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Mathematizing C++ concurrency

Mark Batty, Scott Owens, Susmit Sarkar, Peter Sewell, Tjark Weber
2011 Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '11  
In this paper we establish a mathematical (yet readable) semantics for C++ concurrency.  ...  Shared-memory concurrency in C and C++ is pervasive in systems programming, but has long been poorly defined.  ...  Acknowledgements This work would not have been possible without discussions with members of the C++ Concurrency subcommittee and the cpp-threads mailing list, including Hans Boehm, Lawrence Crowl, Peter  ... 
doi:10.1145/1926385.1926394 dblp:conf/popl/BattyOSSW11 fatcat:i4hrcm7yi5fgbj6kxhfsbv2kja

Mathematizing C++ concurrency

Mark Batty, Scott Owens, Susmit Sarkar, Peter Sewell, Tjark Weber
2011 SIGPLAN notices  
In this paper we establish a mathematical (yet readable) semantics for C++ concurrency.  ...  Shared-memory concurrency in C and C++ is pervasive in systems programming, but has long been poorly defined.  ...  Acknowledgements This work would not have been possible without discussions with members of the C++ Concurrency subcommittee and the cpp-threads mailing list, including Hans Boehm, Lawrence Crowl, Peter  ... 
doi:10.1145/1925844.1926394 fatcat:nhbpkrhadndevmnwfg6v725p3a

A theorem on concurrent Euler lines

C. J. Bradley
2006 Mathematical Gazette  
In the configuration, illustrated in Figure 1, ABC is a triangle with I 1; I 2, I 3 the excentres opposite A, B, C respectively.  ...  -a 2 b(b + c) c(b + c) This reduces to (c 2 -b 2 )x + a(c -a)y + a(a -b)z = 0. (1) Step 2: To find the point of concurrence X of L\, La, L$ The equations of Li and L3 may be obtained from equation (1)  ...  Then the following results hold: (1) L\, L2, L3 are concurrent at a point X with areal coordinates, with respect to ABC as triangle of reference, l a b c \ \b -C* c -a a -bl (2) IxEi (t), 1 2 E 2 (0,13E3  ... 
doi:10.1017/s0025557200180210 fatcat:6if342gimfhnlag4nqk5vdf36m

Justification of concurrent engineering environments based on fuzzy mathematics

M.-C. Wu
1998 International Journal of Production Research  
C. The author also thanks Prof. J. H. Rogerson for providing valuable suggestions on the work.  ...  -C. Wu Mathematical programming Some studies adopt a mathematical programming approach to model the concurrent interaction of product and process factors.  ...  Compared with previously mentioned CE techniques, the mathematical programming approach is relatively more`concurrent'.  ... 
doi:10.1080/002075498193093 fatcat:hday7be3r5hdzj7lvgutuu4cxm

Modeling the dynamics of concurrent computing systems

Juan L.G. Guirao, Fernando L. Pelayo, Jose C. Valverde
2011 Computers and Mathematics with Applications  
This paper presents a very first step on the road to applying the theory of discrete dynamical systems (DDSs) in the analysis of concurrent computing systems.  ...  Petri nets are widely used for modeling and analyzing concurrent systems, because of their graphical nature and the solid mathematical foundations supporting them.  ...  A dynamical system is the mathematical formalization of a deterministic process, created to deal with these kinds of challenges.  ... 
doi:10.1016/j.camwa.2011.01.008 fatcat:3mzrqtvi7jajbhoo77soiqv4wu

Notes on "Modeling the dynamics of concurrent computing systems"

Fernando L. Pelayo, Jose C. Valverde
2012 Computers and Mathematics with Applications  
This opened up a new perspective for working with concurrent computing systems.  ...  Often, this problem is formalized mathematically by adding a parameter in the expression of the evolution operator.  ... 
doi:10.1016/j.camwa.2011.12.079 fatcat:y4hfbie2rfcppcurguysxp6ayi

69. In a Spherical Quadrangle the Arcs Joining the Mid-Points of the Three Pairs of Opposite Sides Are Concurrent

J. C. Palmer
1899 Mathematical Gazette  
That is, the arcs LL', MM', NN' are concurrent. COR.  ...  That is, the arcs LL', MM', NN' are concurrent. COR.  ... 
doi:10.2307/3603493 fatcat:r4uakdp2zvfwnjeey4eiuc372i

Graph-Based Software Design for Managing Complexity and Enabling Concurrency in Multiphysics PDE Software

Patrick K. Notz, Roger P. Pawlowski, James C. Sutherland
2012 ACM Transactions on Mathematical Software  
Mathematical expressions are represented as software objects that directly expose data dependencies.  ...  ACM Transactions on Mathematical Software, Vol. 39, No. 1, Article 1, Publication date: November 2012.  ...  concurrency.  ... 
doi:10.1145/2382585.2382586 fatcat:wnzlpf6ucvd25ope22xk2rr3ui

