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Journal articles on the topic 'Traces of functions'

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Published: 7 June 2025
Last updated: 26 June 2025

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1

Aubry, Jean Marie. "Traces of oscillating functions." Journal of Fourier Analysis and Applications 5, no. 4 (1999): 331–45. http://dx.doi.org/10.1007/bf01259374.

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2

Goffeng, M., and A. S. Usachev. "Weierstrass Functions Separate All Traces." Mathematical Notes 110, no. 5-6 (2021): 796–98. http://dx.doi.org/10.1134/s000143462111016x.

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3

Drury, S. W. "Maximizing traces of matrix functions." Linear Algebra and its Applications 387 (August 2004): 221–34. http://dx.doi.org/10.1016/j.laa.2004.02.029.

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4

Manfredi, Juan J., and Enrique Villamor. "Traces of monotone Sobolev functions." Journal of Geometric Analysis 6, no. 3 (1996): 433–44. http://dx.doi.org/10.1007/bf02921659.

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5

Babadjian, Jean-Francois. "Traces of functions of bounded deformation." Indiana University Mathematics Journal 64, no. 4 (2015): 1271–90. http://dx.doi.org/10.1512/iumj.2015.64.5601.

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6

Berndtsson, Bo, and Joaquim Bruna. "Traces of pluriharmonic functions on curves." Arkiv för Matematik 28, no. 1-2 (1990): 221–30. http://dx.doi.org/10.1007/bf02387377.

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7

Shvartsman, P. A. "Traces of functions of Zygmund class." Siberian Mathematical Journal 28, no. 5 (1988): 853–63. http://dx.doi.org/10.1007/bf00969335.

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8

Sukhov, K. A. "Continuous traces of δ-subharmonic functions". Journal of Mathematical Sciences 194, № 6 (2013): 703–7. http://dx.doi.org/10.1007/s10958-013-1559-3.

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9

Subramanian, P. R. "Generating functions for angular momentum traces." Journal of Physics A: Mathematical and General 19, no. 13 (1986): 2667–70. http://dx.doi.org/10.1088/0305-4470/19/13/030.

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10

Kolsrud, Torbj�rn. "Traces of harmonic functions, capacities, and traces of symmetric Markov processes." Journal of Theoretical Probability 2, no. 4 (1989): 399–418. http://dx.doi.org/10.1007/bf01051874.

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11

Bruinier, Jan Hendrik, and Jens Funke. "Traces of CM values of modular functions." Journal fur die reine und angewandte Mathematik (Crelles Journal) 2006, no. 594 (2006): 1–33. http://dx.doi.org/10.1515/crelle.2006.034.

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12

Impens, Chris. "Real functions as traces of infinite polynomials." Mathematische Annalen 284, no. 1 (1989): 63–73. http://dx.doi.org/10.1007/bf01443505.

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13

Romanov, A. S. "Traces of functions of generalized Sobolev classes." Siberian Mathematical Journal 48, no. 4 (2007): 678–93. http://dx.doi.org/10.1007/s11202-007-0070-9.

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14

Lord, Steven, Denis Potapov, and Fedor Sukochev. "Measures from Dixmier traces and zeta functions." Journal of Functional Analysis 259, no. 8 (2010): 1915–49. http://dx.doi.org/10.1016/j.jfa.2010.06.012.

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15

Eum, Ick Sun, and Ho Yun Jung. "On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5." Open Mathematics 17, no. 1 (2019): 1631–51. http://dx.doi.org/10.1515/math-2019-0115.

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Abstract After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the Fourier coefficients of weakly holomorphic modular forms of weight 3/2 on the congruence subgroups of higher genus by using the Bruinier-Funke modular traces. Extending their work, we construct real-valued class invariants by using the singular values of the generalized Weber functions of level 5 and prove that their Galois traces are Fourier coefficients of a harmonic weak Maass form of weight 3/2 by using Shimura’s reciprocity law.
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16

KANG, SOON-YI, and CHANG HEON KIM. "ARITHMETIC PROPERTIES OF TRACES OF SINGULAR MODULI ON CONGRUENCE SUBGROUPS." International Journal of Number Theory 06, no. 08 (2010): 1755–68. http://dx.doi.org/10.1142/s1793042110003757.

