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1

Bang, S. J., and M. H. Kim. "Zeros of a function given by the series of functions." Applied Mathematics Letters 1, no. 4 (1988): 331–34. http://dx.doi.org/10.1016/0893-9659(88)90144-9.

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2

Franssens, Ghislain R. "Functions with derivatives given by polynomials in the function itself or a related function." Analysis Mathematica 33, no. 1 (March 2007): 17–36. http://dx.doi.org/10.1007/s10474-007-0102-5.

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3

Luo, Ya Wen, Can Kang, and Chuan Lin Zhang. "Copulas with Given Rational Function Sections." Applied Mechanics and Materials 336-338 (July 2013): 2225–28. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.2225.

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We introduce a construction method with rational function horizontal or vertical sections based on the relationship between copula function and its generator. The copulas formula with fraction linear horizontal (vertical) sections is given. In addition, nonexistence about Archimedean copulas with quadratic rational function horizontal or vertical sections has been proved.
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4

Rodriguez, Matthew J. "Ideals attaining a given Hilbert function." Illinois Journal of Mathematics 44, no. 4 (December 2000): 821–27. http://dx.doi.org/10.1215/ijm/1255984693.

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5

Awan, Muhammad, Muhammad Noor, Marcela Mihai, Khalida Noor, and Nousheen Akhtar. "On approximately harmonic h-convex functions depending on a given function." Filomat 33, no. 12 (2019): 3783–93. http://dx.doi.org/10.2298/fil1912783a.

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A new class of harmonic convex function depending on given functions which is called as ?approximately harmonic h-convex functions? is introduced. With the discussion of special cases it is shown that this class unifies other classes of approximately harmonic h-convex function. Some associated integral inequalities with these new classes of harmonic convexity are also obtained. Several special cases of the main results are also discussed.
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6

Averbukh, Yu V. "Differential games with a given value function." Proceedings of the Steklov Institute of Mathematics 266, S1 (September 2009): 40–55. http://dx.doi.org/10.1134/s0081543809060042.

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7

Evans, E. Graham, and Benjamin P. Richert. "POSSIBLE RESOLUTIONS FOR A GIVEN HILBERT FUNCTION." Communications in Algebra 30, no. 2 (February 25, 2002): 897–906. http://dx.doi.org/10.1081/agb-120013189.

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8

Kolomeec, N. A. "Properties of bent functions constructed by a given bent function using subspaces." Prikladnaya diskretnaya matematika. Prilozhenie, no. 12 (September 1, 2019): 50–53. http://dx.doi.org/10.17223/2226308x/12/14.

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9

Zelkin, E. G., V. F. Kravchenko, V. I. Pustovoit, and V. V. Timoshenko. "Approximation of a given function by integral functions of the exponential type." Doklady Physics 45, no. 3 (March 2000): 97–100. http://dx.doi.org/10.1134/1.171715.

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10

Bard, Gregory V. "Determining whether a given cryptographic function is a permutation of another given cryptographic function—A problem in intellectual property." Theoretical Computer Science 800 (December 2019): 3–14. http://dx.doi.org/10.1016/j.tcs.2019.10.010.

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11

Ben-Benjamin, J. S., L. Cohen, N. C. Dias, P. Loughlin, and J. N. Prata. "What is the Wigner Function Closest to a Given Square Integrable Function?" SIAM Journal on Mathematical Analysis 50, no. 5 (January 2018): 5161–97. http://dx.doi.org/10.1137/18m116633x.

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12

Gaál, I. "Integral elements with given discriminant over function fields." Acta Mathematica Hungarica 52, no. 1-2 (March 1988): 133–46. http://dx.doi.org/10.1007/bf01952486.

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13

Bernardi, Alessandra, Joachim Jelisiejew, Pedro Macias Marques, and Kristian Ranestad. "On polynomials with given Hilbert function and applications." Collectanea Mathematica 69, no. 1 (January 11, 2017): 39–64. http://dx.doi.org/10.1007/s13348-016-0190-2.

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14

HED, LISA. "APPROXIMATION OF NEGATIVE PLURISUBHARMONIC FUNCTIONS WITH GIVEN BOUNDARY VALUES." International Journal of Mathematics 21, no. 09 (September 2010): 1135–45. http://dx.doi.org/10.1142/s0129167x10006410.

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In this paper, we study the approximation of negative plurisubharmonic functions with given boundary values. We want to approximate a plurisubharmonic function by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.
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15

Tong, Shih-Hsi, and Daniel C. H. Yang. "Rotor Profiles Synthesis for Lobe Pumps With Given Flow Rate Functions." Journal of Mechanical Design 127, no. 2 (March 1, 2005): 287–94. http://dx.doi.org/10.1115/1.1798271.

