[{"oa":1,"volume":11,"date_updated":"2021-01-12T06:55:26Z","quality_controlled":0,"main_file_link":[{"url":"http://repository.tudelft.nl/view/ir/uuid:c8eca915-d38b-4827-a4d9-e89baabb43a6/","open_access":"1"}],"title":"On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces","extern":1,"intvolume":"        11","publisher":"World Scientific Publishing","publication_status":"published","status":"public","year":"2008","date_created":"2018-12-11T11:55:50Z","month":"12","doi":"10.1142/S0219025708003245","citation":{"apa":"Maas, J., &#38; Van Neerven, J. (2008). On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces. <i>Infinite Dimensional Analysis, Quantum Probability and Related Topics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0219025708003245\">https://doi.org/10.1142/S0219025708003245</a>","ama":"Maas J, Van Neerven J. On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces. <i>Infinite Dimensional Analysis, Quantum Probability and Related Topics</i>. 2008;11(4):603-626. doi:<a href=\"https://doi.org/10.1142/S0219025708003245\">10.1142/S0219025708003245</a>","ista":"Maas J, Van Neerven J. 2008. On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 11(4), 603–626.","short":"J. Maas, J. Van Neerven, Infinite Dimensional Analysis, Quantum Probability and Related Topics 11 (2008) 603–626.","ieee":"J. Maas and J. Van Neerven, “On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces,” <i>Infinite Dimensional Analysis, Quantum Probability and Related Topics</i>, vol. 11, no. 4. World Scientific Publishing, pp. 603–626, 2008.","mla":"Maas, Jan, and Jan Van Neerven. “On the Domain of Non-Symmetric Ornstein-Uhlenbeck Operators in Banach Spaces.” <i>Infinite Dimensional Analysis, Quantum Probability and Related Topics</i>, vol. 11, no. 4, World Scientific Publishing, 2008, pp. 603–26, doi:<a href=\"https://doi.org/10.1142/S0219025708003245\">10.1142/S0219025708003245</a>.","chicago":"Maas, Jan, and Jan Van Neerven. “On the Domain of Non-Symmetric Ornstein-Uhlenbeck Operators in Banach Spaces.” <i>Infinite Dimensional Analysis, Quantum Probability and Related Topics</i>. World Scientific Publishing, 2008. <a href=\"https://doi.org/10.1142/S0219025708003245\">https://doi.org/10.1142/S0219025708003245</a>."},"_id":"2120","type":"journal_article","publist_id":"4914","day":"04","page":"603 - 626","date_published":"2008-12-04T00:00:00Z","issue":"4","author":[{"last_name":"Maas","orcid":"0000-0002-0845-1338","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Jan Maas"},{"full_name":"van Neerven, Jan M","first_name":"Jan","last_name":"Van Neerven"}],"publication":"Infinite Dimensional Analysis, Quantum Probability and Related Topics","acknowledgement":"The authors are supported by the ‘VIDI subsidie’ 639.032.201 of the Netherlands Organization for Scientific Research (NWO) and by the Research Training Network HPRN-CT-2002-00281.","abstract":[{"lang":"eng","text":"We consider the linear stochastic Cauchy problem dX (t) =AX (t) dt +B dWH (t), t≥ 0, where A generates a C0-semigroup on a Banach space E, WH is a cylindrical Brownian motion over a Hilbert space H, and B: H → E is a bounded operator. Assuming the existence of a unique minimal invariant measure μ∞, let Lp denote the realization of the Ornstein-Uhlenbeck operator associated with this problem in Lp (E, μ∞). Under suitable assumptions concerning the invariance of the range of B under the semigroup generated by A, we prove the following domain inclusions, valid for 1 &lt; p ≤ 2: Image omitted. Here WHk, p (E, μinfin; denotes the kth order Sobolev space of functions with Fréchet derivatives up to order k in the direction of H. No symmetry assumptions are made on L p."}]},{"date_published":"2008-04-07T00:00:00Z","author":[{"last_name":"Van Neerven","full_name":"van Neerven, Jan M","first_name":"Jan"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","full_name":"Jan Maas","last_name":"Maas","orcid":"0000-0002-0845-1338"}],"publication":"Electronic Communications in Probability","abstract":[{"lang":"eng","text":"Let H be a separable real Hubert space and let double struck F sign = (ℱt)t∈[0,T] be the augmented filtration generated by an H-cylindrical Brownian motion (WH(t))t∈[0,T] on a probability space (Ω, ℱ ℙ). We prove that if E is a UMD Banach space, 1 ≤ p &lt; ∞, and F ∈ double struck D sign1,p(Ω E) is ℱT-measurable, then F = double struck E sign(F) + ∫0T Pdouble struck F sign(DF) dW H, where D is the Malliavin derivative of F and P double struck F sign is the projection onto the F-adapted elements in a suitable Banach space of Lp-stochastically integrable ℒ(H, E)-valued processes."}],"acknowledgement":"Research supported by ARC Discovery Grant dp0558539. 2research supported by VIDI subsidy 639.032.201 and VICI subsidy 639.033.604 of the Netherlands organisation for scientific research (nwo). ","_id":"2121","publist_id":"4915","type":"journal_article","day":"07","page":"151 - 164","date_created":"2018-12-11T11:55:50Z","month":"04","citation":{"chicago":"Van Neerven, Jan, and Jan Maas. “A Clark-Ocone Formula in UMD Banach Spaces.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2008.","mla":"Van Neerven, Jan, and Jan Maas. “A Clark-Ocone Formula in UMD Banach Spaces.” <i>Electronic Communications in Probability</i>, vol. 13, Institute of Mathematical Statistics, 2008, pp. 151–64.","ieee":"J. Van Neerven and J. Maas, “A Clark-Ocone formula in UMD Banach spaces,” <i>Electronic Communications in Probability</i>, vol. 13. Institute of Mathematical Statistics, pp. 151–164, 2008.","short":"J. Van Neerven, J. Maas, Electronic Communications in Probability 13 (2008) 151–164.","ista":"Van Neerven J, Maas J. 2008. A Clark-Ocone formula in UMD Banach spaces. Electronic Communications in Probability. 13, 151–164.","ama":"Van Neerven J, Maas J. A Clark-Ocone formula in UMD Banach spaces. <i>Electronic Communications in Probability</i>. 2008;13:151-164.","apa":"Van Neerven, J., &#38; Maas, J. (2008). A Clark-Ocone formula in UMD Banach spaces. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics."},"status":"public","year":"2008","extern":1,"intvolume":"        13","publisher":"Institute of Mathematical Statistics","publication_status":"published","main_file_link":[{"url":"http://arxiv.org/abs/0709.2021","open_access":"1"}],"quality_controlled":0,"title":"A Clark-Ocone formula in UMD Banach spaces","volume":13,"date_updated":"2021-01-12T06:55:26Z","oa":1},{"status":"public","year":"2008","doi":"10.1063/1.2948392","citation":{"chicago":"Lemeshko, Mikhail, and Břetislav Friedrich. “An Analytic Model of Rotationally Inelastic Collisions of Polar Molecules in Electric Fields.” <i>Journal of Chemical Physics</i>. American Institute of Physics, 2008. <a href=\"https://doi.org/10.1063/1.2948392\">https://doi.org/10.1063/1.2948392</a>.","mla":"Lemeshko, Mikhail, and Břetislav Friedrich. “An Analytic Model of Rotationally Inelastic Collisions of Polar Molecules in Electric Fields.” <i>Journal of Chemical Physics</i>, vol. 129, no. 2, American Institute of Physics, 2008, doi:<a href=\"https://doi.org/10.1063/1.2948392\">10.1063/1.2948392</a>.","ieee":"M. Lemeshko and B. Friedrich, “An analytic model of rotationally inelastic collisions of polar molecules in electric fields,” <i>Journal of Chemical Physics</i>, vol. 129, no. 2. American Institute of Physics, 2008.","short":"M. Lemeshko, B. Friedrich, Journal of Chemical Physics 129 (2008).","ista":"Lemeshko M, Friedrich B. 2008. An analytic model of rotationally inelastic collisions of polar molecules in electric fields. Journal of Chemical Physics. 