Fractional Differential Equations

The science and technology of ultracapacitors are reviewed for a number of electrode materials, including carbon, mixed metal oxides, and conducting polymers. More work has been done using microporous carbons than with the other materials and most of the commercially available devices use carbon electrodes and an organic electrolytes. The energy density of these devices is 3¯5 Wh/kg with a power density of 300¯500 W/kg for high efficiency (90¯95%) charge/discharges. Projections of future developments using carbon indicate that energy densities of 10 Wh/kg or higher are likely with power densities of 1¯2 kW/kg. A key problem in the fabrication of these advanced devices is the bonding of the thin electrodes to a current collector such the contact resistance is less than 0.1 cm2. Special attention is given in the paper to comparing the power density characteristics of ultracapacitors and batteries. The comparisons should be made at the same charge/discharge efficiency.

Ultracapacitors: Why, How, and Where is the Technology

http://ieeexplore.ieee.org/iel5/5610941/5624686/05624745.pdf

Power electronics

System Identification I

Consider the function defined for $\alpha _{1},\ \alpha _{2} \in \mathbb{R}$ (α 1 2 +α 2 2 ≠ 0) and $\beta _{1},\beta _{2} \in \mathbb{C}$ by the series 

$$\displaystyle{ E_{\alpha _{1},\beta _{1};\alpha _{2},\beta _{2}}(z) \equiv \sum _{k=0}^{\infty } \frac{z^{k}} {\varGamma (\alpha _{1}k +\beta _{1})\varGamma (\alpha _{2}k +\beta _{2})}\ \ (z \in \mathbb{C}). }$$

(6.1.1)

Such a function with positive α 1 > 0, α 2 > 0 and real $\beta _{1},\beta _{2} \in \mathbb{R}$ was introduced by Dzherbashian [Dzh60].

Multi-index Mittag-Leffler Functions

A century has passed regarding wave-particle duality, well an electromagnetic (EM) radiation in dispersionless free space vacuum is represented by a photon, with corpuscular and wave nature. The discussions from the past century aimed at the nature of photon inside a media having dispersion in the refraction property, other than free space.

/pdf/a-new-mechanics-of-corpuscular-wave-transport-of-momentum-2q5xsdk39b.pdf

A new mechanics of corpuscular-wave transport of momentum and energy inside negative indexed material

The market is an indispensable aspect of our lives, enabling us to exchange valuable goods and services. Allocation and pricing are two significant challenges in determining the equilibrium dynamics of a market. With the advent of AI and technology, the way markets function has evolved greatly. With data analytics tools, sellers can engage in personalized pricing to maximize revenue. However, it is shown that personalized pricing is prone to unfairness among consumers. This thesis precisely studies the fairness challenges in personalized pricing. We aim to examine the concept of fairness in the context of monopoly markets that implement feature-based pricing. Our proposal introduces a new form of individual fairness, referred to as α-fairness, which ensures that individuals with similar characteristics are subjected to comparable pricing. To evaluate the loss in revenue to the seller in pursuit of fairness, we additionally introduce the notion of Cost of Fairness (CoF) – the ratio of the expected revenue in optimal feature-based pricing to the expected revenue in the given fair feature-based pricing. First, we investigate the discrete valuation space and present an analytical solution for the most suitable fair feature-based pricing strategy. Our findings indicate that CoF, can be arbitrarily high for any fair pricing strategy. We observe that such valuation spaces are uncommon, so we focus on continuous valuation spaces that are well-studied in economics. With the standard assumption of the revenue function being continuous and concave with respect to the prices, we demonstrate that CoF is strictly less than two, regardless of the model parameters. Finally, we present a polynomial time algorithm that computes a fair feature-based pricing approach, successfully achieving CoF less than two.

Achieving Individually Fair Personalized Pricing

In this paper we have carried out numerical simulation and experimental characterization of two variants of SR (Spiral resonator) viz. TTSR (Two-Turn Spiral Resonator) and NBSR (Non Bianisotropic spiral resonator). The numerical simulation of these develop magnetic inclusion structures are done with commercially available Finite Element Method (FEM) based Ansys HFSS-13 simulation software, and transmission experiment using S-parameter retrieval technique. The experimental characterization of those fabricated structures is used in the parallel plate waveguide experiment (not reported earlier) and then validate our experimental results with the Ansys HFSS-13 simulation software; which in not available in any published literature.

Design and Experimental Characterization of Spiral Resonator variants-TTSR , NBSR

Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation is difficult to find. Usually Laplace-Fourier transformation method, along with methods where solutions are represented in series form is used to find the solution of the fractional wave equation. In this paper we describe the D Alembert s solution of the fractional wave equation with the help of complex fractional transform method. We demonstrate that using this fractional complex transformation method, we obtain the solutions easily as compared to fractional method of characteristics; and get the solution in analytical form. We show that the solution to the fractional wave equation manifests as travelling waves with scaled coordinates, depending on the considered fractional order value.

D Alemberts solution of fractional wave equations using complex fractional transformation

Postoperative immunosuppression has been documented in healthy individuals following elective surgery, trauma, and bums. Both cellular immunity and humoral immunity are depressed transiently, the severity of which is correlated with the length of hospital stay, infectious morbidity, and mortality. The present study was designed to compare the degree of immunosuppression in patients undergoing laparoscopic assisted vaginal hysterectomy (LAVH) versus total abdominal hysterectomy (TAH). Total T cell count, B cell count, and delayed hypersensitivity response to intradermal injection of PPD antigen were documented preoperatively and on postoperative days 3 and 7. There was a significant fall in T cell count on day 3, which tended to normalize by day 7 in the TAH group, but no change was seen in the postoperative T cell count in the LAVH group. No significant change was observed in the B cell count in either group. In the TAH group, two of three patients who showed positive skin response to PPD preoper...

Postoperative Immosuppression in Patients Undergoing Laparoscopic Assisted Vaginal Hysterectomy versus Total Abdominal Hysterectomy: Preliminary Results

Shantanu Das

Papers

A new mechanics of corpuscular-wave transport of momentum and energy inside negative indexed material

Achieving Individually Fair Personalized Pricing

Design and Experimental Characterization of Spiral Resonator variants-TTSR , NBSR

D Alemberts solution of fractional wave equations using complex fractional transformation

Postoperative Immosuppression in Patients Undergoing Laparoscopic Assisted Vaginal Hysterectomy versus Total Abdominal Hysterectomy: Preliminary Results