{"results":[{"id":"crossref_10.1103/3fdc-j3bf","title":"Single-particle strength toward\n                    \u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\n                      \u003cmml:mrow\u003e\n                        \u003cmml:mi\u003eN\u003c/mml:mi\u003e\n                        \u003cmml:mo\u003e=\u003c/mml:mo\u003e\n                        \u003cmml:mn\u003e32\u003c/mml:mn\u003e\n                      \u003c/mml:mrow\u003e\n                    \u003c/mml:math\u003e\n                    : Spectroscopy of\n                    \u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\n                      \u003cmml:msup\u003e\n                        \u003cmml:mi/\u003e\n                        \u003cmml:mn\u003e51\u003c/mml:mn\u003e\n                      \u003c/mml:msup\u003e\n                    \u003c/mml:math\u003e\n                    Ca via the\n                    \u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\n                      \u003cmml:msup\u003e\n                        \u003cmml:mi/\u003e\n                        \u003cmml:mn\u003e50\u003c/mml:mn\u003e\n                      \u003c/mml:msup\u003e\n                    \u003c/mml:math\u003e\n                    Ca(\n                    \u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\n                      \u003cmml:mi\u003ed\u003c/mml:mi\u003e\n                    \u003c/mml:math\u003e\n                    ,\n                    \u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\n                      \u003cmml:mi\u003ep\u003c/mml:mi\u003e\n                    \u003c/mml:math\u003e\n                    ) reaction","authors":[{"name":"Anonymous"}],"abstract":"","source":"CrossRef","year":2026,"language":"en","subjects":null,"doi":"10.1103/3fdc-j3bf","url":"https://doi.org/10.1103/3fdc-j3bf","is_open_access":true,"published_at":"","score":70},{"id":"ss_fe501114ac9885172a3ef5d18eb5ad73b537c09d","title":"Carnot-Carath\\'{e}odory metrics associated to degenerate elliptic operators in three dimensions","authors":[{"name":"L. Korobenko"},{"name":"F. Meister"},{"name":"Olive Ross"}],"abstract":"This note is a companion paper to arXiv:1608.01630 [math.CA]. Here we generalize some of the geometric results of arXiv:1608.01630 [math.CA] to the case of a $3\\times 3$ matrix function $A(x)\\approx \\mathrm{diag}\\{1,f(x_1), g(x_1)\\}$. More precisely, we make explicit calculations of the geodesics in the Carnot-Carath\\'{e}odory space associated to $A$, and provide estimates on the Lebesgue measures of metric balls centered at the origin in that space.","source":"Semantic Scholar","year":2024,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/fe501114ac9885172a3ef5d18eb5ad73b537c09d","is_open_access":true,"published_at":"","score":68},{"id":"ss_4a948d41431b3d5e204f8573622a5bdb0a13f3c8","title":"Unique special solution for discrete Painlevé II","authors":[{"name":"W. Van Assche"}],"abstract":"We show that the discrete Painlevé II equation with starting value $ a_{-1}=-1 $ a−1=−1 has a unique solution for which $ -1 { \\lt } a_n { \\lt } 1 $ −1\u003can\u003c1 for every $ n \\geq ~0 $ n≥ 0. This solution corresponds to the Verblunsky coefficients of a family of orthogonal polynomials on the unit circle. This result was already proved for certain values of the parameter in the equation and recently a full proof was given by Duits and Holcomb [A double scaling limit for the d-PII equation with boundary conditions. arXiv:2304.02918 [math.CA]]. In the present paper we give a different proof that is based on an idea put forward by Tomas Lasic Latimer [Unique positive solutions to q-discrete equations associated with orthogonal polynomials, J. Difference Equ. Appl. 27 (2021), pp. 763–775.] which uses orthogonal polynomials. We also give an upper bound for this special solution.","source":"Semantic