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In this paper we present a complete synthesis procedure for lobe pumps with required flow rate functions. A dimensionless flow rate expression, called the “specific flow rate,” is used for our pump synthesis. This specific flow rate depends only on the pitch and deviation functions of the pump rotor, and it is independent of the individual pump size, neither pumping frequency. Another important design parameter used is the “lobe noncircularity,” which is defined as the ratio of the lobe length to the rotor center distance. It is found that the lobe noncircularity is linearly dependent on the ratio of maximum to minimum flow rate regardless of the type of flow rate function. As a result, our synthesis procedure can be simplified as (1) select a type of desirable flow rate function, (2) from the flow rate function derive the corresponding deviation function, (3) based on the deviation function generate the desired rotor profile, and (4) calculate the real pump size. Another advantage is that by using this method wide classes of lobe pumps can be designed. A detailed design example is presented for illustration. In addition, new lobe profiles are invented based on some typical flow rate functions.
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16

Dũng, Dinh, Charles A. Micchelli, and Vu Nhat Huy. "Approximation by translates of a single function of functions in space induced by the convolution with a given function." Applied Mathematics and Computation 361 (November 2019): 777–87. http://dx.doi.org/10.1016/j.amc.2019.06.034.

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17

Rubio, Franco, and Orlando Hernández. "BUILDING A POLYNOMIAL FUNCTION FROM FIXED POINTS GIVEN PREVIOUSLY." Selecciones Matemáticas 2, no. 1 (June 30, 2015): 54–67. http://dx.doi.org/10.17268/sel.mat.2015.01.06.

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18

Taelman, Lenny. "K3 surfaces over finite fields with given L-function." Algebra & Number Theory 10, no. 5 (July 28, 2016): 1133–46. http://dx.doi.org/10.2140/ant.2016.10.1133.

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19

Bandemer, H. "Some ideas to minimize an empirically given fuzzy function." Optimization 22, no. 1 (January 1991): 139–51. http://dx.doi.org/10.1080/02331939108843652.

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20

STENFLO, ÖRJAN. "ITERATED FUNCTION SYSTEMS WITH A GIVEN CONTINUOUS STATIONARY DISTRIBUTION." Fractals 20, no. 03n04 (September 2012): 197–202. http://dx.doi.org/10.1142/s0218348x1250017x.

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21

Van Iseghem, Jeannette, and Peter R. Graves-Morris. "Approximation of a function given by its Laurent series." Numerical Algorithms 11, no. 1 (December 1996): 339–51. http://dx.doi.org/10.1007/bf02142506.

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22

Maslyuchenko, V. K., and O. V. Maslyuchenko. "Construction of a separately continuous function with given oscillation." Ukrainian Mathematical Journal 50, no. 7 (July 1998): 1080–90. http://dx.doi.org/10.1007/bf02528836.

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23

Zhu, Jian-Feng. "Some estimates for harmonic mappings with given boundary function." Journal of Mathematical Analysis and Applications 411, no. 2 (March 2014): 631–38. http://dx.doi.org/10.1016/j.jmaa.2013.10.001.

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24

Maslyuchenko, Oleksandr V., and Denys P. Onypa. "A quasi-locally constant function with given cluster sets." European Journal of Mathematics 6, no. 1 (January 29, 2020): 72–79. http://dx.doi.org/10.1007/s40879-020-00397-x.

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25

Zaninetti, L. "The Initial Mass Function as given by the fragmentation." Astronomische Nachrichten 326, no. 8 (October 2005): 754–59. http://dx.doi.org/10.1002/asna.200510408.

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26

Alexandrova, T. V., and V. A. Kofanov. "Sharp inequalities of various metrics on the classes of functions with given comparison function." Researches in Mathematics 29, no. 1 (July 5, 2021): 11. http://dx.doi.org/10.15421/242102.

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For any $q > p > 0$, $\omega > 0,$ $d \ge 2 \omega,$ we obtain the following sharp inequality of various metrics$$\|x\|_{L_q(I_{d})} \le \frac{\|\varphi +c\|_{L_q(I_{2\omega})}}{\|\varphi + c \|_{L_p(I_{2\omega})}}\|x\|_{L_p(I_{d})}$$on the set $S_{\varphi}(\omega)$ of $d$-periodic functions $x$ having zeros with given the sine-shaped $2\omega$-periodic comparison function $\varphi$, where $c\in [-\|\varphi\|_\infty, \|\varphi\|_\infty]$ is such that$$\|x_{\pm}\|_{L_p(I_{d})} = \|(\varphi +c)_{\pm}\|_{L_p(I_{2\omega})}\,.$$In particular, we obtain such type inequalities on the Sobolev sets of periodic functions and on the spaces of trigonometric polynomials and polynomial splines with given quotient of the norms $\|x_{+}\|_{L_p(I_{d})} / \|x_-\|_{L_p(I_{d})}$.
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27

Lutz, J. Gary, and Leigh A. Cundari. "Determining the Most Significant Parametric Function for a Given Linear Hypothesis." Journal of Educational Statistics 12, no. 3 (September 1987): 225–33. http://dx.doi.org/10.3102/10769986012003225.

