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SIAM journal on mathematical analysis, ISSN 1095-7154, 2018, Volume 50, Issue 4, pp. 3791 - 3841
In this article we continue our study of higher Sobolev regularity of flexible convex integration solutions to differential inclusions arising from applications in materials sciences... 
Higher Sobolev regularity | Elasticity | Martensitic phase transitions | Convex integration | Weak isometric immersions | Differential inclusion | RIGIDITY RESULT | MATHEMATICS, APPLIED | LINEAR-THEORY | elasticity | higher Sobolev regularity | MICROSTRUCTURES | weak isometric immersions | SURFACE-ENERGY | differential inclusion | convex integration | martensitic phase transitions | PHASE-TRANSITION | ISOMETRIC MAPS
Journal Article
Journal of Complexity, ISSN 0885-064X, 02/2019, Volume 50, pp. 25 - 42
We prove the curse of dimensionality in the worst case setting for multivariate numerical integration for various classes of smooth functions... 
Tractability | [formula omitted]-condition | Thin-shell estimate | Numerical integration | Curse of dimension | Isotropic convex body | condition | MATHEMATICS | MATHEMATICS, APPLIED | CONVEX | SURFACE MEASURE | SPHERE | BODIES | Psi-condition
Journal Article
Proceedings of the National Academy of Sciences - PNAS, ISSN 0027-8424, 5/2012, Volume 109, Issue 19, pp. 7218 - 7223
Journal Article
Complex analysis and operator theory, ISSN 1661-8262, 2018, Volume 13, Issue 4, pp. 1883 - 1893
We study the integration operator between the growth spaces $$H_w^\infty $$ H w ∞ and $$H_u^\infty $$ H u ∞ on the complex plane with arbitrary radial weights w and u... 
Operator Theory | Differentiation operator | 47B38 | Growth space | Analysis | Mathematics, general | Mathematics | Associated weight | Primary 30D15 | Secondary 26A51 | 30H99 | Log-convex weight
Journal Article
Abstract and applied analysis, ISSN 1687-0409, 2012, Volume 2012, pp. 1 - 10
We extend the Montgomery identities for the Riemann-Liouville fractional integrals. We also use these Montgomery identities to establish some new integral... 
MATHEMATICS, APPLIED | Studies | Mathematics | Convex analysis | Inequality
Journal Article
The Journal of geometric analysis, ISSN 1559-002X, 2018, Volume 29, Issue 1, pp. 328 - 369
Journal Article
Journal of Engineering Mechanics, ISSN 0733-9399, 05/2016, Volume 142, Issue 5, p. 4016022
AbstractIn structural dynamics, direct integration algorithms are commonly used to solve the temporally discretized differential equations of motion... 
Technical Papers | Structural dynamics | Accuracy | Nonlinear | Convex optimization | Lyapunov stability | Explicit | Direct integration algorithm | Implicit | Mechanics | Usage | Research | Convex programming
Journal Article
Computational geometry : theory and applications, ISSN 0925-7721, 2013, Volume 46, Issue 3, pp. 232 - 252
Journal Article
IEEE transactions on smart grid, ISSN 1949-3061, 2015, Volume 6, Issue 1, pp. 124 - 134
Microgrid is a key enabling solution to future smart grids by integrating distributed renewable generators and storage systems to efficiently serve the local... 
smart grid | distributed storage | online algorithm | Microgrids | Optimization | Renewable energy sources | renewable energy | Convex optimization | microgrid | Prediction algorithms | energy management | Real-time systems | Energy storage | Load modeling | SYSTEM | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Dynamic programming | Energy management | Renewable resources
Journal Article
Journal of Engineering Mechanics, ISSN 0733-9399, 12/2016, Volume 142, Issue 12, p. 4016098
AbstractIn nonlinear structural dynamics, direct integration algorithms are used to solve the differential equations of motion after they are temporally discretized... 
Technical Papers | Structural dynamics | Nonlinear | Strictly positive realness | Convex optimization | Multi-degree-of-freedom (MDOF) | Lyapunov stability | Explicit | Direct integration algorithm | TIME | POSITIVE REAL LEMMA | ENGINEERING, MECHANICAL | Nonlinear dynamics | Shear | Algorithms | Differential equations | Nonlinearity | Stability analysis | Softening | Dynamical systems
Journal Article
Stochastic partial differential equations : analysis and computations, ISSN 2194-041X, 2018, Volume 6, Issue 4, pp. 618 - 689
Journal Article
Applied categorical structures, ISSN 0927-2852, 2012, Volume 22, Issue 1, pp. 79 - 97
The theory of integration over infinite-dimensional spaces is known to encounter serious difficulties... 
28C20 | Mathematics | Theory of Computation | Point free measures | Boolean rings | 28A60 | Geometry | 16B50 | Convex and Discrete Geometry | Categorical geometry | Segal space | Locales | 03G30 | Mathematical Logic and Foundations | MATHEMATICS | Algebra | Beer
Journal Article
Communications on Stochastic Analysis, ISSN 0973-9599, 2018, Volume 12, Issue 3, pp. 215 - 223
Journal Article
Journal Article
SIAM JOURNAL ON SCIENTIFIC COMPUTING, ISSN 1064-8275, 2019, Volume 41, Issue 5, pp. A3152 - A3181
... available. We present several new families of extended integration formulas that contain such integrals and provide in a special case of our result the multivariate analogues of midpoint, trapezoidal, Hammer, and Simpson rules... 
MATHEMATICS, APPLIED | approximation | cubature formulas | CONVEX | NUMERICAL-INTEGRATION | centroidal Voronoi tessellation | convexity | singularity of integrand | best error estimates | Numerical Analysis | Computer Science
Journal Article