Taming the Load Current of Identical Cells in Matrix

We explore the load current [Formula: see text] for a rectangular array (matrix) of [Formula: see text] identical cells where [Formula: see text] strings (columns) of [Formula: see text] serial cells (rows) are arrayed in parallel. [Formula: see text] is equal to [Formula: see text] with the internal resistance of the cell and the load resistance exchanged. By treating a linear fractional function as a translated inversely-proportional function, we can easily capture the properties of [Formula: see text] and the relative magnitude of [Formula: see text] and [Formula: see text] via their ratio. The limiting behaviors of the load current are discussed beyond the ideal-cell and short-circuit limits. For the given total number of cells, we graphically verify the recent findings on the matrix of cells that produces the maximum load current. Finally, we analyze the possibility of a car starting with lemon cells or AA dry cells in matrix. This work would be useful in creating a high school or university curriculum that unifies identical cells in series, parallel, or matrix.

Using SKPFM to Determine the Influence of Deformation-Induced Dislocations on the Volta Potential of Copper

The variation rule of the Volta potential on deformed copper surfaces with the dislocation density is determined in this study by using electron back-scattered diffraction (EBSD) in conjunction with scanning Kelvin probe force microscopy (SKPFM). The results show that the Volta potential is not linear in the dislocation density. When the dislocation density increases due to the deformation of pure copper, the Volta potential tends to a physical limit. The Volta potential exhibits a fractional function relationship with the dislocation density only for a relatively low shape variable.

Second Generation Current Conveyor Based Floating Fractional Order Memristance Simulator and a New Dynamical System

In recent years, due to its non-volatile memory, non-locality, and weak singularity features, fractional calculations have begun to take place frequently in artificial neural network implementations and learning algorithms. Therefore, there is a need for circuit element implementations providing fractional function behaviors for the physical realization of these neural networks. In this study, a previously defined integer order memristor element equation is changed and a fractional order memristor is given in a similar structure. By using the obtained mathematical equation, frequency-dependent pinched hysteresis loops are obtained. A memristance simulator circuit that provides the proposed mathematical relationship is proposed. Spice simulations of the circuit are run and it is seen that they are in good agreement with the theory. Also, the non-volatility feature has been demonstrated with Spice simulations. The proposed circuit can be realized by using the integrated circuit elements available on the market. With a small connection change, the proposed structure can be used to produce both positive and negative memristance values.

Sparse Principal Component Analysis via Fractional Function Regularity

In this paper, we describe a novel approach to sparse principal component analysis (SPCA) via a nonconvex sparsity-inducing fraction penalty function SPCA (FP-SPCA). Firstly, SPCA is reformulated as a fraction penalty regression problem model. Secondly, an algorithm corresponding to the model is proposed and the convergence of the algorithm is guaranteed. Finally, numerical experiments were carried out on a synthetic data set, and the experimental results show that the FP-SPCA method is more adaptable and has a better performance in the tradeoff between sparsity and explainable variance than SPCA.

Regularity conditions and Farkas-type results for systems with fractional functions

This paper deals with some new versions of Farkas-type results for a system involving cone convex constraint, a geometrical constraint as well as a fractional function. We first introduce some new notions of regularity conditions in terms of the epigraphs of the conjugate functions. By using these regularity conditions, we obtain some new Farkas-type results for this system using an approach based on the theory of conjugate duality for convex or DC optimization problems. Moreover, we also show that some recently obtained results in the literature can be rediscovered as special cases of our main results.

Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered

The radiation fractional function is the fraction of black body radiation below a given value of λT. Edwards and others have distinguished between the traditional, or “external,” radiation fractional function and an “internal” radiation fractional function. The latter is used for linearization of net radiation from a nongray surface when the temperature of an effectively black environment is not far from the surface's temperature, without calculating a separate total absorptivity. This paper examines the analytical approximation involved in the internal fractional function, with results given in terms of the incomplete zeta function. A rigorous upper bound on the difference between the external and internal emissivity is obtained. Calculations using the internal emissivity are compared to exact calculations for several models and materials. A new approach to calculating the internal emissivity is developed, yielding vastly improved accuracy over a wide range of temperature differences. The internal fractional function should be used for evaluating radiation thermal resistances, in particular.