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# zbMATH — the first resource for mathematics

## NoDEA. Nonlinear Differential Equations and Applications

 Short Title: NoDEA, Nonlinear Differ. Equ. Appl. Publisher: Springer (Birkhäuser), Basel ISSN: 1021-9722; 1420-9004/e Online: http://link.springer.com/journal/volumesAndIssues/30 Comments: Indexed cover-to-cover
 Documents Indexed: 1,142 Publications (since 1994) References Indexed: 768 Publications with 19,824 References.
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#### Latest Issues

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#### Authors

 8 Perera, Kanishka 7 Hayashi, Nakao 6 Adimurthi, A. 6 Mannucci, Paola 6 Papageorgiou, Nikolaos S. 6 Tintarev, Kyril 5 Birindelli, Isabeau 5 Gazzola, Filippo 5 Kaikina, Elena Igorevna 5 Loreti, Paola 5 Naumkin, Pavel Ivanovich 5 Peral Alonso, Ireneo 5 Rădulescu, Vicenţiu D. 5 Rossi, Julio Daniel 5 Tesfahun, Achenef 5 Winkler, Michael 5 Xu, Junxiang 4 Abdellaoui, Boumediene 4 Aubin, Jean-Pierre 4 Bessaih, Hakima 4 Boccardo, Lucio 4 Bressan, Alberto 4 Camilli, Fabio 4 Cardaliaguet, Pierre 4 Da Prato, Giuseppe 4 Do Ó, João M. Bezerra 4 Escher, Joachim 4 Feireisl, Eduard 4 Feleqi, Ermal 4 Frankowska, Hélène 4 Giacomoni, Jacques 4 Gianni, Roberto 4 Gomes, Diogo Luís Aguiar 4 Katzourakis, Nikolaos I. 4 Kaufmann, Uriel 4 Leadi, Liamidi A. 4 Liu, Zuhan 4 Messaoudi, Salim A. 4 Pecher, Hartmut 4 Rachinskii, Dmitrii I. 4 Rampazzo, Franco 4 Schneider, Guido 4 Souganidis, Panagiotis E. 4 Squassina, Marco 4 Wang, Zhi-Qiang 3 Aizicovici, Sergiu 3 Amster, Pablo 3 Andreianov, Boris 3 Andreucci, Daniele 3 Arcoya, David 3 Badiale, Marino 3 Bonaccorsi, Stefano 3 Buckdahn, Rainer 3 Cannarsa, Piermarco 3 Capietto, Anna 3 Cardin, Franco 3 Colli, Pierluigi 3 Crasta, Graziano 3 Cuesta, Mabel 3 Cung The Anh 3 D’Abbicco, Marcello 3 Dal Maso, Gianni 3 de Souza, Manassés 3 Demengel, Françoise 3 Donadello, Carlotta 3 Drábek, Pavel 3 Dwivedi, Gaurav 3 Esposito, Luca 3 Figueiredo, Giovany Malcher 3 Galaktionov, Victor Aleksandrovich 3 Garavello, Mauro 3 Grasselli, Maurizio 3 Hoshino, Gaku 3 Ikeda, Masahiro 3 Infante, Gennaro 3 Inui, Takahisa 3 Ishiwata, Michinori 3 Kajikiya, Ryuji 3 Klimsiak, Tomasz 3 Lasiecka, Irena 3 Laurençot, Philippe 3 Li, Yongsheng 3 Liero, Matthias 3 Mácha, Václav 3 Mawhin, Jean L. 3 Moscariello, Gioconda 3 Negrini, Piero 3 Nnang, Hubert 3 Passarelli di Napoli, Antonia 3 Pata, Vittorino 3 Piccoli, Benedetto 3 Pisani, Lorenzo 3 Prouse, Giovanni 3 Pucci, Patrizia 3 Ruzhansky, Michael V. 3 Saintier, Nicolas 3 Schechter, Martin 3 Secchi, Paolo 3 Selberg, Sigmund 3 Spadini, Marco ...and 1,535 more Authors
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#### Fields

 883 Partial differential equations (35-XX) 159 Ordinary differential equations (34-XX) 144 Calculus of variations and optimal control; optimization (49-XX) 88 Fluid mechanics (76-XX) 83 Global analysis, analysis on manifolds (58-XX) 82 Operator theory (47-XX) 74 Dynamical systems and ergodic theory (37-XX) 68 Probability theory and stochastic processes (60-XX) 52 Mechanics of deformable solids (74-XX) 46 Systems theory; control (93-XX) 36 Functional analysis (46-XX) 34 Biology and other natural sciences (92-XX) 29 Mechanics of particles and systems (70-XX) 26 Differential geometry (53-XX) 25 Integral equations (45-XX) 20 Real functions (26-XX) 19 Numerical analysis (65-XX) 19 Statistical mechanics, structure of matter (82-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Quantum theory (81-XX) 12 Classical thermodynamics, heat transfer (80-XX) 10 Optics, electromagnetic theory (78-XX) 8 Measure and integration (28-XX) 8 Potential theory (31-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Operations research, mathematical programming (90-XX) 6 Abstract harmonic analysis (43-XX) 5 Several complex variables and analytic spaces (32-XX) 4 Topological groups, Lie groups (22-XX) 4 Functions of a complex variable (30-XX) 3 Relativity and gravitational theory (83-XX) 3 Information and communication theory, circuits (94-XX) 2 Difference and functional equations (39-XX) 2 General topology (54-XX) 2 Algebraic topology (55-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Convex and discrete geometry (52-XX) 1 Geophysics (86-XX)

