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Any defining role of mast cell or mast cell density in oral squamous cell carcinoma

APPLICATION OF THE DIFFERENTIAL TRANSFORM METHOD TO THE FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED TIMOSHENKO BEAMS

In this study, free vibration characteristics of a functionally graded Timoshenko beam that undergoes flapwise bending vibration is analysed. The energy expressions are derived by introducing several explanotary figures and tables. Applying Hamilton's principle to the energy expressions, governing differential equations of motion and boundary conditions are obtained. In the solution part, the equations of motion, including the parameters for rotary inertia, shear deformation, power law index parameter and slenderness ratio are solved using an efficient mathematical technique, called the differential transform method (DTM). Natural frequencies are calculated and effects of several parameters are investigated

Strategic Generation Capacity Choice under Demand Uncertainty:Analysis of Nash Equilibria in Electricity Markets

Abstract: We analyze a two-stage game of strategic firms facing uncertain demand and exerting market power in decentralized electricity markets. These firms choose their generation capacities at the first stage while anticipating a perfectly competitive future electricity spot market outcome at the second stage; thus it is a closed loop game. In general, such games can be formulated as an equilibrium problem with equilibrium constraints (EPEC) and examples have been posed in the literature that have multiple or no equilibria. Therefore, it is of interest to define general sets of conditions under which solutions exist and are unique, which would enhance the value of such models for policy andmarket intelligence purposes. In this paper, we consider various types of such a closed loop model regarding the underlying price-demand relations (elastic and inelastic demand), the assumed demand uncertainty with a broad class of continuous distributions, and any finite number of players with symmetric or asymmetric costs. We establish sufficient conditions for the random demand’s probability distribution which guarantee existence and uniqueness of equilibria in most of the cases of this closed loop model. We identify a broad class of commonly used continuous probability distributions satisfying these conditions

Generation Capacity Investments in Electricity Markets:Perfect Competition

Abstract: In competitive electricity markets, markets designs based on power exchanges where supply bidding (barring demand-side bidding) is at the sole short run marginal cost may not guarantee resource adequacy. As alternative ways to remedy the resource adequacy problem, we focus on three different market designs in detail when demand is inelastic, namely an energy-only market with VOLL pricing (or a price cap), an additional capacity market, and operating-reserve pricing. We also discuss demand-side bidding (i.e., a price responsive demand) which can be seen as a categorically different alternative to remedy the resource adequacy problem. We consider a perfectly competitive market consisting of three types of agents: generators, a transmission system operator, and consumers; all agents are assumed to have no market power. For each market design, we model and analyze capacity investment choices of firms using a two-stage game where generation capacities are installed in the first stage and generation takes place in future spot markets at the second stage. When future spot market conditions are assumed to be known a priori (i.e., deterministic demand case), we show that all of these two-stage models with different market mechanisms, except operating-reserve pricing, can be cast as single optimization problems. When future spot market conditions are not known in advance (i.e., under demand uncertainty), we essentially have a two-stage stochastic game. Interestingly, an equilibrium point of this stochastic game can be found by solving a two-stage stochastic program, in case of all of the market mechanisms except operating-reserve pricing. In case of operatingreserve pricing, while the formulation of an equivalent deterministic or stochastic optimization problem is possible when operating-reserves are based on observed demand, this simplicity is lost when operatingreserves are based on installed capacities. We generalize these results for other uncertain parameters in spot markets such as fuel costs and transmission capacities. Finally, we illustrate how all these models can be numerically tackled and present numerical experiments. In our numerical experiments, we observe that uncertainty of demand leads to higher total generation capacity expansion and a broader mix of technologies compared to the investment decisions assuming average demand levels. Furthermore for the same VOLL (or price cap) level and under the assumptions of random demand with finite support and no forced outages, energy-onlymarkets with VOLL pricing tend to lead to total generation capacity below the peak load with a certain probability whereas energy markets with a forward capacity market or operating-reserve pricing result in higher investments. Finally, the regulator decisions (e.g., reserve capacity target) in capacity markets and operating-reserve pricing can be chosen in such a way that results in very similar investment levels and fuel mix of generation capacities in b