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Longer titles found: Partition function (mathematics) (view), Partition function (number theory) (view), Partition function (quantum field theory) (view), Partition function (statistical mechanics) (view), Partition function for Interacting RNAs (view), Kostant partition function (view), Rotational partition function (view), Vibrational partition function (view), Translational partition function (view)

searching for Partition function 106 found (421 total)

alternate case: partition function

Arf invariant of a knot (739 words) [view diff] exact match in snippet view article find links to article

Jones showed that the Arf invariant can be obtained by taking the partition function of a signed planar graph associated to a knot diagram. This approach

MapReduce (5,480 words) [view diff] exact match in snippet view article find links to article

a particular reducer by the application's partition function for sharding purposes. The partition function is given the key and the number of reducers

Ramanujan's congruences (954 words) [view diff] exact match in snippet view article find links to article

mathematics, Ramanujan's congruences are the congruences for the partition function p(n) discovered by Srinivasa Ramanujan: p ( 5 k + 4 ) ≡ 0 ( mod 5

Probalign (792 words) [view diff] exact match in snippet view article find links to article

partition function posterior probabilities. Base pair probabilities are estimated using an estimate similar to Boltzmann distribution. The partition function

Einstein solid (1,958 words) [view diff] exact match in snippet view article find links to article

capacities. Heat capacity is obtained through the use of the canonical partition function of a simple quantum harmonic oscillator. Z = ∑ n = 0 ∞ e − E n / k

Self-consistency principle in high energy physics (750 words) [view diff] exact match in snippet view article find links to article

approach to the high energy collisions first proposed by E. Fermi. The partition function of the fireballs can be written in two forms, one in terms of its

Bruria Kaufman (873 words) [view diff] exact match in snippet view article find links to article

applied spinor analysis to rederive the result of Lars Onsager on the partition function of the two-dimensional Ising model, and to the study of the Mössbauer

Supersymmetric localization (383 words) [view diff] exact match in snippet view article find links to article

operators in certain supersymmetric quantum field theories such as the partition function, supersymmetric Wilson loops, etc. The method can be seen as an extension

Field-theoretic simulation (748 words) [view diff] exact match in snippet view article find links to article

possibility is to use Monte Carlo (MC) algorithms, to sample the full partition function integral expressed in field-theoretic representation. The procedure

Field-theoretic simulation (748 words) [view diff] exact match in snippet view article find links to article

possibility is to use Monte Carlo (MC) algorithms, to sample the full partition function integral expressed in field-theoretic representation. The procedure

Modular invariance (90 words) [view diff] exact match in snippet view article find links to article

anomalies. Equivalently, in two-dimensional conformal field theory the torus partition function must be invariant under the modular group SL(2,Z). v t e

Joan van der Waals (895 words) [view diff] exact match in snippet view article find links to article

his paper on the canonical partition function for clathrates, along with J. C. Platteeuw. To create this partition function, van der Waals made a number

H-stable potential (1,041 words) [view diff] exact match in snippet view article find links to article

potential is not H-stable, it is not possible to define a grand canonical partition function in finite volume, because of catastrophic configurations with infinite

Hard hexagon model (1,523 words) [view diff] exact match in snippet view article find links to article

configurations. For a triangular lattice with N sites, the grand partition function is Z ( z ) = ∑ n z n g ( n , N ) = 1 + N z + 1 2 N ( N − 7 ) z 2 +

Gopakumar–Vafa invariant (633 words) [view diff] exact match in snippet view article find links to article

invariants can be viewed as a partition function in topological quantum field theory. They are proposed to be the partition function in Gopakumar–Vafa form:

GSO projection (281 words) [view diff] exact match in snippet view article find links to article

the OPE of any two operators in the set A. Modular invariance — The partition function on the two-torus of the theory containing only the operators in A

A. O. L. Atkin (372 words) [view diff] exact match in snippet view article find links to article

Atkin. Atkin is also known for his work on properties of the integer partition function and the monster module. He was a vocal fan of using computers in mathematics

Thermal quantum field theory (1,167 words) [view diff] exact match in snippet view article find links to article

is recast as a variation in the Euclidean metric. Analysis of the partition function leads to an equivalence between thermal variations and the curvature