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After a hypothesis about some linear statistical model has been tested and rejected (e.g., in an ANOVA), many researchers employ the Scheffe procedure to locate the source(s) of the rejection. This procedure guarantees that there is at least one linear combination of the model parameters (consistent with the hypothesis) that is significantly different from its hypothesized value. This most significant parametric function is not always easy to find, however, because it may not manifest itself in simple functions (such as pairwise contrasts between groups) or in “obvious” functions (such as those suggested by the graph of an interaction). A general solution to this problem is presented along with a practical example of its application.
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28

Devroye, Luc. "Algorithms for Generating Discrete Random Variables with a Given Generating Function or a Given Moment Sequence." SIAM Journal on Scientific and Statistical Computing 12, no. 1 (January 1991): 107–26. http://dx.doi.org/10.1137/0912006.

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29

Pakovich, F. "On Rational Functions Orthogonal to All Powers of a Given Rational Function on a Curve." Moscow Mathematical Journal 13, no. 4 (2013): 693–731. http://dx.doi.org/10.17323/1609-4514-2013-13-4-693-731.

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30

Martin Bibby, Bo, Ib Michael Skovgaard, and Michael Sørensen. "Diffusion-type models with given marginal distribution and autocorrelation function." Bernoulli 11, no. 2 (April 2005): 191–220. http://dx.doi.org/10.3150/bj/1116340291.

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31

Susmaga, Robert. "Analyzing Discretizations of Continuous Attributes Given a Monotonic Discrimination Function." Intelligent Data Analysis 1, no. 3 (July 1, 1997): 157–79. http://dx.doi.org/10.3233/ida-1997-1303.

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32

Rubio, Franco, and Orlando Hernández. "Building a Vectorial function from a fixed point given previously." Selecciones Matemáticas 4, no. 1 (June 30, 2017): 124–38. http://dx.doi.org/10.17268/sel.mat.2017.01.12.

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33

Thunder, Jeffrey Lin. "Counting subspaces of given height defined over a function field." Journal of Number Theory 128, no. 12 (December 2008): 2973–3004. http://dx.doi.org/10.1016/j.jnt.2008.06.011.

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34

MASUMOTO, Yasutaka, and Osamu SAEKI. "A SMOOTH FUNCTION ON A MANIFOLD WITH GIVEN REEB GRAPH." Kyushu Journal of Mathematics 65, no. 1 (2011): 75–84. http://dx.doi.org/10.2206/kyushujm.65.75.

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35

SUSMAGA, R. "Analyzing discretizations of continuous attributes given a monotonic discrimination function." Intelligent Data Analysis 1, no. 1-4 (1997): 157–79. http://dx.doi.org/10.1016/s1088-467x(97)00007-3.

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36

Dikranjan, Dikran, Dmitri Shakhmatov, and Jan Spěvák. "Productivity of sequences with respect to a given weight function." Topology and its Applications 158, no. 3 (February 2011): 298–324. http://dx.doi.org/10.1016/j.topol.2010.11.009.

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37

Schätzle, Reiner. "Hypersurfaces with mean Curvature given by an Ambient Sobolev Function." Journal of Differential Geometry 58, no. 3 (July 2001): 371–420. http://dx.doi.org/10.4310/jdg/1090348353.

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38

Alboul, L., J. Mencía, R. Ramírez, and N. Sadovskaia. "On the determination of the potential function from given orbits." Czechoslovak Mathematical Journal 58, no. 3 (September 2008): 799–821. http://dx.doi.org/10.1007/s10587-008-0052-5.

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39

Murai, Satoshi, and Takayuki Hibi. "The depth of an ideal with a given Hilbert function." Proceedings of the American Mathematical Society 136, no. 05 (January 17, 2008): 1533–39. http://dx.doi.org/10.1090/s0002-9939-08-09067-9.

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40

Kukina, E. G. "The averaged Dehn function relative to a given probability measure." Siberian Mathematical Journal 47, no. 2 (March 2006): 298–300. http://dx.doi.org/10.1007/s11202-006-0042-5.

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41

Kudryavtsev, S. N. "RECOVERING A FUNCTION WITH ITS DERIVATIVES FROM FUNCTION VALUES AT A GIVEN NUMBER OF POINTS." Russian Academy of Sciences. Izvestiya Mathematics 45, no. 3 (June 30, 1995): 505–28. http://dx.doi.org/10.1070/im1995v045n03abeh001666.

