"Version: 20240201"--Title page verso.Includes bibliographical references.1. Manifolds -- 1.1. What is a manifold? -- 1.2. Curves and surfaces in a manifold -- 1.3. Coordinate transformations and summation convention -- 1.4. The local geometry of a manifold -- 1.5. Length, area, and volume -- 1.6. Local Cartesian coordinates and tangent space -- 1.7. The signature of a manifold -- 1.8. N-dimens…
"Version: 20240101"--Title page verso.Includes bibliographical references.1. Introduction -- 1.1. Singularity -- 1.2. Singularities in science and engineering -- 1.3. Acoustic vortex -- 1.4. Singularities in optics -- 1.5. Amplitude, phase and polarization -- 1.6. Brief historical account of optical phase singularities2. Topological features -- 2.1. Introduction -- 2.2. Wavefront shape -- 2.3. …
"Version: 20221201"--Title page verso.Includes bibliographical references.1. Formulas for the sums of the series of reciprocals of the cubic polynomials with integer roots, at least one zero / Radovan Pot?euc?eek -- 2. Polynomials for meshless methods in finding solutions in gradient elasticity problems / N. Fantuzzi, S. Saitta, F. Fabbrocino, R. Vescovini and R. Luciano -- 3. Numerical solutio…
"Version: 20230801"--Title page verso.Includes bibliographical references.1. The static behavior of functionally graded beams / Sahmani Saeid and Safaei Babak -- 2. The static behavior of functionally graded sandwich beams / Akgo?z Bekir and Civalek ?Omer -- 3. The static behavior of functionally graded plates / Shahriar Dastjerdi and Bekir Akgo?z -- 4. The static bending analysis of porous fun…
"Version: 20181001"--Title page verso.Includes bibliographical references.1. Hypergeometric series -- 1.1. Introduction -- 1.2. The Gauss differential equation -- 1.3. Special functions -- 1.4. Properties of the hypergeometric functions -- 1.5. A conjecture2. Group theory: basics -- 2.1. Introduction -- 2.2. Invariances, symmetries, and physics -- 2.3. Discrete groups -- 2.4. The symmetric grou…
"Version: 20190601"--Title page verso.Includes bibliographical references and index.1. Forms of quantum mechanics -- 1.1. The Schr?odinger and Heisenberg pictures -- 1.2. Interaction picture -- 1.3. Density-matrix formulation of quantum mechanics -- 1.4. Further contents of Heisenberg's commutation relations2. Lorentz group and its representations -- 2.1. Lie algebra of the Lorentz group -- 2.2…
"Version: 20181001"--Title page verso.Includes bibliographical references.1. Research and application of reflective microscopy -- 1.1. Introduction -- 1.2. Current situation of research on reflective microscopy -- 1.3. The current situation of application of reflective microscopy -- 1.4. Summary2. Apodization factor and linearly polarized light focusing properties of elliptical mirror -- 2.1. I…
"Version: 20181101"--Title page verso.Includes bibliographical references.1. Introduction -- 1.1. Classical mechanics -- 1.2. Rise of quantum mechanics -- 1.3. Eugene Wigner -- 1.4. Modern devices and simulation -- 1.5. Our approach2. Approaches to quantum transport -- 2.1. Modes and the Landauer formula -- 2.2. The scattering matrix approach -- 2.3. The density matrix -- 2.4. Green's functions…
"Version: 20181101"--Title page verso.Includes bibliographical references.1. Introduction -- 1.1. Singularity -- 1.2. Singularities in science and engineering -- 1.3. Acoustic vortex -- 1.4. Singularities in optics -- 1.5. Amplitude, phase and polarization -- 1.6. Brief historical account of optical phase singularities2. Topological features -- 2.1. Introduction -- 2.2. Wavefront shape -- 2.3. …
"Version: 20181101"--Title page verso.Includes bibliographical references.1. Linear and perturbed equations -- 1.1. Stability analysis -- 1.2. Lyapunov regularity2. Nonlinear differential equations -- 2.1. Continuous dependence and stability of solutions -- 2.2. Orbital Hausdorff dependence of the solutions -- 2.3. Differentiability of solutions3. Semilinear evolution equations -- 3.1. First-or…