We consider the pricing of discretely sampled volatility swaps under a modified Heston model, whose risk-neutralized volatility process contains a stochastic long-run variance level. We derive an analytical forward characteristic function under this model, which has never been presented in the literature before. Based on this, we further obtain an analytical pricing formula for volatility swaps which can guarantee the computational accuracy and efficiency. We also demonstrate the significant impact of the introduced stochastic long-run variance level on volatility swap prices with synthetic as well as calibrated parameters.

In this paper we revisit some classical queueing systems such as the M $^b$ /E $_k$ /1/m and E $_k$ /M $^b$ /1/m queues, for which fast numerical and recursive methods exist to study their main performance measures. We present simple explicit results for the loss probability and queue length distribution of these queueing systems as well as for some related queues such as the M $^b$ /D/1/m queue, the D/M $^b$ /1/m queue, and fluid versions thereof. In order to establish these results we first present a simple analytical solution for the invariant measure of the M/E $_k$ /1 queue that appears to be new.

This study provides an analytic method for the calculation of the cutoff frequencies and waveguide modes of a partially filled eccentric coaxial cable. The method is based on the expressions of the involved electromagnetic fields in bipolar coordinate systems and the validity range of the solution is discussed. It is shown how the waveguide geometry and dielectric parameters may be selected to engineer the lined waveguide's spectral response. Numerical results are included which show good agreement with the corresponding results from full-wave simulations by commercial software.

In the present paper, a general analytical solution is proposed for anisotropic heat conduction through truncated composite spherical shells. The solution is so important in designing the spherical vessels which are usually used to store the CNG, LNG, LPG and other petroleum condensates. Herein, it is supposed that the fiber angle of composite laminate is in range of zero to 90 degrees. Heat convection with ambient flow, an external heat radiation, and a possible internal heat generation are modeled within the heat transfer equation. The exact solution is derived using the complex finite Fourier transform method. The particular solution of transferred equation is found based on the Green’s function and Sturm-Liouville theories. Finally, an inverse integral transformation is applied to form the final analytical solution in physical space. Defining four materials differing in the value of conductivity coefficient in fiber direction, the effects of used composite material and fiber angle on temperature distribution of the spherical shell are investigated in detail.

Supply chains are fundamental to the economy of the world and many supply chains focus on perishable items, such as food, or even clothing that is subject to a limited shelf life due to fashion and seasonable effects. G-networks have not been previously applied to this important area. Thus in this paper, we apply G-networks to supply chain systems and investigate an optimal order allocation problem for a N-node supply chain with perishable products that share the same order source of fresh products. The objective is to find an optimal order allocation strategy to minimize the purchase price per object from the perspective of the customers. An analytical solution based on G-networks with batch removal, together with optimization methods are shown to produce the desired results. The results are illustrated by a numerical example with realistic parameters.

The effect of inertial forces on the Structural Dynamics (SD) behaviour of Elastic Flapping Wings (EFWs) is investigated. In this regard, an analytical modal-based SD solution of EFW undergoing a prescribed rigid body motion is initially derived. The formulated initial-value problem is solved analytically to study the EFW structural responses, and sensitivity with respect to EFWs’ key parameters. As a case study, a rectangular wing undergoing a prescribed sinusoidal motion is simulated. The analytical solution is derived for the first time and helps towards a conceptual understanding of the overall EFW's SD behaviour and its analysis required in their designs. Specifically, the EFW transient and steady response in on-off servo condition is also attended.

Mirage is a camera pose estimation method that analytically solves pose parameters in linear time for multi-camera systems. It utilizes a reference camera pose to calculate the pose by minimizing the 2D projection error between reference and actual pixel coordinates. Previously, Mirage has been successfully applied to trajectory tracking (visual servoing) problem. In this study, a comprehensive evaluation of Mirage is performed by particularly focusing on the area of camera pose estimation. Experiments have been performed using simulated and real data on noisy and noise-free environments. The results are compared with the state-of-the-art techniques. Mirage outperforms other methods by generating fast and accurate results in all tested environments.