Quicksort (9,925 words) [view diff] exact match in snippet view article find links to article

gets swapped with other elements in the partition function. Therefore, the index returned in the partition function isn't necessarily where the actual pivot

Boltzmann distribution (2,496 words) [view diff] exact match in snippet view article find links to article

The partition function can be calculated if we know the energies of the states accessible to the system of interest. For atoms the partition function values

Hansraj Gupta (375 words) [view diff] exact match in snippet view article find links to article

mathematician specialising in number theory, in particular the study of the partition function. Gupta was born 9 October 1902 in Rawalpindi, then part of British

Two-dimensional conformal field theory (5,674 words) [view diff] exact match in snippet view article find links to article

but also their correlation functions are multivalued. The torus partition function is a particular correlation function that depends solely on the spectrum

Entropy (statistical thermodynamics) (2,621 words) [view diff] exact match in snippet view article

_{\text{mic}}} is the microcanonical partition function Z can {\displaystyle Z_{\text{can}}} is the canonical partition function Z gr {\displaystyle {\mathcal

Entropy (statistical thermodynamics) (2,621 words) [view diff] exact match in snippet view article

_{\text{mic}}} is the microcanonical partition function Z can {\displaystyle Z_{\text{can}}} is the canonical partition function Z gr {\displaystyle {\mathcal

Superstatistics (551 words) [view diff] exact match in snippet view article find links to article

}d\beta f(\beta )\exp(-\beta E).} This defines the superstatistical partition function Z = ∑ i = 1 W B ( E i ) {\displaystyle Z=\sum _{i=1}^{W}B(E_{i})}

Critical three-state Potts model (1,747 words) [view diff] exact match in snippet view article find links to article

is considered to be the simplest minimal model with a non-diagonal partition function in Virasoro characters, as well as the simplest non-trivial CFT with

Neutral network (evolution) (2,832 words) [view diff] exact match in snippet view article

a polynomial time DP algorithm for computing the full equilibrium partition function of an RNA secondary structure. This changed the dominant calculation

Hagedorn temperature (975 words) [view diff] exact match in snippet view article find links to article

line of reasoning was well known to be false even to Hagedorn. The partition function for creation of hydrogen–antihydrogen pairs diverges even more rapidly

Spin foam (769 words) [view diff] exact match in snippet view article find links to article

Freidel (FK model) and Jerzy Lewandowski (KKL model). The summary partition function for a spin foam model is Z := ∑ Γ w ( Γ ) [ ∑ j f , i e ∏ f A f (

ViennaRNA Package (801 words) [view diff] exact match in snippet view article find links to article

folding of RNA secondary structures RNA2Dfold Compute MFE structure, partition function and representative sample structures of k,l neighborhoods RNAaliduplex

Two-dimensional critical Ising model (3,287 words) [view diff] exact match in snippet view article find links to article

ϵ , σ {\displaystyle 1,\epsilon ,\sigma } . The modular invariant partition function is Z ( q ) = | χ 0 ( q ) | 2 + | χ 1 16 ( q ) | 2 + | χ 1 2 ( q )

Supersymmetric theory of stochastic dynamics (6,105 words) [view diff] exact match in snippet view article find links to article

the finite-time GTO is larger than unity. Under this condition, the partition function, Z t t ′ = T r M ^ t t ′ = ∑ α e − ( t − t ′ ) H α , {\displaystyle

List of RNA structure prediction software (8,455 words) [view diff] exact match in snippet view article find links to article

1007/BF00818163. S2CID 19344304. McCaskill JS (1990). "The equilibrium partition function and base pair binding probabilities for RNA secondary structure".

Thermal fluctuations (1,707 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\mathcal {Z}}(\beta )} , which is referred to as the partition function, or generating function. The latter name is due to the fact that the

Laser-induced breakdown spectroscopy (2,440 words) [view diff] exact match in snippet view article find links to article

degeneracy of the upper level i (2J+1) U ( T ) {\displaystyle U(T)} is the partition function (unitless) E i {\displaystyle E_{i}} is the energy level of the upper

Nikita Nekrasov (580 words) [view diff] exact match in snippet view article find links to article

gauge theory, quantum integrability, and string theory. The Nekrasov partition function, which he introduced in his 2002 paper, relates in an intricate way

Albert Schwarz (625 words) [view diff] exact match in snippet view article find links to article

