and Applied Analysis 3 delay. In the end, an example is provided to illustrate the effectiveness and the advantages of the results obtained. 2. Preliminaries Let R denote the set of real numbers, R the set of nonnegative real numbers, Z the set of positive integers, and R the n-dimensional real space equipped with the Euclidean norm | · |. Let τ > 0 and PC −τ, 0 ;R {φ : −τ, 0 → Rn|φ t φ t for a...

and Applied Analysis 3 In particular, if x τ0 0, we obtain Dx t Dx t . 2.4 Hence, we can see that Caputo’s derivative is defined for functions for which RiemannLiouville fractional-order derivative exists. Let us write that Grünwald-Letnikov’s notion of fractional-order derivative in a convenient form D q 0x t lim lim h→ 0 nh t−τ0 1 hq [ x t − Sx, h, r, q, 2.5 where S x, h, r, q ∑n r 1 −1 r 1 (...

We have proposed and successfully demonstrated a two step method for localizing defects on an LSI chip. The first step is the same as a conventional laser-SQUID (L-SQUID) imaging where a SQUID and a laser beam are fixed during LSI chip scanning. The second step is a new L-SQUID imaging where a laser beam is stayed at the point, located in the first step results, during SQUID scanning. In the se...

This paper gives three versions of the small gain theorem with restrictions for uncertain time-varying nonlinear systems. The result can be viewed as an extension of the small gain theorem with restrictions for time-invariant nonlinear systems or the small gain theorem without restrictions for time-varying nonlinear systems. The result can be applied to study the stabilization problem or the ou...

Đậu tương là loại cây trồng mẫm cảm với hạn và mặn, do vậy nghiên cứu biện pháp tăng cường khả năng chống chịu mặn của đậu vấn đề đang được quan tâm. Protein DREB nhân tố phiên mã làm biểu hiện các gene liên đến tính tương, tuy nhiên nay còn nhiều ở chưa rõ chức năng. Nghiên này nhằm tạo chuyển phục vụ đánh giá vai trò GmDREB7 đối tương. Các phương biến nạp di truyền, tái sinh, chọn lọc in vitr...

and Applied Analysis 3 Proof. Assume that 1.1 has a nonoscillatory solution x t . Without loss of generality, suppose that it is an eventually positive solution if it is an eventually negative solution, the proof is similar , that is, x t > 0 for all t ≥ t0. We consider the following three cases. Case 1. Suppose that x′ t is oscillatory. Then there exists t1 ≥ t0 such that x′ t1 0. From 1.1 , w...

Galactose-deficient IgA1 (Gd-IgA1) and IgA-IgG complexes are known to play an important role in the pathogenesis of IgA nephropathy (IgAN). We aimed therefore to determine the impact of immunosuppression on the serum levels of Gd-IgA1, total IgA1 and IgA-IgG complexes in IgAN patients. In a retrospective study, serum samples from IgAN patients collected before transplantation (t0) and at 3- and...

A language in which we can express arithmetic and which contains its own satisfaction predicate (in the style of Kripke’s theory of truth) can be formulated using just two nonlogical primitives: ′ (the successor function) and Sat (a satisfaction predicate). Let L be a language with vocabulary: , ( ) ∃ ¬ ∨ = ′ Sat plus the variables x0, x1, x2, . . .. A term is a variable followed by zero or mor...

and Applied Analysis 3 The following are some useful relationships regarding the delta derivative, see 2 . Theorem 2.6 see 2 . Assume that f : T → R and let t ∈ T. i If f is differentiable at t, then f is continuous at t. ii If f is continuous at t and t is right scattered, then f is differentiable at t with fΔ t f σ t − f t σ t − t . 2.1 iii If f is differentiable at t and t is right dense, th...