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## Journal of the Nigerian Mathematical Society

 Short Title: J. Niger. Math. Soc. Publisher: Nigerian Mathematical Society c/o University of Nigeria, Department of Mathematics, Nsukka ISSN: 0189-8965 Online: https://ojs.ictp.it/jnms/index.php/jnms/issue/archivehttps://www.sciencedirect.com/journal/journal-of-the-nigerian-mathematical-society/issueshttps://www.nigerianmathematicalsociety.org/ Comments: Indexed cover-to-cover; This journal is available open access.
 Documents Indexed: 347 Publications (since 1982) References Indexed: 147 Publications with 3,634 References.
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### Fields

 71 Numerical analysis (65-XX) 60 Fluid mechanics (76-XX) 57 Ordinary differential equations (34-XX) 39 Operator theory (47-XX) 37 Classical thermodynamics, heat transfer (80-XX) 30 Partial differential equations (35-XX) 25 Mechanics of deformable solids (74-XX) 20 Biology and other natural sciences (92-XX) 16 Group theory and generalizations (20-XX) 15 Operations research, mathematical programming (90-XX) 13 Functions of a complex variable (30-XX) 12 History and biography (01-XX) 12 Functional analysis (46-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 9 Statistics (62-XX) 8 Differential geometry (53-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Abstract harmonic analysis (43-XX) 7 General topology (54-XX) 6 Combinatorics (05-XX) 6 Probability theory and stochastic processes (60-XX) 5 Integral equations (45-XX) 5 Quantum theory (81-XX) 4 Mechanics of particles and systems (70-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Topological groups, Lie groups (22-XX) 3 Real functions (26-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Algebraic topology (55-XX) 3 Optics, electromagnetic theory (78-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Measure and integration (28-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Manifolds and cell complexes (57-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Mathematical logic and foundations (03-XX) 1 General algebraic systems (08-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Geometry (51-XX) 1 Computer science (68-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX)