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After Zagier proved that the traces of singular moduli are Fourier coefficients of a weakly holomorphic modular form, various arithmetic properties of the traces of singular values of modular functions mostly on the full modular group have been found. The purpose of this paper is to generalize the results for modular functions on congruence subgroups with arbitrary level.
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17

Ferreira, Margarida, Victor Nicolet, Joey Dodds, and Daniel Kroening. "Program Synthesis from Partial Traces." Proceedings of the ACM on Programming Languages 9, PLDI (2025): 1642–65. https://doi.org/10.1145/3729316.

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We present the first technique to synthesize programs that compose side-effecting functions, pure functions, and control flow, from partial traces containing records of only the side-effecting functions. This technique can be applied to synthesize API composing scripts from logs of calls made to those APIs, or a script from traces of system calls made by a workload, for example. All of the provided traces are positive examples, meaning that they describe desired behavior. Our approach does not require negative examples. Instead, it generalizes over the examples and uses cost metrics to prevent over-generalization. Because the problem is too complex for traditional monolithic program synthesis techniques, we propose a new combination of optimizing rewrites and syntax-guided program synthesis. The resulting program is correct by construction, so its output will always be able to reproduce the input traces. We evaluate the quality of the programs synthesized when considering various optimization metrics and the synthesizer's efficiency on real-world benchmarks. The results show that our approach can generate useful real-world programs.
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18

Tullia, Magrini. "Music and functions: an open question." Música Oral del Sur, no. 3 (March 8, 1998): 85–92. https://doi.org/10.5281/zenodo.4626726.

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The belief that music fulfills a role in human society lies at the very foundation of anthropology of music: when Alan P. Merriam traces the roots of the anthropological approach to music in the literature of the late nineteenth century, he points out that «the emphasis was placed [...] upon the part music plays in culture and its functions in the widet social and cultural organization of man» (Merriam 1964:4).
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19

Wu, HaiHua, and XinHan Dong. "Driving functions and traces of the Loewner equation." Science China Mathematics 57, no. 8 (2013): 1615–24. http://dx.doi.org/10.1007/s11425-013-4698-6.

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20

Manfredi, Juan J., and Enrique Villamor. "Traces of monotone functions in weighted Sobolev spaces." Illinois Journal of Mathematics 45, no. 2 (2001): 403–22. http://dx.doi.org/10.1215/ijm/1258138347.

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21

ZVYAGIN, Sergei A., and Tat'yana N. FOMENKO. "Analyzing the protective functions of accounting and traces of illegal economic actions." International Accounting 22, no. 8 (2021): 887–906. http://dx.doi.org/10.24891/ia.24.8.887.

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Subject. The article addresses theoretical and methodological problems related to the analysis of protective functions of accounting process in the system of countering economic crimes and offenses. Objectives. The study focuses on reviewing the condition of protective functions in the accounting system at the current stage. Methods. We apply the systems and logical approaches, general scientific methods of knowledge to develop the framework of categories for accountants to implement the tasks they face to counteract economic crimes. Results. Based on our analysis, we developed a classification of accounting functions; formulated our own definition of protective functions of the accounting process; offered a unique classification of traces of illegal activities impacting the accounting process. The information containing traces of criminal economic impact may be demanded by law enforcement authorities and control and auditing bodies, audit organizations, and interested owners. Conclusions. The offered classification of accounting functions and traces of the impact of illegal activities on accounting process will enable to improve the quality of expert work on detecting, documenting, investigating and preventing illegal economic activities that are associated with accounting system.
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22

Koskela, Pekka, Khanh Ngoc Nguyen, and Zhuang Wang. "Trace Operators on Regular Trees." Analysis and Geometry in Metric Spaces 8, no. 1 (2020): 396–409. http://dx.doi.org/10.1515/agms-2020-0117.

