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Journal articles on the topic 'Generalized cusps'

Author: Grafiati

Published: 16 November 2024

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1

Cervantes, Aldrin, and Miguel A. García-Aspeitia. "Predicting cusps or kinks in Nambu–Goto dynamics." Modern Physics Letters A 30, no. 39 (December 7, 2015): 1550210. http://dx.doi.org/10.1142/s0217732315502107.

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It is known that Nambu–Goto extended objects present some pathological structures, such as cusps and kinks, during their evolution. In this paper, we propose a model through the generalized Raychaudhuri (Rh) equation for membranes to determine if there are cusps and kinks in the worldsheet. We extend the generalized Rh equation for membranes to allow the study of the effect of higher order curvature terms in the action on the issue of cusps and kinks, using it as a tool for determining when a Nambu–Goto string generates cusps or kinks in its evolution. Furthermore, we present three examples where we test graphically this approach.

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2

Acosta, Gabriel, and Ignacio Ojea. "Korn's inequalities for generalized external cusps." Mathematical Methods in the Applied Sciences 39, no. 17 (May 21, 2014): 4935–50. http://dx.doi.org/10.1002/mma.3170.

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3

Ballas, Samuel A., Daryl Cooper, and Arielle Leitner. "Generalized cusps in real projective manifolds: classification." Journal of Topology 13, no. 4 (July 21, 2020): 1455–96. http://dx.doi.org/10.1112/topo.12161.

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4

Ballas, Samuel, Daryl Cooper, and Arielle Leitner. "The moduli space of marked generalized cusps in real projective manifolds." Conformal Geometry and Dynamics of the American Mathematical Society 26, no. 7 (August 17, 2022): 111–64. http://dx.doi.org/10.1090/ecgd/367.

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ln this paper, a generalized cusp is a properly convex manifold with strictly convex boundary that is diffeomorphic to M × [ 0 , ∞ ) M\times [0,\infty ) where M M is a closed Euclidean manifold. These are classified by Ballas, Cooper, and Leitner [J. Topol. 13 (2020), pp. 1455-1496]. The marked moduli space is homeomorphic to a subspace of the space of conjugacy classes of representations of π 1 M \pi _1M . It has one description as a generalization of a trace-variety, and another description involving weight data that is similar to that used to describe semi-simple Lie groups. It is also a bundle over the space of Euclidean similarity (conformally flat) structures on M M , and the fiber is a closed cone in the space of cubic differentials. For 3 3 -dimensional orientable generalized cusps, the fiber is homeomorphic to a cone on a solid torus.

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5

OGATA, Shoetsu. "Generalized Hirzebruch's conjecture for Hilbert-Picard modular cusps." Japanese journal of mathematics. New series 22, no. 2 (1996): 385–410. http://dx.doi.org/10.4099/math1924.22.385.

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6

Ponce, Jean, and David Chelberg. "Finding the limbs and cusps of generalized cylinders." International Journal of Computer Vision 1, no. 3 (October 1988): 195–210. http://dx.doi.org/10.1007/bf00127820.

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7

Jordan, Bruce W., Kenneth A. Ribet, and Anthony J. Scholl. "Modular curves and Néron models of generalized Jacobians." Compositio Mathematica 160, no. 5 (March 26, 2024): 945–81. http://dx.doi.org/10.1112/s0010437x23007662.

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Let $X$ be a smooth geometrically connected projective curve over the field of fractions of a discrete valuation ring $R$ , and $\mathfrak {m}$ a modulus on $X$ , given by a closed subscheme of $X$ which is geometrically reduced. The generalized Jacobian $J_\mathfrak {m}$ of $X$ with respect to $\mathfrak {m}$ is then an extension of the Jacobian of $X$ by a torus. We describe its Néron model, together with the character and component groups of the special fibre, in terms of a regular model of $X$ over $R$ . This generalizes Raynaud's well-known description for the usual Jacobian. We also give some computations for generalized Jacobians of modular curves $X_0(N)$ with moduli supported on the cusps.

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8

McREYNOLDS, D. B. "Cusps of Hilbert modular varieties." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 3 (May 2008): 749–59. http://dx.doi.org/10.1017/s0305004107001004.

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AbstractMotivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifoldMto be diffeomorphic to a cusp cross-section of a Hilbert modular variety. Specialized to Hilbert modular surfaces, this proves that every Sol 3–manifold is diffeo morphic to a cusp cross-section of a (generalized) Hilbert modular surface. We also deduce an obstruction to geometric bounding in this setting. Consequently, there exist Sol 3–manifolds that cannot arise as a cusp cross-section of a 1–cusped nonsingular Hilbert modular surface.

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De los Ríos, Patricio, Laksmanan Kanagu, Chokkalingam Lathasumathi, and Chelladurai Stella. "Radular morphology by using SEM in Pugilina cochlidium (Gastropoda: Melongenidae) populations, from Thondi coast-Palk Bay in Tamil Nadu-South East coast of India." Brazilian Journal of Biology 80, no. 4 (December 2020): 783–89. http://dx.doi.org/10.1590/1519-6984.220076.