An analytical solution is launched for Twin-cell Composite Box Beam (TCCBB) considering the impact of shear lag effects of concrete slab and twin-cell steel girder. To in-depth explore its mechanical mechanism, a new warping displacement mode of wide flange is chosen to meet the essential deformation feature of this TCCBB model by authors. Combining the virtual work principle with the thin-walled beam theory, its governing equations and boundary conditions are established for the TCCBB model. Closed form solutions for longitudinal strain and its shear lag coefficients are also derived under concentrated loads. What's more, experiment investigation and related parameter impact analysis are carried out for this established TCCBB model. Through this research, it shows that the proposed method can be applied to describe and predict shear lag behaviors for this type of composite structure. That further suggests that it provides a certain reference value for engineering design and its late reinforcement and maintenance in the composite structure.

In this paper, He's homotopy perturbation method is utilized to obtain the analytical solution for the nonlinear natural frequency of functionally graded nanobeam. The functionally graded nanobeam is modeled using the Eringen's nonlocal elasticity theory based on Euler-Bernoulli beam theory with von Karman nonlinearity relation. The boundary conditions of problem are considered with both sides simply supported and simply supported-clamped. The Galerkin's method is utilized to decrease the nonlinear partial differential equation to a nonlinear second-order ordinary differential equation. Based on numerical results, homotopy perturbation method convergence is illustrated. According to obtained results, it is seen that the second term of the homotopy perturbation method gives extremely precise solution.

This paper is concerned with a low-dimensional dynamical system model for analytically solving partial differential equations (PDEs). The model proposed is based on a posterior optimal truncated weighted residue (POT-WR) method, by which an infinite dimensional PDE is optimally truncated and analytically solved in required condition of accuracy. To end that, a POT-WR condition for PDE under consideration is used as a dynamically optimal control criterion with the solving process. A set of bases needs to be constructed without any reference database in order to establish a space to describe low-dimensional dynamical system that is required. The Lagrangian multiplier is introduced to release the constraints due to the Galerkin projection, and a penalty function is also employed to remove the orthogonal constraints. According to the extreme principle, a set of ordinary differential equations is thus obtained by taking the variational operation of the generalized optimal function. A conjugate gradient algorithm by FORTRAN code is developed to solve the ordinary differential equations. The two examples of one-dimensional heat transfer equation and nonlinear Burgers’ equation show that the analytical results on the method proposed are good agreement with the numerical simulations and analytical solutions in references, and the dominant characteristics of the dynamics are well captured in case of few bases used only.

In the present study, an exact solution for free vibration analysis of piezoelectric nanobeams based on the nonlocal theory is obtained. The Euler beam model for a long and thin beam structure is employed, together with the electric potential satisfying the surface free charge condition for free vibration analysis. The governing equations and the boundary conditions are derived using Hamilton's principle. These equations are solved analytically for the vibration frequencies of beams with various end conditions. The model has been verified with the previously published works and found a good agreement with them. A detailed parametric study is conducted to discuss the influences of the nonlocal parameter, on the vibration characteristics of piezoelectric nanobeams. The exact vibration solutions should serve as benchmark results for verifying numerically obtained solutions based on other beam models and solution techniques.

In this paper, free vibration analysis of functionally graded rectangular plate is investigated based on the first order shear deformation theory and the effect of in-plane displacements on the natural frequencies of such plate is studied. The governing equations of motion are obtained, which are five coupled partial differential equations, without any simplification. Some mathematical manipulation leads us to decouple the equations. The decoupled equations are solved by the Levy's method for various boundary conditions. As the results show, in some boundary conditions the in-plane displacements cause a drastic change of frequencies. In other words, neglecting the in-plane displacement, which is assumed in some papers, is not proper for these boundary conditions. However, in the other boundary conditions, the natural frequencies are not significantly affected by the in-plane displacements. The results for various boundary conditions are discussed in detail and some interpretations for these differences are provided. Besides to the comparisons, the accurate natural frequencies of the plate for six different boundary conditions with several aspect ratios, thickness-length ratios and power law indices are presented. The natural frequencies of Mindlin functionally graded rectangular plates with considering the in-plane displacements are reported for the first time and can be used as benchmark.