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42

BETSAKOS, DIMITRIOS. "HOLOMORPHIC FUNCTIONS WITH IMAGE OF GIVEN LOGARITHMIC OR ELLIPTIC CAPACITY." Journal of the Australian Mathematical Society 94, no. 2 (March 8, 2013): 145–57. http://dx.doi.org/10.1017/s1446788712000559.

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AbstractFor holomorphic functions $f$ in the unit disk $ \mathbb{D} $ with $f(0)= 0$, we prove a modulus growth bound involving the logarithmic capacity (transfinite diameter) of the image. We show that the pertinent extremal functions map the unit disk conformally onto the interior of an ellipse. We prove a modulus growth bound for elliptically schlicht functions in terms of the elliptic capacity ${\mathrm{d} }_{\mathrm{e} } f( \mathbb{D} )$ of the image. We also show that the function ${\mathrm{d} }_{\mathrm{e} } f(r \mathbb{D} )/ r$ is increasing for $0\lt r\lt 1$.
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43

Aryanti, Maya Lisa. "Interjections Functioned as Pragmatic Markers and Given/ New Information." Celt: A Journal of Culture, English Language Teaching & Literature 18, no. 1 (July 23, 2018): 84. http://dx.doi.org/10.24167/celt.v18i1.570.

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The purposes of this research are to find out the functions of the interjections functioned as pragmatic markers and what they indicate to, to find out which information the interjections denote and to find out how many functions the interjections functioned as pragmatic markers possibly have. The data are five different interjections taken from five different novels. The results of this research are concerning to the functions of the interjections functioned as pragmatic markers. Generally, the functions are utterance initial, attention marker and a response signal. Further, interjections functioned as pragmatic markers take form as attitude, feelings or both. The interjections denote given/old information, new information and both. The last result is that it is possible for interjections to have more than one function. To sum up, interjections functioned as pragmatic markers have roles and forms in discourses. In addition, interjections functioned as pragmatic markers denote information.
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44

Kofanov, V. A. "Sharp upper bounds of norms of functions and their derivatives on classes of functions with given comparison function." Ukrainian Mathematical Journal 63, no. 7 (November 29, 2011): 1118–35. http://dx.doi.org/10.1007/s11253-011-0567-z.

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45

Belhaouari, Samir Brahim, Yassine Hamdi, and Abdelouahed Hamdi. "Revisited Carmichael’s Reduced Totient Function." Mathematics 9, no. 15 (July 29, 2021): 1800. http://dx.doi.org/10.3390/math9151800.

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The modified Totient function of Carmichael λ(.) is revisited, where important properties have been highlighted. Particularly, an iterative scheme is given for calculating the λ(.) function. A comparison between the Euler φ and the reduced totient λ(.) functions aiming to quantify the reduction between is given.
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46

Gaidabura, A. E., and V. A. Kofanov. "Sharp Remez-type Inequalities of Various Metrics in the Classes of Functions with Given Comparison Function." Ukrainian Mathematical Journal 69, no. 11 (April 2018): 1710–26. http://dx.doi.org/10.1007/s11253-018-1465-4.

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47

Lutz, J. Gary, and Leigh A. Cundari. "Determining the Most Significant Parametric Function for a Given Linear Multivariate Hypothesis." Journal of Educational Statistics 14, no. 1 (March 1989): 21–28. http://dx.doi.org/10.3102/10769986014001021.

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After a hypothesis about some linear multivariate statistical model has been tested and rejected (e.g., in a MANOVA), many researchers employ simultaneous test procedures to locate the source(s) of the rejection. If the global test was conducted using Roy’s largest root criterion, then this procedure guarantees at least one linear combination of the model parameters relative to some linear combination of the dependent variables that is significantly different from its hypothesized value. This most significant parametric function is not always easy to find, however, because it may not manifest itself in simple or “obvious” functions. A general solution to this problem is presented along with a practical example of its application.
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48

Vetro, Francesca. "Fixed point belonging to the zero-set of a given function." Journal of Nonlinear Sciences and Applications 11, no. 03 (February 22, 2018): 417–24. http://dx.doi.org/10.22436/jnsa.011.03.09.

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49

Arnold, Vladimir I. "On the problem of realization of a given Gaussian curvature function." Topological Methods in Nonlinear Analysis 11, no. 2 (June 1, 1998): 199. http://dx.doi.org/10.12775/tmna.1998.013.

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50

Thunder, Jeffrey Lin, and Martin Widmer. "Counting points of fixed degree and given height over function fields." Bulletin of the London Mathematical Society 45, no. 2 (November 7, 2012): 283–300. http://dx.doi.org/10.1112/blms/bds087.

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