In this study, high energy energy derivatives of TEX with different carbon-containing fullerenes at different temperature conditions were studied using density functional theory. For this purpose, the materials were first geometric optimized, then the thermodynamic parameters were calculated for all of them. Then, the process of changing the energy-dependent parameters such as specific heat cap...

In this study, based on nonlocal differential constitutive relations of Eringen, the first order shear deformation theory of plates (FSDT) is reformulated for vibration of nano-plates considering the initial geometric imperfection. The dynamic analog of the von Kármán nonlinear strain-displacement relations is used to derive equations of motion for the nano-plate. When dealing with nonlineariti...

The classical shell theory, first-order shear deformation theory, and third-order shear deformation theory are employed to study the natural frequencies of functionally graded cylindrical shells. The governing equations of motion describing the vibration behavior of functionally graded cylindrical shells are derived by Hamilton’s principle. Resulting equations are solved using the Navier-type s...

In this talk we discuss and characterize multivariate geometric distributions with lack-of-memory (LM) property. First, a multivariate extension of the univariate geometric law is derived using a discrete analogue of the Marshall-Olkin exponential “shock model”. It is shown that only the subclass of multivariate LM distributions with positively correlated components can be obtained in this way....

Geometric phases of simple harmonic oscillator system are studied. Complete sets of ”eigenfunctions” are constructed, which depend on the way of choosing classical solutions. For an eigenfunction, two different motions of the probability distribution function (pulsation of the width and oscillation of the center) contribute to the geometric phase which can be given in terms of the parameters of...

We address the safety-critical control problem for systems whose dynamics evolve on manifolds using the concepts of control Lyapunov functions (CLFs) and control Barrier functions (CBFs). We first extend the concepts of CLFs and CBFs from Cartesian spaces to manifolds, resulting in geometric CLFs and CBFs. We then formulate a state-dependent online quadratic program (QP) that imposes the constr...

In this article we consider rough differential equations (RDEs) driven by non-geometric rough paths, using the concept of branched rough paths introduced in [Gub10]. We first show that branched rough paths can equivalently be defined as γ-Hölder continuous paths in some Lie group, akin to geometric rough paths. We then show that every branched rough path can be encoded in a geometric rough path...