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Abstract Radula in all melongeninae species is rather uniform and characterized by bicuspid lateral teeth with strongly curved cusps and sub rectangular rachidians, bearing usually 3 cusps. The aim of the present study was to describe the radula of 2 Pugilina cochlidium populations using SEM. The radula in 2 species proves itself as a rachiglossate type showing the radular formula of 1 + R + 1. The first population hasthe central tooth wide with sharp cusps equal in length, emanate from posterior margin of tooth base. The lateral teeth have 2 cusps and are long, sharp, pointed and bent towards the rachidian tooth. Whereas the second population, the central tooth is narrow with sharp cusps equal in length, emanate from posterior margin of tooth base. The lateral teeth have 2 cusps and are broad, longer, sharp, pointed and bent towards the rachidian tooth. They are typically sickle shaped with broad strong base. In both populations the rachidian tooth is subquadrate with 3 big cusps in the middle, but in the second population the base of the rachidian is concave while in the first population it is straight. In the present study the median rachidian of the second population, has a broad basal region when compared to first. This similar observation has been made in Chicoreus virgineus ponderosus and Siratus virgineus ponderosus. In the present study, since 2 populations exhibit the same generalized rachiglossate pattern it does not offer much scope for systematic diagnosis below generic level.

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10

BRUINIER, JAN HENDRIK, and MARKUS SCHWAGENSCHEIDT. "A CONVERSE THEOREM FOR BORCHERDS PRODUCTS ON." Nagoya Mathematical Journal 240 (March 1, 2019): 237–56. http://dx.doi.org/10.1017/nmj.2019.3.

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We show that every Fricke-invariant meromorphic modular form for $\unicode[STIX]{x1D6E4}_{0}(N)$ whose divisor on $X_{0}(N)$ is defined over $\mathbb{Q}$ and supported on Heegner divisors and the cusps is a generalized Borcherds product associated to a harmonic Maass form of weight $1/2$. Further, we derive a criterion for the finiteness of the multiplier systems of generalized Borcherds products in terms of the vanishing of the central derivatives of $L$-functions of certain weight $2$ newforms. We also prove similar results for twisted Borcherds products.

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11

Kettner, Frank, Etienne Côté, and Robert M. Kirberger. "Quadricuspid Aortic Valve and Associated Abnormalities in a Dog." Journal of the American Animal Hospital Association 41, no. 6 (November 1, 2005): 406–12. http://dx.doi.org/10.5326/0410406.

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An 11-month-old, female Scottish terrier was presented with a history of a heart murmur. The electrocardiogram showed signs of left ventricular enlargement, and radiography confirmed generalized cardiomegaly. Echocardiography revealed four equally sized aortic valve cusps. A ventricular septal defect, with systolic left-to-right shunting, and aortic regurgitation into both ventricles were also present. The dog was free of clinical signs 1 year after diagnosis.

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12

Hunsicker, Eugenie, Nikolaos Roidos, and Alexander Strohmaier. "Scattering theory of the $p$-form Laplacian on manifolds with generalized cusps." Journal of Spectral Theory 4, no. 1 (2014): 177–209. http://dx.doi.org/10.4171/jst/66.

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13

He, Yang-Hui, and John McKay. "Sporadic and Exceptional." inSTEMM Journal 1, S1 (January 24, 2024): 61–85. http://dx.doi.org/10.56725/instemm.v1is1.8.

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We study the web of correspondences linking the exceptional Lie algebras E8,7,6 and the sporadic simple groups Monster, Baby and the largest Fischer group. This is done via the investigation of classical enumerative problems on del Pezzo surfaces in relation to the cusps of certain subgroups of PSL(2,R) for the relevant McKay-Thompson series in Generalized Moonshine. We also study Conway's sporadic group, as well as its association with the Horrocks-Mumford bundle.

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14

Asha Rathod, Mayuri Bachhav, Gaurang Mistry, Rasha Ansari, Nilay Karnik, and Tanupriya Bhatia. "Minimally Invasive Approach for Full Mouth Rehabilitation Using Table-Tops in A Patient with Generalized Attrition." Journal of Advanced Zoology 44, no. 4 (December 6, 2023): 1058–62. http://dx.doi.org/10.17762/jaz.v44i4.2513.

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Currently A table-top is a conservative treatment approach limited to the thickness of the occlusal table with margins placed supragingivally for covering all the cusps of teeth. Its indications include patients with occlusal wear due to attrition or abrasion, teeth with cracks/fracture lines and endodontically treated teeth. The present case report demonstrates its potential in the field of prosthodontics to achieve full mouth rehabilitation through a minimally invasive approach

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15

Wei, Fu-Tsun, and Takao Yamazaki. "Rational torsion of generalized Jacobians of modular and Drinfeld modular curves." Forum Mathematicum 31, no. 3 (May 1, 2019): 647–59. http://dx.doi.org/10.1515/forum-2018-0141.

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Abstract We consider the generalized Jacobian {\widetilde{J}} of the modular curve {X_{0}(N)} of level N with respect to a reduced divisor consisting of all cusps. Supposing N is square free, we explicitly determine the structure of the {\mathbb{Q}} -rational torsion points on {\widetilde{J}} up to 6-primary torsion. The result depicts a fuller picture than [18] where the case of prime power level was studied. We also obtain an analogous result for Drinfeld modular curves. Our proof relies on similar results for classical Jacobians due to Ohta, Papikian and the first author. We also discuss the Hecke action on {\widetilde{J}} and its Eisenstein property.

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16

Galvão, B. R. L., V. C. Mota, and A. J. C. Varandas. "Modeling cusps in adiabatic potential energy surfaces using a generalized Jahn-Teller coordinate." Chemical Physics Letters 660 (September 2016): 55–59. http://dx.doi.org/10.1016/j.cplett.2016.07.029.