### Citations contained in zbMATH Open

107 Publications have been cited 287 times in 239 Documents Cited by Year
Third Hankel determinant for bounded turning functions of order alpha. Zbl 1353.30013
Krishna, D. Vamshee; Venkateswarlu, B.; RamReddy, T.
2015
Numerical solution for hydromagnetic boundary layer flow and heat transfer past a stretching surface embedded in non-Darcy porous medium with fluid-particle suspension. Zbl 1349.76892
Gireesha, B. J.; Mahanthesh, B.; Manjunatha, P. T.; Gorla, R. S. R.
2015
Nonlinear radiative heat transfer in MHD three-dimensional flow of water based nanofluid over a non-linearly stretching sheet with convective boundary condition. Zbl 1349.76899
Mahanthesh, B.; Gireesha, B. J.; Gorla, Rama Subba Reddy
2016
Effects of thermophoresis, variable viscosity and thermal conductivity on free convective heat and mass transfer of non-Darcian MHD dissipative Casson fluid flow with suction and $$n$$th order of chemical reaction. Zbl 1349.76883
Animasaun, I. L.
2015
The flow of second grade fluid over a stretching sheet with variable thermal conductivity and viscosity in the presence of heat source/sink. Zbl 1349.76007
Akinbobola, Temitope E.; Okoya, Samuel S.
2015
Casson fluid flow with variable thermo-physical property along exponentially stretching sheet with suction and exponentially decaying internal heat generation using the homotopy analysis method. Zbl 1349.76884
2016
Radiative heat transfer of variable viscosity and thermal conductivity effects on inclined magnetic field with dissipation in a non-Darcy medium. Zbl 1349.76905
Salawu, S. O.; Dada, M. S.
2016
Nonresonant oscillation for some third-order differential equations. I. Zbl 0599.34055
Ezeilo, J. O. C.; Onyia, J.
1984
Radiation, inclined magnetic field and cross-diffusion effects on flow over a stretching surface. Zbl 1349.76904
Raju, C. S. K.; Sandeep, N.; Sulochana, C.; Sugunamma, V.; Babu, M. Jayachandra
2015
The solution by iteration of nonlinear equations in certain Banach spaces. Zbl 0609.47069
Chidume, C. E.
1986
Temperature dependent viscosity and thermal conductivity effects on hydromagnetic flow over a slendering stretching sheet. Zbl 1349.76889
Devi, S. P. Anjali; Prakash, M.
2015
Heat transfer enhancement of $$Cu - Al_2O_3$$/Water hybrid nanofluid flow over a stretching sheet. Zbl 1474.76095
Uma Devi. S, Suriya; Anjali Devi, S. P.
2017
Parameter uniform numerical method for singularly perturbed parabolic differential difference equations. Zbl 1474.65321
Woldaregay, Mesfin M.; Duressa, Gemechis F.
2019
Some examples of finite Osborn loops. Zbl 1294.20078
Isere, A. O.; Adeniran, J. O.; Solarin, A. R. T.
2012
Mathematical recipe for HIV elimination in Nigeria. Zbl 1251.34072
Garba, Salisu M.; Gumel, A. B.
2010
Solution of a class of fourth order singular singularly perturbed boundary value problems by quintic B-spline method. Zbl 1353.65082
Lodhi, Ram Kishun; Mishra, Hradyesh Kumar
2016
The time optimal control problem of linear neutral functional systems. Zbl 0535.49013
Chukwu, Ethelbert N.
1982
Picard iteration process for a general class of contractive mappings. Zbl 1341.47079
Chidume, C. E.; Olaleru, J. O.
2014
A new class of exponential fitting numerical integrators for initial value problems in ordinary differential equations. Zbl 1171.65406
Abhulimen, C. E.; Otunta, F. O.
2009
Barzilai-Borwein-like method for solving large-scale non-linear systems of equations. Zbl 1474.65145
2017
Approximation of common solutions of equilibrium and fixed point problems for certain classes of mappings. Zbl 1366.47013
Isiogugu, F. O.; Udomene, A.; Osilike, M. O.
2011
Thermal stability analysis of reactive hydromagnetic third-grade fluid through a channel with convective cooling. Zbl 1290.76009
2013
On $$n$$-weak amenability of semigroup algebras. Zbl 1300.46039
Mewomo, O. T.; Ogunsola, O. J.
2013
Fluid flow and heat transfer in a collapsible tube with heat source or sink. Zbl 1349.74114
Odejide, S. A.
2015
Extension of generalized recursive tau method to non-linear ordinary differential equations. Zbl 1353.65070
2016
Melting heat transfer effects on stagnation point flow of micropolar fluid with variable dynamic viscosity and thermal conductivity at constant vortex viscosity. Zbl 1360.80005
2016
Effects of diffusion-thermo and thermo-diffusion on two-phase boundary layer flow past a stretching sheet with fluid-particle suspension and chemical reaction: a numerical study. Zbl 1349.76079
Lakshmi, K. L. Krupa; Gireesha, B. J.; Gorla, Rama. S. R.; Mahanthesh, B.
2016
Dynamic behaviour under moving concentrated masses of elastically supported finite Bernoulli-Euler beam on Winkler foundation. Zbl 1171.74369
Oni, S. T.; Awodola, T. O.
2009
Higher order boundary value problems with integral boundary conditions at resonance on the half-line. Zbl 1474.34127
Iyase, S. A.; Imaga, O. F.
2019
A class of 2-step continuous hybrid implicit linear multistep method for IVPs. Zbl 1288.65105
Ehigie, J. O.; Okunuga, S. A.; Sofoluwe, A. B.
2011
The boundedness of solutions of certain nonlinear third order ordinary differential equations. Zbl 1300.34076
Omeike, M. O.; Olutimo, A. L.; Oyetunde, O. O.
2012
On boundedness and stability of solutions of certain third order delay differential equation. Zbl 1288.34060
Ogundare, B. S.
2012
Stability and ultimate boundedness of solutions of a certain third order nonlinear vector differential equation. Zbl 1288.34048
Olutimo, A. L.
2012
Fixed point and convergence theorems for certain classes of mappings. Zbl 1320.47053
Isiogugu, F. O.; Osilike, M. O.
2012
Approximate analytical solutions for pipe flow of a third grade fluid with variable models of viscosities and heat generation/absorption. Zbl 1288.76006
Jayeoba, O. J.; Okoya, S. S.
2012
Boundedness of solutions of some third order non-autonomous ordinary differential equations. Zbl 1293.34051
Adams, D. O.; Omeike, M. O.; Mewomo, O. T.; Olusola, I. O.
2013
On approximate character amenability of Banach algebras. Zbl 1300.46040
Mewomo, O. T.; Okelo, N. B.
2013
Accurate and automatic integration of stiff and non stiff (ODE) systems via spectral decomposition. Zbl 1251.65098
Jibunoh, C. C.
2010
Sur les structures pseudo-riemanniennes plates des variétés compactes. (On flat pseudo-Riemannian structures on compact manifolds). Zbl 0684.53047
Furness, P. M. D.; Fedida, E.
1989
Remarks on the second duals of Banach algebras. Zbl 0572.46044
Pym, John
1983
Implicit two-derivative Runge-Kutta collocation methods for systems of initial value problems. Zbl 1353.65079
Yakubu, D. G.; Kwami, A. M.
2015
An exponential method for accurate and automatic integration of nonlinear (stiff and nonstiff) ODE systems. Zbl 1353.65071
Jibunoh, C. C.
2015
A family of continuous third derivative block methods for solving stiff systems of first order ordinary differential equations. Zbl 1353.65068
Akinfenwa, O. A.; Akinnukawe, B.; Mudasiru, S. B.
2015
MHD radiative boundary layer flow of nanofluid past a vertical plate with internal heat generation/absorption, viscous and ohmic dissipation effects. Zbl 1349.76891
Ganga, B.; Ansari, S. Mohamed Yusuff; Ganesh, N. Vishnu; Hakeem, A. K. Abdul
2015
Some extensions and generalizations of Eneström-Kakeya theorem. Zbl 1351.26027
2015
On common fixed points and multipled fixed points of contractive mappings in metric-type spaces. Zbl 06653871
Olaoluwa, Hallowed; Olaleru, Johnson
2015
Mathematical model for velocity and temperature of gravity-driven convective optically thick nanofluid flow past an oscillating vertical plate in presence of magnetic field and radiation. Zbl 1349.76895
Kataria, Hari R.; Mittal, Akhil S.
2015
Influence of chemical reaction, radiation and rotation on MHD nanofluid flow past a permeable flat plate in porous medium. Zbl 1349.76876
Reddy, J. V. Ramana; Sugunamma, V.; Sandeep, N.; Sulochana, C.
2016
Similarity solution of 3D Casson nanofluid flow over a stretching sheet with convective boundary conditions. Zbl 1349.76909
Sulochana, C.; Ashwinkumar, G. P.; Sandeep, N.
2016
Magneto-hydrodynamic mixed convection of a non-Newtonian power-law nanofluid past a moving vertical plate with variable density. Zbl 1349.76898
2016
Unsteady hydromagnetic chemically reacting mixed convection flow over a permeable stretching surface with slip and thermal radiation. Zbl 1349.76887
Daba, Mitiku; Devaraj, Ponnaian
2016
Nonuniform nonresonance conditions in the periodic-Dirichlet problem for semilinear wave equations with jumping nonlinearities. Zbl 0652.35074
Mawhin, J.; Ward, J.
1984
Value of a differential game problem with multiple players in a certain Hilbert space. Zbl 1474.49083
2017
Chebyshev wavelet collocation method for the numerical solution of ordinary differential equations. Zbl 1474.65258
Shiralashetti, S. C.; Deshi, A. B.
2017
A class of implicit five step block method for general second order ordinary differential equations. Zbl 1288.65103
Umaru, Mohammed
2011
Implicit iteration method for common fixed points of a finite family of asymptotically $$\phi$$-demicontractive mappings. Zbl 1366.47012
Igbokwe, D. I.; Udofia, E. U.
2011
Outings after “Behind the closed door(s)”: a review of the research publications of Professor Haroon Ọladipọ Tẹjumọla. II. Zbl 1288.01026
Afuwapẹ, Anthony Uyi
2012
Integral conditions of existence and non-existence of periodic solutions of some sixth and fifth order ordinary differential equations. Zbl 1300.34093
Tejumola, H. O.
2012
Demidovic’s limiting regime to a certain fourth order nonlinear differential equation: another result. Zbl 1300.34123
2012
Analytical solution to MHD micropolar fluid flow past a vertical plate in a slip-flow regime in the presence of thermal diffusion and thermal radiation. Zbl 1290.76161
Oahimire, J. I.; Olajuwon, B. I.; Waheed, M. A.; Abiala, I. O.
2013
On the dynamic analysis of a tapered Timoshenko beam under a uniform partially distributed moving load. Zbl 1290.74022
Isede, H. A.; Gbadeyan, J. A.
2013
Vibrations of a simply supported plate under moving masses and resting on Pasternak elastic foundation with stiffness variation. Zbl 1290.74025
Oni, S. T.; Awodola, T. O.
2013
An augmented cubic line search algorithm for solving high-dimensional nonlinear optimization problems. Zbl 1290.90085
Nwaeze, I.; Isienyi, S. U.; Li, Zhengui
2013
Strong convergence of a modified averaging iterative algorithm for asymptotically nonexpansive maps. Zbl 1366.47025
Osilike, M. O.; Chima, E. E.; Nwokoro, P. U.; Ogbuisi, F. U.
2013
Hyponormality-preserving finite rank perturbations of terraced matrices. Zbl 1290.47019
Rhaly, H. C. jun.
2013
On uniform ultimate boundedness of the solutions of certain non-autonomous nonlinear differential equations of the third-order. Zbl 1251.34071
Afuwape, Anthony Uyi; Carvajal, Yamir Elena
2010
Solutions for the nonlinear second order two-point boundary value problems with eigenvalues $$\lambda-m^2\pi^2\;(m-1,2,\dots)$$. Zbl 1251.34037
2010
On screw dislocation in a multiphase lamellar inclusion. Zbl 1349.74134
Ogbonna, Nkem
2015
On the generalization of the error and error estimation process of Ortiz’s recursive formulation of the tau method. Zbl 1353.65088
Yisa, B. M.; Adeniyi, R. B.
2015
Finding a continuous-time Markov chain via sparse stochastic matrices in manpower systems. Zbl 1349.91238
Osagiede, Augustine A.; Ekhosuehi, V. U.
2015
Heat transfer with radiation and temperature dependent heat source in MHD free convection flow in a porous medium between two vertical wavy walls. Zbl 1349.76888
Dada, M. S.; Disu, A. B.
2015
Vortical structures on spherical surfaces. Zbl 1349.76043
