Judul: pH and Organoleptic Analysis Of Kefir Leri Due To The Addition Of Bee Honey (Apis cerana)
Abstrak: Kefir merupakan salah satu olahan dari susu yang telah difermentasi, memiliki cita rasa asam dan alkohol. Bahan baku pembuatan kefir bisa berasal dari protein hewani atau nabati. Air leri merupakan limbah yang dihasilkan dari air pencucian beras dan belum banyak dimanfaatkan oleh masyarakat. Kefir memiliki cita rasa yang sangat asam sehingga minat masyarakat terhadap kefir cenderung kurang. Oleh karena itu, dibutuhkan susu pemanis dalam kefir. Pemanis yang memungkinkan untuk ditambahkan dalam pembuatan kefir yaitu madu. Penelitian ini bertujuan untuk mengukur perubahan pH dan pengujian organoleptik pada proses pembuatan kefir berbahan dasar air leri beras, ketan hitam, dan ketan putih akibat penambahan madu (A. cerana). Metode penelitian meliputi analisis pH, uji organoleptik dan uji total asam. Interaksi lama fermentasi dan variasi volume madu berpengaruh nyata terhadap pH. Nilai pH terendah yaitu 3.03 Uji organoleptik kefir air leri menunjukkan tingkat kesukaan tertinggi pada penambahan madu 30 mL oleh kefir air leri pada rasa dan aroma sedangkan pada tekstur dan warna tingkat kesukaan tertinggi dengan penambahan madu 20 mL. Uji total asam tertinggi pada kefir air leri ketan putih sebesar 1.17%. Simpulan dari penelitian ini air leri beras, ketan hitam, dan ketan putih dapat digunakan sebagai bahan dasar pembuatan kefir., Kefir is a product of fermented milk and has a sour and alcoholic taste. The raw materials for making kefir can come from animal or vegetable protein. Leri water is a waste product from rice washing water that has not been widely used by the community. Kefir tastes sour, so people tend to be less interested in kefir. So it adds sweetener milk to the kefir. A sweetener that can be added when making kefir is honey. The purpose of This study aims to measure changes in pH and organoleptic testing in the process of making kefir based on rice leri, black sticky rice, and white sticky rice due to the addition of honey (A. cerana). Research methods include pH analysis, sensory testing and total acid testing. The interaction of fermentation time and honey volume change had a significant effect on pH. The minimum pH is 3.03. The sensory test of Larry Kefir showed that the preference for taste and aroma was highest for Larry Kefir with 30ml of honey, while the texture and color preference for 20ml of honey was the highest. The highest total acid test for white sticky rice kefir was 1.17%. The study concluded that rice wine water, black glutinous rice and white glutinous rice can be used as basic ingredients for making kefir.
Keyword: Air leri, Madu Apis cerana, pH, organoleptik, total asam, Leri Water, Apis cerana honey, pH, organoleptic, total acid

Judul: pH and Organoleptic Characteristics of Kefir Made from Leri Water With the Addition of Bee Honey ( Trigona sp.)
Abstrak: Kefir merupakan salah satu minuman fermentasi yang dibuat dengan menambahkan kefir grains (bibit kefir) ke dalam susu kemudian difermentasi sehingga menghasilkan rasa, warna, dan konsistensi seperti yoghurt dan beraroma alkohol. Umumnya, kefir terbuat dari bahan dasar susu hewani seperti susu sapi, susu kambing, ataupun susu nabati. Namun, susu masih mengandung laktosa yang cukup tinggi sehingga tidak dapat dikonsumsi oleh penderita lactose intolerance. Selain itu, pengolahan kefir dari bahan dasar berupa cairan seperti air leri yang mengandung gula masih terbatas. Kandungan gula yang tedapat pada air leri masih terbatas sehingga madu dapat digunakan sebagai sumber gula alami yang akan membantu fermentasi kefir. Oleh karena itu, penelitian ini bertujuan menganalisis kualitas kefir berbahan dasar air leri dengan penambahan madu lebah (Trigona sp.). Metode penelitian meliputi analisis pH dan uji organoleptik. Berdasarkan hasil penelitian menunjukkan variasi penambahan volume madu Trigona sp. berpengaruh nyata terhadap pH. Nilai pH terbaik dari ketiga sampel ialah sampel ketan putih dengan konsentrasi 50% dengan penambahan madu 10 mL dengan nilai pH berada pada 3.80. Semakin banyak madu yang ditambahkan akan menyebabkan nilai pH kefir air leri menurun. Uji organoleptik menunjukkan hasil dimana panelis lebih menyukai kefir ketan putih konsentrasi 50% dengan penambahan madu 10 mL. Simpulan dari penelitian ini selain susu, kefir dapat menggunakan air leri ketan putih dengan konsentrasi 50% dengan penambahan madu 10 mL sebagai bahan dasar dalam pembuatan kefir., Kefir is a fermented beverage made by adding kefir grains to milk and then fermenting it to produce a yogurt-like taste, color, and consistency. Generally, kefir is made from animal milk, such as cow's milk, goat's milk, or vegetable milk. However, milk still contains lactose which is high enough so that it cannot be consumed by people with lactose intolerance. In addition, the processing of kefir from basic ingredients in the form of liquids such as leri water which contains sugar is still limited. The sugar content in leri water is still limited, so honey can be used as a natural sugar source that will help ferment kefir. Therefore, this study aims to analyze the quality of kefir made from leri water with the addition of bee honey (Trigona sp.). Research methods include pH analysis and organoleptic tests. Based on the results of the study showed variations in the volume addition of Trigona sp. significant effect on pH. The best pH value of the three samples was a sample of white sticky rice with a concentration of 50% with the addition of 10 mL of honey with a pH value of 3.80. The more honey added will cause the pH value of the kefir water to decrease. The organoleptic test showed that the panelists preferred the 50% concentration of white glutinous kefir with the addition of 10 mL of honey. The conclusion from this research is that in addition to milk, kefir can use white glutinous rice water with a concentration of 50% with the addition of 10 mL of honey as a basic ingredient in making kefir.
Keyword: Air leri, Madu Trigona sp., pH, Organoleptik., Leri water, Trigona sp. honey, pH, Organoleptic

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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