.1016/j.ymben.2015.04.001.

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Malachivskyy, P. S., Ya V. Pizyur, and R. P. Malachivsky. "Chebyshev Approximation by a Rational Expression for Functions of Many Variables." Cybernetics and Systems Analysis 56, no. 5 (2020): 811–19. http://dx.doi.org/10.1007/s10559-020-00302-0.

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Boissinot, M., L. A. Kuhn, P. Lee, et al. "Rational Design and Expression of a Heparin-Targeted Human Superoxide Dismutase." Biochemical and Biophysical Research Communications 190, no. 1 (1993): 250–56. http://dx.doi.org/10.1006/bbrc.1993.1038.

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34

Elsayed, E. M. "Expression and behavior of the solutions of some rational recursive sequences." Mathematical Methods in the Applied Sciences 39, no. 18 (2016): 5682–94. http://dx.doi.org/10.1002/mma.3953.

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35

Carew, Jennifer S., Claudia M. Espitia, Weiguo Zhao, et al. "Rational cotargeting of HDAC6 and BET proteins yields synergistic antimyeloma activity." Blood Advances 3, no. 8 (2019): 1318–29. http://dx.doi.org/10.1182/bloodadvances.2018026484.

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Abstract Inhibition of bromodomain and extra terminal (BET) protein family members, including BRD4, decreases the expression of c-MYC and other key oncogenic factors and also significantly induces histone deacetylase 6 (HDAC6) expression. On the basis of the role of HDAC6 in malignant pathogenesis, we hypothesized that rational cotargeting of HDAC6 and BET family proteins may represent a novel approach that yields synergistic antimyeloma activity. We used genetic and pharmacologic approaches to selectively impair HDAC6 and BET function and evaluated the consequential impact on myeloma pathogen

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WHITEFIELD, STEPHEN, and GEOFFREY EVANS. "Political Culture Versus Rational Choice: Explaining Responses to Transition in the Czech Republic and Slovakia." British Journal of Political Science 29, no. 1 (1999): 129–54. http://dx.doi.org/10.1017/s000712349900006x.

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There has been considerable disagreement among political scientists over the relative merits of political culture versus rational choice explanations of democratic and liberal norms and commitments. However, empirical tests of their relative explanatory power using quantitative evidence have been in short supply. This article employs national probability sample surveys conducted in 1994 to assess differences between Czechs and Slovaks in the expression of democratic norms and liberal attitudes with respect to economic, political, social and ethnic issues. The applicability of an explanation fo

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Hamer, Dean H., Sven Bocklandt, Louise McHugh, et al. "Rational Design of Drugs That Induce Human Immunodeficiency Virus Replication." Journal of Virology 77, no. 19 (2003): 10227–36. http://dx.doi.org/10.1128/jvi.77.19.10227-10236.2003.

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ABSTRACT Drugs that induce human immunodeficiency virus type 1 (HIV-1) replication could be used in combination with highly active antiretroviral therapy (HAART) to reduce the size of the latent reservoir that is in part responsible for viral persistence. Protein kinase C (PKC) is a logical target for such drugs because it activates HIV-1 transcription through multiple mechanisms. Here we show that HIV-1 gene expression can be induced by potent synthetic analogues of the lipid second messenger diacylglycerol (DAG) synthesized on a five-member ring platform that reduces the entropy of binding r

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Gómez-Abad, Cristina, Helena Pisonero, Carmen Blanco-Aparicio, et al. "PIM2 inhibition as a rational therapeutic approach in B-cell lymphoma." Blood 118, no. 20 (2011): 5517–27. http://dx.doi.org/10.1182/blood-2011-03-344374.

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Abstract PIM serine/threonine kinases are overexpressed, translocated, or amplified in multiple B-cell lymphoma types. We have explored the frequency and relevance of PIM expression in different B-cell lymphoma types and investigated whether PIM inhibition could be a rational therapeutic approach. Increased expression of PIM2 was detected in subsets of mantle cell lymphoma, diffuse large B-cell lymphoma (DLBLC), follicular lymphoma, marginal zone lymphoma-mucosa–associated lymphoid tissue type, chronic lymphocytic leukemia, and nodal marginal zone lymphoma cases. Increased PIM2 protein express

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Gity, Sogol, Farah Lotfi Kashani, Shahram Vaziri, and Hooman Namvar. "Comparison of the Effectiveness of Written Emotional Expression and Rational Emotive Behavior Therapy on the Health of Infertile Women." International Journal of Education and Cognitive Sciences 5, no. 4 (2024): 121–30. https://doi.org/10.61838/kman.ijecs.5.4.13.

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Purpose: The present study aimed to compare the effectiveness of the written emotional expression strategy and rational emotive behavior therapy (REBT) on the health of infertile women. Methods and Materials: The research method is quasi-experimental, and data collection was conducted using a pre-test, post-test, and follow-up design (three groups), with two experimental groups and one control group. The statistical population of this study consisted of all infertile women living in Tehran in 2023, who had visited infertility centers due to fertility problems and had been classified as inferti

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Inglehart, Ronald. "Mapping Global Values." Comparative Sociology 5, no. 2-3 (2006): 115–36. http://dx.doi.org/10.1163/156913306778667401.