Ifidon, E. O.; Oghre, E. O.
2015
Existence results for a fourth order multipoint boundary value problem at resonance. Zbl 1354.34042
Iyase, S. A.
2015
Dufour and Soret effects on steady MHD convective flow of a fluid in a porous medium with temperature dependent viscosity: homotopy analysis approach. Zbl 1349.76902
Omowaye, A. J.; Fagbade, A. I.; Ajayi, A. O.
2015
Nested balanced incomplete block designs of harmonised series. Zbl 1349.62351
Saka, A. J.; Adeleke, B. L.
2015
The efficiency of second derivative multistep methods for the numerical integration of stiff systems. Zbl 1353.65080
Yakubu, D. G.; Markus, S.
2016
Effects of thermal radiation, Soret and Dufour on an unsteady heat and mass transfer flow of a chemically reacting fluid past a semi-infinite vertical plate with viscous dissipation. Zbl 1349.76878
Alao, F. I.; Fagbade, A. I.; Falodun, B. O.
2016
Effect of temperature dependent properties on thermal radiative loading of planar surfaces with distinct heaters. Zbl 1349.74116
2016
Homotopy analysis solution of MHD slip flow past an exponentially stretching inclined sheet with Soret-Dufour effects. Zbl 1349.76908
Sravanthi, C. S.
2016
Impact of velocity slip and joule heating on MHD peristaltic flow through a porous medium with chemical reaction. Zbl 1349.76897
Machireddy, Gnaneswara Reddy; Kattamreddy, Venugopal Reddy
2016
Functions with separable orbits on foundation semigroups. Zbl 0541.22001
Dzinotyiweyi, Heneri A.; Milnes, Paul
1982
Periodic solutions of certain sixth order differential equations. Zbl 0543.34030
Ezeilo, J. O. C.
1982
A topological construction in the theory of compact semigroups. Zbl 0557.22004
Pym, John
1983
Rational torsion points on elliptic curves defined over quadratic fields. Zbl 0558.14020
Kenku, M. A.
1983
Mathematical analysis of an age-structured vaccination model for measles. Zbl 1334.92230
Garba, S. M.; Gumel, A. B.; Hussaini, N.
2014
Dynamic behaviour of non-prismatic Rayleigh beam on Pasternak foundation and under partially distributed masses moving at varying velocities. Zbl 1334.74050
Oni, S. T.; Ogunbamike, O. K.
2014
A note on just-in-time scheduling on flow shop machines. Zbl 1335.90030
Adamu, M. O.; Budlender, N.; Idowu, G. A.
2014
On some autotopisms of non-Steiner central loops. Zbl 1162.20045
Jaiyéọlá, T. G.; Adéníran, J. O.
2008
Accurate numerical differentiation by continuous integrators for ordinary differential equations. Zbl 1153.65068
Onumanyi, P.; Fatokun, J.; Adejo, B. O.
2008
Hybrid iteration method for fixed points of $$k$$-strictly pseudocontractive mappings of Browder-Petryshyn type. Zbl 1222.47107
Osilike, M. O.; Isiogugu, F. O.; Nwokoro, P. U.
2008
A fractional reaction diffusion model for tumor invasion. Zbl 1147.92308
Oyesanya, M. O.; Atabong, T. A.
2008
$$\lambda$$-sequences and fixed point theorems $$G$$-metric type spaces. Zbl 1474.54155
Gaba, Yaé Ulrich
2016
A hybrid-extragradient iterative method for split monotone variational inclusion, mixed equilibrium problem and fixed point problem for a nonexpansive mapping. Zbl 1479.47067
Kazmi, K. R.; Rizvi, S. H.; Ali, Rehan
2016
Bound states of pseudo-harmonic oscillator in the presence of magnetic field. Zbl 1474.81028
Oyewumi, K. J.; Titiloye, E. O.; Alabi, A. B.; Falaye, B. J.
2016
Thermal diffusion, radiation and inclined magnetic field effects on oscillatory flow in an asymmetric channel in presence of heat source and chemical reaction. Zbl 1474.76099
2016
Non-standard higher-order $$G$$-strand partial differential equations on matrix Lie algebra. Zbl 1474.17039
El-Nabulsi, R. A.
2017
Criticality and thermal explosion in the flow of reactive viscous third grade fluid flow in a cylindrical pipe with surface cooling. Zbl 1474.65174
Ogunseye, Hammed; Okoya, S. S.
2017
Higher order compact finite difference method for singularly perturbed one dimensional reaction diffusion problems. Zbl 1474.65191
Edosa, Feyisa; File, Gemechis
2017
An efficient family of second derivative Runge-Kutta collocation methods for oscillatory systems. Zbl 1474.35048
Yakubu, D. G.; Aminu, M.; Tumba, P.; Abdulhameed, M.
2018
On a quasilinear wave equation with memory and nonlinear source terms. Zbl 1474.35456
2018
The fuzzy subgroups for the abelian structure $$\mathbb{Z}_8\times\mathbb{Z}_{2^n}$$, $$n>2$$. Zbl 1477.20141
Adebisi, S. A.; Ogiugo, M.; Enioluwafe, M.
2020
Solving systems of nonlinear equations using improved double direction method. Zbl 1476.65075
Halilu, A. S.; Waziri, M. Y.
2020
Local nonsimilarity solutions for mixed convective flow over a stretching sheet in the presence of chemical reaction and Hall current. Zbl 1502.35116
Lawal, M. O.; Ajadi, S. O.
2020
Parameter uniform numerical method for singularly perturbed parabolic differential difference equations. Zbl 1474.65321
Woldaregay, Mesfin M.; Duressa, Gemechis F.
2019
Higher order boundary value problems with integral boundary conditions at resonance on the half-line. Zbl 1474.34127
Iyase, S. A.; Imaga, O. F.
2019
Flexural vibration to partially distributed masses of non-uniform Rayleigh beam resting on Vlasov foundation with general boundary conditions. Zbl 1477.74043
Ogunbamike, O. K.; Oni, S. T.
2019
Analytical solutions for the flow of a reactive third-grade fluid with temperature dependent viscosity models in a pipe. Zbl 1477.76104
Jayeoba, Oladimeji J.; Okoya, Samuel S.
2019
Algorithms for a system of variational inequality problems and fixed point problems with demicontractive mappings. Zbl 1486.47114
Sow, T. M. M.; Sene, M.; Ndiaye, M.; El Yekheir, Y. B.; Djitte, N.
2019
Approximation of solutions of generalized mixed equilibrium problems and fixed points of multivalued asymptotically quasinonexpansive mappings. Zbl 1486.47104
Ali, Bashir; Umar, Lawal
2019
An efficient family of second derivative Runge-Kutta collocation methods for oscillatory systems. Zbl 1474.35048
Yakubu, D. G.; Aminu, M.; Tumba, P.; Abdulhameed, M.
2018
On a quasilinear wave equation with memory and nonlinear source terms. Zbl 1474.35456
2018
Heat transfer enhancement of $$Cu - Al_2O_3$$/Water hybrid nanofluid flow over a stretching sheet. Zbl 1474.76095
Uma Devi. S, Suriya; Anjali Devi, S. P.
2017
Barzilai-Borwein-like method for solving large-scale non-linear systems of equations. Zbl 1474.65145
2017
Value of a differential game problem with multiple players in a certain Hilbert space. Zbl 1474.49083
2017
Chebyshev wavelet collocation method for the numerical solution of ordinary differential equations. Zbl 1474.65258
Shiralashetti, S. C.; Deshi, A. B.
2017
Non-standard higher-order $$G$$-strand partial differential equations on matrix Lie algebra. Zbl 1474.17039
El-Nabulsi, R. A.
2017
Criticality and thermal explosion in the flow of reactive viscous third grade fluid flow in a cylindrical pipe with surface cooling. Zbl 1474.65174
Ogunseye, Hammed; Okoya, S. S.
2017
Higher order compact finite difference method for singularly perturbed one dimensional reaction diffusion problems. Zbl 1474.65191
Edosa, Feyisa; File, Gemechis
2017
Nonlinear radiative heat transfer in MHD three-dimensional flow of water based nanofluid over a non-linearly stretching sheet with convective boundary condition. Zbl 1349.76899
Mahanthesh, B.; Gireesha, B. J.; Gorla, Rama Subba Reddy
2016
Casson fluid flow with variable thermo-physical property along exponentially stretching sheet with suction and exponentially decaying internal heat generation using the homotopy analysis method. Zbl 1349.76884
2016
Radiative heat transfer of variable viscosity and thermal conductivity effects on inclined magnetic field with dissipation in a non-Darcy medium. Zbl 1349.76905
Salawu, S. O.; Dada, M. S.
2016
Solution of a class of fourth order singular singularly perturbed boundary value problems by quintic B-spline method. Zbl 1353.65082
Lodhi, Ram Kishun; Mishra, Hradyesh Kumar
2016
Extension of generalized recursive tau method to non-linear ordinary differential equations. Zbl 1353.65070
2016
Melting heat transfer effects on stagnation point flow of micropolar fluid with variable dynamic viscosity and thermal conductivity at constant vortex viscosity. Zbl 1360.80005
2016
Effects of diffusion-thermo and thermo-diffusion on two-phase boundary layer flow past a stretching sheet with fluid-particle suspension and chemical reaction: a numerical study. Zbl 1349.76079
Lakshmi, K. L. Krupa; Gireesha, B. J.; Gorla, Rama. S. R.; Mahanthesh, B.
2016
Influence of chemical reaction, radiation and rotation on MHD nanofluid flow past a permeable flat plate in porous medium. Zbl 1349.76876
Reddy, J. V. Ramana; Sugunamma, V.; Sandeep, N.; Sulochana, C.
2016
Similarity solution of 3D Casson nanofluid flow over a stretching sheet with convective boundary conditions. Zbl 1349.76909
Sulochana, C.; Ashwinkumar, G. P.; Sandeep, N.
2016
Magneto-hydrodynamic mixed convection of a non-Newtonian power-law nanofluid past a moving vertical plate with variable density. Zbl 1349.76898
2016
Unsteady hydromagnetic chemically reacting mixed convection flow over a permeable stretching surface with slip and thermal radiation. Zbl 1349.76887
Daba, Mitiku; Devaraj, Ponnaian
2016
The efficiency of second derivative multistep methods for the numerical integration of stiff systems. Zbl 1353.65080
Yakubu, D. G.; Markus, S.
2016
Effects of thermal radiation, Soret and Dufour on an unsteady heat and mass transfer flow of a chemically reacting fluid past a semi-infinite vertical plate with viscous dissipation. Zbl 1349.76878
Alao, F. I.; Fagbade, A. I.; Falodun, B. O.
2016
Effect of temperature dependent properties on thermal radiative loading of planar surfaces with distinct heaters. Zbl 1349.74116
2016
Homotopy analysis solution of MHD slip flow past an exponentially stretching inclined sheet with Soret-Dufour effects. Zbl 1349.76908
Sravanthi, C. S.
2016
Impact of velocity slip and joule heating on MHD peristaltic flow through a porous medium with chemical reaction. Zbl 1349.76897
Machireddy, Gnaneswara Reddy; Kattamreddy, Venugopal Reddy
2016
$$\lambda$$-sequences and fixed point theorems $$G$$-metric type spaces. Zbl 1474.54155
Gaba, Yaé Ulrich
2016
A hybrid-extragradient iterative method for split monotone variational inclusion, mixed equilibrium problem and fixed point problem for a nonexpansive mapping. Zbl 1479.47067
Kazmi, K. R.; Rizvi, S. H.; Ali, Rehan
2016
Bound states of pseudo-harmonic oscillator in the presence of magnetic field. Zbl 1474.81028
Oyewumi, K. J.; Titiloye, E. O.; Alabi, A. B.; Falaye, B. J.
2016
Thermal diffusion, radiation and inclined magnetic field effects on oscillatory flow in an asymmetric channel in presence of heat source and chemical reaction. Zbl 1474.76099
2016
Third Hankel determinant for bounded turning functions of order alpha. Zbl 1353.30013
Krishna, D. Vamshee; Venkateswarlu, B.; RamReddy, T.
2015
Numerical solution for hydromagnetic boundary layer flow and heat transfer past a stretching surface embedded in non-Darcy porous medium with fluid-particle suspension. Zbl 1349.76892
Gireesha, B. J.; Mahanthesh, B.; Manjunatha, P. T.; Gorla, R. S. R.
2015
Effects of thermophoresis, variable viscosity and thermal conductivity on free convective heat and mass transfer of non-Darcian MHD dissipative Casson fluid flow with suction and $$n$$th order of chemical reaction. Zbl 1349.76883
Animasaun, I. L.
2015
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...and 7 more Documents
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text:
# How large a solar panel would I need to electrolyse 1 liter of water?

