PPAD-hardness for constant-δ approximate competitive equilibria in SPLC Fisher markets requires the PCP-for-PPAD conjecture, which the paper proves is necessary to establish such hardness.
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11 Pith papers cite this work. Polarity classification is still indexing.
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Graphical Algebraic Geometry creates universal diagrammatic languages for commutative algebras and affine varieties that also characterize the qudit ZH calculus for quantum computation.
Phase-field peridynamics degrades bond energies continuously via a bond phase-field parameter while using kinematic degradation to preserve nonlocal deformation gradient accuracy, with an analytically derived normalization constant for thermodynamic consistency.
New algorithm computes holonomic submodule of partial Weyl closure via non-commutative Rabinowitsch trick, implemented in Julia with reported speedups over Singular and Macaulay2.
Monte-Carlo simulations with an ML potential demonstrate that coherency strain removes the Ag-Cu miscibility gap in Ag_xCu_{1-x}GaSe2, producing complete mixing.
Volumetric growth in linear elasticity is cast as a constrained optimization problem that determines the growth tensor at each step while satisfying equilibrium, mass balance, and irreversibility.
Derives exact distributions for two-step restricted-angle 2D random walks, numerical solutions for general steps, large-step approximations, and exact support characterization.
Relativistic SOC corrections to the magnetic moment operator create an abnormal magnetic moment, render spin-orbital decomposition ambiguous, and require a new Kubo formula for the kinetic magnetoelectric effect that includes noncommuting position and partial-B operators.
Generalized Markov operators on deficient topological measures admit unique invariants under Kantorovich-Rubinstein contractions; a new equivariant generalized sample median is introduced; topological measures on spaces of covering dimension at most 1 coincide with Radon measures.
The paper constructs asymptotic expansions for one-phase and two-phase soliton-like and peakon-like solutions of the variable-coefficient Camassa-Holm equation with small dispersion and proves their asymptotic accuracy.
Existence of solutions is shown for the third operator of the Connaughton-Newell model when the interaction kernel is constant and the source term is well-behaved.
citing papers explorer
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Fisher Markets with Approximately Optimal Bundles and the Need for a PCP Theorem for PPAD
PPAD-hardness for constant-δ approximate competitive equilibria in SPLC Fisher markets requires the PCP-for-PPAD conjecture, which the paper proves is necessary to establish such hardness.
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Graphical Algebraic Geometry: From Ideals and Varieties to Quantum Calculi
Graphical Algebraic Geometry creates universal diagrammatic languages for commutative algebras and affine varieties that also characterize the qudit ZH calculus for quantum computation.
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Phase-Field Peridynamics
Phase-field peridynamics degrades bond energies continuously via a bond phase-field parameter while using kinematic degradation to preserve nonlocal deformation gradient accuracy, with an analytically derived normalization constant for thermodynamic consistency.
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Computing a holonomic submodule of the partial Weyl closure
New algorithm computes holonomic submodule of partial Weyl closure via non-commutative Rabinowitsch trick, implemented in Julia with reported speedups over Singular and Macaulay2.
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Chemo-mechanical coupling stabilizes mixed $\mathrm{Ag}_{x}\mathrm{Cu}_{1-x}\mathrm{GaSe}_{2}$ solar-cell absorbers: Insights from Monte-Carlo simulations assisted by ab initio informed machine-learning potentials
Monte-Carlo simulations with an ML potential demonstrate that coherency strain removes the Ag-Cu miscibility gap in Ag_xCu_{1-x}GaSe2, producing complete mixing.
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Volumetric Growth in Linear Elasticity Driven by an Optimality Criterion
Volumetric growth in linear elasticity is cast as a constrained optimization problem that determines the growth tensor at each step while satisfying equilibrium, mass balance, and irreversibility.
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On the Distribution of a Two-Dimensional Random Walk with Restricted Angles
Derives exact distributions for two-step restricted-angle 2D random walks, numerical solutions for general steps, large-step approximations, and exact support characterization.
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Magnetic moment of electrons in systems with spin-orbit coupling
Relativistic SOC corrections to the magnetic moment operator create an abnormal magnetic moment, render spin-orbital decomposition ambiguous, and require a new Kubo formula for the kinetic magnetoelectric effect that includes noncommuting position and partial-B operators.
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Image transformations, Markov operators, and sample median
Generalized Markov operators on deficient topological measures admit unique invariants under Kantorovich-Rubinstein contractions; a new equivariant generalized sample median is introduced; topological measures on spaces of covering dimension at most 1 coincide with Radon measures.
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Soliton-like solutions of the Camassa--Holm equation with variable coefficients and a small dispersion
The paper constructs asymptotic expansions for one-phase and two-phase soliton-like and peakon-like solutions of the variable-coefficient Camassa-Holm equation with small dispersion and proves their asymptotic accuracy.
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Existence of Solutions of the third term of the Connaughton-Newell Model with a source term
Existence of solutions is shown for the third operator of the Connaughton-Newell model when the interaction kernel is constant and the source term is well-behaved.