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17

Douçot, Benoit, Franco Nori, and R. Rammal. "FILLING LANDAU LEVELS: FERMI SEA GROUND STATE ENERGY, COMPETING INTERACTIONS AND MARGINAL DISPERSIONS IN GENERALIZED FLUX PHASES." International Journal of Modern Physics B 06, no. 05n06 (March 1992): 563–83. http://dx.doi.org/10.1142/s0217979292000347.

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ABSTRACT: We review recent studies on the energetics of fermions confined to a two dimensional square lattice, and the relations of these results to mean-field approaches to the t−J model. Our goal has been to compute the kinetic energy of the Fermi sea of the spinless fermions for any value of the (1) fermion concentration, (2) magnetic flux, and (3) frustration. For the unfrustrated case, we confirm that the ground state energy, χ(Φ), is a minimum for Φ=π(1−δ), which corresponds to one flux quantum per spinless fermion. We then proceed to do a systematic study of frustration effects, coming from longer range couplings, which modify the picture obtained for the unfrustrated case. The frustrating influence of the kinetic energy of the holes (e.g., by breaking magnetic bonds and suppressing the long-range order present in the undoped systems) is the main focus of this work. We find that, in general, E(Φ) always exhibits cusp-like minima which position moves linearly as a function of the fermion density x. Frustration can induce a competition between different local minima. By first considering the local minima for one particle only, we can understand most of the qualitative features of E(Φ). These local minima occur at simple rational fractions of Φ0, and when the flux slightly deviates from these values a one-particle Landau level structure develops. It is precisely such a spectrum that generates a family of cusps that “move away” from the original flux value as x is increased. Every cusp corresponds to an integer number of filled Landau levels, and the minimum energy cusp corresponds to the one level case. Furthermore, we use perturbation theory, valid for low fermion density x, in order to analyze quantitatively the behavior of the cusp-like energy minima; which originate from the Landau level structure when the flux is close to a rational value. If the flux is slightly away from a given rational value [Formula: see text] each of the q subbands generates a secondary Landau level structure. We have derived a t2−t3 phase diagram indicating regions of similar behavior (i.e., adiabatic continuations can be performed with each region, preserving the E(Φ) structure) and the boundaries between them. We have studied several points belonging to those boundaries and found that anomalous behavior, (e.g., cancelation of the k2 term in the dispersion relation) induced by frustration, can occur.

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18

Hangjian, Zhang, Zhang Guicang, and Wang Lu. "The Shape Analysis of DTB-like and DT B-spline-like Curves." Journal of Mathematics and Informatics 24 (2023): 01–21. http://dx.doi.org/10.22457/jmi.v24a01216.

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In the field of computer-aided design and related applications, the free curve with parameters shows its strong function. But an excellent curve with parameters need to eliminate unnecessary cusps and inflection points, so shape analysis is needed for some specific curves. We have already shown many excellent properties of the DTB-like curves and DT B-spline-like curves. Thus the shape features like convexity, loops, inflection points, and cusps of the DTB-like curves, and DT B-spline-like curves are further discussed in this paper. And the necessary and sufficient conditions for the existence of shape features of the corresponding DTB-like curves and DT B-spline-like curves are given. And the shape features distribution all be generalized into tables and diagrams, which are useful for industrial design. In addition, the effect of shape parameters on the shape features diagram and its adjustment ability to the shape of corresponding curves are analyzed, respectively. The work in this paper enables users to determine how to set parameter values so that the generated curve could be a global convex or local convex curve, has a required inflection point, or eliminate the unnecessary one, and could be adjusted to another aimed shape.

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19

GRIEP, STINE, and JULIAN GLOS. "Description of tadpoles of the frogs Heterixalus tricolor, H. carbonei and H. luteostriatus (Anura: Hyperoliidae) from western Madagascar." Zootaxa 4767, no. 2 (April 24, 2020): 332–44. http://dx.doi.org/10.11646/zootaxa.4767.2.8.

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The genus Heterixalus is endemic to Madagascar. It contains eleven species of small to medium-sized tree frogs that typically inhabit open areas like swamps and rice fields. We describe the larval stages of three sympatric species that occur in western Madagascar: H. tricolor, H. carbonei, and H. luteostriatus. Similar to other species of this genus, the tadpoles of these species have a depressed, ovoid body-form and a generalized oral disc. The labial tooth row formula is 1/3(1). Examined phenotypes differed marginally between species. Compared to H. tricolor and H. carbonei, H. luteostriatus showed fewer cusps on the fork-like labial teeth, a lower ventral fin, and a shorter tail. The high morphological resemblance implicates an ecological similarity between species. Highly overlapping niches raise questions on how species co-occur.

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20

He, Lingchao, and Zhonglong Zhao. "Multiple lump solutions and dynamics of the generalized (3+1)-dimensional KP equation." Modern Physics Letters B 34, no. 15 (March 27, 2020): 2050167. http://dx.doi.org/10.1142/s0217984920501675.

