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The Fast Fourier Transform (FFT) method for solving the 1-D heat diffusion equation offers an efficient approach for resolving partial differential equations (PDEs) with various time steps . FFT is used to transform the 1-D heat diffusion equation into the frequency domain and back to the time domain through inverse FFT. Using mathematical modeling with initial and Dirichlet boundary conditions, the numerical solutions produced by FFT are compared with analytical solutions. The accuracy of the method is validated using MAE and MSE calculated in Matlab. At several time intervals , the obtained MAE and MSE values indicate a good agreement between the numerical and analytical solutions, with very small errors. Numerical stability analysis confirms the reliability of the FFT method across various  The variation in time step  has a significant impact on the accuracy and stability of the solution. Smaller time steps improve accuracy and stability but require longer computation times. The optimal time step selected in this study is  Increasing the number of discretization points  also enhances accuracy but implies an increase in computational load and memory usage. The FFT method demonstrates good numerical consistency with increasing  

In this paper, Spline techniques have become prominent lately due to their effectiveness in addressing singular perturbation boundary value problems. These issues, defined by a boundary layer or a minor parameter associated with a derivative term, pose difficulties due to swift fluctuations in solutions adjacent to the boundary. Solutions to singularly perturbed involving both positive and negative changes in a spatial variable are shown in this review article. The methods presented here are algorithmic in nature. The singular perturbation that arises in neural activity simulation and the approaches proposed by numerous investigators between 2004 and 2024 are the only ones covered in this review. A variety of types of singularly perturbed were reviewed, including ordinary delay differential . Discovering what numerical and analytical strategies have been created in the past decade to address these types of issues is the primary objective of this review. Its secondary objective is to encourage academics to come up with novel, strong approaches to resolving related issues.

Innovation communication is a way of conveying the discovery of new ideas to society so that social change occurs. A new innovation that is a solution to Jasa Raharja services which is caused by the high number of accidents in Pekanbaru City. In-person support services take a lot of time and take a long time, online updates make it easier for users of these support services. This research aims to analyze the communication innovation of raharja services in implementing online compensation services for accident victims in Pekanbaru city. This research uses qualitative research methods, with data collection techniques using interviews and analyzing the media used in the innovation diffusion process. As for determining research subjects, a purposive technique was used with five informants, then the data analysis technique used Miles and Huberman data analysis techniques which included data collection, data reduction, data presentation and conclusion drawing. This research uses Rogers and Shoemaker's theory of diffusion of innovation. This theory examines messages in the form of new ideas or thoughts, which cause social change.From the research results, this innovation communication has 4 stages, namely. In this research it can be concluded based on the results of the analysis using Roger's theory which has 4 points, This innovation distribution explains that the involvement of communicators provides information in the form of socialization in the form of a content that states information about how to claim or submit compensation from Jasa Raharja. A communicator does not only work alone, this communicator is the Head of Public Relations, Jasa Raharja, who works together with the compensation service staff to collaborate with the community to make it easier and more affordable. With new innovations, since 2009, compensation services for accident victims have gone from conventional forms to online services. This communication channel uses social media, namely in the form of Instagram and Tik Tok, then uses print media, television media and radio media. By implementing the Innovation Division, it has made progress, but of course there are still new innovations, of course this is influenced by factors that hinder the establishment of this innovation, one of which is awareness. The awareness of users or local people who use vehicles in traffic, whether land, sea or air, of course they do not have awareness.

Dandruff is one of the problems that cause a lack of confidence. The triggering microorganism is Candida albicans. The innovation in the skin of red dragon fruit has the potential as an antibacterial and antifungal because it contains several active compounds such as alkaloids, terpenoids and flavonoids. This study aims to find out at what concentration the anti-dandruff activity on the growth of Candida albicans fungus in the formulation of dragon fruit peel extract shampoo preparation (Hylocereus polyrhizus). This research method is an experimental research using the disc paper diffusion method which consists of making dragon fruit peel extract with the maceration method using 96% ethanol solvent. The extract is formulated in shampoo with concentrations of 20.40 and 80%. The results of this study were in the organoleptis test in the form of a viscous liquid, soft sticky texture, brown and menthol flavor. pH test 6.13, 6.71, 6.39, 5.49. Test the height of the foam 5.8cm, 6.0cm, 6.5cm, 10.3cm. Viscosity test 500 Cp, 612 Cp, 635 Cp, 624 Cp. Homogeneity test is homogeneous. Anti-dandruff shampoo activity test of kontro (+), control (-), concentration of 20%, 40%, 80% with an average of 21.95 mm, 0.00 mm, 22.9 mm, 26.07 mm, 28.52 mm. The conclusion of this study is that the formulation of dragon fruit peel extract shampoo (Hylocereus polyrhizus) has provided an inhibitory effect on the growth of Candida albicans fungus with the strongest inhibitory concentration produced in formulation III with a concentration of 80% of 28.52 mm.    

