LEADER 03069nam 2200589 450 001 9910788734603321 005 20170822144323.0 010 $a1-4704-0218-1 035 $a(CKB)3360000000464813 035 $a(EBL)3114373 035 $a(SSID)ssj0000889211 035 $a(PQKBManifestationID)11478759 035 $a(PQKBTitleCode)TC0000889211 035 $a(PQKBWorkID)10876022 035 $a(PQKB)10457235 035 $a(MiAaPQ)EBC3114373 035 $a(RPAM)1655616 035 $a(PPN)195415132 035 $a(EXLCZ)993360000000464813 100 $a19971112d1998 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aShort-time geometry of random heat kernels /$fRichard B. Sowers 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1998. 215 $a1 online resource (145 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 629 300 $a"March 1998, volume 132, number 629 (end of volume)." 311 $a0-8218-0649-1 320 $aIncludes bibliographical references. 327 $a""Contents""; ""Chapter 1. Introduction""; ""A?1.1. The Short-Time Problem""; ""A?1.2. The Main Results and Some Examples""; ""A?1.3. Notation and Assumptions""; ""Chapter 2. Guessing the Dominant Asymptotics""; ""A?2.1. A Simpler Problem""; ""A?2.2. A Minimization Problem""; ""A?2.3. A Rate Function and Approximation for the Random Heat Kernel""; ""A?2.4. Representation Results for the Secondary and Tertiary Terms""; ""Chapter 3. Initial Condition and Evolution of the Approximate Kernel""; ""A?3.1. The Short-Time Behavior of the Approximation""; ""A?3.2. The Evolution of the Approximation"" 327 $a""Chapter 4. The Minakshisundaram-Pleijel Coefficients""""A?4.1. An Ansatz""; ""A?4.2. Some Results on Multiple Wiener Integrals""; ""A?4.3. The Minakshisundaram-Pleijel Expansion""; ""Chapter 5. Error Estimates, Proof of the Main Theorem, and Extensions""; ""A?5.1. Setup of Equations""; ""A?5.2. Estimates on the Continuity of SPDE's""; ""A?5.3. The Near-Field Error""; ""A?5.4. The Far-Field Error""; ""A?5.5. Proof of the Main Theorem""; ""A?5.6. Extensions""; ""Appendices""; ""Appendix A: The Jacobi Flow""; ""Appendix B: Some Results on Multiple Wiener Integrals"" 327 $a""Appendix C: Garsia-Rodemich-Rumsey Estimates""""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 629. 606 $aHeat equation 606 $aStochastic partial differential equations 606 $aFilters (Mathematics) 615 0$aHeat equation. 615 0$aStochastic partial differential equations. 615 0$aFilters (Mathematics) 676 $a510 s 676 $a519.2 700 $aSowers$b R. B$g(Richard Bucher),$f1965-$01580679 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788734603321 996 $aShort-time geometry of random heat kernels$93861786 997 $aUNINA LEADER 05071nam 22006731 450 001 9910955725503321 005 20240405120946.0 010 $a9783038130376 010 $a3038130370 035 $a(CKB)2550000001143176 035 $a(EBL)1865195 035 $a(SSID)ssj0000760459 035 $a(PQKBManifestationID)11510643 035 $a(PQKBTitleCode)TC0000760459 035 $a(PQKBWorkID)10810888 035 $a(PQKB)11773063 035 $a(Au-PeEL)EBL1865195 035 $a(CaPaEBR)ebr10814646 035 $a(OCoLC)868922183 035 $a(MiAaPQ)EBC1865195 035 $a(EXLCZ)992550000001143176 100 $a20051020h20052005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMacro-, meso-, micro- and nano-mechanics of materials $especial issue containing the proceedings of the International Symposium on Macro-, Meso-, Micro- and Nano-Mechanics of Materials : (MM2003) : 8-10 December, 2003, Hong Kong /$fedited by Tong Yi-Zhang and Jang-Kyo Kim ; organized by Department of Mechanical Enginering, Hong Kong University of Science and Technology 205 $a1st ed. 210 1$aUetikon-Zuerich, Switzerland :$cTrans Tech Publications Ltd,$d[2005] 210 4$dİ2005 215 $a1 online resource (208 p.) 225 1 $aAdvanced materials research ;$vvolume 9 300 $a"MM2003 was originally incepted to honor Professor Pin Tong ... on the occasion of his 65th birthday."