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Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control. Zbl 1147.35055
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Second order mean field games with degenerate diffusion and local coupling. Zbl 1344.49061
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Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent. Zbl 1308.35097
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A new proof of partial regularity of solutions to Navier-Stokes equations. Zbl 1142.35066
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Asymptotic behavior of a semilinear problem in heat conduction with memory. Zbl 0912.45009
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Existence of entire solutions for a class of quasilinear elliptic equations. Zbl 1273.35137
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Initial-boundary value problems for nonlinear systems of conservation laws. Zbl 0868.35069
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A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data. Zbl 1373.35166
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Regularity for minimizers of functionals with $$p-q$$ growth. Zbl 0928.35044
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Equivalence between entropy and renormalized solutions for parabolic equations with smooth measure data. Zbl 1151.35045
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Multivalued evolution equations with nonlocal initial conditions in Banach spaces. Zbl 1145.35076
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2007
Bound states to critical quasilinear Schrödinger equations. Zbl 1252.35048
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2012
Hamilton-Jacobi equations constrained on networks. Zbl 1268.35120
Achdou, Yves; Camilli, Fabio; Cutrì, Alessandra; Tchou, Nicoletta
2013
Loss of positivity in a nonlinear scalar heat equation. Zbl 1112.34017
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2006
On the partial differential equations of electrostatic MEMS devices. II: Dynamic case. Zbl 1146.35381
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2008
Weak KAM theorem on non compact manifolds. Zbl 1139.49027
2007
The Cauchy problem for the Novikov equation. Zbl 1268.35026
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2013
Regularity criteria for the 3D magneto-micropolar fluid equations in the Morrey-Campanato space. Zbl 1191.35214
2010
Remarks on scattering for nonlinear Schrödinger equations. Zbl 0991.35082
Nakanishi, Kenji; Ozawa, Tohru
2002
Generalized Morrey spaces for non-doubling measures. Zbl 1173.42317
Sawano, Yoshihiro
2008
A multiplicity result via Ljusternick-Schnirelmann category and Morse theory for a fractional Schrödinger equation in $$\mathbb{R}^N$$. Zbl 1375.35599
Figueiredo, Giovany M.; Siciliano, Gaetano
2016
On the internal and boundary stabilization of Timoshenko beams. Zbl 1163.74037
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2008
Multiple solutions for a class of Kirchhoff type problems with concave nonlinearity. Zbl 1262.35106
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2012
Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow. Zbl 1268.35087
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2013
Self-improving property of nonlinear higher order parabolic systems near the boundary. Zbl 1194.35087
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2010
$$H^s$$ versus $$C^0$$-weighted minimizers. Zbl 1339.35201
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2015
Global solutions of abstract semilinear parabolic equations with memory terms. Zbl 1052.35085
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2003
Sum of weighted Lebesgue spaces and nonlinear elliptic equations. Zbl 1234.35102
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2011
Symmetry breaking in a bounded symmetry domain. Zbl 1210.35114
Wang, Hwai-chiuan; Wu, Tsung-fang
2004
A weighted eigenvalue problem for the $$p$$-Laplacian plus a potential. Zbl 1174.35089
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2009
Conservation laws with continuous flux functions. Zbl 0961.35088
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1996
Nontrivial solutions to boundary value problems for semilinear strongly degenerate elliptic differential equations. Zbl 1247.35028
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Stochastic McKean-Vlasov equations. Zbl 0830.60091
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1995
Multiplicity results for elliptic fractional equations with subcritical term. Zbl 1322.49025
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Infinitely many solutions for a fourth-order elastic beam equation. Zbl 1222.34023
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2011
Existence and uniqueness for $$p$$-Laplace equations involving singular nonlinearities. Zbl 1341.35074
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2016
Existence for stationary mean-field games with congestion and quadratic Hamiltonians. Zbl 1343.91003
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2015
Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem. Zbl 1102.35040
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2004
Some remarks on critical point theory for nondifferentiable functionals. Zbl 0923.35049
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1999
$$L^\infty$$-estimates for nonlinear elliptic Neumann boundary value problems. Zbl 1193.35070
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2010
Fractional Choquard equation with critical nonlinearities. Zbl 1387.35608
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Small-amplitude limit cycles in polynomial Liénard systems. Zbl 0855.34030
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2015
An improved Hardy-Sobolev inequality in $$W^{1,p}$$ and its application to Schrödinger operators. Zbl 1089.35035
2005
Justification of modulation equations for hyperbolic systems via normal forms. Zbl 0890.35082
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1998
Chemotaxis: from kinetic equations to aggregate dynamics. Zbl 1270.35048
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Monotonicity and symmetry of solutions of elliptic systems in general domains. Zbl 0822.35039
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1994
The fractional Neumann and Robin type boundary conditions for the regional fractional $$p$$-Laplacian. Zbl 1338.35484
2016
General decay of solutions of a nonlinear system of viscoelastic wave equations. Zbl 1246.35040
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2011
Multiple solutions of nonlinear elliptic systems. Zbl 1146.35346
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2005
Uniqueness of positive solutions for a nonlinear elliptic system. Zbl 1181.35063
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Homogenization and behaviour of optimal controls for the wave equation in domains with oscillating boundary. Zbl 1149.35312
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2007
Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains. Zbl 1327.45004
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2015
The Bénard problem with random perturbations: Dissipativity and invariant measures. Zbl 0876.35082
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1997
Sharp Gagliardo-Nirenberg inequalities via $$p$$-Laplacian type equations. Zbl 1175.39012
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2008
Quasi-periodic solutions of forced Kirchhoff equation. Zbl 1373.37166
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1998
Hölder estimates for viscosity solutions of equations of fractional $$p$$-Laplace type. Zbl 1380.35097
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A non-existence theorem for a semilinear Dirichlet problem involving critical exponent on halfspaces of the Heisenberg group. Zbl 0961.35054
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1999
The blow-up rate for semilinear parabolic problems on general domains. Zbl 0993.35046
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2001
Global existence for a class of generalized systems for irreversible phase changes. Zbl 1004.35061
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2002
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1994
$$C^{1,\alpha}$$-regularity for electrorheological fluids in two dimensions. Zbl 1132.76301
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Molinet, Luc; Talhouk, Raafat
2004
Existence and concentration of positive solutions for a class of gradient systems. Zbl 1146.35345
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2005
Resolutions of the prescribed volume form equation. Zbl 0857.35025
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1996
On absolutely minimizing Lipschitz extensions and PDE $$\bigtriangleup_{\infty}(u)=0$$. Zbl 1154.35055
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2007
Cantor families of periodic solutions of wave equations with $$C^{k}$$ nonlinearities. Zbl 1155.35004
Berti, Massimiliano; Bolle, Philippe
2008
Multiple solutions for asymptotically linear elliptic systems. Zbl 1170.35384
Zhao, Fukun; Zhao, Leiga; Ding, Yanheng
2008
Maximal regularity for a free boundary problem. Zbl 0842.35083
Escher, Joachim; Simonett, Gieri
1995
On a class of nonhomogeneous fractional quasilinear equations in $$\mathbb R^n$$ with exponential growth. Zbl 1322.35168
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2015
Multiple equilibria, periodic solutions and a priori bounds for solutions in superlinear parabolic problems. Zbl 1058.35120
Quittner, Pavol
2004
On $$p$$-superlinear equations with a nonhomogeneous differential operator. Zbl 1283.35029
Aizicovici, Sergiu; Papageorgiou, Nikolaos S.; Staicu, Vasile
2013
On relations of the adjoint state to the value function for optimal control problems with state constraints. Zbl 1269.49035
Frankowska, Hélène; Mazzola, Marco
2013
On a Schrödinger equation with periodic potential and critical growth in $$\mathbb{R}^{2}$$. Zbl 1146.35363
do Ó, João Marcos; Ruf, Bernhard
2006
The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results. Zbl 1056.35086
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2001
Existence and multiplicity of solutions for semilinear elliptic systems. Zbl 0814.35036
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1994
Critical dimensions and higher order Sobolev inequalities with remainder terms. Zbl 0990.46021
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2001
Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension. Zbl 1375.35500
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2017
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1995
Nonautonomous fractional problems with exponential growth. Zbl 1332.35389
do Ó, João Marcos; Miyagaki, Olímpio H.; Squassina, Marco
2015
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Perera, Kanishka
2004
Remarks on variational methods and lower-upper solutions. Zbl 0941.35031
Conti, Monica; Merizzi, Luca; Terracini, Susanna
1999
Probabilistic approach to homogenization of viscosity solutions of parabolic PDEs. Zbl 0953.35017
Buckdahn, Rainer; Hu, Ying; Peng, Shige
1999
On the Bellman equation for some unbounded control problems. Zbl 0894.49017
Bardi, Martino; Da Lio, Francesca
1997
Multi-peak solutions for a class of nonlinear Schrödinger equations. Zbl 1001.35030
Pistoia, Angela
2002
Approaching optimality in blow-up results for Keller-Segel systems with logistic-type dampening. Zbl 1471.35062
Fuest, Mario
2021
On the stochastic Dullin-Gottwald-Holm equation: global existence and wave-breaking phenomena. Zbl 1456.60161
Rohde, Christian; Tang, Hao
2021
Scattering and asymptotic order for the wave equations with the scale-invariant damping and mass. Zbl 1458.35271
Inui, Takahisa; Mizutani, Haruya
2021
Pohozaev-type identities for differential operators driven by homogeneous vector fields. Zbl 1456.35092
Biagi, Stefano; Pinamonti, Andrea; Vecchi, Eugenio
2021
Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons. Zbl 07309484
Dohnal, Tomáš; Romani, Giulio
2021
Non-uniqueness of delta shocks and contact discontinuities in the multi-dimensional model of Chaplygin gas. Zbl 1460.35269
Březina, Jan; Kreml, Ondřej; Mácha, Václav
2021
Comparison principle for Hamilton-Jacobi-Bellman equations via a bootstrapping procedure. Zbl 1462.49050
Kraaij, Richard C.; Schlottke, Mikola C.
2021
Periodic solutions to reversible second order autonomous DDEs in prescribed symmetric nonconvex domains. Zbl 07385274
Balanov, Zalman; Hirano, Norimichi; Krawcewicz, Wiesław; Liao, Fangfang; Murza, Adrian
2021
Scattering threshold for the focusing coupled Schrödinger system revisited. Zbl 07385278
Saanouni, Tarek
2021
Quasi-radial solutions for the Lane-Emden problem in the ball. Zbl 1437.35336
2020
Existence and regularity results for viscous Hamilton-Jacobi equations with Caputo time-fractional derivative. Zbl 1452.35234
Camilli, Fabio; Goffi, Alessandro
2020
Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear terms. Zbl 1456.35049
Palmieri, Alessandro; Takamura, Hiroyuki
2020
Deterministic mean field games with control on the acceleration. Zbl 1442.35463
Achdou, Yves; Mannucci, Paola; Marchi, Claudio; Tchou, Nicoletta
2020
Calderon-Zygmund-Stampacchia theory for infinite energy solutions of nonlinear elliptic equations with singular drift. Zbl 1448.35144
Boccardo, L.; Buccheri, S.; Cirmi, G. R.
2020
Positive vector solutions for a Schrödinger system with external source terms. Zbl 1460.35123
Long, Wei; Peng, Shuangjie
2020
Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups. Zbl 1432.22015
Kassymov, Aidyn; Ruzhansky, Michael; Suragan, Durvudkhan
2020
Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains. Zbl 1436.35096
Lancelotti, Sergio; Molle, Riccardo
2020
Sharp semi-concavity in a non-autonomous control problem and $$L^p$$ estimates in an optimal-exit MFG. Zbl 1437.91053
Dweik, Samer; Mazanti, Guilherme