. Avocado seeds are one of the plants used as a medicine for diabetes mellitus with the Latin name (Persea americana Mill.). Avocado seeds contain compounds such as alkaloids, flavonoids, saponins, tannins and triterpenoids which are beneficial for health. This study aims to determine the effect of avocado seed extract (Persea americana Mill.) on the growth of Staphylococcus aureus bacteria in diabetic wounds using the disc diffusion method. The extraction process is by maceration using 96% ethanol. The treatment was repeated 4 times with extract concentrations of 25%, 50%, 75%, 100%, as a positive control Ciprofloxacin and DMSO (Dimetyl Sulfoxide) as a negative control. The results of phytochemical screening show that avocado seeds contain alkaloids, flavonoids, saponins, tannins and triterpenoids. Based on the results of research conducted, avocado seed extract can inhibit the growth of Staphylococcus aureus bacteria as an inhibition zone is formed. The most effective concentration in inhibiting the growth of Staphylococcus aureus bacteria is at 100% concentration of 10.14 mm.

Gangrenous wounds are wounds that occur due to diabetes complications caused by nerve damage and poor blood circulation which makes diabetic wounds unable to prevent infection. Infection is caused by the growth of microbes. High levels of sugar in the blood of DM sufferers provide food for microbes to reproduce. One of the bacteria that causes gangrene is Staphylococcus aureus. Plants that can be used as antibacterials are cherry leaves, also known as seri (Muntingia calabura L.), which contain tannins, terpenoids, saponins, flavonoids and polyphenols. This research aims to identify the antibacterial activity of cherry leaf extract against Staphylococcus aureus bacteria from DM wound wipes. This research was carried out in an experimental laboratory by applying the disc diffusion research method. The resistance is measured through the clear zone that extends around the paper disc. Kersen leaf extract was obtained through a maceration process with 96% ethanol solvent to obtain a thick extract of 0.074%. The test concentrations used were 12.5%, 25%, 50% and 75%. Positive control tetracycline 500 mg and negative control DMSO (dimethyl sulfoxide). The results of this research show that Kersen leaf extract inhibits the growth of Staphylococcus aureus bacteria in diabetic wounds. In concentrations of 12.5%, 25%, 50%, and 75%, the average diameter obtained was 2.70 mm, 4.67 mm, 6.30 mm, 7.89 mm. Conclusion: the effect of ethanol extract of cherry leaves on the growth of Staphylococcus aureus bacteria in diabetic wounds is antibacterial.

African leaf plants (Vernonia amygdalina Del.) is one of tradisional medicine and has pharmacological contain secondary metabolite such as Flavonoids, Saponin, Tanin and Alkaloid. This study aimed to determine the antibacterial activity of African leaf extract (Vernonia amygdalina Del.) in handsoap formulation on the growth of Escherichia coli. African left extract was obtained from maceration process with ethanol and phytochrmical screening was carried out.This study uses concentration of 0,5%, 1% and 2%. Antibacterial activity testing using scratch and disc diffusion methods. Tis study also evaluated the pyshical quality of the preparation which included organoleptic observation, homogeneity test, high foam test and antibacterial activity test. Antibacterial activity testing using scratch and disc disfusion methods. African pyctochemical screening was carried out. The result showed that the percentage of African leaf extract yield was 24,958%. The pH test gets a pH of 10-11 and 5-6 cm foam height test. The highest concentration of positive control of preparation containing alcohol (Dettol) with an average number og 4,72 mm ± 1,45 mm. Liquid soap preparation 1% with a diameter of inhibition of 3,93 mm ± 1,97 mm. The result of this study inhibit the growth of Eshcherichia coli bacteria.