68. In a Spherical Quadrangle the Arcs Joining the Middle Points of the Three Pairs of Opposite Sides Are Concurrent

J. C. Palmer
1898 Mathematical Gazette  
THE MATHEMATICAL GAZETTE.  ...  MATHEMATICAL NOTES. MATHEMATICAL NOTES. The fact of the problem being given in a work on trigonometry does not appear to render a geometrical solution inadmissible.  ... 
doi:10.2307/3603167 fatcat:i5cbqf4ldrczxoa5u5mqe4cyna

A model on the impact of treating typhoid with anti-malarial: dynamics of malaria concurrent and co-infection with typhoid

Okaka C. Akinyi, Mugisha J.Y.T., Manyonge A., Ouma C.
2015 International Journal of Mathematical Analysis  
In this paper we have formulated a mathematical model of malariatyphoid concurrent and co-infection to establish the effect of misdiagnosing typhoid as malaria and hence treating it with anti-malarials  ...  I acknowledge with thanks the department of Mathematics of Makerere University for their assistance and hospitality, School of Mathematics Maseno University for their continued support and the Kenya National  ...  In this study we have developed a mathematical model for the dynamics of misdiagnosis of typhoid as malaria in malaria-tyhpoid concurrent and co-infection.  ... 
doi:10.12988/ijma.2015.412403 fatcat:6r4ssd6jzrgkvjpouozyd3hs64

Dynamic multi-rigid-body systems with concurrent distributed contacts

J. C. Trinkle, J. A. Tzitzouris, J. S. Pang
2001 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
Consider a system of rigid bodies with multiple concurrent contacts.  ...  The generalized dynamic multi-rigid-body problem with concurrent distributed frictional contacts is to find contact forces (c in , c it , c io , c ir ) and accelerations (a in , a it , a io , a ir ) satisfying  ...  The Model The derivation of our mathematical model describing the motion of a system of rigid bodies with locally planar, finite areas of contact is analogous to the model with isolated point contacts  ... 
doi:10.1098/rsta.2001.0911 fatcat:xn2cb76wyjbu3mtnj55dq4qsqy

Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: Mathematical modelling guides dose optimisation to minimise neutropenia

Morgan Craig, Antony R. Humphries, Fahima Nekka, Jacques Bélair, Jun Li, Michael C. Mackey
2015 Journal of Theoretical Biology  
Based on up-to-date knowledge and rational considerations, we develop here a physiologically-realistic model to mathematically characterise the neutrophil production in the bone marrow which we then integrate  ...  Accordingly, we model the increase in the death rate for the stem cells during chemotherapy as γ chemo S (C p (t)) = γ homeo S + h S C p , (17) where γ chemo Concurrently, the rate of proliferation of  ...  Then at C = C max we have from Equation (A4) xE max = E max C max EC 50 + C max ⇐⇒ x = C max EC 50 + C max ⇐⇒ xEC 50 = C max (1 − x) ⇐⇒ EC 50 = C max 1 x − 1 .  ... 
doi:10.1016/j.jtbi.2015.08.015 pmid:26343861 fatcat:kycn4x6phjao3nyy3ostflnhyq

Page 692 of School Science and Mathematics Vol. 55, Issue 488 [page]

1955 School Science and Mathematics  
692 SCHOOL SCIENCE AND MATHEMATICS nometry that R=a/(2 sin A) =6/(2 sin B)=c/(2 sin C) A B = XZ = 8R sin — sin sin — - 3 3 3 =ZY=YZ, Extension of Morley’s Theorem So far we have used only the adjacent  ...  Hopkins, Mathematical Gazette, Vol. XXXIV, 1950, p. 129, “Some Theorems of Concurrence and Col- linearity.” See also A. G. Burgess. Proc. Edinburgh Math. Soc. Vol.  ... 

SUMMARY OF EVENTS

1950 Science  
Education Q Section on Education-2:30 P.M.; Concurrent Session A; Parlor C, Statler.  ...  on Mathematics-10:00 A.M.; Symposium: Mathematics in Applied Science, Part I; Club Room C, FG3 Section on Botanical Sciences and the Ecological Society of America-9:00 A.M.; Joint Symposium: The Structure  ... 
doi:10.1126/science.112.2919.676 pmid:17811028 fatcat:5a4z5orhfzd6nhx25zmu4j3fvu

Page 404 of Mathematics Magazine Vol. 19, Issue 8 [page]

1945 Mathematics Magazine  
NATIONAL MATHEMATICS MAGAZINE theorems and corollaries. Theorem VIII. The lines FA’,DR,KL are concurrent at a point 5. Corollary I. The lines DB’,EP,LM are concurrent at a point e. Corollary II.  ...  The points C,X,Y,J,W,vy are collinear. Theorem XI. The points A,N,6,p,r’ are collinear. Corollary I. The points B,N,e,s,«’ are collinear. Corollary II. The points C,N,¢,7,u' are collinear.  ... 
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