129(2).","ama":"Lemeshko M, Friedrich B. An analytic model of rotationally inelastic collisions of polar molecules in electric fields. <i>Journal of Chemical Physics</i>. 2008;129(2). doi:<a href=\"https://doi.org/10.1063/1.2948392\">10.1063/1.2948392</a>","apa":"Lemeshko, M., &#38; Friedrich, B. (2008). An analytic model of rotationally inelastic collisions of polar molecules in electric fields. <i>Journal of Chemical Physics</i>. American Institute of Physics. <a href=\"https://doi.org/10.1063/1.2948392\">https://doi.org/10.1063/1.2948392</a>"},"date_created":"2018-12-11T11:55:58Z","month":"07","type":"journal_article","_id":"2146","publist_id":"4878","day":"01","publication":"Journal of Chemical Physics","abstract":[{"lang":"eng","text":"We present an analytic model of thermal state-to-state rotationally inelastic collisions of polar molecules in electric fields. The model is based on the Fraunhofer scattering of matter waves and requires Legendre moments characterizing the “shape” of the target in the body-fixed frame as its input. The electric field orients the target in the space-fixed frame and thereby effects a striking alteration of the dynamical observables: both the phase and amplitude of the oscillations in the partial differential cross sections undergo characteristic field-dependent changes that transgress into the partial integral cross sections. As the cross sections can be evaluated for a field applied parallel or perpendicular to the relative velocity, the model also offers predictions about steric asymmetry. We exemplify the field-dependent quantum collision dynamics with the behavior of the Ne–OCS(Σ1) and Ar–NO(Π2) systems. A comparison with the close-coupling calculations available for the latter system [Chem. Phys. Lett.313, 491 (1999)] demonstrates the model’s ability to qualitatively explain the field dependence of all the scattering features observed."}],"issue":"2","date_published":"2008-07-01T00:00:00Z","author":[{"last_name":"Lemeshko","orcid":"0000-0002-6990-7802","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","first_name":"Mikhail","full_name":"Mikhail Lemeshko"},{"last_name":"Friedrich","first_name":"Břetislav","full_name":"Friedrich, Břetislav"}],"oa":1,"date_updated":"2021-01-12T06:55:35Z","volume":129,"main_file_link":[{"url":"http://arxiv.org/abs/0804.3318","open_access":"1"}],"quality_controlled":0,"title":"An analytic model of rotationally inelastic collisions of polar molecules in electric fields","publisher":"American Institute of Physics","publication_status":"published","extern":1,"intvolume":"       129"},{"citation":{"ama":"Lemeshko M, Friedrich B. Kvantový Zenonův jev aneb co nesejde z očí, nezestárne. <i>Chemicke Listy</i>. 2008;102(10):880-883.","apa":"Lemeshko, M., &#38; Friedrich, B. (2008). Kvantový Zenonův jev aneb co nesejde z očí, nezestárne. <i>Chemicke Listy</i>. Czech Society of Chemical Engineering.","ista":"Lemeshko M, Friedrich B. 2008. Kvantový Zenonův jev aneb co nesejde z očí, nezestárne. Chemicke Listy. 102(10), 880–883.","ieee":"M. Lemeshko and B. Friedrich, “Kvantový Zenonův jev aneb co nesejde z očí, nezestárne,” <i>Chemicke Listy</i>, vol. 102, no. 10. Czech Society of Chemical Engineering, pp. 880–883, 2008.","short":"M. Lemeshko, B. Friedrich, Chemicke Listy 102 (2008) 880–883.","mla":"Lemeshko, Mikhail, and Břetislav Friedrich. “Kvantový Zenonův Jev Aneb Co Nesejde z Očí, Nezestárne.” <i>Chemicke Listy</i>, vol. 102, no. 10, Czech Society of Chemical Engineering, 2008, pp. 880–83.","chicago":"Lemeshko, Mikhail, and Břetislav Friedrich. “Kvantový Zenonův Jev Aneb Co Nesejde z Očí, Nezestárne.” <i>Chemicke Listy</i>. Czech Society of Chemical Engineering, 2008."},"date_created":"2018-12-11T11:55:59Z","month":"10","status":"public","year":"2008","publication":"Chemicke Listy","abstract":[{"lang":"eng","text":"We present the physics of the quantum Zeno effect, whose gist is often expressed by invoking the adage &quot;a watched pot never boils&quot;. We review aspects of the theoretical and experimental work done on the effect since its inception in 1977, and mention some applications. We dedicate the article - with our very best wishes - to Rudolf Zahradnik at the occasion of his great jubilee. Perhaps Rudolf's lasting youthfulness and freshness are due to that he himself had been frequently observed throughout his life: until the political turn-around in 1989 by those who wished, by their surveillance, to prevent Rudolf from spoiling the youth by his personal culture and his passion for science and things beautiful and useful in general. This attempt had failed. Out of gratitude, the youth has infected Rudolf with its youthfulness. Chronically. Since 1989, Rudolf has been closely watched by the public at large. For the same traits of his as before, but with the opposite goal and for the benefit of all generations. We relish keeping him in sight..."}],"issue":"10","author":[{"last_name":"Lemeshko","orcid":"0000-0002-6990-7802","first_name":"Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","full_name":"Mikhail Lemeshko"},{"last_name":"Friedrich","full_name":"Friedrich, Břetislav","first_name":"Břetislav"}],"date_published":"2008-10-01T00:00:00Z","page":"880 - 883","_id":"2147","type":"review","publist_id":"4877","day":"01","date_updated":"2020-07-14T12:45:29Z","volume":102,"publication_status":"published","publisher":"Czech Society of Chemical Engineering","extern":1,"intvolume":"       102","quality_controlled":0,"title":"Kvantový Zenonův jev aneb co nesejde z očí, nezestárne"},{"day":"01","_id":"2148","publist_id":"4876","type":"journal_article","page":"667 - 681","author":[{"full_name":"Pokrovski, Gleb S","first_name":"Gleb","last_name":"Pokrovski"},{"first_name":"Jacques","full_name":"Roux, Jacques L","last_name":"Roux"},{"full_name":"Hazemann, Jean L","first_name":"Jean","last_name":"Hazemann"},{"full_name":"Borisova, Anastassia Y","first_name":"Anastassia","last_name":"Borisova"},{"full_name":"Gonchar, Anastasia A","first_name":"Anastasia","last_name":"Gonchar"},{"orcid":"0000-0002-6990-7802","last_name":"Lemeshko","full_name":"Mikhail Lemeshko","first_name":"Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87"}],"date_published":"2008-04-01T00:00:00Z","issue":"2","publication":"Mineralogical Magazine","abstract":[{"text":"Despite the growing geological evidence that fluid boiling and vapour-liquid separation affect the distribution of metals in magmatic-hydrothermal systems significantly, there are few experimental data on the chemical status and partitioning of metals in the vapour and liquid phases. Here we report on an in situ measurement, using X-ray absorption fine structure (XAFS) spectroscopy, of antimony speciation and partitioning in the system Sb2O3-H2O-NaCl-HCl at 400°C and pressures 270–300 bar corresponding to the vapour-liquid equilibrium. Experiments were performed using a spectroscopic cell which allows simultaneous determination of the total concentration and atomic environment of the absorbing element (Sb) in each phase. Results show