2020
An example of multiple mean field limits in ergodic differential games. Zbl 1434.91010
Cardaliaguet, Pierre; Rainer, Catherine
2020
Critical parameters for reaction-diffusion equations involving space-time fractional derivatives. Zbl 1442.35207
Asogwa, Sunday A.; Foondun, Mohammud; Mijena, Jebessa B.; Nane, Erkan
2020
Stabilizability in optimal control. Zbl 1451.93293
Lai, Anna Chiara; Motta, Monica
2020
The influence of data regularity in the critical exponent for a class of semilinear evolution equations. Zbl 1450.35054
Ebert, Marcelo R.; da Luz, Cleverson R.; Palma, Maíra F. G.
2020
Elastodynamic Griffith fracture on prescribed crack paths with kinks. Zbl 1432.35134
Dal Maso, Gianni; Larsen, Christopher J.; Toader, Rodica
2020
On principal frequencies, volume and inradius in convex sets. Zbl 1433.35204
Brasco, Lorenzo; Mazzoleni, Dario
2020
Dirichlet-boundary value problem for one dimensional nonlinear Schrödinger equations with large initial and boundary data. Zbl 1437.35628
Hayashi, Nakao; Kaikina, Elena I.; Ogawa, Takayoshi
2020
$$\mathbf{L^2}$$-decay rate for the critical nonlinear Schrödinger equation with a small smooth data. Zbl 1437.35640
Ogawa, Takayoshi; Sato, Takuya
2020
A nonlinear Bismut-Elworthy formula for HJB equations with quadratic Hamiltonian in Banach spaces. Zbl 1443.60058
Addona, Davide; Bandini, Elena; Masiero, Federica
2020
The stochastic nonlinear Schrödinger equation in unbounded domains and non-compact manifolds. Zbl 1448.35426
Hornung, Fabian
2020
On the behavior in time of solutions to motion of non-Newtonian fluids. Zbl 1454.76010
Moscariello, Gioconda; Porzio, Maria Michaela
2020
On the regularity of very weak solutions for linear elliptic equations in divergence form. Zbl 1452.35056
La Manna, Domenico Angelo; Leone, Chiara; Schiattarella, Roberta
2020
The initial-boundary value problem for the Kawahara equation on the half-line. Zbl 1448.35440
Cavalcante, Márcio; Kwak, Chulkwang
2020
Optimal regularity for all time for entropy solutions of conservation laws in $$BV^s$$. Zbl 1452.35097
Ghoshal, Shyam Sundar; Guelmame, Billel; Jana, Animesh; Junca, Stéphane
2020
Strong backward uniqueness for sublinear parabolic equations. Zbl 1452.35004
Arya, Vedansh; Banerjee, Agnid
2020
Fundamental properties and asymptotic shapes of the singular and classical radial solutions for supercritical semilinear elliptic equations. Zbl 1454.35188
Miyamoto, Yasuhito; Naito, Yūki
2020
Vanishing viscosity limit for the compressible Navier-Stokes system via measure-valued solutions. Zbl 1465.35330
Basarić, Danica
2020
Mass-constrained ground states of the stationary NLSE on periodic metric graphs. Zbl 1428.35650
Dovetta, Simone
2019
Scattering threshold for the focusing Choquard equation. Zbl 07141584
Saanouni, Tarek
2019
Nonlocal Kirchhoff problems with Trudinger – Moser critical nonlinearities. Zbl 1422.35054
Miyagaki, Olímpio H.; Pucci, Patrizia
2019
The Burgers’ equation with stochastic transport: shock formation, local and global existence of smooth solutions. Zbl 1430.35280
Alonso-Orán, Diego; Bethencourt de León, Aythami; Takao, So
2019
$${\mathcal{C}}^{1, \gamma }$$ regularity for singular or degenerate fully nonlinear equations and applications. Zbl 1428.35132
Birindelli, Isabeau; Demengel, Françoise; Leoni, Fabiana
2019
Large solutions of fully nonlinear equations: existence and uniqueness. Zbl 1427.35060
Mohammed, Ahmed; Vitolo, Antonio
2019
Front propagation for integro-differential KPP reaction-diffusion equations in periodic media. Zbl 1423.35212
Souganidis, Panagiotis E.; Tarfulea, Andrei
2019
Harnack inequalities and qualitative properties for some quasilinear elliptic equations. Zbl 1427.35088
Montoro, Luigi
2019
On the long time convergence of potential MFG. Zbl 1418.49004
Masoero, Marco
2019
Uniqueness of the nonlinear Schrödinger equation driven by jump processes. Zbl 1418.60073
de Bouard, Anne; Hausenblas, Erika; Ondreját, Martin
2019
Global existence for a class of viscous systems of conservation laws. Zbl 1437.35130
Alasio, Luca; Marchesani, Stefano
2019
Does repulsion-type directional preference in chemotactic migration continue to regularize Keller-Segel systems when coupled to the Navier-Stokes equations? Zbl 1429.92042
Winkler, Michael
2019
Anti-symmetry of the second eigenfunction of the fractional Laplace operator in a 3-D ball. Zbl 07031087
Ferreira, Rui A. C.
2019
Hamilton-Jacobi-Bellman equations with time-measurable data and infinite horizon. Zbl 1409.49006
Basco, V.; Frankowska, H.
2019
Stationary wave profiles for nonlocal particle models of traffic flow on rough roads. Zbl 07161227
Chien, Jereme; Shen, Wen
2019
Localized solutions of nonlinear Schrödinger systems with critical frequency for infinite attractive case. Zbl 1428.35118
Chang, Xiaojun; Sato, Yohei
2019
Periodic solutions to parameter-dependent equations with a $$\phi$$-Laplacian type operator. Zbl 1434.34037
Feltrin, Guglielmo; Sovrano, Elisa; Zanolin, Fabio
2019
Large Prandtl number asymptotics in randomly forced turbulent convection. Zbl 1427.76242
Földes, Juraj; Glatt-Holtz, Nathan E.; Richards, Geordie
2019
An application of a global lifting method for homogeneous Hörmander vector fields to the Gibbons conjecture. Zbl 1428.35013
Biagi, Stefano
2019
Existence of solutions for the magnetohydrodynamics with power-law type nonlinear viscous fluid. Zbl 1417.76045
Kang, Kyungkeun; Kim, Jae-Myoung
2019
Weighted anisotropic Hardy and Rellich type inequalities for general vector fields. Zbl 1421.35009
Ruzhansky, Michael; Sabitbek, Bolys; Suragan, Durvudkhan
2019
Around a singular solution of a nonlocal nonlinear heat equation. Zbl 1407.35105
Biler, Piotr; Pilarczyk, Dominika
2019
Escaping orbits are rare in the quasi-periodic Littlewood boundedness problem. Zbl 1427.37050
Schließauf, Henrik
2019
A simple variational approach to weakly coupled competitive elliptic systems. Zbl 1422.35043
Clapp, Mónica; Szulkin, Andrzej
2019
Smoluchowski’s discrete coagulation equation with forcing. Zbl 1422.34088
Kuehn, Christian; Throm, Sebastian
2019
The Rayleigh-Taylor instability for the verigin problem with and without phase transition. Zbl 1418.35310
Prüss, Jan; Simonett, Gieri; Wilke, Mathias
2019
The Enskog process for hard and soft potentials. Zbl 1419.35148
Friesen, Martin; Rüdiger, Barbara; Sundar, Padmanabhan
2019
The Strichartz estimates for the damped wave equation and the behavior of solutions for the energy critical nonlinear equation. Zbl 1435.35253
Inui, Takahisa
2019
Nonlocal conservation laws with time delay. Zbl 1439.35325
Keimer, Alexander; Pflug, Lukas
2019
Profile decomposition in Sobolev spaces of non-compact manifolds. Zbl 1444.46026
Sandeep, Kunnath; Tintarev, Cyril
2019
Stability of semi-wavefronts for delayed reaction-diffusion equations. Zbl 1423.35211
Solar, Abraham
2019
Periodic solutions of perturbed central Hamiltonian systems. Zbl 1439.34042
Gallo, Anna Chiara
2019
Incompressible Euler limit of the Boltzmann equation in the whole space and a periodic box. Zbl 1428.35269
Wu, Weijun; Zhou, Fujun; Li, Yongsheng
2019
Analysis of a perturbed Cahn-Hilliard model for Langmuir-Blodgett films. Zbl 1423.35157
Bonacini, Marco; Davoli, Elisa; Morandotti, Marco
2019
The self-improving property of higher integrability in the obstacle problem for the porous medium equation. Zbl 1423.35227
Cho, Yumi; Scheven, Christoph
2019
Uniqueness structure of weakly coupled systems of ergodic problems of Hamilton-Jacobi equations. Zbl 1437.35160
Terai, Kengo
2019
The $$\infty$$-eigenvalue problem with a sign-changing weight. Zbl 1417.35078
Kaufmann, Uriel; Rossi, Julio D.; Terra, Joana
2019
Asymptotic profile of solutions for semilinear wave equations with structural damping. Zbl 1437.35505
Yamazaki, Taeko
2019
A note on the upper perturbation property and removable sets for fully nonlinear degenerate elliptic PDE. Zbl 07031084
Święch, Andrzej
2019
Stable solutions in potential mean field game systems. Zbl 1390.35365
Briani, Ariela; Cardaliaguet, Pierre
2018
The prescribed mean curvature equation in weakly regular domains. Zbl 1391.49041
Leonardi, Gian Paolo; Saracco, Giorgio
2018
Nehari method for locally Lipschitz functionals with examples in problems in the space of bounded variation functions. Zbl 1419.35050
Figueiredo, Giovany M.; Pimenta, Marcos T. O.
2018
Existence and uniqueness results for possibly singular nonlinear elliptic equations with measure data. Zbl 1398.35050
De Cave, Linda Maria; Durastanti, Riccardo; Oliva, Francescantonio
2018
The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis-Nirenberg problem. Zbl 1407.35201
Bonder, Julián Fernández; Saintier, Nicolas; Silva, Analía
2018
Existence and asymptotic behavior of sign-changing solutions for fractional Kirchhoff-type problems in low dimensions. Zbl 1417.35032
Chen, Sitong; Tang, Xianhua; Liao, Fangfang
2018
Annular rearrangements, incompressible axi-symmetric whirls and $$L^1$$-local minimisers of the distortion energy. Zbl 1393.35037
Morris, Charles; Taheri, Ali
2018
Homogenization of Cahn-Hilliard-type equations via evolutionary $$\Gamma$$-convergence. Zbl 1412.35024
Liero, Matthias; Reichelt, Sina
2018
Regularity estimates for BMO-weak solutions of quasilinear elliptic equations with inhomogeneous boundary conditions. Zbl 1391.35169
Phan, Tuoc
2018
Positive solutions of an elliptic Neumann problem with a sublinear indefinite nonlinearity. Zbl 1391.35159
Kaufmann, Uriel; Ramos Quoirin, Humberto; Umezu, Kenichiro
2018
On existence and uniqueness of viscosity solutions for second order fully nonlinear PDEs with Caputo time fractional derivatives. Zbl 1392.35330
Namba, Tokinaga
2018
About reaction-diffusion systems involving the Holling-type II and the Beddington-DeAngelis functional responses for predator-prey models. Zbl 1392.35181
Conforto, F.; Desvillettes, Laurent; Soresina, C.
2018
A boundary estimate for singular parabolic diffusion equations. Zbl 1401.35206
Gianazza, Ugo; Liao, Naian; Lukkari, Teemu
2018
Liouville-type theorems with finite Morse index for semilinear $$\Delta_{\lambda}$$-Laplace operators. Zbl 1395.35095
Rahal, Belgacem
2018
$$p$$-Laplacian problems involving critical Hardy-Sobolev exponents. Zbl 1401.35109
Perera, Kanishka; Zou, Wenming
2018
Uniqueness of closed self-similar solutions to $$\sigma_k^\alpha$$-curvature flow. Zbl 1409.53057
Gao, Shanze; Li, Haizhong; Ma, Hui
2018
Robust Stackelberg controllability for the Navier-Stokes equations. Zbl 1407.35154
Montoya, Cristhian; de Teresa, Luz
2018
Carleman estimate for a linearized bidomain model in electrocardiology and its applications. Zbl 1403.35062
Wu, Bin; Yan, Lin; Gao, Ying; Chen, Qun
2018
Capacity solution to a coupled system of parabolic-elliptic equations in Orlicz-Sobolev spaces. Zbl 1391.35233
Moussa, H.; Ortegón Gallego, F.; Rhoudaf, M.
2018
Sign-changing solutions for elliptic problems with singular gradient terms and $$L^{1}(\Omega )$$ data. Zbl 1400.35122
Buccheri, Stefano
2018
On a dynamic boundary condition for singular degenerate parabolic equations in a half space. Zbl 1407.35096
Giga, Yoshikazu; Hamamuki, Nao
2018
Critical exponent for the semilinear wave equations with a damping increasing in the far field. Zbl 1415.35207
Nishihara, Kenji; Sobajima, Motohiro; Wakasugi, Yuta
2018
Formation of singularities of spherically symmetric solutions to the 3D compressible Euler equations and Euler-Poisson equations. Zbl 1416.35197
Li, Hai-Liang; Wang, Yuexun
2018
Liouville type theorems for stable solutions of the weighted elliptic system with the advection term: $$p \geq \vartheta >1$$. Zbl 1391.35090
Hu, Liang-Gen
2018
Dual variational methods for a nonlinear Helmholtz system. Zbl 1397.35093
Mandel, Rainer; Scheider, Dominic
2018
A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in $$W^{1,n}$$. Zbl 1388.49011
Crismale, Vito; Orlando, Gianluca
2018
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 65 Rădulescu, Vicenţiu D. 59 Papageorgiou, Nikolaos S. 48 Tang, Xianhua 32 Alves, Claudianor Oliveira 31 O’Regan, Donal 29 Messaoudi, Salim A. 29 Wu, Tsungfang 28 Molica Bisci, Giovanni 27 Pucci, Patrizia 26 Ambrosio, Vincenzo 26 Figueiredo, Giovany Malcher 26 Roubíček, Tomáš 24 Do Ó, João M. Bezerra 24 Goodrich, Christopher S. 23 Byun, Sun-Sig 23 Gomes, Diogo Luís Aguiar 23 Yin, Zhaoyang 22 Afrouzi, Ghasem Alizadeh 22 Repovš, Dušan D. 22 Rossi, Julio Daniel 22 Sreenadh, Konijeti 22 Zou, Wenming 21 Mahmudov, Elimhan N. 21 Miyagaki, Olimpio Hiroshi 21 Stefanelli, Ulisse 21 Wang, Zhi-Qiang 20 Su, Jiabao 19 Camilli, Fabio 19 Passarelli di Napoli, Antonia 19 Ramos Quoirin, Humberto 18 Zhan, Huashui 18 Zhang, Binlin 17 Cung The Anh 17 Flandoli, Franco 17 Katzourakis, Nikolaos I. 17 Sciunzi, Berardino 17 Umezu, Kenichiro 17 Winkler, Michael 16 Boscaggin, Alberto 16 Guo, Boling 16 Mielke, Alexander 16 Mugnai, Dimitri 16 Nguyễn Văn Hoàng 16 Rossi, Riccarda 16 Sawano, Yoshihiro 16 Schneider, Guido 16 Squassina, Marco 16 Wei, Juncheng 16 Xu, Junxiang 15 de Souza, Manassés 15 Heidarkhani, Shapour 15 Mihăilescu, Mihai 15 Mingione, Giuseppe 15 Winkert, Patrick 15 Yin, Jingxue 15 Zhang, Jihui 14 Aouaoui, Sami 14 Fiscella, Alessio 14 Furtado, Marcelo Fernandes 14 Galaktionov, Victor Aleksandrovich 14 Infante, Gennaro 14 Kaufmann, Uriel 14 Liu, Lishan 14 Lu, Guozhen 14 Marchi, Claudio 14 Mitake, Hiroyoshi 14 Perera, Kanishka 14 Vauchelet, Nicolas 14 Warma, Mahamadi 14 Wu, Jiahong 14 Wu, Yonghong 14 Zhang, Jian 14 Zhang, Wen 13 Agarwal, Ravi P. 13 Bonheure, Denis 13 Brzeźniak, Zdzisław 13 Cannarsa, Piermarco 13 Chen, Caisheng 13 Cheng, Bitao 13 Coclite, Giuseppe Maria 13 Feng, Baowei 13 Frankowska, Hélène 13 Giacomoni, Jacques 13 Klimsiak, Tomasz 13 Li, Shujie 13 Liu, Zhaoli 13 Schechter, Martin 13 Tan, Zhong 13 Tintarev, Kyril 13 Xiang, Mingqi 13 Yamazaki, Kazuo 13 Yang, Yunyan 13 Zhang, Ting 13 Zhang, Zhitao 12 Akagi, Goro 12 Andreianov, Boris 12 Breit, Dominic 12 Cirant, Marco 12 Da Silva, Edcarlos Domingos 12 Dambrosio, Walter ...and 5,879 more Authors
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text:
# pCDN:Emulator