The use of antibiotics can cause drug resistance if their use is not appropriate, so alternative treatment from plants is needed, one of which is soursop leaves (Annona muricata L.). Chemical substances contained in soursop leaves can prevent development until they can kill bacteria, one of which is flavonoids. The purpose of this study was to determine whether soursop leaf methanol extract (Annona muricata L.) at concentrations of 25%, 50%, 75% can inhibit the growth of Staphylococcus aureus bacteria and can determine at what concentration soursop leaf extract (Annona muricata L.) can effectively inhibit Staphylococcus aureus. The simplisia extract was done by maceration strategy using methanol as a solvent. The antibacterial testing method uses the disc diffusion method and uses clindamycin as a positive control and distilled water as a negative control. The results showed that Annona muricata L. extract can provide antibacterial action at concentration variants of 25%, 50% and 75% which is characterized by the presence of transparent areas with an average diameter of 8.97mm, 11.36 mm and 13.3mm respectively with positive control with a diameter of 23.25 and negative control with a diameter of 0 mm. Soursop leaf methanol extract (Annona muricata L.) is able to suppress the growth of Staphylococcus aureus bacteria with the most effective concentration variant of 75%.    

The purpose of this discussion is to see how the dynamics of multicultural education in the surrounding environment, based on the definition, purpose, basis, how multicultural and cultural education diffusion, as well as the conceptual framework. Where the methodology used in this research is in the form of Library Research, namely researchers utilize research methods by collecting, studying, and understanding sources regarding multicultural education, Data collection in this method is using how to analyze and reconstruct existing references, such as books, journal articles, and studies that have been carried out by previous research. Study materials obtained from sources in the form of scientific articles both national and international, books, magazines, online news. multicultural education is needed as an effort to transform awareness so that differences in culture, customs, religion, and ethnicity can be embraced. Multicultural education also teaches a culture that has always existed until now.

The skin is the widest organ that makes up the human body which is the outermost and covers the entire surface of the body. The outermost location causes the skin to receive stimulation for the first time such as touch stimulation, pain, or bad influences from outside. This causes the skin to stretch due to disease. One of the most common skin diseases suffered by people is acne. Acne occurs generally triggered by the bacterium Propionibacterium acnes (gram positive bacteria). Effective acne treatment can use antibiotics, but inappropriate use of antibiotics can lead to resistance. Therefore it is necessary to have alternative therapies from plants that have the potential as antibacterial. One of the natural ingredients from plants that have antibacterial properties is mangosteen (Garcinia mangostana Linn.)This research was conducted using a descriptive experimental method with the aim of knowing the presence of antibacterial activity in cream preparations of ethanol extract of mangosteen rind (Garcinia mangostana Linn.) against Propionibacterium acnes bacteria as seen from the inhibition of bacteria with varying concentrations of 10%, 15% and 25% by using paper disc diffusion method and solid liquid dilution method. The positive control used clindamycin cream and the negative control used 1% DMSO. Analysis of the diameter of the inhibition data was carried out using the One Way ANOVA test. The preparation formulation that has the largest diameter in the diffusion test is F3 with a concentration of 25% with an average inhibition of 6.36 in the medium category.  The MIC and KBM values in the dilution method were at a concentration of 12.5%. The results of a normally distributed One Way ANOVA are measured with a value (P> 0.05). Mangosteen peel extract (Garcinia mangostana Linn.) has antibacterial activity against Propionibacterium acnes bacteria.    

Innovation Development (PI) is a program as concrete evidence of the application of knowledge that has been obtained during the lecture period in accordance with the Accounting and Management Study Program. The innovation development process consists of all decisions and activities, and their impacts, that occur from the recognition of a need or a problem, through research, development and commercialization of an innovation, through the diffusion and adoption of ana innovation by users with all consequences. The target of this activity is Micro, Small and Medium Enterprises (MSMes) in Batu Ampar Village. After we conducted interviews with MSMes in Batu Ampar Subdistrict and set targets for the MSMes that we will provide assistance to, namely the development business of Mrs. Nurmawati’s “Disco Bean” MSMEs. Which is located on Jalan LKMD 2 Rt.33 No.37 Batu Ampar Village, North Balikpapan District. The problem faced by MSME players are that they do not have their own innovation or characteristics in packaging development, and there is also a lack of marketing targets and a lack of understanding about social media in this digital era. Apart from that, this business is only done by word of mouth, so that Mrs. Nurmawati’s business is not known to many people