I am interested to know how large a solar panel one would need to produce pure oxygen and pure hydrogen from sea water.

I already found the required energy here:

If you assume perfect efficiency.....in terms of power, this is 3.67 kW for one hour.

## migrated from earthscience.stackexchange.comDec 16 '15 at 11:33

This question came from our site for those interested in the geology, meteorology, oceanography, and environmental sciences.

• I don't think you mean hydrolise. Electrolysis, perhaps? (by the way, we do have a site dedicated to Chemistry) – EnergyNumbers Dec 14 '15 at 14:10
• Thanks - the word is 'electrolise'. (it is also possible I might be better served on another site - let's wait and see) – Hugh Jones Dec 14 '15 at 14:35

The flippant answer is "it depends how long you're prepared to wait". But, let's assume that you want to electrolyse a litre of water an in hour.

You've identified above that the energy needed to electrolyse one litre of water is 3.67kWh, or 3.67kW for one hour (assuming no losses in the process). So what we need is a solar system capable of delivering 3.67kW.

Let's assume that we're in a temperate latitude, that the sky is clear, and that it's the middle of the day. That should give us around a 1kW/m^2 of energy, in the form of light, reaching the ground. Decent (but not bleeding-edge) photovoltaic panels are around 15% efficient, so we'll get around 150W out of them for each square metre of area. That means that in this scenario, we'd need 24m^2 of solar panels.

That's a lot. It gets worse if you want to do this continuously, rather than as a one-off, because the average power of sunlight reaching the ground in temperate climes, including cloudy days and including nighttime, is around 250kW/m^2, one quarter of the peak value. So then you need 100m^2 of solar panels.

Let's look at it another way, and say that we have 20m^2 of rooftop available. That would mean that you produced an average of 20 x 250 x 0.15 = 750W, which works out to splitting around 5 litres of water per day.

Looking at it from systems I can buy rather than theory, if you want 1 litre per hour you need 3.67kW of hydrolysis output from your system, but the hydrolosis is not 100% efficient. There are two main options, and they're both a bit over 50% efficient:

Wikipedia says

Reported working efficiencies are in the range 60-75% for alkaline and 65–90% for PEM.

You will need 3.67kW/0.60 = 6.1kW of input power. But you will have other losses, so should aim for 7kW or more.

In the US that looks to cost about $US10,000 as a DIY kit, or$OZ11,000 here. In Australia it's common to put slightly more panels on than your inverter is rated for so that you get peak power for longer. I would try to put 7.5kW or 8kW of panels on that 7kW inverter (almost all of them will do that, it's a question of maximum input voltage) so that you get 7kW out of the system more often.

format: plain


text:
# BayesSampling

library(BayesSampling)

# Bayes linear estimation for finite population

## 1. Introduction

Surveys have long been an important way of obtaining accurate information from a finite population. For instance, governments need to obtain descriptive statistics of the population for purposes of evaluating and implementing their policies. For those concerned with official statistics in the first third of the twentieth century, the major issue was to establish a standard of acceptable practice. Neyman (1934) created such a framework by introducing the role of randomization methods in the sampling process. He advocated the use of the randomization distribution induced by the sampling design to evaluate the frequentist properties of alternative procedures. He also introduced the idea of stratification with optimal sample size allocation and the use of unequal selection probabilities. His work was recognized as the cornerstone of design-based sample survey theory and inspired many other authors. For example, Horvitz and Thompson (1952) proposed a general theory of unequal probability sampling and the probability weighted estimation method, the so-called “Horvitz and Thompson’s estimator”.

The design-based sample survey theory has been very appealing to official statistics agencies around the world. As pointed out by Skinner, Holt and Smith (1989), page 2, the main reason is that it is essentially distribution-free. Indeed, all advances in survey sampling theory from Neyman onwards have been strongly influenced by the descriptive use of survey sampling. The consequence of this has been a lack of theoretical developments related to the analytic use of surveys, in particular for prediction purposes. In some specific situations, the design-based approach has proved to be inefficient, providing inadequate predictors. For instance, estimation in small domains and the presence of the non-response cannot be dealt with by the design-based approach without some implicit assumptions, which is equivalent to assuming a model. Supporters of the design-based approach argue that model-based inference largely depends on the model assumptions, which might not be true. On the other hand, interval inference for target population parameters (usually totals or means) relies on the Central Limit Theorem, which cannot be applied in many practical situations, where the sample size is not large enough and/or independence assumptions of the random variables involved are not realistic.

Basu (1971) did not accept estimates of population quantities which depend on the sampling rule, like the inclusion probabilities. He argued that this estimation procedure does not satisfy the likelihood principle, at which he was adept. Basu (1971) created the circus elephant example to show that the Horvitz-Thompson estimator could lead to inappropriate estimates and proposed an alternative estimator. The question that arises is whether it is possible to conciliate both approaches. In the superpopulation model context, Zacks (2002) showed that some design-based estimators can be recovered by using a general regression model approach. Little (2003) claims that: “careful model specification sensitive to the survey design can address the concerns with model specifications, and Bayesian statistics provide a coherent and unified treatment of descriptive and analytic survey inference”. He gave some illustrative examples of how standard design-based inference can be derived from the Bayesian perspective, using some models with non-informative prior distributions.

In the Bayesian context, another appealing proposal to conciliate the design-based and model-based approaches was proposed by Smouse (1984). The method incorporates prior information in finite population inference models by relying on Bayesian least squares techniques and requires only the specification of first and second moments of the distributions involved, describing prior knowledge about the structures present in the population. The approach is an alternative to the methods of randomization and appears midway between two extreme views: on the one hand the design-based procedures and on the other those based on superpopulation models. O’Hagan (1985), in an unpublished report, presented the Bayes linear estimators in some specific sample survey contexts and O’Hagan (1987) also derived Bayes linear estimators for some randomized response models. O’Hagan (1985) dealt with several population structures, such as stratification and clustering, by assuming suitable hypotheses about the first and second moments and showed how some common design-based estimators can be obtained as a particular case of his more general approach. He also pointed out that his estimates do not account for non-informative sampling. He quoted Scott (1977) and commented that informative sampling should be carried out by a full Bayesian analysis. An important reference about informative sampling dealing with hierarchical models can be found in Pfeffermann, Moura and Silva (2006).