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

# Emulator

To perform stress test on our pCDN server within our Lab, we develop an emulator that sends client-to-server request on behalf of many clients. We configure the emulator's NIC in promiscuous mode. The emulator is connected to the pCDN server using a dedicated GigE subnet. The emulator takes a few parameters, such as number of clients, frequency of publishing new podcasts, and average download speed on P2P networks. Using empirically derived traffic models, the emulator maps these parameters to individual requests and sends these parameters to the pCDN server. To recreate highly-stressed loads, the emulator should be scalable in the sense that multiple of them can be run in parallel.

We build the traffic models by performing and analyzing smaller-scaled Planetlab experiments. Assume we have $p$ pCDN clients. Every client joins the pCDN network for a random time $t_j$ seconds, it then leave the network for another random time $t_l$ seconds. We assume that the content provider produces a 30 MB podcast every hour, and the online clients download each podcast whenever it becomes available. Individual downloads are completed within a random time (determined by a random download rate). The pCDN server is configured to record all messages. We try several $p$ values, such as 50, 100, 150, 200, 250, 300.

To accelerate the experiments, we may scale dow the time and file sizes by a factor of 60. As a result, we can cover a 10-day experiment in a 4-hr run.

# Messages Exchanged between Clients and Servers

• Join/JoinAck
• Leave/LeaveAck
• Query/Response
• Stat/StatAck
• Session Stat: One message is sent when a session is completed
• Host Stat: One message is sent for ping packet stats.
• Path Stat: One message is sent for each sender.
• Update: A update message is sent when (i) download starts, (ii) download ends, and (iii) every 10-min during downloads.
• Heartbeat: One message is sent every 30-min.

# Additional Statistics for the pCDN server

## Periodical Logs (Say, every 10 mins)

1. Current message queue length
2. Number of dropped messages
3. Current CPU load and memory usage
4. Mean/Max processing time for each message (from received to freed)
5. Number of files, number of peers, average number of files per peer, and average peers per file.

## Real-Time Logged Events (When dbg_leve == MESSAGE or finer-grained)

1. JoinMsg: Peer (IP:Port)
2. LeaveMsg: Peer (IP:Port)
3. QueryMsg: Receiver (IP:Port), FileID (MD5 hash), # of senders, Sender IDs (IPs:Ports)
4. InsertPeer: Peer (IP:Port)
5. RemovePeer: Peer(IP:Port), ReasonCode (1: leave; 2: heartbeat timer expiers)

format: plain


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# According to Exodus 20:8-11 when is the Sabbath to be observed?

Which day is the correct Sabbath as prescribed in the ten commandments found in Exodus 20:8-11?

8 “Remember the Sabbath day by keeping it holy. 9 Six days you shall labor and do all your work, 10 but the seventh day is a sabbath to the Lord your God. On it you shall not do any work, neither you, nor your son or daughter, nor your male or female servant, nor your animals, nor any foreigner residing in your towns. 11 For in six days the Lord made the heavens and the earth, the sea, and all that is in them, but he rested on the seventh day. Therefore the Lord blessed the Sabbath day and made it holy.

The command to observe the Sabbath established a system of reckoning time. Unlike months and years which can be counted and tracked by the moon and the sun, the seven-day cycle has no natural or astronomical markers. It can only be observed on the correct day by correctly and continually counting days. There is no Scripture which names days of the week; therefore there is no Scriptural basis for stating which named day of the week is the first day or the seventh day.

The naming of the days is an extra-Biblical custom and the precise alignment of man’s names for the days of the week to the LORD God’s numbered days of the rest, is a matter of tradition. It is generally accepted the Sabbath corresponds to Saturday where it is observed by the Jewish people. In general, Christians choose to observe the "Sabbath" on Sunday. The two traditions can be characterized by why the specific day of the week was chosen:

Christian Tradition: Sunday - remember the resurrection of Jesus

Legally, the day which is named is the last day of the week. It is called "the Sabbath" and it is to be recognized by what takes place on this day:

Six days shall work be done, but on the seventh day is a Sabbath of solemn rest, a holy convocation. You shall do no work. It is a Sabbath to the LORD in all your dwelling places. (Leviticus 23:3)1

The Sabbath is a day of solemn rest, a holy convocation, and a lack of work.2 "Convocation" means gathering together, a place of assembly, a recitation, or reading. [H4744-miqra']

The question of the Sabbath and the first day of the week is discussed elsewhere on this site: In Acts 20:7, why is the phrase τῇ μιᾷ τῶν σαββάτων translated “the first day of the week” when it could mean “the first Sabbath”? and Did Acts 20:7 take place on Sunday midnight or Monday midnight? Regardless of how the language is understood in terms of the day of the week, a Christian tradition of gathering for worship (based on Acts 20:7) is one which falls the day after the Jewish tradition of the Sabbath.

The actions described in Acts 20 do not necessarily mean Paul and his companions did not also observe the Sabbath on the previous day. Given the numerous references in Acts to Paul in the synagogue on the Sabbath and the references to his observing the Passover and other feast days, it is more likely he observed the Sabbath and gathered the following day.

The reference to creation establishes both the cycle and how the days are recognized:

…And there was evening and there was morning, the first day. (Genesis 1:5)
…And there was evening and there was morning, the second day. (Genesis 1:8)
…And there was evening and there was morning, the third day. (Genesis 1:13)
…And there was evening and there was morning, the fourth day. (Genesis 1:19)
…And there was evening and there was morning, the fifth day. (Genesis 1:23)
…And there was evening and there was morning, the sixth day. (Genesis 1:31)
And on the seventh day God finished his work that he had done, and he rested on the seventh day from all his work that he had done. So God blessed the seventh day and made it holy, because on it God rested from all his work that he had done in creation. (Genesis 2:2-3)

As can be seen, the unique description is at the end of the cycle. By way of comparison, the LORD’s calendar also includes annual days to observe. These days are observed in specific months. Like days, months are numbered. However, the first month is also identified by name:

Observe the month of Abib and keep the Passover to the LORD your God, for in the month of Abib the LORD your God brought you out of Egypt by night. (Deuteronomy 16:1)

In the first month, which is the month of Nisan… (Esther 3:7)

Knowing the name of the first month properly aligns when the counting starts. This feature of the weekly calendar is absent from Scripture. While there is no certain way to identify which day of the week is the first day, the Sabbath day was identified by the LORD:

Then the LORD said to Moses, “Behold, I am about to rain bread from heaven for you, and the people shall go out and gather a day's portion every day, that I may test them, whether they will walk in my law or not. On the sixth day, when they prepare what they bring in, it will be twice as much as they gather daily.” (Exodus 16:4-5)

Six days you shall gather it, but on the seventh day, which is a Sabbath, there will be none. On the seventh day some of the people went out to gather, but they found none. (Exodus 16:26-27)

The Sabbath day was marked (before the Ten commandments) by the lack of manna. This continued for the 40-years the Israelites were in the wilderness. Thus the Jewish tradition has its roots not only in the commandment to work six days and rest on the seventh; it has the tradition of knowing which day is the seventh day. Unless they lost rack, miscounted, or stopped counting, the Sabbath Day is the day known on man's calendar as Saturday.

