scholarly journals A computational proof of complexity of some restricted counting problems

2011 ◽  
Vol 412 (23) ◽  
pp. 2468-2485 ◽  
Author(s):  
Jin-Yi Cai ◽  
Pinyan Lu ◽  
Mingji Xia
Keyword(s):  
Counting Problems

Media Clips: Boulder Lottery; The Probability of Slot Machines

2013 ◽  
Vol 107 (3) ◽  
pp. 172-175
Author(s):  
Kristy B. McGowan ◽  
Nathan J. Lowe Spicer
Keyword(s):  
Slot Machines ◽  
Counting Problems ◽  
State Lottery ◽  
The Media

Students analyze items from the media to answer mathematical questions related to the article. The clips this month, from the Colorado State lottery and a Marilyn vos Savant column on probability, involve probability and counting problems.

Informing Practice: Counting Using Sets of Outcomes

2012 ◽  
Vol 18 (3) ◽  
pp. 132-135 ◽  
Author(s):  
Elise Lockwood
Keyword(s):  
Counting Problems

A branch of mathematics—combinatorics—is explored through counting problems.

scholarly journals LOOPS, SURFACES AND GRASSMANN REPRESENTATION IN TWO- AND THREE-DIMENSIONAL ISING MODELS

1999 ◽  
Vol 14 (29) ◽  
pp. 4549-4574 ◽  
Author(s):  
C. R. GATTRINGER ◽  
S. JAIMUNGAL ◽  
G. W. SEMENOFF
Keyword(s):  
Three Dimensional ◽  
Ising Models ◽  
Algebraic Representation ◽  
Simple Derivation ◽  
Counting Problems ◽  
Intrinsic Geometry ◽  
Geometry Factor ◽  
Loop Expansion ◽  
Loop Surface

We construct an algebraic representation of the geometrical objects (loop and surface variables) dual to the spins in 2 and 3D Ising models. This algebraic calculus is simpler than dealing with the geometrical objects, in particular when analyzing geometry factors and counting problems. For the 2D case we give the corrected loop expansion of the free energy and the radius of convergence for this series. For the 3D case we give a simple derivation of the geometry factor which prevents overcounting of surfaces in the intrinsic geometry representation of the partition function, and find a classification of the surfaces to be summed over. For 2 and 3D we derive a compact formula for 2n-point functions in loop (surface) representation.

Definability of optimization and counting problems

2004 ◽  
pp. 251-262
Author(s):  
Richard Lassaigne ◽  
Michel de Rougemont
Keyword(s):  
Counting Problems

scholarly journals Dating of seasonal snow/firn accumulation layers using pollen analysis

2005 ◽  
Vol 51 (174) ◽  
pp. 483-490 ◽  
Author(s):  
Fumio Nakazawa ◽  
Koji Fujita ◽  
Nozomu Takeuchi ◽  
Toshiyuki Fujiki ◽  
Jun Uetake ◽  
...  
Keyword(s):  
Wind Erosion ◽  
Pollen Grains ◽  
Ice Cores ◽  
Altai Mountains ◽  
Counting Problems ◽  
Annual Layer ◽  
Alpine Glaciers ◽  
Pollen Species ◽  
Dating Method ◽  
Precipitation Records

AbstractReliable chronologies in ice cores and snow pits from many alpine glaciers in latitudes between 60° N and 60° S are often difficult to establish owing to problems with annual-layer counting. Problems arise from melting, wind erosion and the negligible amount of precipitation in some seasons, all of which tend to obscure the seasonal variations in δ18O and chemical concentrations that are typically used to date ice cores. However, alpine glaciers contain many species of pollen grains that peak at particular times of the year. We used the peaks in Betulaceae, Pinus, Artemisia and a combination of Abies and Picea pollen species to determine the four seasonal layers of a snow pit on Belukha glacier in Russia’s Altai Mountains. Comparing the pollen-dated profiles with wind and precipitation records allows us to determine where a seasonal layer is missing. Thus, the pollen-dating method described here may be a useful tool to measure the annual snow deposition on alpine glaciers, even when some seasonal layers are eroded by wind or missing due to negligible precipitation.

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