Afrika Matematika最新文献

Simplex and MacDonald codes have received significant attention from researchers since the inception of coding theory. In this work, we present the construction of linear torsion codes for simplex and MacDonald codes over the ring ({mathcal {R}}={mathcal {R}}_{1}{mathcal {R}}_{2}{mathcal {R}}_{3}). We have introduced a novel family of linear codes over ({mathbb {F}}_{p}). These codes have been extensively examined with respect to their properties, such as code minimality, weight distribution, and their applications in secret sharing schemes. In addition to this investigation, we have discovered that these codes are also applicable to the association schemes of linear torsion codes for simplex and MacDonald codes over. ({mathcal {R}}={mathcal {R}}_{1}{mathcal {R}}_{2}{mathcal {R}}_{3}).

The Suzuki simple group Sz(8) has an automorphism group 3. Using the electronic Atlas [22], the group Sz(8) : 3 has an absolutely irreducible module of dimension 12 over ({mathbb {F}}_{2}.) Therefore a split extension group of the form (2^{12}{:}(Sz(8){:}3):= {overline{G}}) exists. In this paper we study this group, where we determine its conjugacy classes and character table using the coset analysis technique together with Clifford-Fischer Theory. We determined the inertia factor groups of ({overline{G}}) by analysing the maximal subgroups of Sz(8) : 3 and maximal of the maximal subgroups of Sz(8) : 3 together with various other information. It turns out that the character table of ({overline{G}}) is a (43 times 43) complex valued matrix, while the Fischer matrices are all integer valued matrices with sizes ranging from 1 to 7.

In this paper, we show that canal and tubular surfaces can be obtained by special curves. Also, we give the equations of the canal and tubular surfaces given by the different frames. Besides, these surfaces are obtained by quaternion and homothetic motion.

In this paper we establish the spacetime manifold as a partially ordered set via the casual structure. We show that these partially ordered sets are naturally continuous as a suitable way below relation can be established via the chronological order. We further consider those classes of spacetimes on which a lattice structure can be endowed by physically defining the joins and meets. By considering the physical properties of null geodesics on the spacetime manifold we show that these lattices are necessarily distributive. These lattices are then continuous as a result of the equivalence between the way below relation and chronology. This enables us to define the Scott topology on the spacetime manifold and describe it on an equal footing as any other continuous lattice. We further show that the Scott topology is a proper subset of Alexandroff topology, which must be the manifold topology for the strongly causal spacetimes, (and hence a coarser topology than Alexandroff). In the process we find some interesting results on the sobriety of these manifolds. We prove that they are necessarily not sober under the Scott topology but regain their sobriety under Alexandroff topology. We also define a dual Scott topology on these manifolds by endowing them with bicontinuous poset structure and show that the join of the Scott topology with the dual is the Alexandroff topology. We also discuss the previous works done in this topic and how the present work generalises those results to some extent.

We introduce screen slant lightlike submanifolds of metallic semi-Riemannian manifolds. We find necessary and sufficient conditions for the induced connection to be a metric connection. Moreover, we investigate some equivalent conditions for integrability of such submanifolds.

Let (Xsubset mathbb {P}^r) be an integral and non-degenerate variety. For any (qin mathbb {P}^r) its X-rank (r_X(q)) is the minimal cardinality of a finite subset of X whose linear span contains q. The solution set (mathcal {S}(X,q)) of (qin mathbb {P}^r) is the set of all (Ssubset X) such that (#S=r_X(q)) and S spans q. We prove that if (Xne mathbb {P}^r) there is at least one q with (#mathcal {S}(X,q)>1) and that for almost all pairs (X, q) we have (dim mathcal {S}(X,q)>0).

The present article attempts to obtain numerical solutions for the GEW equation with the Lie–Trotter splitting algorithm. For this reason, in accordance with the rules of the algorithm, the main problem is split into two sub-equations, linear and non-linear. By applying Galerkin finite element method with cubic B-spline to each sub-equation, two numerical schemes are obtained and two problems for them are discussed. Error norms (L_{2}) and (L_{infty }) and three conservation properties (I_{1},I_{2}) and (I_{3}) are calculated to measure the reliability and performance of the proposed technique and find new approximate solutions. The results generated as a result of the calculation are compared with those produced by other methods in the literature. Stability analysis is examined using the Fourier method to indicate that the numerical approach is unconditionally stable. Based on the results obtained, it can be seen that this technique may be preferred to be applied to other partial differential equations such as the equation discussed in the current study.

Through this research, we introduce two new forms of the half-discrete Hilbert inequality for three variables. In addition, we show that the constants that appear on the right-hand of inequalities are the best. Also, we introduce the equivalence forms of the two inequalities.

In this paper we obtain coefficient characterization, extreme points and distortion bounds for the classes of ( p- )valent harmonic functions defined by (q-)derivative operator. Some of our results improve and generalize previously known results.

An existence result for quasilinear elliptic systems with nonstandard growth/coercive conditions, (W^{-1}L_{overline{M}})-data and no sign condition is proved.