1. All Scripture is from the English Standard Version
2. Rest and not working are described as separate actions. Solemn or Sabbath rest would mean complete rest encompassing the mind. So do not think about or plan work.

By "true" I believe you mean "the one described in Exodus 20". If so then it is as it says, the seventh day. The Jews reckoned their days beginning at sundown and the first day began on sundown of what is secularly called "Saturday":

KJV Genesis 1:5 And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.

The seventh day (aka the "sabbath") begins on what is secularly called Friday at sundown until Saturday at sundown.

There are other sabbaths such as every seventh year:

King James Bible Leviticus 25:4 But in the seventh year shall be a sabbath of rest unto the land, a sabbath for the LORD: thou shalt neither sow thy field, nor prune thy vineyard.

The "Sunday Sabbath" is a pagan tradition that has been established as a pseudo-sabbath by many religious groups but has no true basis in scripture.

Luke 23 (KJV)

51 (The same had not consented to the counsel and deed of them;) he was of Arimathaea, a city of the Jews: who also himself waited for the kingdom of God.

52 This man went unto Pilate, and begged the body of Jesus.

53 And he took it down, and wrapped it in linen, and laid it in a sepulchre that was hewn in stone, wherein never man before was laid.

54 And that day was the preparation, and the sabbath drew on.

55 And the women also, which came with him from Galilee, followed after, and beheld the sepulchre, and how his body was laid.

56 And they returned, and prepared spices and ointments; and rested the sabbath day according to the commandment.

Jesus was crucified on the preparation day.

The women prepared spices for Jesus' body the same preparation day and rested according to the commandment that you referred to, in Exo 20:8-11.

Luke continues:

Luke 24 (KJV)

1 Now upon the first day of the week, very early in the morning, they came unto the sepulchre, bringing the spices which they had prepared, and certain others with them.

2 And they found the stone rolled away from the sepulchre.

Across the world Christians recognize the day of Jesus' crucifixion as Good Friday. They recognize the first day, when Jesus rose from the dead as Easter Sunday.

Thus, the day between the preparation day and the first day is the day when Jesus' body remained in the tomb, the 7th day we call in the secular world, Saturday.

The true sabbath is that which Paul speaks of in Hebrews 4:9 :

There remaineth therefore a rest to the people of God [KJV]

There doth remain, then, a sabbatic rest to the people of God [Young's Literal]

There remaineth, therefore, yet a rest to the people of God [Tyndale]

Having created, God rested. There was no more to do, regarding the first creation. It was there, for a purpose. Thereafter, God's work was to do with that (spiritual) purpose.

The Law entered in due to the activity of Serpent, then woman, then man. It entered in because of transgression, it was 'added' (laid down, tithemi) because of transgression, Galatians 3:19.

But that was not God's rest, as the writer to the Hebrews proves - there remaineth a rest. The rest was not a legal one, for the Law gives nobody rest, day nor night.

They that are of faith, these are Abraham's true children, Galatians 3:7. And to these is the promise made of a rest, perpetually, in Christ.

They that first heard these things, entered not in, through unbelief, Galatians 4:6, so the rest remains. It remains to be entered in by faith.

Which is why we are to fear, Hebrews 4:1, lest we enter not in to the promise, but come short of it, through unbelief.

As to days, one man esteemeth one day above another; another esteemeth every day, Romans 14:5. Let no man judge another, therefore, in respect of an holyday or of the sabbath, Colossians 2:16 . . .

. . . which are but a shadow of things to come.

But the body, is of Christ.

• What does this answer have to do with the OP's question regarding Exodus 20:8-11? – Abu Munir Ibn Ibrahim Oct 13 '17 at 11:25
• @AbuMunirIbnIbrahim If you check the edit above, you will see that someone has changed the heading which the original OP wrote. – Nigel J Oct 13 '17 at 11:48
• The title was indeed changed to bring the question on-topic. Your answer relates to the off-topic version of the question. It is a theological response, not a hermeneutic answer. – Abu Munir Ibn Ibrahim Oct 13 '17 at 12:01
• I believe it answers the question. Fundamentally. – Nigel J Oct 13 '17 at 17:11

Shabbat and the reality of traditions. Today's shabbat in Judaism is a tradition born under the Roman pressure in the 2nd century AD. Jews in Ysrael under the last Sanhedrin and his leader Hillel II, did a compromising choice due to the romman pressure. They kept the observance of the "chodesh", New Moon and adopted the saturday as the shabbat. Contantine changed the Julian calendar and put Sun-day as the First day of the week to honor the day of the sun, been a sun worshiper. Until the 4th century, "saturn-day" was the first day of the week. THE SHABBAT Ps 104:19 He made the moon for appointed times; The sun knows its going down. Appointed times: H4150 מוֹעֵד mowed (mo-ade') n-m. מֹעֵד moed (mo-ade') מוֹעָדָה mow`adah (mo-aw-daw') [feminine, 2 Chronicles 8:13] 1. (properly) an appointment, i.e. a fixed time or season. 2. (specifically) a festival.

The text in Hebrew shows that "appointed times "moedim" (plural) are determined by the moon, and the seasons by the sun. Gen 1:14 And Elohim said, “Let lights come to be in the expanse of the heavens to separate the day from the night, and let them be for signs and appointed times, and for days and years,

The Moedim are clearly listed in the book of Vayiqra (Leveticus), and the First of them is: Lv 23:1 And יהוה spoke to Mosheh, saying, Lv 23:2 “Speak to the children of Yisra’ĕl, and say to them, ‘The appointed times (Moedim) of יהוה, which you are to proclaim as set-apart gatherings, My appointed times (Moedim), are these: Lv 23:3 ‘Six days work is done, but the seventh day is a Sabbath of rest, a set-apart gathering. You do no work, it is a Sabbath to יהוה in all your dwellings.

The First of all moedim is the SHABBAT. In the First century this is what Philo of Alexandria write concerning the shabbat:

“Again, the periodical changes of the moon, take place according to the number seven, that star having the greatest sympathy with the things on earth. And the changes which the moon works in the air, it perfects chiefly in accordance with its own configurations on each seventh day. At all events, all mortal things, as I have said before, drawing their more divine nature from the heaven, are moved in a manner which tends to their preservation in accordance with this number seven. … Accordingly, on the seventh day, Elohim caused to rest from all his works which he had made.” …

Notice that Philo says the moon is perfect in its shape or appearance at seven day intervals. Had a Hebrew speaking Israelite written this he would have said “it perfects chiefly in accordance with its own configurations on each Sabbath day instead of each “seventh” day

The Decalogue XXX (159),

But to the seventh day of the week he has assigned the greatest festivals, those of the longest duration, at the periods of the equinox (Tekufah) both vernal and autumnal in each year; appointing two festivals for these two epochs, each lasting seven days; the one which takes place in the spring being for the perfection of what is being sown, and the one which falls in autumn being a feast of thanksgiving for the bringing home of all the fruits which the trees have produced”…

Equinox: Ps 19:4 Their line has gone out through all the earth, And their words to the end of the world. In them He set up a tent for the sun, Ps 19:5 And it is like a bridegroom coming out of his room, It rejoices like a strong man to run the path. Ps 19:6 Its rising is from one end of the heavens, And its circuit to the other end; And naught is hidden from its heat.

Circuit: H8622 תְּקוּפָה tquwphah (tek-oo-faw') n-f. תְּקֻפָה tquphah (tek-oo-faw') 1. a revolution. 2. (of the sun) course. Ex 34:22 'And a feast of weeks thou dost observe for thyself; first-fruits of wheat-harvest; and the feast of in-gathering, at the revolution of the year (Tekufah).

Another translation give the verse as follow: Ex 34:22 “And perform the Festival of Shaḇu‘ot "c" for yourself, of the first-fruits of wheat harvest, and the Festival of Ingathering "d" at the turn of the year (Tekufah in the Hebrew text). Footnotes: c Feast of Weeks. d Festival of Sukkot (Booths). Ex 34:22 וְחַג שָׁבֻעֹת תַּעֲשֶׂה לְךָ בִּכּוּרֵי קְצִיר חִטִּים וְחַג הָֽאָסִיף תְּקוּפַת הַשָּׁנָֽה׃

Speaking of “lunar” intervals, in Special Laws I. (178), Philo writes…

“…there is one principle of reason by which the moon waxes and wanes in equal intervals, both as it increases and diminishes in illumination; the seven lambs because it receives the perfect shapes in periods of seven days—the half-moon in the first seven day period after its conjunction with the sun, full moon in the second; and when it makes its return again, the first is to half-moon, then it ceases at its conjunction with the sun.”

Flavius Josephus lived from about 37 CE to 100 CE and undoes the Gregorian calendar in a different fashion but nonetheless supports the Creation Calendar and the lunar Sabbaths. There are in Scripture several passages that prevent any child of the King from ever accidentally falling into the wrong calendar for worship. Exodus 12:2-6 and Leviticus 23:4-14 introduce us to three fixed date work days. Abib 10, Abib 14 and Abib 16.

The 10th day of Abib is the day to set aside the Passover lamb. This is a work/commerce day. A sheepherder may have a suitable lamb, but a fisherman or a tent-maker may not. Abib 10 is the day to PURCHASE a suitable lamb. Abib 10 floats on the Gregorian calendar [translation: satyrday falls on Abib 10 at times]. Commerce is prohibited on Sabbath and there is NO legislation in Torah to purchase the Passover lamb on either the 9th or 11th of Abib IF satyrday just happens to land on Abib 10.

The 14th day of Abib is always the preparation day for the first day of Unleavened Bread. Matthew 27:62, Mark 15:42, Luke 23:54--24:1, John 19:14, 31, 42—John 20:1. Satyrday falls on Abib 14 from time to time. The fact is that the 10th, 14th and 16th of Abib are, without exception, commanded work days. The barley could be harvested on the 16th after the Wave Sheaf had been offered, Leviticus 23:9-14. Can we harvest our fields on Sabbath?