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Abstract We consider different notions of boundary traces for functions in Sobolev spaces defined on regular trees and show that the almost everywhere existence of these traces is independent of the chosen definition of a trace.
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23

Björn, Anders, Jana Björn, and Nageswari Shanmugalingam. "Sobolev Extensions of Hölder Continuous and Characteristic Functions on Metric Spaces." Canadian Journal of Mathematics 59, no. 6 (2007): 1135–53. http://dx.doi.org/10.4153/cjm-2007-049-7.

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AbstractWe study when characteristic and Hölder continuous functions are traces of Sobolev functions on doubling metric measure spaces. We provide analytic and geometric conditions sufficient for extending characteristic and Hölder continuous functions into globally defined Sobolev functions.
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24

Shamoyan, Romi, and Olivera Mihic. "On traces of holomorphic functions on the unit polyball." Applicable Analysis and Discrete Mathematics 3, no. 2 (2009): 198–211. http://dx.doi.org/10.2298/aadm0902198s.

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25

LIEB, ELLIOTT H., and GERT K. PEDERSEN. "CONVEX MULTIVARIABLE TRACE FUNCTIONS." Reviews in Mathematical Physics 14, no. 07n08 (2002): 631–48. http://dx.doi.org/10.1142/s0129055x02001260.

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For any densely defined, lower semi-continuous trace τ on a C*-algebra A with mutually commuting C*-subalgebras A1, A2, … An, and a convex function f of n variables, we give a short proof of the fact that the function (x1, x2, …, xn)→ τ (f (x1, x2, …, xn)) is convex on the space [Formula: see text]. If furthermore the function f is log-convex or root-convex, so is the corresponding trace function. We also introduce a generalization of log-convexity and root-convexity called ℓ-convexity, show how it applies to traces, and give some examples. In particular we show that the Kadison–Fuglede determinant is concave and that the trace of an operator mean is always dominated by the corresponding mean of the trace values.
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26

LASSOUED, DHAOU. "A Study of Functions on the Torus and Multi-periodic Functions." Kragujevac Journal of Mathematics 50, no. 2 (2024): 297–337. http://dx.doi.org/10.46793/kgjmat2602.297l.

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In this paper, we are concerned with functions defined on the cube Qm = [−π, π] m and functions defined on the torus T m. Especially, the harmonic analysis of Sobolev-type spaces is carefully studied. We analyze in particular periodic distributions and distributions on the torus. We introduce a space similar to H1 0 , for which we prove a Poincaré-Wirtinger inequality. We prove that the usual Rellich-Kondrachov result does not hold for these last space because of the lack of compactness. A result of absolute continuity and density of regular functions is then established and a theorem of traces is obtained.
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27

Pankka, Pekka, Pietro Poggi-Corradini, and Kai Rajala. "Sharp Exponential Integrability for Traces of Monotone Sobolev Functions." Nagoya Mathematical Journal 192 (2008): 137–49. http://dx.doi.org/10.1017/s0027763000026015.

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AbstractWe answer a question posed in [12] on exponential integrability of functions of restricted n-energy. We use geometric methods to obtain a sharp exponential integrability result for boundary traces of monotone Sobolev functions defined on the unit ball.
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28

TRENEER, STEPHANIE. "CONGRUENCES FOR THE COEFFICIENTS OF WEAKLY HOLOMORPHIC MODULAR FORMS." Proceedings of the London Mathematical Society 93, no. 2 (2006): 304–24. http://dx.doi.org/10.1112/s0024611506015814.

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Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. We show that this type of phenomenon is completely general, by finding similar congruences for the coefficients of any weakly holomorphic modular form on any congruence subgroup $\Gamma_0 (N)$. In particular, we give congruences for a wide class of partition functions and for traces of CM values of arbitrary modular functions on certain congruence subgroups of prime level.
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29

Buffa, Vito, and Michele Miranda Jr. "Rough traces of BV functions in metric measure spaces." Annales Fennici Mathematici 46, no. 1 (2021): 309–33. http://dx.doi.org/10.5186/aasfm.2021.4625.

