in this paper we demonstrate the existence of a set of polynomials pi , 1 i  n , which arepositive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in thelagrange interpolation process. in other words, if a  a1  an  b is a given finite sequence of realnumbers, then pi (a j )  ij (ij is the kronecker delta symbol ) ; moreover, the sum of ...

Second-order parabolic equations are natural generalizations of the heat equation and we will study in this section the existence, uniqueness, and regularity of appropriately defined weak solutions. 1.1. Formulation of Weak Solutions. 1.1.1. Notations. In this note, we assume Ω to be an open, bounded domain in R n , and set Ω T = Ω × (0, T ]. We study the following initial/boundary-value proble...

Let Q(A) be number of comparisons done on input array A: (A) For 1 ≤ i < j < n let R ij be the event that rank i element is compared with rank j element. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. Q(A) = ∑ 1≤i<j≤n X ij and hence by linearity of expectation,

For $m,n\in\mathbb{N}$ let $X=(X_{ij})_{i\leq m,j\leq n}$ be a random matrix, $A=(a_{ij})_{i\leq real deterministic and $X_A=(a_{ij}X_{ij})_{i\leq the corresponding structured matrix. We study expected operator norm of $X_A$ considered as between $\ell_p^n$ $\ell_q^m$ for $1\leq p,q \leq \infty$. prove optimal bounds up to logarithmic terms when underlying matrix $X$ has i.i.d. Gaussian entries...

In many area of medical research, a relation analysis between one response variable and some explanatory variables is desirable. Regression is the most common tool in this situation. If we have some assumptions for such normality for response variable, we could use it. In this paper we propose a nonparametric regression that does not have normality assumption for response variable and we focus ...

Water temperature controls the physiology, growth rate, distribution, and behavior of most plankton populations in sea thus affects energy transfer marine ecosystems. The present study focuses on influence seasonal changes surface phytoplankton size distribution copepods Arraial do Cabo Upwelling System (Brazil), where a wind-driven coastal upwelling can lead to multiple distinct bottom-up casc...

Let Q(A) be number of comparisons done on input array A: (A) For 1 ≤ i < j < n let R ij be the event that rank i element is compared with rank j element. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. Q(A) = ∑ 1≤i<j≤n X ij and hence by linearity of expectation,

and Applied Analysis 3 holding for any t ∈ 0, T . Here ( a ij x e j k ) t : ∫ t 0 a ij x, t, τ · e j k x, τ dτ 2.4 are Volterra integral operators with kernels a ij x, t, τ ; a hk ij 0 x, t are instantaneous elastic coefficients out-of-integral terms and a ij x : a hk ij 0 x, t a ij x ; fi0 are components of a vector of external forces; φi x, t are components of a vector of boundary traction on...

in this paper, the notion of fuzzy n-polygroups (fn -polygroups) is introduced and some related properties are investigated. in this regards, the concepts of normal  f-subpolygroups and homomorphisms of fn-polygroups are adopted. also, the quotient of fn-polygroups by defining regular relations are studied. finally, the classical isomorphism theorems of groups are generalized to fn-polygroups p...