## 2. Bayes linear estimation for finite population

The Bayes approach has been found to be successful in many applications, particularly when the data analysis has been improved by expert judgments. But while Bayesian models have many appealing features, their application often involves the full specification of a prior distribution for a large number of parameters. Goldstein and Wooff (2007), section 1.2, argue that as the complexity of the problem increases, our actual ability to fully specify the prior and/or the sampling model in detail is impaired. They conclude that in such situations, there is a need to develop methods based on partial belief specification.

Hartigan (1969) proposed an estimation method, termed Bayes linear estimation approach, that only requires the specification of first and second moments. The resulting estimators have the property of minimizing posterior squared error loss among all estimators that are linear in the data and can be thought of as approximations to posterior means. The Bayes linear estimation approach is fully employed in this article and is briefly described below.

### 2.1 Bayes linear approach

Let $$y_s$$ be the vector with observations and $$\theta$$ be the parameter to be estimated. For each value of $$\theta$$ and each possible estimate $$d$$, belonging to the parametric space $$\Theta$$, we associate a quadratic loss function $$L(\theta, d) = (\theta - d)' (\theta - d) = tr (\theta - d) (\theta - d)'$$. The main interest is to find the value of $$d$$ that minimizes $$r(d) = E [L (\theta, d) | y_s]$$, the conditional expected value of the quadratic loss function given the data.

Suppose that the joint distribution of $$\theta$$ and $$y_s$$ is partially specified by only their first two moments:

$$$\tag{2.1} \begin{pmatrix} \theta\\ y_s \end{pmatrix} \hspace{0.1cm} \sim \hspace{0.1cm} \begin{bmatrix} \begin{pmatrix} a\\ \text{f} \end{pmatrix},\begin{pmatrix} R & AQ\\ QA^{'} & Q \end{pmatrix} \end{bmatrix}$$$

where $$a$$ and $$f$$, respectively, denote mean vectors and $$R$$, $$AQ$$ and $$Q$$ the covariance matrix elements of $$\theta$$ and $$y_s$$.

The Bayes linear estimator (BLE) of $$\theta$$ is the value of $$d$$ that minimizes the expected value of this quadratic loss function within the class of all linear estimates of the form $$d = d(y_s) = h + H y_s$$, for some vector $$h$$ and matrix $$H$$. Thus, the BLE of $$\theta$$, $$\hat{d}$$, and its associated variance, $$\hat{V} (\hat{d})$$, are respectively given by:

$$$\tag{2.2} \hat{d} = a + A(y_s - \text{f}) \hspace{0.7cm} \text{and} \hspace{0.7cm} \hat{V}(\hat{d}) = R - AQA^{'}$$$

It should be noted that the BLE depends on the specification of the first and second moments of the joint distribution partially specified in (2.1).

From the Bayes linear approach applied to the general linear regression model for finite population prediction, the paper shows how to obtain some particular design-based estimators, as in simple random sampling and stratified simple random sampling.

## 3. Functions

The package contain the main following functions:

• BLE_Reg() - general function (base for the rest of the functions)
• BLE_SRS() - Simple Random Sample case
• BLE_SSRS() - Stratified Simple Random Sample case
• BLE_Ratio() - Ratio Estimator case


text:
Filter (mathematics) explained

In mathematics, a filter is a special subset of a partially ordered set. Filters appear in order and lattice theory, but can also be found in topology, from where they originate. The dual notion of a filter is an order ideal.

Filters were introduced by Henri Cartan in 1937[1] [2] and subsequently used by Bourbaki in their book Topologie Générale as an alternative to the similar notion of a net developed in 1922 by E. H. Moore and H. L. Smith.

Motivation

Intuitively, a filter in a partially ordered set (poset), P, is a subset of P that includes as members those elements that are large enough to satisfy some given criterion. For example, if x is an element of the poset, then the set of elements that are above x is a filter, called the principal filter at x. (If x and y are incomparable elements of the poset, then neither of the principal filters at x and y is contained in the other one, and conversely.)

Similarly, a filter on a set contains those subsets that are sufficiently large to contain some given thing. For example, if the set is the real line and x is one of its points, then the family of sets that include x in their interior is a filter, called the filter of neighbourhoods of x. The thing in this case is slightly larger than x, but it still doesn't contain any other specific point of the line.

The above interpretations explain conditions 1 and 3 in the section General definition: Clearly the empty set is not "large enough", and clearly the collection of "large enough" things should be "upward-closed". However, they do not really, without elaboration, explain condition 2 of the general definition. For, why should two "large enough" things contain a common "large enough" thing?

Alternatively, a filter can be viewed as a "locating scheme": When trying to locate something (a point or a subset) in the space X, call a filter the collection of subsets of X that might contain "what is looked for". Then this "filter" should possess the following natural structure:

1. A locating scheme must be non-empty in order to be of any use at all.
2. If two subsets, E and F, both might contain "what is looked for", then so might their intersection. Thus the filter should be closed with respect to finite intersection.
3. If a set E might contain "what is looked for", so does every superset of it. Thus the filter is upward-closed.

An ultrafilter can be viewed as a "perfect locating scheme" where each subset E of the space X can be used in deciding whether "what is looked for" might lie in E.

From this interpretation, compactness (see the mathematical characterization below) can be viewed as the property that "no location scheme can end up with nothing", or, to put it another way, "always something will be found".

The mathematical notion of filter provides a precise language to treat these situations in a rigorous and general way, which is useful in analysis, general topology and logic.

General definition: Filter on a partially ordered set

A subset of a partially ordered set is a filter if the following conditions hold:

1. is non-empty.
2. is downward directed: For every, there is some such that and .
3. is an upper set or upward-closed: For every and, implies that .

A filter is proper if it is not equal to the whole set .This condition is sometimes added to the definition of a filter.

While the above definition is the most general way to define a filter for arbitrary posets, it was originally defined for lattices only. In this case, the above definition can be characterized by the following equivalent statement:A subset of a lattice is a filter, if and only if it is a non-empty upper set that is closed under finite infima (or meets), i.e., for all, it is also the case that is in F.[3] A subset of is a filter basis if the upper set generated by is all of . Note that every filter is its own basis.

The smallest filter that contains a given element is a principal filter and is a principal element in this situation.The principal filter for is just given by the set

\{x\inP\midp\leqx\}

and is denoted by prefixing with an upward arrow:

The dual notion of a filter, i.e. the concept obtained by reversing all and exchanging ∧ with ∨, is ideal.Because of this duality, the discussion of filters usually boils down to the discussion of ideals.Hence, most additional information on this topic (including the definition of maximal filters and prime filters) is to be found in the article on ideals.There is a separate article on ultrafilters.

Filter on a set

Definition of a filter

There are two competing definitions of a "filter on a set," both of which require that a filter be a dual ideal. One definition defines "filter" as a synonym of "dual ideal" while the other defines "filter" to mean a dual ideal that is also proper.

Warning: It is recommended that readers always check how "filter" is defined when reading mathematical literature.

Given a set, a canonical partial ordering can be defined on the powerset by subset inclusion, turning into a lattice. A "dual ideal" is just a filter with respect to this partial ordering. Note that if then there is exactly one dual ideal on, which is .

Filter definition 1: Dual ideal

The article uses the following definition of "filter on a set."

Filter definition 2: Proper dual ideal

The other definition of "filter on a set" is the original definition of a "filter" given by Henri Cartan, which required that a filter on a set be a dual ideal that does not contain the empty set:

The only non-proper filter on is . Much mathematical literature, especially that related to Topology, defines "filter" to mean a non-degenerate dual ideal.

Filter bases, subbases, and comparison

Filter bases and subbases

A subset of is called a prefilter, filter base, or filter basis if is non-empty and the intersection of any two members of is a superset of some member(s) of . If the empty set is not a member of, we say is a proper filter base.

Given a filter base, the filter generated or spanned by is defined as the minimum filter containing . It is the family of all those subsets of which are supersets of some member(s) of . Every filter is also a filter base, so the process of passing from filter base to filter may be viewed as a sort of completion.

For every subset of there is a smallest (possibly nonproper) filter containing, called the filter generated or spanned by .Similarly as for a filter spanned by a filter base, a filter spanned by a subset is the minimum filter containing .It is constructed by taking all finite intersections of, which then form a filter base for . This filter is proper if and only if every finite intersection of elements of is non-empty, and in that case we say that is a filter subbase.

Finer/equivalent filter bases

If and are two filter bases on, one says is finer than (or that is a refinement of) if for each, there is a such that . If also is finer than, one says that they are equivalent filter bases.