A12(7):1405–1429, 1997. V. Kac, A. Schwarz, Geometric interpretation of the partition function of 2D gravity, Phys. Lett. B257 (1991), nos. 3–4, 329–334. A. A. Belavin

Chern–Simons form (611 words) [view diff] exact match in snippet view article find links to article

University of Texas. Retrieved June 7, 2019. Schwartz, A. S. (1978). "The partition function of degenerate quadratic functional and Ray-Singer invariants". Letters

Ultraviolet catastrophe (1,050 words) [view diff] exact match in snippet view article find links to article

λ is the wavelength of light. By applying this new energy to the partition function in statistical mechanics, Planck's assumptions led to the correct

Al-Salam–Chihara polynomials (403 words) [view diff] exact match in snippet view article find links to article

28(2), 199-218. Ishikawa, M., & Zeng, J. (2009). The Andrews–Stanley partition function and Al-Salam–Chihara polynomials. Discrete Mathematics, 309(1), 151-175

Massless free scalar bosons in two dimensions (3,687 words) [view diff] exact match in snippet view article find links to article

the compactified free boson CFT exists on any Riemann surface. Its partition function on the torus C Z + τ Z {\displaystyle {\frac {\mathbb {C} }{\mathbb

Rudin–Shapiro sequence (2,732 words) [view diff] exact match in snippet view article find links to article

S(N,x)=\sum _{0\leq n<2^{N}}\exp(2\pi ixu(n,N)).} Recall that the partition function of the one-dimensional Ising model can be defined as follows. Fix

List of sequence alignment software (2,358 words) [view diff] exact match in snippet view article find links to article

Nucleotide Local B. Ma et al. 2002–2004 ProbA (also propA) Stochastic partition function sampling via dynamic programming Both Global U. Mückstein 2002 PyMOL

Selberg integral (1,012 words) [view diff] exact match in snippet view article find links to article

Dyson (1963), who were unaware of Selberg's earlier work. It is the partition function for a gas of point charges moving on a line that are attracted to

Euler numbers (2,049 words) [view diff] case mismatch in snippet view article find links to article

A1. Malenfant, J. (2011). "Finite, Closed-form Expressions for the Partition Function and for Euler, Bernoulli, and Stirling Numbers". arXiv:1103.1585 [math

Likelihood function (8,546 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbf {T} (x)} ⁠, minus the normalization factor (log-partition function) ⁠ A ( η ) {\displaystyle A({\boldsymbol {\eta }})} ⁠. Thus for example

Jennifer Tour Chayes (1,216 words) [view diff] exact match in snippet view article find links to article

Chayes, Jennifer; M. Biskup; C. Borgs; L. Kleinwaks; Kotecky (2004), "Partition function zeros at first-order phase transitions: A general analysis", Communications

Dyadic transformation (4,718 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \beta } be the inverse temperature for the system, the partition function for this model is given by Z = ∑ { σ i = ± 1 , i ∈ Z 2 N } ∏ i ∈ Z

Glossary of string theory (5,167 words) [view diff] exact match in snippet view article find links to article

Coleman–Mandula theorem. Hagedorn temperature The temperature above which the partition function diverges due to the exponentially increasing number of string states

George Stanley Rushbrooke (755 words) [view diff] exact match in snippet view article find links to article

1098/rspa.1953.0017. Rushbrooke, G S; Eve, J (1962). "High-temperature partition function and refated noncrossing polygons for the simple cubic lattice". Journal

Black hole thermodynamics (3,223 words) [view diff] exact match in snippet view article find links to article

microstate ensemble for black holes is the microcanonical ensemble. The partition function for black holes results in a negative heat capacity. In canonical

Network entropy (3,470 words) [view diff] exact match in snippet view article find links to article

)=Tr[e^{-\beta L}]} is a normalizing factor which plays the role of the partition function, and β {\displaystyle \beta } is a tunable parameter which allows

Instanton (6,385 words) [view diff] exact match in snippet view article find links to article

{\text{Im}}Z_{k}} whereby Z k {\displaystyle Z_{k}} is the canonical partition function, which is calculated by taking the trace of the Boltzmann operator

Goldbach's conjecture (3,720 words) [view diff] exact match in snippet view article find links to article

are believed to be of roughly comparable difficulty. The Goldbach partition function is the function that associates to each even integer the number of

