in this paper, we prove the hyers-ulam stability in$beta$-homogeneous probabilistic modular spaces via fixed point method for the functional equation[f(x+ky)+f(x-ky)=f(x+y)+f(x-y)+frac{2(k+1)}{k}f(ky)-2(k+1)f(y)]for fixed integers $k$ with $kneq 0,pm1.$

Three modular reduction algorithms for large integers are compared with respect to their performance in portable software: the classical algorithm, Barrett’s algorithm and Montgomery’s algorithm. These algorithms are a time critical step in the implementation of the modular exponentiation operation. For each of these algorithms their application in the modular exponentiation operation is consid...

A 45-year-old female presented with symptoms of hyperthyroidism and hot nodules in the right lobe, which was diagnosed as nodular goiter by fine-needle aspiration. An anomalous thyroidectomy and difficult dissection with multiple rotations were performed around the trachea. As a remark, the pathology confirmed the presence of goiter with modular nodules (Figure 1). A macroscopic photograph show...

We begin with some general remarks. Let X be a smooth projective variety of dimension n over a field k. For any positive integer p < n, it is of interest to understand, modulo a natural equivalence, the algebraic cycles Y = ∑ j mjYj lying on X, with each Yj closed and irreducible of codimension p, together with codimension p + 1 algebraic cycles Zj = ∑ i rijZij lying on Yj , for all j. There is...

‎In this paper‎, ‎we use the concept of $C$-class functions introduced‎ ‎by Ansari [4] to prove the existence and uniqueness of‎ ‎common fixed point for self-mappings in modular spaces of integral‎ ‎inequality‎. ‎Our results extended and generalized previous known‎ ‎results in this direction‎.