Analysis of solution trajectories of linear fractional order systems

The behavior of solution trajectories usually changes if we replace the classical derivative in a system by a fractional one. In this article, we throw a light on the relation between two trajectories $X(t)$ and $Y(t)$ of such a system, where the initial point $Y(0)$ is at some point $X(t_1)$ of trajectory $X(t)$. In contrast with classical systems, trajectories $X$ and $Y$ do not follow the same path. Further, we provide a Frenet apparatus of both trajectories in various cases and discuss their effect.Comment: 19 pages, 17 figure

ROLE OF GANDHAK RASAYAN IN SHUSHKA VICHARCHIKA (ECZEMA)

In Ayurveda context, eleven types Kshudrakushtha are described and Vicharchika (Eczema) is one of them. In ancient text, there described many lines of treatmentsof Vicharchika (Eczema) like leech application, local application and many oral medicines. Gandhak Rasayanais one of the oral medicines described for many skin diseases.For this study, 30 patients of Shushka vicharchika (Dry Eczema)having complaint of Kandu, Daha, Ruja, Sparshaasahatva, Tvakvaivarnya were selected.Vicharchika (Eczema)is Kaphajavyadhi and Raktadushti is also observed. Gandhak Rasayana (Bharat Bhaishajya Ratnakar 1153) mainly acts on skin, blood and it is Rasayana in action. So it more or less acts on all Doshas and Dhatus. Gandhak isushnaveeryatmaka and Katu rasa Vipaki so acts as best Kaphghna and Kledaghna. During making of Gandhak Rasayana different twelve Drawyabhavanas are given to Shudhagandhak. These drugs helps to destroy the Samprapti of Vichrchika due to its Ushnavirya and Katukashay rasa. Some Bhavanadravyas has property of Madhur rasa, Sheet Virya due to which they acts as Pittaghna and Raktaprasadana and helps to cure Vicharchika (Eczema).Daha, Kandu, Ruja and Sparshaasahatva were significantly reduced. Also significant relief in Tvak-vaivarnyata was observed

TOXICOLOGICAL STUDY OF SHASHILEKHA VATI WITH SPECIAL REFERENCE TO ITS CHRONIC TOXICITY STUDY IN ALBINO MICE

Safety is the major concern today. It mainly depends on the method of preparation. To assess the quality of a finished product, there should be some basic standards as well as methods of preparation. Shashilekha Vati is one such Herbo-mineral compound used in the treatment of Vitiligo. A chronic Toxicity Study for Shashilekha Vati carried out in the National Toxicology Centre (N.T.C.) Pune to establish the tolerability and to evaluate the effective and non-toxic human dose of Shashilekha Vati by assessing the histopathological and subjective changes in animals. Young (6-8 wks old) male and female Swiss albino mice (28-32 gms of weight), bred at the N.T.C. were used for the study. The duration of the chronic toxicity study was of 3 months (90 days). Shashilekha Vati was prepared according to the method mentioned in the classical text of Yogaratnakara. During the course of the study, all the animal belonging to the entire different groups were observed for food intake, signs of toxicity, histo-pathological study. Clinical parameters (food intake, body weight, sings of Toxicity) indicate safety of Shashilekha Vati for Human Dose Group. Histological findings for day 90; for Ten Times Human Dose Group showed degenerative changes in the liver and kidneys. While it shows mild to moderate degenerative changes in Ten Times Human Dose. The study showed positive results as the Shashilekha Vati is safe and non toxic when given in human dose

Predictive Models for ABS and TPMS based on Gaussian Naïve Bays

The car industry is currently preoccupied with the issue of safety. The increasing number of accidents occurring around the world as a result of automobile problems is a major contributing factor to these incidents. The amount of complicated electronics that is used in vehicles is becoming more prevalent every day. A great effort has been made in evaluating vehicle features in relation to vehicle components. Through such systems, a smart architecture and complex function designs are involved. During all of this vehicle transformation and evolution, the automotive industry recognises a high demand for vehicle safety. While designing and manufacturing this system, automotive experts understand a need for a strict monitoring and feedback system for complex vehicle architecture, which can notify the end user if there is any indication of a failure ahead of time. In order to effectively participate in vehicle design activities, it is critical to grasp the significance of safety features. Tire system failures and braking system failures have played a large role in several recent traffic accidents. The failures of the tyre system and the braking system in the vehicle are addressed in this study. While investigating this system, it is discovered that it is supported by complex electrical systems, which include an ECU (electronic controller unit), sensors, and a wire system. Through the use of these technologies, censored data can be processed in a timely manner and made available for diagnostic purposes. Nevertheless, car diagnostics is needed after any vehicle failure but that does not serve the aim of maintaining vehicle safety. As a result, predictive analysis or predictive diagnostics may be a viable option for informing the driver about the health of a particular vehicle component in advance. In this study, the author discusses the concepts of vehicle prognostics for the tyre pressure monitor system and the antilock braking system, which are accomplished using a statistical method of machine learning. In today's world, machine learning is expanding in breadth, and the world is becoming more aware of its enormous potential in the field of data analytics. It is the purpose of this study to introduce methodologies by which machine learning can assist vehicle predictive analytics to attain the intended goal of vehicle safety.The author of this article discusses how Bayesian statistics may be used to produce predictions in the form of probability estimation. The prediction's outcome is thoroughly analysed