Unruh effect (2,946 words) [view diff] exact match in snippet view article find links to article

} A path integral with real time coordinate is dual to a thermal partition function, related by a Wick rotation. The periodicity β {\displaystyle \beta

Rotamer (3,949 words) [view diff] exact match in snippet view article find links to article

the absolute temperature. The denominator of the right side is the partition function. The effects of electrostatic and steric interactions of the substituents

Vertex operator algebra (8,938 words) [view diff] exact match in snippet view article find links to article

–z−n–1∂z as n ranges over integers greater than 1. The module then has partition function T r V q L 0 = ∑ n ∈ R dim ⁡ V n q n = ∏ n ≥ 2 ( 1 − q n ) − 1 {\displaystyle

Connective constant (2,354 words) [view diff] exact match in snippet view article find links to article

to b {\displaystyle b} . The aim of the proof is to show that the partition function Z ( x ) = ∑ γ : a → H x ℓ ( γ ) = ∑ n = 0 ∞ c n x n {\displaystyle

Fundamental thermodynamic relation (2,676 words) [view diff] exact match in snippet view article find links to article

{\textstyle \Pr(i)\propto f(E_{i},T)} . The normalization factor (partition function) is therefore Z = ∑ i f ( E i , T ) . {\displaystyle Z=\sum _{i}f(E_{i}

Radial distribution function (4,541 words) [view diff] exact match in snippet view article find links to article

\mathbf {r} _{N})=\sum _{i=1}^{N}U_{1}(\mathbf {r} _{i})} , then the partition function factorizes, and the probability of an elementary configuration decomposes

Multi-key quicksort (700 words) [view diff] exact match in snippet view article find links to article

., a[length(a)−1][d] or some random character in that range. The partition function is a variant of the one used in ordinary three-way quicksort: it rearranges

Light-front quantization applications (9,006 words) [view diff] exact match in snippet view article find links to article

partition function in light-front quantization has been developed and numerical methods are under development for evaluating this partition function in

Entropic gravity (3,736 words) [view diff] exact match in snippet view article find links to article

C.; Jeynes, C. (21 April 2021). "Entropic uncertainty principle, partition function and holographic principle derived from Liouville's Theorem". Physics

Superselection (2,429 words) [view diff] exact match in snippet view article find links to article

path integral, this is a quantum phase transition, in a classical partition function, a classical phase transition. So as t moves toward more negative

Robert Churchhouse (867 words) [view diff] exact match in snippet view article find links to article

Churchhouse, Robet F. (1969). "Congruence properties of the binary partition function". Mathematical Proceedings of the Cambridge Philosophical Society

Partial sorting (952 words) [view diff] no match in snippet view article find links to article

pivot falls in position k or later, we recurse only on the left partition: function partial_quicksort(A, i, j, k) is if i < j then p ← pivot(A, i, j)

Kramers–Wannier duality (1,653 words) [view diff] exact match in snippet view article find links to article

=1/kT} . The low temperature expansion of the N {\displaystyle N} spin partition function Z N {\displaystyle Z_{N}} for (K*,L*) obtained from the standard expansion

Kramers–Wannier duality (1,653 words) [view diff] exact match in snippet view article find links to article

=1/kT} . The low temperature expansion of the N {\displaystyle N} spin partition function Z N {\displaystyle Z_{N}} for (K*,L*) obtained from the standard expansion

N-vector model (1,193 words) [view diff] exact match in snippet view article find links to article

vectors, the corresponding lines combine into closed loops, and the partition function becomes a sum over loop configurations: Z = ∑ L ∈ L K E ( L ) n |

Bethe lattice (1,948 words) [view diff] exact match in snippet view article find links to article

magnetic field. The Ising model on the Bethe lattice is defined by the partition function Z = ∑ { σ } exp ⁡ ( K ∑ ( i , j ) σ i σ j + h ∑ i σ i ) . {\displaystyle

Maxwell–Jüttner distribution (2,911 words) [view diff] exact match in snippet view article find links to article

obtains: Hence, Or The inverse of the normalization constant gives the partition function Z ≡ 1 N : {\displaystyle Z\equiv {\frac {1}{N}}:} Therefore, the normalized

Louise Gray Young (552 words) [view diff] exact match in snippet view article find links to article