that quantitative vapour-brine separation of a supercritical aqueous salt fluid can be achieved by a controlled decompression and monitoring the X-ray absorbance of the fluid phase. Antimony concentrations in equilibrium with Sb2O3 (cubic, senarmontite) in the coexisting vapour and liquid phases and corresponding SbIII vapour-liquid partitioning coefficients are in agreement with recent data obtained using batch-reactor solubility techniques. The XAFS spectra analysis shows that hydroxy-chloride complexes, probably Sb(OH)2Cl0, are dominant both in the vapour and liquid phase in a salt-water system at acidic conditions. This first in situ XAFS study of element fractionation between coexisting volatile and dense phases opens new possibilities for systematic investigations of vapour-brine and fluid-melt immiscibility phenomena, avoiding many experimental artifacts common in less direct techniques.","lang":"eng"}],"year":"2008","status":"public","month":"04","date_created":"2018-12-11T11:55:59Z","doi":"10.1180/minmag.2008.072.2.667 ","citation":{"ista":"Pokrovski G, Roux J, Hazemann J, Borisova A, Gonchar A, Lemeshko M. 2008. In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation of antimony at hydrothermal conditions. Mineralogical Magazine. 72(2), 667–681.","apa":"Pokrovski, G., Roux, J., Hazemann, J., Borisova, A., Gonchar, A., &#38; Lemeshko, M. (2008). In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation of antimony at hydrothermal conditions. <i>Mineralogical Magazine</i>. Mineralogical Society. <a href=\"https://doi.org/10.1180/minmag.2008.072.2.667 \">https://doi.org/10.1180/minmag.2008.072.2.667 </a>","ama":"Pokrovski G, Roux J, Hazemann J, Borisova A, Gonchar A, Lemeshko M. In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation of antimony at hydrothermal conditions. <i>Mineralogical Magazine</i>. 2008;72(2):667-681. doi:<a href=\"https://doi.org/10.1180/minmag.2008.072.2.667 \">10.1180/minmag.2008.072.2.667 </a>","chicago":"Pokrovski, Gleb, Jacques Roux, Jean Hazemann, Anastassia Borisova, Anastasia Gonchar, and Mikhail Lemeshko. “In Situ X-Ray Absorption Spectroscopy Measurement of Vapour-Brine Fractionation of Antimony at Hydrothermal Conditions.” <i>Mineralogical Magazine</i>. Mineralogical Society, 2008. <a href=\"https://doi.org/10.1180/minmag.2008.072.2.667 \">https://doi.org/10.1180/minmag.2008.072.2.667 </a>.","mla":"Pokrovski, Gleb, et al. “In Situ X-Ray Absorption Spectroscopy Measurement of Vapour-Brine Fractionation of Antimony at Hydrothermal Conditions.” <i>Mineralogical Magazine</i>, vol. 72, no. 2, Mineralogical Society, 2008, pp. 667–81, doi:<a href=\"https://doi.org/10.1180/minmag.2008.072.2.667 \">10.1180/minmag.2008.072.2.667 </a>.","ieee":"G. Pokrovski, J. Roux, J. Hazemann, A. Borisova, A. Gonchar, and M. Lemeshko, “In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation of antimony at hydrothermal conditions,” <i>Mineralogical Magazine</i>, vol. 72, no. 2. Mineralogical Society, pp. 667–681, 2008.","short":"G. Pokrovski, J. Roux, J. Hazemann, A. Borisova, A. Gonchar, M. Lemeshko, Mineralogical Magazine 72 (2008) 667–681."},"title":"In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation of antimony at hydrothermal conditions","quality_controlled":0,"intvolume":"        72","extern":1,"publisher":"Mineralogical Society","publication_status":"published","volume":72,"date_updated":"2021-01-12T06:55:36Z"},{"publication_status":"published","publisher":"John Wiley and Sons Ltd","extern":1,"intvolume":"        96","quality_controlled":0,"title":"On the representation of integers by quadratic forms","date_updated":"2021-01-12T06:56:13Z","volume":96,"abstract":[{"text":"Let n ≥ 4 and let Q ∈ [X1, ..., Xn] be a non-singular quadratic form. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q = 0, and when Q is positive definite we provide improved upper bounds for the greatest positive integer k for which the equation Q = k is insoluble in integers, despite being soluble modulo every prime power.","lang":"eng"}],"publication":"Proceedings of the London Mathematical Society","date_published":"2008-03-01T00:00:00Z","issue":"2","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","full_name":"Timothy Browning","last_name":"Browning","orcid":"0000-0002-8314-0177"},{"last_name":"Dietmann","full_name":"Dietmann, Rainer","first_name":"Rainer"}],"page":"389 - 416","_id":"224","publist_id":"7688","type":"journal_article","day":"01","citation":{"ista":"Browning TD, Dietmann R. 2008. On the representation of integers by quadratic forms. Proceedings of the London Mathematical Society. 96(2), 389–416.","ama":"Browning TD, Dietmann R. On the representation of integers by quadratic forms. <i>Proceedings of the London Mathematical Society</i>. 2008;96(2):389-416. doi:<a href=\"https://doi.org/10.1112/plms/pdm032\">10.1112/plms/pdm032</a>","apa":"Browning, T. D., &#38; Dietmann, R. (2008). On the representation of integers by quadratic forms. <i>Proceedings of the London Mathematical Society</i>. John Wiley and Sons Ltd. <a href=\"https://doi.org/10.1112/plms/pdm032\">https://doi.org/10.1112/plms/pdm032</a>","mla":"Browning, Timothy D., and Rainer Dietmann. “On the Representation of Integers by Quadratic Forms.” <i>Proceedings of the London Mathematical Society</i>, vol. 96, no. 2, John Wiley and Sons Ltd, 2008, pp. 389–416, doi:<a href=\"https://doi.org/10.1112/plms/pdm032\">10.1112/plms/pdm032</a>.","chicago":"Browning, Timothy D, and Rainer Dietmann. “On the Representation of Integers by Quadratic Forms.” <i>Proceedings of the London Mathematical Society</i>. John Wiley and Sons Ltd, 2008. <a href=\"https://doi.org/10.1112/plms/pdm032\">https://doi.org/10.1112/plms/pdm032</a>.","ieee":"T. D. Browning and R. Dietmann, “On the representation of integers by quadratic forms,” <i>Proceedings of the London Mathematical Society</i>, vol. 96, no. 2. John Wiley and Sons Ltd, pp. 389–416, 2008.","short":"T.D. Browning, R. Dietmann, Proceedings of the London Mathematical Society 96 (2008) 389–416."},"doi":"10.1112/plms/pdm032","date_created":"2018-12-11T11:45:18Z","month":"03","status":"public","year":"2008"},{"status":"public","year":"2008","month":"11","date_created":"2018-12-11T11:45:18Z","citation":{"ista":"De La Bretèche R, Browning TD. 2008. Binary linear forms as sums of two squares. Compositio Mathematica. 144(6), 1375–1402.","apa":"De La Bretèche, R., &#38; Browning, T. D. (2008). Binary linear forms as sums of two squares. <i>Compositio Mathematica</i>. Cambridge University Press. <a href=\"https://doi.org/10.1112/S0010437X08003692\">https://doi.org/10.1112/S0010437X08003692</a>","ama":"De La Bretèche R, Browning TD. Binary linear forms as sums of two squares. <i>Compositio Mathematica</i>. 2008;144(6):1375-1402. doi:<a href=\"https://doi.org/10.1112/S0010437X08003692\">10.1112/S0010437X08003692</a>","chicago":"De La Bretèche, Régis, and Timothy D Browning. “Binary Linear Forms as Sums of Two Squares.” <i>Compositio Mathematica</i>. Cambridge University Press, 2008. <a href=\"https://doi.org/10.1112/S0010437X08003692\">https://doi.org/10.1112/S0010437X08003692</a>.","mla":"De La Bretèche, Régis, and Timothy D. Browning. “Binary Linear Forms as Sums of Two Squares.” <i>Compositio Mathematica</i>, vol. 144, no. 6, Cambridge University Press, 2008, pp. 1375–402, doi:<a href=\"https://doi.org/10.1112/S0010437X08003692\">10.1112/S0010437X08003692</a>.","short":"R. De La Bretèche, T.D. Browning, Compositio Mathematica 144 (2008) 1375–1402.","ieee":"R. De La Bretèche and T. D. Browning, “Binary linear forms as sums of two squares,” <i>Compositio Mathematica</i>, vol. 144, no. 6. Cambridge University Press, pp. 1375–1402, 2008."