Diarrhea is a disease characterized by frequent bowel movements with watery or watery stool conditions. Symptoms are infections in the intestinal tract due to bacteria, viruses, or other parasitic microorganisms. Not a few cases of diarrhea caused by Escherichia coli bacteria. Plants that can be used as antibacterial one of them is guava leaves variates Australia.  Has biological activity as an antibacterial, because it contains several active compounds, such as: tannins, terpenoids, alkaloids, flavonoids, and essential oils. The purpose of this study was to determine the active compounds contained in guava leaves of Australian variates and their antibacterial activity. The extraction method used is maceration with 70% ethanol solvent.  Testing its antibacterial activity with the disc diffusion method to see the inhibition zone, then testing the KHM value with liquid diffusion and testing the KBM value with solid diffusion. The results showed that guava leaf extract of Australian variates has antibacterial activity against Eschericia coli ATCC 25922 bacteria.  The average diameter of the inhibitory zone in Australian guava leaf extract concentrations of 25%, 12.5%, 6.25%, 3.125%, 1.562%, respectively was 6.6 mm, 3.3 mm, 2.6 mm, 0.83 mm, 1.33 mm. The KHM and KBM values of the liquid dilution test and solid dilution of Australian guava leaf extract in this study were expressed at a concentration of 12.5%.

Robusta coffee is one of the plants used as a drink and has an efficacious content that can be modified to be used as a cure for diarrhea. This research was conducted To determine the effect of synbiotic coffee with a combination of coffee, prebiotic inulin chicory, probiotic B. bifidum, and glucose on the growth and antibacterial activity of the probiotic Bifidobacterium bifidum BRL-130. Organoleptic testing of synbiotic coffee was performed on 30 panelists, then the growth test used the total plate count method, and the antibacterial test used the paper diffusion method. The organoleptic test showed that the selected formula 1 had the highest average taste of 3.76. In the symbiotic coffee growth test, the best results were obtained in week 1 of plain water with a temperature of 40°C with the number of colonies 5.95 x108 CFU/mL. Antibacterial activity test using paper disc diffusion method with a variation of the selected formula 1 treatment control, 2 treatment control pure robusta coffee powder, positive control of ciprofloxacin antibiotic, and negative control of aquadest solvent. The antibacterial activity of synbiotic coffee against E. coli showed that there was an inhibitory response in formula 1 against Escherichia coli bacteria in the first week of storage, 12.3±1.1 mm with strong criteria.  

Pharmaceutical biotechnology products in the form of hand washing soap with an active ingredient of telang flower kombucha fermented solution have the potential to inhibit the growth of Staphylococcus capitis, Bacillus cereus, and Pantoea dispersa bacteria. The aim of this study was to formulate and prepare hand washing soap with an active ingredient in a solution of seagrass kombucha fermentation to inhibit the growth of Staphylococcus capitis, Bacillus cereus, and Pantoea dispersa. This research is an experimental laboratory by making 4 hand washing soap preparations, which consist of a hand washing soap base without an active substance. Hand washing soap base added to a solution of fermented butterfly pea flower kombucha at a sugar concentration of 20%, 30%, and 40%. Disc diffusion is a method used to calculate the average diameter of the inhibition zone for the three tested bacterial growth. The research data obtained were analyzed through one way ANOVA and post hoc analysis. The results of the ANOVA test proved that the obtained p value <0.05, which means that there were significant differences in the three treatment groups in inhibiting the growth of the three test bacteria. The post hoc analysis results also proved that 40% concentration was the best concentration in inhibiting the growth of the three tested bacteria, namely 18.34 mm (S. capitis/strong), 16.39 mm (B. cereus/strong), and 13.33 mm (P. disperse/strong).

Jackfruit leaves are one of the medical plants that have many benefits. In general, jackfruit leaves are known as animal feed, but behind their function as animal feed, jackfruit leaves have health benefits because jackfruit leaves contain antimicrobials including flavonoids, tannins, saponins that can dissolve in water and can work to damage cytoplasmic membranes and denature cell proteins bacteria. Staphylococcus aureus is a gram-positive bacterium and is arranged in clusters (like grapes). Some infectious diseases caused by these bacteria are impetigo, boils, acne, wound infections, toxic shock syndrome, and other types of pathogenic. This study was conducted to determine the effect of jackfruit leaf extract dissolved using 70% ethanol as a solvent on the growth of staphylococcus aureus bacteria. The method used is the maceration method for the phytochemical screening test, and the disc diffusion method for the antibacterial activity test. The results of the phytochemical screening contained secondary metabolite compounds in jackfruit leaves and for the results of the antibacterial activity test of jackfruit leaf ethanol extract against the growth of staphylococcus aureus bacteria there was antibacterial activity inhibition with high inhibition at 80% concentration with a diameter of 13mm.