1016/0019-1035(70)90007-2 L Gray Young. (August 1971). "Calculation of the partition function for 14N216O". Journal of Quantitative Spectroscopy and Radiative Transfer

Spenta R. Wadia (857 words) [view diff] exact match in snippet view article find links to article

Hawking’s calculation in gravity; vii) for dualities involving the partition function and S-matrix of fermions and bosons coupled to 2+1 dim Chern-Simons

Game theory (15,399 words) [view diff] exact match in snippet view article find links to article

Lucas, William F. (1963), " n {\displaystyle n} -person games in partition function form", Naval Research Logistics Quarterly, 10 (4): 281–298, doi:10

Density of states (5,573 words) [view diff] exact match in snippet view article find links to article

states can also be understood as the derivative of the microcanonical partition function Z m ( E ) {\displaystyle Z_{m}(E)} (that is, the total number of states

Specific heat capacity (8,537 words) [view diff] case mismatch in snippet view article find links to article

New York, NY: University Science Books. pp. 83–85. "6.6: Electronic Partition Function". Chemistry LibreTexts. 2020-11-26. Retrieved 2024-12-16. Bonhoeffer

Atiyah–Singer index theorem (7,553 words) [view diff] exact match in snippet view article find links to article

displaying short descriptions of redirect targets Witten index – Modified partition function Atiyah & Singer 1963. Kayani 2020. Hamilton 2020, p. 11. Gel'fand

Dynamic programming (9,283 words) [view diff] exact match in snippet view article find links to article

"Cooperative phenomena in homopolymers: An alternative formulation of the partition function", Biopolymers, 13 (7): 1511–1512, doi:10.1002/bip.1974.360130719 Gurskiĭ

Cyclometer (3,070 words) [view diff] case mismatch in snippet view article find links to article

partitions of n (the partition numbers)" https://oeis.org/A000041; "Partition Function P(n)", stating "gives the number of ways of writing the integer n

Belleville washer (2,570 words) [view diff] exact match in snippet view article find links to article

to stack n {\displaystyle {n}} washers is defined by the integer partition function p(n) and increases rapidly with large n {\displaystyle {n}} , allowing

Gaussian network model (4,574 words) [view diff] exact match in snippet view article find links to article

^{-1}\right)^{-1}\Delta X\right)\right\}} The normalization constant, also the partition function ZX, is given by Z X = ∫ 0 ∞ exp ⁡ { − 1 2 ( Δ X T ( k B T γ Γ − 1

Yang–Baxter equation (3,340 words) [view diff] exact match in snippet view article find links to article

Bibcode:1944PhRv...65..117O. doi:10.1103/PhysRev.65.117. Baxter, R. J. (1972). "Partition function of the Eight-Vertex lattice model". Annals of Physics. 70 (1). Elsevier:

Probabilistic soft logic (2,120 words) [view diff] exact match in snippet view article find links to article

}\exp(\sum _{i=1}^{k}w_{i}\phi _{i}(\mathbf {x} ,\mathbf {y} ))} is the partition function. This density is a logarithmically convex function, and thus the common

Combining rules (1,898 words) [view diff] exact match in snippet view article find links to article

Delhommelle, Jerome (14 March 2014). "Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. III. Impact of combining rules

Robert Penner (1,273 words) [view diff] exact match in snippet view article find links to article

punctured surfaces including the so-called Penner matrix model, the basic partition function for Riemann's moduli space. Extending the foregoing to orientation-preserving

Random energy model (1,433 words) [view diff] exact match in snippet view article find links to article

temperature β c = 2 ln ⁡ 2 {\displaystyle \beta _{c}=2{\sqrt {\ln 2}}} . Partition function Z ( β ) = ∑ s e − β H ( s ) {\displaystyle Z(\beta )=\sum _{s}e^{-\beta

Stirling numbers of the first kind (7,262 words) [view diff] exact match in snippet view article find links to article

Malenfant, Jerome (2011). "Finite, closed-form expressions for the partition function and for Euler, Bernoulli, and Stirling numbers". arXiv:1103.1585 [math

Nucleic acid structure prediction (3,715 words) [view diff] exact match in snippet view article find links to article

PMC 514697. PMID 15294028. McCaskill JS (1990). "The equilibrium partition function and base pair binding probabilities for RNA secondary structure".