},"doi":"10.1112/S0010437X08003692","_id":"225","type":"journal_article","publist_id":"7687","day":"01","page":"1375 - 1402","author":[{"last_name":"De La Bretèche","full_name":"de la Bretèche, Régis","first_name":"Régis"},{"first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Timothy Browning","last_name":"Browning","orcid":"0000-0002-8314-0177"}],"date_published":"2008-11-01T00:00:00Z","issue":"6","abstract":[{"text":"We revisit recent work of Heath-Brown on the average order of the quantity r(L1(x))⋯r(L4(x)), for suitable binary linear forms L1,...,L4, as x=(x1,x2) ranges over quite general regions in ℤ2. In addition to improving the error term in Heath-Browns estimate, we generalise his result to cover a wider class of linear forms.","lang":"eng"}],"acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council","publication":"Compositio Mathematica","volume":144,"date_updated":"2021-01-12T06:56:17Z","quality_controlled":0,"title":"Binary linear forms as sums of two squares","intvolume":"       144","extern":1,"publication_status":"published","publisher":"Cambridge University Press"},{"conference":{"name":"QMath: Mathematical Results in Quantum Physics"},"oa":1,"date_updated":"2021-01-12T06:56:50Z","quality_controlled":0,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0802.0446"}],"title":" Spectral properties of the BCS gap equation of superfluidity","publisher":"World Scientific Publishing","publication_status":"published","extern":1,"status":"public","year":"2008","doi":"10.1142/9789812832382_0009","citation":{"chicago":"Hainzl, Christian, and Robert Seiringer. “ Spectral Properties of the BCS Gap Equation of Superfluidity,” 117–36. World Scientific Publishing, 2008. <a href=\"https://doi.org/10.1142/9789812832382_0009\">https://doi.org/10.1142/9789812832382_0009</a>.","mla":"Hainzl, Christian, and Robert Seiringer. <i> Spectral Properties of the BCS Gap Equation of Superfluidity</i>. World Scientific Publishing, 2008, pp. 117–36, doi:<a href=\"https://doi.org/10.1142/9789812832382_0009\">10.1142/9789812832382_0009</a>.","short":"C. Hainzl, R. Seiringer, in:, World Scientific Publishing, 2008, pp. 117–136.","ieee":"C. Hainzl and R. Seiringer, “ Spectral properties of the BCS gap equation of superfluidity,” presented at the QMath: Mathematical Results in Quantum Physics, 2008, pp. 117–136.","ista":"Hainzl C, Seiringer R. 2008.  Spectral properties of the BCS gap equation of superfluidity. QMath: Mathematical Results in Quantum Physics, 117–136.","apa":"Hainzl, C., &#38; Seiringer, R. (2008).  Spectral properties of the BCS gap equation of superfluidity (pp. 117–136). Presented at the QMath: Mathematical Results in Quantum Physics, World Scientific Publishing. <a href=\"https://doi.org/10.1142/9789812832382_0009\">https://doi.org/10.1142/9789812832382_0009</a>","ama":"Hainzl C, Seiringer R.  Spectral properties of the BCS gap equation of superfluidity. In: World Scientific Publishing; 2008:117-136. doi:<a href=\"https://doi.org/10.1142/9789812832382_0009\">10.1142/9789812832382_0009</a>"},"month":"08","date_created":"2018-12-11T11:57:02Z","page":"117 - 136","publist_id":"4595","_id":"2331","type":"conference","day":"01","abstract":[{"text":"We present a review of recent work on the mathematical aspects of the BCS gap equation, covering our results of Ref. 9 as well our recent joint work with Hamza and Solovej and with Frank and Naboko, respectively. In addition, we mention some related new results.","lang":"eng"}],"date_published":"2008-08-01T00:00:00Z","author":[{"last_name":"Hainzl","full_name":"Hainzl, Christian","first_name":"Christian"},{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Robert Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}]},{"day":"30","type":"conference","_id":"2332","publist_id":"4594","page":"241 - 254","author":[{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"date_published":"2008-12-30T00:00:00Z","abstract":[{"text":"We present a rigorous proof of the appearance of quantized vortices in dilute trapped Bose gases with repulsive two-body interactions subject to rotation, which was obtained recently in joint work with Elliott Lieb.14 Starting from the many-body Schrödinger equation, we show that the ground state of such gases is, in a suitable limit, well described by the nonlinear Gross-Pitaevskii equation. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.","lang":"eng"}],"year":"2008","status":"public","month":"12","date_created":"2018-12-11T11:57:02Z","doi":"10.1142/9789812832382_0017","citation":{"mla":"Seiringer, Robert. <i>Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases</i>. World Scientific Publishing, 2008, pp. 241–54, doi:<a href=\"https://doi.org/10.1142/9789812832382_0017\">10.1142/9789812832382_0017</a>.","chicago":"Seiringer, Robert. “Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases,” 241–54. World Scientific Publishing, 2008. <a href=\"https://doi.org/10.1142/9789812832382_0017\">https://doi.org/10.1142/9789812832382_0017</a>.","ieee":"R. Seiringer, “Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases,” presented at the QMath: Mathematical Results in Quantum Physics, 2008, pp. 241–254.","short":"R. Seiringer, in:, World Scientific Publishing, 2008, pp. 241–254.","ista":"Seiringer R. 2008. Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases. QMath: Mathematical Results in Quantum Physics, 241–254.","ama":"Seiringer R. Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases. In: World Scientific Publishing; 2008:241-254. doi:<a href=\"https://doi.org/10.1142/9789812832382_0017\">10.1142/9789812832382_0017</a>","apa":"Seiringer, R. (2008). Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases (pp. 241–254). Presented at the QMath: Mathematical Results in Quantum Physics, World Scientific Publishing. <a href=\"https://doi.org/10.1142/9789812832382_0017\">https://doi.org/10.1142/9789812832382_0017</a>"},"title":"Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases","quality_controlled":0,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0801.0427"}],"extern":1,"publisher":"World Scientific Publishing","publication_status":"published","oa":1,"conference":{"name":"QMath: Mathematical Results in Quantum Physics"},"date_updated":"2021-01-12T06:56:50Z"},{"publisher":"Springer","publication_status":"published","extern":1,"intvolume":"       279","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0608069"}],"quality_controlled":0,"title":"Free energy of a dilute Bose gas: Lower bound","date_updated":"2021-01-12T06:57:06Z","volume":279,"oa":1,"publication":"Communications in Mathematical Physics","abstract":[{"lang":"eng","text":"A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density Q and temperature T. In the dilute regime, i.e., when a3 1, where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2 2}-[ - c]2+). Here, c(T) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and [ · ]+ = max{ ·, 0} denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., T ~ 2/3 or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [17] for estimating correlations to temperatures below the critical one."