AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

(ρ, τ, σ)-Derivations of Dendriform Algebras

We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras.

Root Systems Lie Algebras

A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.

Some results on derivations of MV-algebras

In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

2D Curves in Conformal Hyperquaternion Algebras H⊗2m

The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H⊗2m in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H⊗2m is the object of this work.

Biserial Incidence Algebras

Let K be an algebraically closed field and A be a finite dimensional algebra over K. In this paper we give a classification of biserial incidence algebras with quiver methods.

Linear Commuting Maps on Parabolic Subalgebras of Finite-dimensional Simple Lie Algebras

A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.

Fuzzy Foldness of P-Ideals in BCI-Algebras

This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we construct a computer-program for studying the foldness theory of P-ideals in BCI-algebras.

Generalized Kinematics Analysis of Hybrid Mechanisms Based on Screw Theory and Lie Groups Lie Algebras

Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms,and the generalized analysis method and concise kinematics transfer matrix are obtained.In this study,first,according to the kinematics analysis of serial mechanisms,the basic principles of Lie groups and Lie algebras are briefly explained in dealing with the spatial switching and differential operations of screw vectors.Then,based on the standard ideas of Lie operations,the method for kinematics analysis of parallel mechanisms is derived,and Jacobian matrix and Hessian matrix are formulated recursively and in a closed form.Then,according to the mapping relationship between the parallel joints and corresponding equivalent series joints,a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are examined.A case study is performed to verify the calculated matrices wherein a humanoid hybrid robotic arm with a parallel-series-parallel configuration is considered as an example.The results of a simulation experiment indicate that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practically feasible.

Nonlinear Jordan Triple Derivations of Triangular Algebras

In this paper, it is proved that every nonlinear Jordan triple derivation on triangular algebra is an additive derivation.

Reconsidering “Does the Sum Rule Hold at the Big Bang?” with Pre Planckian HUP, and Division Algebras

In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. the solution in 2012 was that the author stated that quantum measures in 4 dimensions would not work, mandating, if measure theory were used, imbedding in higher dimensions was necessary for a singularity. The idea was to use the methodology of String Theory as to come up with a way out of the impasse if higher dimensions do not exist. We revisit this question, taking into account a derived HUP, for metric tensors if we look at Pre-Planckian space-time introducing a pre-quantum mechanical HUP which may be a way to ascertain a solution not mandating higher dimensions, as well as introducing cautions as to what will disrupt the offered solution. Note that first, measurable spaces allow disjoint sets. Also, that smooth relations alone do not define separability or admit sets Planck’s length, if it exists, is a natural way to get about the “bad effects” of a cosmic singularity at the beginning of space-time evolution, but if a development is to be believed, namely by Stoica in the article, about removing the cosmic singularity as a breakdown point in relativity, there is nothing which forbids space-time from collapsing to a point. Without the use of a Pre Planckian HUP, for metric tensors, the quantum measures in four dimensions break down. We try to ascertain if a Pre Planckian HUP is sufficient to avoid this pathology and also look at if division algebras which can link Octonionic geometry and E8, to Quark spinors, in the standard model and add sufficient definition to the standard model are necessary and sufficient conditions for a metric tensor HUP which may remove this breakdown of the sum rule in the onset of the “Big Bang”.

Three Clifford Algebras for Four Kinds of Interactions

Three Clifford algebras are sufficient to describe all interactions of modern physics: The Clifford algebra of the usual space is enough to describe all aspects of electromagnetism, including the quantum wave of the electron. The Clifford algebra of space-time is enough for electro-weak interactions. To get the gauge group of the standard model, with electro-weak and strong interactions, a third algebra is sufficient, with only two more dimensions of space. The Clifford algebra of space allows us to include also gravitation. We discuss the advantages of our approach.

Introduction to Lie Algebras and Their Representations

This paper is made up of a desire for me to contribute to this beautiful field of mathematics that I have encountered in recent years. In addition, I would like to mention that I am not aware that there are papers in our Balkans on Lie algebra, although this is only an introductory part for which in the near future in collaboration with several professors from abroad I will do a book in our mother tongue on Lie groups and algebras. The main content of this paper is similar to the books that have been published regarding Lie algebras, from basic definition and example, structure, killing form, classification to root system. In my opinion, this paper is important in relation to Lie algebras, because it will be helpful to all those who write papers on algebra, as well as the fact that the paper will be written in Montenegrin, which is understood by almost more than 70 percent of the population. For me, this work has the significance of being useful to all who need it.

Contractions of Certain Lie Algebras in the Context of the DLF-Theory

Contractions of the Lie algebras d = u(2), f = u(1 ,1) to the oscillator Lie algebra l are realized via the adjoint action of SU(2,2) when d, l, f are viewed as subalgebras of su(2,2). Here D, L, F are the corresponding (four-dimensional) real Lie groups endowed with bi-invariant metrics of Lorentzian signature. Similar contractions of (seven-dimensional) isometry Lie algebras iso(D), iso(F) to iso(L) are determined. The group SU(2,2) acts on each of the D, L, F by conformal transformation which is a core feature of the DLF-theory. Also, d and f are contracted to T, S-abelian subalgebras, generating parallel translations, T, and proper conformal transformations, S (from the decomposition of su(2,2) as a graded algebra T + Ω + S, where Ω is the extended Lorentz Lie algebra of dimension 7).

Epimorphisms between Finite 4-Valued Modal Algebras

In this paper, we determine conditions for the existence of an epimorphism between two finite 4-valued modal algebras and state a method to obtain it. Furthermore, we obtain formulas which generalize those indicated by R. Sikorski for finite Boolean algebras [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380037003200340036003100310038000000 , and by M. Abad and A. V. Figallo for finite 3-valued ukasiewicz algebras [2] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380037003200340036003100320031000000 .

Meta-Invariant Operators over Cayley-Dickson Algebras and Spectra

A class of meta-invariant operators over Cayley-Dickson algebra is studied. Their spectral theory is investigated. More- over, theorems about spectra of generalized unitary operators and their semigroups are demonstrated.

Stratification Analysis of Certain Nakayama Algebras

Our purpose in these notes is to present a result for a specific Nakayama Algebra. In essence, it affirms that for any order of simple modules, the cyclic Nakayama Algebras with relations (i.e. ) are not standardly stratified or costandardly stratified.

Non-Linear Semi-Quantum Hamiltonians and Its Associated Lie Algebras

We show that the non-linear semi-quantum Hamiltonians which may be expressed as(whereis the set of generators of some Lie algebra and are the classical conjugated canonical variables) always close a partial semi Lie algebra under commutation and, because of this, it is always possible to integrate the mean values of the quantum degrees of freedom of the semi-quantum non-linear system in the fashion:(whereis the Maximum Entropy Principle density operator) and, so, these kind of Hamiltonians always have associated dynamic invariants which are expressed in terms of the quantum degrees of freedom’s mean values. Those invariants are useful to characterize the kind of dynamics (regular or irregular) the system displays given that they can be fixed by means of the initial conditions imposed on the semi-quantum non-linear system.