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In this paper, the bilinear method is employed to investigate the multiple lump solutions of the generalized (3[Formula: see text]+[Formula: see text]1)-dimensional KP equation. With the aid of the variable transformation, this equation is reduced to a dimensionally reduced equation. The reduced equation can be transformed into a bilinear equation. On the basis of the bilinear forms and a special quadratic function, the 1-lump solution is constructed, which has a positive peak and two negative peaks. Three polynomial functions are introduced to derive the 3-lump solutions. The 3-lump wave has a “triangular” structure. As the parameters tend to zero, the 3-lump wave becomes the lump wave with two adjacent cusps. The 6-lump solutions are constructed. Four kinds of lump waves appear as the parameters increase. In addition, the high-order 8-lump solutions are also obtained. All the peaks of the 6-lump and the 8-lump wave tend to the same height when the parameters are sufficiently large. The dynamical behaviors of the multiple lump solutions are discussed. All the results are useful in explaining the dynamical phenomena of the generalized (3[Formula: see text]+[Formula: see text]1)-dimensional KP equation.

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21

CUMMINS, C. J., and N. S. HAGHIGHI. "ON FOURIER COEFFICIENTS OF MODULAR FORMS." Bulletin of the Australian Mathematical Society 83, no. 1 (November 26, 2010): 50–62. http://dx.doi.org/10.1017/s0004972710001887.

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AbstractRecursive formulae satisfied by the Fourier coefficients of meromorphic modular forms on groups of genus zero have been investigated by several authors. Bruinier et al. [‘The arithmetic of the values of modular functions and the divisors of modular forms’, Compositio Math. 140(3) (2004), 552–566] found recurrences for SL(2,ℤ); Ahlgren [‘The theta-operator and the divisors of modular forms on genus zero subgroups’, Math. Res. Lett.10(5–6) (2003), 787–798] investigated the groups Γ0(p); Atkinson [‘Divisors of modular forms on Γ0(4)’, J. Number Theory112(1) (2005), 189–204] considered Γ0(4), and S. Y. Choi [‘The values of modular functions and modular forms’, Canad. Math. Bull.49(4) (2006), 526–535] found the corresponding formulae for the groups Γ+0(p). In this paper we generalize these results and find recursive formulae for the Fourier coefficients of any meromorphic modular form f on any genus-zero group Γ commensurable with SL(2,ℤ) , including noncongruence groups and expansions at irregular cusps. The form of the recurrence relations is well suited for the computation of the Fourier coefficients of the functions and forms on the groups which occur in monstrous and generalized moonshine. The required initial data has, in many cases, been computed by Norton (private communication).

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22

Leitner, Arielle. "A classification of subgroups of SL(4,R) isomorphic to R3 and generalized cusps in projective 3 manifolds." Topology and its Applications 206 (June 2016): 241–54. http://dx.doi.org/10.1016/j.topol.2016.04.005.

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23

Levine, Timothy P., Gregory J. Matthews, Lydia A. Salama, and Alan Yee. "Anteroposterior skeletofacial classification and its relationship to maxillary second molar buccopalatal angulation." Angle Orthodontist 90, no. 6 (September 8, 2020): 851–56. http://dx.doi.org/10.2319/121719-809.1.

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ABSTRACT Objective To compare second molar angulation to the occlusal plane with cephalometric measurements corresponding to AP skeletal discrepancy. Materials and Methods 72 patients' pre-orthodontic records were analyzed. A plane was constructed along the cusps of the upper second molar and measured to a proxy for the occlusal plane. The angle between the planes was measured. ANB, Wits appraisal, U1-SN, IMPA, A-B perpendicular to Frankfort, and overjet were measured on the patients' cephalograms. Generalized additive mixed model analysis was performed to analyze the relationship between the second molar angulation and the cephalometric measurements. Results All six cephalometric measurements showed a significant relationship with the second molar angulation, with Class III patients having a larger angle than Class II and I patients. Conclusions Class III patients have upper second molars that are significantly tipped from the occlusal plane. The second molars require special attention for correction prior to orthognathic surgery for Class III patients in order to avoid deleterious effects from the malpositioned teeth.

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24

Cho, Munjin, and Hyesuk LeePark. "A Study on Effects of Multiple Exemplar Instruction on Derived Intraverbal Responses within Stimuli Equivalence in children with Autism spectrum disorder." Journal of Behavior Analysis and Support 10, no. 2 (August 2023): 1–27. http://dx.doi.org/10.22874/kaba.2023.10.2.1.

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This study was to investigate effects of the Multiple Examplar Instruction(MEI) on untaught tact as Naming and untaught Intraverbal using stimuli within equivalent relations. 4 and 5 year old children with Autism Spectrum Disorder participated in the study. A multiple baselines across participants with multiple probes design was used. Direct instruction on part of possible stimulus-response relations with the stimulus equivalence relations were delivered in order to establish reinforcement history within that relations. Probe for untaught stimulus-response within the stimulus equivalence relations, derived intraverbal and derived tact as Naming were conducted. The participant showed low level of correct derived responses with the equivalence relations. A MEI was implemented where the participant learned to respond within the equivalence relations a type of relational frame. The participants showed derived intraverbal and tact responses within the frame and generalized the responding to a novel set of stimuli. Possible source for inconsistent responding across stimuli were discussed in term of behavioral cusps and stimulus control.

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25

Viertel, BRUNO, MICHAEL VEITH, SUSANNE SCHICK, ALAN CHANNING, STEPHEN KIGOOLO, OSCAR BAEZA-URREA, ULRICH SINSCH, and STEFAN LÖTTERS. "The stream-dwelling larva of the Ruwenzori River Frog, Amietia ruwenzorica, its buccal cavity and pathology of chytridiomycosis." Zootaxa 3400, no. 1 (July 26, 2012): 43. http://dx.doi.org/10.11646/zootaxa.3400.1.3.