}],"issue":"3","date_published":"2008-05-01T00:00:00Z","author":[{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Robert Seiringer"}],"page":"595 - 636","type":"journal_article","_id":"2374","publist_id":"4551","day":"01","citation":{"mla":"Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.” <i>Communications in Mathematical Physics</i>, vol. 279, no. 3, Springer, 2008, pp. 595–636, doi:<a href=\"https://doi.org/10.1007/s00220-008-0428-2\">10.1007/s00220-008-0428-2</a>.","chicago":"Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.” <i>Communications in Mathematical Physics</i>. Springer, 2008. <a href=\"https://doi.org/10.1007/s00220-008-0428-2\">https://doi.org/10.1007/s00220-008-0428-2</a>.","ieee":"R. Seiringer, “Free energy of a dilute Bose gas: Lower bound,” <i>Communications in Mathematical Physics</i>, vol. 279, no. 3. Springer, pp. 595–636, 2008.","short":"R. Seiringer, Communications in Mathematical Physics 279 (2008) 595–636.","ista":"Seiringer R. 2008. Free energy of a dilute Bose gas: Lower bound. Communications in Mathematical Physics. 279(3), 595–636.","ama":"Seiringer R. Free energy of a dilute Bose gas: Lower bound. <i>Communications in Mathematical Physics</i>. 2008;279(3):595-636. doi:<a href=\"https://doi.org/10.1007/s00220-008-0428-2\">10.1007/s00220-008-0428-2</a>","apa":"Seiringer, R. (2008). Free energy of a dilute Bose gas: Lower bound. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-008-0428-2\">https://doi.org/10.1007/s00220-008-0428-2</a>"},"doi":"10.1007/s00220-008-0428-2","date_created":"2018-12-11T11:57:17Z","month":"05","status":"public","year":"2008"},{"year":"2008","status":"public","date_created":"2018-12-11T11:57:18Z","month":"05","citation":{"chicago":"Hainzl, Christian, and Robert Seiringer. “Critical Temperature and Energy Gap for the BCS Equation.” <i>Physical Review B - Condensed Matter and Materials Physics</i>. American Physical Society, 2008. <a href=\"https://doi.org/10.1103/PhysRevB.77.184517\">https://doi.org/10.1103/PhysRevB.77.184517</a>.","mla":"Hainzl, Christian, and Robert Seiringer. “Critical Temperature and Energy Gap for the BCS Equation.” <i>Physical Review B - Condensed Matter and Materials Physics</i>, vol. 77, no. 18, American Physical Society, 2008, doi:<a href=\"https://doi.org/10.1103/PhysRevB.77.184517\">10.1103/PhysRevB.77.184517</a>.","ieee":"C. Hainzl and R. Seiringer, “Critical temperature and energy gap for the BCS equation,” <i>Physical Review B - Condensed Matter and Materials Physics</i>, vol. 77, no. 18. American Physical Society, 2008.","short":"C. Hainzl, R. Seiringer, Physical Review B - Condensed Matter and Materials Physics 77 (2008).","ista":"Hainzl C, Seiringer R. 2008. Critical temperature and energy gap for the BCS equation. Physical Review B - Condensed Matter and Materials Physics. 77(18).","ama":"Hainzl C, Seiringer R. Critical temperature and energy gap for the BCS equation. <i>Physical Review B - Condensed Matter and Materials Physics</i>. 2008;77(18). doi:<a href=\"https://doi.org/10.1103/PhysRevB.77.184517\">10.1103/PhysRevB.77.184517</a>","apa":"Hainzl, C., &#38; Seiringer, R. (2008). Critical temperature and energy gap for the BCS equation. <i>Physical Review B - Condensed Matter and Materials Physics</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevB.77.184517\">https://doi.org/10.1103/PhysRevB.77.184517</a>"},"doi":"10.1103/PhysRevB.77.184517","day":"28","type":"journal_article","_id":"2376","publist_id":"4550","issue":"18","date_published":"2008-05-28T00:00:00Z","author":[{"full_name":"Hainzl, Christian","first_name":"Christian","last_name":"Hainzl"},{"full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"abstract":[{"text":"We derive upper and lower bounds on the critical temperature Tc and the energy gap Ξ (at zero temperature) for the BCS gap equation, describing spin- 1 2 fermions interacting via a local two-body interaction potential λV(x). At weak coupling λ 1 and under appropriate assumptions on V(x), our bounds show that Tc ∼A exp(-B/λ) and Ξ∼C exp(-B/λ) for some explicit coefficients A, B, and C depending on the interaction V(x) and the chemical potential μ. The ratio A/C turns out to be a universal constant, independent of both V(x) and μ. Our analysis is valid for any μ; for small μ, or low density, our formulas reduce to well-known expressions involving the scattering length of V(x).","lang":"eng"}],"publication":"Physical Review B - Condensed Matter and Materials Physics","oa":1,"volume":77,"date_updated":"2021-01-12T06:57:06Z","title":"Critical temperature and energy gap for the BCS equation","quality_controlled":0,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0801.4159"}],"intvolume":"        77","extern":1,"publisher":"American Physical Society","publication_status":"published"},{"day":"01","publist_id":"4548","_id":"2377","type":"journal_article","page":"99 - 107","author":[{"first_name":"Christian","full_name":"Hainzl, Christian","last_name":"Hainzl"},{"full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"date_published":"2008-06-01T00:00:00Z","issue":"2-3","abstract":[{"text":"We prove that the critical temperature for the BCS gap equation is given by T c = μ ( 8\\π e γ-2+ o(1)) e π/(2μa) in the low density limit μ→ 0, with γ denoting Euler's constant. The formula holds for a suitable class of interaction potentials with negative scattering length a in the absence of bound states.","lang":"eng"}],"publication":"Letters in Mathematical Physics","year":"2008","status":"public","date_created":"2018-12-11T11:57:19Z","month":"06","doi":"10.1007/s11005-008-0242-y","citation":{"ieee":"C. Hainzl and R. Seiringer, “The BCS critical temperature for potentials with negative scattering length,” <i>Letters in Mathematical Physics</i>, vol. 84, no. 2–3. Springer, pp. 99–107, 2008.","short":"C. Hainzl, R. Seiringer, Letters in Mathematical Physics 84 (2008) 99–107.","mla":"Hainzl, Christian, and Robert Seiringer. “The BCS Critical Temperature for Potentials with Negative Scattering Length.” <i>Letters in Mathematical Physics</i>, vol. 84, no. 2–3, Springer, 2008, pp. 99–107, doi:<a href=\"https://doi.org/10.1007/s11005-008-0242-y\">10.1007/s11005-008-0242-y</a>.","chicago":"Hainzl, Christian, and Robert Seiringer. “The BCS Critical Temperature for Potentials with Negative Scattering Length.” <i>Letters in Mathematical Physics</i>. Springer, 2008. <a href=\"https://doi.org/10.1007/s11005-008-0242-y\">https://doi.org/10.1007/s11005-008-0242-y</a>.","ama":"Hainzl C, Seiringer R. The BCS critical temperature for potentials with negative scattering length. <i>Letters in Mathematical Physics</i>. 2008;84(2-3):99-107. doi:<a href=\"https://doi.org/10.1007/s11005-008-0242-y\">10.1007/s11005-008-0242-y</a>","apa":"Hainzl, C., &#38; Seiringer, R. (2008). The BCS critical temperature for potentials with negative scattering length. <i>Letters in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s11005-008-0242-y\">https://doi.org/10.1007/s11005-008-0242-y</a>","ista":"Hainzl C, Seiringer R. 2008. The BCS critical temperature for potentials with negative scattering length. Letters in Mathematical Physics. 