About fuzzy fixed point theorem in the generalized fuzzy fractal space.

The Banach fixed point theorem has applications in several branches of science. Many authors prove this theorem in different types of fuzzy metric spaces and fuzzy fractal spaces. The aim of this paper is to prove the Banach fixed point theorem in a new generalized space called multi fuzzy fractal space

Fractal Image Compression Using Modified Operator (IFS)

Image data Compression based on fractal theory is fundamentally dierent from conventional compression methods, its idea is to generate a contraction operator whose fixed point approximates the original image in a complete metric space of images. The specication of such operator can be stored as the fractal code for the original image. The contraction mapping principle implies that the iteration of the stored operator starting from arbitrary initial image will recover its xed point which is an approximation for the original image. This Contraction mapping is usually constructed using the partitioned IFS(PIFS) technique which relies on the assertion that parts of the image resemble other parts of the same image. It then, nds the fractal code for each part by searching for another larger similar part. This high costly search makes fractal image compression dicult to be implemented in practice, even it has the advantages of a high compression ratio, a low loss ratio, and the resolution independence of the compression rate. In this paper, we investigate fractal image compression(FIC) using Iterated Function Systems(IFS). After reviewing the standard scheme, we state a mathematical formulation for the practical aspect. We then propose a modied IFS that relies on the fact  that, there are very smooth parts in certain images. From the view point of mathematics, we present the modied operator, proving its properties that make it not only a fractal operator but also more eective than the standard one. The experimental results are presented and the performance of the proposed algorithm is discussed

Efficiency analysis for public key systems based on fractal functions.

In the last decade, dynamical systems were utilized to develop cryptosystems, which ushered the era of continuous value cryptography that transformed the practical region from finite field to real numbers. Approach: Taking the security threats and privacy issues into consideration, fractals functions were incorporated into public-key cryptosystem due to their complicated mathematical structure and deterministic nature that meet the cryptographic requirements. In this study we propose a new public key cryptosystem based on Iterated Function Systems (IFS). Results: In the proposed protocol, the attractor of the IFS is used to obtain public key from private one, which is then used with the attractor again to encrypt and decrypt the messages. By exchanging the generated public keys using one of the well known key exchange protocols, both parties can calculate a unique shared key. This is used as a number of iteration to generate the fractal attractor and mask the Hutchinson operator, so that, the known attacks will not work anymore. The algorithm is implemented and compared to the classical one, to verify its efficiency and security. We conclude that public key systems based on IFS transformation perform more efficiently than RSA cryptosystems in terms of key size and key space

IFS on the multi-fuzzy fractal space.

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based” algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition

A Comparison of Dissection-method and Diathermy Tonsillectomies

Objective: To compare the dissection and diathermy methds of tonsillectomy and evaluate their advantages and disadvantages during surgery and convalescence.Methods and Setting: Patients who had tonsillectomy at Aga Khan University Hospital, between January 1994-December 1997.Results: Four year retrospective analysis was done of 200 patients who underwent tonsillectomy by either electrocautery or dissection method. One hundred and eleven underwent tonsillectomy by electrocautery and the other 79 had their tonsils removed by dissection-method and 2 had a combination of both. The average intra­operative blood loss was 10 ml with cautery and 65 ml with dissection method. The average operative time was 15.7 minutes with cautery and 26.9 minutes for dissection. We found higher amounts of blood loss and intra­operative time with dissection method than electrocautery. In comparing diathermy dissection method tonsillectomies, there was marked difference between two, in pen-operative blood loss and operative time.Conclusion: Although post-operative bleeding, pain and infection are complications of both techniques and in our study their incidence in similar in both, but intra-operative blood loss and time are two important factors,technique is a more effective technique in our set up based on which we can conclude that electrocauter

Memory embedded non-intrusive reduced order modeling of non-ergodic flows

Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two but the novel non-intrusive approach presented in this study is an attempt at taking all three into account effectively compared to their traditional counterparts. Based on dimensionality reduction using proper orthogonal decomposition (POD), we introduce a long short-term memory (LSTM) neural network architecture together with a principal interval decomposition (PID) framework as an enabler to account for localized modal deformation, which is a key element in accurate reduced order modeling of convective flows. Our applications for convection dominated systems governed by Burgers, Navier-Stokes, and Boussinesq equations demonstrate that the proposed approach yields significantly more accurate predictions than the POD-Galerkin method, and could be a key enabler towards near real-time predictions of unsteady flows

SERUM LIPID LEVELS IN PERIODONTITIS PATIENTS: A CASE-CONTROL STUDY

Objective: We aimed to evaluate serum lipid levels in periodontitis patients and compared with healthy subjects.Methods: A case-control study was conducted among 30 participants in the age group of 35-60 y, including 15 subjects in case group with community periodontal index (CPI) score of ≥2 and 15 subjects in the control group with a CPI score of ≤ 1 based on their periodontal status. Fasting blood samples were taken for measurement of lipid profiles, including total cholesterol, triglyceride (TG), high-density lipoprotein (HDL), low-density lipoprotein (LDL), and very low-density lipoprotein (VLDL) using an enzymatic method. Odds ratio and independent t-test at *p=0.05 significance level were calculated.Results: Periodontitis patients were 4.1 times at risk to have high triglyceride, 1.3 times at risk to have high total cholesterol and 0.3times at risk to have higher HDL. Independent t-test showed higher total cholesterol/HDL ratio (*p=0.033) and lowered HDL levels (*p=0.027) in periodontitis patients.Conclusion: Periodontitis group has significantly higher total cholesterol/high-density lipoprotein ratio and lower high-density lipoprotein levels when compared to the healthy group

Evaluation of Retention among Acid-etch and Self-etch Sealants: An in vivo Study

Aim: The aim of the study is to evaluate the retention of fissure sealants following the use of self-etch priming agent and traditional acid-etch method. Materials and methods: Thirty subjects around the age 8 to 12 years old school children was recruited to this study by two dental professionals. Paired lower molars were the principal  unit of analysis. Pit and fissure sealant placement lower molars  followed by traditional acid-etching done on 36 and self-etch primer (3M ESPE) on 46. After 6 months the retention was evaluated using Smales RJ and Wong KC (1999) retention evaluation criteria. The Chi-square test was used to evaluate the difference in the retention rates. Results: The total retention in the self-etch sealant group seems to be high, the difference between the groups was not statistically significant. The chi-square computed value was found to b e c2 = 0.417, df = 1 and p = 0.519. This means that there was no significance difference between the retention rate of self-etch sealant compared to conventional acid-etch technique. Hence, this study conclude that self-etch primer (3M ESPE Adper) is effective in bonding sealant to enamel and that the simplified method dramatically shortens treatment time and treatment complexity