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Tadpoles of Amietia ruwenzorica (Pyxicephalidae, Cacosterninae) were collected in the Ruwenzori Mountains, Uganda(identified by DNA barcoding). The ventrally directed enlarged oral disc with a high number of labial tooth rows (LTRF9(4)/9(1)) and the narrow tail with robust caudal musculature characterise them as stream-dwellers. We name this mor-photype the 'common or standard type of stream-adaptation', because special additional adhesive organs are missing in A.ruwenzorica. The uniserially arranged oral teeth of the spoon-shaped type with 16 to 18 cusps per tooth are known fromother anuran larvae, especially from pyxicephalids. The buccal morphology resembles generalized tadpoles with some re-strictions and all features of a suspension-feeding pyxicephalid larva are present in A. ruwenzorica. This leads us to theconclusion that tadpoles of this species are suspension-feeders scraping periphyton off the surface and ingesting bottomand deposit particles. Histopathological and scanning electron microscopy investigations demonstrated the presence of theamphibian chytrid fungus (Batrachochytrium dendrobatidis) in part of our material resulting in signs of chytridiomycosis indicated by the loss of labial teeth and by corrosion of jaw sheaths.

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26

Marston, Philip L., and Gregory Kaduchak. "Generalized rainbows and unfolded glories of oblate drops: organization for multiple internal reflections and extension of cusps into Alexander's dark band." Applied Optics 33, no. 21 (July 20, 1994): 4702. http://dx.doi.org/10.1364/ao.33.004702.

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27

LANGER, ADRIAN. "LOGARITHMIC ORBIFOLD EULER NUMBERS OF SURFACES WITH APPLICATIONS." Proceedings of the London Mathematical Society 86, no. 2 (March 2003): 358–96. http://dx.doi.org/10.1112/s0024611502013874.

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We introduce orbifold Euler numbers for normal surfaces with boundary $\mathbb{Q}$-divisors. These numbers behave multiplicatively under finite maps and in the log canonical case we prove that they satisfy the Bogomolov–Miyaoka–Yau type inequality. Existence of such a generalization was earlier conjectured by G. Megyesi [Proc. London Math. Soc. (3) 78 (1999) 241–282]. Most of the paper is devoted to properties of local orbifold Euler numbers and to their computation.As a first application we show that our results imply a generalized version of R. Holzapfel's ‘proportionality theorem’ [Ball and surface arithmetics, Aspects of Mathematics E29 (Vieweg, Braunschweig, 1998)]. Then we show a simple proof of a necessary condition for the logarithmic comparison theorem which recovers an earlier result by F. Calderón-Moreno, F. Castro-Jiménez, D. Mond and L. Narváez-Macarro [Comment. Math. Helv. 77 (2002) 24–38].Then we prove effective versions of Bogomolov's result on boundedness of rational curves in some surfaces of general type (conjectured by G. Tian [Springer Lecture Notes in Mathematics 1646 (1996) 143–185)]. Finally, we give some applications to singularities of plane curves; for example, we improve F. Hirzebruch's bound on the maximal number of cusps of a plane curve.2000 Mathematical Subject Classification: 14J17, 14J29, 14C17.

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28

Assing, Edgar, and Andrew Corbett. "Voronoï summation via switching cusps." Monatshefte für Mathematik 194, no. 4 (February 22, 2021): 657–85. http://dx.doi.org/10.1007/s00605-021-01537-5.

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AbstractWe consider the Fourier expansion of a Hecke (resp. Hecke–Maaß) cusp form of general level N at the various cusps of $$\Gamma _{0}(N)\backslash \mathbb {H}$$ Γ 0 ( N ) \ H . We explain how to compute these coefficients via the local theory of p-adic Whittaker functions and establish a classical Voronoï summation formula allowing an arbitrary additive twist. Our discussion has applications to bounding sums of Fourier coefficients and understanding the (generalised) Atkin–Lehner relations.

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29

ARTIGIANI, MAURO, LUCA MARCHESE, and CORINNA ULCIGRAI. "Persistent Hall rays for Lagrange spectra at cusps of Riemann surfaces." Ergodic Theory and Dynamical Systems 40, no. 8 (February 11, 2019): 2017–72. http://dx.doi.org/10.1017/etds.2018.143.

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We study Lagrange spectra at cusps of finite area Riemann surfaces. These spectra are penetration spectra that describe the asymptotic depths of penetration of geodesics in the cusps. Their study is in particular motivated by Diophantine approximation on Fuchsian groups. In the classical case of the modular surface and classical Diophantine approximation, Hall proved in 1947 that the classical Lagrange spectrum contains a half-line, known as a Hall ray. We generalize this result to the context of Riemann surfaces with cusps and Diophantine approximation on Fuchsian groups. One can measure excursion into a cusp both with respect to a natural height function or, more generally, with respect to any proper function. We prove the existence of a Hall ray for the Lagrange spectrum of any non-cocompact, finite covolume Fuchsian group with respect to any given cusp, both when the penetration is measured by a height function induced by the imaginary part as well as by any proper function close to it with respect to the Lipschitz norm. This shows that Hall rays are stable under (Lipschitz) perturbations. As a main tool, we use the boundary expansion developed by Bowen and Series to code geodesics and produce a geometric continued fraction-like expansion and some of the ideas in Hall’s original argument. A key element in the proof of the results for proper functions is a generalization of Hall’s theorem on the sum of Cantor sets, where we consider functions which are small perturbations in the Lipschitz norm of the sum.