84(2–3), 99–107."},"title":"The BCS critical temperature for potentials with negative scattering length","main_file_link":[{"url":"http://arxiv.org/abs/0803.3324","open_access":"1"}],"quality_controlled":0,"extern":1,"intvolume":"        84","publisher":"Springer","publication_status":"published","oa":1,"volume":84,"date_updated":"2021-01-12T06:57:07Z"},{"publication_status":"published","publisher":"Springer","extern":1,"intvolume":"       131","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0712.2810"}],"quality_controlled":0,"title":"Ground state energy of the low density hubbard model","date_updated":"2021-01-12T06:57:07Z","volume":131,"oa":1,"publication":"Journal of Statistical Physics","abstract":[{"lang":"eng","text":"We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8πaσ uσ d , where σ u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case."}],"issue":"6","date_published":"2008-06-01T00:00:00Z","author":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Robert Seiringer","last_name":"Seiringer","orcid":"0000-0002-6781-0521"},{"last_name":"Yin","first_name":"Jun","full_name":"Yin, Jun"}],"page":"1139 - 1154","_id":"2378","type":"journal_article","publist_id":"4549","day":"01","citation":{"mla":"Seiringer, Robert, and Jun Yin. “Ground State Energy of the Low Density Hubbard Model.” <i>Journal of Statistical Physics</i>, vol. 131, no. 6, Springer, 2008, pp. 1139–54, doi:<a href=\"https://doi.org/10.1007/s10955-008-9527-x\">10.1007/s10955-008-9527-x</a>.","chicago":"Seiringer, Robert, and Jun Yin. “Ground State Energy of the Low Density Hubbard Model.” <i>Journal of Statistical Physics</i>. Springer, 2008. <a href=\"https://doi.org/10.1007/s10955-008-9527-x\">https://doi.org/10.1007/s10955-008-9527-x</a>.","short":"R. Seiringer, J. Yin, Journal of Statistical Physics 131 (2008) 1139–1154.","ieee":"R. Seiringer and J. Yin, “Ground state energy of the low density hubbard model,” <i>Journal of Statistical Physics</i>, vol. 131, no. 6. Springer, pp. 1139–1154, 2008.","ista":"Seiringer R, Yin J. 2008. Ground state energy of the low density hubbard model. Journal of Statistical Physics. 131(6), 1139–1154.","ama":"Seiringer R, Yin J. Ground state energy of the low density hubbard model. <i>Journal of Statistical Physics</i>. 2008;131(6):1139-1154. doi:<a href=\"https://doi.org/10.1007/s10955-008-9527-x\">10.1007/s10955-008-9527-x</a>","apa":"Seiringer, R., &#38; Yin, J. (2008). Ground state energy of the low density hubbard model. <i>Journal of Statistical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s10955-008-9527-x\">https://doi.org/10.1007/s10955-008-9527-x</a>"},"doi":"10.1007/s10955-008-9527-x","month":"06","date_created":"2018-12-11T11:57:19Z","status":"public","year":"2008"},{"type":"journal_article","_id":"2379","publist_id":"4546","day":"01","page":"925 - 950","date_published":"2008-01-01T00:00:00Z","author":[{"last_name":"Frank","full_name":"Frank, Rupert L","first_name":"Rupert"},{"last_name":"Lieb","first_name":"Élliott","full_name":"Lieb, Élliott H"},{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"issue":"4","publication":"Journal of the American Mathematical Society","status":"public","year":"2008","date_created":"2018-12-11T11:57:19Z","month":"01","citation":{"apa":"Frank, R., Lieb, É., &#38; Seiringer, R. (2008). Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. <i>Journal of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/S0894-0347-07-00582-6\">https://doi.org/10.1090/S0894-0347-07-00582-6</a>","ama":"Frank R, Lieb É, Seiringer R. Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. <i>Journal of the American Mathematical Society</i>. 2008;21(4):925-950. doi:<a href=\"https://doi.org/10.1090/S0894-0347-07-00582-6\">10.1090/S0894-0347-07-00582-6</a>","ista":"Frank R, Lieb É, Seiringer R. 2008. Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Journal of the American Mathematical Society. 21(4), 925–950.","short":"R. Frank, É. Lieb, R. Seiringer, Journal of the American Mathematical Society 21 (2008) 925–950.","ieee":"R. Frank, É. Lieb, and R. Seiringer, “Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators,” <i>Journal of the American Mathematical Society</i>, vol. 21, no. 4. American Mathematical Society, pp. 925–950, 2008.","mla":"Frank, Rupert, et al. “Hardy-Lieb-Thirring Inequalities for Fractional Schrödinger Operators.” <i>Journal of the American Mathematical Society</i>, vol. 21, no. 4, American Mathematical Society, 2008, pp. 925–50, doi:<a href=\"https://doi.org/10.1090/S0894-0347-07-00582-6\">10.1090/S0894-0347-07-00582-6</a>.","chicago":"Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Hardy-Lieb-Thirring Inequalities for Fractional Schrödinger Operators.” <i>Journal of the American Mathematical Society</i>. American Mathematical Society, 2008. <a href=\"https://doi.org/10.1090/S0894-0347-07-00582-6\">https://doi.org/10.1090/S0894-0347-07-00582-6</a>."},"doi":"10.1090/S0894-0347-07-00582-6","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math/0610593"}],"quality_controlled":0,"title":"Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators","extern":1,"intvolume":"        21","publication_status":"published","publisher":"American Mathematical Society","oa":1,"volume":21,"date_updated":"2021-01-12T06:57:07Z"},{"day":"01","publist_id":"4547","_id":"2380","type":"journal_article","page":"349 - 367","date_published":"2008-07-01T00:00:00Z","author":[{"full_name":"Hainzl, Christian","first_name":"Christian","last_name":"Hainzl"},{"last_name":"Hamza","first_name":"Eman","full_name":"Hamza, Eman"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Robert Seiringer","last_name":"Seiringer","orcid":"0000-0002-6781-0521"},{"full_name":"Solovej, Jan P","first_name":"Jan","last_name":"Solovej"}],"issue":"2","abstract":[{"text":"The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.","lang":"eng"}],"publication":"Communications in Mathematical Physics","year":"2008","status":"public","month":"07","date_created":"2018-12-11T11:57:20Z","citation":{"ista":"Hainzl C, Hamza E, Seiringer R, Solovej J. 2008. The BCS functional for general pair interactions. Communications in Mathematical Physics. 281(2), 349–367.","ama":"Hainzl C, Hamza E, Seiringer R, Solovej J. The BCS functional for general pair interactions. <i>Communications in Mathematical Physics</i>. 2008;281(2):349-367. doi:<a href=\"https://doi.org/10.1007/s00220-008-0489-2\">10.1007/s00220-008-0489-2</a>","apa":"Hainzl, C., Hamza, E., Seiringer, R., &#38; Solovej, J. (2008). The BCS functional for general pair interactions. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-008-0489-2\">https://doi.org/10.1007/s00220-008-0489-2</a>","chicago":"Hainzl, Christian, Eman Hamza, Robert Seiringer, and Jan Solovej. “The BCS Functional for General Pair Interactions.” <i>Communications in Mathematical Physics</i>. Springer, 2008. <a href=\"https://doi.org/10.1007/s00220-008-0489-2\">https://doi.org/10.1007/s00220-008-0489-2</a>.","mla":"Hainzl, Christian, et al. “The BCS Functional for General Pair Interactions.” <i>Communications in Mathematical Physics</i>, vol. 281, no. 2, Springer, 2008, pp. 349–67, doi:<a href=\"https://doi.org/10.1007/s00220-008-0489-2\">10.1007/s00220-008-0489-2</a>.","ieee":"C. Hainzl, E. Hamza, R. Seiringer, and J. Solovej, “The BCS functional for general pair interactions,” <i>Communications in Mathematical Physics</i>, vol. 281, no. 2. Springer, pp. 349–367, 2008.","short":"C. Hainzl, E. Hamza, R. Seiringer, J. Solovej, Communications in Mathematical Physics 281 (2008) 349–367."