A new factor theorem on absolute matrix summability method

In this paper, we have a new matrix generalization with absolute matrix summability factor of an infinite series by using quasi-β-power increasing sequences. That theorem also includes some new and known results dealing with some basic summability methods

ANALISIS TINGKAT KESULITAN SISWA DALAM KEMAMPUAN MENYELESAIKAN MASALAH MATEMATIKA MATERI PERSAMAAN KUADRAT

Penelitian ini bertujuan untuk menganalisis kesulitan – kesulitan siswa dalam menyelesaikan masalah matematika pada materi Persamaan Kuadrat Dan Fungsi Kuadrat, Teorema Faktor Dan Teorema Sisa Metode yang digunakan adalah menggunakan tes dan wawancara. Tes dilakukan kepada siswa sedangkan wawacara dilakukan kepada guru dan siswa. Sekolah yang merupakan tempat penelitian adalah SMA Advent Purwodadi sekolah ini adalah merupakan sekolah satu atap (SATAP) yang terdiri dari 300 siswa dari berbagai daerah Hasil wawancara guru menyatakan bahwa guru tidak terlalu mengalami kesulitan dalam mengajar materi Persamaan Kuadrat Dan Fungsi Kuadrat, Teorema Faktor Dan Teorema Sisa guru akan mengalami kesulitan apabila sudah masuk pada bentuk akar, sedangkan kesalahan yang dilakukan siswa bervariasi yaitu kesalahan fakta, kesalahan konsep, kesalahan prinsip dan kesalahan operasi. Solusi yang di tawarkan adalah pembelajaran dengan memberikan soal open- ended pada materi persamaan kuadrat dan untuk menentukan grafik fungsi kuadrat yaitu dengan mengkontruksi prinsip.ABSTRACTThis study aims to analyze the difficulties of students in solving mathematical problems in the material Quadratic Equations and Quadratic Functions, Factor Theorem and Time Theorem The method used is to use tests and interviews. Tests are conducted on students while interviews are conducted on teachers and students. The school which is a place of research is Adventist Purwodadi High School. This school is a one-roof school (SATAP) consisting of 300 students from various regions. The teacher's interview results state that the teacher has no difficulty in teaching the material Quadratic Equations and Quadratic Functions, Theorem Factors and Theorems The rest of the teachers will experience difficulties if they have entered the root form, while the mistakes made by students vary, namely fact errors, concept errors, principle errors and operating errors. The solution offered is learning by giving open-ended questions to the material in quadratic equations and to determine the graph of quadratic functions, namely by constructing the principle.

A new factor theorem for generalized absolute Riesz summability

The aim of this paper is to consider an absolute summability method and generalize a theorem concerning $\left|\bar{N},p_{n}\right|_{k}$ summability of infinite series to ${\varphi-\mid{\bar{N},p_n;\delta}\mid}_k$ summability of infinite series by using almost increasing sequence. Furthermore, it is explained that a well known result dealing with $\left|\bar{N},p_{n}\right|_{k}$ summability is obtained when this generalization is restricted under special conditions.

POLISH MODELS AND SOFIC ENTROPY

We deduce properties of the Koopman representation of a positive entropy probability measure-preserving action of a countable, discrete, sofic group. Our main result may be regarded as a ‘representation-theoretic’ version of Sinaǐ’s factor theorem. We show that probability measure-preserving actions with completely positive entropy of an infinite sofic group must be mixing and, if the group is nonamenable, have spectral gap. This implies that if$\unicode[STIX]{x1D6E4}$is a nonamenable group and$\unicode[STIX]{x1D6E4}\curvearrowright (X,\unicode[STIX]{x1D707})$is a probability measure-preserving action which is not strongly ergodic, then no action orbit equivalent to$\unicode[STIX]{x1D6E4}\curvearrowright (X,\unicode[STIX]{x1D707})$has completely positive entropy. Crucial to these results is a formula for entropy in the presence of a Polish, but a priori noncompact, model.