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30

Bown, Thomas M., and John G. Fleagle. "Systematics, Biostratigraphy, and Dental Evolution of the Palaeothentidae, Later Oligocene to Early–Middle Miocene (Deseadan–Santacrucian) Caenolestoid Marsupials of South America." Journal of Paleontology 67, S29 (March 1993): 1–76. http://dx.doi.org/10.1017/s0022336000062107.

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The family Palaeothentidae contains some of the dentally more specialized of the small-bodied marsupials of South America and was a clade almost equivalent with the Abderitidae in having been the most abundant caenolestoids. They were unquestionably the most diverse, containing two subfamilies, nine genera, and 19 species, with a distribution ranging from Colombia to Tierra del Fuego. The best and most continuous record of the Palaeothentidae is from Patagonian Argentina where eight genera and 17 species are recognized. There, the Palaeothentidae ranged in age from the Deseadan (later Oligocene) through the late Santacrucian (middle Miocene—the Santacrucian record lasting from about 19.4 m.y. to considerably less than 16.05 m.y. before the present). The family appears to have survived longer in Colombia. The palaeothentine Palaeothentes boliviensis (Bolivia) and the incertae sedis genus and species Hondathentes cazador (Colombia) are the only taxa restricted to an extra-Argentine distribution.Two palaeothentid subfamilies are recognized. The subfamily Acdestinae is new and is erected to accommodate four genera and five species of herbivorous to frugivorous palaeothentids known from the Deseadan through the middle–late Santacrucian. Three of those genera are new (Acdestoides, Acdestodon, and Trelewthentes), as are three acdestine species placed in the genera Acdestodon, Trelewthentes, and Acdestis. The largely faunivorous Palaeothentinae includes four genera and 13 species; the genera Propalaeothentes and Carlothentes are new and new species are described for the genera Propalaeothentes (2) and Palaeothentes (3). Carlothentes is named for Ameghino's Deseadan species Epanorthus chubutensis, and Ameghino's genus Pilchenia is resurrected to accommodate Deseadan P. lucina. New species include: Acdestodon bonapartei, Trelewthentes rothi, Acdestis lemairei, Palaeothentes marshalli, P. migueli, P. pascuali, and Propalaeothentes hatcheri.The Palaeothentinae contains more generalized palaeothentid species than does the Acdestinae, but also includes some very specialized forms. The most generalized known palaeothentid is the Colombian Hondathentes cazador. Both the Acdestinae and Palaeothentinae have large- and small-bodied species; Palaeothentes aratae was the largest palaeothentid (about 550 g), and P. pascuali n. sp. the smallest (about 50 g). The oldest known members of both subfamilies consist of five of the six largest palaeothentids.The evolutionary history of the Palaeothentidae is complicated by thick sequences containing no fossils, several lacunae in sequences that yield fossils, and a continent-wide distribution of localities. By far the densest and most continuous record of the family exists in the coastal Santa Cruz Formation of Patagonian Argentina. Three major clades exist within the Palaeothentidae: 1) the incertae sedis species Hondathentes cazador; 2) the Acdestinae; and 3) the Palaeothentinae (including the new genus Propalaeothentes). The evolution of dental characters in these clades is documented with the aid of 719 new specimens (about 80% of the hypodigm of the family), most of which (about 90% of the new specimens) have precise stratigraphic data.Biostratigraphic study of the new samples was assisted by a new technique of temporal analysis of paleosols and by radiometric age determinations, the latter indicating that the upper part of the Pinturas Formation (16.6 Ma) is older than the lower part of the Santa Cruz Formation (16.4 Ma) and that the top of the marine Monte León Formation (Grupo Patagonica) is older than either (19.4 Ma).Fifty-two gnathic and dental characters were used to identify the taxonomy and to reconstruct the phylogeny of the Palaeothentidae. Analysis of sequencing of appearances of derived characters documents rampant convergences at all taxonomic levels and considerable phenotypic plasticity (variable percent representation of different mutable character morphs) in the organization of the palaeothentid dentition. Certain highly generalized character states survive for the duration of the family in some lineages, whereas others are phenotypically lost for a time and then reappear as a minor percentage of character variability. In general, replacement faunas of palaeothentids were morphologically more generalized than their antecedent forms. The high rate of character mutability and the survival and reappearance of generalized dental characters in the Palaeothentidae were probably related to massive events of pyroclastic deposition that periodically caused at least local extinctions of small mammal populations throughout the duration of the Patagonian middle Tertiary. Dental character regression indicates that palaeothentids arose prior to the Deseadan from a relatively large-bodied marsupial having generalized tribosphenic molars with more or less bunodont cusps; probably an unknown member of the Didelphidae.

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31

TAKLOO-BIGHASH, RAMIN. "A REMARK ON A PAPER OF AHLGREN, BERNDT, YEE, AND ZAHARESCU." International Journal of Number Theory 02, no. 01 (March 2006): 111–14. http://dx.doi.org/10.1142/s1793042106000450.

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A classical theorem of Ramanujan relates an integral of Dedekind eta-function to a special value of a Dirichlet L-function at s = 2. Ahlgren, Berndt, Yee and Zaharescu have generalized this result [1]. In this paper, we generalize this result to the context of holomorphic cusp forms on the upper half space.

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32

RAMAKRISHNAN, B., and BRUNDABAN SAHU. "RANKIN’S METHOD AND JACOBI FORMS OF SEVERAL VARIABLES." Journal of the Australian Mathematical Society 88, no. 1 (January 26, 2010): 131–43. http://dx.doi.org/10.1017/s1446788709000330.