Scholar","year":2023,"language":"en","subjects":["Mathematics"],"doi":"10.1080/10236198.2023.2294919","url":"https://www.semanticscholar.org/paper/4a948d41431b3d5e204f8573622a5bdb0a13f3c8","pdf_url":"https://lirias.kuleuven.be/bitstream/20.500.12942/731339/2/dPII_unique.pdf","is_open_access":true,"citations":2,"published_at":"","score":67.06},{"id":"ss_0340946c67b0500fee4a876c34ecd12d93b9bdc3","title":"Further Double Sums of Dunkl and Gasper","authors":[{"name":"W. Chu"}],"abstract":"","source":"Semantic Scholar","year":2017,"language":"en","subjects":["Mathematics"],"doi":"10.1007/S00025-016-0594-Z","url":"https://www.semanticscholar.org/paper/0340946c67b0500fee4a876c34ecd12d93b9bdc3","is_open_access":true,"citations":2,"published_at":"","score":61.06},{"id":"ss_39dcfbb006688782248e17edca1da5e56fcacf34","title":"Mahler equations and rationality","authors":[{"name":"Reinhard Schafke"},{"name":"M. Singer"}],"abstract":"We give another proof of a result of Adamczewski and Bell concerning Mahler equations: A formal power series satisfying a $p-$ and a $q-$Mahler equation over ${\\mathbb C}(x)$ with multiplicatively independent positive integers $p$ and $q$ is a rational function. The proof presented here is self-contained and is essentially a compilation of proofs contained in the recent preprint \"Consistent systems of linear differential and difference equations\", arXiv:1605.02616 [math.CA], by the same authors.","source":"Semantic Scholar","year":2016,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/39dcfbb006688782248e17edca1da5e56fcacf34","is_open_access":true,"citations":4,"published_at":"","score":60.12},{"id":"ss_e0671cd0bd856b27f3258e5880dbb29fa2b8bd58","title":"On a Whitney extension problem for convex functions","authors":[{"name":"D. Azagra"},{"name":"Carlos Mudarra"}],"abstract":"","source":"Semantic Scholar","year":2015,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/e0671cd0bd856b27f3258e5880dbb29fa2b8bd58","is_open_access":true,"citations":2,"published_at":"","score":59.06},{"id":"ss_5f01c94e807e85e2a78dc8c28f7dd81cbddbf209","title":"Some inequalities related to two expansions of (1+1/x)x$(1+1/x)^{x}$","authors":[{"name":"Bijun Ren"},{"name":"X. Li"}],"abstract":"AbstractWe prove the following theorem: Let (1+1x)x=e(1−∑k=1∞bk(1+x)k)=e(1−∑k=1∞dk(1112+x)k),σm(x)=∑k=1mbk(1+x)kandSm(x)=∑k=1mdk(1112+x)k. $$\\begin{aligned}\u0026 \\biggl(1+\\frac{1}{x} \\biggr)^{x}=e \\Biggl(1- \\sum _{k=1}^{\\infty}\\frac{b_{k}}{ (1+x )^{k}} \\Biggr)=e \\Biggl(1-\\sum _{k=1}^{\\infty}\\frac{d_{k}}{ (\\frac{11}{12}+x )^{k}} \\Biggr), \\\\\u0026 \\sigma_{m}(x)=\\sum_{k=1}^{m} \\frac{b_{k}}{ (1+x )^{k}} \\quad\\mbox{and}\\quad S_{m}(x)=\\sum_{k=1}^{m} \\frac{d_{k}}{ (\\frac{11}{12}+x )^{k}}. \\end{aligned}$$ (1)If m≥6$m\\geq6$ is even, we have Sm(x)\u003eσm(x)$S_{m}(x)\u003e\\sigma_{m}(x)$ for all x\u003e0$x\u003e0$.(2)If m≥7$m\\geq7$ is odd, we have Sm(x)\u003eσm(x)$S_{m}(x)\u003e\\sigma_{m}(x)$ for all x\u003e1$x\u003e1$. This provides an intuitive explanation for the main result in Mortici and Hu (On an infinite series for (1+1/x)x$(1+ 1/x)^{x}$, 2014, arXiv:1406.7814 [math.CA]).","source":"Semantic Scholar","year":2015,"language":"en","subjects":["Mathematics"],"doi":"10.1186/S13660-015-0928-5","url":"https://www.semanticscholar.org/paper/5f01c94e807e85e2a78dc8c28f7dd81cbddbf209","pdf_url":"https://doi.org/10.1186/s13660-015-0928-5","is_open_access":true,"citations":1,"published_at":"","score":59.03},{"id":"crossref_10.1103/physrevc.85.044606","title":"Microscopic study of Ca\u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\u003cmml:mo\u003e+\u003c/mml:mo\u003e\u003c/mml:math\u003eCa fusion","authors":[{"name":"R. Keser"},{"name":"A. S. Umar"},{"name":"V. E. Oberacker"}],"abstract":"","source":"CrossRef","year":2012,"language":"en","subjects":null,"doi":"10.1103/physrevc.85.044606","url":"https://doi.org/10.1103/physrevc.85.044606","pdf_url":"http://link.aps.org/accepted/10.1103/PhysRevC.85.044606","is_open_access":true,"citations":74,"published_at":"","score":58.22},{"id":"crossref_10.1103/physrevc.87.024303","title":"Giant resonances in\u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\u003cmml:msup\u003e\u003cmml:mrow/\u003e\u003cmml:mn\u003e40\u003c/mml:mn\u003e\u003c/mml:msup\u003e\u003c/mml:math\u003eCa and\u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\u003cmml:msup\u003e\u003cmml:mrow/\u003e\u003cmml:mn\u003e48\u003c/mml:mn\u003e\u003c/mml:msup\u003e\u003c/mml:math\u003eCa","authors":[{"name":"M. R. Anders"},{"name":"S. Shlomo"},{"name":"Tapas Sil"},{"name":"D. H. Youngblood"},{"name":"Y.