• If and are filter bases, then is finer than if and only if the filter spanned by contains the filter spanned by . Therefore, and are equivalent filter bases if and only if they generate the same filter.
• For filter bases,, and, if is finer than and is finer than then is finer than . Thus the refinement relation is a preorder on the set of filter bases, and the passage from filter base to filter is an instance of passing from a preordering to the associated partial ordering.

Examples

• Let be a set and be a non-empty subset of . Then is a filter base. The filter it generates (i.e., the collection of all subsets containing) is called the principal filter generated by .
• A filter is said to be a free filter if the intersection of all of its members is empty. A proper principal filter is not free. Since the intersection of any finite number of members of a filter is also a member, no proper filter on a finite set is free, and indeed is the principal filter generated by the common intersection of all of its members. A nonprincipal filter on an infinite set is not necessarily free.
• The Fréchet filter on an infinite set is the set of all subsets of that have finite complement. A filter on is free if and only if it includes the Fréchet filter.
• More generally, if

(X,\mu)

is a measure space for which

\mu(X)=infty

, the collection of all

A\subseteqX

such that

\mu(X\setminusA)<infty

forms a filter. The Fréchet filter is the case where

X=\N

and

\mu

is the counting measure.

\{\{N,N+1,N+2,...\}\midN\in\{1,2,3,...\}\}

is called a filter base of tails of the sequence of natural numbers

(1,2,3,...)

. A filter base of tails can be made of any net

(x\alpha)\alpha

using the construction

\{\{x\alpha\mid\alpha\inA,\alpha0\leq\alpha\}\mid\alpha0\inA\}

, where the filter that this filter base generates is called the net's eventuality filter. Therefore, all nets generate a filter base (and therefore a filter). Since all sequences are nets, this holds for sequences as well.

Filters in model theory

See also: Filter quantifier. For every filter F on a set S, the set function defined by

m(A)= \begin{cases} 1&ifA\inF\\ 0&ifS\setminusA\inF\\ undefined&otherwise \end{cases}

is finitely additive — a "measure" if that term is construed rather loosely. Therefore, the statement

\left\{x\inS\mid\varphi(x)\right\}\inF

can be considered somewhat analogous to the statement that

\varphi

holds "almost everywhere". That interpretation of membership in a filter is used (for motivation, although it is not needed for actual proofs) in the theory of ultraproducts in model theory, a branch of mathematical logic.

Filters in topology

See main article: Filters in topology.

In topology and analysis, filters are used to define convergence in a manner similar to the role of sequences in a metric space.

In topology and related areas of mathematics, a filter is a generalization of a net. Both nets and filters provide very general contexts to unify the various notions of limit to arbitrary topological spaces.

A sequence is usually indexed by the natural numbers, which are a totally ordered set. Thus, limits in first-countable spaces can be described by sequences. However, if the space is not first-countable, nets or filters must be used. Nets generalize the notion of a sequence by requiring the index set simply be a directed set. Filters can be thought of as sets built from multiple nets. Therefore, both the limit of a filter and the limit of a net are conceptually the same as the limit of a sequence.

Neighbourhood bases

Let X be a topological space and x a point of X.

• Take Nx to be the neighbourhood filter at point x for X. This means that Nx is the set of all topological neighbourhoods of the point x. It can be verified that Nx is a filter. A neighbourhood system is another name for a neighbourhood filter.
• To say that N is a neighbourhood base at x for X means that each subset V0 of X is a neighbourhood of x if and only if there exists N0N such that N0V0. Every neighbourhood base at x is a filter base that generates the neighbourhood filter at x.

Convergent filter bases

Let X be a topological space and x a point of X.

• To say that a filter base B converges to x, denoted Bx, means that for every neighbourhood U of x, there is a B0B such that B0U. In this case, x is called a limit of B and B is called a convergent filter base.
• Every neighbourhood base N of x converges to x.
• If N is a neighbourhood base at x and C is a filter base on X, then Cx if C is finer than N. If N is the upward closed neighborhood filter, then the converse holds as well: any basis of a convergent filter refines the neighborhood filter.
• If YX, a point p ∈ X is called a limit point of Y in X if and only if each neighborhood U of p in X intersects Y. This happens if and only if there is a filter base of subsets of Y that converges to p in X.
• For YX, the following are equivalent:
• (i) There exists a filter base F whose elements are all contained in Y such that Fx.
• (ii) There exists a filter F such that Y is an element of F and Fx.
• (iii) The point x lies in the closure of Y.

Indeed:

(i) implies (ii): if F is a filter base satisfying the properties of (i), then the filter associated to F satisfies the properties of (ii).

(ii) implies (iii): if U is any open neighborhood of x then by the definition of convergence U contains an element of F; since also Y is an element of F, U and Y have non-empty intersection.

(iii) implies (i): Define

F=\{U\capY\midU\inNx\}

. Then F is a filter base satisfying the properties of (i).

Clustering

Let be a topological space and x a point of X.

Definition: A filter base on is said to cluster at (or have as a cluster point) if and only if each element of has non-empty intersection with each neighbourhood of .

• If a filter base clusters at and is finer than a filter base, then also clusters at .
• Every limit of a filter base is also a cluster point of the base.
• A filter base that has as a cluster point may not converge to . But there is a finer filter base that does. For example, the filter base of finite intersections of sets of the subbase .
• For a filter base, the set is the set of all cluster points of (the closure of B0 is . Assume that is a complete lattice.
• The limit inferior of is the infimum of the set of all cluster points of .
• The limit superior of is the supremum of the set of all cluster points of .
• is a convergent filter base if and only if its limit inferior and limit superior agree; in this case, the value on which they agree is the limit of the filter base.

Properties of a topological space

Let X be a topological space.

• X is a Hausdorff space if and only if every filter base on X has at most one limit.
• X is compact if and only if every filter base on X clusters or has a cluster point.
• X is compact if and only if every filter base on X is a subset of a convergent filter base.
• X is compact if and only if every ultrafilter on X converges.

Functions between topological spaces

Let and be topological spaces, let be a filter base on, and let be a function. The image of under, denoted by, is defined as the set, which necessarily forms a filter base on .

• is continuous at if and only if for every filter base on, implies .

Cauchy filters

Let

(X,d)

be a metric space.
• To say that a filter base B on X is Cauchy means that for each real number ε > 0, there is a B0B such that the metric diameter of B0 is less than ε.
• Take (xn) to be a sequence in metric space X. (xn) is a Cauchy sequence if and only if the filter base {{xN, xN +1, ...} N ∈ } is Cauchy.

More generally, given a uniform space X, a filter F on X is called a Cauchy filter if for every entourage U there is an AF with (x, y) ∈ U for all x, yA. In a metric space this agrees with the previous definition. X is said to be complete if every Cauchy filter converges. Conversely, on a uniform space every convergent filter is a Cauchy filter. Moreover, every cluster point of a Cauchy filter is a limit point.

A compact uniform space is complete: on a compact space each filter has a cluster point, and if the filter is Cauchy, such a cluster point is a limit point. Further, a uniformity is compact if and only if it is complete and totally bounded.

Most generally, a Cauchy space is a set equipped with a class of filters declared to be Cauchy. These are required to have the following properties:

1. for each x in X, the ultrafilter at x, U(x), is Cauchy.
2. if F is a Cauchy filter, and F is a subset of a filter G, then G is Cauchy.
3. if F and G are Cauchy filters and each member of F intersects each member of G, then FG is Cauchy.

The Cauchy filters on a uniform space have these properties, so every uniform space (hence every metric space) defines a Cauchy space.

References

• Nicolas Bourbaki, General Topology (Topologie Générale), (Ch. 1-4): Provides a good reference for filters in general topology (Chapter I) and for Cauchy filters in uniform spaces (Chapter II)
• Burris, Stanley N., and H.P. Sankappanavar, H. P., 1981. A Course in Universal Algebra. Springer-Verlag. .
• Stephen Willard, General Topology, (1970) Addison-Wesley Publishing Company, Reading Massachusetts. (Provides an introductory review of filters in topology.)


text:
FLOC 2022: FEDERATED LOGIC CONFERENCE 2022
LICS ON FRIDAY, AUGUST 5TH
Days:
previous day
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View: session overviewtalk overviewside by side with other conferences

08:30-09:00Coffee & Refreshments
09:00-10:00 Session 73E: Invited talk by Mikolaj Bojanczyk

Transducers of polynomial growth

Abstract: The polyregular functions are a class of string-to-string functions that have polynomial size outputs, and which can be defined using finite state models. There are many equivalent definitions of this class, with roots in automata theory, programming  languages and logic. The talk surveys recent results on polyregular functions. It presents five of the equivalent definitions, and gives self-contained proofs for most of the equivalences. Decision problems as well as restricted subclasses of the polyregular functions are also discussed.