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AbstractFollowing R. A. Rankin’s method, D. Zagier computed the nth Rankin–Cohen bracket of a modular form g of weight k1 with the Eisenstein series of weight k2, computed the inner product of this Rankin–Cohen bracket with a cusp form f of weight k=k1+k2+2n and showed that this inner product gives, up to a constant, the special value of the Rankin–Selberg convolution of f and g. This result was generalized to Jacobi forms of degree 1 by Y. Choie and W. Kohnen. In this paper, we generalize this result to Jacobi forms defined over ℋ×ℂ(g,1).

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33

Ogata, Shōetsu. "Infinitesimal deformations of generalized cusp singularities." Tohoku Mathematical Journal 39, no. 2 (1987): 237–48. http://dx.doi.org/10.2748/tmj/1178228327.

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34

Choie, Youngju, and Min Ho Lee. "Mellin Transforms of Mixed Cusp Forms." Canadian Mathematical Bulletin 42, no. 3 (September 1, 1999): 263–73. http://dx.doi.org/10.4153/cmb-1999-032-3.

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AbstractWe define generalized Mellin transforms of mixed cusp forms, show their convergence, and prove that the function obtained by such a Mellin transform of a mixed cusp form satisfies a certain functional equation. We also prove that a mixed cusp form can be identified with a holomorphic form of the highest degree on an elliptic variety.

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35

Lee, Min Ho. "Generalized jacobi cusp forms and elliptic surfaces." Complex Variables, Theory and Application: An International Journal 36, no. 2 (October 1998): 133–48. http://dx.doi.org/10.1080/17476939808815104.

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36

KAO, LIEN-YUNG. "Manhattan curves for hyperbolic surfaces with cusps." Ergodic Theory and Dynamical Systems 40, no. 7 (December 4, 2018): 1843–74. http://dx.doi.org/10.1017/etds.2018.124.

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In this paper, we study an interesting curve, the so-called Manhattan curve, associated with a pair of boundary-preserving Fuchsian representations of a (non-compact) surface; in particular, representations corresponding to Riemann surfaces with cusps. Using thermodynamic formalism (for countable state Markov shifts), we prove the analyticity of the Manhattan curve. Moreover, we derive several dynamical and geometric rigidity results, which generalize results of Burger [Intersection, the Manhattan curve, and Patterson–Sullivan theory in rank 2. Int. Math. Res. Not.1993(7) (1993), 217–225] and Sharp [The Manhattan curve and the correlation of length spectra on hyperbolic surfaces. Math. Z.228(4) (1998), 745–750] for convex cocompact Fuchsian representations.

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37

MILLER, ALISON, and AARON PIXTON. "ARITHMETIC TRACES OF NON-HOLOMORPHIC MODULAR INVARIANTS." International Journal of Number Theory 06, no. 01 (February 2010): 69–87. http://dx.doi.org/10.1142/s1793042110002818.

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We extend results of Bringmann and Ono that relate certain generalized traces of Maass–Poincaré series to Fourier coefficients of modular forms of half-integral weight. By specializing to cases in which these traces are usual traces of algebraic numbers, we generalize results of Zagier describing arithmetic traces associated to modular forms. We define correspondences [Formula: see text] and [Formula: see text]. We show that if f is a modular form of non-positive weight 2 - 2 λ and odd level N, holomorphic away from the cusp at infinity, then the traces of values at Heegner points of a certain iterated non-holomorphic derivative of f are equal to Fourier coefficients of the half-integral weight modular forms [Formula: see text].

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38

Meng, Qing, and Bin He. "Exact Peakon, Compacton, Solitary Wave, and Periodic Wave Solutions for a Generalized KdV Equation." Mathematical Problems in Engineering 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/602432.

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We employ the approaches of both dynamical system and numerical simulation to investigate a generalized KdV equation, which is presented by Yin (2012). Some peakon, compacton, solitary wave, smooth periodic wave, and periodic cusp wave solutions are obtained, and the planar graphs of the compactons and the periodic cusp waves are simulated.

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39

Gaigalas, Edmundas. "Apie mišraus tipo parabolines formas." Lietuvos matematikos rinkinys 43 (December 22, 2003): 29–31. http://dx.doi.org/10.15388/lmr.2003.32313.

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40

López-López, Jorge L., and Yesenia Villicaña-Molina. "On cusps of hyperbolic once-punctured torus bundles over the circle." Revista Colombiana de Matemáticas 56, no. 2 (April 17, 2023): 157–78. http://dx.doi.org/10.15446/recolma.v56n2.108373.

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The geometry of certain canonical triangulation of once-punctured torus bundles over the circle is applied to the problem of computing their cusp tori. We are also concerned with the problem of finding the limit points of the set formed by such cusp tori, inside the moduli space of the torus. Our discussion generalizes examples which were elaborated by H. Helling (unpublished) and F. Guéritaud.

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41

Tsalugelashvili, N., and T. Vepkhvadze. "The Construction of the Bases of Some Eight Level Cusp Form Spaces." Georgian Mathematical Journal 7, no. 4 (December 2000): 793–98. http://dx.doi.org/10.1515/gmj.2000.793.

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42

Kumar, Balesh, Jay Mehta, and G. K. Viswanadham. "Some remarks on the Fourier coefficients of cusp forms." International Journal of Number Theory 16, no. 09 (June 16, 2020): 1935–43. http://dx.doi.org/10.1142/s1793042120500992.

