The derivative and tangent operators of a motion in Lorentzian space

2017 ◽  
Vol 14 (04) ◽  
pp. 1750058 ◽  
Author(s):  
Olgun Durmaz ◽  
Buşra Aktaş ◽  
Hali̇t Gündoğan

In this paper, by using Lorentzian matrix multiplication, [Formula: see text]-Tangent operator is obtained in Lorentzian space. The [Formula: see text]-Tangent operators related with planar, spherical and spatial motion are computed via special matrix groups. [Formula: see text]-Tangent operators are related to vectors. Some illustrative examples for applications of [Formula: see text]-Tangent operators are also presented.

Aksioma ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 110-124
Author(s):  
Fausan Fausan ◽  
Gandung Sugita ◽  
Sukayasa Sukayasa

Abstrak: Penelitian ini merupakan penelitian kualitatif yang bertujuan untuk memperoleh profil kesalahan yang dilakukan siswa dalam menyelesaikan soal matriks berdasarkan jenis kelamin di SMA Negeri 7 Palu. Data dikumpulkan dengan cara metode tes dan wawancara. Subjek penelitian terdiri dari satu siswa laki-laki (SH) dan satu siswa perempuan (DS). Hasil Penelitian menunjukkan bahwa kesalahan konseptual yang dilakukan siswa laki-laki (SH) yaitu : 1) kesalahan tidak memahami konsep rumus perkalian matriks, 2) kesalahan konsep perkalian matriks, 3) kesalahan tidak menerapkan rumus invers, 4) kesalahan konsep invers matriks dan 5)  kesalahan konsep adjoin. Kesalahan prosedural yang dilakukan siswa laki-laki berupa 1) kesalahan dalam melakukan perhitungan, 2) kesalahan tidak menyederhanakan dan 3) kesalahan tidak menuliskan tanda operasi pada matriks. Sedangkan kesalahan konseptual yang dilakukan siswa perempuan (DS) yaitu: 1) kesalahan tidak memahami konsep rumus perkalian matriks, 2) kesalahan konsep perkalian matriks, 3) kesalahan konsep adjoin dan 4) kesalahan konsep invers matriks. Kesalahan prosedural yang dilakukan siswa perempuan berupa 1) kesalahan dalam melakukan perhitungan. Siswa laki-laki banyak melakukan kesalahan dari pada siswa perempuan dikarenakan, siswa laki-laki tidak teliti dan terburu-buru dalam menyelesaikan soal matriks. Sedangkan siswa perempuan tidak terlalu banyak melakukan kesalahan dikarenakan cenderung lebih teliti dan cermat dalam menyelesaikan soal matriks. Kata kunci: Profil Kesalahan, Jenis Kelamin dan Matriks Abstract: This research is a qualitative research which aims to obtain a profile of errors students make in solving matrix problems based on sex in SMA 7 Palu. Data was collected by means of test and interview methods. The research subjects consisted of one male student (SH) and one female student (DS). The results showed that the conceptual errors made by male students (SH) were: 1) errors not understanding the concept of matrix multiplication formula, 2) errors in matrix multiplication concepts, 3) errors not applying inverse formulas, 4) inverse matrix concept errors and 5 ) the error of the adjoin concept. Procedural errors made by male students in the form of 1) errors in making calculations, 2) errors do not simplify and 3) errors do not write the operation mark on the matrix. Whereas the conceptual errors made by female students (DS) are: 1) errors do not understand the concept of matrix multiplication formula, 2) errors in the concept of matrix multiplication, 3) errors in adjoining concepts and 4) inverse matrix concept errors. Procedural errors made by female students in the form of 1) errors in carrying out calculations. Male students make a lot of mistakes than female students because , male students are not careful and in a hurry to solve the matrix problem. Whereas female students don't make too many mistakes becausethey tend to be more thorough and careful in solving matrix problems. Keywords: Error Profile, Gender and Matrix


2018 ◽  
Vol 52 (2-3-4) ◽  
pp. 253-268
Author(s):  
Özlem Salehi ◽  
Flavio D’Alessandro ◽  
A.C. Cem Say

We investigate the language classes recognized by group automata over matrix groups. For the case of 2 × 2 matrices, we prove that the corresponding group automata for rational matrix groups are more powerful than the corresponding group automata for integer matrix groups. Finite automata over some special matrix groups, such as the discrete Heisenberg group and the Baumslag-Solitar group are also examined. We also introduce the notion of time complexity for group automata and demonstrate some separations among related classes. The case of linear-time bounds is examined in detail throughout our repertory of matrix group automata.


2005 ◽  
Vol 15 (02) ◽  
pp. 367-394 ◽  
Author(s):  
ALICE C. NIEMEYER

The members of the class C6 in Aschbacher's structure theorem for subgroups of the general linear group GL (d,q) are the normalizers of certain absolutely irreducible, symplectic-type r-groups, where r is a prime, d a power of r and q ≡ 1 ( mod r). For a prime r > 2 and d = r, we present a constructive one-sided Monte Carlo algorithm to recognize whether or not a given subgroup G of GL (r,q) contains a normal extra-special r-group of order r3 and exponent r. In the former case the algorithm returns a homomorphism from G into SL (2,r) with kernel being the extra-special r-group times the center.


Author(s):  
Yaniv Aspis ◽  
Krysia Broda ◽  
Alessandra Russo ◽  
Jorge Lobo

We introduce a novel approach for the computation of stable and supported models of normal logic programs in continuous vector spaces by a gradient-based search method. Specifically, the application of the immediate consequence operator of a program reduct can be computed in a vector space. To do this, Herbrand interpretations of a propositional program are embedded as 0-1 vectors in $\mathbb{R}^N$ and program reducts are represented as matrices in $\mathbb{R}^{N \times N}$. Using these representations we prove that the underlying semantics of a normal logic program is captured through matrix multiplication and a differentiable operation. As supported and stable models of a normal logic program can now be seen as fixed points in a continuous space, non-monotonic deduction can be performed using an optimisation process such as Newton's method. We report the results of several experiments using synthetically generated programs that demonstrate the feasibility of the approach and highlight how different parameter values can affect the behaviour of the system.


1983 ◽  
Author(s):  
I. V. Ramakrishnan ◽  
P. J. Varman

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