Location: Taub 1
10:00-10:30 Session 75: Poster Session

Daniel Gratzer. Normalization for multimodal type theory

Clemens Grabmayer. Milner's Proof System for Regular Expressions Modulo Bisimilarity is Complete

Soumodev Mal. On the Satisfiability of Context-free String Constraints with Subword Ordering

Matthias Naaf. Zero-One Laws and Almost Sure Valuations of First-Order Logic in Semiring Semantics

Jana Hofmann. Deciding Hyperproperties combined with Functional Specifications

10:30-11:00Coffee Break
11:00-12:30 Session 76G: Verification

"Verification": 6 papers (12 min presentation + 2-3 min Q&A)

Location: Taub 1
11:00
On the Satisfiability of Context-free String Constraints with Subword Ordering
PRESENTER: Soumodev Mal

ABSTRACT. We consider a variant of string constraints given by membership constraints in context-free languages and subword relation between variables. The satisfiability problem for this variant turns out to be undecidable. We consider a fragment in which the subword order constraints do not impose any cyclic dependency between variables. We show that this fragment is NEXPTIME-complete. As an application of our result, we settle the complexity of control state reachability in acyclic lossy channel pushdown systems, an important distributed system model. The problem was shown to be decidable by Atig et al. in 2008. However, no elementary upper bound was known. We show that this problem is NEXPTIME-complete.

11:15
The complexity of soundness in workflow nets

ABSTRACT. Workflow nets are a popular variant of Petri nets that allow for the algorithmic formal analysis of business processes. The central decision problems concerning workflow nets deal with soundness, where the initial and final configurations are specified. Intuitively, soundness states that from every reachable configuration one can reach the final configuration. We settle the widely open complexity of the three main variants of soundness: classical, structural and generalised soundness. The first two are EXPSPACE-complete, and, surprisingly, the latter is PSPACE-complete, thus computationally simpler.

11:30
Lower Bounds for the Reachability Problem in Fixed Dimensional VASSes

ABSTRACT. We study the complexity of the reachability problem for Vector Addition Systems with States (VASSes) in fixed dimensions. We provide four lower bounds improving the currently known state-of-art: 1) NP-hardness for unary flat 4-VASSes (VASSes in dimension 4), 2) PSpace-hardness for unary 5-VASSes, 3) ExpSpace-hardness for binary 6-VASSes and 4) Tower-hardness for unary 8-VASSes.

11:45
Probabilistic Verification Beyond Context-Freeness
PRESENTER: Andrzej Murawski

ABSTRACT. Probabilistic pushdown automata (recursive state machines) are a widely known model of probabilistic computation associated with many decidable problems about termination (time) and linear-time model checking. Higher-order recursion schemes (HORS) are a prominent formalism for the analysis of higher-order computation. Recent studies showed that, for the probabilistic variant of HORS, even the basic problem of determining whether a scheme terminates almost surely is undecidable. Moreover, the undecidability already holds for order-2 schemes (order-1 schemes are known to correspond to pushdown automata). Motivated by these results, we study restricted probabilistic tree-stack automata (rPTSA), which in the nondeterministic setting are known to characterise a proper extension of context-free languages, namely, the multiple context-free languages. We show that several verification problems, such as almost-sure termination, positive almost-sure termination and omega-regular model checking are decidable for this class. At the level of higher-order recursion schemes, this corresponds to being able to verify a probabilistic version of the so-called affine-additive higher-order recursion schemes (PAHORS). PAHORS extend order-1 recursion schemes and are incomparable with order-2 schemes.

12:00
Ramsey Quantifiers over Automatic Structures: Complexity and Applications to Verification

ABSTRACT. Automatic structures are infinite structures that are finitely represented by synchronized finite-state automata. We investigate Ramsey quantifiers over automatic structures, which express the existence of infinite cliques in an edge relation, and observe connections to two problems in verification: (1) reachability with (generalized) Büchi conditions in regular model checking can be seen as Ramsey quantification over transitive automatic graphs, (2) checking monadic decomposability of automatic relations can be viewed as Ramsey quantification over co-transitive automatic graphs. We provide a comprehensive complexity landscape of Ramsey quantifiers, all between NL and EXP, which yields a wealth of new results with precise complexity.

12:15
The complexity of bidirected reachability in valence systems
PRESENTER: Georg Zetzsche

ABSTRACT. An infinite-state system is bidirected (sometimes called reversible) if for every transition, there exists another with opposite effect. We study reachability in bidirected systems in the framework of valence systems, an abstract model featuring finitely many control states and an infinite-state storage that is specified by a finite graph. Picking suitable graphs yields counters as in vector addition systems, pushdowns, integer counters, and combinations. We provide a comprehensive complexity analysis. For example, the complexity of bidirected reachability drops substantially (often to polynomial time) from that of general reachability, for almost every storage mechanism where general reachability is known to be decidable.

12:30-14:00Lunch Break

Lunch will be held in Taub lobby (CP, LICS, ICLP) and in The Grand Water Research Institute (KR, FSCD, SAT).

14:00-15:30 Session 78D: Complexity and Circuits

"Complexity and Circuits": 6 papers (12 min presentation + 2-3 min Q&A)

Location: Taub 1
14:00
Separating LREC from LFP

ABSTRACT. LREC= is an extension of first-order logic with a logarithmic recursion operator. It was introduced by Grohe et al. and shown to capture the complexity class L (log-space) over trees and interval graphs. It does not capture L in general as it is contained in FPC - fixed-point logic with counting. We show that this containment is strict. In particular, we show that the path systems problem, a classic P-complete problem which is definable in LFP - fixed-point logic - is not definable in LREC. This shows that the logarithmic recursion mechanism is provably weaker than general least fixed points.

14:15
Reasonable Space for the Lambda-Calculus, Logarithmically
PRESENTER: Gabriele Vanoni

ABSTRACT. Can the lambda-calculus be considered as a reasonable computational model? Can we use it for measuring the time and space consumption of algorithms? While the literature contains positive answers about time, much less is known about space. This paper presents a new reasonable space cost model for the lambda-calculus, given by the space used by a variant over the Krivine abstract machine, and which is the first one able to account for logarithmic space. Moreover, we study the time behavior of our machine and show how to transport the results to the call-by-value lambda-calculus.

14:30
Cyclic Implicit Complexity
PRESENTER: Gianluca Curzi

ABSTRACT. Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have been proposed. However, little is known about the complexity theoretic aspects of circular proofs, which exhibit sophisticated loop structures atypical of more common 'recursion schemes'.

This paper attempts to bridge the gap between circular proofs and implicit computational complexity (ICC). Namely we introduce a circular proof system based on Bellantoni and Cook's famous safe-normal function algebra, and we identify proof theoretical constraints, inspired by ICC, to characterise the polynomial-time and elementary computable functions. Along the way we introduce new recursion theoretic implicit characterisations of these classes that may be of interest in their own right.

14:45
PRESENTER: Klara Nosan

ABSTRACT. We study the Radical Identity Testing problem (RIT): Given an algebraic circuit representing a multivariate polynomial $f(x_1, \dots, x_k)$ and nonnegative integers $a_1, \dots, a_k$ and $d_1, \dots, d_k$, written in binary, test whether the polynomial vanishes at the real radicals $\sqrt[d_1]{a_1}, \dots,\sqrt[d_k]{a_k}$, i.e., test whether $f(\sqrt[d_1]{a_1}, \dots, \sqrt[d_k]{a_k}) = 0$. We place the problem in coNP assuming the Generalised Riemann Hypothesis (GRH), improving on the straightforward PSPACE upper bound obtained by reduction to the existential theory of reals. Next we consider a restricted version, called 2-RIT, where the radicals are square roots of prime numbers, written in binary. It was known since the work of Chen and Kao that 2-RIT is at least as hard as the polynomial identity testing problem, however no better upper bound than PSPACE was known prior to our work. We show that 2-RIT is in coRP assuming GRH and in coNP unconditionally. Our proof relies on theorems from algebraic and analytic number theory, such as the Chebotarev density theorem and quadratic reciprocity.