Ralph Kenna (3,225 words) [view diff] case mismatch in snippet view article find links to article

R.; Lang, C.B. (1991). "Finite-Size Scaling and the Zeroes of the Partition Function in the φ 4 4 {\displaystyle \varphi _{4}^{4}} Model". Physics Letters

Probabilistic context-free grammar (5,242 words) [view diff] case mismatch in snippet view article find links to article

AAAI Press. pp. 143–153. McCaskill J. S. (1990). "The Equilibrium Partition Function and Base Pair Binding Probabilities for RNA Secondary Structure".

Theoretical astronomy (3,882 words) [view diff] exact match in snippet view article find links to article

deduce Feynman's imaginary-time functional integral for the canonical partition function. Reaction equations and large reaction networks are an important tool

John McCaskill (940 words) [view diff] exact match in snippet view article find links to article

doi:10.1002/9780470141243.ch4 McCaskill, John (1990). "The equilibrium partition function and base pair binding probabilities for RNA secondary structure".

Correlation function (statistical mechanics) (3,959 words) [view diff] exact match in snippet view article

plays a significant role in nonequilibrium statistical mechanics as partition function does in equilibrium statistical mechancis. For instance, transport

Lambert series (3,873 words) [view diff] exact match in snippet view article find links to article

products whose lower triangular entries are given in terms of the partition function and the Möbius function by the divisor sums s n , k ( − 1 ) = ∑ d

Bernoulli number (13,056 words) [view diff] exact match in snippet view article find links to article

Malenfant, Jerome (2011), "Finite, closed-form expressions for the partition function and for Euler, Bernoulli, and Stirling numbers", arXiv:1103.1585 [math

Higher-spin theory (5,905 words) [view diff] exact match in snippet view article find links to article

sense. One begins with the free O ( N ) {\displaystyle O(N)} model partition function and performs a change of variables by passing from the O ( N ) {\displaystyle

Twelvefold way (5,609 words) [view diff] exact match in snippet view article find links to article

answer in terms of combinatorial functions (Stirling numbers and the partition function for a given number of parts). The incorporation of classical enumeration

Martin H. Krieger (1,858 words) [view diff] case mismatch in snippet view article find links to article

Mathematical Physics: Structure, Tricks, and Lacunae in Derivations of the Partition Function of the Two-Dimensional Ising Model and in Proofs of The Stability

Superradiant phase transition (2,436 words) [view diff] exact match in snippet view article find links to article

the Rabi frequency. One can approximately calculate the canonical partition function Z = ∑ ± , n e − β E ± ( n ) ≈ ∑ ± ∫ e − β E ± ( n ) d n = ∫ e Φ (

Classical nucleation theory (4,710 words) [view diff] exact match in snippet view article find links to article

methods of statistical mechanics hold at least approximately. The grand partition function is Q = ∑ N = 0 ∞ z N ∑ μ S | N e − β H N ( μ S ) , z ≡ e β μ . {\displaystyle

Aquilanti–Mundim deformed Arrhenius model (4,903 words) [view diff] exact match in snippet view article find links to article

functions of the reactants, and Q ‡ {\displaystyle Q^{\ddagger }} is the partition function of the activated complex. In Ref., the significance of the parameter

Frank A. Weinhold (1,956 words) [view diff] exact match in snippet view article find links to article

water and other pure substances. QCE predictions are based on a model partition function composed from an equilibrium mixture of molecular clusters {Mn}, each

Virasoro conformal block (6,417 words) [view diff] exact match in snippet view article find links to article

spectrum can be derived from the modular invariance of the torus partition function, leading in particular to the ADE classification of minimal models

Light front quantization (12,723 words) [view diff] exact match in snippet view article find links to article

Develop numerical methods/computer codes to directly evaluate the partition function (viz. thermodynamic potential) as the basic thermodynamic quantity

Leiden algorithm (3,129 words) [view diff] no match in snippet view article find links to article

P_refined. */ end for return P_refined /* return newly refined partition. */ function refine_partition_subset(Graph G, Partition P, Subset S) R = {v |

Deaths in November 1988 (4,919 words) [view diff] exact match in snippet view article find links to article

II Luftwaffe fighter ace. Hansraj Gupta, 86, Indian mathematician (partition function). Wieland Herzfelde, 92, German publisher and writer. Richard Lonsdale