Judul: Analisis Fisikokimia  Madu Lebah Hutan (Apis dorsata) Multilokasi Indonesia dengan Variasi Suhu  Pemanasan
Abstrak: Madu merupakan cairan manis alami yang dihasilkan oleh lebah dari berbagai sumber nektar. Madu hutan memenuhi 75% kebutuhan madu di Indonesia. Sifat fisikokimia perlu diketahui untuk menentukan kualitas madu. Penelitian ini bertujuan menentukan sifat fisik dan kimia madu lebah hutan (Apis dorsata) yang berasal dari Garut, Ujung Kulon, Danau Sentarum, dan Flores yang diberi perlakuan panas, serta menentukan jenis madu yang unggul dan suhu perlakuan yang optimal. Sampel madu yang digunakan berasal dari. Perlakuan panas tidak berpengaruh nyata (P>0,05) terhadap fisikokimia madu, kecuali kadar gula pereduksi. Seluruh sampel madu dinyatakan lulus SNI, terkecuali madu asal Flores dengan kadar gula pereduksi dibawah SNI pada pemanasan suhu 65℃ dan 121℃ yaitu sebesar 59,55% dan 55,93%. Madu asal Danau Sentarum memiliki sifat fisikokimia yang lebih unggul pada parameter kelarutan, keasaman, HMF, gula pereduksi, dan sukrosa. Madu ditemukan optimal pada suhu ruang atau tanpa perlakuan panas. Madu Danau Sentarum memiliki rata-rata kelarutan, keasaman, dan kadar HMF yang lebih rendah dari madu asal daerah lain, yaitu secara berurutan sebesar 3 ml madu/ml akuades, 35,75 ml NaOH/kg, dan 1,934 mg/kg., Honey is a naturally sweet liquid produced by bees from various sources of nectar. Forest honey meets 75% of Indonesia's honey needs. Physicochemical properties need to be known to determine the quality of honey. This study aims to determine the physical and chemical properties of forest bee honey (Apis dorsata) originating from Garut, Ujung Kulon, Danau Sentarum, and Flores which were given heat treatment, as well as to determine the superior type of honey and the optimal treatment temperature. The honey samples used were from . Heat treatment had no significant effect (P>0.05) on the physicochemistry of honey, except for reducing sugar content. All honey samples passed SNI, except for honey from Flores with reducing sugar content below SNI at 65℃ and 121℃ heating, namely 59.55% and 55.93%, respectively. Honey from Danau Sentarum has superior physicochemical properties in the parameters of solubility, acidity, HMF, reducing sugar, and sucrose. Honey was found to be optimal at room temperature or without heat treatment. Danau Sentarum honey has lower average solubility, acidity, and HMF content than honey from other regions, which are 3 ml honey/ml aquadest, 35.75 ml NaOH/kg, and 1.934 mg/kg respectively.
Keyword: honey, Apis dorsata, honey physicochemistry, honey heating

Judul: Physicochemical Analysis of Kelulut Honey from Various Locations in Indonesia with Various Heating Temperatures
Abstrak: Madu kelulut dikenal sebagai stingless bee honey atau madu Meliponinae. Penelitian bertujuan untuk mengidentifikasi sifat fisikokimia madu Kelulut dari lokasi Serang, Bogor, Bangka, Sumedang, Garut, Klaten, dan Batu Ampar dengan ragam suhu pemanasan. Sifat fisikokimia yang diuji pada penelitain ini meliputi intensitas warna, total padatan terlarut, kadar air, viskositas, kelarutan, hidroksimetilfurfural, keasaman, gula pereduksi, dan sukrosa. pada madu dengan variasi suhu pemanasan yakni suhu ruang (25 °C), 65 °C and 121 °C. Hasil penelitian ini menunjukkan adanya perubahan sifat fisik maupun kimia yang terjadi pada madu diakibatkan pemanasan. Salah satunya adalah nilai gula pereduksi yang menunjukkan penurunan yang konsisten pada kedua ragam suhu pemanasan. Madu Garut pada perlakuan suhu normal memiliki kadar air sebesar 18,5 %b/b, keasaman sebesar 170 ml NaOH/kg, hidroksimetilfurfural sebesar 27,4 mg/kg, gula pereduksi sebesar 70,8 %b/b, dan sukrosa sebesar 1,4 %b/b, sehingga memiliki kesesuaian dan memenuhi Standar Nasional Indonesia. Hasil dari penelitian semua madu mengalami perubahan karakteristik fisik maupun kimia., Kelulut honey is known as stingless bee honey or Meliponinae honey. The study aimed to identify the physicochemical properties of Kelulut honey from Serang, Bogor, Bangka, Sumedang, Garut, Klaten, and Batu Ampar with various heating temperatures. The physicochemical properties tested in this research include colour intensity, total soluble solids, moisture content, viscosity, solubility, hydroxymethylfurfural, acidity, reducing sugar, and sucrose in honey with variations in heating temperature, namely room temperature (25 °C), 65 °C and 121 °C. The results of this study show that there are changes in physical and chemical properties occur in honey due to heating. One of them is the value of Reducing Sugar which shows a consistent decrease in both heating temperature variations. Garut honey in the normal temperature treatment has a moisture content of 18.5 %w/w, the acidity of 170 ml NaOH/kg, hydroxymethylfurfural of 27.4 mg/kg, reducing sugar of 70.8 %w/w, and sucrose of 1.4 %w/w, so it has conformity and meets the Indonesian National Standard. The results of the research all honey experienced changes in physical and chemical characteristics.
Keyword: honey, heating, physicochemistry, stingless bee

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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