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43

Balibrea, F., and J. C. Valverde. "Cusp and generalized flip bifurcations under higher degree conditions." Nonlinear Analysis: Theory, Methods & Applications 52, no. 2 (January 2003): 405–19. http://dx.doi.org/10.1016/s0362-546x(01)00908-7.

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44

Buttcane, Jack, and Rizwanur Khan. "On the fourth moment of Hecke–Maass forms and the random wave conjecture." Compositio Mathematica 153, no. 7 (May 2, 2017): 1479–511. http://dx.doi.org/10.1112/s0010437x17007199.

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Conditionally on the generalized Lindelöf hypothesis, we obtain an asymptotic for the fourth moment of Hecke–Maass cusp forms of large Laplacian eigenvalue for the full modular group. This lends support to the random wave conjecture.

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45

Rozier, Simon, and Raphaël Errani. "Collisionless Relaxation from Near-equilibrium Configurations: Linear Theory and Application to Tidal Stripping." Astrophysical Journal 971, no. 1 (August 1, 2024): 91. http://dx.doi.org/10.3847/1538-4357/ad4c6e.

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Abstract Placed slightly out of dynamical equilibrium, an isolated stellar system quickly returns toward a steady virialized state. We study this process of collisionless relaxation using the matrix method of linear response theory. We show that the full phase-space distribution of the final virialized state can be recovered directly from the disequilibrium initial conditions, without the need to compute the time evolution of the system. This shortcut allows us to determine the final virialized configuration with minimal computational effort. Complementing this result, we develop tools to model the system's full time evolution in the linear approximation. In particular, we show that moments of the velocity distribution can be efficiently computed using a generalized moment matrix. We apply our linear methods to study the relaxation of energy-truncated Hernquist spheres, mimicking the tidal stripping of a cuspy dark matter subhalo. Comparison of our linear predictions against controlled, isolated N-body simulations shows agreement at percent level for the parts of the system where a linear response to the perturbation is expected. We find that relaxation generates a tangential velocity anisotropy in the intermediate regions, despite the initial disequilibrium state having isotropic kinematics. Our results also strengthen the case for relaxation depleting the amplitude of the density cusp, without affecting its asymptotic slope. Finally, we compare the linear theory against an N-body simulation of tidal stripping on a radial orbit, confirming that the theory still accurately predicts density and velocity dispersion profiles for most of the system.

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LI, JIBIN, and ZHIJUN QIAO. "BIFURCATIONS AND EXACT TRAVELING WAVE SOLUTIONS OF THE GENERALIZED TWO-COMPONENT CAMASSA–HOLM EQUATION." International Journal of Bifurcation and Chaos 22, no. 12 (December 2012): 1250305. http://dx.doi.org/10.1142/s0218127412503051.

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In this paper, we apply the method of dynamical systems to a generalized two-component Camassa–Holm system. Through analysis, we obtain solitary wave solutions, kink and anti-kink wave solutions, cusp wave solutions, breaking wave solutions, and smooth and nonsmooth periodic wave solutions. To guarantee the existence of these solutions, we give constraint conditions among the parameters associated with the generalized Camassa–Holm system. Choosing some special parameters, we obtain exact parametric representations of the traveling wave solutions.

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47

Marston, Philip L. "Cusp diffraction catastrophe from spheroids: generalized rainbows and inverse scattering." Optics Letters 10, no. 12 (December 1, 1985): 588. http://dx.doi.org/10.1364/ol.10.000588.

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48

SPRING, DAVID. "DIRECTED EMBEDDINGS OF CLOSED MANIFOLDS." Communications in Contemporary Mathematics 07, no. 05 (October 2005): 707–25. http://dx.doi.org/10.1142/s0219199705001891.

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Gromov's theorem on directed embeddings of open manifolds is generalized to the case of closed manifolds, where the embeddings are directed with respect to a given codimension ≥ 1 foliation on the manifold. Applications include directed embeddings with prescribed codimension 1 cusp singularities.

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49

van den Ban, Erik P., Job J. Kuit, and Henrik Schlichtkrull. "K-invariant cusp forms for reductive symmetric spaces of split rank one." Forum Mathematicum 31, no. 2 (March 1, 2019): 341–49. http://dx.doi.org/10.1515/forum-2018-0150.

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AbstractLet {G/H} be a reductive symmetric space of split rank one and let K be a maximal compact subgroup of G. In a previous article the first two authors introduced a notion of cusp forms for {G/H}. We show that the space of cusp forms coincides with the closure of the space of K-finite generalized matrix coefficients of discrete series representations if and only if there exist no K-spherical discrete series representations. Moreover, we prove that every K-spherical discrete series representation occurs with multiplicity one in the Plancherel decomposition of {G/H}.

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50

Laurinčikas, Antanas, Darius Šiaučiūnas, and Adelė Vaiginytė. "Extension of the discrete universality theorem for zeta-functions of certain cusp forms." Nonlinear Analysis: Modelling and Control 23, no. 6 (November 21, 2018): 961–73. http://dx.doi.org/10.15388/na.2018.6.10.

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In the paper, an universality theorem on the approximation of analytic functions by generalized discrete shifts of zeta functions of Hecke-eigen cusp forms is obtained. These shifts are defined by using the function having continuous derivative satisfying certain natural growth conditions and, on positive integers, uniformly distributed modulo 1.

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