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30

Romanov, A. S. "On the traces of Sobolev functions on Lipschitz surfaces." Doklady Mathematics 95, no. 3 (2017): 243–46. http://dx.doi.org/10.1134/s1064562417030127.

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31

Koskela, Pekka, Juan J. Manfredi, and Enrique Villamor. "Regularity theory and traces of $\mathcal {A}$-harmonic functions." Transactions of the American Mathematical Society 348, no. 2 (1996): 755–66. http://dx.doi.org/10.1090/s0002-9947-96-01430-4.

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32

Buffa, Annalisa, and Giuseppe Geymonat. "On traces of functions in for Lipschitz domains in." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 332, no. 8 (2001): 699–704. http://dx.doi.org/10.1016/s0764-4442(01)01881-x.

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33

Bruna, Joaquim, and Joaquin M. Ortega. "Traces on curves of Sobolev spaces of holomorphic functions." Arkiv för Matematik 29, no. 1-2 (1991): 25–49. http://dx.doi.org/10.1007/bf02384329.

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34

Aubry, Jean-Marie, Delphine Maman, and Stéphane Seuret. "Local behavior of traces of Besov functions: Prevalent results." Journal of Functional Analysis 264, no. 3 (2013): 631–60. http://dx.doi.org/10.1016/j.jfa.2012.11.012.

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35

Alpay, Daniel, and Juliette Leblond. "Traces of Hardy functions and reproducing kernel Hilbert spaces." Archiv der Mathematik 64, no. 6 (1995): 490–99. http://dx.doi.org/10.1007/bf01195131.

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36

Kałamajska, Agnieszka, and Miroslav Krbec. "Traces of Orlicz-Sobolev functions under general growth restrictions." Mathematische Nachrichten 286, no. 7 (2012): 730–42. http://dx.doi.org/10.1002/mana.201100185.

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37

Harlan, William S. "Simultaneous velocity filtering of hyperbolic reflections and balancing of offset‐dependent wavelets." GEOPHYSICS 54, no. 11 (1989): 1455–65. http://dx.doi.org/10.1190/1.1442609.

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Hyperbolic reflections and convolutional wavelets are fundamental models for seismic data processing. Each sample of a “stacked” zero‐offset section can parameterize an impulsive hyperbolic reflection in a midpoint gather. Convolutional wavelets can model source waveforms and near‐surface filtering at the shot and geophone positions. An optimized inversion of the combined modeling equations for hyperbolic traveltimes and convolutional wavelets makes explicit any interdependence and nonuniqueness in these two sets of parameters. I first estimate stacked traces that best model the recorded data and then find nonimpulsive wavelets to improve the fit with the data. These wavelets are used for a new estimate of the stacked traces, and so on. Estimated stacked traces model short average wavelets with a superposition of approximately parallel hyperbolas; estimated wavelets adjust the phases and amplitudes of inconsistent traces, including static shifts. Deconvolution of land data with estimated wavelets makes wavelets consistent over offset; remaining static shifts are midpoint‐consistent. This phase balancing improves the resolution of stacked data and of velocity analyses. If precise velocity functions are not known, then many stacked traces can be inverted simultaneously, each with a different velocity function. However, the increased number of overlain hyperbolas can more easily model the effects of inconsistent wavelets. As a compromise, I limit velocity functions to reasonable regions selected from a stacking velocity analysis—a few functions cover velocities of primary and multiple reflections. Multiple reflections are modeled separately and then subtracted from marine data. The model can be extended to include more complicated amplitude changes in reflectivity. Migrated reflectivity functions would add an extra constraint on the continuity of reflections over midpoint. Including the effect of dip moveout in the model would make stacking and migration velocities equivalent.
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38

Gupta, Dhawal, Scott M. Jordan, Shreyas Chaudhari, Bo Liu, Philip S. Thomas, and Bruno Castro da Silva. "From Past to Future: Rethinking Eligibility Traces." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 11 (2024): 12253–60. http://dx.doi.org/10.1609/aaai.v38i11.29115.