15:00
Complexity of Modular Circuits
PRESENTER: Piotr Kawałek

ABSTRACT. We study how the complexity of modular circuits computing AND depends on the depth of the circuits and the prime factorization of the modulus they use. In particular, our construction of subexponential circuits of depth 2 for AND helps us to classify (modulo Exponential Time Hypothesis) modular circuits with respect to the complexity of their satisfiability. We also study a precise correlation between this complexity and the sizes of modular circuits realizing AND. On the other hand showing that AND can be computed by a polynomial size probabilistic modular circuit of depth 2 (with O(log n) random bits) providing a probabilistic computational model that can not be derandomized.

We apply our methods to determine (modulo ETH) the complexity of solving equations over groups of symmetries of regular polygons with an odd number of sides. These groups form a paradigm for some of the remaining cases in characterizing finite groups with respect to the complexity of their equation solving.

15:15
Choiceless Polynomial Time with Witnessed Symmetric Choice

ABSTRACT. We extend Choiceless Polynomial Time (CPT), the currently only remaining promising candidate in the quest for a logic capturing PTime, so that this extended logic has the following property: for every class of structures for which isomorphism is definable, the logic automatically captures PTime.

For the construction of this logic we extend CPT by a witnessed symmetric choice operator. This operator allows for choices from definable orbits. But, to ensure polynomial time evaluation, automorphisms have to be provided to certify that the choice set is indeed an orbit.

We argue that, in this logic, definable isomorphism implies definable canonization. Thereby, our construction removes the non-trivial step of extending isomorphism definability results to canonization. This step was a part of proofs that show that CPT or other logics capture PTime on a particular class of structures. The step typically required substantial extra effort.

15:30-16:00Coffee Break
16:00-16:45 Session 81C: CSP, SAT and Boolean Algebra

"CSP, SAT, Boolean algebra": 3 papers (12 min presentation + 2-3 min Q&A)

Location: Taub 1
16:00
On Almost-Uniform Generation of SAT Solutions: The power of 3-wise independent hashing

ABSTRACT. Given epsilon and a Boolean formula F, the problem of almost-uniform generation seeks to generate solutions such that every solution is generated with a probability that is within (1+epsilon)-multiplicative factor of 1/#F where #F is the number of solutions of F. The problem of almost-uniform generation was shown to be inter-reducible to that of randomized approximate counting in the seminal work of Jerrum, Valiant, and Vazirani (TCS, 1986). The proposed reduction, however, requires a linear number of calls to approximate counter, and therefore, provides an O(n log (n) log (n/epsilon)) algorithm that employs pairwise independent hash functions.

In this work, we propose a new algorithm that makes only one call to the approximate counter, and in turn, provides an O( log n * log (1/epsilon) + 1/epsilon) algorithm for an almost-uniform generation. The key ingredient of our approach is a beautiful combination of the usage of approximate counting and 3-wise independent hash functions. Since the standard tabulation-based hash family proposed by Carter and Wegman (STOC 1977) is known to be 3-wise independent, our scheme can be highly efficient in practical applications where a SAT solver is typically used in lieu of a NP oracle. We demonstrate that theoretical improvements translate to practice; in particular, we conduct a comprehensive study over 562 benchmarks and demonstrate that while JVV would time out for 544 out of 562 instances, our proposed scheme can handle all the 562 instances. To the best of our knowledge, this is the first almost-uniform generation scheme that can handle practical instances from real-world applications. We also present a nuanced analysis focusing on the both the size of SAT queries as well as the number of queries.

16:15
Smooth approximations and CSPs over finitely bounded homogeneous structures
PRESENTER: Michael Pinsker

ABSTRACT. We introduce the novel machinery of smooth approximations, and apply it to confirm the CSP dichotomy conjecture for first-order reducts of the random tournament, and to give new short proofs of the conjecture for various homogeneous graphs including the random graph (STOC'11, ICALP'16), and for expansions of the order of the rationals (STOC'08). Apart from obtaining these dichotomy results, we show how our new proof technique allows to unify and significantly simplify the previous results from the literature. For all but the last structure, we moreover characterise for the first time those CSPs which are solvable by local consistency methods, again using the same machinery.

16:30
A first-order completeness result about characteristic Boolean algebras in classical realizability

ABSTRACT. We prove the following completeness result about classical realizability: given any Boolean algebra with at least two elements, there exists a Krivine-style classical realizability model whose characteristic Boolean algebra is elementarily equivalent to it. This is done by controlling precisely which combinations of so-called "angelic" (or "may") and "demonic" (or "must") nondeterminism exist in the underlying model of computation.

16:50-17:30 Session 83: Award Session: Kleene award, LICS Test-of-Time award, Church award

Award Session: Kleene award, LICS Test-of-Time award, Church award

Location: Taub 1


text:
# Expression

If it is true that
$\dfrac{ l + 15 w}{ w} = 6$
, then the value of the expression
$\dfrac{ 13 l}{ 12 w}$
is:

Result

x =  -9.75

#### Solution:

$x = (6-15)\cdot \dfrac{ 13}{ 12} \doteq -9.75$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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text:
# XeLaTeX + \setmainfont{CMU Serif} produces wrong characters

When I'm compiling with XeLaTeX and I use \setmainfont{CMU Serif}, the resulting characters are off by one. This means that an a becomes a b, a 1 becomes a 2, etc.

\documentclass{article}

\usepackage{fontspec}

\setmainfont{CMU Serif}

\begin{document}
Test test2

12345
\end{document}

However, when I use \setmainfont{cmunrm.otf}, using the filename, the output is correct:

When I use \setmainfont{CMU Sans Serif}, the output is also correct, but if I use \setmainfont{CMU Serif Extra}, for example, the output is wrong again, so it seems that there's something wrong with the Serif CMU fonts?

What causes this, and how can I solve it?

Edit: The console output after running xelatex -output-driver="xdvipdfmx -v" test.tex is at http://pastebin.com/nb19aPuc.The log at http://pastebin.com/qgSC07YY. Interesting stuff seems to begin around line 349.

The output of fc-list | grep 'CMU Serif' (http://pastebin.com/BNWzyRkH) seems to suggest that there's not something wrong with the installation of the font.

I'm running MikTex 2.9 on Windows 10 x64, with all packages updated to the latest version (at least, according to the MikTex update tool).

• Welcome to TeX.SX! You seem to have a wrong font somewhere. Can you try running xelatex -output-driver="xdvipdfmx -v" file (where file is your file name, of course) and add the final part of the console output? Chances are that you'll be able to spot what goes wrong. What OS are you on? And what TeX distribution? – egreg Feb 27 '16 at 23:00
• Thanks for the help :). See the edit for more information. – BrtH Feb 27 '16 at 23:15
• There's nothing at the pastebin for the console output – egreg Feb 27 '16 at 23:27
• Oh, strange. A new one: pastebin.com/CaHy2UFB. It's not all that interesting though. – BrtH Feb 27 '16 at 23:30
• No, apparently the relevant information is not shown. Unfortunately I can't test MiKTeX. – egreg Feb 27 '16 at 23:32

Probably type1 fonts are used as native fonts. The old xdvipdfmx was broken for native type1 fonts. In the upcoming xdvipdfmx, which will be in TeX Live 2016, the bugs are fixed. In any case, even in the case of the new xdvipdfmx in which the bugs are fixed, I recommend you to hide

C:/MiKTeX-2.9/fonts/type1

for fontconfig. If you hide the type1 fonts, you will obtain required results even by using the broken xdvipdfmx.

• Commenting out <dir>C:\MiKTeX-2.9\fonts\type1</dir> in C:\Users\username\AppData\Roaming\MiKTeX\2.9\fontconfig\config\localfonts.conf indeed solved the problem. Thanks! However, the file says "DO NOT EDIT THIS FILE! (...) Instead, edit the configuration file localfonts2.conf.". But the file localfonts2.conf only specifies extra folders to add, not folders to delete, as far as I can tell. Would you know of an option to permanently disable a folder? – BrtH Feb 28 '16 at 13:14

I checked your file. It works and gives the right result.

\begin{document}
\setmainfont{CMU Serif Extra}
\noindent Test test2 \\
12345 \\
\setmainfont{CMU Serif}
Test test2 \\
12345
\end{document}

Check: MiKTeX Options -> Formats -> xelatex (non exclude) -> Build. Further:

Update Formats, Refresh FNDB. There should be no errors. Else, try logging in as admin.

My setup: This is XeTeX, Version 3.14159265-2.6-0.99998 (MiKTeX 2.9.6500 64-bit)