Question
An infinite hierarchy of quantities with this property arises from the Korteweg–de Vries (“COR-tuh-veg-duh-VREEZ”) equation because it is fully integrable. In most scenarios, the Poisson bracket of the Hamiltonian with quantities with this property equals zero. Quantities conjugate to “cyclic” or “ignorable” coordinates of a Lagrangian (“luh-GRONZH-ee-un”) have this property. The correspondence of quantities with this property to differentiable symmetries of the action is described by (*) Noether’s theorem (“NUR-turz”). By definition, kinetic energy has this property in elastic collisions. In the absence of external forces, momentum has this property because its time derivative equals zero. For 10 points, name this property of quantities that do not change as a system evolves. ■END■
Summary
2023 PACE NSC | 06/10/2023 | Y | 35 | 100% | 6% | 0% | 78.09 |
Buzzes
Player | Team | Opponent | Buzz Position | Value |
---|---|---|---|---|
Ali Hamzeh | Kinkaid | University Lab | 38 | 0 |
Michael Karpov | Barrington A | Rockford Auburn A | 47 | 20 |
Shreyas Singh | University Lab | Kinkaid | 60 | 20 |
Charles Heydt | Midtown | Lincoln-Way East | 64 | 10 |
Joshua Fan | Richard Montgomery | Detroit Catholic Central A | 65 | 0 |
Sam Macchi | Belmont | Hunter A | 65 | 10 |
Anvith Vanukuri | William Fremd | Maggie Walker A | 65 | 10 |
Dylan Cheng | Thomas Jefferson A | Detroit Country Day | 65 | 10 |
Aneesh Swaminathan | Plymouth | Dallas County | 67 | 10 |
Sohum Sukhatankar | St. Mark's | Winston Churchill A | 67 | 0 |
Aakash Sanjay | Johns Creek A | Dunbar | 69 | 10 |
Aatreyo Bhattacharyya | Mira Loma | Thomas Jefferson B | 72 | 10 |
Sanjay Ranjith | Thomas Jefferson D | Walter Payton | 72 | 10 |
Evan Lin | Woodland | Canyon Crest | 74 | 10 |
Anthony Chalhoub | Detroit Catholic Central B | Detroit Catholic Central C | 74 | 10 |
Ryan Dai | Carbondale | Chattahoochee B | 75 | 10 |
Jingyi Wu | Stevenson A | Winston Churchill B | 75 | 10 |
Kyunghwan Lim | Chattahoochee A | Choate Rosemary Hall | 75 | 10 |
Rohan Dalal | Johns Creek B | Winnebago | 75 | 10 |
Vincent Wang | Irvington A | Heights | 75 | 10 |
Hatice Caliskan | Carl Sandburg | Innovation Academy A | 75 | 10 |
Brielle Rach | Rockford Auburn B | Maggie Walker B | 75 | 10 |
Yashwanth Bajji | Troy | Solon | 75 | 10 |
Aaryan Sumesh | Thomas Jefferson C | Northmont A | 75 | 10 |
Kaushik Gollamudi | Barrington B | Maggie Walker C | 75 | 10 |
Aryan Pathak | Lake Highland | Cincinnati Hills Christian | 75 | 10 |
Miles Sierra | Waukee | Moberly | 78 | 10 |
Jeffrey Liu | Hinsdale Central | New Brighton | 78 | 10 |
Nolan King | Elkhorn North | Hunter B | 78 | 10 |
David Bertolasi | Belvidere | Washington | 78 | 10 |
Armaan Ahmed | Mercer County | Hoover B | 79 | 10 |
Thomas Belcher | Saint Joseph | Stevenson B | 81 | 10 |
Anna Rosato | John Adams A | Innovation Academy B | 105 | 10 |
Anish Jindal | Parkway West | Mexico | 106 | 10 |
Jacob Barta | Detroit Catholic Central A | Richard Montgomery | 107 | 10 |
Andy Yu | Winston Churchill A | St. Mark's | 108 | 10 |
Kevin Adler | Northmont B | West Point | 108 | 10 |
Eavan Kelly | John Adams B | Norman | 108 | 10 |