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In this paper, we introduce a fresh perspective on the challenges of credit assignment and policy evaluation. First, we delve into the nuances of eligibility traces and explore instances where their updates may result in unexpected credit assignment to preceding states. From this investigation emerges the concept of a novel value function, which we refer to as the ????????????? ????? ????????. Unlike traditional state value functions, bidirectional value functions account for both future expected returns (rewards anticipated from the current state onward) and past expected returns (cumulative rewards from the episode's start to the present). We derive principled update equations to learn this value function and, through experimentation, demonstrate its efficacy in enhancing the process of policy evaluation. In particular, our results indicate that the proposed learning approach can, in certain challenging contexts, perform policy evaluation more rapidly than TD(λ)–a method that learns forward value functions, v^π, ????????. Overall, our findings present a new perspective on eligibility traces and potential advantages associated with the novel value function it inspires, especially for policy evaluation.
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39

MESYAN, ZACHARY, and LIA VAŠ. "TRACES ON SEMIGROUP RINGS AND LEAVITT PATH ALGEBRAS." Glasgow Mathematical Journal 58, no. 1 (2015): 97–118. http://dx.doi.org/10.1017/s0017089515000087.

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AbstractThe trace on matrix rings, along with the augmentation map and Kaplansky trace on group rings, are some of the many examples of linear functions on algebras that vanish on all commutators. We generalize and unify these examples by studying traces on (contracted) semigroup rings over commutative rings. We show that every such ring admits a minimal trace (i.e., one that vanishes only on sums of commutators), classify all minimal traces on these rings, and give applications to various classes of semigroup rings and quotients thereof. We then study traces on Leavitt path algebras (which are quotients of contracted semigroup rings), where we describe all linear traces in terms of central maps on graph inverse semigroups and, under mild assumptions, those Leavitt path algebras that admit faithful traces.
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40

Cho, Peter J., and Henry H. Kim. "Central limit theorem for Artin L-functions." International Journal of Number Theory 13, no. 01 (2016): 1–14. http://dx.doi.org/10.1142/s1793042117500014.

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We show that the sum of the traces of Frobenius elements of Artin [Formula: see text]-functions in a family of [Formula: see text]-fields satisfies the Gaussian distribution under certain counting conjectures. We prove the counting conjectures for [Formula: see text] and [Formula: see text]-fields. We also prove a central limit theorem for the [Formula: see text]-functions of modular forms on congruence subgroups [Formula: see text] as [Formula: see text].
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41

Ihnatsyeva, Lizaveta, and Antti V. Vähäkangas. "Characterization of traces of smooth functions on Ahlfors regular sets." Journal of Functional Analysis 265, no. 9 (2013): 1870–915. http://dx.doi.org/10.1016/j.jfa.2013.07.006.

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42

Celada, Pietro, and Alessandra Lunardi. "Traces of Sobolev functions on regular surfaces in infinite dimensions." Journal of Functional Analysis 266, no. 4 (2014): 1948–87. http://dx.doi.org/10.1016/j.jfa.2013.11.013.

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43

Shcherbina, N. V. "Traces of pluriharmonic functions on the boundaries of analytic varieties." Mathematische Zeitschrift 213, no. 1 (1993): 171–77. http://dx.doi.org/10.1007/bf03025716.

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44

Chacón-Cortés, L. F., and W. A. Zúñiga-Galindo. "Heat Traces and Spectral Zeta Functions for $p$-adic Laplacians." St. Petersburg Mathematical Journal 29, no. 3 (2018): 529–44. http://dx.doi.org/10.1090/spmj/1505.

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45

Gulisashvili, A. B. "Traces of differential functions on subsets of the euclidean space." Journal of Soviet Mathematics 42, no. 2 (1988): 1573–83. http://dx.doi.org/10.1007/bf01665043.

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46

Vybíral, Jan, та Winfried Sickel. "Traces of functions with a dominating mixed derivative in ℝ3". Czechoslovak Mathematical Journal 57, № 4 (2007): 1239–73. http://dx.doi.org/10.1007/s10587-007-0122-0.

