Approximation of derivations on proper JCQ*-algebras

In this paper, we prove the generalized Hyers-Ulam stability of proper JCQ*-derivations on JCQ*-triples associated to the general (m,n)-Cauchy-Jensen additive functional equation

Lotmanian explosion: From peripheral space to dislocated time

The problem of the “shift” in Lotmanian thought in his last period (the so-called Lotmanian explosion) still remains a subject of controversy for those who are interested in the scholarly heritage of Lotman. Besides explanations pointing out the “circumstantial” factors (for example, the historical context or influence from other thinkers) which brought about changes in Lotman’s views, it is important to identify a dimension of substantial “internal” changes which took place in the theoretical system itself. Regarding the essential changes relating to the concept of explosion as a movement from a ‘spatial’, more specifically ‘centre-periphery’ model to a ‘temporal’, namely ‘dislocated time’ model, the present article will focus on revealing the theoretical implication of this movement. The concept of explosion as an exceptional moment of ‘time out of joint’ was an active alternative to a theoretical breakthrough which was introduced in the process of overcoming the limitations of a previous ‘spatial’ model

On the stability of a nonic functional equation in quasi-normed spaces

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation: where $9 ! = 362880$ in quasi-normed spaces

On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on Links

We study the algebraic and geometric structures for closed orientable 3-manifolds obtained by Dehn surgery along the family of hyperbolic links with certain surgery coefficients and moreover, the geometric presentations of the fundamental group of these manifolds. We prove that our surgery manifolds are 2-fold cyclic covering of 3-sphere branched over certain link by applying the Montesinos theorem in Montesinos-Amilibia (1975). In particular, our result includes the topological classification of the closed 3-manifolds obtained by Dehn surgery on the Whitehead link, according to Mednykh and Vesnin (1998), and the hyperbolic link +1 of +1 components in Cavicchioli and Paoluzzi (2000)

On The Stability Problem of Quadratic Functional Equations in 2-Banach Spaces

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and Gavruta for the quadratic functional equation: f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 4f(x) - 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by the quadratic functional equation in normed spaces to 2-Banach spaces

Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications

We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. As applications of the analytical structure, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional equation fx⊕y=fx⊕fy in tangle space which is a set of real tangles with analytic structure and describe the DNA recombination as the action of some enzymes on tangle space

Juvenile idiopathic arthritis: Diagnosis and differential diagnosis

Juvenile idiopathic arthritis (JIA) is comprised of a heterogeneous group of several disease subtypes that are characterized by the onset of arthritis before the age of 16 years and has symptoms lasting at least 6 weeks. The previous classification of JIA included seven different categories, whereas its current classification was compiled by the International League of the Association for Rheumatology, and replaced the previous terms of "juvenile chronic arthritis" and "juvenile rheumatoid arthritis," which were used in Europe or North America, respectively, with the single nomenclature of JIA. As mentioned above, JIA is defined as arthritis of unknown etiology that manifests itself before the age of 16 years and persists for at least 6 weeks, while excluding other known conditions. The clinical symptoms of JIA can be quite variable. Several symptoms that are characteristic of arthritis are not necessarily diagnostic of JIA and may have multiple etiologies that can be differentiated with careful examination of patient history. The disease may develop over days or sometimes weeks, thereby making the diagnosis difficult at the time of presentation. To make a clinical diagnosis of JIA, the first step is to exclude arthritis with known etiologies. Of note, late treatment due to excessive delay of diagnosis can cause severe damage to joints and other organs and impair skeletal maturation. Therefore, early detection of JIA is critical to ensure prompt treatment and to prevent long-term complications including the likelihood of disability in childhood

Homomorphisms and derivations on C*-ternary algebras assocoated with a generalized Cauchy-Jensen type additive functional equation

In this paper, we prove the generalized Hyers-Ulam stability of C∗-ternary homomorphisms and C∗-ternary derivations on C∗-ternary algebras associated with the generalized Cauchy-Jensen type additive functional equation for all xi; xj ∈ X where n ∈ Z+ is a fixed integer with n ≥ 3. &nbsp