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AbstractModernization goes through two main phases, each of which brings distinctive changes in people's worldviews. The Industrial Revolution was linked with a shift from traditional to secular-rational values, bringing bureaucratization, centralization, standardization and the secularization of authority. In the post-industrial phase of modernization, a shift from survival values to self-expression values, brings increasing emancipation from both religious and secular-rational authority. Rising mass emphasis on self-expression values makes democracy increasingly likely to emerge.Although the

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Temesi, Ottó K., Albert Karacs, Nguyen Q. Chinh, and Lajos K. Varga. "Temperature Dependence of Hardness of High Entropy Alloys." Metals 15, no. 6 (2025): 623. https://doi.org/10.3390/met15060623.

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Correlations have been found for the base value of hardness (as the ratio between the heat of fusion and molar volume) and the softening temperature (as the ratio of heat of fusion and specific heat capacity). The relative change of bulk hardness as a function of temperature, H(T), is studied by three new parametric formulas beside the well-known exponential decay and Arrhenius-type expressions. Mathematically, two formulas can be considered as deriving from the exponential decay; the third one is a new rational fraction expression based on the power of normalized temperature. The normalizing

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Li, Wei Vivian, and Jingyi Jessica Li. "A statistical simulator scDesign for rational scRNA-seq experimental design." Bioinformatics 35, no. 14 (2019): i41—i50. http://dx.doi.org/10.1093/bioinformatics/btz321.

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Abstract Motivation Single-cell RNA sequencing (scRNA-seq) has revolutionized biological sciences by revealing genome-wide gene expression levels within individual cells. However, a critical challenge faced by researchers is how to optimize the choices of sequencing platforms, sequencing depths and cell numbers in designing scRNA-seq experiments, so as to balance the exploration of the depth and breadth of transcriptome information. Results Here we present a flexible and robust simulator, scDesign, the first statistical framework for researchers to quantitatively assess practical scRNA-seq exp

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Ma, Yangyang. "Rational Exploration of Compassion Education." Journal of Higher Education Teaching 1, no. 3 (2024): 81–86. http://dx.doi.org/10.62517/jhet.202415312.

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With the rapid development of modern industry in China, people's lifestyle and quality of life have been significantly improved compared with the past. The strong appeal of social groups for a better life and strengthening the construction of spiritual civilization has become the vane to guide the new development of society. However, with the rapid development of social material civilization, people's spiritual civilization construction is becoming increasingly backward, especially the lack of compassion development of adolescent groups. Compassion is the true expression of human nature. It no

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Carter, Jason Lee, and Xuemei Wu. "An Examination of the Rational Model in Business Education in the Greater Bay Area (Guangdong, Hong Kong, and Macau) for Curriculum Revision and Development Aimed at Improving Graduates’ Employability Potential." Asian Journal of University Education 16, no. 2 (2020): 141. http://dx.doi.org/10.24191/ajue.v16i2.9153.

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The rational action model are techniques and processes of decision-making from data for effective decision-making. Business leaders are strategizing for their futures for their future employment needs in the Greater Bay Area region of Hong Kong, Macau, and the Guangdong province. Tertiary business curriculum revision and development efforts are focused on properly preparing graduates’ productive decision-making skillsets that ultimately increases their employability. This qualitative study examines the perspectives of regional business leaders for the knowledge and use of rational action in th

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Potseiko, P. G., and E. Rovba. "Vallée Poussin sums of rational Fourier–Chebyshev integral operators and approximations of the Markov function." St. Petersburg Mathematical Journal 35, no. 5 (2024): 879–96. https://doi.org/10.1090/spmj/1834.

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Rational approximations of the Markov function on the segment [ − 1 , 1 ] [-1,1] are studied. The Vallée Poussin sums of rational integral Fourier–Chebyshev operators as an approximation apparatus with a fixed number of geometrically distinct poles are chosen. For the constructed rational approximation method, integral representations of approximations and upper estimates of uniform approximations are established. For the Markov function with a measure whose derivative is a function that has a power-law singularity on the segment [ − 1 , 1 ] [-1, 1] , upper estimates of pointwise and uniform a

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Cebolla, A. "Rational design of a bacterial transcriptional cascade for amplifying gene expression capacity." Nucleic Acids Research 29, no. 3 (2001): 759–66. http://dx.doi.org/10.1093/nar/29.3.759.

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I.T. Al-Dosary, Khalil. "Explicit Expression for First Integral of a Rational Type of Kolmogorov Systems." International Journal of Mathematical Trends and Technology 12, no. 2 (2014): 69–74. http://dx.doi.org/10.14445/22315373/ijmtt-v12p511.

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Nehlsen, Kristina, Leonor da Gama-Norton, Roland Schucht, Hansjörg Hauser, and Dagmar Wirth. "Towards rational engineering of cells: Recombinant gene expression in defined chromosomal loci." BMC Proceedings 5, Suppl 8 (2011): O6. http://dx.doi.org/10.1186/1753-6561-5-s8-o6.

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Babu, V. Amarendra, O. Bhanu Sekhar, and K. Bhanu Chander. "Common fixed point theorem for almost weak contraction maps with rational expression." Nonlinear Analysis and Differential Equations 5 (2017): 43–52. http://dx.doi.org/10.12988/nade.2017.61084.

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Bianchi, Elisabetta, Sara Venturini, Antonello Pessi, Anna Tramontano, and Maurizio Sollazzo. "High Level Expression and Rational Mutagenesis of a Designed Protein, the Minibody." Journal of Molecular Biology 236, no. 2 (1994): 649–59. http://dx.doi.org/10.1006/jmbi.1994.1174.

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