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: Quality Analysis of Cow's Milk Kefir with the  Addition of Forest Honey During Low Temperature Storage. supervised
Abstrak: Kefir merupakan produk olahan susu yang sangat asam dengan beragam manfaat kesehatan. Penambahan madu hutan berperan meningkatkan kualitas fungsional dan cita rasa pada kefir sehingga mudah diterima konsumen. Penelitian bertujuan menganalisis pengaruh penambahan madu dan lama penyimpanan terhadap karakteristik fisikokimia, organoleptik, dan antioksidan kefir susu sapi pada suhu refrigerator. Penelitian dilaksanakan dengan rancangan acak kelompok pola faktorial 3x3 dengan tiga kali pengulangan. Faktor pertama adalah penambahan madu (0%, 5%, 10%, dan 15%) dan faktor kedua adalah lama penyimpanan (0, 7, dan 14 hari). Analisis variansi dan uji Tukey digunakan untuk menganalisis data. Hasil penelitian menunjukkan bahwa penambahan madu berpengaruh nyata (p<0,05) pada aktivitas air dan kapasitas antioksidan. Kefir dengan kapasitas antioksidan tertinggi dihasilkan pada penambahan madu 10% dengan lama simpan 0 hari. Penelitian ini mengonfirmasi bahwa penambahan madu dan lama penyimpanan secara nyata memengaruhi karakteristik kefir susu sapi dengan perlakuan terbaik yakni penambahan sebesar 10% madu dengan lama simpan 0 hari., Kefir is a highly acidic dairy product with various health benefits. The addition of forest honey plays a role in improving the quality and taste of kefir. The aim of this study was to analyze the effect of honey addition and storage time on the physicochemical, organoleptic and antioxidant characteristics of cow's milk kefir during refrigerator storage. The study was conducted with a 3x3 factorial randomized block design with three replications. The first factor was the addition of honey (0%, 5%, 10%, and 15%) and the second factor was storage time (0, 7, and 14 days). Analysis of variance and Tukey’s test were used to analyze the data. The results showed that the addition of honey had a significant effect (p<0,05) on water activity and antioxidant capacity. Kefir with the highest antioxidant capacity was produced by adding 10% honey with a storage time of 0 days. The high concentration of added honey increased the panelists preference for kefir acceptance. This study confirmed that the addition of honey and storage time significantly affected the characteristics of cow's milk kefir. The best treatment was 10% addition of honey with a storage time of 0 days.
Keyword: antioxidant, honey, kefir, storage

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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