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47

Gregoratti, M. "Traces of Sobolev functions with one square integrable directional derivative." Mathematical Methods in the Applied Sciences 29, no. 2 (2005): 157–71. http://dx.doi.org/10.1002/mma.669.

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48

MASUMOTO, SHUHEI. "THE JIANG–SU ALGEBRA AS A FRAÏSSÉ LIMIT." Journal of Symbolic Logic 82, no. 4 (2017): 1541–59. http://dx.doi.org/10.1017/jsl.2016.52.

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AbstractIn this paper, we give a self-contained and quite elementary proof that the class of all dimension drop algebras together with their distinguished faithful traces forms a Fraïssé class with the Jiang–Su algebra as its limit. We also show that the UHF algebras can be realized as Fraïssé limits of classes of C*-algebras of matrix-valued continuous functions on [0,1] with faithful traces.
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49

Fiordalisi, Francesco. "Logarithmic intertwining operators and genus-one correlation functions." Communications in Contemporary Mathematics 18, no. 06 (2016): 1650026. http://dx.doi.org/10.1142/s0219199716500267.

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This is the first of two papers in which we study the modular invariance of pseudotraces of logarithmic intertwining operators. We construct and study genus-one correlation functions for logarithmic intertwining operators among generalized modules over a positive-energy and [Formula: see text]-cofinite vertex operator algebra [Formula: see text]. We consider grading-restricted generalized [Formula: see text]-modules which admit a right action of some associative algebra [Formula: see text], and intertwining operators among such modules which commute with the action of [Formula: see text] ([Formula: see text]-intertwining operators). We obtain duality properties, i.e. suitable associativity and commutativity properties, for [Formula: see text]-intertwining operators. Using pseudotraces introduced by Miyamoto and studied by Arike, we define formal [Formula: see text]-traces of products of [Formula: see text]-intertwining operators, and obtain certain identities for these formal series. This allows us to show that the formal [Formula: see text]-traces satisfy a system of differential equations with regular singular points, and therefore are absolutely convergent in a suitable region and can be extended to yield multivalued analytic functions, called genus-one correlation functions. Furthermore, we show that the space of solutions of these differential equations is invariant under the action of the modular group.
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50

Kopcha, V., R. Fridmanskyi, and N. Kopcha. "Legal investigation of crime trace tracks: facilitating effective detection and prevention of crimes." Uzhhorod National University Herald. Series: Law 2, no. 72 (2022): 211–18. http://dx.doi.org/10.24144/2307-3322.2022.72.67.

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This article is devoted to the coverage of legal research of traces at the crime scene, which contribute to the effective detection and prevention of crimes, and determine the development and functioning of trasology.
 The authors point to the research and organization of the volume. Their main functions are manifested in the accumulation of achievements of trasological research in theory and practice, the optimal development of trasology and dactyloscopy, which contribute to the effective detection and prevention of crimes. These are the most important starting points that underlie its construction and development.
 The commission of many crimes is accompanied by certain changes in the environment. Such changes are called traces of a crime. The trace is a reflection of criminal acts, individual elements of a criminal act. In the forensic sense, the value of traces is due to the existing relationship between the crime and its reflection (traces).
 In modern criminology, the concept of trace should be considered in several aspects. In a broad sense, it should be the result of any material change in the primary situation as a result of the crime: the appearance or disappearance of certain objects, violation of the original position, location, condition of various objects (eg, lost property at the scene, fragments broken window glass). At the present stage of development of criminology as traces are considered: sound traces, odor traces, traces-microparticles, traces-substances, traces of the genetic code of man.
 Traditionally, trasology studies traces only in a narrow sense, namely, materially fixed reflections of the external structure of one object on another (traces-reflections). Traces-reflections arise as a result of interaction of two objects and have rather wide distribution: these are traces of human hands, feet, footwear, teeth, vehicles, tools and tools, etc. Traces-reflection is the main subject of study in trasology.
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