},"doi":"10.1007/s00220-008-0489-2","title":"The BCS functional for general pair interactions","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0703086"}],"quality_controlled":0,"intvolume":"       281","extern":1,"publisher":"Springer","publication_status":"published","oa":1,"volume":281,"date_updated":"2021-01-12T06:57:08Z"},{"month":"12","date_created":"2018-12-11T11:57:20Z","citation":{"mla":"Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations and Sharp Hardy Inequalities.” <i>Journal of Functional Analysis</i>, vol. 255, no. 12, Academic Press, 2008, pp. 3407–30, doi:<a href=\"https://doi.org/10.1016/j.jfa.2008.05.015\">10.1016/j.jfa.2008.05.015</a>.","chicago":"Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations and Sharp Hardy Inequalities.” <i>Journal of Functional Analysis</i>. Academic Press, 2008. <a href=\"https://doi.org/10.1016/j.jfa.2008.05.015\">https://doi.org/10.1016/j.jfa.2008.05.015</a>.","ieee":"R. Frank and R. Seiringer, “Non-linear ground state representations and sharp Hardy inequalities,” <i>Journal of Functional Analysis</i>, vol. 255, no. 12. Academic Press, pp. 3407–3430, 2008.","short":"R. Frank, R. Seiringer, Journal of Functional Analysis 255 (2008) 3407–3430.","ista":"Frank R, Seiringer R. 2008. Non-linear ground state representations and sharp Hardy inequalities. Journal of Functional Analysis. 255(12), 3407–3430.","apa":"Frank, R., &#38; Seiringer, R. (2008). Non-linear ground state representations and sharp Hardy inequalities. <i>Journal of Functional Analysis</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jfa.2008.05.015\">https://doi.org/10.1016/j.jfa.2008.05.015</a>","ama":"Frank R, Seiringer R. Non-linear ground state representations and sharp Hardy inequalities. <i>Journal of Functional Analysis</i>. 2008;255(12):3407-3430. doi:<a href=\"https://doi.org/10.1016/j.jfa.2008.05.015\">10.1016/j.jfa.2008.05.015</a>"},"doi":"10.1016/j.jfa.2008.05.015","status":"public","year":"2008","date_published":"2008-12-15T00:00:00Z","author":[{"full_name":"Frank, Rupert L","first_name":"Rupert","last_name":"Frank"},{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"issue":"12","publication":"Journal of Functional Analysis","abstract":[{"text":"We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.","lang":"eng"}],"publist_id":"4543","_id":"2381","type":"journal_article","day":"15","page":"3407 - 3430","volume":255,"date_updated":"2021-01-12T06:57:08Z","oa":1,"intvolume":"       255","extern":1,"publication_status":"published","publisher":"Academic Press","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0803.0503"}],"quality_controlled":0,"title":"Non-linear ground state representations and sharp Hardy inequalities"},{"volume":284,"date_updated":"2021-01-12T06:57:08Z","oa":1,"extern":1,"intvolume":"       284","publisher":"Springer","publication_status":"published","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0709.4022"}],"quality_controlled":0,"title":"The Lieb-Liniger model as a limit of dilute bosons in three dimensions","month":"12","date_created":"2018-12-11T11:57:21Z","doi":"10.1007/s00220-008-0521-6","citation":{"ieee":"R. Seiringer and J. Yin, “The Lieb-Liniger model as a limit of dilute bosons in three dimensions,” <i>Communications in Mathematical Physics</i>, vol. 284, no. 2. Springer, pp. 459–479, 2008.","short":"R. Seiringer, J. Yin, Communications in Mathematical Physics 284 (2008) 459–479.","chicago":"Seiringer, Robert, and Jun Yin. “The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions.” <i>Communications in Mathematical Physics</i>. Springer, 2008. <a href=\"https://doi.org/10.1007/s00220-008-0521-6\">https://doi.org/10.1007/s00220-008-0521-6</a>.","mla":"Seiringer, Robert, and Jun Yin. “The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions.” <i>Communications in Mathematical Physics</i>, vol. 284, no. 2, Springer, 2008, pp. 459–79, doi:<a href=\"https://doi.org/10.1007/s00220-008-0521-6\">10.1007/s00220-008-0521-6</a>.","apa":"Seiringer, R., &#38; Yin, J. (2008). The Lieb-Liniger model as a limit of dilute bosons in three dimensions. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-008-0521-6\">https://doi.org/10.1007/s00220-008-0521-6</a>","ama":"Seiringer R, Yin J. The Lieb-Liniger model as a limit of dilute bosons in three dimensions. <i>Communications in Mathematical Physics</i>. 2008;284(2):459-479. doi:<a href=\"https://doi.org/10.1007/s00220-008-0521-6\">10.1007/s00220-008-0521-6</a>","ista":"Seiringer R, Yin J. 2008. The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in Mathematical Physics. 284(2), 459–479."},"status":"public","year":"2008","date_published":"2008-12-01T00:00:00Z","issue":"2","author":[{"full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"},{"last_name":"Yin","first_name":"Jun","full_name":"Yin, Jun"}],"publication":"Communications in Mathematical Physics","abstract":[{"lang":"eng","text":"We show that the Lieb-Liniger model for one-dimensional bosons with repulsive δ-function interaction can be rigorously derived via a scaling limit from a dilute three-dimensional Bose gas with arbitrary repulsive interaction potential of finite scattering length. For this purpose, we prove bounds on both the eigenvalues and corresponding eigenfunctions of three-dimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the Lieb-Liniger model. In particular, if both the scattering length a and the radius r of the cylindrical trap go to zero, the Lieb-Liniger model with coupling constant g ∼ a/r 2 is derived. Our bounds are uniform in g in the whole parameter range 0 ≤ g ≤ ∞, and apply to the Hamiltonian for three-dimensional bosons in a spectral window of size ∼ r -2 above the ground state energy."}],"_id":"2382","publist_id":"4544","type":"journal_article","day":"01","page":"459 - 479"},{"page":"1283 - 1307","day":"01","type":"journal_article","_id":"2383","publist_id":"4545","publication":"Reviews in Mathematical Physics","abstract":[{"text":"We study the relativistic electron-positron field at positive temperature in the Hartree-Fock approximation. We consider both the case with and without exchange terms, and investigate the existence and properties of minimizers. Our approach is non-perturbative in the sense that the relevant electron subspace is determined in a self-consistent way. The present work is an extension of previous work by Hainzl, Lewin, Séré and Solovej where the case of zero temperature was considered.","lang":"eng"}],"author":[{"first_name":"Christian","full_name":"Hainzl, Christian","last_name":"Hainzl"},{"last_name":"Lewin","first_name":"Mathieu","full_name":"Lewin, Mathieu"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"date_published":"2008-11-01T00:00:00Z","issue":"10","year":"2008","status":"public","doi":"10.1142/S0129055X08003547","citation":{"ama":"Hainzl C, Lewin M, Seiringer R. A nonlinear model for relativistic electrons at positive temperature. <i>Reviews in Mathematical Physics</i>. 