Singular points in the solution trajectories of fractional order dynamical systems

Dynamical systems involving non-local derivative operators are of great importance in Mathematical analysis and applications. This article deals with the dynamics of fractional order systems involving Caputo derivatives. We take a review of the solutions of linear dynamical systems ${}_0^C\mathrm{D}_t^\alpha X(t)=AX(t)$, where the coefficient matrix $A$ is in canonical form. We describe exact solutions for all the cases of canonical forms and sketch phase portraits of planar systems. We discuss the behavior of the trajectories when the eigenvalues $\lambda$ of $A$ are at the boundary of stable region i.e. $|arg(\lambda)|=\frac{\alpha\pi}{2}$. Further, we discuss the existence of singular points in the trajectories of such systems in a region of $\mathbb{C}$ viz. Region II. It is conjectured that there exists singular point in the solution trajectories if and only if $\lambda\in$ Region II.Comment: 12 pages, 22 figure

Nonexistence of invariant manifolds in fractional order dynamical systems

Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in planar polynomial systems. We provide the conditions for the invariance of linear subspaces in fractional order systems. Further, we provide an important result showing the nonexistence of invariant manifolds (other than linear subspaces) in fractional order systems.Comment: 27 pages, 15 figure

Can we split fractional derivative while analyzing fractional differential equations?

Fractional derivatives are generalization to classical integer-order derivatives. The rules which are true for classical derivative need not hold for the fractional derivatives, for example, we cannot simply add the fractional orders $\alpha$ and $\beta$ in ${}_0^{C}\mathrm{D}_t^\alpha {}_0^{C}\mathrm{D}_t^\beta$ to produce the fractional derivative ${}_0^{C}\mathrm{D}_t^{\alpha+\beta}$ of order $\alpha+\beta$, in general. In this article we discuss the details of such compositions and propose the conditions to split a linear fractional differential equation into the systems involving lower order derivatives. Further, we provide some examples, which show that the related results in the literature are sufficient but not necessary conditions.Comment: 16 page

Model-based Reinforcement Learning with Parametrized Physical Models and Optimism-Driven Exploration

In this paper, we present a robotic model-based reinforcement learning method that combines ideas from model identification and model predictive control. We use a feature-based representation of the dynamics that allows the dynamics model to be fitted with a simple least squares procedure, and the features are identified from a high-level specification of the robot's morphology, consisting of the number and connectivity structure of its links. Model predictive control is then used to choose the actions under an optimistic model of the dynamics, which produces an efficient and goal-directed exploration strategy. We present real time experimental results on standard benchmark problems involving the pendulum, cartpole, and double pendulum systems. Experiments indicate that our method is able to learn a range of benchmark tasks substantially faster than the previous best methods. To evaluate our approach on a realistic robotic control task, we also demonstrate real time control of a simulated 7 degree of freedom arm.Comment: 8 page

Rediscovery, resurrection and lectotypification of endemic Isoetes sampathkumarnii L. N. Rao from India

An interesting species of Isoetes was collected from Jambughoda, Wildlife Sanctuary, Gujarat. After a review of literature and comparison of the morphological characters with type specimens, it was identified as I. sampathkumarnii L. N. Rao. It is endemic species of south India and rediscovered after a lapse of 63 years. The species shows several features that make it unique in the genus. Earlier, I. sampathkumarnii was also treated as synonym of I. coromandelina L.f. and I. sahyadrii Mahabala. However, it has an idiosyncratic velum character and spore ornamentation that makes it different from other species. Hence, the authors resurrected it as a distinct species. The original material is ambiguous hence, a lectotype of I. sampathkumarnii has been designated here