If there is a continuous 7 day cycle, every few years either the 10th, 14th or 16th will fall on a Satyrday. Evidence: Abib 10 fell on a “Saturday” in 2003. The 14th fell on “Saturday” in 2004. YHVH never instructed Israel to do common work on a rest day Sabbath. He is not the Author of confusion.

It is Abib 16 that Josephus writes about, his words hammering the counterfeit calendar and its proponents. Please understand that Josephus is writing to a non-Israelite audience. In The Antiquities of the Jews, Book 3, Chapter 10, section 5, he has this to say about the Passover season:

(248) “In the month of Xanthicus, which is by us called Nisan, and is the beginning of the year, on the fourteenth day of the lunar month, when the sun is in Aries (for in this month it was that we were delivered from bondage under the Egyptians, and law ordained that we should every year slay that sacrifice which I before told you we slew when we came out of Egypt, and which was called the Passover; and so we do celebrate this Passover in companies, leaving nothing of what we sacrifice till the day following. (249) The feast of unleavened bread succeeds that of the Passover, and falls on the fifteenth day of the month and continued seven days, wherein they feed on unleavened bread… (250) But on the second day of unleavened bread, which is the sixteenth day of the month, they first partake of the fruits of the earth, for before that day, they do not touch them. …. (251) They take a handful of ears, and dry them, then beat them small and purge the barley from the bran; they then bring one tenth deal to the altar, to Elohim; and, casting one handful of it upon the fire they leaven the rest for use of the priest; and after this it is that they may publicly or privately reap their harvest.”

Josephus is explaining to the Gentile nations how the barley could be harvested on the 16th, and says exactly what Leviticus 23 says about the feast of Passover, Unleavened Bread and wavesheaf.

In the fourteenth day of the first month at even is YHVH’s passover. And on the fifteenth day of the same month is the feast of unleavened bread unto YHVH: seven days ye must eat unleavened bread. In the first day ye shall have an holy convocation: ye shall do no servile work therein. But ye shall offer an offering made by fire unto YHVH seven days: in the seventh day is an holy convocation: ye shall do no servile work therein. And YHVH spake unto Moses, saying, Speak unto the children of Israel, and say unto them, When ye be come into the land which I give unto you, and shall reap the harvest thereof, then ye shall bring a sheaf of the firstfruits of your harvest unto the priest: And he shall wave the sheaf before YHVH, to be accepted for you: on the morrow after the sabbath the priest shall wave it. Leviticus 23:5-11

Here are a few more historical accounts of Israel’s lunar Sabbath…

The first is found in the Talmud the Steinsaltz Edition”, Volume XIV Tractate Ta’anit Part II (1995 by Israel Institute for Talmudic Publications and Milta Books), pages 205-206. It says the following regarding the destruction of Solomon’s Temple in Jerusalem by Nebuchadnezzar’s army:

Page 205: “Then late on the day of the ninth, close to nightfall, they set the Temple on fire, and it continued to burn the entire next day, on the tenth.” Page 206: “When the Temple was destroyed for the first time at the hands of Nebuzaradan [the captain of the guard], that day was the ninth of Av, and it was the day following Shabbat, and it was the year following the Sabbatical Year.... And similarly when the Temple was destroyed a second time at the hands of Titus, the destruction occurred on the very same day, on the ninth of Av.”

Guess what day the ninth day of Av was when Titus destroyed the temple? (The day after the weekly Sabbath, naturally.) If I’ve done the math right, the ninth day of the month follows the 8th day of the month. Correct? If the 8th day of the month is the Sabbath, so are the 15th, 22nd and 29th days of the month.

The historian Josephus records Sabbaths that can be pinpointed and they are on the 8th, 15th, 22nd, and 29th and the New moon was not counted as one of the six workdays. Josephus records an interesting type of strategy by General Pompey and the Romans. The Roman’s saw that the Hebrews did not fight on the Sabbath unless attacked. So, the Romans simply moved their engines and battering rams up to the walls on the Sabbath day, which otherwise they could not do, and on the next day, they battered the city. See page 369-370. Antiquities of the Jews Book 14, Chapter 4, section 3.

When, according to Exodus 20:8-11 is the Sabbath to be observed?

Answer: the Sabbath is to be observed on the 7th day, after a 6 days period of work.

Your Sabbath starts on the evening before your day off work. In society this day is by convenience celebrated on the same day by everybody. In theory, this is Friday for most Muslims, Saturday for most Jews, and Sunday for most Christians. In practice, however, this day may be different for some people, due to unforeseen circumstances, or necessary societal work responsibilities. There is a passage in the Bible that can be leaned upon for Sabbath flexibility, namely 2 Chronicles 30. Mark 2:27 also supports my argument.

Mark 2:27 (NIV) "Then he said to them, “The Sabbath was made for man, not man for the Sabbath".


text:
# Rebar Grid Weight with Lapping Factors

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The Rebar Grid Weight with Lapping Factors calculator computes the total weight of rebar in one or more mats of rebar in a concrete slab including lapping.

INSTRUCTIONS: Choose your preferred units and enter the following:

• (L) The length of the slab
• (W) The width of the slab
• (oC) The on-center spacing of the rebar spacing (defaults 18")
• (i) The inset distance from the side of the slab to the rebar grid (default of 3").
• (m) The number of mats.  (default is one).
• (rS) The size of rebar  which is used to compute the diameter for lapping considerations.
• (rL) The length of the pre-cut reinforcement bars being used to determine if lapping is required.
• (LF)  The lapping factor is the multiple of the diameter of the rebar to specify the lapping distance.  40 (default) and 60 are common.

Weight of Rebar: The calculator returns the weight of rebar in pounds.   However, this can be automatically converted into other weight units (e.g. kilograms or tons) via the pull-down menu.  Tocompute the length of reinforcement bars, use the Rebar LENGTH Calculator.

### General Information

The user inputs are as follows:                   Rebar Grid (one mat) with no lapping

• The slab is defined by a length (l) and a width (w).
• The user enters an on-center (oC) for the rebar spacing, which defaults to 18".
• The user can also input an inset (i) for the distance from the side of the slab to the first row of the rebar grid,  The inset has a default of 3".
• The user can specify the number of mats (m).  The default is one.
• The user can specify the length of the pre-cut reinforcement bars being used (rL) which is used to determine if lapping is required.
• The user can specify the size of rebar (rS).  This is the size of rebar which is used to compute the diameter for lapping considerations.
• The user can specify the lapping factor(lF).  This is the multiple of the diameter of the rebar to specify the lapping distance.  40 (default) and 60 are common.

## Description

This calculator computes the length of a simple rectangular grid of rebar. Rebar Specifications   It employs lapping for dimensions (length or width) in excess of the user specified rebar lengths (rL: see Lapping below).  A tolerance for determining the need for an extra rebar is set to less than one inch  for a spacing fraction above the tolerance.

### Lapping

When the dimensions of your slab or wall exceed the length of a single piece of rebar, it is required to lap bars and tie them to create the added length.  There are a few considerations.  First, the length of the lap is often specified as 40 times the diameter of the rebar.  In this case, 40 is lapping factor.  60 is also a common factor, but the engineering specifications should always be applied.  See these YouTube videos to better understand rebar lap:

Second, the typical length of rebar is 40' and 60' in the United States.

See how much the rebar will weigh - Rebar Weight


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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 3, Pages 506–519 (Mi tvp731)

On the Chebyshev–Cramér asymptotic expansions

I. A. Ibragimov

Abstract: Let $\xi_1,…,\xi_n,…$ be a sequence of independent identically distributed random variables with a distribution function (d.f.) $F(x)$ and let $\mathbf E\xi_i=0$, $\mathbf D\xi_i=1$. Denote $\mathbf P\{\frac1{\sqrt n}\sum_1^n\xi_i<x\}=F_n(x)$. Let $\beta_1,\beta_2,…,\beta_n,…$ be a numerical sequence such that $\beta_1=\mathbf E\xi_1=0$, $\beta_2=\mathbf E\xi_1^2=1$ and the other $\beta_s$ are arbitrary. Let us connect with the $\beta$-sequence the sequence $\{Q_n(x)\}$ of the Chebyshev–Cramér polynomials constructed in such a way as if $\{\beta_n\}$ were the sequence of moments of some distribution. We investigate the rate of convergence of the difference
$$\sup\limits_n|F_n(x)-[\Phi(x)+\frac1{\sqrt{2\pi}}e^{-x^2/2}\sum_{s=1}^k\frac{Q_s(x)}{n^{s/2}}]|$$
to zero (here $\Phi(x)$ is the normal d.f.).

Full text: PDF file (661 kB)

English version:
Theory of Probability and its Applications, 1967, 12:3, 455–469

Bibliographic databases:

Citation: I. A. Ibragimov, “On the Chebyshev–Cramér asymptotic expansions”, Teor. Veroyatnost. i Primenen., 12:3 (1967), 506–519; Theory Probab. Appl., 12:3 (1967), 455–469

Citation in format AMSBIB
\Bibitem{Ibr67}
\by I.~A.~Ibragimov
\paper On the Chebyshev--Cram\'er asymptotic expansions
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 3
\pages 506--519
\mathnet{http://mi.mathnet.ru/tvp731}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=216550}
\zmath{https://zbmath.org/?q=an:0201.51001}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 3
\pages 455--469
\crossref{https://doi.org/10.1137/1112055}

• http://mi.mathnet.ru/eng/tvp731
• http://mi.mathnet.ru/eng/tvp/v12/i3/p506

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This publication is cited in the following articles:
1. M. A. Lifshits, Ya. Yu. Nikitin, V. V. Petrov, A. Yu. Zaitsev, A. A. Zinger, “Toward the history of the Saint Petersburg school of probability and statistics. I. Limit theorems for sums of independent random variables”, Vestn. St Petersb. Univ. Math., 51:2 (2018), 144–163


text:
# Regularity properties of ideals and ultrafilters

@article{Taylor1979RegularityPO,
title={Regularity properties of ideals and ultrafilters},
author={Alan D. Taylor},
journal={Annals of Mathematical Logic},
year={1979},
volume={16},
pages={33-55}
}
• Alan D. Taylor
• Published 1 May 1979
• Mathematics
• Annals of Mathematical Logic

### Martin's Maximum, saturated ideals and non-regular ultrafilters. Part II

• Mathematics
• 1988
We prove, assuming the existence of a huge cardinal, the consistency of fully non-regular ultrafilters on the successor of any regular cardinal. We also construct ultrafilters with ultraproducts of

### Nonregular ideals

Most of the regularity properties of ideals introduced by Taylor are equivalent at successor cardinals. For $\kappa = \mu^+$ with $\mathrm{cf}(\mu)$ uncountable, we can rid the universe of dense

### The nonstationary ideal in the ℙmax extension

• P. Larson
• Mathematics
Journal of Symbolic Logic
• 2007
The Boolean algebra induced by the nonstationary ideal on ω1 in this model is studied and it is shown that the induced quotient does not have a simply definable form.

