11,561 research outputs found
Bicomplex Third-order Jacobsthal Quaternions
The aim of this work is to consider the bicomplex third-order Jacobsthal
quaternions and to present some properties involving this sequence, including
the Binet-style formulae and the generating functions. Furthermore, Cassini's
identity and d'Ocagne's identity for this type of bicomplex quaternions are
given, and a different way to find the -th term of this sequence is stated
using the determinant of a four-diagonal matrix whose entries are bicomplex
third-order quaternions.Comment: 11 page
The Gelin-Ces\`aro identity in some third-order Jacobsthal sequences
In this paper, we deal with two families of third-order Jacobsthal sequences.
The first family consists of generalizations of the Jacobsthal sequence. We
show that the Gelin-Ces\`aro identity is satisfied. Also, we define a family of
generalized third-order Jacobsthal sequences by the recurrence relation
with initials conditions ,
and , where , and
are non-zero real numbers. Many sequences in the literature are special cases
of this sequence. We find the generating function and Binet's formula of the
sequence. Then we show that the Cassini and Gelin-Ces\`aro identities are
satisfied by the indices of this generalized sequence.Comment: 11 page
Multipliers and weighted d-bar estimates
We study some size estimates for the solution of the equation d-bar u=f in
one variable. The new ingredient is the use of holomorphic functions with
precise growth restrictions in the construction of explicit solutions to the
equation.Comment: 16 pages, 2 figure
New Identities for Padovan Numbers
In \cite{Choi-Jo}, the () subscripted Tribonacci numbers
are studied. This work is devoted to study a new generalization of Fibonacci
numbers called Padovan numbers. In particular, the subscripted Padovan
numbers will be expressed by three step apart Padovan numbers for any
, where
Identities involving Narayana numbers
Narayana's cows problem is a problem similar to the Fibonacci's rabbit
problem. We define the numbers which are the solutions of this problem as
Narayana's cows numbers. Narayana's cows sequence satisfies the third order
recurrence relation () with initial condition
, . In this paper, the subscripted Narayana
numbers will be expressed by three step apart Narayana numbers for any
(). Furthermore, we study the sum
of step apart Narayana numbers for
any .Comment: Submitted to journa
On a Generalization for Tribonacci Quaternions
Let denote the third order linear recursive sequence defined by the
initial values , and and the recursion
if , where , , and are
real constants. The are generalized Tribonacci numbers and
reduce to the usual Tribonacci numbers when and to the -bonacci
numbers when and . In this study, we introduced a quaternion
sequence which has not been introduced before. We show that the new quaternion
sequence that we introduced includes the previously introduced Tribonacci,
Padovan, Narayana and Third order Jacobsthal quaternion sequences. We obtained
the Binet formula, summation formula and the norm value for this new quaternion
sequence
Some Properties of Horadam quaternions
In this paper, we consider the generalized Fibonacci quaternion which is the
Horadam quaternion sequence. Then we used the Binet's formula to show some
properties of the Horadam quaternion. We get some generalized identities of the
Horadam number and generalized Fibonacci quuaternion
Potts model coupled to causal triangulations
In this work we study the annealed Potts model coupled to two dimensional
causal triangulations with periodic boundary condition. Using duality on a
torus, we provide a relation between the free energy of the Potts model coupled
CTs and its dual. This duality relation follows from the FK representation for
the Potts model. In order to determine a region where the critical curve for
the model can be located we use the duality relation and the high-temperature
expansion. This is done by outlining a region where the infinite-volume Gibbs
measure exists and is unique and a region where the finite-volume Gibbs mea-
sure has no weak limit (in fact, does not exist if the volume is large enough).
We also provide lower and upper bounds for the infinite- volume free energy
The Third Order Jacobsthal Octonions: Some Combinatorial Properties
Various families of octonion number sequences (such as Fibonacci octonion,
Pell octonion and Jacobsthal octonion) have been established by a number of
authors in many different ways. In addition, formulas and identities involving
these number sequences have been presented. In this paper, we aim at
establishing new classes of octonion numbers associated with the third order
Jacobsthal and third order Jacobsthal-Lucas numbers. We introduce the third
order Jacobsthal octonions and the third order Jacobsthal-Lucas octonions and
give some of their properties. We derive the relations between third order
Jacobsthal octonions and third order Jacobsthal-Lucas octonions
The unifying formula for all Tribonacci-type octonions sequences and their properties
Various families of octonion number sequences (such as Fibonacci octonion,
Pell octonion and Jacobsthal octonion) have been established by a number of
authors in many different ways. In addition, formulas and identities involving
these number sequences have been presented. In this paper, we aim at
establishing new classes of octonion numbers associated with the generalized
Tribonacci numbers. We introduce the Tribonacci and generalized Tribonacci
octonions (such as Narayana octonion, Padovan octonion and third-order
Jacobsthal octonion) and give some of their properties. We derive the relations
between generalized Tribonacci numbers and Tribonacci octonions.Comment: arXiv admin note: text overlap with arXiv:1710.0060
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