INTERACTIVE APPLICATION DEVELOPMENT BASED ON THE JOINT USE OF THE HASKELL FUNCTIONAL PROGRAMMING LANGUAGE AND Qt FRAMEWORK

The Haskell language allows you to efficiently implement computational algorithms. Higher-order functions, composition of functions, lazy calculations allow you to create functional programs with a clear structure that most fully reflect the logic of the algorithm being implemented. This allows you to get programs that are more compact and more flexible to make changes. Also, the use of pure functions allows you to avoid errors associated with the influence of the “side effect”. The I / O operations required for user interaction use special constructs and functions with a “side effect”, which violates the functional purity of the Haskell language. The approach considered in the article involves the allocation of two parts in an interactive application: interface (front-end) and computing (back-end), interacting with each other by exchanging parameters. The interface part of the application organizes the interaction with the user through the graphical user interface, and the computational part provides the algorithm implementation. To implement front-end is proposed to use the Qt Creator framework with C++ language, and to implement the back-end – the Haskell language. Using a shared address space (files) for data exchange minimizes the impact of the “outside world” on the Haskell program. We also consider a possible way of the software implementation of this approach and example of its applying to develop an application for solve the k-shortest path problem in a graph.

Analisis Kemampuan Pemahaman Konsep Matematis Siswa Pada Materi Komposisi Fungsi

<p>Aspek pemahaman konsep matematis menjadi dasar utama siswa dalam menyelesaikan permasalahan matematika. Tujuan penelitian ini adalah memberikan deskripsi kemampuan pemahaman konsep matematis siswa kelas XI SMKN 1 Kudus dalam menyelesaikan soal komposisi fungsi. Indikator pemahaman matematis pada penelitian ini mengacu kriteria mengukur kemampuan pemahaman matematis Thompson, sehingga peneliti dapat mengukur dan mengetahui bagaimana kemampuan pemahaman matematis subjek penelitian. Penelitian menggunakan metode deskriptif kualitatif. Subjek dalam penelitian ini adalah 3 siswa kelas XI Tata Boga 3 dengan menggunakan teknik <em>purposive sampling</em>. Instrumen penelitian menggunakan 3 buah soal materi komposisi fungsi berupa tes tertulis berbentuk uraian yang telah disesuaikan dengan indikator pemahaman matematis yang digunakan. Setelah rangkaian proses analisis data dilakukan, hasil penelitian menunjukkan bahwa kemampuan pemahaman matematis dari ketiga subjek penelitian tergolong sangat tinggi berdasarkan tabel klasifikasi kemampuan pemahaman matematis, yaitu sebesar 86%. Secara garis besar, subjek menyelesaikan soal tes yang diberikan sesuai dengan aturan konsep, notasi, dan istilah dalam materi komposisi fungsi, meskipun masih terdapat kesalahan miskonsep yang dilakukan.</p><p><em><br /></em></p><p><em>The aspect of understanding mathematical concepts is the main basis for students in solving math problems. The purpose of this research is to describe the ability of students to understand mathematical concepts in class XI SMKN 1 Kudus in solving the composition of functions. Indicators of mathematical understanding in this study refer to the criteria for measuring Thompson's mathematical understanding so that researchers can measure and find out how the subject's mathematical understanding ability. This research used a qualitative descriptive method. The subjects in this study were 3 students of class XI “Tata Boga” 3 using the purposive sampling technique. The research instrument used 3 questions about the composition of the function in the form of a written test in the form of a description which has been adjusted to the indicators of mathematical understanding. After a series of data analysis processes were carried out, the results of this study indicated that the mathematical comprehension ability of the three research subjects was classified as very high based on the classification table of mathematical comprehension abilities, which was 86%. The subject completed the test questions given in accordance with the concept rules, notations, and terms in the function composition material, although there were still misconceptions that were made.</em></p>

Total disconnectedness of Julia sets of random quadratic polynomials

For a sequence of complex parameters $(c_n)$ we consider the composition of functions $f_{c_n} (z) = z^2 + c_n$ , the non-autonomous version of the classical quadratic dynamical system. The definitions of Julia and Fatou sets are naturally generalized to this setting. We answer a question posed by Brück, Büger and Reitz, whether the Julia set for such a sequence is almost always totally disconnected, if the values $c_n$ are chosen randomly from a large disc. Our proof is easily generalized to answer a lot of other related questions regarding typical connectivity of the random Julia set. In fact we prove the statement for a much larger family of sets than just discs; in particular if one picks $c_n$ randomly from the main cardioid of the Mandelbrot set, then the Julia set is still almost always totally disconnected.

