Sound-absorbing coatings are of great importance in noise control, thus to make them technically and economically effective, their design optimization is a necessity. Multi-layered homogeneous linings, intended to provide a certain level of absorption, have recently been of much interest among the anechoic coatings. In the present work, first, a mathematical model, called Transfer Matrix Method (TMM) is introduced and validated to properly predict the acoustic response of cavity-less multi-layers. Next, a two-loop optimization technique aimed at maximizing the mean value of echo reduction and minimizing the layers’ total thickness is developed. The outer loop (GP) focuses on the number and order of the layers, while the inner (ICA) is dedicated to the thickness modification of each layer. Finally, results are demonstrated for some specific cases, where promising solutions are found for different constraints and conditions. As an example, comparing a homogeneous coating invented by the GP-ICA (#Generation 50 of Section 5.3) with a typical cavity-included coating used for sound absorption shows that the thickness of this new coating is reduced by nearly two-thirds (from 50 mm to 18 mm), while the first hit of the 20 dB band of Echo Reduction (ER) has reduced by 65 % (from 20 kHz to 7 kHz), and almost did not fall from this level until the end of the frequency domain of interest (40 kHz). That’s while the conventional coating frequency response dropped soon after hitting the 20 dB threshold.

Acne is a very common skin disease. Scars are seen in 95% of patients with acne. Although numerous treatments have been recommended to cure acne scars, researchers are still searching for a single modality to treat the complication due to its variety in shape and depth. In other words, a combination of available methods is required to reach satisfactory results. We compared the effects of fractional carbon dioxide (CO2) laser alone and in combination with subcision.Methods: This clinical trial study was performed in Skin Diseases and Leishmaniasis Research Center (Isfahan, Iran) during 2011-12. Eligible patients with atrophic acne scars were treated with fractional CO2 laser alone (five sessions with three-week interval) on right side of the face and fractional CO2 laser plus subcision (one session using both followed by four sessions of fractional CO2 laser, all with three-week intervals) on the left side. The subjects were visited one, two, and six months after the treatment. Patient satisfaction rate was analyzed by SPSS20.Findings: The average of recovery rate was 54.7% using the combination method and 43.0% using laser alone (P<0.001). The mean patient satisfaction rate according to visual analogue scale (VAS) score was significantly higher with the combination method than with laser alone (6.6 vs. 5.2; P<0.001). Bruising was only seen with the combination method and lasted for one week in 57.0% of patients and for two weeks in 43.0%. Erythema was a side effect of both methods. Post-inflammatory pigmentation and hyperpigmentation were only caused by the combination method. None of the patients had persistent side effects after six months.Conclusion: Using a combination of subcision and laser had suitable results regarding scar recovery and satisfaction rate. However, bruising, post-inflammatory pigmentation, and hyperpigmentation were the side effects of this method. In general, subcision plus laser can be beneficial in the treatment of atrophic acne scars.

Fractional programming is a significant nonlinear planning tool within operation research‎. ‎It finds applications in diverse domains such as resource allocation‎, ‎transportation‎, ‎production programming‎, ‎performance evaluation‎, ‎and finance‎. ‎In practical scenarios‎, ‎uncertainties often make it challenging to determine precise coefficients for mathematical models‎. ‎Consequently‎, ‎utilizing indefinite coefficients instead of definite ones is recommended in such cases‎. ‎Grey systems theory‎, ‎along with probability theory‎, ‎randomness‎, ‎fuzzy logic‎, ‎and rough sets‎, ‎is an approach that addresses uncertainty‎. ‎In this study‎, ‎we address the problem of linear fractional programming with grey coefficients in the objective function‎. ‎To tackle this problem‎, ‎a novel approach based on the variable change technique proposed by Charnes and Cooper‎, ‎along with the convex combination of intervals‎, ‎is employed‎. ‎The article presents an algorithm that determines the solution to the grey fractional programming problem using grey numbers‎, ‎thus capturing the uncertainty inherent in the objective function‎. ‎To demonstrate the effectiveness of the proposed method‎, ‎an example is solved using the suggested approach‎. ‎The result is compared with solutions obtained using the whitening method‎, ‎employing Hu and Wong's technique and the Center and Greyness Degree Ranking method‎. ‎The comparison confirms the superiority of the proposed method over the whitening method‎, ‎thus suggesting adopting the grey system approach in such situations‎.

There is no data on the effect of maximum and minimum premedication dose of atropine on work performance of heart and amount of Fractional Shortening (FS) in rabbit echocardiography, so this study was designed for evaluation of probability of the above effect.24 White New Zealand rabbits, clinically healthy with no consideration in sex and age, weighting 1.5±0.3 kg in four groups consisting six animals for access to the purpose of study were evaluated.Injection of atropine with maximum and minimum dosage for first and second groups and injection of distilled water for third and fourth groups were observed. Calculations of FS for left ventricles in statutory times were done by echocardiography with no knowledge about injection solution.Determinations for Mean, Standard Deviation, Minimum and Maximum amount for FS were 37.29, 3.355, 30 and 43 respectively. Determinations for Mean and Standard Deviation for FS in group one, before injection and in minutes 2, 5, 15 and 30 after injection were 36.33±3.011, 35.33±2.944, 36.17±4.119, 36.83±3.251 and 37.00±2.449 respectively. Determinations for Mean and Standard Deviation for FS in group two, before injection and in minutes 2, 5, 15 and 30 after injection were 39.17±2.994, 39.00±3.347, 36.50±3.017, 35.50±6.025 and 36.83±5.811 respectively. Determinations for Mean and Standard Deviation for FS in group three, before injection and in minutes 2, 5, 15 and 30 after injection were 36.17±2.483, 33.83±3.061, 34.33±2.805, 35.00±2.828 and 33.67±4.885 respectively. Determinations for Mean and Standard Deviation for FS in group four, before injection and in minutes 2, 5, 15 and 30 after injection were 37.50±4.550, 34.17±4.622, 37.17±3.125, 36.50±1.225 and 37.50±2.811 respectively.As a conclusion, Stability of heart performance was observed after using maximum dose of atropine.

In this article, we study a new nonlinear Langevin equation of two fractional orders with fractional boundary value conditions which is a generalization of previous Langevin equations. Based on Banach and Schauder fixed point theorems, the existence and uniqueness of solutions of this equation are investigated. Moreover, our hypotheses are simpler than similar works.

In this paper, the fractional Sumudu decomposition method (FSDM) is employed to handle the time-fractional PDEs and system of time-fractional PDEs. The fractional derivative is described in the Caputo sense. The approximate solutions are obtained by using FSDM, which is the coupling method of fractional decomposition method and Sumudu transform. The method, in general, is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

In this paper, we investigate the solutions of a class of-Hilfer fractional differential equations with the initial values in the sense of-fractional integral by using the successive approximation techniques. Next, the continuous dependence of a solution for the given Cauchy-type problem is presented.