The goal of the combustion research is to achieve optimum combustion mode. Reaction Front velocity is one of the most important parameter that is studied in this field. Most biomass consumed at the present time is burned in fixed or moving beds. Fixed-bed combustion systems are characterized by the slow combustion of large particles subjected to an oxidizing ambient. In this paper a model for propagation of a reaction front of wood particles in a fixed Bed is presented. Once the bed is ignited, an apparent flame zone is formed at the bed's top surface and the flame front moves downwards into the bed of fuel at a speed depending on fuel type and operating parameters. Effect of different parameters such as air flow rate through the bed, primary air temperature, moisture content, particle size and number density of fuel particles on the reaction front velocity has been studied. In order to compare the results of this model with the associated experimental data three species of wood fuels are studied and the agreement is found to be satisfactory.

An analytical solution to compute the 3D steady state temperature distribution in abearing ring is presented in this paper. The ring is formed by a hollow cylinder of finitelength. Its radial external surface is subjected to localized, identical heat sources,equally spaced in the azimuth direction. This surface is also subjected to convectivecooling while as the internal surface is maintained at a uniform temperature. Thedeveloped solution is explicit and does not impose any restriction on the geometrical orphysical parameters.

In this paper, we extend the results in the literature for boundary layer flow over a horizontal plate, by considering the buoyancy force term in the momentum equation. Using a similarity transformation, we transform the partial differential equations of the problem into coupled nonlinear ordinary differential equations. We first analyse several special cases dealing with the properties of the exact and approximate solutions. Then, for the general problem, we construct series solutions for arbitrary values of the physical parameters. Furthermore, we obtain numerical solutions for several sets of values of the parameters. The numerical results thus obtained are presented through graphs and tables and the effects of the physical parameters on the flow and heat transfer characteristics are discussed. The results obtained reveal many interesting behaviours that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

The present work considers the turbulent air flow inside an annular high speed rotor-stator cavity opened to the atmosphere at the periphery, where the pre-swirl ratio of the fluid is low. The interdisk spacing is sufficiently large so that the boundary layers developed on each disk are separated and the flow belongs to the regime IV of Daily and Nece (ASME J. Basic Eng. 82 (1960) 217–232). In such a system, the solid body rotation of the core predicted by Batchelor (J. Mech. Appl. Math. 4 (1951) 29–41) in case of infinite disks is not always observed: the flow behaviour in the whole interdisk spacing is governed by the level of the pre-swirl velocity of the fluid which is closely linked to the peripheral geometry (Debuchy et al., Int. J. Rotating Machinery, (2007)). In the first part of the paper, experimental results performed by hot-wire probes introduced through the stator including mean radial and tangential velocity components, as well as three turbulent correlations, are presented for several peripheral boundary conditions leading to the same value of the pre-swirl ratio. In the second part, comparisons between experiments, numerical and analytical results are provided. The numerical approach is based on the Reynolds Stress Modeling (RSM) developed by Elena and Schiestel (Int. J. Heat Fluid Flow 17 (1996) 283–289). A good agreement between the different approaches is obtained for the mean and turbulent fields and especially for the distribution of the core swirl ratio.

The present paper uses an analytical approach to derive approximate closed-form solutions for the asset moments of a real-business-cycle model with idiosyncratic risk. To preserve analytical tractability, risk sharing is completely shut down. Further, the firm is assumed to maximize a variant of value maximization, given that its usual objective is no longer well defined under market incompleteness. When idiosyncratic risk is incorporated into the model, the asset moments can be decomposed into their value under identical households plus a new idiosyncratic term. Under full constrained persistence, in which case the same household determines the asset moments every period, the model is able to generate the risk premium in the data with reasonable parameter values, but it cannot generate the risk return trade-off. While the quantitative impact of idiosyncratic risk is smaller when there is only some persistence in who is constrained, the qualitative predictions are unaltered.