Mathematical Approach in Colitis-Related Colon Cancer Genomics

Ulcerative colitis or Crohn's illness patients are in danger of colon cancer due to chronic inflammation, resulting from the reaction of the immune system to bacterial disease caused by genetic alterations in the colonic mucosa. Somatic cells gain genomic changes, such as TP53 that regulates MUC2 production and APC alterations linked with 𝛽-catenin and MUC1 contribution in the slight proliferation of cells. Mathematical modeling describes developmental modifications and uses the phrases to link parameter to curves of age-dependent incidence of epidemiological cancer. By using the long-lasting investigation of IBD patients to gather the genomic estimations for increasingly exact computations of IBD-explicit developmental parameters as initiation, birth, and death. Colon cancer genetic trajectory follows the structure of the composition of functions that leads to malignancies. Models of population level can be utilized to consolidate epidemiological information and in this manner describe malignant growth advancement in a population with IBD.

PELEVELAN PEMAHAMAN KONSEP KOMPOSISI FUNGSI BERDASAR TAKSONOMI SOLO (STRUCTURE OF OBSERVES LEARNING OUTCOMES)

This qualitative descriptive study aims to describe the level of student understanding of function composition based on the SOLO taxonomy. This research was conducted at Madrasah Aliyah Islamiyah Balen on science class X students school year 2019/2020 with 20 subjects. Sampling using stratified sampling techniques (conditional sample) and purposive sampling (sample aims) see the results of written tests that refer to the grid of test questions and sampling data sources with specific considerations. Analysis of the level of understanding with PKLM1, PKLM2, PKLR1, PKLR2, PKLE1, and PKLE2. Data analysis using the test method and interview method and test the data's validity using the triangulation of data sources and triangulation of methods. The results showed three levels of students' understanding of the composition of functions based on SOLO taxonomy, namely multi structural, relational, and extended abstract. Penelitian deskriptif kualitatif ini bertujuan untuk mendeskripsikan level pemahaman siswa pada konsep komposisi fungsi berdasar taksonomi SOLO. Penelitian ini dilakukan di Madrasah Aliyah Islamiyah Balen pada siswa kelas X IPA tahun ajaran 2019/2020 dengan jumlah 20 siswa. Pengambilan sampel menggunakan teknik stratified sampling (sampel bersyarat) dan purposive sampling (sampel bertujuan) yaitu melihat hasil tes tulis yang mengacu pada kisi-kisi soal tes serta pengambilan sampel sumber data dengan pertimbangan tertentu. Analisis level pemahaman dengan subyek PKLM1, PKLM2, PKLR1, PKLR2, PKLE1, dan PKLE2. Analisis data menggunakan metode tes dan metode wawancara, serta uji keabsahan data menggunakan triangulasi sumber data dan triangulasi metode. Hasil penelitian menunjukkan ada tiga level pemahaman siswa pada konsep komposisi fungsi berdasar taksonomi SOLO yaitu multistruktural, relasional, dan extended abstract.

Magnifiers in Some Generalization of the Full Transformation Semigroups

An element a of a semigroup S is called a left [right] magnifier if there exists a proper subset M of S such that a M = S ( M a = S ) . Let T ( X ) denote the semigroup of all transformations on a nonempty set X under the composition of functions, P = { X i ∣ i ∈ Λ } be a partition, and ρ be an equivalence relation on the set X. In this paper, we focus on the properties of magnifiers of the set T ρ ( X , P ) = { f ∈ T ( X ) ∣ ∀ ( x , y ) ∈ ρ , ( x f , y f ) ∈ ρ and X i f ⊆ X i for all i ∈ Λ } , which is a subsemigroup of T ( X ) , and provide the necessary and sufficient conditions for elements in T ρ ( X , P ) to be left or right magnifiers.

A criterion of perfect balance for shift-composition of functions over a finite alphabet

We prove a criterion of perfect balance for sliding superposition of functions over an arbitrary finite alphabet. We also give examples of applying this result to the construction of perfectly balanced functions that are not permutations with respect to the first and to the last variable.