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

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

DRUG UTILIZATION STUDY IN THE ORTHOPEDICS OUTPATIENT DEPARTMENT OF A TERTIARY CARE HOSPITAL IN MAHARASHTRA

Objective: The objective of this study was to analyze the pattern of drug utilization in outpatients of orthopedics department from a tertiary care hospital.Material and Methods: In this retrospective study, prescriptions of randomly selected patients attending orthopedics clinic were screened to analyze a number of medicines per prescription. Number and percentages of prescribed medicines were calculated.Results: In this study, 512 patients (male 260 [50.8%] and females 252 [49.2%]) were included in the study. The total number of prescribed medicines was 1562, accounting for 3.1 medicines per patient. A total number of oral, parenteral, and topical medicines were 1375 (88%), 176 (11.3%), and 11 (0.7%), respectively. Nonsteroidal anti-inflammatory agents (NSAIDs), antacid/anti-ulcerants, and antimicrobial agents were 641 (41%), 371 (23.8%), and 102 (6.5%), respectively. A total of 54 (52.9%), 29 (28.4%), 9 (8.8%), 6 (5.9%), 3 (2.9%), and 1 (1%) patients were prescribed fluoroquinolones, beta-lactam antibiotics, metronidazole, trimethoprim plus sulfamethoxazole, macrolides, and doxycycline, respectively. For 371 (23.8%) patients, anti-ulcerant and antiulcer were prescribed, among which ranitidine was the most common prescription [353 (95.1%)]Conclusion: Number of medicines prescribed per patient in orthopedic clinic was 3.1. NSAIDs and antacid/anti-ulcerants were the most commonly prescribed medicines

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

Improved Third Party Auditing Approach For Shared Data In The Cloud With Efficient Revocation of User

Verify the integrity of the shared information publically, users within the cluster to ensure that shared information all got to figure out the signatures on blocks. Sharing information by different users in different blocks of information typically changes entirely by individual users are signed. Once a user has canceled the cluster, for security reasons, blocks that antecedently the revoked by signed by associate an existing user must sign in nursing again. The Direct transfer of information sharing that same methodology, half and this user to sign in again over the cancellation of existing user in nursing associate permits, mostly due to the size of share data within is disabled. Over the course of this paper, we share information with the user in mind affordable revocation is a completely unique integrity of public auditing mechanisms to propose is a trend. Proxy re-signature thought of using signatures we didn’t order that transfer existing user and blocks by themselves again to sign on behalf of the current cloud blocks users. User to sign in again over are knowledge with the rest of the latest version of the cluster is the cancellation, to allow for a trend. In addition, a public vouchers are often part of the shared although some information has been signed by the cloud while cannot share to retrieve information from the cloud, complete information to audit the integrity of is ready. In addition, our systems at the same time by multiple auditing functions to support verification, auditing is in batch. Experimental results show that our system fairly can improve the efficiency of user cancellation. DOI: 10.17762/ijritcc2321-8169.15073

Retrospective analysis of prescriptions in the management of lepra reactions: Results of a single center study from tertiary hospital in Maharashtra

Objective: To examine pattern of lepra reaction andmedicines used in the treatment of lepra reactions in a tertiary hospital.Material methods: In this retrospective study, prescriptions of patients treated for the lepra reactions were reviewed to find out prevalence of type 1 and type 2 reactions and medicines used in the treatment of lepra reactions.Results:A total of66 patients (male 59.1%; female 40.9%) with mean age of 36.6 (+13.1) years were included in the study. Multibacillary leprosy was present in 93.7% patients.  A total of 39 (60%) patients had type 2 reaction whereas 26 (40%) had type 1 reaction. Mean number of medicines per patients was 7.5. Prednisolone was used in 62 (93.9%) patients with mean duration of 33.32 (+33.2) days whereas chloroquine was used in 52 (78.8%) patients for 36.6 (+27.9) days. Thalidomide was used in 25 (37.9%) patients. Analgesic and anti-inflammatory and anti-acidity drugs were used in 63 (95.4%) patients each whereas paracetamol was given to 41 (62.1%) patients. Antihistamine, antimicrobial agent and vitamins were given to 27 (40.9%), 27 (40.9%) and 35 (53.0%) patients respectively.Conclusion:Lepra 2 reaction is more common than lepra 1 reaction.  Prednisolone and chloroquine are the two most commonly used medicines in the treatment of lepra reaction. Similarly, thalidomide, older drug has emerged as common treatment for lepra reaction

QR Code Approach for Examination Process

Using the QR codes is one of the most intriguing ways of digitally connecting consumers to the internet via mobile phones since the mobile phones have become a basic necessity thing of everyone The detection of QR codes, a type of 2D barcode, as described in the literature consists merely in the determination of the boundaries of the symbol region in images obtained with the specific intent of highlighting the symbol .In order to improve the practical application property of the two-dimensional barcode Quick Response (QR) code, we investigate the coding and decoding process of the QR code image. The barcode is a real mechanism for data reads. Data can be stored, embedded and through the scanning device to show. The store of data which being read. In this paper, we present a methodology for creating QR code approach for virtual word examination process by using different techniques like SHA256, encoding, decoding, and Error correction. DOI: 10.17762/ijritcc2321-8169.15024

Biochemical composition, nutritional analysis and antioxidant activity of Buchanania lanzan Spreng fruits

Buchanania lanzan Spreng belongs to the family Anacardiaceae. The primary focus of this study was to examine phytochemical, proximate, antioxidant property and GCMS evaluation of unripe and ripen fruit of B. lanzan Spreng. The phytochemical studies showed that alkaloids, phenols, flavones, saponins, coumarins, glycosides and tannins are present in both ripen and unripe fruits. The proximate evaluation confirmed that crude fat (14.5%) and protein (6.37±0.69 g/100g) is high in ripen fruit. In unripe fruit (11.3%) crude fat and protein (4.11%) is less percent. The carotenoid (5.58 ± 0.5 mg/100g) and catalase (0.226±0.074 mg/100g) activity is higher in unripe fruit. The total polyphenol (6.4±0.8 mg/100g) and peroxidase (0.362±0.017 mg/100g) content show greater activity in ripen fruit. In DPPH and FRAP highest activity showed in methanol extract of ripen and unripe fruit than the other solvent. GC-MS evaluation showed many bioactive compounds present in unripe and ripen fruit. It is concluded that nutritional and bioactive ability is high in ripen and unripe fruits of B. lanzan. The fruits of B.lanzan are a good source of nutrition and medicinally important