On characteristic twists of multiple Dirichlet series associated to Siegel cusp forms

We define a twisted two complex variables Rankin-Selberg convolution of Siegel cusp forms of degree 2. We find its group of functional equations and prove its analytic continuation to . As an application we obtain a non-vanishing result for special values of the Fourier Jacobi coefficients. We also prove the analytic properties for the characteristic twists of convolutions of Jacobi cusp forms. Research Supported by Fondecyt grants 1061147, 7060241.     

Common Fixed Points of Continuous Mappings on S-Metric Spaces

Mathematical Notes - The aim of this paper is to obtain some common fixed point results on an S-metric space. For this purpose, we prove new generalized common fixed point theorems using the...     

A new concatenated type construction for LCD codes and isometry codes

We give a new concatenated type construction for linear codes with complementary dual (LCD) over small finite fields. In this construction,we need a special class of inner codes that we call isometry codes. Our construction generalizes a recent construction of Carlet et al. (2014–2016) and of Güneri et al. (2016). In particular, it allows us to construct LCD codes with improved parameters directly.     

Mappings of Butson-type Hadamard matrices

A $\mathrm{BH}(q,n)$ Butson-type Hadamard matrix $H$ is an $n\times n$ matrix over the complex $q$th roots of unity that fulfils $H{H}^1=n{I}_n$. It is well known that a $\mathrm{BH}(4,n)$ matrix can be used to construct a $\mathrm{BH}(2,2n)$ matrix, that is, a real Hadamard matrix. This method is here generalised to construct a $\mathrm{BH}(q,pn)$ matrix from a $\mathrm{BH}(pq,n)$ matrix, where $q$ has at most two distinct prime divisors, one of them being $p$. Moreover, an algorithm for finding the domain of the mapping from its codomain in the case $p=q=2$ is developed and used to classify the $\mathrm{BH}(4,16)$ matrices from a classification of the $\mathrm{BH}(2,32)$ matrices.     

On the <Emphasis Type="Italic">p</Emphasis>-ary (cubic) bent and plateaued (vectorial) functions

Plateaued functions play a significant role in cryptography, sequences for communications, and the related combinatorics and designs. Comparing to their importance, those functions have not been studied in detail in a general framework. Our motivation is to bring further results on the characterizations of bent and plateaued functions, and to introduce new tools which allow us firstly a better understanding of their structure and secondly to get methods for handling and designing such functions. We first characterize bent functions in terms of all even moments of the Walsh transform, and then plateaued (vectorial) functions in terms of the value distribution of the second-order derivatives. Moreover, we devote to cubic functions the characterization of plateaued functions in terms of the value distribution of the second-order derivatives, and hence this reveals non-existence of homogeneous cubic bent (and also (homogeneous) cubic plateaued for some cases) functions in odd characteristic. We use a rank notion which generalizes the rank notion of quadratic functions. This rank notion reveals new results about (homogeneous) cubic plateaued functions. Furthermore, we observe non-existence of a function whose absolute Walsh transform takes exactly 3 distinct values (one being zero). We finally provide a new class of functions whose absolute Walsh transform takes exactly 4 distinct values (one being zero).     

Compact-like operators in lattice-normed spaces

A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_{\alpha }$, the net $T{x}_{\alpha }$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators such as compact, weakly compact, order weakly compact, $AM$-compact operators, etc. Similar to $M$-weakly and $L$-weakly compact operators, we define $p$-$M$-weakly and $p$-$L$-weakly compact operators and study some of their properties. We also study $up$-continuous and $up$-compact operators between lattice-normed vector lattices.     

Comparing the development of the multiplication of fractions in Turkish and American textbooks

This study analyzed the methods used to teach the multiplication of fractions in Turkish and American textbooks. Two Turkish textbooks and two American textbooks, Everyday Mathematics (EM) and Connected Mathematics 3 (CM), were analyzed. The analyses focused on the content and the nature of the mathematical problems presented in the textbooks. The findings of the study showed that the American textbooks aimed at developing conceptual understanding first and then procedural fluency, whereas the Turkish textbooks aimed at developing both concurrently. The American textbooks provided more opportunities for different computational strategies. The solutions to most problems in all textbooks required a single computational step, a numerical answer, and procedural knowledge. Furthermore, compared with the Turkish textbooks, the American textbooks contained a greater number of problems that required high-level cognitive skills such as mathematical reasoning.     

The adjacency-Jacobsthal-Hurwitz sequences in groups

In [3 Deveci, O., Aküzüm, Y. (in press). The adjacency-Jacobsthal-Hurwitz type numbers. Filomat. [Google Scholar]], Deveci and Aküzüm defined the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind. In this work, firstly we produce the cyclic groups from the multiplicative orders of the generating matrices of the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind when read modulo λ and we study the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind modulo λ. Then, we give the relationship between the orders of the cyclic groups obtained and the periods of the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind modulo λ. Further, we extend the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind to groups and then we examine these sequences in the quaternion group Q₈ in detail.     

On the Strong Solutions and the Structural Stability of the g-Bénard Problem

In this paper, we study a type of modified Boussinesq equations which is called g-Bénard problem. We show the existence and uniqueness of strong solutions of the problem in two dimensions, and then, we investigate the continuous dependence of the solutions on the viscosity parameter.     

Real matrix representations of complex split quaternions with applications

In this paper, we introduce 8×8 real matrix representations of complex split quaternions. Then, the relations between real matrix representations of split and complex split quaternions are stated. Moreover, we investigate some linear split and complex split quaternionic equations with split Fibonacci and complex split Fibonacci quaternion coefficients. Finally, we also give some numerical examples as applications of real matrix representation of complex split quaternions.