-W. Lui"},{"name":"Krishichayan"}],"abstract":"","source":"CrossRef","year":2013,"language":"en","subjects":null,"doi":"10.1103/physrevc.87.024303","url":"https://doi.org/10.1103/physrevc.87.024303","pdf_url":"http://link.aps.org/accepted/10.1103/PhysRevC.87.024303","is_open_access":true,"citations":16,"published_at":"","score":57.48},{"id":"ss_432c461e5701a2def561af61862fbe13da75d21b","title":"Recurrence relations of the multi-indexed orthogonal polynomials V: Racah and q-Racah types","authors":[{"name":"S. Odake"}],"abstract":"In Paper II, we presented conjectures of the recurrence relations with constant coefficients for the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types. In this paper we present a proof for the Laguerre and Jacobi cases. Their bispectral properties are also discussed, which gives a method to obtain the coefficients of the recurrence relations explicitly. This paper extends to the Laguerre and Jacobi cases the bispectral techniques recently introduced by Gomez-Ullate et al. [J. Approx. Theory 204, 1 (2016); e-print arXiv:1506.03651 [math.CA]] to derive explicit expressions for the coefficients of the recurrence relations satisfied by exceptional polynomials of Hermite type.","source":"Semantic Scholar","year":2013,"language":"en","subjects":["Physics","Mathematics"],"doi":"10.1063/1.4921230","url":"https://www.semanticscholar.org/paper/432c461e5701a2def561af61862fbe13da75d21b","pdf_url":"http://arxiv.org/pdf/1303.5820","is_open_access":true,"citations":10,"published_at":"","score":57.3},{"id":"ss_ee9128a6b87bc26f219d986909356fe922007b63","title":"Ap\\'ery's theorem and problems for the values of Riemann's zeta function and their $q$-analogues","authors":[{"name":"W. Zudilin"}],"abstract":"This monograph is intended to be considered as my habilitation (D.Sc.) thesis; because of that and as everything has already appeared in English, it is performed exclusively in Russian. The monograph comprises a detailed introduction and seven chapters that represent part of my work influenced by Ap\\'ery's proof from 1978 of the irrationality of $\\zeta(2)$ and $\\zeta(3)$, the values of Riemann's zeta function. Chapter 1 is about\"at least one of the four numbers $\\zeta(5)$, $\\zeta(7)$, $\\zeta(9)$ and $\\zeta(11)$ is irrational\"(based in part on arXiv:math.NT/0206176). Chapter 2 explains a connection between the generalized multiple integrals introduced by Beukers in his proof of Ap\\'ery's result and the very-well-poised hypergeometric series; it is based on arXiv:math.CA/0206177. Chapter 3 surveys some arithmetic and hypergeometric $q$-analogies and establishes the irrationality measure $\\mu(\\zeta_q(2))0.5803^k$ for the distance from $(3/2)^k$ to the nearest integer, with the English version published in J. Th\\'eor. Nombres Bordeaux 19 (2007), 313--325. Chapter 6 reproduces the solution (from arXiv:math.CA/0311195) to the problem of Asmus Schmidt about generalized Ap\\'ery's numbers. Finally, Chapter 7 is about expressing the special $L$-values as periods (in the sense of Kontsevich and Zagier), in particular, as values of hypergeometric functions; it is based on the publication in Springer Proc. Math. Stat. 43 (2013), 381--395.","source":"Semantic Scholar","year":2013,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/ee9128a6b87bc26f219d986909356fe922007b63","is_open_access":true,"citations":2,"published_at":"","score":57.06},{"id":"ss_f2a4c952e7d9869adf6eb930dbd03e288ceea6d4","title":"Two