U ovom radu detaljnije se proučavaju svojstva logaritamske spirale zadane upolarnom sustavu te je stoga u uvodu najprije ukratko objašnjen polarni sustav. Usredišnjem dijelu rada obrazloženo je svojstvo logaritamske spirale koja sve svojeradijalne zrake siječe pod istim konstantnim kutom. Također, objašnjena je prirodnajednadžba logaritamske spirale i izvedena njezina jednadžba. Naglašen je odnoszakrivljenosti i polumjera kružnice zakrivljenosti u svakoj točki logaritamske spirales motivacijom definiranja i izvođenja parametarskih jednadžbi evolute logaritamskespirale. Dokazano je da logaritamska spirala i njezina evoluta imaju jednakuprirodnu jednadžbu.

Proučava se evoluta proizvoljne krivulje u ravnini i pritom se izvode formule za izračunanje parametarskih jednadžbi evolute krivulje zadane vektorskom jednadžbom, odnosno parametarskim jednadžbama, a potom i za krivulje zadane ekplicitnom, implicitnom i polarnom jednadžbom. Opisat će se konstrukcija evolute i obrazložit njezina svojstva. Detaljnije će se analizirati i grafički prikazati evolute nekih ravninskih krivulja. Također, objasnit će se konstrukcija evolvente krivulje i argumentirat njezina povezanost s evolutom.

With the steady increase in the number of Internet users, email remains the most popular and extensively used communication means. Therefore, email management is an important and growing problem for individuals and organizations. In this paper, we deal with the classification of emails into two main categories, Business and Personal. To find the best performing solution for this problem, a comprehensive set of experiments has been conducted with the deep learning algorithms: Bidirectional Long-Short Term Memory (BiLSTM) and Attention-based BiLSTM (BiLSTM+Att), together with traditional Machine Learning (ML) algorithms: Stochastic Gradient Descent (SGD) optimization applied on Support Vector Machine (SVM) and Extremely Randomized Trees (ERT) ensemble method. The variations of individual email and conversational email thread arc representations have been explored to reach the best classification generalization on the selected task. A special contribution of this paper is the extraction of a large number of additional lexical, conversational, expressional, emotional, and moral features, which proved very useful for differentiation between personal and official written conversations. The experiments were performed on the publicly available Enron email benchmark corpora on which we obtained the State-Of-the-Art (SOA) results. As part of the submission, we have made our work publicly available to the scientific community for research purposes.

In this paper we will give a similar factorization as in [3, 4], where Svrtan and Meljanac examined certain matrix factorizations on Fock-like representation of a multiparametric quon algebra on the free associative algebra of noncommuting polynomials equipped with multiparametric partial derivatives. In order to replace these matrix factorizations (given from the right) by twisted algebra computation, we first consider the natural action of the symmetric group Sn on the polynomial ring Rn in n 2 commuting variables X a b and also introduce a twisted group algebra (defined by the action of Sn on Rn) which we denote by A(Sn). Here we consider some factorizations given from the left because they will be more suitable in calculating the constants (= the elements which are annihilated by all multiparametric partial derivatives) in the free algebra of noncommuting polynomials.

In this paper we study the rose curves in the polar coordinate system. Therefore, we first briefly describe their shape in the context of shapes in nature, architecture and also in cuisine. Then we describe the biography of Luigi Guido Grandi, who was the first to define the rose curve. We also introduce the polar coordinate system and explain how each point is related to the radial coordinate (or radius) and the angular coordinate (or polar angle), both called polar coordinates. We explain in detail the polar equation of a rose curve, where the radius is defined as the cosine function of the polar angle multiplied by a real constant called the angular frequency, which is considered here as a positive real number. In this way, we have considered the angular frequency as a positive integer (odd or even), as a positive rational number in the form of an irreducible fraction, or as a positive irrational number. We have explained and shown by some pictures that a rose curve is usually complete for any continuous interval subset of the set of real numbers, whose length depends on the angular frequency. In fact, a rose curve is incomplete only if the angular frequency is an irrational number. MSC Classification: 51A50 , 53A04 , 97G60 , 97I20