An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x ∧ y) has polynomially related classical and quantum bounded-error complexities. We solve a variant of this question. For every f, we prove that the task of computing, on input x and y, both of the quantities f(x∧y) and f(x∨y) has polynomially related c...

It is proved that if 0 < q ≤ (1− 3 √ 2 + 3 √ 4)/3, then the zero function is the only solution f : IR → IR of (1) satisfying (2) and bounded in a neighbourhood of at least one point of the set (3). The paper concerns bounded solutions f : IR → IR of the functional equation f(qx) = 1 4q [f(x − 1) + f(x + 1) + 2f(x)] (1) such that f(x) = 0 for | x |> Q (2) where q is a fixed number from the open ...

In this paper, we consider the Frobenius pushforward endofunctor F * ${F}_{\ast}$ of bounded derived category finitely generated modules over an $F$ -finite noetherian local ring. We completely determine categorical entropy in sense Dimitrov, Haiden, Katzarkov, and Kontsevich.

The notation and terminology used in this paper have been introduced in the following papers: [19], [18], [4], [5], [20], [11], [10], [14], [17], [1], [6], [16], [24], [25], [21], [13], [12], [22], [2], [9], [8], [3], and [7]. For simplicity, we use the following convention: E, F , G are real normed spaces, f is a function from E into F , g is a function from F into G, a, b are points of E, and...

"The objective of this paper is to obtain an upper bound the third order Hankel determinant for inverse function f, when f belongs reciprocal bounded turning functions with new approach."

For a system A = (A1, . . . , An) of linear operators whose real linear combinations have spectra contained in a fixed sector in C and satisfy resolvent bounds there, functions f(A) of the system A of operators can be formed for monogenic functions f having decay at zero and infinity in a corresponding sector in R. In the case that the operators A1, . . . , An commute with each other and satisf...

Using a multivariable Faa di Bruno formula we give conditions on transformations τ : [0, 1] → X where X is a closed and bounded subset of R such that f ◦ τ is of bounded variation in the sense of Hardy and Krause for all f ∈ C(X ). We give similar conditions for f◦τ to be smooth enough for scrambled net sampling to attain O(n−3/2+ ) accuracy. Some popular symmetric transformations to the simple...

We study an extension of the second-order calculus of bounded quantiication, System F , with bounded existential types. Surprisingly, the most natural formulation of this extension lacks the important minimal typing property of F , which ensures that the set of types possessed by a typeable term can be characterized by a single least element. We consider alternative formulations and give an alg...

The author deals with the quasilinear parabolic equation ut = [uα + g(u)]∆u + buα+1+f(u,∇u) with Dirichlet boundary conditions in a bounded domain Ω, where f and g are lower order terms. He shows that, under suitable conditions on f and g, whether the solution is bounded or blows up in a finite time depends only on the first eigenvalue of −∆ in Ω with Dirichlet boundary condition. For some spec...

The notation and terminology used in this paper have been introduced in the following papers: [19], [18], [4], [5], [20], [11], [10], [14], [17], [1], [6], [16], [24], [25], [21], [13], [12], [22], [2], [9], [8], [3], and [7]. For simplicity, we use the following convention: E, F , G are real normed spaces, f is a function from E into F , g is a function from F into G, a, b are points of E, and...