weight estimate for the Hilbert transform and corona decomposition for non-doubling measures","authors":[{"name":"F. Nazarov"},{"name":"S. Treil"},{"name":"A. Volberg"}],"abstract":"This article was written in 2005 and subsequently lost (at least by the third author). Recently it resurfaced due to one of the colleagues to whom a hard copy has been sent in 2005. We consider here a problem of finding necessary and sufficient conditions for the boundedness of two weight Calder\\'on-Zygmund operators. We give such necessary and sufficient conditions in very natural terms, if the operator is the Hilbert transform, and the weights satisfy some very natural condition. The condition on weights was lifted in a recent paper of Michael Lacey, Eric Sawyer and Ignacio Uriarte-Tuero: \"A characterization of the two weight norm inequality for the Hilbert transform\", arXiv:1001.4043 [math.CA] 31 January 2010. The paper of Lacey--Sawyer-Uriarte-Tuero alliviated the \"pivotal\" condition used in a present article and replaced it by the very interesting and correct energy condition, which, unlike the \"pivotal\" condition turned out to be also necessary. The paper of Lacey-Sawyer-Uriarte-Tuero used the present article in its main aspect. The thrust of the present article is to use the methods of nonhomogeneous Harmonoc Analysis together with a several paraproducts arising from a certain stopping time argument. In view of the importance of the present article for Lacey--Sawyer-Uriarte-Tuero's paper arXiv:1001.4043 [math.CA] 31 January 2010, we present it to the attention of the reader. Drawing no parallels, \"Darwin spent 1838-1859 getting ready to publish \"On the Origin of Species\" without actually publishing it, only brooding over beaks of finches\".","source":"Semantic Scholar","year":2010,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/f2a4c952e7d9869adf6eb930dbd03e288ceea6d4","is_open_access":true,"citations":85,"published_at":"","score":56.55},{"id":"doaj_10.2168/LMCS-8(4:16)2012","title":"The Structure of Differential Invariants and Differential Cut Elimination","authors":[{"name":"Andre Platzer"}],"abstract":"The biggest challenge in hybrid systems verification is the handling of\ndifferential equations. Because computable closed-form solutions only exist for\nvery simple differential equations, proof certificates have been proposed for\nmore scalable verification. Search procedures for these proof certificates are\nstill rather ad-hoc, though, because the problem structure is only understood\npoorly. We investigate differential invariants, which define an induction\nprinciple for differential equations and which can be checked for invariance\nalong a differential equation just by using their differential structure,\nwithout having to solve them. We study the structural properties of\ndifferential invariants. To analyze trade-offs for proof search complexity, we\nidentify more than a dozen relations between several classes of differential\ninvariants and compare their deductive power. As our main results, we analyze\nthe deductive power of differential cuts and the deductive power of\ndifferential invariants with auxiliary differential variables. We refute the\ndifferential cut elimination hypothesis and show that, unlike standard cuts,\ndifferential cuts are fundamental proof principles that strictly increase the\ndeductive power. We also prove that the deductive power increases further when\nadding auxiliary differential variables to the dynamics.","source":"DOAJ","year":2012,"language":"","subjects":["Logic","Electronic computers. Computer science"],"doi":"10.2168/LMCS-8(4:16)2012","url":"https://lmcs.episciences.org/809/pdf","pdf_url":"https://lmcs.episciences.org/809/pdf","is_open_access":true,"published_at":"","score":56},{"id":"ss_d949eab32406df8c19d562804ebb4b0df8d68b71","title":"Sharp $A_2$ estimates of Haar shifts via Bellman function","authors":[{"name":"S. Treil"}],"abstract":"We