Suppose we are given a particular fixed-length hash function h : 256-bits→ 128-bits. How can we use h to compute a 128-bit strong collision-free hash of a 512-bit input block? We consider several possible ways to extend h to a hash function H : 512-bits→ 128-bits. In the following, we suppose that m is 512-bits long, and we write m = m1m2, where m1 and m2 are 256 bits each. Method 1 Define H(m)...

the aim of this paper is to prove some inequalities for p-valent meromorphic functions in thepunctured unit disk δ* and find important corollaries.

the rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. the rational bi-cubic function involves six parameters in each rectangular patch. data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

The vasopressin-regulated urea transporter (UT)-A1 is a transmembrane protein with two glycosylated forms of 97 and 117 kDa; both are derived from a single 88-kDa core protein. However, the precise molecular sites and the function for UT-A1 N-glycosylation are not known. In this study, we compared Madin-Darby canine kidney cells stably expressing wild-type (WT) UT-A1 to Madin-Darby canine kidne...

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

The rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. The rational bi-cubic function involves six parameters in each rectangular patch. Data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

making use of an extended fractional differintegral operator ( introduced recently by patel and mishra), we introduce a new subclass of multivalent analytic functions and investigate certain interesting properties of this subclass.

1. Suppose that the matrix Mk is of dimension nk × nk+1, k ∈ {1, . . . , h}. We wish to compute the product M1M2 · · ·Mh. Notice that the order of multiplication makes a difference. For example, if (n1, n2, n3, n4) = (1, 10, 1, 10), the calculation (M1M2)M3 requires 20 scalar multiplications, but the calculation M1(M2M3) requires 200 scalar multiplications. Indeed, multiplying a m × n matrix by...