### Separating ultrafilters on uncountable cardinals

• Mathematics
• 1984
A uniform ultrafilterU on κ is said to be λ-separating if distinct elements of the ultrapower never projectU to the same uniform ultrafilterV on λ. It is shown that, in the presence of CH, an

### The nonstationary ideal in the P max extension

The forcing construction Pmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω1 is in some sense maximal. In this paper we study the Boolean algebra induced by the

### Ideals and Generic Elementary Embeddings

This chapter covers the technique of generic elementary embeddings. These embeddings are closely analogous to conventional large cardinal embeddings, the difference being that they are definable in

### Almost disjoint refinement of families of subsets of

• Mathematics
• 1980
Without any set-theoretic assumptions, we prove that every uniform ultrafilter on the set N of all natural numbers has a Comfort system, that is, an almost disjoint refinement. Moreover, we describe

### Distributive ideals and partition relations

It is a theorem of Rowbottom [12] that if κ is measurable and I is a normal prime ideal on κ, then for each λ < κ, In this paper a natural structural property of ideals, distributivity, is considered

### SATURATION PROPERTIES OF IDEALS IN GENERIC EXTENSIONS

• Mathematics
• 2010
We consider saturation properties of ideals in models obtained by forcing with countable chain condition partial orderings. As sample results, we mention the following. If M[G] is obtained from a

## References

SHOWING 1-8 OF 8 REFERENCES

### On splitting stationary subsets of large cardinals

• Mathematics
Journal of Symbolic Logic
• 1977
Abstract Let κ denote a regular uncountable cardinal and NS the normal ideal of nonstationary subsets of κ. Our results concern the well-known open question whether NS fails to be κ+-saturated, i.e.,

### Kurepa's Hypothesis and a problem of Ulam on families of measures

We prove that if Kurepa's Hypothesis holds, then on a set of cardinality ℵ1, there does not exist a family of ℵ1 non-trivial measures such that each subset is measurable with respect to at least one

### Regularity of ultrafilters

• Mathematics
• 1974
If there arek++ eventually functions fromk+ intok or if there arek++ eventually different functions fromk+ then uniform ultrafilters onk+ are (k, k+)-regular.

### Iterated Cohen extensions and Souslin's problem*

• Mathematics
• 1971
We can characterize the real line, up to order isomorphism, by the following list of properties: R is order complete, order dense, has no first or last elements, and contains a countable dense

### Some remarks on set theory

Let there be given n ordinals a,, a2, , * , a,n. It is well known that every ordinal can be written uniquely as the sum of indecomposable ordinals. (An ordinal is said to be indecomposable if it is


text:
## Kakuro

Kakuro is a puzzle given on a grid of red and white cells. The digits 1 to 9 must be filled into all the white cells so that they satisfy the clues given in some of the red cells. The clues specify the sum of the numbers in the row of successive white cells to the right or the column of successive white cells below. No row or column of successive white cells can have a digit repeated. In other words, we can write $4=1+3$ but not $4=2+2$.

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Related topic: Su Doku

# Kapenta

### Kapenta: the old saws

 (2) 3=1+2 4=1+3 5=1+4=2+3 6=2+4 7=3+4 (3) 6=1+2+3 7=1+2+4 8=1+3+4 9=2+3+4 (4) 10=1+2+3+4

Kapenta has the same rules as Kakuro except that the only digits allowed are 1, 2, 3 and 4. Since the second rule allows no repeats, this means that no clue can be longer than 4. All possible clues are given in this table. There is only one clue with a non-unique partition. We will write 62 and 72 when these two numbers are used in a clue for 2 white cells, but 63 and 73 otherwise.

When A and B are two clues which uniquely determine the number at their intersection, we write A∩B for that unique number (a∩B=B∩A). Among all 15 intersecting clues that could be placed in a 2×2 block, only the following 3 exist: 3∩4=1, 3∩62=2 and 4∩72=3. One also has 8 others: 3∩8=1=4∩73, 3∩9=2=62∩63, 4∩9=3=72∩63 and 62∩8=4=72∩73. The following 2 have no solutions: 3∩72 and 4∩62,. Everything else has multiple solutions.

### The simplest templates: M=3,4

The counting for the template with M=3 has already been done. There are 3 essentially different solutions, labelled by the clues (3,4), (3,62) and (4,72). Under a reflection in the dotted diagonal, each generates another puzzle by interchanging the clues. There are 3 essentially different puzzles with M=3, each doubled if we count symmetry related puzzles separately.

These M=3 puzzles can each be extended to M=4 in two ways because [Cc] can be filled in two ways: either [Cc]=[Bb], or [Cc] is the fourth different digit. Clearly, therefore, M=4 puzzles are labelled by 3 clues (W,X,Y). There are 6 essentially different puzzles, each doubled under symmetries.

### The templates M=5,6 inside 2×3 blocks

For every unique solution with M=4 inside 2×2 blocks, one can extend one of the rows or columns by one cell. Then there are two ways to fill this new cell, implying that the corresponding clue can be one out fo two. Therefore, there are 12 essentially different puzzles on this template, each doubled under interchange of the two equivalent rows or columns.

The rectangular 2×3 block allows unique solutions for Kapenta, unlike for Kaquadro. First, the two long clues cannot be the same, and no two of the three short clues can be the same, otherwise a permutation of any solution also yields a solution. To find all the solutions, start from the M=5 template analyzed above. There are two cases. In one case, the 5th cell value was different from either of the values in the parallel smaller clue. In this case, the new white cell added to that can be filled in exactly one way, since it cannot have any of the two values in one direction and one value in the other direction. In the second case, the new cell could have one of two values.

### M=6,7 inside a 3×3 block

Carrying on the counting from the M=5 case, the new square can be filled in any of 3 ways. Hence there are 24 essentially different puzzles, each doubled under symmetry. The puzzles are labelled by the clues (A,B,C,D).

So here is the counting for M=7. Bb can be filled in 3 different ways. Each filling determines [Bc] and [Cb], and they are different. Now [Cc] can be filled in 2 different ways: [Cc]=[Bb] and [Cc]≠[Bb]. For each choice of [Cc], there are 2 ways of filling each of Cd and Dc. Of these exactly half have [Cd]≠[Dc], so [Dd] can be filled in either of 2 ways. The remainder can be filled in either of 3 ways. Therefore there are a total of 60 solutions, which lie in 30 essentially different classes. Each puzzle can be uniquely labelled by the clues (A,B,C,D,E).

The distinction between Kaquadro and Kapenta on this template is crucial. In Kaquadro, solving [Bb] gave an unique filling of the template. In Kapenta one needs to solve [Bb] and [Cc] independently. Extensions of this template to L intersecting 2×2 blocks, giving M=3L+1 has similar properties. In Kaquadro all such blocks were fixed as soon as [Bb] was solved. In Kapenta (and its larger siblings), these require solution of L free variables.

© Sourendu Gupta. Mail me if you want to reproduce any part of this page. My mailing address is a simple (satisfactory) puzzle for you to solve. Created on 30 November, 2006. Last modified on 4 December, 2006.


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# Introductory Guide to Competitive Programming with C++

Jun 17, 2020 - 13 min read
Aaron Xie

To many, competitive programming isn’t just about typing out code. It’s a sport that takes years to master and become fully adept.

In fact, competitive programming isn’t just a hobby. Participating in competitions has many benefits: getting a job, improving logical analysis skills, and expanding your creativity.

In today’s article, we’ll introduce you to competitive programming and learn about the major concepts you’ll need to enter your first competition. We’ll also turn to Yash Kumar, a world finalist at ACM ICPC, for his thoughts and experiences with competitive programming.

We will cover the following:

## What is competitive programming?

Competitive programming is a sport, perhaps even a form of art. It’s an activity that requires creativity and analytical thinking to tackle difficult coding problems.

Competitive programming includes events (usually held over the internet) where participants, called sport programmers, solve specific problems or puzzles.

Judging, usually done by host machines, is usually based on the number of problems solved under a time constraint. The goal is to write source code that solves a given logical or mathematical problem.

These competitions have been around since the 1970s, and interest in the events has grown significantly over the years, including international contests and a worldwide community. These events are recognized by several large companies, like Facebook and Google.

• Well-defined problems: In a competition, you will be given a few problems. These problems will be well-defined, i.e. you are given constraints of variables, assumptions, and any other limitations.

• Computer programs: You will be writing computer programs and source code that solve the given problem. It’s important to note that these computer programs are simple command-line programs, not fancy GUIs or web applications.

• Specified limits: You will be asked to develop a program with a specified time and memory limit. This constraint will force you to problem-solve and develop creative ideas. You will also be constrained to a set of allowed programming languages.

Competitive programmers participate in contests like ACM ICPC, Google CodeJam, Facebook HackerCup, and many more. In these competitions, competitive programmers use their knowledge of algorithms, data structures, logical reasons, and other skills to solve difficult algorithmic problems.

This is especially difficult because competitors are required to develop programs in a limited time frame. The most common programming languages for competitive programming are Java and C++ due to their relative run-time efficiency compared to other languages like Python or JavaScript.

### Benefits of competitive programming

When we asked Yash Kumar, a world finalist at ACM ICPC and creator of Educative’s course, Competitive Programming in C++, about why he started competing in competitions, he said:

“It started out as just a hobby. There were constant challenges, new topics to learn, and participating in contests always made it an interesting learning experience. It didn’t start as something I was doing to crack software developer interviews, but it did help a lot. It soon became about demonstrating my skill in online and onsite competitions. Obviously, I had no income back then so prizes were an added bonus.”