--Pref. 311 08$a9780878499793 311 08$a0878499792 320 $aIncludes bibliographical references and indexes. 327 $aMacro-, Meso-, Micro- and Nano-Mechanics of Materials; Preface; Table of Contents; Finite Element Analysis of Particle Reinforced Composite Using Different Cell Models; Active Finite Element Method for Simulating the Contraction Behavior of a Muscle-Tendon Complex; Microstructure of the Fiber/Matrix of Chafer Cuticle; Residual Stress and Stress-Strain Relationship of Electrodeposited Nickel Coatings; Failure of Thermal Barrier Ceramic Coating Induced by Buckling Due to Temperature Gradient and Creep; Cyclic Stress-Strain Behavior and Thermomechanical Effect in Metal Matrix Composites 327 $aOptimization of Residual Thermal Stress in SiC/C Plasma Facing Material for Future Tokamak Facilities of ChinaInfluence of Surface Properties on Microscratch Durability of Aluminum Nitride Semiconductor Processing Component; Thermal Shock and Thermal Fatigue of Ferroelectric Thin Film due to Pulsed Laser Heating; Fatigue Damage of Materials with Small Crack Calculated by the Ratio-Method under Cyclic Loading ; Dynamic Strength of Steel Welds under High Strain Rate Loading; Synthesis and Mechanical Properties of Nanostructured Mg-Al-Nd Alloys 327 $aStudy on Fracture Behaviors of High-Density Polyethylene Pipe Material Based on Local ApproachEffects of Gun Tube Profile and Sabot on Stresses and Velocity of Long Rod Penetrator; Numerical Study on Cracking Process of Masonry Structure; Micromechanical Model for Simulating Hydraulic Fractures of Rock ; Residual Stress and Surface Molding Conditions in Thin Wall Injection Molding; Symplectic Solution for a Plane Couple Stress Problem; Multi-Scale and Finite Element Analysis of the Mixed Boundary Value Problem in a Perforated Domain under Coupled Thermoelasticity 327 $aSimulation of Multiple Hydraulic Fracturing in Non-Uniform Pore Pressure FieldMechanics Framework for Micron-Scale Planar Structures ; A Piezoelectric Screw Dislocation Interacting with a Dielectric Crack in a Hexagonal Piezoelectric Material ; Surface Electrode Problems in Piezoelectric Materials; Keywords Index; Authors Index 330 $aThis compilation of selected papers has, as its principal objective, the discussion of state-of-the-art technologies and recent developments in the macro-, meso-, micro- and nano-mechanics of materials and structures. The focus is on the most recent advances in strength, fracture and mechanics of micro- and nano-structured materials. It also serves to narrow the gaps between conventional macro-/meso- systems and the emerging micro-/nano- materials technologies. The papers are arranged into two categories: ""Composite Materials; Thin Films and Coatings"" and ""Fracture, Fatigue and Strengths of 410 0$aAdvanced materials research ;$vv. 9. 606 $aMaterials$vCongresses 606 $aStrength of materials$vCongresses 615 0$aMaterials 615 0$aStrength of materials 676 $a620.11292 701 $aKim$b Jang-Kyo$0627307 701 $aZhang$b Tong-Yi$f1949-$01815422 712 02$aHong Kong University of Science and Technology.$bDepartment of Mechanical Engineering. 712 12$aInternational Symposium on Macro-, Meso-, Micro and Nano-Mechanics of Materials 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910955725503321 996 $aMacro-, meso-, micro- and nano-mechanics of materials$94370392 997 $aUNINA