use the Bellman function method to give an elementary proof of a sharp weighted estimate for the Haar shifts, which is linear in the $A_2$ norm of the weight and in the complexity of the shift. Together with the representation of a general Calder\\'{o}n--Zygmund operator as a weighted average (over all dyadic lattices) of Haar shifts, (cf. arXiv:1010.0755v2[math.CA], arXiv:1007.4330v1[math.CA]) it gives a significantly simpler proof of the so-called the $A_2$ conjecture. The main estimate is a very general fact about concave functions, which can be very useful in other problems of martingale Harmonic Analysis. Concave functions of such type appear as the Bellman functions for bounds on the bilinear form of martingale multipliers, thus the main estimate allows for the transference of the results for simplest possible martingale multipliers to more general martingale transforms. Note that (although this is not important for the $A_2$ conjecture for general Calder\\'{o}n--Zygmund operators) this elementary proof gives the best known (linear) growth in the complexity of the shift.","source":"Semantic Scholar","year":2011,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/d949eab32406df8c19d562804ebb4b0df8d68b71","is_open_access":true,"citations":33,"published_at":"","score":55.99},{"id":"crossref_10.1103/physrevc.84.051601","title":"Absence of a maximum in the\u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\u003cmml:mi\u003eS\u003c/mml:mi\u003e\u003c/mml:math\u003efactor at deep sub-barrier energies in the fusion reaction\u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\u003cmml:msup\u003e\u003cmml:mrow/\u003e\u003cmml:mn\u003e40\u003c/mml:mn\u003e\u003c/mml:msup\u003e\u003c/mml:math\u003eCa + \u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"\u003e\u003cmml:msup\u003e\u003cmml:mrow/\u003e\u003cmml:mn\u003e40\u003c/mml:mn\u003e\u003c/mml:msup\u003e\u003c/mml:math\u003eCa","authors":[{"name":"Şerban Mişicu"},{"name":"Florin Carstoiu"}],"abstract":"","source":"CrossRef","year":2011,"language":"en","subjects":null,"doi":"10.1103/physrevc.84.051601","url":"https://doi.org/10.1103/physrevc.84.051601","is_open_access":true,"citations":10,"published_at":"","score":55.3},{"id":"ss_18152db3bd5cf93408f856d1bf962cfee3cf6b53","title":"The proof of Muqattash-Yahdi conjecture","authors":[{"name":"C. Mortici"}],"abstract":"","source":"Semantic Scholar","year":2010,"language":"en","subjects":["Computer Science","Mathematics"],"doi":"10.1016/j.mcm.2009.12.030","url":"https://www.semanticscholar.org/paper/18152db3bd5cf93408f856d1bf962cfee3cf6b53","pdf_url":"https://doi.org/10.1016/j.mcm.2009.12.030","is_open_access":true,"citations":38,"published_at":"","score":55.14},{"id":"arxiv_1107.2425","title":"On the orthogonality of q-classical polynomials of the Hahn class II","authors":[{"name":"R. Alvarez-Nodarse"},{"name":"R. Sevinik-Adiguzel"},{"name":"H. Taseli"}],"abstract":"In this article, the study of the orthogonality properties of $q$-polynomials of the Hahn class started in the initial article by R. Álvarez-Nodarse, R. Sevinik-Adıgüzel, and H. Taşeli, \\textit{On the orthogonality of $q$-classical polynomials of the Hahn class I} is proceeded. To be more specific, the orthogonality properties of the $q$-polynomials belonging to the $\\emptyset$-Hermite-Laguerre/Jacobi, $\\emptyset$-Jacobi/Hermite-Laguerre, 0-Laguerre/Jacobi-Bessel and 0-Jacobi/Laguerre-Bessel cases are studied by taking into account the idea considered in the initial paper. In particular, a new orthogonality relation for the $q$-Meixner polynomials is established.","source":"arXiv","year":2011,"language":"en","subjects":["math.CA"],"url":"https://arxiv.org/abs/1107.2425","pdf_url":"https://arxiv.org/pdf/1107.2425","is_open_access":true,"published_at":"2011-07-12T22:00:17Z","score":55}],"total":1262543,"page":1,"page_size":20,"sources":["arXiv","DOAJ","Semantic Scholar","CrossRef"],"query":"math.CA"}