Let X ,Y are linear space. In this paper, we prove the generalized Hyers-Ulam stability of the following quartic equation n ∑ k=2 ( k ∑ i1=2 k+1 ∑ i2=i1+1 . . . n ∑ in−k+1=in−k+1 ) f ( n ∑ i=1,i =i1,...,in−k+1 xi − n−k+1 ∑ r=1 xir )

The articles [11], [7], [14], [13], [15], [5], [6], [2], [12], [1], [10], [8], [9], [3], and [4] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: A, B denote ordinal numbers, K, M, N denote cardinal numbers, x, y, z, X , Y , Z, Z1, Z2 denote sets, n denotes a natural number, and f , g denote functions. Let I1 be a function. We say that I1 is car...

Two methods are compared for measuring the kinetic parameters of apolipoprotein A-I and A-I1 metabolism in human plasma. In the first, high density lipoprotein apoproteins were radioiodinated in situ in the lipoprotein particle (endogenous apoprotein labeling) while in the second, individually labeled apolipoprotein A-I or A-I1 was incorporated into the particle by in vitro incubation (exogenou...

Cilia and flagella are highly conserved motile and sensory organelles in eukaryotes, and defects in ciliary assembly and motility cause many ciliopathies. The two-headed I1 inner arm dynein is a critical regulator of ciliary and flagellar beating. To understand I1 architecture and function better, we analyzed the 3D structure and composition of the I1 dynein in Chlamydomonas axonemes by cryoele...

The cardiac muscle protein titin, responsible for developing passive elasticity and extensibility of muscle, possesses about 40 immunoglobulin-like (Ig) domains in its I-band region. Atomic force microscopy (AFM) and steered molecular dynamics (SMD) have been successfully combined to investigate the reversible unfolding of individual Ig domains. However, previous SMD studies of titin I-band mod...

1.1 Addresses, Areas and Regions We iteratively define an area A as a special subspace of a d-dimensional cube as follows: Split the cube with respect to every dimension in the middle, resulting in 2 subcubes numbered in some arbitrary but fixed order (for our implementation and this paper we used Z-ordering) from 1 to 2. An area A1 of level 1 consists of the first i1 closed subcubes. i1 determ...

(1) Let S be an order sorted signature, U0 be a strict non-empty order sorted algebra of S, and A be a subset of U0. Then A is an order sorted generator set of U0 if and only if for every OSSubset O of U0 such that O = OSClA holds OSGenO = U0. Let us consider S, let U0 be a monotone order sorted algebra of S, and let I1 be an order sorted generator set of U0. We say that I1 is osfree if and onl...