Keywords: گروه بحرانی; primary; 05C50; secondary; 05C25; Graph Laplacian; Critical group; Abelian sandpile; Chip-firing; Matrix-tree theorem;
مقالات ISI گروه بحرانی (ترجمه نشده)
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Keywords: گروه بحرانی; Arithmetical graph; Ballot number; Catalan number; Critical group; Sandpile group; Laplacian;
Keywords: گروه بحرانی; Invariant factors; Elementary divisors; Smith normal form; Critical group; Jacobian group; Sandpile group; Adjacency matrix; Laplacian; Chip-firing; Moore graph;
Keywords: گروه بحرانی; 58E05; 34C25; Periodic solution; Hamiltonian system; Resonance; Critical group; Maslov-type index;
Keywords: گروه بحرانی; Spanning trees; Break divisors; Matrix-tree theorem; Jacobian; Tropical Jacobian; Sandpile group; Critical group; Bernardi process; Geometric bijections;
Keywords: گروه بحرانی; primary; 13F20; secondary; 13P10; 05C50; 05E99; Critical ideals; Algebraic co-rank; Twin vertices; Replication; Duplication; Critical group;
Keywords: گروه بحرانی; Smith normal form; Diagonal form; Critical group; Random matrix; Jacobi–Trudi matrix; Varchenko matrix
Keywords: گروه بحرانی; Critical group; Clique-inserted graph; Regular graph; Cycle space; Bond space;
Keywords: گروه بحرانی; Critical ideal; Critical group; Generalized Laplacian matrix; Forbidden induced subgraph
The critical group of the Kneser graph on 2-subsets of an n-element set
Keywords: گروه بحرانی; 05C50; Invariant factors; Elementary divisors; Smith normal form; Critical group; Jacobian group; Sandpile group; Laplacian matrix; Kneser graph;
On a problem of L.A. Shemetkov on superradical formations of finite groups
Keywords: گروه بحرانی; 20D10; 20D20; Finite group; Saturated formation; Critical group;
Integer invariants of abelian Cayley graphs
Keywords: گروه بحرانی; 05C50Cayley graphs; Invariant factors; Elementary divisors; Smith normal form; Smith group; Critical group; Association schemes; Adjacency matrix; Cartesian product of graphs; n-Cube; Laplacian
Existence and multiplicity results for partially superquadratic elliptic systems
Keywords: گروه بحرانی; Elliptic system; Critical group; Nontrivial solution;
On the critical ideals of graphs
Keywords: گروه بحرانی; primary, 13F20; secondary, 13P10, 05C50, 05E99Critical ideals; Critical group; Generalized Laplacian matrix; Determinantal ideal; Gröbner basis; Stability number; Clique number; Cycle; Complete graph
Nontrivial solutions of a second order difference systems with multiple resonance
Keywords: گروه بحرانی; Difference systems; Multiple resonance; Critical group; Morse theory;
Multiple sign-changing solutions to the Sturm-Liouville boundary value problem with resonance
Keywords: گروه بحرانی; Sturm-Liouville boundary value problem; Sign-changing solution; Topological degree; Fixed point index; Critical group;
Nontrivial solutions for discrete boundary value problems with multiple resonance via computations of the critical groups
Keywords: گروه بحرانی; Difference equations; Multiple resonance; Critical group; Morse theory
On the sandpile group of the cone of a graph
Keywords: گروه بحرانی; Primary: 05C25; Secondary: 05C50, 05E99; Sandpile group; Critical group; Graph homomorphism; Cartesian product; Hypercube;
Existence of solutions for 2mth-order periodic boundary value problems
Keywords: گروه بحرانی; 2mth-order PBVP; Nontrivial solutions; Critical group; Morse theory;
Solutions to a gradient system with resonance at both zero and infinity
Keywords: گروه بحرانی; 35J10; 35J65; 58E05Gradient system; Resonance; Critical group; Morse theory; Local linking
Multiple solutions of some boundary value problems with parameters
Keywords: گروه بحرانی; Boundary value problem; Critical group; Morse theory
Multiple sign-changing solutions to semilinear elliptic resonant problems
Keywords: گروه بحرانی; Sign-changing solution; Elliptic resonant problem; Topological degree; Critical group
Modelling radioactivity in the Irish Sea: From discharge to dose
Keywords: گروه بحرانی; Modelling; Radionuclides; Irish Sea; Dose; Critical group; Transport processes
Critical groups for homeomorphism classes of graphs
Keywords: گروه بحرانی; Critical group; Laplacian matrix; Homeomorphism class; Cyclic group
Multiple solutions to fourth-order boundary value problems
Keywords: گروه بحرانی; Fourth-order boundary value problem; Multiple solutions; Critical point; Critical group; Morse theory
Nontrivial solutions for some fourth order boundary value problems with parameters
Keywords: گروه بحرانی; Boundary value problem; Variational methods; Critical group; Critical point; Morse theory
Existence of multiple nontrivial solutions for semilinear elliptic problems
Keywords: گروه بحرانی; Minimax method; Critical group; Morse theory; Multiple solutions
Multiple solutions of some nonlinear fourth-order beam equations
Keywords: گروه بحرانی; Boundary value problems; Critical points; Critical group; Morse inequality
Multiplicity results for quasi-linear problems
Keywords: گروه بحرانی; 58E05; 35J65; 49B27pp-Laplacian; Variational method; Critical group; Multiple solution; Morse theory
Multi-bump solutions for a strongly indefinite semilinear Schrödinger equation without symmetry or convexity assumptions
Keywords: گروه بحرانی; 35J20; 35J70Semilinear Schrödinger equation; Multi-bump solutions; Critical group; Reduction methods
Multiple nontrivial solutions for some fourth-order semilinear elliptic problems
Keywords: گروه بحرانی; Critical group; Homological nontrivial critical point; Morse theory; Local linking; Multiple solutions; Travelling waves;