The number of certain integral polynomials and nonrecursive sets of integers, Part 1

The Number of Certain Integral Polynomials and Nonrecursive Sets of Integers, Part 2

We present some examples of mathematically natural nonrecursive sets of integers and relations on integers by combining results from Part 1, from recursion theory, and from the negative solution to Hilbert’s 10th Problem.

The Number of Certain Integral Polynomials

Given r > 2, we establish a good upper bound for the number of multivariate polynomials (with as many variables and with as large degree as we wish) with integer coefficients mapping the “cube” with real coordinates from [−r, r] into [−t, t]. This directly translates to a nice statement in logic (more specifically recursion theory) with a corresponding phase transition case of 2 being open. We ...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

On the average number of sharp crossings of certain Gaussian random polynomials

Spectra of certain types of polynomials and tiling of integers with translates of finite sets

Definition 1.1 is motivated by a conjecture of Fuglede [2], which asserts that a measurable set E ⊂ Rn tiles Rn by translations if and only if the space L2(E) has an orthogonal basis consisting of exponential functions {e}λ∈Λ; the set Λ is called a spectrum for E. For recent work on Fuglede’s conjecture see e.g. [4], [5], [6], [7], [8], [9], [11], [12], [13], [14], [15], [16], [18], [20], [21],...