2008;20(10):1283-1307. doi:<a href=\"https://doi.org/10.1142/S0129055X08003547\">10.1142/S0129055X08003547</a>","apa":"Hainzl, C., Lewin, M., &#38; Seiringer, R. (2008). A nonlinear model for relativistic electrons at positive temperature. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129055X08003547\">https://doi.org/10.1142/S0129055X08003547</a>","ista":"Hainzl C, Lewin M, Seiringer R. 2008. A nonlinear model for relativistic electrons at positive temperature. Reviews in Mathematical Physics. 20(10), 1283–1307.","ieee":"C. Hainzl, M. Lewin, and R. Seiringer, “A nonlinear model for relativistic electrons at positive temperature,” <i>Reviews in Mathematical Physics</i>, vol. 20, no. 10. World Scientific Publishing, pp. 1283–1307, 2008.","short":"C. Hainzl, M. Lewin, R. Seiringer, Reviews in Mathematical Physics 20 (2008) 1283–1307.","mla":"Hainzl, Christian, et al. “A Nonlinear Model for Relativistic Electrons at Positive Temperature.” <i>Reviews in Mathematical Physics</i>, vol. 20, no. 10, World Scientific Publishing, 2008, pp. 1283–307, doi:<a href=\"https://doi.org/10.1142/S0129055X08003547\">10.1142/S0129055X08003547</a>.","chicago":"Hainzl, Christian, Mathieu Lewin, and Robert Seiringer. “A Nonlinear Model for Relativistic Electrons at Positive Temperature.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2008. <a href=\"https://doi.org/10.1142/S0129055X08003547\">https://doi.org/10.1142/S0129055X08003547</a>."},"date_created":"2018-12-11T11:57:21Z","month":"11","title":"A nonlinear model for relativistic electrons at positive temperature","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0802.4054"}],"quality_controlled":0,"publisher":"World Scientific Publishing","publication_status":"published","intvolume":"        20","extern":1,"oa":1,"date_updated":"2021-01-12T06:57:09Z","volume":20},{"publisher":"American Mathematical Society","publication_status":"published","extern":1,"intvolume":"       453","quality_controlled":0,"title":"k-Sets and k-facets","date_updated":"2021-01-12T06:57:21Z","volume":453,"publication":"Surveys on Discrete and Computational Geometry: Twenty Years Later","author":[{"full_name":"Uli Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","orcid":"0000-0002-1494-0568","last_name":"Wagner"}],"date_published":"2008-01-01T00:00:00Z","page":"443 - 514","type":"book_chapter","_id":"2415","publist_id":"4510","day":"01","citation":{"ama":"Wagner U. k-Sets and k-facets. In: Goodman J, Pach J, Pollack R, eds. <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i>. Vol 453. American Mathematical Society; 2008:443-514. doi:<a href=\"https://doi.org/10.1090/conm/453\">10.1090/conm/453</a>","apa":"Wagner, U. (2008). k-Sets and k-facets. In J. Goodman, J. Pach, &#38; R. Pollack (Eds.), <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i> (Vol. 453, pp. 443–514). American Mathematical Society. <a href=\"https://doi.org/10.1090/conm/453\">https://doi.org/10.1090/conm/453</a>","ista":"Wagner U. 2008.k-Sets and k-facets. In: Surveys on Discrete and Computational Geometry: Twenty Years Later. Contemporary Mathematics, vol. 453, 443–514.","ieee":"U. Wagner, “k-Sets and k-facets,” in <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i>, vol. 453, J. Goodman, J. Pach, and R. Pollack, Eds. American Mathematical Society, 2008, pp. 443–514.","short":"U. Wagner, in:, J. Goodman, J. Pach, R. Pollack (Eds.), Surveys on Discrete and Computational Geometry: Twenty Years Later, American Mathematical Society, 2008, pp. 443–514.","mla":"Wagner, Uli. “K-Sets and k-Facets.” <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i>, edited by Jacob Goodman et al., vol. 453, American Mathematical Society, 2008, pp. 443–514, doi:<a href=\"https://doi.org/10.1090/conm/453\">10.1090/conm/453</a>.","chicago":"Wagner, Uli. “K-Sets and k-Facets.” In <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i>, edited by Jacob Goodman, János Pach, and Richard Pollack, 453:443–514. American Mathematical Society, 2008. <a href=\"https://doi.org/10.1090/conm/453\">https://doi.org/10.1090/conm/453</a>."},"doi":"10.1090/conm/453","date_created":"2018-12-11T11:57:32Z","month":"01","editor":[{"last_name":"Goodman","first_name":"Jacob","full_name":"Goodman, Jacob E"},{"last_name":"Pach","full_name":"Pach, János","first_name":"János"},{"first_name":"Richard","full_name":"Pollack, Richard","last_name":"Pollack"}],"status":"public","year":"2008","alternative_title":["Contemporary Mathematics"]},{"quality_controlled":0,"title":"On center regions and balls containing many points","intvolume":"      5092","extern":1,"publication_status":"published","publisher":"Springer","conference":{"name":"COCOON: Conference on Computing and Combinatorics"},"volume":5092,"date_updated":"2021-01-12T06:57:27Z","_id":"2432","type":"conference","publist_id":"4482","day":"01","page":"363 - 373","author":[{"last_name":"Smorodinsky","full_name":"Smorodinsky, Shakhar","first_name":"Shakhar"},{"last_name":"Sulovský","first_name":"Marek","full_name":"Sulovský, Marek"},{"full_name":"Uli Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","orcid":"0000-0002-1494-0568","last_name":"Wagner"}],"date_published":"2008-01-01T00:00:00Z","abstract":[{"text":"We study the disk containment problem introduced by Neumann-Lara and Urrutia and its generalization to higher dimensions. We relate the problem to centerpoints and lower centerpoints of point sets. Moreover, we show that for any set of n points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing A contains at least roughly 4/5ed 3n points of S. This improves previous bounds for which the constant was exponentially small in d. We also consider a generalization of the planar disk containment problem to families of pseudodisks.","lang":"eng"}],"status":"public","year":"2008","alternative_title":["LNCS"],"date_created":"2018-12-11T11:57:38Z","month":"01","doi":"10.1007/978-3-540-69733-6_36","citation":{"ista":"Smorodinsky S, Sulovský M, Wagner U. 2008. On center regions and balls containing many points. COCOON: Conference on Computing and Combinatorics, LNCS, vol. 5092, 363–373.","ama":"Smorodinsky S, Sulovský M, Wagner U. On center regions and balls containing many points. In: Vol 5092. Springer; 2008:363-373. doi:<a href=\"https://doi.org/10.1007/978-3-540-69733-6_36\">10.1007/978-3-540-69733-6_36</a>","apa":"Smorodinsky, S., Sulovský, M., &#38; Wagner, U. (2008). On center regions and balls containing many points (Vol. 5092, pp. 363–373). Presented at the COCOON: Conference on Computing and Combinatorics, Springer. <a href=\"https://doi.org/10.1007/978-3-540-69733-6_36\">https://doi.org/10.1007/978-3-540-69733-6_36</a>","chicago":"Smorodinsky, Shakhar, Marek Sulovský, and Uli Wagner. “On Center Regions and Balls Containing Many Points,” 5092:363–73. Springer, 2008. <a href=\"https://doi.org/10.1007/978-3-540-69733-6_36\">https://doi.org/10.1007/978-3-540-69733-6_36</a>.","mla":"Smorodinsky, Shakhar, et al. <i>On Center Regions and Balls Containing Many Points</i>. Vol. 5092, Springer, 2008, pp. 363–73, doi:<a href=\"https://doi.org/10.1007/978-3-540-69733-6_36\">10.1007/978-3-540-69733-6_36</a>.","short":"S. Smorodinsky, M. Sulovský, U. Wagner, in:, Springer, 2008, pp. 363–373.","ieee":"S. Smorodinsky, M. Sulovský, and U. Wagner, “On center regions and balls containing many points,” presented at the COCOON: Conference on Computing and Combinatorics, 2008, vol. 5092, pp. 363–373."}}]