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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
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
Analysis and PDE, ISSN 2157-5045, 2017, Volume 10, Issue 3, pp. 695 - 727
.... In particular, we focus on degenerate, i.e., "flexible", weak solutions that can be constructed through methods of convex integration a la Nash and Kuiper and establish... 
Convex integration | Rigidity and flexibility | Developable surfaces | H-principle | Monge-Ampére equation | DISSIPATION | MATHEMATICS, APPLIED | CODIMENSION | Monge-Ampere equation | developable surfaces | PERONA-MALIK EQUATION | ISOMETRIC IMMERSIONS | DIFFERENTIAL INCLUSION | GRADIENT RANGE | MATHEMATICS | convex integration | REGULARITY | h-principle | MAPPINGS | WEAK SOLUTIONS | EULER EQUATIONS | rigidity and flexibility
Journal Article
Proceedings of the National Academy of Sciences of the United States of America, 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
Nonlinear Analysis, ISSN 0362-546X, 2012, Volume 75, Issue 3, pp. 1188 - 1201
Starting from explicit expressions for the subdifferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions... 
Epi-pointed functions | Conjugate function | Integration | [formula omitted]-subdifferential | Lower semicontinuous convex envelope | ε-subdifferential | epsilon-subdifferential | CRITERIA | MATHEMATICS, APPLIED | DIFFERENTIABILITY | CALCULUS | PROPERTY | REPRESENTATION | MONOTONICITY | CONVEX-FUNCTIONS | MATHEMATICS | Conjugates | Envelopes | Nonlinearity | Construction | Banach space
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2015, Volume 47, Issue 4, pp. 2770 - 2794
.... We finally fulfill this density hypothesis by convex integration based on certain approximations from an explicit formula of lamination convex hull of some matrix set involved. 
Convex integration | Infinitely many weak solutions on convex domains | Perona-Malik equation | Differential inclusion | Baire's category method | EXISTENCE | MATHEMATICS, APPLIED | ENERGY | differential inclusion | convex integration | infinitely many weak solutions on convex domains | DIFFUSION-EQUATIONS
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