The skills needed for competitive programming have long-lasting benefits to your career as a developer. There are numerous benefits to participating in competitive programming, including:

### Getting hired

Participating in competitive programming can make you a desirable candidate for companies. When you participate in large competitions like the ACM International Collegiate Programming Contest, you have a good chance of being on the radar of companies like Apple, Facebook, IBM, Google, and more.

Tech companies track competitions and events to find potential employees. Large competitive programming events are extremely prestigious and difficult to succeed in, so if you do well, that is an indicator of your technical talent and abilities.

That’s why many companies have actually sponsored programming competitions.

### Teamwork skills

When you participate in these competitions, you will often work in teams, meaning that you learn how to interact with teammates during high-pressure moments. This is an incredibly important skill.

When you are working as a software engineer, you will almost always work with other individuals, meaning that companies care a lot about your communication and team skills. Also, most teams will have a leader.

If you are the leader of the team, this demonstrates management skills, making you even more of a desirable candidate. Companies want to know that you can work effectively and comfortably with your teammates.

### Interview prep

When you are trying to get an engineering job, companies will test you for your knowledge of data structures and algorithms. When you participate in competitive programming, you work to develop an advanced understanding of these concepts.

Furthermore, the environment for the coding interview and competitive programming is quite similar. They are both high-pressure environments, in which you have to engage in problem-solving.

While many others may not be able to adjust to this environment, your competition experience gives you an advantage.

### Makes you faster and more focused

When you train and participate in programming competitions, you become more disciplined, faster, and more efficient. In this environment, you solve problems and code with a tight deadline. This teaches you how to focus on a task and efficiently execute.

Though competitive programming helps you get a job, Yash wanted to make it clear that you should not start competitive programming solely for the purpose of getting a job:

"This is something I’ve stressed about in the course as well. You can get a job by taking an interview preparation course and practicing a limited set of topics. You don’t showcase your competitive programming talent anywhere for a decent job.

This is a sport and should be treated like one. You do it because you enjoy the time you put into it and get something to show for it. Competitive programming will definitely help you with your job interviews, but you don’t have to do CP to prepare for those.”

## How does competitive programming work?

### Prerequisites

Programming languages. Before getting started with competitive programming, you want to have a good knowledge of a programming language and basic data structures. C++ is the most used language in competitive programming due to its speed.

Data Structures and Algorithms. After choosing your languages of choice, you need to review the fundamentals of data structures and algorithms. Understanding data structures and algorithms are the heart of competitive programming, as they are the way to solve the problems you are given.

Applications and Time Complexity. Beyond just knowing the concepts, you need to know what, when, and where to apply them. This means knowing which data structure should be used for a certain problem for the most optimal solution. You’ll need to understand the concepts of time and space complexity, like Big O Notation. This is key when being a competitive programmer because much of your placing revolves around how quickly you can solve the problem.

Practice, practice, practice. So, you’ve determined your programming language of choice and learned about data structures and algorithms. Now, you should continue practicing. You want to start practicing on some online platforms before participating in an official contest.

### The Competition

If you’re ready to participate in an official competition, here are some to consider:

• International Collegiate Programming Contest (ACM ICPC)
• TopCoder
• The International Olympiad in Informatics (IOI)
• The International Conference on Functional Programming (ICFP).

Google also hosts a number of programming contests like Google Code Jam, Google Hash Code, and Google Kickstart. Here’s a word of advice from Yash before you get started:

“Competitive programming is a sport, if you don’t enjoy the process, it’s probably not for you. Developers are problem solvers, using existing knowledge to solve an unknown problem. CP makes you a better problem solver than non-CP developers. The same is the reason why many companies will go beyond a typical SD interview into CP to hire better problem solvers, especially at earlier levels.”

So what do the competitions look like? A majority of the programming problems and challenges you will be given are mathematical or logical in nature, typically involved one of the following categories: combinatorics, number theory, graph theory, geometry, string analysis, and data structures. The process of solving a problem normally involves two steps.

• First, constructing an efficient algorithm.
• Second, implementing the algorithm in a suitable programming language.

Typically, you’ll be judged automatically by host machines. All the solutions submitted by contestants will be run on the judge against a series of test cases. Most of the time, problems have an all-or-none marking system, meaning that the solution is either accepted or rejected. The faster you complete an accepted solution, the higher the online judges will rank you.

## Fundamentals of competitive programming

### C++ refresher

C++ is by far the most popular programming language for competitive programmers. It offers a library called STL (Standard Template Library). STL is a collection of C++ template classes that provides common data structures and functions.

C++ is followed by other languages like Java, an Object Oriented Programming language. Java offers extensive libraries for data structures called Collections. Still, it’s a bit slower than C++, which is a downside.

Another popular language in competition programming is Python because of its user-friendly functionality, as the code is significantly shorter and more concise than other programming languages. The downside to using Python is that it is quite slow compared to C/C++ and Java.

## Continue the learning.

Educative’s Competitive Programming course covers theory, code samples, step-by-step solved sample problems, illustrations, useful practice problems, and tips and tricks for faster implementation! All from your browser with no extra downloads.

Become a Competitive Programmer

### Complexity analysis

Before you dive into data structures and algorithms, it’s important that we cover complexity analysis, which is a way to describe an algorithm’s performance and efficiency as the input grows larger. It’s important that you analyze your algorithm’s runtime complexity to determine whether your solution is going to meet the time limit.

There are three cases to consider:

• Best case
• Average case
• Worst case

When you are participating in a competition, you want to focus on the worst-case analysis. Typically, the inputs will force your solution to its worst-case performance.

Big O notation is an asymptotic analysis that describes how long an algorithm takes to perform. In other words, it’s used to talk about how efficient or complex an algorithm is.

### Data structures

A data structure is a container that stores data in a specific layout. This “layout” allows a data structure to be efficient in some operations and inefficient in others.

Understanding data structures is integral to participate in competitive programming, as you will be faced with making decisions on what data structure to utilize to most efficiently solve the problem you are given. If you’ve taken a computer science course in college, you most likely are familiar with data structures. You should cover:

• Arrays
• Stacks
• Queues
• Binary Tree
• Binary Search Tree
• Graphs
• Tries
• Hash tables
• Heap

Looking for a refresher on data structures? Visit our Top Data Structures and Algorithms to know article.

### Number Theory

Competitive programming deals with a lot of math, so it’s important to review mathematical concepts used by developers. Let’s review some of the main topics covered in competitions. These basic fundamentals can make or break your success!

Algebra:

• Natural numbers are all positive integers starting from 1 (ex: 1, 2, 3, 4, 5, 6, 7…)

• Sum of the first n integers is calculated $n(n+1)/2$

• Factorial is denoted by $n!$, i.e. $n! = 1 * 2 * 3...* n$

• Prime numbers are natural numbers greater than 1 that can not be made by multiple other whole numbers

Arithmetic Sequence:

Arithmetic sequences are a series of numbers such that the difference between each consecutive number is constant. For example, an arithmetic sequence could be 1,3,5,7…, since the common difference is 2.

Sum of an arithmetic sequence with $n$ terms is $=n[2a + d(n-1)]/2$ with $n$ denoting the number of terms, $a$ denoting the first term, and $d$ denoting the common difference.

Geometric Sequence:

Geometric sequences are a series of numbers such that the next term is obtained by multiply the previous term with a common multiplier. For example, 2, 4, 8, 16, 32. The common multiplier is 2.

Sum of a geometric sequence with $n$ terms is $a(1-r^n)/(1-r)$ where $r$ is the common multiplier, $n$ is the number of terms, and $a$ is the first term.

Algorithmic paradigms are general strategies for solving a problem. There are four popular forms of algorithmic paradigms: brute force, divide & conquer, greedy algorithms, and dynamic programming. For today, you will learn about Brute Force and Dynamic Programming (DP).

Brute force algorithms are exhaustive methods of solving a problem by trial and error. It takes advantage of sheer computing power and tries every single possibility to find a solution. An example of a brute force algorithm is linear search, a method to find a target value by iterating through every single value in a list.

Dynamic Programming is an algorithmic strategy for solving a problem by breaking it down into smaller subproblems by utilizing the fact that the optimal solution to the original problem depends upon the optimal solution to its subproblems.

### Graph algorithm

A graph is a non-linear data structure that consists of nodes and edges. These nodes can also be referred to as vertices. Below is a visualization of a graph.

The set of vertices V = (5, 3, 7, 9, 2) and the set of edges E = (52, 37, 72, 29, 95, 32)

Popular Graph concepts to learn:

• Depth First Search (DFS)

• Shortest path from source to all vertices (Dijkstra)

• Shortest path from every vertex to every other vertex (Floyd Warshall)

"Get yourself around people who enjoy CP. Having a group like this definitely was one of the top reasons why CP never became boring for me. Discussing new problems late at night with your friends after a competition might sound nerdy but having a motivated circle will keep you motivated.

I often see students spending months on CP theory and never participating in a competition (online or onsite), fearing that they don’t know enough to start competing, or fearing the pressure of a timed contest. Writing accurate and fast code is a huge part of CP and this can only be improved by getting into a live contest."

## Wrapping up and Resources

Now you have a sense of what competitive programming is and what concepts you’ll need to brush up on before competing.

Yash has compiled his years of experience and passion for competitive programming into a one-stop-shop course for beginners. His guide walks you through the process, insider tricks, and all the concepts you’ll need to master. Get started with Competitive Programming in C++: The Keys to Success.


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# A strength smooth tunnel is dug through a spherical planet and is perpendicular to the planet’s axis of rotation, which is fixed in space. The planet rotates with the angular velocity ω so that objects in the tunnel have no acceleration relative to the tunnel. Find the value of ω.

Q: A strength smooth tunnel is dug through a spherical planet and is perpendicular to the planet’s axis of rotation, which is fixed in space. The planet rotates with the angular velocity ω so that objects in the tunnel have no acceleration relative to the tunnel. Find the value of ω.

(a) $\sqrt{\frac{4}{3}} \pi G \rho_0$

(b) $\sqrt{\frac{2}{3}} \pi G \rho_0$

(c) $\sqrt{\frac{1}{3}} \pi G \rho_0$

(d) $2 \sqrt{\frac{4}{3}} \pi G \rho_0$

Ans: (a)